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 |
|---|---|---|---|---|---|
4,037,459 | [
"https://math.stackexchange.com/questions/4037459",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/890127/"
] | This is the question I got and I'm not sure how to approach it.
Let <span class="math-container">$f: A → B$</span> and <span class="math-container">$g: B → A$</span> be two functions, such that <span class="math-container">$g ∘ f(x) = x$</span> for all <span class="math-container">$a ∈ A$</span>. Prove that <span class... | To show <span class="math-container">$g$</span> surjective, pick any <span class="math-container">$a \in A$</span> and since <span class="math-container">$g(f(a)) = a$</span>, let <span class="math-container">$b = f(a)\in B$</span> then <span class="math-container">$g(b) = a$</span> showing <span class="math-container"... | <span class="math-container">$f$</span> injective: If <span class="math-container">$f(x_1)=f(x_2)$</span>, then, applying <span class="math-container">$g$</span> yields <span class="math-container">$x_1=g(f(x_1))=g(f(x_2))=x_2$</span>.
<span class="math-container">$g$</span> surjective: If <span class="math-container">... | https://math.stackexchange.com |
15,612 | [
"https://chemistry.stackexchange.com/questions/15612",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7603/"
] | We have always studied about metals reacting with dilute and concentrated acids, but I do not understand what will happen if the same metal reacts with an acid that is neither concentrated nor dilute?
| This question is a bit vague, but briefly, the reason some acids behave differently at high and low concentration is because changing the activities of components in the solution changes the redox potential of the various possible reactions.
Let's take the reaction of iron with sulfuric acid as an example. This is not... | Some metals react explosively with water (Alkali metals, Group 1, sodium, potassium), and water is neutral. Some metals do not react even with very strong and consentraded acids (platinum).
Some acids are strong, some are weak. Even vitamine C is an acid, but so also are sulferic acid and nitric acid. Consentration a... | https://chemistry.stackexchange.com |
43,365 | [
"https://electronics.stackexchange.com/questions/43365",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/13848/"
] | How to determine the feedback resistor in negative feedback op-amp configuration ? How does the feedback resistor affect the signal output of op-amp ? What is the consequence of using high resistance or low resistance in feedback circuit ?
| The transfer function of the inverting amplifier is
\$ V_{OUT} = -\dfrac{R_{feedback}}{R_{in}} \cdot V_{IN} \$
For the non-inverting amplifier it is
\$ V_{OUT} = \left(1 + \dfrac{R_{feedback}}{R_{g}}\right) \cdot V_{IN} \$
where \$R_g\$ is the resistor to ground.
So the gain is determined by a resistance ratio, ... | The feedback resistance divided by the input resistance gives the closed-loop gain of the circuit. Don't set it lower than double what the op-amp can tolerate as a load: in the typical inverting configuration the inverting input is a virtual earth so Rf is in parallel with the external load. On the other hand setting i... | https://electronics.stackexchange.com |
647,605 | [
"https://physics.stackexchange.com/questions/647605",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/305356/"
] | If I understand properly, QM says a particle can only be entangled with one other particle. How then can you get entangled ensembles of particles, required for example in various theories of decoherence or in notions of fast scrambling in black holes or in tensor networks? I'm sure I'm missing something, and those ex... | No, it means that you are measuring the electric potential relative to the potential of the plane rather than the potential at infinity.
Note that the potential at infinity, which you call <span class="math-container">$V(\infty)$</span>, is only meaningful to talk about if <span class="math-container">$\lim_{|\mathbf r... | If we postulate some charge <span class="math-container">$q$</span> at a distance from ground, this does not mean that ground has the opposite charge; that opposite charge could be anywhere.
We define ground as the reference from which all other potentials are measured. It has an undefined charge, however any charge it... | https://physics.stackexchange.com |
71,712 | [
"https://mechanics.stackexchange.com/questions/71712",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/52861/"
] | I just got my engine back from the rebuilders.
1965 Pontiac 389
They have crank timing Mark at tdc on the front pulley.
The distributor is not installed.
The problem is that I don't know if piston 1 is firing or exhausting
Is it true that if the timing marks on the cam gear and the crank gear are lined up then Piston... | If the crank and cam are both aligned , it is TDC firing. While the crank rotates twice and can be either TDC firing or exhaust , the cam only rotates once and is at TDC firing every time its mark is aligned with the crank mark .
| Best option is to remove spark plug from #1 cylinder and turn over the engine while your finger is in the spark plug hole, when you feel the compression pushing your finger out that is the compression stroke, now continue to turn the engine slowly until the mark lines up on 0 degrees on the timing cover, now set the di... | https://mechanics.stackexchange.com |
8,253 | [
"https://electronics.stackexchange.com/questions/8253",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2064/"
] | OK, so the uA741 is 42 years old now. For its time it may have been a great opamp; the requirements weren't as high as today, and there was far less competition. But I was wondering what's the 741's appeal today.
<blockquote>
<ul>
<li>it's slow. GBW 1MHz, slew rate < 0.5 V/us </li>
<li>it's not low power,... | It's an <em>ideal</em> op amp to learn the basics on due to its <em>non-ideal</em> nature. The first thing we learn is infinite input impedance, infinite gain, as well as a few other silly things. The 741 obeys none of these idealities, forcing students to learn the hard way how to cope. They see bandwidth limitations ... | Is it really <em>used</em> per se, or simply kept around for legacy designs? Changing an op-amp in an application where those specific parameters are important (i.e. feedback loops) can be problematic at best (or outright dangerous at worst) - best to let sleeping dogs lie in these situations, sometimes...
I can speak... | https://electronics.stackexchange.com |
53,389 | [
"https://physics.stackexchange.com/questions/53389",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6764/"
] | QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$:
$$P = \left|\psi\right|^2.$$
If I write down a wave function like this $\psi = \psi_0 e^{i(kx - \omega t)}$, I find $\psi_0$ inside.
If $\psi$ is called <strong>probability amplitude</strong>... | <strong>INCLUDING AN EXTENSION</strong>
$\psi_o$ is, as mentioned previously, the normalisation constant which is calculated by doing the integral $\int_V|\psi|^2dV$ and setting its value equal to 1 (hence normalization). This will give you the equation for $\psi_o$. If your interest is to find the probablity amplitu... | $\psi_0$ is the initial amplitude and $\psi$ is the amplitude after some amount of time (or more appropriately, the amplitude after some change in spacetime coordinates). The function you have provided: $\psi=\psi_0e^{i(kx-\omega t)}$; is a function of space and time. So it tells me that given some initial function $... | https://physics.stackexchange.com |
58,845 | [
"https://datascience.stackexchange.com/questions/58845",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/23556/"
] | Using tensorflow-gpu 2.0.0rc0. I want to choose whether it uses the GPU or the CPU.
| I've seen some suggestions elsewhere, but they are old and do not apply very well to newer TF versions. What worked for me was this:
<pre class="lang-py prettyprint-override"><code>import os
os.environ["CUDA_VISIBLE_DEVICES"] = "-1"
</code></pre>
When that variable is defined and equal to -1, TF uses the CPU even whe... | For TF2:
<pre><code>try:
# Disable all GPUS
tf.config.set_visible_devices([], 'GPU')
visible_devices = tf.config.get_visible_devices()
for device in visible_devices:
assert device.device_type != 'GPU'
except:
# Invalid device or cannot modify virtual devices once initialized.
pass
</cod... | https://datascience.stackexchange.com |
436,412 | [
"https://stats.stackexchange.com/questions/436412",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/41307/"
] | I am running an ANOVA and computing bootstrapped CIs for my effect sizes. I am using for this the Measures of Effect Size Toolbox for Matlab.
