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
values |
|---|---|---|---|---|---|
41,536 | [
"https://stats.stackexchange.com/questions/41536",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10890/"
] | I am trying to build a model where the response is a proportion (it is actually the share of votes a party gets in constituencies). Its distribution is not normal, so I decided to model it with a beta distribution. I also have several predictors.
However, I don't know how to write it in BUGS/JAGS/STAN (JAGS would be ... | The beta regression approach is to reparameterize in terms of $\mu$ and $\phi$. Where $\mu$ will be the equivalent to y_hat that you predict. In this parameterization you will have $\alpha=\mu\times\phi$ and $\beta=(1-\mu) \times \phi$. Then you can model $\mu$ as the logit of the linear combination. $\phi$ can eit... | Greg Snow gave a great answer. For completeness, here is the equivalent in Stan syntax. Although Stan has a beta distribution that you could use, it is faster to work out the logarithm of the beta density yourself because the constants <code>log(y)</code> and <code>log(1-y)</code> can be calculated once at the outset (... | https://stats.stackexchange.com |
183,882 | [
"https://physics.stackexchange.com/questions/183882",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57094/"
] | Assume a particle in 3D euclidean space. Its kinetic energy:
$$
T = \frac{1}{2}m\left(\dot x^2 + \dot y^2 + \dot z^2\right)
$$
I need to change to spherical coordinates and find its kinetic energy:
$$
T = \frac{1}{2}m\left(\dot r^2 + r^2\dot\theta^2 + r^2\sin^2\theta\dot\phi^2\right)
$$
Its well known that:
$$
x = r... | There is an effortless way, if you accept geometrical reasoning.
You know, that $T = \frac 1 2 m \vec v^2 = \frac 1 2 m \lvert \vec v \rvert^2$. Furthermore, spherical coordinates are orthogonal, therefore you can just write:
$$\lvert \vec v \rvert = \sqrt{v_\phi^2 + v_\theta^2 + v_r^2}$$
Geometrically, one easily f... | When you find the total (squared) value of some vector in an orthogonal basis, such as the Cartesian system $(x,y,z)$ or indeed the spherical system $(r,\theta,\phi)$, what you're doing is simply adding the squared values of each component of the vector.
Taking the velocity, let's think about the different components:... | https://physics.stackexchange.com |
66,552 | [
"https://dba.stackexchange.com/questions/66552",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/38059/"
] | Is it possible to search a column within a table for a numerical value range of 1-2000 and then copy each full row into a different table? By doing so technically splitting the table into smaller parts.
| Addressing the question behind the question:
<blockquote>
Maybe you can answer this. Is it possible to search a column within a table for a numerical value range of 1-2000 and then copy each full row into a different table?
</blockquote>
If you already have a column by which you can "partition" the table, then you ... | You can add a column with a unique row number by using the row_number() function:
<pre><code> SELECT LINKRECID ,
FLAGS ,
USERID ,
FOLDER ,
FOLDER2 ,
ACCOUNTNO ,
CREATEON ,
MAILSIZE ,
MAILDATE ,
MAILTIME ,
... | https://dba.stackexchange.com |
143,245 | [
"https://stats.stackexchange.com/questions/143245",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/71899/"
] | Is it possible to do a power analysis for a 2-sided Kolmogorov Smirnov test in R?
I am testing whether two empirical distributions differ using ks.test(), and am looking to add a power analysis.
I haven't been able to find any built-in power analyses for KS tests in R. Any suggestions?
<strong>Edit</strong>: These a... | Finding power against exponential scale-shift alternatives is reasonably straightforward.
However, I don't know that you should be using values calculated <em>from</em> your data to work out what the power might have been. That sort of post hoc power calculation tends to result in counter-intuitive (and often misleadin... | Since Kolmogorov-Smirnov is non-parametric so by definition there can be no applicable power analysis. To have some sort of estimation, you need to assume a background model (and thus divert from the non-parametric world...) and use it to compute one of the following: sample-size, MDE, or power (i.e., you fix/choose tw... | https://stats.stackexchange.com |
64,029 | [
"https://datascience.stackexchange.com/questions/64029",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/86192/"
] | I have a lot of sentences (500k) which looks like this:
<pre><code>"Penalty missed! Bad penalty by Felipe Brisola - Riga FC - shot with right foot is very close to the goal. Felipe Brisola should be disappointed."
"Penalty saved! Damir Kojasevic - Sutjeska Niksic - fails to capitalise on this great opportunity, s... | Named Entity Recognition (NER) would extract names of people, organizations and such. Example:
<pre><code>"Penalty missed! Bad penalty by <person>Felipe Brisola</person> - <organization>Riga FC</organization> - shot with right foot is very close to the goal. <person>Felipe Brisola</p... | You can use dependency parsing and POS tagging from spaCy here. This will help on 'Actions' tagging and with some additional brain storming, you should be able to train your model on the rest of statements as well.
| https://datascience.stackexchange.com |
631,315 | [
"https://physics.stackexchange.com/questions/631315",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275227/"
] | In many youtube videos about building low power radio transmeters , I have seen a piece of regular wire or extension cord used as a antenna. But , it seems like telecommunication antennas have specific geometry (like dipole antenna , dish antenna etc).But why do we have to follow specific geometry for designing antenna... | at high (radio) frequencies, extension cord ("zip cord") wire has large power losses and is generally unsuitable for <em>transmitting</em> antennas.
telecomm antennas are built so as to produce as much electromagnetic radiation as possible, and point it in the desired direction. They have a wide variety of sh... | The geometry of antenna changes its radiation pattern. This pattern is important for reception also (reciprocity theorem). One have to adapt this pattern in order to obtain a certain directivity of antenna. Also the geometry defines which polarization of electromagnetic wave will be emitted and, in case of reception, ... | https://physics.stackexchange.com |
311,040 | [
"https://physics.stackexchange.com/questions/311040",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | While solving various problems on impulsive forces, I find it very non-intuitive apply the principle of conservation of energy. When suddenly a force of very short duration is exerted, it is obvious that the work done by the force has to be zero because the force acted for a very short stint of time, hence we can assum... | In "collision" type problems the use of the conservation of energy is usually restricted to those collisions which are elastic (kinetic energy conserved) and those where a given amount of energy is inputted to the system e.g. an explosion).<br>
For all other such problems the energy route is very difficult to follow so... | In case of impulsive forces to apply energy conservation we have to write first energy equation before impact
After impact we have to consider momentum changed by it and write second energy equation
| https://physics.stackexchange.com |
213,558 | [
"https://physics.stackexchange.com/questions/213558",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/72439/"
] | I know that this sounds really stupid but, when I think of the Minkowski space I cannot imagine a null curve, only null lines. For me, the only possible way to have one is to change the basis of the space for one that is not orthogonal, and that don't make any practical sense for me. And almost the same goes to null su... | Regarding null curves in flat space, how about
$$
X(t) = (t,x,y) = (\tau, \cos(\tau), \sin(\tau)) .
$$
Then
$$
V(t) = (\dot t, \dot x, \dot y) = (1,-\sin(\tau), \cos(\tau))
$$
in which case $V^2 = 0$.
| Any particle moving in $\mathbb{R}^3$ along any curve with constant speed $|v|=c$ will trace a null curve in Minkowski space.
| https://physics.stackexchange.com |
2,390,165 | [
"https://math.stackexchange.com/questions/2390165",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/466946/"
] | <blockquote>
Let $\{a,b\}\subset\mathbb{R}$. Show that:
$$a^2+b^2+ \frac{1}{a^2}+ \frac{b}{a} \geq \sqrt{3}$$
</blockquote>
I am unable to apply AM-GM inequality in the given problem.
| We need to prove that
$$b^2+\frac{1}{a}\cdot{b}+a^2+\frac{1}{a^2}-\sqrt3\geq0,$$
for which we need $\Delta\leq0$ or
$$\frac{1}{a^2}-4\left(a^2+\frac{1}{a^2}-\sqrt3\right)\leq0$$ or
$$4a^2+\frac{3}{a^2}\geq4\sqrt3,$$ which is AM-GM:
$$4a^2+\frac{3}{a^2}\geq2\sqrt{4a^2\cdot\frac{3}{a^2}}=4\sqrt3.$$
Done!
| it is equivalent to
$$\left(ab+\frac{1}{2}\right)^2+\left(a^2-\frac{\sqrt{3}}{2}\right)^2\geq 0$$
| https://math.stackexchange.com |
24,192 | [
"https://physics.stackexchange.com/questions/24192",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8820/"
] | I am an amateur learning about the Higgs because I was interested in what the LHC's purpose is.
I read that as a particle passes through space, it is actually passing through a Higgs field and there are little Higgs particles that accumulate on the moving particle, which is where mass and momentum come from.
But that... | The Higgs ether does not pick out a preferred velocity--- it is the same in all reference frames. Because of this, it can't impart a resistance to velocity, since any velocity is symmetric with any other. There is no Higgs drag. But it can impart a resistance to change in velocity, and this is a change mass. The most i... | <blockquote>
I read that s a particle passes through space, it is actually passing through a Higgs field and there are little Higgs particles that accumulate on the moving particle, which is where mass and momentum come from.
</blockquote>
That's one way that people try to describe the Higgs mechanism to non-special... | https://physics.stackexchange.com |
124,744 | [
"https://cs.stackexchange.com/questions/124744",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/31249/"
] | For a mental exercise, I decided to try out my own simple sorting algorithm which processes an array of integers in any order, and as it passes thru them all, records the highest and the lowest. So imagine an array of size 10 with elements (9, 2, 4, 1, 6, 8, 5, 3, 7, 0) in that order. We want the algorithm to sort th... | Given the word <span class="math-container">$w = ab^p ab^p$</span>, clearly <span class="math-container">$w\in L \land |w|=2\cdot(p+1)\geq p$</span>.
Now, consider the division <span class="math-container">$w=xyz$</span> where <span class="math-container">$|xy|\leq p \land |y|>0$</span> then
<ul>
<li><strong>Case... | Your language is not regular. Indeed, let <span class="math-container">$n$</span> be the pumping lemma constant, and consider the word <span class="math-container">$ab^nab^na = a(b^na)^2 \in L$</span>. Suppose that your language were regular. Then you could write <span class="math-container">$ab^nab^na = xyz$</span>, w... | https://cs.stackexchange.com |
408,332 | [
"https://electronics.stackexchange.com/questions/408332",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/201588/"
] | So lets say I used 2's complement to put <code>-17</code> in binary and then I added it to <code>+27</code>, e.g.:
<pre><code> +27 0001 1011b
+ -17 1110 1111b
-------------------
+10 0000 1010b
</code></pre>
This calculation here should have an overflow of 1. <strong>Where did this overflow of 1 go?</stro... | There are many ways to explain it. Here is one.
Eight-bit signed binary can represent integers as low as -128<sub>DECIMAL</sub> and as high as +127<sub>DECIMAL</sub>. So, why can it not represent the next greater integer, +128<sub>DECIMAL</sub>?
Answer: it could represent +128<sub>DECIMAL</sub>. The trouble is, the r... | Carry and overflow are not the same thing.
The MSB of a 2's-complement number is the sign bit. The bit you're talking about is the carry-out from the addition of the MSBs. There is an "overflow" only if the signs of the operands are identical AND the sign bit of the result and that carry-out are not identical. If the ... | https://electronics.stackexchange.com |
40,646 | [
"https://stats.stackexchange.com/questions/40646",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/16040/"
] | The mean is not good in this case, because there are galleries that have an artist with a high rank and several other artists with way lower ranks. I'm thinking about doing a weighted mean, but I don't know how to split the weights to the ranking ranges. Any ideas? Thank you.
| How about simply summing the <em>qualities</em> of the artists, where ranks are probably not the best measure for the quality, but if that's all you have...
Isn't it the case that a gallery with ten soso artists is better than one with five soso artists?
Also think about whether a gallery with ten works of a single a... | Maybe just quote the top one and say how many of their works are there. The quantity of art is quite important isn't it?