To my surprise, if I re-run the same line of code, i.e. compute the same thing for the same data, the lower&upper margins of the CI are slightly different each time.
I know... | A bootstrap resample consists of data points <span class="math-container">$(x_1^*, x_2^*, \cdots x_n^*)$</span> which are sampled <em>with replacement</em> from the original data <span class="math-container">$(x_1, x_2, \cdots x_n)$</span>. Technically, a Bootstrap procedure should consider <em>all of the possible boot... | Each time you repeat the process, you are taking a different set of samples. Those different samples will give slightly different results.
If you set a random seed, you will get the same results every time (which is why random seeds are useful). I don’t know the Matlab command for it, but R is set.seed(2019) and Pytho... | https://stats.stackexchange.com |
405,706 | [
"https://mathoverflow.net/questions/405706",
"https://mathoverflow.net",
"https://mathoverflow.net/users/384338/"
] | I want to prove the following statement:
<blockquote>
Let <span class="math-container">$u$</span> be a vertex in a <span class="math-container">$2$</span>-connected graph <span class="math-container">$G$</span>. Then <span class="math-container">$G$</span> has two spanning trees such that for every vertex <span class="... | Note first that every pseudo-Riemmanian manifold admits a null vector field which is not identically <span class="math-container">$0$</span> (just construct one locally and multiply it by a bump function). So by "non-zero vector field" I assume you mean "nowhere vanishing".
Let <span class="math-con... | Such manifolds are precisely the Riemannian ones and their “opposites”.
Suppose <span class="math-container">$M$</span> is a pseudo-Riemannian manifold whose signature is not trivial in one direction or the other. We work in a neighbourhood of a point and will define a vector field with arbitrarily small support, so we... | https://mathoverflow.net |
199,601 | [
"https://electronics.stackexchange.com/questions/199601",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/91119/"
] | I have just bought a breadboard, but I have notinced that the components are hard to insert into the holes (and sometimes only one pin go in and the another one go out, like a LED).<br>
In videos I see people insert componenets into breadboard very easily.
<hr>
Is it normal because it is a new breadboard?<br>
Will it b... | I have had this happen to me and it was essentially a faulty breadboard. The components should easily go in and out if the breadboard is good. I have managed to loosen up my bad breadboards by forcing large tough component legs(like pin header) into and out of the stiff holes repeatedly, they eventually become more acc... | problem solved by using a male jumber wire, I put then remove it in every hole (and reapeted it 3 times).<br>
I will also try using a pin header as HighInBC mentiond
| https://electronics.stackexchange.com |
207,763 | [
"https://mathoverflow.net/questions/207763",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34575/"
] | Are there some outstanding results using some version of Helly's theorem in a totally different area (whatever that means) than convex geometry?
| <ul>
<li>Applications of Helly's theorem to linear programming are discussed
in this <A HREF="http://web.cs.ucdavis.edu/~amenta/pubs/ninathesis.pdf">thesis</A>.</li>
<li>Then there are applications to the theory of approximation of
continuous functions by polynomials (<A HREF="http://www.maths.manchester.ac.uk/~khudian... | The famous Krasnoselsky criteria for star-shaped regions is based on Helly theorem. It is important in embedding theorems for Sobolev spaces.
| https://mathoverflow.net |
21,595 | [
"https://stats.stackexchange.com/questions/21595",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6096/"
] | I understand the rationale that underpins representative sampling (i.e. to avoid bias so that the sample 'broadly' represents the target population).
Suppose the size of the target population is 600 and the population comprises of four types of units as follows:
<ul>
<li>100 white units</li>
<li>250 black units</li>... | <em>One</em>. <strong>Any sample for which every population member has a known, non-zero (but not necessarily equal) probability of being selected.</strong> So long as you know the probability, you can use post-stratification weighting to help your inference to population.
<em>Two</em>. <strong>Both.</strong> Arguab... | Adding to @PeterEllis excellent reply, there are many types of sample that are representative, and they each have strengths and weaknesses. However, a good start is simple random sampling without replacement. This would entail randomly choosing numbers between 1 and 600 and using the corresponding units in your sample.... | https://stats.stackexchange.com |
120,683 | [
"https://softwareengineering.stackexchange.com/questions/120683",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/40805/"
] | I am teaching the course "Introduction in Programming" for the first-year students and would like to find interesting examples where the datatype size in bits, chosen by design, led to certain known restrictions or important values.
Here are some examples:
<ol>
<li>Due to the fact that the Bell teleprinter used 7-bit... | IPv4 is a very good example where a limited spec size caused a very expensive problem down the line. 4.3 billion addresses just aren't enough anymore. Now ISPs around the world are desparately rolling out IPv6 with a 128-bit address space which translates into an address for every atom in your body or something like th... | The year 2000 problem was similar, except that people used decimal numbers instead of binary, and encoded just two last digits. This can be a useful example if explaining to someone who has little experience with binary.
FAT12/FAT16/FAT32 were adapted to cover for bigger and bigger storage.
TeX has some interesting p... | https://softwareengineering.stackexchange.com |
98,724 | [
"https://mathoverflow.net/questions/98724",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24196/"
] | Hi everybody
Let $U$ be the domain (as shown in the picture) and $\bar{U}$ its closure, further more set $\partial_r U$ to be the reflecting boundary and $\partial_a U$ the absorbing one. The process $(X_t)_{t\geq 0}$ is chosen as described above and $\tau=\inf(t\geq 0, X_t \in \partial_a U)$ is the first hitting time... | How about transforming the corner conformally into a part of a line? The process would transform into a time-changed Brownian motion, again with normal reflection (since the map is conformal up to the boundary, with the only exception at that corner point, and I guess the process never hits that point). And then use th... | First of all I would like to thank all of you for your advice - it really helps to know that there is sombebody out there you can turn to (if the people who are actually supposed to be helping and supporting you are both not avaliable and not interested)
The comformal map argument seems to work. Unfortunately I found ... | https://mathoverflow.net |
315,025 | [
"https://electronics.stackexchange.com/questions/315025",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/154231/"
] | Suppose you have a resistor that leads to a parallel connection of a capacitor and an output wire. I am having tremendous difficulty understanding how the capacitor steals all the current that would not otherwise leak into the output wire, reproducing the frequency that entered in, only with a different amplitude from ... | Looks like a bullet type crimp connector to me or maybe a small spade connector.
| Looks like what is called a “parallel splice”. If this is a high-temperature application then you want them made of nickel. These can be hard to find in a variety of sizes, but a search of the popular distributors for “crimp nickel” or “splice nickel” should turn up something.
| https://electronics.stackexchange.com |
2,152,410 | [
"https://math.stackexchange.com/questions/2152410",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/365922/"
] | I know that convergence almost everywhere implies convergences in measure(sometime it said locally). I also know that convergence in measure implies the existence of subsequence which is convergent almost everywhere.
However I wonder if there are some additional conditions from which the convergence in measure will i... | If the convergence in measure is rapid enough, then a.e. convergence will follow. Suppose $(f_n)$ converges in measure on the measure space $(E,\mathcal E,\mu)$. If $\mu(\{x\in E: |f_n(x)-f(x)|>\epsilon\})$ converges to $0$ so rapidly that $\sum_n\mu(\{x\in E: |f_n(x)-f(x)|>\epsilon\})<\infty$ for each $\epsil... | Let <span class="math-container">$f,f_n: X \rightarrow \mathbb{R}$</span> be measurable and <span class="math-container">$f_n \rightarrow f$</span> in measure <span class="math-container">$\mu$</span>. If <span class="math-container">$f_n$</span> is monotone increasing then <span class="math-container">$f_n \rightarrow... | https://math.stackexchange.com |
4,487,761 | [
"https://math.stackexchange.com/questions/4487761",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1072684/"
] | Let <span class="math-container">$X$</span> be a scheme over a field <span class="math-container">$k$</span>. Let <span class="math-container">$R$</span> be the <span class="math-container">$k$</span>-algebra of global sections of <span class="math-container">$X$</span>'s structure sheaf.
Is there any way to view schem... | You absolutely can. For any ring <span class="math-container">$A$</span> and scheme <span class="math-container">$X$</span>, we have a natural bijection <span class="math-container">$$Hom( X, Spec(A) ) \to Hom( A, \Gamma( X, O_X) ), $$</span>
where the left side is scheme morphisms and the right side is ring morphisms.... | If you stipulate that <span class="math-container">$X\to \operatorname{Spec}(k[t])$</span> is a morphism of <span class="math-container">$k$</span>-schemes, then yes! In this case, <span class="math-container">$\pi:X\to \operatorname{Spec}(k[t])$</span> corresponds to a <span class="math-container">$k$</span>-algebra h... | https://math.stackexchange.com |
2,017,271 | [
"https://math.stackexchange.com/questions/2017271",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/390095/"
] | Is there a mathematical equation for:
2 + 2^2 + 2^3 + 2^4 + 2^5 + ... 2^n
I'm not sure what this type of pattern is called.
| It is the sum of the $n$ first terms of a geometric progression of ratio $2$ and first term $2$ and so one has
$$2+2^2+\cdots+2^n=2\times {2^n-1\over 2-1}=2^{n+1}-2$$
| This is called a geometric series. There is a well-known formula for summing finite geometric series:
$$ar+ar^2+...+ar^n = \frac{ar^{n+1}-ar}{r-1}$$
Here's a proof:
Let $S = ar+ar^2+...+ar^n$. Then, we have that
$$rS = ar^2+ar^3+...+ar^{n+1}$$
Now, consider $rS-S$. Note that almost all of the terms cancel:
$$rS-S... | https://math.stackexchange.com |
188,733 | [
"https://security.stackexchange.com/questions/188733",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/172073/"
] | I get that people don't want to encourage other people to implement their own algorithms/implementations of algorithms due to safety issues. But on the other hand, questions about creating your own implementation are "shut down" immediately with the words " the first problem is: you are implementing it yourself". How c... | No, it doesn't matter. Every algorithm we use today was implemented by someone and then became a standard. The reason why it's not used as a practice is:
<ol>
<li>Security. A new method of hashing/encrypting/whatever needs a lot of time in order to be tested thoroughly, or even be further developed. It's not safe to l... | <blockquote>
How can one be able to learn more about security if not implementing such things himself and learning from his faults ?!
</blockquote>
Of course trying to implement it is a good way to learn, <strong>but only if you confront it to test and inspection by experts and state it as such</strong>, without tr... | https://security.stackexchange.com |
57,038 | [
"https://physics.stackexchange.com/questions/57038",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15874/"
] | I've got: $Q=\frac{Er^2}{k}$
how to check the units?
I start with $\left[\frac{\text V}{\text m} \, \text m^2\right]$, tried replacing $[ \text V ]$ with $\left[ \frac{\text J}{\text C} \right]$, but it's not leading me to $[\text C]$.
| First of all note that $k$ is not dimensionless, it is $k = \frac{1}{4 \pi \varepsilon_0}$, and $\varepsilon_0$ has dimensions of $\frac{ \text C^2}{ \text {N m}^2}$. So you have already $\frac{ \text{V C}^2 \text m^2}{ \text {N m m} ^2}$. Also, <em>volt</em> can be expanded as $ \text V = \frac{ \text {N m}}{ \text C}... | When in doubt, break everything down into a set of indivisible units: kilograms, meters, seconds, and coulombs. So ask yourself what is a joule in terms of those units, and also consider that the constant $k$ has units. You can figure out what those units are by writing out Coulomb's law.
Edit: the units of $\epsilo... | https://physics.stackexchange.com |
574,686 | [
"https://physics.stackexchange.com/questions/574686",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/257479/"
] | Let us assume that all we know till now is that two types of charges exist. One of them is possessed by an elementary particle called an <em>electron</em> and the other by another elementary particle called a <em>proton</em>. We also know that the effect of a proton on another proton is the same as that of an electron ... | I think your question is a little unclear, so let me know if I've misunderstood what you were asking.
If your question is about how we know that the electron and the proton have the same magnitude but opposite signs, it's simple (at least in theory): create a Hydrogen atom. It has one proton and one electron, and it's ... | It’s actually the other way round. Observations lead to formulating the math in this particular way. As it should be in science. Following is a brief history of the same.
The world around us by and large is neutral. It was only when electricity was discovered, we had to come up with the concept of charges. One thing to... | https://physics.stackexchange.com |
402,931 | [
"https://physics.stackexchange.com/questions/402931",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/157704/"
] | In Section 35.7 of Misner, Thorne, and Wheeler, p. 955, an "effective" stress energy momentum tensor for gravitational waves is defined:
$$T^{\text{GW}}_{\mu \nu} = \frac{1}{32 \pi} \left< \bar{h}_{\alpha \beta, \mu} \bar{h}^{\alpha \beta}_{\space\space,\nu} - \frac{1}{2}\bar{h}_{,\mu}\bar{h}_{\nu} - \bar{h}^{\alph... | The treatment of this in section 35.7 of MTW says they're only presenting the result, whereas the actual derivation is given in section 35.13, p. 964. The basic idea is as follows. First you take the vacuum field equation $R_{\mu\nu}=0$, and expand it in powers of the wave's amplitude $A$. They argue that the term line... | A previous answer contains some correct statements but does not clearly answer the question IMO, so here goes.