Summary statistic of all ranks: if you have outliers at the top you may want to use a robust measure. Look up robust statistics on wikipedia. These include the median and trimmed means, or Winsoriza... | https://stats.stackexchange.com |
23,091 | [
"https://mathoverflow.net/questions/23091",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4333/"
] | I'm stuck on a technicality concerning singularities.
Basically, I have to show that the singularities of a $\mathbf{certain}$ normal projective variety over $\mathbf{C}$ are rational. (I won't bother you with the exact set-up. For, it's possible that I'm even wrong.)
My idea was to use a theorem of Viehweg and sho... | Say $X=\mathbb A^n$ and $D_1,\dots, D_n$, the components of $D$, are the coordinate hyperplanes $x_i=0$, for simplicity. You can assume that WLOG, because your $(X,D)$ is isomorphic to this one in étale topology.
$\pi_1(X\setminus D) = \mathbb Z^n$. So the cover $V\to U$ corresponds to a finite quotient of $\m... | I'm not sure if I understand what you are doing correctly, but let me take a guess.
Say you have $f : Y \to X$ which is finite and etale outside of a simple normal crossings divisor $D$ on $X$.
Consider the pair $(X, (1-\varepsilon)D)$ where $\varepsilon > 0$ is a very small positive number. This pair is "Kawa... | https://mathoverflow.net |
195,860 | [
"https://electronics.stackexchange.com/questions/195860",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/89336/"
] | I understand the concept of the transconductance but it's not clear what does the transconductance efficiency (gm/Id) mean. Since gm is the variation of Id to the Vgs or vin voltage... What is the variation of Id to Vgs by Id???
| The cover is made of plastic that is opaque to visible light but transparent to infra-red. It probably attenuates the infra-red a small amount but not enough to affect operation.
The cover is basically for aesthetics - it will work fine without it.
Learning remote controls also have an IR photo-diode where there may ... | After working with IR for years, and observing numberless products, I conclude that the reason just: tradition, and a bit of aesthetics.
But with a caveat.
For <strong><em>receivers</em></strong>, the bandpass window is critical for rejecting the visible band: sunlight and bright room lighting. Even when using mod... | https://electronics.stackexchange.com |
117,301 | [
"https://softwareengineering.stackexchange.com/questions/117301",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5512/"
] | In a lot of cases I might have an existing class with some behavior:
<pre><code>class Lion
{
public void Eat(Herbivore herbivore) { ... }
}
</code></pre>
...and I have a unit test...
<pre><code>[TestMethod]
public void Lion_can_eat_herbivore()
{
var herbivore = buildHerbivoreForEating();
var test = Build... | This is great because it shows how tests truly drive the way you think about design. You are sensing problems in the design and asking the right questions.
There are two ways of looking at this.
IHerbivoreEater is a contract. All IHerbivoreEaters must have an Eat method which accepts a Herbivore. Now, your tests do n... | <blockquote>
It seems redundant to test the same code multiple times, but there are cases where the subclass can and does override the functionality of the base class
</blockquote>
In a round-about way you're asking whether its appropriate to use white-box knowledge to omit some tests. From a black-box perspective, ... | https://softwareengineering.stackexchange.com |
478,794 | [
"https://stats.stackexchange.com/questions/478794",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/245251/"
] | I am comparing different classification models and for a given model (let's say logistic regression), everytime I run it, it obviously produces a slightly different value for the Accuracy and for the AUC. Since, I want to compare the different models, I want a pretty stable metric, so I thought of running each algorith... | First thing to do is to make sure that you're not overfitting. If there is no such strong signal, then averaging out performance metrics you mentioned make sense. And, producing a basic confidence intervals (or +- std intervals) out of different runs of the same algorithm is a common practice in research papers.
| Computing it multiple times can be more useful for specific algorithms. Let's take an example : while a regression will do the same thing if you use it on the exact same data (ie if you split your train and test with a random state to each time have the exact same rows), an algorithm like random forest will randomly ta... | https://stats.stackexchange.com |
712,757 | [
"https://math.stackexchange.com/questions/712757",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/87845/"
] | Similar to how lines have slopes defined in terms of $\Delta y$ and $\Delta x$, why can't planes have slopes defined in therms of $\Delta x$, $\Delta y$, and $\Delta z$?
Couldn't these could be represented in terms of a vector: $$\left[ \begin{array}{c} \Delta x \\ \Delta y \\ \Delta z \end{array} \right]$$
Why is i... | A point and a normal vector is a convenient parameterization for a plane because it is coordinate-independent. Sometimes planes are parameterized by a point and a gradient ("slope") instead, for instance you can represent the plane
$$z = ax+by+c$$
with the point $(1,1,a+b+c)$ and gradient $\nabla_{x,y}z = (a,b)$. But... | This is a great question... however all will be answered in Integral Calculus. :P A simple explanation is that you are now in 3D space. A plane is flat, so you use instead a "normal vector" which is perpendicular to the plane for these types of calculations.
Look up how gradients and planes are used to calculate slope... | https://math.stackexchange.com |
59,560 | [
"https://mathoverflow.net/questions/59560",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13905/"
] | Let $(X,\mathfrak{M},\mu)$ be a positive finite measure space, then
define $\rho(A,B)=\int_X |\chi_A-\chi_B|d\mu$.
Is $(\mathfrak{M},\rho)$ a complete metric space(modulo sets of measure 0)?
I am trying very hard to look for any references, but I cannot find any.
So, if $(\mathfrak{M},\rho)$ is a complete metric spa... | To complement Michael Renardy's response, a reference is: "1.12.6. Theorem" in Bogachev's Measure Theory, Volume 1. The proof goes as follows. Take any Cauchy sequence in the metric, then pass to a subsequence in which the mutual distances converge to zero very fast, then the original sequence converges in the metric t... | This is known as the Nikodym metric. It is complete.
| https://mathoverflow.net |
11,033 | [
"https://stats.stackexchange.com/questions/11033",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/333/"
] | I have a model fitted (from the literature). I also have the raw data for the predictive variables.
What's the equation I should be using to get probabilities? Basically, how do I combine raw data and coefficients to get probabilities?
| Here is the applied researcher's answer (using the statistics package R).
First, let's create some data, i.e. I am simulating data for a simple bivariate logistic regression model $log(\frac{p}{1-p})=\beta_0 + \beta_1 \cdot x$:
<pre><code>> set.seed(3124)
>
> ## Formula for converting logit to probabilities... | The link function of a logistic model is $f: x \mapsto \log \tfrac{x}{1 - x}$. Its inverse is $g: x \mapsto \tfrac{\exp x}{1 + \exp x}$.
In a logistic model, the left-hand side is the logit of $\pi$, the probability of success:
$f(\pi) = \beta_0 + x_1 \beta_1 + x_2 \beta_2 + \ldots$
Therefore, if you want $\pi$ you ... | https://stats.stackexchange.com |
64,968 | [
"https://security.stackexchange.com/questions/64968",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/42544/"
] | I was playing with OWASP Mutillidae II and in one page I've found a vulnerability. In the address bar I've wrote something like this:
<pre><code>127.0.0.1/.../?page=text-file-viewer.php/"><script>alert("test");</script>
</code></pre>
The alert box pops up, but I don't understand why? I know what happe... | The address bar doesn't do anything. It's the <em>web application</em> which appearently takes the URL and inserts it right into the HTML markup, leading to a cross-site scripting vulnerability.
This happens either server-side or client-side: Either the PHP script delivers the page with the URL already in it, or there... | That is the same as filling a form which has an input field named <strong>page</strong> with the following data
<pre><code>text-file-viewer.php/"><script>alert("test");</script>
</code></pre>
If you get the alert pop-up, the server is writing the user input as is.
| https://security.stackexchange.com |
203,265 | [
"https://mathoverflow.net/questions/203265",
"https://mathoverflow.net",
"https://mathoverflow.net/users/44768/"
] | In his paper <em>QFT and Jones Polynomials</em>, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated surgeries on knots." (page 383).
Is there an analogous statement/theorem for 4-manifolds? Such as obtaining other 4-m... | If an $n$-dimensional smooth manifold $X'$ is obtained from $X$ by doing some surgeries, then there is an $(n+1)$-dimensional smooth cobordism $W$ from $X$ to $X'$; vice-versa, any handle decomposition of such a cobordism induces a sequence of surgeries.
Hence, the equivalence relation of "being obtained from one anot... | It is a theorem of Iwase that every 4-manifold can be obtained from a connected sum of a number of $\pm CP^2$ and $S^1\times B^3$ by surgery along tori:
Iwase, Dehn surgery along a torus T2-knot II, Japan Jour. of Math vol.16,
no.2 (1990), 171-196
| https://mathoverflow.net |
142,413 | [
"https://physics.stackexchange.com/questions/142413",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/40408/"
] | My Professor in QFT did a move which I cannot follow:
Given the state $$\hat\phi|0\rangle = \int \frac{d^3p}{(2\pi)^3 2 E_p} a^\dagger_p e^{- i p_\mu x^\mu}|0\rangle,$$ he wanted to show that this state is an eigenstate of the position operator. Therefore he applied the position operator in the momentum representatio... | Here is the answer (I will not consider the constants on the denominator of your Fourier transform for simplicity, however they are there ;-) ). When you write the operator $\hat{\phi}$ you have to be careful. I will drop the hats, because it will be clearer I think (maybe here the hat stands for an operator and not fo... | This issue is a bit confused in textbooks, however the statement of the professor is <strong>physically wrong</strong> (mathematically all the procedure can be rigorously justified using the theory of distributions). The point is that the claimed position operator is not the position operator because it is not even sel... | https://physics.stackexchange.com |
545,817 | [
"https://physics.stackexchange.com/questions/545817",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/232396/"
] | My understanding is that there are 5 implicit assumptions when introducing the Lagrangian formulation.
Assumptions:
<ol>
<li>We appear to know that the principle of stationary action is true for the universe</li>
<li>We define Kinetic energy of the system to be to be <span class="math-container">$T = \sum f(\mathcal{... | Partially answering your question, but the Universe is not time-translation invariant.
From Noether's theorem, we know that we can connect symmetries with conserved quantities, and as you said energy conservation is connected to time-translation invariance. However, universal expansion breaks time-translation invaria... | The lagrangian formalism doesn't require that the state of the system be time-translation invariant. It only requires that the differential equations governing the system be so.
The universe is not time-translation invariant, and nobody has ever imagined that it was.
<blockquote>
Also, how do we know that the durat... | https://physics.stackexchange.com |
77,763 | [
"https://electronics.stackexchange.com/questions/77763",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/26864/"
] | When are inductors really used? I have read that the elements are typically quite hard to implement into circuits given their physical characteristics. I also read that if inductors are placed in circuits there is a imlpementation method that actually places them flat and coils around itself on a plane, but it's appare... | Good question.. one common use is in a filter. A capacitor passes a high frequency signal easily, but resists low frequency ones. While an inductor does the opposite: it pass low-frequency easily, and impedes high frequency. In fact, inside most speaker enclosures you'll find an inductor used on the woofer to pass ... | Energy stored in a capacitor comes out again in the opposite direction from which it went in.
Energy stored in an inductor comes out in the <em>same</em> direction as it went in.
This lets you build resonant LC circuits where enegy circulates between a capacitor an inductor at a particular frequency: this is the trad... | https://electronics.stackexchange.com |
267,876 | [
"https://softwareengineering.stackexchange.com/questions/267876",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/52500/"
] | I am creating a DLL that I want to distribute to public to use it the way they want. This DLL contains common utility functions. People can use it on any operating system and with any language or framework. So, I want to ask that the DLL created using .NET 3.5 or above is accessible from other languages, operating syst... | A .NET DLL contains Intermediate Language which requires the .NET runtime to execute it and probably some .NET base libraries that it uses/depends on.
This means that the DLL can only be used on hardware/operating systems that have a matching .NET Framework available.