In the equation
<span class="math-container">$$G^{\text{B}}_{\mu \nu} = 8 \pi \left(T^{\text{GW}}_{\mu \nu} + T^{\text{other fields}}_{\mu \nu} \right)$$</span>
<span class="math-container">$G^{\rm B}_{\mu\... | https://physics.stackexchange.com |
422,823 | [
"https://electronics.stackexchange.com/questions/422823",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/66790/"
] | I'm working on Intel FPGA. The Timing Analyzer (STA Engine) gives Fmax summary for both slow Models but <strong>none</strong> for the fast model <strong>WHY?</strong>. I didn't find any setting for this in documentation or in GUI.
(let me know if there is any!)
I suppose Timing Analyzer should give some value of Fmax ... | Timing analysis is for checking for worst-case timing issues.
For the clock period (setup time), you're interested in the worst case paths, the paths with the longest delay during the worst possible (slowest) operating conditions. This requires the slow model.
For hold time, you're interested in the worst case p... | The actual, real-life, maximum operating frequency of your circuit is limited by its behavior with slow models. Giving you a number for fmax with fast models would be misleading.
You need the fast models to look for hold time violations.
| https://electronics.stackexchange.com |
643,736 | [
"https://electronics.stackexchange.com/questions/643736",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/325465/"
] | I need to provide supply voltage to take measurements and also get measured signal from same current transformer, which will be placed on AC line. Current transformer parameters, such as internal inductance and internal resistance are known. Upper voltage limit from current transformer 48 V. The problem is that I canno... | In case there are no critical EMC or high speed signal issues, then normally the software engineer is allowed to dictate which pins to use and group them as per how the GPIO peripheral port registers are defined in the MCU. That is, your option "Connect them to pins that share the same register inside the PIC"... | <strong>Where</strong> you have options, you can give some thought to physical connections if you expect layout to be gnarly, or you can give some thought to logical arrangement if you expect to need to wring the last bit of speed out of the MCU, but often these days it's not so important - we often have luxurious amou... | https://electronics.stackexchange.com |
753,540 | [
"https://physics.stackexchange.com/questions/753540",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/324226/"
] | By definition, any electronic circuits placed under super-conducting conditions (very low temperatures) will not dissipate energy to the surroundings as the resistance is 0.
If a computer was placed under such conditions, would it consume any electric energy? The question only considers the energy changes within the co... | The issue of superconductors comes into play for "the peripherals" on the board, so to speak, but at a fundamental level, computation is done by representing bits with a voltage threshold, and the manipulations of computation are done by raising and lowering those voltages. For the sake of argument, if <span ... | Unfortunately, this question misses the point of computer circuitry. Yes, conductors are important, but what makes a computer do computations is not the conductors but rather the transistors. There is no such thing as a supertransistor.
It is unlikely that you could design a computer without components that consume ene... | https://physics.stackexchange.com |
397,878 | [
"https://stats.stackexchange.com/questions/397878",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/77446/"
] | What is the point of using the identity matrix as weighting matrix in GMM?
GMM is the minimizer of the distance <span class="math-container">$g_n(\delta)'\hat{W}g_n({\delta})$</span>, where <span class="math-container">$g_n = \frac{1}{n}\sum_ix_i\epsilon_i$</span>. If we set <span class="math-container">$\hat{W}=I$</s... | Yes, getting a first step estimator is the canonical use. Of course, the error terms in <span class="math-container">$$S = \frac{1}{n}\sum_i\epsilon_i^2x_ix_i'$$</span> are not observable, so that you need to replace them with something feasible. As the efficient GMM estimator depends on <span class="math-container">$\... | This second answer addresses the question posed in the comment to the first answer as to why the specific choice of <span class="math-container">$W$</span> results in an efficient GMM estimator.
The efficient weighting matrix results from the general one by setting <span class="math-container">$W=S^{-1}$</span> to get ... | https://stats.stackexchange.com |
21,022 | [
"https://electronics.stackexchange.com/questions/21022",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6193/"
] | I have a two way switch (for an outlet), and it was for 16 AMP.
I went to a store and asked for a new one, and when I got home and was starting to assemble it, I noticed the new one was 10 AMP...
Is it ok to use a lower AMP model, or should I get a 16 (or more) AMP?
I am almost positive the charge on each outlet won... | If the circuit is 15A, you need at least a 15A switch, and preferably have some headroom; 16A is not that much. The 10A switch won't do. Problems to be expected: fast burning in of contacts (= wear-out) and possibly welding of the contacts (= dead switch).
| A major rule when dealing with mains power is that every cable, socket, switch, etc. must generally be capable of passing through all the current passed by the smallest upstream breaker without starting a fire or creating a hazardous condition. Even if a wire or switch is only expected to pass half an amp, if it's fed... | https://electronics.stackexchange.com |
220,364 | [
"https://security.stackexchange.com/questions/220364",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/159776/"
] | Does it make sense to log a user out from a web service after the user's IP address is changed?
I understand that a change of an IP address might indicate a man-in-the-middle attack. Then again IP addresses of end user devices (mobile phones) might change frequently when switching from network provider to local WLAN.
... | If you want to implement a security measure, you need to know what you secure yourself against. In this case, you want to secure yourself against a Man-in-the-Middle attack.
As you said yourself, a change of IP address is not a good indicator for that, for actually two reasons:
<ul>
<li>There are many reasons why an ... | The <strong><em>only</em></strong> consideration is the one of <strong><em>risk</em></strong>.
<em>Controls</em> (like this control) are put in place to mitigate <em>risks</em>. What risks are you trying to mitigate? You say that it might mitigate MitM. Ok. Is that your web service's responsibility to do that? Does it... | https://security.stackexchange.com |
2,391,293 | [
"https://math.stackexchange.com/questions/2391293",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/104171/"
] | I am lookinf for an idea to prove this inequality: $$\frac{1}{2}\cdot \frac{3}{4}\cdot\frac{5}{6}...\frac{2n-1}{2n}<\frac{1}{\sqrt{2n+1}}$$ without induction.
I can use induction to prove it .Thanks in advance for your hint,solution and idea.
| $$\underbrace{\frac12\cdot\frac23}_{<\left(\frac12\right)^2}\cdot\underbrace{\frac34\cdot\frac45}_{<\left(\frac34\right)^2}\cdots\underbrace{\frac{2n-1}{2n}\cdot\frac{2n}{2n+1}}_{<\left(\frac{2n}{2n-1}\right)^2}=\frac1{2n+1}$$
| $$\frac{1}{2}\cdot \frac{3}{4}\cdot\frac{5}{6}...\frac{2n-1}{2n}=\sqrt{\frac{3}{4}\cdot\frac{3\cdot5\cdot5\cdot7...\cdot(2n-3)(2n-1)\cdot(2n-1)}{4^2\cdot6^2...(2n-2)^2\cdot4n^2}}<$$
$$<\sqrt{\frac{3(2n-1)}{16n^2}}<\frac{1}{\sqrt{2n+1}}$$
| https://math.stackexchange.com |
80,529 | [
"https://softwareengineering.stackexchange.com/questions/80529",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/26678/"
] | I am an entry level developer with 1 year of experience. I have worked on a large scale project which I have played around 80% of the project work, those 5 months were terrible to me - late nights spent working, even Sundays.
i have worked on whole Process Model , doing some of my colleagues work ,DB Design ,client fe... | Taking what you said at face value, and assuming that the seniors didn't spend their nights and weekends fixing or rewriting the code that you wrote ;-) ...
...there is no reason to stay where your work goes unrecognized and unrewarded.
Caveat: do not take career advice from strangers on the Internet.
| Honestly - as an entry level developer with 1 year of experience - you might be overestimating your contribution if you are saying you've done 80% of the work.
In large scale projects, a very large portion of the work involves requirements gathering. Testing, pricing, marketing, etc. also play a very large role. If, ... | https://softwareengineering.stackexchange.com |
68,800 | [
"https://math.stackexchange.com/questions/68800",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1457/"
] | What are some examples of functions which are continuous, but whose inverse is not continuous?
<strong>nb:</strong> I changed the question after a few comments, so some of the below no longer make sense. Sorry.
| Define $f: [0,1) \cup [2,3] \rightarrow [0,2]$ by
$$f(x)=\begin{cases} x & x \in [0,1) \\ x-1 & x \in [2,3] \end{cases}$$
| A bijective map that is continuous but with non-continuous inverse is the following parametrization of the unit circle $\mathbb{S}^1$:
$$f: \colon [0, 2\pi) \to \mathbb{S}^1, \qquad f(\theta)=e^{i \theta}.$$
This map cannot have continuous inverse, because $\mathbb{S}^1$ is compact, while $[0, 2\pi)$ is not. Indeed,... | https://math.stackexchange.com |
9,092 | [
"https://engineering.stackexchange.com/questions/9092",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/6640/"
] | Boiling temperature of Acetylene is -84°C and that of Petrol is 95°C (at Atmospheric Pressure). So the spark is efficient to ignite the compressed Acetylene and run the Engine. But why wont that work ? Is any other factor that I miss or misunderstood ?
| There are certainly a few reasons why acetylene is not a very practical fuel for an IC engine.
Perhaps the most important is that it is inherently unstable and tends to explode under pressure, this makes it much more difficulty to store as it must be dissolved in acetone in an inert matrix, unlike say propane which c... | Due to the dangers involved with storing and transporting compressed or liquid acetylene, you would probably have to make use of an onboard acetylene generator, fueled with calcium carbide.
Acetylene generators are safe, but generally produce hot gas, which reduces specific power, and has a tendency towards preignitio... | https://engineering.stackexchange.com |
15 | [
"https://physics.stackexchange.com/questions/15",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57/"
] | I know that there's big controversy between two groups of physicists:
<ol>
<li>those who support string theory (most of them, I think)</li>
<li>and those who oppose it.</li>
</ol>
One of the arguments of the second group is that there's no way to disprove the correctness of the string theory.
So my question is if th... | One can disprove string theory by many observations that will almost certain not occur, for example:
<ol>
<li>By detecting <strong>Lorentz violation</strong> at high energies: string theory predicts that the Lorentz symmetry is exact at any energy scale; recent experiments by the Fermi satellite and others have showed... | Since many people seem to have very odd ideas about this, let's address this from a much simpler point of view.
Let's suppose you have a friend who only knows math at the level of arithmetic of positive integers. You try to tell him about the existence of negative numbers, and he tells you,
<blockquote>
That's s... | https://physics.stackexchange.com |
57,351 | [
"https://mathoverflow.net/questions/57351",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6269/"
] | Let $A$ be a unital $C^{*}$-algebra and $\phi:A \rightarrow A$ be a completely positive map, i.e. $\phi^{(n)}:M_{n}(A) \rightarrow M_{n}(A)$ preserves positivity for any natural number $n$, where $\phi^{(n)}((A_{ij})_{ij})=(\phi(A_{ij}))_{ij}$. It is well-known that the norm $\|\phi\|=sup_{\|x\|\leq 1}\{\|\phi(x)\|\}=\... | This answer deals with the case that $\phi$ is non-unital. In this case, $\phi$
must be of the form $\phi(a)=ha$, where $h$ is a positive element in the center
of $A$.
Unfortunately, the solution I've got is somewhat long (hopefully correct): Let us assume that $\phi$ is contractive (otherwise one can rescale). Sinc... | If I am not mistaken, the map $\phi$ should be automatically equal to $id$ under such conditions. if $\psi:A\rightarrow B$ is a positive map between two $C^*$-algebras then it is bounded and $||\psi||\leq 2||\psi(1)||$. But $\psi(1)=id(1)-\phi(1)=0$, if we assume that $\phi$ is unital. therefore $\phi=id$.
| https://mathoverflow.net |
603,965 | [
"https://electronics.stackexchange.com/questions/603965",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35373/"
] | I want to show a program state with LEDs. There are 22 steps, each step is represented by an LED.
<ul>
<li>only one LED is on at a time</li>
<li>the sequence is set (forward or backwards).</li>
</ul>
I have only one pin left on my MCU, maybe two.
Basically, I'd like to have the pin work as a 'clock'. For every pulse, t... | I'd use 3 4017 counters, chained together. Just clock the chain from your microcontroller. The 4017 is very cheap, has an output for each LED (so no decoding), and can be set up very easily to be chained. You would need 3 for your application. The 23 pin output should just reset them all to restart the count.
Edit: You... | Upgrade you MCU to one with more pins. It will be cheaper than adding more parts.
| https://electronics.stackexchange.com |
249,936 | [
"https://softwareengineering.stackexchange.com/questions/249936",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7693/"
] | I'm in the process of designing an API, part of which involves writing POCOs to a database.
In C#, we have the <code>DateTime</code> structure. The "default" value for this (<code>DateTime.MinValue</code>) is 01/01/0001.
Part of the API serializes POCOs to the database. If a date field is optional, it should <em>re... | Violating a best practice is not an exceptional condition. If you want to declare that 01/01/0001 is an invalid value, then throw an exception for that, specifically.
Looking forward to the day when my IDE throws an <code>InvalidBraceStyleException</code>.
| A date of <code>01/01/0001</code> would usually indicate a bug. Someone probably has used a default-initialized variable.
Your intention basically is to have a runtime assert to guard against a specific class of bugs. That's a valid thing to do. In fact it is done all the time.
Consider having this validation as a la... | https://softwareengineering.stackexchange.com |
396,567 | [
"https://softwareengineering.stackexchange.com/questions/396567",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/157621/"
] | I find myself often looking up questions online, and many solutions include dictionaries. However, whenever I try to implement them, I get this horrible reek in my code. For example every time I want to use a value:
<pre><code>int x;
if (dict.TryGetValue("key", out x)) {
DoSomethingWith(x);
}
</code></pre>
That's... | Dictionaries (C# or otherwise) are simply a container where you look up a value based on a key. In many languages it's more correctly identified as a Map with the most common implementation being a HashMap.