Writing code for <em>all</em> possible platforms ... | A DLL is a format used for shared libraries by the Microsoft Windows operating system. Other operating systems use other formats, and since DLLs are binary they cannot generally be used on other processor architectures such as ARM devices. Therefore, DLLs are of no or little use under Mac OS X, on Linux-based operating... | https://softwareengineering.stackexchange.com |
191,223 | [
"https://dba.stackexchange.com/questions/191223",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/138385/"
] | I am currently comparing performance of PostgreSQL with several other SQL systems. I am aware of the <code>\timing</code> option to turn on timing queries. However, I would very much like to automate the process of copying the statements executed and the query speed below it. I imagine there is a simple way to log this... | There are different ways to achieve the goal.
<pre><code>SQL> select to_char(trunc(add_months(sysdate,-12*5),'YEAR'),'YYYYMM') from dual;
</code></pre>
OR
<pre><code>SQL> select to_char(trunc(SYSDATE - interval '5' year,'YEAR'),'YYYYMM') from dual;
</code></pre>
Regarding the second one, what happens if the SYSD... | SQL>
<pre><code>select trunc(sysdate)AS TODAY,
2 ADD_MONTHS(TRUNC(SYSDATE), 12 * 5 * -1) AS minus_5_year from dual;
</code></pre>
Result:
<pre><code>TODAY MINUS_5_YEAR
----------- ------------
04/03/2021 04/03/2016
</code></pre>
<h2><strong>for leap day</strong></h2>
SQL>
<pre><code>select to_date('29/02/... | https://dba.stackexchange.com |
3,239 | [
"https://mathoverflow.net/questions/3239",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1047/"
] | There are many proofs based on a "tertium non datur"-approach (e.g. prove that there exist two irrational numbers a and b such that a^b is rational).
But according to Gödel's First Incompleteness Theorem, where he provides a constructive example of a contingent proposition, which is neither deductively (syntactically)... | You are confused.
The best way out of your confusion is to maintain a very careful distinction between strings of formal symbols and their mathematical meanings. Godel's theorem is, on its most primitive level, a theorem about which strings of formal symbols can be obtained from other strings by certain formal manipul... | You're missing the distinction between <em>truth</em> and <em>proof</em>. Godel's Theorem says there are statements which are neither <em>provable</em> nor <em>disprovable</em> (from a given set of axioms). Those statements are still either true or false in a given universe. Godel just says your axioms aren't good enou... | https://mathoverflow.net |
21,257 | [
"https://stats.stackexchange.com/questions/21257",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3691/"
] | I am performing simple (first-order terms) linear regression on data having several categorical variables (i.e. factors), and it is often desired that for each factor, one of the levels should add nothing to the regressand, and the other levels should add positive values to the regressand. When I perform a regression ... | Thanks to whuber's comment, and Seb's answer, I have put together the following function which I believe does what I want. Hopefully it will be useful to someone. Comments are welcome.
<pre><code># take a dataframe, and re-level it such that the levels of the factors are
# assigned positive coefficients by lm()
# NO... | Here is an attampt of doing what you wanted.
<pre><code> # Setting up some sample data
require(dummies)
df <- data.frame(categorial=rep(c(1,2,3), each=20), x=rnorm(60))
flevels <- dummy(df$categorial)
df$categorial <- factor(df$categorial)
df$y=20 + df$x*3 + flevels%*%c(3,1,2) + rnorm(60)*2
</code></pre... | https://stats.stackexchange.com |
103,903 | [
"https://softwareengineering.stackexchange.com/questions/103903",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27417/"
] | At the beginning of every iteration our whiteboard is covered with "not started" stories estimated in IDEAL HOURS. On a daily basis we update these estimates to keep track of each task's progress. I think we are doing it wrong. The original estimates are in ideal hours and our daily "re-assessment" in ELAPSED TIME. Thi... | We never update our original estimates. Instead we just also log total time spent on the ticket. This gives us better information so we can review are estimation process and drive out any issues. We also check to make sure our estimates are as close to consistent in terms of actual effort.
| Reestimating tasks during sprint is non-sense. It will just spoil burndown chart and it will not change commitment you already did.
Anyway in my opinion whole point of "estimating" tasks is waste. What you will get by estimating these tasks?
<ul>
<li>Will the estimate will make your product better? </li>
<li>Will th... | https://softwareengineering.stackexchange.com |
232,689 | [
"https://electronics.stackexchange.com/questions/232689",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51619/"
] | I am maintaining and developing software in C for S12X micro controllers. The ISR for each interrupts (like I2C, Timer Interrupts etc) are very lengthy, like around 20 to 30 lines with several calculations inside the ISR for several interrupts.
From what I have read the ISR should be as short as possible. Am I correct... | In general, keeping interrupts short is a good idea. How rigidly you need to follow this advice obviously depends on what you are trying to do, and we don't know that. Good engineering involves knowing when it's safe to leave your guidelines.
Debugging?? At this level, whatever helps you see what's going on. From y... | Adding to the above point a good way to deal with interrupts inside the ISR is that you just set a variable inside the interrupt and clear the interrupt status register flags. And in the main you just keep checking continuosly if this variable is set or not. If it is set then reset it first and do whatever you where ab... | https://electronics.stackexchange.com |
378,434 | [
"https://electronics.stackexchange.com/questions/378434",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/183336/"
] | Is it possible to measure the output of a Variable Frequency Drive without relying on it's display data? I tried to measure the line voltage with a DMM and current with a clamp meter but it shows inaccurate results. I'm running the motor at 50Hz and the carrier frequency is 6kHz if that matters.
Thank you in advance!
| Getting the PCB itself manufactured probably doesn't cost extra. The features you need are <em>milling slots</em> and <em>castellated holes</em>. These are already part of the base service for many PCB shops.
In your example the space for the component is at the edge of the board, so it gets made the same time they ro... | Common enough. The process is called "Z-axis milling". Used for LEDs sometimes too.
You can even bury low-profile parts such as bypass capacitors and resistors in cavities entirely within multilayer PCBs.
It requires extra steps so expect extra costs or MOQ or both. For small quantities the costs may be prohibitiv... | https://electronics.stackexchange.com |
1,378,459 | [
"https://math.stackexchange.com/questions/1378459",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/176662/"
] | Prove that for all $\xi \in \mathbb{C}$,
$$\int_{-\infty}^{\infty}e^{-\pi x^2}\cdot e^{-2\pi ix\xi}dx = e^{\pi\xi^2}$$
I don't really know how to compute this integral. Can you please help me?
| Here is a solution avoiding the residu theorem or any change of variables over the complex plane.
Let $g(\xi)$ be the left hand side :$$g(\xi)=\int_{\mathbb R} e^{-\pi x^2}e^{-2i\pi x\xi}dx.$$
One can easily check that $f:\mathbb R\times \mathbb C\rightarrow \mathbb C$ given by $f:(x,\xi)\mapsto e^{-\pi x^2}e^{-2i\pi ... | By noticing that
$$a x^{2} + b x = \left( \sqrt{a} x + \frac{b}{2 \sqrt{a}} \right)^{2} - \frac{b^{2}}{4 a}$$
then
\begin{align}
I &= \int_{-\infty}^{\infty} e^{-a x^{2} - b x} \, dx \\
&= e^{\frac{b^{2}}{4 a}} \, \int_{-\infty}^{\infty} e^{- \left( \sqrt{a} x + \frac{b}{2 \sqrt{a}} \right)^{2}} \, dx
\end{al... | https://math.stackexchange.com |
488,999 | [
"https://physics.stackexchange.com/questions/488999",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/169942/"
] | Consider a quantum spin chain of length <span class="math-container">$N$</span>. Each site/spin has the local Hilbert space <span class="math-container">$\mathbb{C}^d$</span> and so for the whole chain the Hilbert space is <span class="math-container">$(\mathbb{C}^d)^{\otimes N}$</span>. Now for periodic boundaries, we... | So just to extend my comment as an answer: Consider a two-body Hamiltonian <span class="math-container">$h$</span> defined on <span class="math-container">$\mathbb{C}^d \otimes \mathbb{C}^d$</span>, it can always be expanded as <span class="math-container">$h=\sum_p A^{(p)} \otimes B^{(p)}$</span>, where <span class="m... | You seem to be confused by the basis-dependent definition of a tensor product.
<span class="math-container">$$A \otimes B = \left( \begin{array}{cccc}
a_{11} b_{11} & a_{11}b_{12} & a_{12}b_{11} & a_{12}b_{12} \\
a_{11} b_{21} & a_{11}b_{22} & a_{12}b_{21} & a_{12}b_{22} \\
a_{21} b_{11} &... | https://physics.stackexchange.com |
37,609 | [
"https://dba.stackexchange.com/questions/37609",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10832/"
] | We have recently upgraded from SQL Server 2005 to SQL Server 2012. Under SQL Server 2005 there is no option to create compressed backups as there is in 2012.
If you attempt <code>BACKUP DATABASE ... WITH (COMPRESSION);</code> to a file that has already been initialized without compression, the <code>BACKUP DATABASE</... | I created the following stored procedure that can be used to determine if a database backup file is initialized for compression:
<pre><code>CREATE PROCEDURE IsBackupFileCompressed
(
@BackupFileName nvarchar(255)
, @UseXPFileExists bit = 1
)
AS
BEGIN
/*
Inspects the header of the given backup file t... | Maybe instead of backing up over and over again to the same file, you should consider using <code>WITH INIT</code> and a new file always. I think it is simpler to manage multiple backup files, all with their own timestamp embedded into the filename, and be able to archive/purge each file individually. When you keep dum... | https://dba.stackexchange.com |
89,330 | [
"https://mathoverflow.net/questions/89330",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11546/"
] | Suppose we have $\langle K(n)\rangle$ and $\langle K(n-1) \rangle$ for some fixed prime $p$. do we know whether or not $\langle K(n) \rangle \geq \langle K(n-1) \rangle$ or $\langle K(n-1) \rangle \geq \langle K(n) \rangle$?
It seems to me that the first relation is accurate if we somehow restricted ourselves to finit... | It is standard that $K(n)\wedge K(m)=0$ for $n\neq m$. One way to think about this is as follows: if $E$ and $F$ are complex oriented ring spectra then the corresponding formal group laws become isomorphic over $\pi_*(E\wedge F)$, but it is easy to see that formal group laws of different heights can only become isomor... | Neil's answer is great. I just wanted to add that in fact the Bousfield classes of the Morava $K$-theories are minimal non-zero classes in the Bousfield lattice. In particular, $\langle K(n) \rangle$ and $\langle K(n-1) \rangle$ are not comparable.
| https://mathoverflow.net |
357,879 | [
"https://mathoverflow.net/questions/357879",
"https://mathoverflow.net",
"https://mathoverflow.net/users/123273/"
] | There is a supermartingale convergence theorem which is often cited in texts which use Stochastic Approximation Theory and Reinforcement Learning, in particular the famous book "Neuro-dynamic Programming" the theorem is:
"Let <span class="math-container">$Y_t, X_t, Z_t, t = 1,2,3,....$</span> be three sequences of ran... | Here's one approach.
First notice that
<span class="math-container">$$
R_t: = Y_{t} + \sum_{i=1}^{t-1} X_i - \sum_{i=1}^{t-1} Z_i
$$</span>
is a supermartingale, since
<span class="math-container">$$
R_{t+1} - R_t = Y_{t+1} - Y_t + X_t - Z_t,
$$</span>
giving
<span class="math-container">$$
E(R_{t+1} - R_t | \mathc... | As far as I know this statement was first proved by Robbins and Siegmund in their paper "A convergence theorem for non negative almost supermartingales and some applications" from 1971.
| https://mathoverflow.net |
137,460 | [
"https://physics.stackexchange.com/questions/137460",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59953/"
] | I heard this quote a lot (especially from my teachers) and I always wanted to know whether or not it was actually true. I think that its partially true; a chain with one weak link is weaker than a chain with a lot of links that are slightly weak. So does the force just spread out or what actually happens?
| Instead of working with angles (which are very easy to mess up in 3D), I would just go directly to a transformation matrix. I had to solve a very similar problem to this when tracking charged particles through magnetic fields and all the angles and rotations kept messing me up (probably due to subtle sign errors). So, ... | <blockquote>
Is my approach fundamentally wrong or am I just making a silly computational error?