The problem to consider is what happens when a key does not exist. Some languages behave by returning <code>nu... | Some good answers here on the general principles of hashtables/dictionaries. But I thought I'd touch on your code example,
<pre><code>int x;
if (dict.TryGetValue("key", out x))
{
DoSomethingWith(x);
}
</code></pre>
As of C# 7 (which I think is around two years old), that can be simplified to:
<pre><code>if (dic... | https://softwareengineering.stackexchange.com |
261,410 | [
"https://mathoverflow.net/questions/261410",
"https://mathoverflow.net",
"https://mathoverflow.net/users/66131/"
] | Let $z_1,z_2,\dots,z_n\in\Bbb{C}$ be distinct and $w_1,w_2,\dots,w_n\in\Bbb{C}$ be arbitrary. Suppose $f, g$ are two polynomials of degree less than $n$ such that
$$f(z_j)=w_j,\qquad g(z_j)=\bar{w}_j \qquad\text{for $1\leq j\leq n$}.$$
Define $\Omega(z)=\prod_{j=1}^n(z-z_j)$. The following puzzles me.
<blockquote>
<... | For $n\ge 3$, let's take $z_j$, for $1\le j\le n$, be the $n$-th roots of unity, and $w_j:=z_j+4\bar{z_j}$, so that the assumption are satisfied by $$f(z):=z+4z^{n-1}$$ $$g(z):=4z+z^{n-1}.$$ However,
$$ |g'(z_k)|=|4+(n-1) z_k^{-2}| \le n+3<\phantom{Z} $$ $$ \phantom{ZZZZ} <4n-5\le|1+4(n-1) z_k^{-2}|= |f'... | This Matlab program shows that your conjecture is in general not true for $n\geq 3$
<pre><code>n = 3;
z = rand(1, n) + 1i * rand(1, n)
w = rand(1, n) + 1i * rand(1, n)
f = polyfit(z, w, n-1);
g = polyfit(z, conj(w), n - 1);
% note that Omega(z_i) = 0 and Omega(z) = z^n+q(z) where deg(q)<=n-1 and
% hence q(z_i)=-... | https://mathoverflow.net |
166,251 | [
"https://physics.stackexchange.com/questions/166251",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/63806/"
] | I'd like to know if it is possible to compute positronium mass and lifetime from a QED approach.
I'm searching for some literature on how to treat resonances in QED (or general QFT) ; most of the articles I've found are about corrections to these results, I'm searching for the beginning of these computations.
| To find the lifetime you can use a mixture between QED and non relativistic QM.
You use QED to find the cross-section of $e^+ e^- \rightarrow \gamma\gamma$ which is to first order in perturbation theory for the singlet state
$\frac{4\pi}{cv}\left(\frac{\alpha}{m}\right)^2$.
Then you must multiply this by the electron l... | Volume 4 of Landau & Lifshitz give an excellent account on both points. I am going to give a summary of it.
The following abreviations will be used (apart from well-known <span class="math-container">$c$</span> and <span class="math-container">$\hbar$</span> ) :
<span class="math-container">$m$</span> electron resp... | https://physics.stackexchange.com |
68,394 | [
"https://electronics.stackexchange.com/questions/68394",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7548/"
] | With a mobile two-way radio you have the radio, an antenna mount kit and the actual whip antenna.
The antenna needs to be trimed to the correct length so to match the freequency you are Tx/Rx on.
When you install the antenna mount kit though, you cut the feedline length without regard to electrical length. Why can... | The reason you trim the antenna itself is so that the impedance at its base matches that of the transmission line (usually 50Ω for most RF applications).
It is a property of transmission lines in general that if it is terminated at both ends by its characteristic impedance, then the current and voltage measured ... | The antenna feed-line is usually coaxial cable and it intentionally does not radiate significant amounts of RF energy <em>by design</em>. A propeller shaft on a boat wouldn't work without the propeller and the coax cable is equivalent to the shaft. Speaker cables don't make audible sounds (well maybe very tiny ones if ... | https://electronics.stackexchange.com |
343,376 | [
"https://softwareengineering.stackexchange.com/questions/343376",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/242862/"
] | Consider an ORM that maps tables to classes, and columns to properties. How should it handle a property that maps to an identity column for non-inserted objects?
For example,
<pre><code>[Table("MyTable")]
public class MyMappedType
{
[Column("Id")]
public int Id
{
get
{
// ..... | You answered yourself already. There is a reason most other ORMs go with option #2.
#1 should not even be considered, as throwing an exception from a property is extremely counterintuitive for the final user.
#3 is better, and mostly mirrors #2, in the sense that it assigns a default value (<code>null</code> in this ... | One solution could be to avoid working directly with ORM entities before they have been inserted into the database, and not to use ORM entities in your business logic.
If you need to work with the <em>data</em> before inserting it, then a common solution would be to create a separate model for that data which is no... | https://softwareengineering.stackexchange.com |
428,595 | [
"https://physics.stackexchange.com/questions/428595",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/47373/"
] | In order to describe one-particle states of spin-1 in a Lagrangian description, we need to use a field $A_\mu$. This is a 4-vector up to gauge transformations, which means that under Lorentz transformations $\Lambda^\mu_\nu$ the field $A_\mu$ transforms as
$$
A_\mu \rightarrow \Lambda^\nu_{\,\,\mu}\, A_\nu + \partial_... | Your equation of motion does not make sense. Try instead
$$
\gamma^{\mu} \left( \partial_{\mu} + i A_{\mu} \right) \psi = 0
$$
Then follows
$$
\partial_{\mu} J^{\mu} = \partial_{\mu} \bar{\psi} \gamma^{\mu} \psi
+ \bar{\psi} \gamma^{\mu} \partial_{\mu} \psi
= + i A_{\mu} \bar{\psi} \gamma^{\mu} \psi - i\bar{\psi}\ga... | The current $j^\mu\equiv\bar{\psi}\gamma^\mu\psi$ is conserved because the Lagrangian is invariant under the global U(1) symmetry $\psi\rightarrow e^{i\alpha}\psi$.
The QED Lagrangian is invariant under the local U(1) symmetry $\psi\rightarrow e^{i\alpha(x)}\psi$.
Since the global U(1) symmetry is a subset of the l... | https://physics.stackexchange.com |
505,236 | [
"https://electronics.stackexchange.com/questions/505236",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/255159/"
] | I'm planning on making a small desk toy involving LEDs and a motor to turn a reflective element, and I just want to know if what I'm planning is safe or not.
I want to use a series resistor to limit current to the motor. I only need the motor to turn slowly (no exact RPM defined), and I don't need variable motor speed ... | You can use a series resistor to reduce the speed of a small DC motor by reducing the voltage, but the effectiveness of that will be very limited. You can probably reduce the speed to 20 percent of the normal speed. The speed will vary with load variation. If you want something less than a few revolutions per second, t... | You can use a belt drive or gears to make it turn slower.
If that adds too much complexion for the application, you can use a diode instead of the resistor, so that the motor can draw more current in ramping up the speed. Resistor will have a higher voltage drop on higher currents. With a diode the current dependency i... | https://electronics.stackexchange.com |
15,420 | [
"https://engineering.stackexchange.com/questions/15420",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/11361/"
] | Why does chilled water emerge from the water pipe of air conditioner?
I feel that instead, lukewarm water should come out, the reason being the air conditioner air from the room and also, electricity produces heat energy so as a result warm water should come out. So what is the correct reason for this?
| An air conditioning system is basically a refrigerator, it passes air over a heat exchanger to cool it ie it injects cold air into a space, it doesn't 'suck' anything out'.
The water which comes out of the waste pipe is just condensed water vapour from the incoming warm air, the waste heat form the exchanger goes el... | I'm not quite sure of the context of the question or what the water pipeline you are referring to is since most air conditioners that are in homes do not use water, but rather refrigerants. If you are talking about the condensate line from the coil as Chris thought, then yes that is water vapor from the air. Warmer air... | https://engineering.stackexchange.com |
29,462 | [
"https://stats.stackexchange.com/questions/29462",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11609/"
] | Is it correct to say that the Hidden State Sequence in a Hidden Markov Model is a Markov Chain?
Thanks
| Yes, it's definitely a Markov chain because the observed variables define the transition probabilities from every <em>latent variable configuration</em> to every other. (That is, they yield an $n \times n$ matrix of probabilities where $n$ is the number of latent variable configurations.)
Usually you can say more abo... | Yes, A hidden Markov model is a bivariate stochastic process
$\{(X_t,Y_t)\}_{t\geq0}$, defined on a product space $(\mathsf{X}
\times \mathsf{Y},\mathcal{X} \otimes \mathcal{Y})$, where
$\{X_t\}_{t\geq0}$ is a Markov chain taking
values in $\mathsf{X}$... | https://stats.stackexchange.com |
47,176 | [
"https://mechanics.stackexchange.com/questions/47176",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/28020/"
] | something got in and caused these scratches.
can/will they cause blowby if reused?
<img src="https://i.stack.imgur.com/kwHZI.jpg" alt="piston damage">
I figure if the placement of its .018 mil piston ring gaps matter, then the gaps from these scratch just may as well.
I already took off any high spots. and could cut ... | The piston will be fine - it is the rings that provide the seal with the bore. As long as the rings move freely side to side then it will seal as it should.
If the rings stick then that should be addressed.
| The foreign object damage to the piston means there is very likely similar damage to the bore . New rings can not fix that problem.
| https://mechanics.stackexchange.com |
820,211 | [
"https://math.stackexchange.com/questions/820211",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/103063/"
] | Let $X_1, \cdots, X_n$ be $iid$ normal random variables with unknown mean $\mu$ and known variance $\sigma^2$. How to find $E[\Phi(\bar X)]$, where $\bar X:=\frac{\sum_{i=1}^nX_i}{n}$, please? I guess the answer should be $\Phi(\mu)$. Here is how I started. Note that $Y:= \bar X$ is also normal with mean $\mu$ and vari... | The constant of integration is arbitrary and two anti-derivatives are equivalent if they differ by a constant.
For example, since
$$
\int0\,\mathrm{d}x=C
$$
we get not only
$$
\int\cos(x)\,\mathrm{d}x=\sin(x)+C
$$
but also
$$
\begin{align}
\int\cos(x)\,\mathrm{d}x
&=\int(\color{#C00000}{\cos(x)}+\color{#00A000}{0}... | There is no other constant, because you see, $\int\sin 2\theta\, d\theta = \dfrac{1 - \cos 2\theta}{2} = \sin^2 \theta$. Oh, what's that, you're saying it's just $\dfrac{-\cos 2\theta}{2}$? Well okay then, I'll say that $\int x\, dx = \dfrac{x^2}{2} -\dfrac{1}{4}$.
I hope you see what's going on. There's no <em>unique... | https://math.stackexchange.com |
65,289 | [
"https://biology.stackexchange.com/questions/65289",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/31076/"
] | If I have a GST 26kDa polyclonal antibody, will it bind to the GST 28kDa protein as well?
| If the sequence of the 26 kDa form is included within the sequence of the 28 kDa form then the answer is 'probably yes'.
However if the N- or C-terminus of the short form is an important/dominant epitope and it is masked in the long form (by being extended) then the activity of the serum against the long form could b... | As Alan said, it depends but I'd guess that, yes, it probably does.
Given that you are using polyclonal antibodies against a not so dramatic extension, I'd say it's even more likely that you'll see signal. The various antibodies within the polyclonal mixture will bind different parts of the smaller protein, so unless ... | https://biology.stackexchange.com |
19,732 | [
"https://engineering.stackexchange.com/questions/19732",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/14841/"
] | What kind of motor is suitable for the below requirements?
<ol>
<li>2700 rpm, needs to be accurate, not +- few rpms. I think the best approach is to use a hall effect sensor and adjust current/voltage on the fly? Or a better idea?</li>
<li>Be as noiseless as possible. The noise 12V square fan motors make is perfect.</... | A brushless motor controlled by an electronic speed controller can produce an accurate and relatively powerful system.
Most BLDC motors used for hobby r/c equipment would be suitable and these are capable of supporting a significant axial and tangential load.
When operating at low RPMs (2700 RPM is slow) good qual... | I suggest a synchronous motor in order to obtain desired the rpm, it runs at a constant speed irrespective of and load there are various methods to control speed. The sound produced is dependent on the design-friction and others things.
In synchronous motors the stater and rotor rotates at the same speed. However, you... | https://engineering.stackexchange.com |
14,921 | [
"https://electronics.stackexchange.com/questions/14921",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10598/"
] | How would you go about designing a PCB with weight constraints? Suppose, the PCB has a weight constraint that say it must weight less than 140grams.
In searching for parts and components, I realized most if not all components' datasheets do not have any weight information. For example, I need to use two DB25 connector... | It sounds to me like you're going the wrong direction with the hardware you have available. If you're using a USB network adapter, it's probably one of those where you have to install drivers in the OS to make it work. And if you have to do this, then you've got your work cut out for you trying to interface an Arduin... | As Kellenjb has said in a comment:
<blockquote>
if the datasheet doesn't have enough info to make it work then you should look for a different part
</blockquote>
I think that this is excellent advice, especially if you're a beginner. Much better to spend time and effort designing, rather than wondering what the (po... | https://electronics.stackexchange.com |
224,205 | [
"https://physics.stackexchange.com/questions/224205",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65707/"
] | Consider the following two situations:
A: You wake up in an elevator that is in free fall in a gravitational field.
B: You wake up in an elevator that is floating in a vacuum.
Is it possible to distinguish between these two situations?