</blockquote>
You made a number of computational errors. The purpose of this answer is to show what you did wrong, and how to fix it. That said, I recommend using Mark H's approach.
<br>
Your first error was that you m... | https://physics.stackexchange.com |
144,763 | [
"https://cs.stackexchange.com/questions/144763",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/143833/"
] | Recently I'm studying 3SAT problem, which is a NP-complete problem. I feel that it's easy to find a boolean formula which is satisfiable,but how about boolean formulas which are unsatisfiable， namely 3-co-SAT problem.
Can you help me provide some examples of 3-co-SAT?
The definition of 3SAT problem is supplemented here... | There is no problem with assuming <span class="math-container">$ \neg q$</span> towards a contradiction and showing that this implies <span class="math-container">$q$</span>.
Here is an example, adapted from Euclid's proof that there are infinitely many primes.
Let <span class="math-container">$p$</span> be a prime num... | I'll add some steps to make it very clear. You want to prove q.
You can take any statement s, then say "either s or not s is true", and then prove "if s is true then q is true" and "if not s is true then q is true". That happens actually quite often; you might have the statement "x ≤ ... | https://cs.stackexchange.com |
67,364 | [
"https://physics.stackexchange.com/questions/67364",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25513/"
] | I've heard before that everything in physics can be thought of as either a field, or its excitation. Is there some intuitive explanation of how I can look at gravity, light, electromagnetism, etc as a field/excitation?
| A field is just something that has a value at every spatial coordinate (or close to that). It is easy to think of gravity and electric/magnetic fields. Consider gravity, no matter where you go, you can always state the value of gravity at that position (and it's direction but that is not a necessary condition). For exa... | A classical field is simply a space-time function $\Phi(x,y,z,t)$, whose parameters are space-time coordinates $x,y,z,t$, and $\Phi$ is a quantity depending of the considered problem.
For instance, the temperature $T$ could vary from time to time, and vary from one place to another place, so you can modelize this tem... | https://physics.stackexchange.com |
142,995 | [
"https://softwareengineering.stackexchange.com/questions/142995",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11107/"
] | Let's say we have a winform application with a buttonclick event. The buttonclick handles everything from the UI configuration to the database call and data manipulation. So you end up with a method that is 100's of lines of code long. Outside the fact that this code can't be considered test-able for various reasons... | Find a suitable paradigm like Model-View-Controller, and discuss it specifically.
I think you will find that your developers will immediately see the benefits of following a pre-defined architectural standard. You will also be talking about something concrete, rather than pie-in-the-sky abstract concepts.
ASP.NET MV... | This is going to require a time investment. If people are committed to practices like "duct-tape programming", avoiding unit tests, writing static-procedural code in an OO language, etc, speeches about decoupling and test seams are not going to sway them. Speeches about anything probably won't sway them.
Keep to you... | https://softwareengineering.stackexchange.com |
146,722 | [
"https://mathoverflow.net/questions/146722",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | A well known theorem by Scott says:
<strong>If $\kappa$ is a measurable cardinal and $\mu$ a normal measure on it and $\mu (\lbrace\lambda\in\kappa~|~2^{\lambda}=\lambda^{+}\rbrace)=1$ then $2^{\kappa}=\kappa^{+}$.</strong>
So:
<strong>If $\text{GCH}$ is false in a measurable cardinal then there is a smaller cardina... | The statement is not true.
<strong>Theorem.</strong> If $\kappa$ is strongly unfoldable and the GCH holds below $\kappa$, then it holds at $\kappa$ also.
This is just because the strongly unfoldable cardinals are $\Sigma_2$-reflecting, and the result also holds for any $\Sigma_2$-reflecting cardinal. The strongly unf... | As far as I know the best results in this direction are due to Levinski (see his paper "Filters and large cardinals").
The following results are taken from the above paper. First a few definitions:
A premeasure on $\kappa$ is a normal filter $F$ on $\kappa$ such that $P(\kappa)/I$ is $\kappa^+-$distributive, $I$ the ... | https://mathoverflow.net |
456,596 | [
"https://electronics.stackexchange.com/questions/456596",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/183348/"
] | I think this question is ok in the electronics stack and not the programming stack (I hope).
I have a simple code written in C, on a TM4C123 evaluation board. It uses the two on board switches to control the colour of the on board RGB LED.
The switches are configured in software with pull up resistors and the PORTF ... | As you noted, you have a logic flaw where several of your if statements might be true simultaneously. This should be solved with the equivalent of <code>switch</code>, namely <code>if() else if() ...</code>. This is the least of the problems though.
The root of your problems seems to be the lack of "debouncing", which... | This is one of the possible solutions to my question, which is based on Peter Smith's comment. I replaced the AND assignments in the IF statement condition with a Boolean equal to operator.
Below is the corrected code which is now working and functions how I described it should in the question:
<pre><code>#include "i... | https://electronics.stackexchange.com |
124,146 | [
"https://softwareengineering.stackexchange.com/questions/124146",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/40538/"
] | It's often said that the software industry is immature compared to manufacturing. Specifically with regard to being process driven.
<strong>Question</strong>:
Can we as developers learn from the processes of the manufacturing industry? Can adopting their processes increase the success rate of software development?
... | The fundamental difference between software development and manufacturing is that for software, the design phase is practically the entire thing. The actual production (assembly line part in traditional manufacturing) is a matter of copying a few files around. In software, the product design <em>is</em> the product.
S... | If you wanted to write the same exact software over and over again (as opposed to simply copying it) you could do that very efficiently via an assembly line.
But software creation is not a repetative task, each module is uniqe. That is why the comparison to manufacturing is invalid.
| https://softwareengineering.stackexchange.com |
32,986 | [
"https://electronics.stackexchange.com/questions/32986",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9079/"
] | I'm designing a high current linear regulator and learning about real opamps as opposed to ideal ones described in tutorials all over the net as I go.
<img src="https://i.stack.imgur.com/WpaA0.png" alt="Linear regulator schematics">
My initial voltage regulation design was stable enough under the resistive load, but ... | The first rule of a control system is to never get information late. Unfortunately, this is exactly what low pass filters in the feedback path do. In particular, R13, C8, R12, C3, and C6 are going to cause stability problems in current limit mode. Also the fact the IC3B is being run open loop means the current shut ... | This system has two loops - a voltage loop based around VSET, and a current loop based around ISET. The current loop output modifies the voltage loop reference, which changes the output voltage, which changes the load current and voila, you have a closed-loop system.
If the current detection is meant as a fail-safe ov... | https://electronics.stackexchange.com |
987,348 | [
"https://math.stackexchange.com/questions/987348",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/186710/"
] | If $X = (X_1,X_2)$ and $Y = (Y_1,Y_2)$ , $X$ and $Y$ are stochastically independent can $X_1$ and $Y_1$ be dependent?
| Let us consider that all variables are continuous and let us consider probability density functions $f$ that are distinguished by their arguments.
The independence of $X$ and $Y$ means
$$f(X,Y)=f(X)(Y)$$
The right hand side can be written using the chain rule as
$$f(X)f(Y) = f(X_2,X_1)f(Y_2,Y_1)=f(X_2|X_1)f(X_1)f(Y_2|... | <strong>Hint</strong>:
$$
P(X_1\in A,Y_1\in B)=P(X\in A\times\mathbb{R},Y\in B\times\mathbb{R}).
$$
| https://math.stackexchange.com |
19,631 | [
"https://softwareengineering.stackexchange.com/questions/19631",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3239/"
] | I think it's safe to assume that for most programmers, producing documentation is not as fun as actually coding. I think it's also safe to assume that most good programmers recognize the need for useful documentation, and the code that they write is not an exception by any stretch of the imagination.
So, I'd like to k... | Our Wiki.
Because people actually use it and update it.
I think the nature of a Wiki lends itself to the way developers want to work which is just get the facts down and move on.
It's quick and easy, searching makes it simple to find what you're looking for which minimises the chance of duplication (and the subseq... | Well written tests. They describe what the code should do, and demonstrate that it works.
Since they are automatically run with every build, they are never out of date.
| https://softwareengineering.stackexchange.com |
1,083,993 | [
"https://math.stackexchange.com/questions/1083993",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/145527/"
] | Find the Asymptotes of the function $f(x)=3^x / (3^x+1)$
No way for Vertical asymptotes since the denominator can not be zero
Also, there is no slant asymptote since we will have horizontal asymptotes ( this is the only reason I have )
we are left with horizontal asymptote, there are two : I found one but I could no... | Common sense: In the first place, recall that $3^x\to0$ as $x\to-\infty$. And if you don't recall that, look at this:
\begin{align}
3^0 & = 1 \\
3^{-1} & = 1/3 \\
3^{-2} & = 1/9 \\
& {}\ \ \vdots
\end{align}
every time $x$ gets one step closer to $-\infty$, then $3^x$ gets $1/3$ as big. So it approach... | There are $2$ horizontal asymptotes: $y =0$ and $y = 1$ that correspond to $x \to -\infty$, and $x \to +\infty$. To see it clearer we write: $y = 1-\dfrac{1}{3^x+1}$
| https://math.stackexchange.com |
189,274 | [
"https://softwareengineering.stackexchange.com/questions/189274",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23347/"
] | We are considering to impose a single standard code format in our project (auto format with save actions in Eclipse). The reason is that currently there is a big difference in the code formats used by several (>10) developers which makes it harder for one developer to work on the code of another developer. The same Jav... | I currently work at a place where a standard code format is enforced and the code is automatically formatted when saving the file, just like you are about to do. As a new member of the company I found that the common formatting rules gave me a warm and fuzzy feeling that "these guys know what they are doing", so I coul... | Yes, that is good to have one code format styles for all developers.
Design the code style formats and import that to all developers eclipse.
This will help when we are <code>merging</code> code to 'Version control' system.
| https://softwareengineering.stackexchange.com |
3,983,556 | [
"https://math.stackexchange.com/questions/3983556",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/558071/"
] | I am referring book Topology Without Tears
(i)In the book it is said,<span class="math-container">$\mathcal{B}$</span> collection of all 'open rectangles' <span class="math-container">$\{(x,y):(x,y)\in \mathbb{R}^2,a<x<b,c<y<d\}$</span> in the plane which have sides parallel to the <span class="math-contain... | By <span class="math-container">$B(x,r)$</span> I will denote an open ball around <span class="math-container">$x$</span> of radius <span class="math-container">$r$</span>.
Intersection of two open discs need not be a disc. But it can be written as union of open discs. Take two open discs <span class="math-container">$... | Beside the expressions of @freakish, notice that since your triangles have parallel bases, and therefore other sides too, the intersection of those becomes equilateral one too, also its base is parallel to others.
| https://math.stackexchange.com |
587,050 | [
"https://physics.stackexchange.com/questions/587050",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251995/"
] | Let's say that we have a gaseous or liquidus compound (I don't know if elements or compounds make a difference, take this as a thought experiment), and we have a tungsten or steel block that's 5cm (or less, you choose) thick. Is there any physical method for that gas or liquid to pass through that thick heavy metal blo... | Yes, some gases can diffuse into and through metal. It is the bane of the high-vacuum engineer's life. Hydrogen is the worst because it tends to dissociate into atoms at the surface and the nucleus, a single proton, can then leave its electron behind and wander through the metal lattice until it picks up another electr... | Not really, but sort of.
Helium atoms do not form molecules, and the atoms are small. They fit between the spaces in iron, and can diffuse around inside.
This is not a fast process. That is to say, it does not create a measurable leak.
I have heard of one case where that actually created a problem, though I have forgot... | https://physics.stackexchange.com |
110,231 | [
"https://physics.stackexchange.com/questions/110231",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/37286/"
] | As stated in the heading: Is $\frac{\partial}{\partial \Phi(y)} \Phi (x) = \delta(x-y)$ correct? Here denotes $\Phi(x)$ denotes a scalar field. And if yes, why? Any reference where I can read about this would be great.
| It is not. The correct identity is $$\frac{\delta}{\delta \Phi(y)} \Phi (x) = \delta(x-y)$$
where the derivative is the <strong>functional derivative</strong>.
If $F : D(F)\ni \Phi \mapsto F(\Phi)\in \mathbb C$ is a function from a space of functions $D(F)$ to $\mathbb C$, the <em>functional derivative</em> of $F$, if... | The functional differentiation identity is given by$^{\dagger}$
$$\frac{\delta}{\delta J(x)}J(y)=\delta^{(d)}(x-y) \quad \implies \frac{\delta}{\delta J(x)} \int \mathrm{d}^d y \, J(y)\phi(y)=\phi(x) \qquad (1)$$
The identity is the natural generalization, as Peskin and Schroeder state, of the discrete identities,
... | https://physics.stackexchange.com |
550,090 | [
"https://physics.stackexchange.com/questions/550090",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262085/"
] | I have a doubt about the work done by elastic force.
The general formula of the work is: <span class="math-container">$W_{Fe} = \frac{1}{2}k(x_0^2-x^2)$</span>; if we take that the state in which the spring is at rest, we have: <span class="math-container">$W_{Fe} = -\frac{1}{2}kx^2$</span> for both cases where the sp... | You can characterise isometries as those linear maps that can be written in the form
<span class="math-container">$$V = \sum_{k=1}^d |u_k'\rangle\!\langle u_k| \in \operatorname{Lin}(\mathcal H,\mathcal H'),$$</span>
where <span class="math-container">$\{|u_k\rangle\}_k$</span> is an orthonormal basis for <span class="... | A partial isometry is mapping a sub-vector space <span class="math-container">$K$</span> of a Hilbert space <span class="math-container">$H$</span> onto another sub-vector space <span class="math-container">$K'$</span> of the same dimension <em>isometrically</em>, that is
<span class="math-container">$$(V\psi, V\phi) ... | https://physics.stackexchange.com |
74,154 | [
"https://physics.stackexchange.com/questions/74154",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21805/"
] | From Wikipedia: The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product:
$$W = Fd.$$
If I lift some object from a ground, the force to be put in above equation is the gravitational force $mg$.
But while I am moving the object upwards, again... | You are getting confused between work done by a <em>single force</em> and <em>total work done</em> on a body. When you substitute $F=mg$ in the above equation<sup><strong>[1]</strong></sup>, you are calculating the work done <em>by the gravitational force</em>, only the gravitational force and nothing else.
Substituti... | When you accelerate the object the applied force is greated than gravity. The formula is
$$ F = m ( g + \ddot{y} ) $$
where $\ddot{y}$ is the upwards acceleration. The work put in the system is equal to the work needed to lift the object (potential energy) plus the work needed to move the object (kinetic energy).
Th... | https://physics.stackexchange.com |
3,072 | [
"https://mechanics.stackexchange.com/questions/3072",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1497/"
] | I have a 2001 Dodge Durango, and the passenger-side brake light will not work, even after replacing the bulb.
The bulb that I replaced was obviously burned out. I double-checked the new bulb, and it looks fine. I checked the connectors on the inside of the bulb housing, and it looks fine as well--very clean. I thought... | I finally got this figured out.
The housing inside the actual tail-light assembly had become deformed, I guess due to heat, thus keeping the light-bulb housing from making proper contact with the tail-light assembly. A new tail-light assembly fixed the issue.
Thanks, everyone, for your help with this issue.
UPDATE:... | Last time I saw that problem it ended up being the socket on the vehicle. Could also potentially be wiring of course.
| https://mechanics.stackexchange.com |
113,911 | [
"https://mathoverflow.net/questions/113911",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27760/"
] | Suppose $G$ is a finite group and $F$ is a field. Is $F[G\wr S_n]$ a cellular algebra ?. If so, what is a cellular basis for that algebra.
| I don't believe that $F[G]$ is cellular in general. My reason (and this is not a proof) is that cellular algebras are typically quasi-hereditary (which implies finite cohomological dimension) and group algebras are not close to quasi-hereditary.
| Just noticed this discussion. We invented "cyclic cellularity" precisely to make the argument for wreath products work. Our argument wouldn't work without the cyclic condition.
All standard examples of cellular algebras are in fact cyclic cellular, so one doesn't lose much by imposing this extra hypothesis.
| https://mathoverflow.net |
16,471 | [
"https://mathoverflow.net/questions/16471",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4267/"
] | Consider the set of random variables with zero mean and finite second moment. This is a vector space, and $\langle X, Y \rangle = E[XY]$ is a valid inner product on it. Uncorrelated random variables correspond to orthogonal vectors in this space.
Questions:
(i) Does there exist a similar geometric interpretation for... | There is a Hilbert space interpretation of independence, which follows from the interpretation of conditional expectation as an orthogonal projection, though it may be more complicated than you had in mind.
Say your underlying probability space is $(\Omega, \mathcal{F}, \mathbb{P})$, and write $L^2(\mathcal{F})$ for ... | (i) Not if I understood you correctly. A Hilbert space is so very symmetric that given that orthogonality is necessary but not sufficient for independence, there isn't anything else to look for. To be precise, any set of orthogonal vectors can be carried onto any other set of orthogonal vectors of the same cardinality ... | https://mathoverflow.net |
210,081 | [
"https://physics.stackexchange.com/questions/210081",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/43712/"
] | For a coherent state <span class="math-container">$$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_n\frac{\alpha^n}{\sqrt{n!}}|n\rangle$$</span> please show me how to prove,<br />
<span class="math-container">$$
\mathrm{Tr}\left[|\alpha\rangle\langle\alpha|\hat{A}\right]=\langle\alpha|\hat{A}|\alpha\rangle,
$$</span>
whe... | Let $|n'\rangle$ be a basis of the Hilbert space, then
$$
\textrm{tr}\Big[|\alpha\rangle\langle\alpha|A\Big]=\sum_{n'}\langle n'|\alpha\rangle\langle\alpha|A|n'\rangle=\sum_{n'}\langle\alpha|A|n'\rangle\langle n'|\alpha\rangle = \langle\alpha|A\left(\sum_{n'}|n'\rangle \langle n'|\right)|\alpha\rangle=\langle\alpha|A|\... | Another way to see this is to observe that any state $|\psi⟩\in\mathcal H$ can be extended to an orthonormal basis of the Hilbert space, and in that basis the trace $\operatorname{Tr}\left(|\psi⟩⟨\psi|\hat A\right)$ is exactly $⟨\psi|\hat A|\psi⟩$.
More explicitly, for any $|\psi⟩\in\mathcal H$ there exists a sequence... | https://physics.stackexchange.com |
582,198 | [
"https://physics.stackexchange.com/questions/582198",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/226508/"
] | In a lot of literature the notion of different Hilbert spaces has been mentioned. In QFT, for non-interacting theories the Hilbert space is a called a 'Fock space', this is different from the interacting theory 'Physical Hilbert Space'.
When the notion of Hilbert spaces was introduced to me it was described as the spac... | I'll start with a generic perspective, and then I'll apply it to the question about Hilbert space. Here's the generic perspective:
<ul>
<li>Sometimes we use one mathematical thing to represent another mathematical thing. Here, a <strong>representation</strong> is a mapping from <span class="math-container">$A$</span> t... | The single-particle Hilbert space is the space of functions <span class="math-container">$\psi: \, \mathbb{R} \to \mathbb{C}$</span> [with value <span class="math-container">$\psi(\vec{r})$</span>] with finite <span class="math-container">$L^2$</span> norm (normalizable functions). Furthermore boundary conditions may l... | https://physics.stackexchange.com |
282,556 | [
"https://electronics.stackexchange.com/questions/282556",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/137089/"
] | In my case I am working on passive analog filters, but I think the question applies to any other type of analog filter design. Typically I think the process for designing analog filters is to calculate the desired components using equations, or perhaps if we're with a large company we might use filtershop. We will th... | <em>zener diodes (or diodes in general) only conducts current in one direction</em>
That is only partly true, Zener diodes will also conduct when the reverse voltage exceeds a certain value. Here that value is 2.4 V (they are 2.4 V zeners). Add to that the forward voltage of the other Zener (about 0.7 V) and the two Z... | <blockquote>
zener diodes ... only conducts current in one direction.
</blockquote>
On the contrary, the defining behaviour of Zener diodes is that they conduct in both directions, albeit with different forward voltages. That is, forward biased, they typically behave like a regular silicon diode, and have a forward ... | https://electronics.stackexchange.com |
453,341 | [
"https://physics.stackexchange.com/questions/453341",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/210715/"
] | I have basis knowledge in special relativity, but I haven't studied it for too long and I'm stuck in a simple thought experiment. Assume that there is a spaceship departing from the earth at speed of light (I know it is not possible but it's just a thought experiment). There is a clock in the spaceship with time 00:00 ... | Commenters are objecting that a clock cannot travel at the speed of light, so let's modify your thought experiment to preserve its spirit but eliminate that objection:
A beam of light travels from the earth, passing mileposts that are placed every light-second. Each time it passes a milepost, it triggers a mechanism ... | What you did here was throwing away special relativity and pointing out that the result is in contradiction with special relativity.
As you correctly said, any time interval on the spaceship corresponds to an infinitely long time for a stationary observer, and the signal will never be even sent from that perspective, ... | https://physics.stackexchange.com |
321,378 | [
"https://electronics.stackexchange.com/questions/321378",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/109827/"
] | I am planning to buy an oscilloscope. I always used oscilloscopes which come with an LCD display. But I found there are USB oscilloscopes as well which can be connected to PC and get data from the PC. Since I already have a laptop I felt like that's a better choice.
But is there any disadvantage in terms of accuracy/... | Although this is a very opinion-based matter, there are two things to keep in mind. I presume here, with "USB scope" you refer to an oscilloscope that has no display or controls, and requires a computer to operate. I presume you do not mean an oscilloscope that can be connected to a computer, since any modern scope is ... | A USB scope can be useful as a lower cost alternative to a non-USB scope. But it will tie up your laptop if at the same time as testing electronics you wish to look at schematics.
Also be aware that the typical modern standlone LCD screen scope that is in the typical hobbiest or single engineer budget price range is ... | https://electronics.stackexchange.com |
72,589 | [
"https://biology.stackexchange.com/questions/72589",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/42023/"
] | So the question is if:
a deletion of a codon for the amino acid lysine (AAG) is more or less likely to cause nonfunctionality of the protein than:
<ol>
<li>Insertion of an additional base (C) within the start codon for this protein</li>
<li>Mutation of the stop codon (TAG) to an arginine codon (CGC)</li>
</ol>
My a... | I think the question is fairly confusingly worded, so good job on your attempt based on that.
<ol>
<li>If a C is inserted <em>within</em> the start codon, I presume that is referring to making a sequence that was originally ATGXXX and making it either ACTGXXX or ATCGXXX. Either insertion means the start codon will be ... | I would interpret "within the start codon" as meaning changing ATG to ACTG or ATCG or ATGC. All of which are going to destroy the start codon, which is likely to ruin the protein.
Whereas adding extra amino acids at the end might not affect the protein function of the rest of the protein. Protein functions tend to b... | https://biology.stackexchange.com |
2,573 | [
"https://stats.stackexchange.com/questions/2573",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | If we want to visibly see the distribution of a continuous data, which one among histogram and pdf should be used?
What are the differences, not formula wise, between histogram and pdf?
| To clarify Dirks point :
Say your data is a sample of a normal distribution. You could construct the following plot:
<img src="https://i.stack.imgur.com/i4NXE.png" alt="alt text">
The red line is the empirical density estimate, the blue line is the theoretical pdf of the underlying normal distribution. Note that the... | A histogram is pre-computer age estimate of a density. A density estimate is an alternative.
These days we use both, and there is a rich literature about which defaults one should use.
A pdf, on the other hand, is a closed-form expression for a <em>given</em> distribution. That is different from describing your dat... | https://stats.stackexchange.com |
345,381 | [
"https://physics.stackexchange.com/questions/345381",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/32222/"
] | It was claimed that if an iceberg melts in the ocean, the sea level won't change as the ice displaces as much water as there will be melted water. The other claim was that the sea level should rise because oceans contain salt, so the water in oceans is denser than the water in the ice. Which one is the correct reasonin... | The Archimedes principle says that a floating body will displace an amount of fluid that is equal to its weight.
Since the iceberg floats, it weighs the same as the water it displaces. If it had the same salt concentration as the ocean, then once thawed, it would occupy exactly the same volume as it displaced and the ... | The one you're not contemplating: that the sea level rises because of melting of ice that's currently over land. As noted in Rodrigo's answer, when sea ice melts there is no change in the water level, and if the ice is made from fresh water then there will be a small change due to the mismatch in densities. However, th... | https://physics.stackexchange.com |
119,039 | [
"https://physics.stackexchange.com/questions/119039",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16177/"
] | I seem to recall that $r^2 \dot{\theta}$ is a conserved quantity in orbital mechanics, which I just proved using the Euler-Lagrange equations. Namely via:
$ \mathcal{L} = \frac{m}{2} (\dot{r}^2+r^2 \dot{\theta}^2)+\frac{GMm}{r}$
$\frac{\partial{\mathcal{L}}}{\partial \theta}=\frac{d}{dt}\frac{\partial\mathcal{L}}{\pa... | $mr^2\dot\theta$ is the angular momentum, which is conserved. The quantity $r^2\dot\theta$ is conserved if $m$ is independent of time, but it doesn't have a name that I know of.
| You have a mistake in your calculation. Its $mr^2\dot\theta$ which is equal to a constant. This is the angular momentum which we know is conserved.
| https://physics.stackexchange.com |
34,294 | [
"https://scicomp.stackexchange.com/questions/34294",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/26978/"
] | After some parallel computations, I need to write the results in a file and for plotting reasons, I want them in ASCII format. Because of performance issues, I want to avoid to <code>MPI_SEND</code> the data to the master process and make him print. Thus, I am wondering if there is a way to write directly in ASCII with... | It's possible to use VTK library and its parallel IO built-in mechanism to write the files from each rank to different file and ParaView could combine them again to show you the visualization. Also, I should say I don't have a FORTRAN example and unfortunately VTK doesn't support FORTRAN officially. So, I'll show you a... | The problem with output from parallel processes is that they all go through ssh tunnels, and there is no guarantee in what order they will arrive. Even if you use Send/Recv to sequentialize them.
You could do the following:
<pre><code>mpirun -np 8 program_script
</code></pre>
where program_script:
<pre><code>#!/bin... | https://scicomp.stackexchange.com |
118,589 | [
"https://security.stackexchange.com/questions/118589",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/105613/"
] | Sites like PersonalCapital require you submit your account login details for every one of your banking account providers.
Could personal capital potentially log into your financial accounts and make changes? What if personal capital is hacked?
These sites don't really seem safe to me, since they ask for financial a... | It all comes down to the old adage: <em>"Good IT security is <strong>hard</strong>"</em>.
While none of the concerns are <em>known</em> by us here to be fatal (we can't know your whole business and client model), they do raise serious doubts or at least things to really think hard about, and are worth taking soberly.... | I didn't read all the details you wrote, I just want to make a general observation: you're planning on <em>re-implementing</em> part of an existing standard. Most likely, in a few months you'll realize you need another feature and you'll have to re-implement some more of that standard. Unless you're a genius cryptograp... | https://security.stackexchange.com |
108,170 | [
"https://mathoverflow.net/questions/108170",
"https://mathoverflow.net",
"https://mathoverflow.net/users/26809/"
] | Is there a hyperreal-valued finitely additive measure on all the subsets of [0,1), or at least the Borel ones, that
<ol>
<li>assigns $b-a$ to $[a,b)$ and to $(a,b]$ for all $a\lt b,$ and </li>
<li>assigns an infinitesimal--ideally, the same one--to each singleton?</li>
</ol>
It's (1) that's a problem. The Bernstein... | Yes, by compactness.
Let $R$ denote your favorite hyperreal ordered field
and let $\delta\in R$ be a positive infinitesimal.
Let $\mathcal{E}$ denote the set of all
(standard) finite Boolean subalgebras of $\mathcal{P}([0,1))$.
For every $A\in\mathcal{E}$,
let $\lambda_A(I)$ be the (exact) length of $I$
for all h... | I think this is a very interesting question.
In response to your comment, let me argue that if 1 holds and the measure is additive, then the singleton values are all the same. This is the sense in which the strong form of 2 follows from the weak form of 2.
To see this, following Sean's comment, observe that $\mu
(\{... | https://mathoverflow.net |
65,441 | [
"https://cs.stackexchange.com/questions/65441",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/60648/"
] | Let $A = (Q,Σ,\delta,q_0,F)$ be an NFA such that $L = L(A)$.
We define a DFA $A'=(Q',Σ,\delta,q_0',F')$ as:
$$
Q'=2^Q, \qquad q_0'=\{q_0\}\\F'=\{q\in Q \mid q'\cap F \neq\emptyset\}
$$
My question is how we know what elements $Q'$ has? What is the formal definition to obtain these elements? Because it can contain al... | Condition $A$ is <em>stronger than</em> condition $B$ if $A$ implies $B$. That is, if $B$ holds in all situations in which $A$ holds. Conversely, if $A$ is stronger than $B$, then $B$ is weaker than $A$. Note that, from the definition, $A$ is stronger and weaker than itself, si... | The consequence rule is a necessary${}^*$ piece of glue we typically apply in a few select situations around loops.
<ol>
<li>We're trying to prove $\{\psi\}\mathbf{while}~g~\mathbf{do}~P~\mathbf{od}\{\phi\}$ but the standard rule
$$\frac{\{I\land g\}P\{I\}}{\{I\}\mathbf{while}~g~\mathbf{do}~P~\mathbf{od}\{I\land\neg ... | https://cs.stackexchange.com |
1,317,406 | [
"https://math.stackexchange.com/questions/1317406",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $A_p$ be the set of all numbers whose prime factors are all in first $p$ prime numbers.
example: $A_2= \{2,3,4,6,9,12,16,18,\ldots \}$ (all of these numbers can be generated by repeatedly multiplying only $2$ and $3$ the first two prime numbers).
as $p \to \infty$
intuition is that this set would cover all of na... | You haven't really defined a meaning for your $A_\infty$, unless you think "the first infinity prime numbers" make sense.
If you <em>choose</em> a definition for $A_\infty$ -- such as the union of all $A_p$ for <em>finite</em> $p$,
$$ A_\infty = \bigcup_{p\in\mathbb N} A_p $$
then it will be easy to show that $A_\inft... | I would be more comfortable calling it $A_n$ than $A_p$ because the letter $p$ is often used to refer only to a prime number.
Probably the concept you need is that of a <b>union</b> of sets, and that is <b>not</b> defined by saying $n\to\infty$. The union
$$
\bigcup_{n\in\mathbb N} A_n \tag 1
$$
is defined by saying ... | https://math.stackexchange.com |
51,361 | [
"https://stats.stackexchange.com/questions/51361",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/21566/"
] | This might be a basic question, but I want to be sure that what I'm doing is right. I have a model that suggests that variable X causes both Y and Z. When I regress Y on X, or Z on X, I get positive and significant coefficients as expected.
Now, when I regress Z on Y, I still get a positive significant coefficient.
<... | As a start:
<pre><code>f <- function(x1,x2,a,b1,b2) {a * (b1^x1) * (b2^x2) }
# generate some data
x1 <- 1:10
x2 <- c(2,3,5,4,6,7,8,10,9,11)
set.seed(44)
y <- 2*exp(x1/4) + rnorm(10)*2
dat <- data.frame(x1,x2, y)
# fit a nonlinear model
fm <- nls(y ~ f(x1,x2,a,b1,b2), data = dat, start = c(a=1, b1=1... | Huub Hoofs' approach above worked! Thank you. Here is the technique I utilized to plot a visualization of the model:
<pre><code># x1 is the variable we want to show on the x-axis
plot(x1, y)
# generate a range of values for x1 in small increments to create a smooth line
xRange <- seq(min(x1), max(x1), length.out ... | https://stats.stackexchange.com |
3,021,887 | [
"https://math.stackexchange.com/questions/3021887",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/593845/"
] | The problem is as follows:
Let <span class="math-container">$F$</span> be a field and <span class="math-container">$K \leqslant F$</span>. Let <span class="math-container">$f(x)$</span> and <span class="math-container">$g(x) \in K[x]$</span>, where <span class="math-container">$f$</span> and <span class="math-containe... | Well I'll be honest, your work doesn't make much sense past a certain point.
Specifically not only do <span class="math-container">$b(x)$</span> and <span class="math-container">$c(x)$</span> not need to be in <span class="math-container">$K$</span>, they probably aren't since they're polynomials in <span class="math-... | By Bezout, <span class="math-container">$\,f,g$</span> coprime <span class="math-container">$\,\Rightarrow h f + h' g = 1\ $</span> so evaluating at <span class="math-container">$\,x=a\,$</span> yields <span class="math-container">$\,0 = 1\,$</span> in <span class="math-container">$F\, \Rightarrow\!\Leftarrow$</span>
| https://math.stackexchange.com |
38,344 | [
"https://electronics.stackexchange.com/questions/38344",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5694/"
] | I have been working with some board layouts that include a test point for every net on the circuit (or close to it). This lead me to a search for other topics about test points and general design-for-test procedures and guidelines around here, but I found nothing. So, my question is a bit broad and ill-defined, but her... | I add test points to a majority of the boards I work on - unless the client specifies otherwise. I won't add test point for <em>every</em> net, but power and ground nets definitely get a test point. When we get a batch of boards back from the fab house, I grab the DMM and "Ohm out" the test points, to make sure nothing... | <ul>
<li>Always have the bare board (PCB) 100% tested against the netlist you supply. If you are depending on controlled impedances, have the board fab for that too.</li>
<li>JTAG doesn't add to the cost of the board or require additional chips, just a connector. But make sure you can seperate the chains, e.g. one for ... | https://electronics.stackexchange.com |
112,378 | [
"https://electronics.stackexchange.com/questions/112378",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43634/"
] | <img src="https://i.stack.imgur.com/6rqln.png" alt="exercise">
I'm having trouble finding the voltage between the points 0 and 1. Can anyone help me? By applying KVL on each closed loop I find that Vi+IiRi is constant for every "i" but I don't know how to find the current flowing trough each resistor and therefore the... | After seeing Horta's answer, I got another way to do it.
Replacing each branch with its Norton's equivalent, we get
<img src="https://i.stack.imgur.com/tviFA.png" alt="schematic">
$$\style{font-size:700%}\Downarrow$$
<img src="https://i.stack.imgur.com/UK253m.png" alt="schematic">
Where,
$$I_x = \sum_{i=1}^{n}{\f... | Using node analysis:
$$ \frac{V_1 - V_p}{R_1} + \frac{V_2 - V_p}{R_2} ... = 0 $$
$$ \frac{V_1}{R_1} - \frac{V_p}{R_1} + \frac{V_2}{R_2} - \frac{V_p}{R_2} ... = 0 $$
$$ V_p(1/R_1+1/R_2...) =\frac{V_1}{R_1}+\frac{V_2}{R_2} ... $$
$$ V_p = (\frac{V_1}{R_1}+\frac{V_2}{R_2}...)\times\frac{1}{(\frac{1}{R1}+\frac{1}{R2}+.... | https://electronics.stackexchange.com |
1,429,921 | [
"https://math.stackexchange.com/questions/1429921",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/269600/"
] | I have some trouble with my homework. The problem is to simplify the following trigonometric expression:
$$
\frac{\sin150^{\circ}-\cos240^{\circ}}{\cot730^{\circ}\cot800^{\circ}+\tan730^{\circ}\tan800^{\circ}}
$$
I know that $\sin{150^{\circ}} = \sin{\frac{5\pi}{3}} = \frac{1}{2}$ and $\cos240^{\circ} = \cos{\frac{4\... | What division really means is the inverse of multiplication. So 1/0 means the number you multiply by zero to get one. However, it is a property that x*0 = 0 for all x. This is the reason we say 1/0 is undefined.
This is all a consequence of the interplay of operations (addition and multiplication) on the space of rea... | Both expressions
$$\frac 10 \quad\text{ and }\quad \frac 1{-0}$$
do not make sense with the usual rules of the real numbers.
(If they did, then $0$ would have a multiplicative inverse. Namely, there would exist a real number $x$ such that $0\cdot x = 1$. But it is straight forward to show there is no such number $x... | https://math.stackexchange.com |
315,771 | [
"https://physics.stackexchange.com/questions/315771",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/132386/"
] | I'm having tremendous difficulty accepting the reality of this phenomenon. I have read countless analogies of balls hitting trains and moving walls, etc but I still cannot reconcile why the rebounding object gains TWICE the larger mass's velocity WRT the sun/station platform/whatever. It feels like it is gaining someth... | Let's consider a ping pong ball and a paddle. First throw the ball at a stationary paddle. The ball bounces back. The ball approaches the paddle with speed v and leaves with speed v.
Important point 1: The ball doesn't end up at the speed of the paddle (which is $0$ in this case). As it hits and slows to a stop, it f... | The Planet’s orbit is basically adding its knetic energy to the craft.Here’s an analogy.
Imagine trying to throw a ball.If you throw the ball while standing still,it’s going to go pretty far.But if you throw the ball while moving,it’s going to go really far.
| https://physics.stackexchange.com |
1,552,935 | [
"https://math.stackexchange.com/questions/1552935",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/294619/"
] | I have to slove the following differential equation with separation of the variables (without any initial conditions)
$xy'=\frac{1}{y^2}-y$
This is what I have done so far
$x\frac{dy}{dx}=\frac{1-y^3}{y^2}$
$\int \frac{dx}{x}=\int \frac{y^2 dy}{1-y^3}$
${\rm ln} \ \vert x \vert +c_1=-\frac{1}{3} {\rm ln} \ \vert 1... | It is the second term that is always zero (because $d^2a = 0$), no matter what $k$ is. The first term is zero because $da$ has odd degree. In general
$$ x \wedge y = (-1)^{|x||y|} y \wedge x$$
where $|x|,|y|$ are the degrees of $x,y$. In particular, if $x$ has odd degree then $x \wedge x = 0$.
| As levap writes in their answer, it <em>is</em> true that $da \wedge da = 0$ for forms $a$ of even degree $k$: The exterior derivative $da$ has degree $k + 1$, and so by the commutation rule $$\alpha \wedge \beta = (-1)^{|\alpha| |\beta|} \beta \wedge \alpha,$$ (where $|\gamma|$ denotes the degree of $\gamma$) we have ... | https://math.stackexchange.com |
29,573 | [
"https://cs.stackexchange.com/questions/29573",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/21307/"
] | I am confused between these two terminologies: recursively enumerable language, recursively enumerable set.
Do they have the exactly same meaning?
| No they do not have <em>exactly</em> the same meaning. A language is a set of strings, whereas a set can be virtually anything. Usually such a set is a set of (natural) numbers, but we also can consider sets of graphs.
However, when the sets are accepted or generated by Turing machines, then they have to be represente... | The language describes the set, it defines how to decide if a given element is part of the set or not.
The complexity in your given case for that decision is recursively enumberable.
You could create a Turing Machine to make this decision, or an computer program in any other prorgamming language like e.g. Java.
<br/>... | https://cs.stackexchange.com |
331,437 | [
"https://stats.stackexchange.com/questions/331437",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/191627/"
] | Whilst studying I stumbled on this problem, which I wish to check if my understanding is correct.
Imagine we have a biased coin with probability <strong>'k'</strong> of getting a head when flipped.
Now <strong>A</strong> defines the number of times a biased coin is thrown until getting the 1st Head. On the other hand,... | \begin{align}
p(1,b) &= P(A=1, B=b) \\
&= P(B=b|A=1)P(A=1) \\
&=P(B=b|A=1)k \\
&=\begin{cases}0 & , b=1 \\ k^{b-2}(1-k)k
&, b > 1\end{cases} \\
&=\begin{cases}0 & , b=1 \\ k^{b-1}(1-k)
&, b > 1\end{cases} \\
\end{align}
<ul>
<li>Try to compute $p(a,1)$ similarly as an exercis... | A variable X~Geo(p) where p is the probability of success for each trial. Since the probability of getting heads is 'k',
A ~ Geo(k)
And since B is the complement of A, their probabilities must sum to one. So,
B~Geo((1-k)). The rest of your work seems correct.
| https://stats.stackexchange.com |
8,049 | [
"https://physics.stackexchange.com/questions/8049",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2359/"
] | Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground state, and half the time the atom is produced in the excited state, but other than that you get the exact same atom every tim... | These systems are <em>not</em> distiguishable. The average density matrix is the same, and the probability distribution obtained by performing any measurement depends only on the average density matrix.
For the first system, the density matrix is
$$\frac{1}{2} \left[\left(\begin{array}{cc}1&0\cr 0&0\end{array}... | Case 1: $\frac{1}{2}\left[\left|0\right>\left<0\right|+\left|1\right>\left<1\right|\right]$.
Case 2, average over phases $0$ to $2\pi$: $$\frac{\int\left[(\left|0\right>+e^{i\theta}\left|1\right>)
(\left<0\right|+e^{-i\theta}\left<1\right|)\right]d\theta}
{\... | https://physics.stackexchange.com |
108,777 | [
"https://electronics.stackexchange.com/questions/108777",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35783/"
] | I'm finding a bit of a problem when trying to solve this question:
<hr>
<em>Show that the leakage current for the capacitor is given by</em>
\$ I = \dfrac{Q}{KP} \$
<hr>
where \$Q\$ is the charge on the plates, \$K\$ is the dielectric constant and \$P\$ is
the resistivity of the dielectric.
I know the concept behi... | Current is defined as voltage divided by resistance.
Therefore, you need to find a way to relate charge to voltage, and resistivity to resistance.
Voltage on a capacitor is charge divided by capacitance. Capacitance is related to plate area, spacing and dielectric constant.
Resistance is resistivity multiplied by th... | <span class="math-container">\$ \vec{j} = \sigma \vec{E} \$</span>
<span class="math-container">\$ i = \displaystyle \int\vec{j}.\vec{ds}\$</span>
<span class="math-container">\$ i = \sigma\displaystyle \int\vec{E}.\vec{ds}= \sigma E \displaystyle \int {ds} = \sigma E*S\$</span>
<span class="math-container">\$ i=\... | https://electronics.stackexchange.com |
80,377 | [
"https://stats.stackexchange.com/questions/80377",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/36491/"
] | I am not a community ecologist, but these days I am working on community ecology data.
What I couldn't understand, apart from the mathematics of these distances, is the criteria for each distance to use and in what situations it can be applied. For instance, what to use with count data? How to convert slope angle betw... | Unfortunately, in most situations there is not a clear-cut answer to your question. That is, for any given application, there are surely many distance metrics which will yield similar and accurate answers. Considering that there are dozens, and probably hundreds, of valid distance metrics actively being used, the notio... | Choosing the right distance is not an elementary task. When we want to make a cluster analysis on a data set, different results could appear using different distances, so it's very important to be careful in which distance to choose because we can make a false good artefact that capture well the variability, but actual... | https://stats.stackexchange.com |
48,043 | [
"https://engineering.stackexchange.com/questions/48043",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/35641/"
] | I'm an advanced industrial engineering student and I'm currently looking for some "final project" material. I have this idea of a product where you can plug in a type K thermocouple at the end of a meter long wire to your smartphone via the minijack port, as to mesure mainly kitchen-like temperatures (you kno... | The only input possibility is for the thermocouple to act as a microphone or audio source. There are several reasons why this wouldn't work.
<ol>
<li>There will most likely be a DC blocking capacitor on the audio input. This will block your thermocouple signal.</li>
<li>There will be a bias voltage of a volt or two on ... | This probably won't work the way you describe. However, what you could do is use a generic thermocouple amplifier to generate a dc voltage from the thermocouple and then use a voltage-to-frequency converter to generate a frequency proportional to temperature. Input that signal to your phone/laptop. Run an FFT on the ph... | https://engineering.stackexchange.com |
3,514,707 | [
"https://math.stackexchange.com/questions/3514707",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/718627/"
] | I have to prove the following:
<span class="math-container">$$f''(x)=\lim_{h\rightarrow0} \frac{f(x+h)+f(x-h)-2f(x)}{h^2}$$</span>
I tried to just apply the definition of derivative, namely:
<span class="math-container">$$f'(x)=\lim_{h\rightarrow0} \frac{f(x+h)-f(x)}{h}$$</span>
Then this:
<span class="math-containe... | There is a particular natural connection between equivalence relations and partitions. Each partition corresponds to an equivalence relation, and each equivalence relation corresponds to a partition. Going back and forth along this correspondence will get you back where you started.
The correspondence is this: Given a... | The partition <span class="math-container">$P$</span> is a set <span class="math-container">$\{A_\lambda\mid\lambda\in\Lambda\}$</span> of subsets of <span class="math-container">$A$</span>. The relation <span class="math-container">$R$</span> is the one defined by<span class="math-container">$$a\mathrel Ra'\iff\text{f... | https://math.stackexchange.com |
289,288 | [
"https://dba.stackexchange.com/questions/289288",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/202993/"
] | I m planning to add a key column index in one of the existing non clustered index in a big table which have millions of rows rather than create a new non clustered index. Is that any way for me to know how much the extra space consumed by the index by adding a new key column in existing non clustered index and is that ... | It depends on the size of the values in the column you are adding. As David suggests the most accurate way of knowing is to create an index in a dev or test environment and see what effect it has there.
You can estimate though. If the added column is 8 bytes long (a <code>datetime</code> column for instance) and there ... | <blockquote>
Is that any way for me to know how much the extra space consumed by the index by adding a new key column
</blockquote>
Create a new index and check its size:
<pre><code>select schema_name(t.schema_id) schema_name,
t.name table_name,
i.name index_name,
ps.used_page_count / 8. / 1024 s... | https://dba.stackexchange.com |
21,502 | [
"https://mechanics.stackexchange.com/questions/21502",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/12455/"
] | I have a 2008 F150 160k miles and all of the warning lights came on (Check engine, ABS, low tire, parking brake, 4x4 Hi and 4x4 Low from what I remember). The odometer was just a blank green screen. I turned the truck off and the radio didn't turn off like it normally does when I open the door. After turning it on a... | It sounds to me like the fault is within the instrument binnacle or associated wiring as opposed to the lights being genuine warning lights. It sounds like a classic "shorting out" problem. This could be caused by a loose connection or poorly installed accessory (immobilizer, aftermarket radio, etc...)
I'd be inclin... | This can be the key cylinder switch or the harness connector at the other end. These are known to come loose. Find the large harness coming off the key cylinder and follow it all the way to the firewall. Check any connector you come to by opening it, checking for moisture and corrosion, and reassembling it. Check the l... | https://mechanics.stackexchange.com |
643,230 | [
"https://physics.stackexchange.com/questions/643230",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/134133/"
] | GOAL: I would like to compute the local absorption of light in material from an RCWA simulation. The RCWA tool can output the time-averaged (and input-normalized) Poynting vector.
The time-averaged Poynting vector is given as:
<span class="math-container">$$\textbf{S}=1/2*Re\big[\textbf{E(x,y,z,w)} \times \textbf{H*(x,... | Your equation with <span class="math-container">$\nabla \mathbf{P}$</span> makes sense if this is the
divergence <span class="math-container">$\mathbf{\nabla}\cdot \mathbf{P}$</span>. That is, the Poynting
vector is the energy flux, i.e. the energy per unit are per unit time.
To calculate the absorption, you want the n... | The previous answer is complete with respect to the original question, i.e. if you want to explicitly use the time-averaged Poynting vector. However, the RCWA simulation gives you the electric and magnetic field (in frequency domain) and those can be used directly to calculate the absorption (more convenient and accura... | https://physics.stackexchange.com |
1,399,130 | [
"https://math.stackexchange.com/questions/1399130",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/206994/"
] | The question is to find all group homomorphisms from $\Bbb{Z}$ and $\Bbb{Z}/n\Bbb{Z}$ into $(\Bbb{C},+)$, $(\Bbb{C}^{\times},\cdot)$ and $(S^1,\cdot)$.
How should this be tackled? What should be in your arsenal in order to confront this quesion?
I have read about homomorphisms, all I know is that if $\phi:\ G\ \longr... | $f\colon\mathbf Z\to G$, where $G$ is any <em>abelian</em> group:
As $f(n)=f(n\cdot 1)=nf(1)$, $f$ is defined by the sole value of $f(1)$, which is arbitrary. Hence $\;\operatorname{Hom}_{\mathbf Z}(\mathbf Z,G)\simeq G$ (the index $\mathbf Z$ in Hom stresses the fact that abelian groups are $\mathbf Z$-modules).
$... | The three facts you know about group homomorphisms are sufficient to answer the question, if you are familiar with the groups mentioned. I will sketch how to find all group homomorphisms from $\Bbb{Z}$ to $(\Bbb{C},+)$ as an example. For the other groups a similar approach will work.
If $\varphi:\ \Bbb{Z}\ \longrighta... | https://math.stackexchange.com |
376,048 | [
"https://electronics.stackexchange.com/questions/376048",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3814/"
] | I recently replaced a set of incandescent bulbs from the interior of my old car with some very inexpensive festoon LEDs. Unfortunately the LEDs are not 100% compatible with the lighting system as dimming is accomplished via pulsing the voltage signal. The pulsing effectively dims the incandescent bulb, but causes the... | There's a visual difference between flicker and blink...
Flicker (if you can see it) would be something like 40-60 Hz.
Blinking would be much lower, maybe 10 Hz or less.
The difference is important, because flicker can be solved with a cap, but blinking could indicate that there is a bit of a problem that won't be s... | It would make more sense to bypass your current incandescent bulb dimming system, as it is looking to power a much heavier load than you are proposing.
Are their enough lights on all the time to achieve a significant power savings/ reduced load on your electrical system?
I would determine if you still want to do thi... | https://electronics.stackexchange.com |
104,682 | [
"https://stats.stackexchange.com/questions/104682",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12565/"
] | I have 2 population samples for which I want to assess whether they have comparable demographics. What is the right way to test this, that includes multivariate combinations ?
I.e I would like to check that both datasets have:
<ul>
<li>the same proportion of men</li>
<li>the same proportion of age [0-18]</li>
<li>the... | The model has 7 parameters because of the 3-category categorical variable which will have 2 ``main effects'' parameters in the model (1 of the categories is omitted as the reference category). There will also be a parameter for the interaction between each of the levels of the categorical variable with the continuous ... | I think you need to consider your categorical variable d as three different dummy variables following the value d can take. That would make two more variables, hence 7 variables in total. Does that make any sense?
| https://stats.stackexchange.com |
96,647 | [
"https://electronics.stackexchange.com/questions/96647",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7523/"
] | I'm told that a 1% transformer costs more than a 5% transformer of the same power rating. I understand that the 5% transformer has higher output impedance, which seems to imply more windings and thinner wire. Is this the only construction difference between a 1% and 5% transformer of the same power rating? Or are there... | From ABB's <em>Transformer Handbook</em>, 3e:
<blockquote>
3.9 Short Circuit Impedance
Users have sometimes particular requirements regarding the
short-circuit impedance. Such requirements may be determined by:
<ul>
<li>parallel operation with existing units</li>
<li>limitation of voltage drop</li>
... | For any transformer we have some basic equations
$$
V = N \frac{d\phi}{dt} = N \cdot A \frac{dB}{dt}$$
Here ϕ is flux, B is flux density, N is turns and A area.
For a given size core you can work out the number of turns required on the primary to prevent saturation. All magnetic materials will saturate if you apply ... | https://electronics.stackexchange.com |
623,547 | [
"https://electronics.stackexchange.com/questions/623547",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/315693/"
] | I'm trying to wire this module. I'm just confused as to what the difference is between the two triangles and how would I connect them?
<img src="https://i.stack.imgur.com/jlUiV.jpg" width="500" height="750">
| That appears to be internal to the module, likely +24VDC and 0VDC. If so then you should only need to deal with the pinout on the left.
| The white triangle is the analog common reference net, often called “ground” or “0V”.
The black triangle represents a connection to the positive supply rail.
The connection of two lines to the black triangle is unfortunate and confusing. It looks as if the black triangle was some sort of a differential stage or an op-a... | https://electronics.stackexchange.com |
603,907 | [
"https://stats.stackexchange.com/questions/603907",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/378941/"
] | I have a group, people, and have converted their heights into z-scores.
I separated the groups into male and female and wanted to test whether there is a statistically significant difference between the groups. Is a t-test suitable for this purpose?
The means and SDs of the groups are not identical because the z-score ... | In short, yes. As long as you converted the heights to z-scores <em>before</em> splitting them into groups, then it is valid to perform a t-test. Z-scoring as you have described it is sometimes referred to as "standardizing" data, and it is a common preprocessing step in many analysis pipelines. This is becau... | <h4>Explanation</h4>
As Dave and Sal already mentioned, this can certainly be achieved with essentially the same results, but it will slightly change the interpretation of the results. I will provide a worked example to show you why.
<h4>Simulating Your Data</h4>
I demonstrate with an example in R with some simulated d... | https://stats.stackexchange.com |
325,597 | [
"https://softwareengineering.stackexchange.com/questions/325597",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/236985/"
] | I'm writing a program in which I fscanf a file and write to the same memory address repeatedly. I tried the following:
<pre><code>FILE *f = fopen(fname, "r");
int* num;
while(fscanf(f, "%d,", num) != EOF)
{
printf("%d\n", *num);
}
</code></pre>
which, when I run it, produces Bus Error 10, which means to the be... | IMHO, no. Sometimes, a commit is just too large to be explained in enough detail in the message, for it not to require exploring the '<code>diff</code>'.
However, I would change the <em>why</em> to a <em>what</em> (described in broad strokes). This way, a developer can get a good idea of what was affected by that comm... | The git mantra states
<blockquote>
commit often
</blockquote>
Commits shouldn't be done after a complete module have been coded. Commits should be done after changes that work and add something organic no the goal of the project.
If you abide to that mantra and commit often and write a clear commit message, then ... | https://softwareengineering.stackexchange.com |
76,422 | [
"https://mathoverflow.net/questions/76422",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4053/"
] | Let $G$ be a group of automorphisms of the countable atomless Boolean algebra $B$. Suppose that every orbit of $G$ on $B$ is an antichain. Does it follow that $G$ preserves a non-zero (probability) measure on $B$?
Does the answer change if we extend $B$ to some complete or $\sigma$-complete algebra, and the action o... | Let <span class="math-container">$G$</span> be a torsion group. Then every action of <span class="math-container">$G$</span> on every Boolean algebra has only antichains as orbits (indeed <span class="math-container">$gA<A$</span> implies <span class="math-container">$g^nA<A$</span> for every <span class="math-co... | Regarding the question is your last paragraph, there is the following often-studied but not-quite-equivalent-to-your property:
<ul>
<li>A Boolean algebra $\mathbb{B}$ is <em>almost homogeneous</em> if for every nonzero $a,b\in\mathbb{B}$ there is an automorphism $\pi$ with $0\lt \pi(a)\wedge b$. Similarly, a group $G$... | https://mathoverflow.net |
85,904 | [
"https://mathoverflow.net/questions/85904",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6818/"
] | My brother asked me a question which I didn't know the answer to.
Are there theorems about existence, uniqueness and stability of solutions of ODEs of the followin type
$$
\frac{d^2 y}{dt^2} = f(t,y,\frac{dy}{dt})H(g(y)),
$$
where $f$ and $g$ are Lipschitz functions and $H$ is the Heaviside function?
If there are ... | Your question already has the answer in it for $n=2$. Take a connected complex curve $L\subset\mathbb{C}^2$ that is dense in $\mathbb{C}^2$. Then $L$ is Lagrangian for the real part of the holomorphic $2$-form $\Upsilon = dz^1\wedge dz^2$. This real part of $\Upsilon$ is equivalent to the standard symplectic structu... | This is more a remark than an answer.
The typical solution of the typical polynomial ODE is uniformized by the Poincaré disc not by the complex line.
Indeed, after the work of McQuillan, it is known that the existence of a non-algebraic leaf uniformized by $\mathbb C$ imposes strong restrictions on the polynomial ve... | https://mathoverflow.net |
115,648 | [
"https://electronics.stackexchange.com/questions/115648",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/41557/"
] | How can I calculate how many LEDs in parallel I can light with three 1.2V batteries in series?
How long will 3.000mAh batteries last in that case? Do I have to put a resistor at only one of the parallel lines or in every line?
| You'll always want a single resistor per LED. If you don't, only one LED will really be lit to its full brightness. The rest won't be at a similar brightness because their V-I curve will be slightly different due to process differences.
To calculate how many LEDs you can supply in parallel, all you need to do is deter... | Your first step would be to look at the LED's datasheet to determine the current. Common LED currents are around 25mA, though they vary widely depending on the construction, age, brightness, and so on.
Once you find the current, you should be able to determine the total current drawn by each series string. The number ... | https://electronics.stackexchange.com |
352,935 | [
"https://softwareengineering.stackexchange.com/questions/352935",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/278155/"
] | We have a ASP.NET Web API that provides a REST API for our Single Page Application. We use DTOs/POCOs to pass data through this API.
The problem is now, that these DTOs are getting bigger over time, so now we want to refactor the DTOs.
I am looking for "best practices" how to design a DTO: Currently we have small DTO... | As a best practice, try and make your DTOs as concise as possible. Only return what you need to return. Only use what you need to use. If that means a few extra DTOs, so be it.
In your example, a task contains a user. One probably doesn't need a full user object there, maybe just the name of the user that is assign... | Unless your system is based strictly on CRUD operations, your DTO's are too granular. Try creating endpoints that embody business processes or artifacts. This approach maps nicely to a business logic layer, and to Eric Evans' "domain-driven design."
For example, let's say you have an endpoint that returns data for a... | https://softwareengineering.stackexchange.com |
192,803 | [
"https://security.stackexchange.com/questions/192803",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/27627/"
] | Let's say I know that there is a computer than is heavily infested with viruses (but I do not know which kind of viruses) and needs to be nuked from orbit. And on that computer is a very important picture, png format, that I absolutely must have and can not lose. Which one will give me least chance of catching a virus?... | I would recommend downloading a live Linux distribution (Ubuntu is great for this), create a bootable USB device on a clean computer, and booting your infected computer with this USB drive.
With Linux running, you can copy all pictures to another USB drive, without any Windows malware interfering.
Virus attaching the... | The PNG file is unlikely to be maliciously modified in a way that would infect a patched computer. If the computers on your home network are up to date on their patches (and don't have open file shares, etc), it's unlikely that the infected computer will infect the others just from being connected to the network.
<blo... | https://security.stackexchange.com |
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