It seems to me that Newton's second law formulated in a local coordinate system ... | What happens is that for a conductor limited in real space and not grounded the net charge can't change (if is 0 it has to remain 0), so on the face towards the external charge it accumulates a charge to balance the electric field inside the conductor, but on the other face it accumulates a charge opposite in sign, to ... | The charge is induced inside an conductor so as to balance the electric field of the external charge.In steady state condition electric field inside the conductor is always zero,external electric fiels is cancelled by the induced charges on the surface of the conductors.
| https://physics.stackexchange.com |
639,183 | [
"https://physics.stackexchange.com/questions/639183",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/245292/"
] | I read that a rope applies a force equal to its tension wherever it touches (pulls)
Suppose a rope is connected to a block then why do we ignore the normal force by the rope ? Or its the tension force in disguiuse ?
Does a rope apply both Tension and normal ??
| It is the tension force in disguise. The block has its weight acting downwards. This is counteracted by the tension in the rope. Since this force works in the opposite direction, you can call this the normal force in disguise. If the force is not balanced, the block would move upwards or downwards.
| acoording to newtons third law every action has equal and opposite reaction.
Normal force is an example of a reaction force.
Tension is just a pulling force that a rope gives to the object it is attached to.
It has nothing to do with normal force.
the force with which the block pulls the force back can be called normal... | https://physics.stackexchange.com |
857,866 | [
"https://math.stackexchange.com/questions/857866",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/157361/"
] | Let $r_k$ be the rational numbers in $\mathbb{R}$.
(1).Is $\cup_{k=1}^\infty (r_k-\frac{1}{k^2}, r_k+\frac{1}{k^2}) = \mathbb{R}$?
(2).Is $\cup_{k=1}^\infty (r_k-\frac{1}{k}, r_k+\frac{1}{k}) = \mathbb{R}$?
(1).Because $m(\mathbb{R})=+\infty, \sum_{k=1}^\infty \frac{1}{k^2}<+\infty$, so $\mathbb{R} \setminus\cup... | One can choose an enumeration $\{r_k\}_{k=1}^\infty$ of the rationals so that (2) fails.
Define $A = \{2^k : k \in \Bbb N\}$.
Let $\{r_k\}_{k=1}^\infty$ be an enumeration of the rationals such that
$$
\{k \in \Bbb N : r_k \in \Bbb Q \cap [0, \infty)\} = A.
$$
This is possible since $A$, $\Bbb N - A$, $\Bbb Q \cap [0... | I think (2) depends on how you enumerate the rationals. For example lets say you dont want $e$ in the image. Then enumerate the rationals so that if $q$ is a rational and
$e-q \sim \frac{1}{n}$ the make sure that if $r_k=q$ we have $k > n$.
(better is given in Ayman's answer and in the comments afterwards).
Conver... | https://math.stackexchange.com |
177,834 | [
"https://security.stackexchange.com/questions/177834",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/34530/"
] | There are countless “how-to” articles and best practices recommending use of an offline root certificate authority (CA). Though as the title suggests, is this recommendation obsolete?
The context of my question is for small to medium enterprises. NOT large enterprises (or otherwise) with multiple tiers of subordinate ... | I think we need to consider here definitions of the word "offline".
As you suggest, the following are conflicting requirements:
<ul>
<li>Have the Root CA be powered off except when issuing / revoking a Subordinate CA cert.</li>
<li>Have the Root CA issue frequent CRLs.</li>
</ul>
The solution I see deployed most oft... | One other thing, there is no reason an offline root CA can't publish it's certificate revocation list (CRL) to another location that is online. The lifetime of a CRL can be extended to a very large time period using this command:
<pre><code>certutil -setreg CA\CRLPeriodUnits 6
certutil -setreg CA\CRLPeriod "Years"
</c... | https://security.stackexchange.com |
145,167 | [
"https://physics.stackexchange.com/questions/145167",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52659/"
] | I am given the following (probably simple) exercise, but I think I misunderstand something:
Let $\psi_{a,b}(r_1,r_2)$ be a two-particle state, calculate the probability density for distinguishable and indistinguishable particles.
I don't quite understand what this exercise wants me to do: If $\psi_{a,b}(r_1,r_2)$ ,... | The probability density to find one particle at $r_1$ and the other particle at $r_2$ is the absolute square of the wave-function. The question is, so I understand, how does the wave-function look like.
If the particles a and b are distinguishable, the wave-function looks as given in the exercise.
However, if the parti... | Think ψa,b(r1,r2) as a variable in a function space. you need to find the subset of these that have the required properties. The set for the distinguishable particles should be different from the set for indistinguishable particles. I suspect notation abuse in the identical/distinguishable theory of particles. its not... | https://physics.stackexchange.com |
109,643 | [
"https://mathoverflow.net/questions/109643",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2565/"
] | Edit: I have reworded the question.
This may be a basic question but I am having trouble figuring out the correct answer. I want to find a local coordinate chart that fits a d-dimensional submanifold in $\mathbb{R}^N$. I am given two points $p_1, p_2 \in \mathbb{R}^N$ and corresponding orthonormal bases $(\phi_1, \... | This isn't really a formula so much as a conceptual construction.
First suppose that $d=n-1.$
Let $T_1=span(\phi_1,..., \phi_{n-1})$ and $T_2=span(\tau_1,...,\tau_{n-1})$ be the tangent subspaces of $T{\mathbb R}^N$ at $p_1$ and $p_2,$ respectively. We can think of these as hyperplanes in real N-space so that ther... | There isn't a formula for what you're looking for. At least, the formula can't make sense for all initial data <em>and</em> depend continuously on that initial data.
Your initial data is two points in the Stiefel manifold $V_{n,d}$, together with two points in $\mathbb R^n$. If you were to find an embedding $B^d \to ... | https://mathoverflow.net |
142,173 | [
"https://softwareengineering.stackexchange.com/questions/142173",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/21461/"
] | I have read a lot of computer architecture textbooks, and I wonder why most of them (if not all) used MIPS as the architecture to teach. Why MIPS and not Intel or AMD or something else? What makes the architecture suitable for teaching?
| The MIPS architecture is derived from an architecture specifically designed at Stanford for educational use and for research into CPU ISAs and architectural implementations. Early academic RISC architecture were designed such that they could be implemented (included layout) by small teams of graduate or upper-division... | Intel and AMD have a large share of the Desktop market. Other processor families are much more common in devices outside that fairly small area of influence. MIPS is also a RISC architecture which are generally thought of as being easier to learn. You learn a small number of commands that can be combined orthogonally a... | https://softwareengineering.stackexchange.com |
2,948,329 | [
"https://math.stackexchange.com/questions/2948329",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/350248/"
] | I don't know whether it's correct but I wish to show that <span class="math-container">$g_1g_2=g_2g_1 \Leftrightarrow g_1=g_2^{-1}$</span> for any <span class="math-container">$g_1\neq g_2$</span> in <span class="math-container">$\langle x,y : xyx^{-1}y=e\rangle$</span>
I was trying to work be definition, taking <span... | The statement <span class="math-container">$g_1g_2 = g_2g_1 \implies g_1 = g_2^{-1}$</span> for any <span class="math-container">$g_1$</span>, <span class="math-container">$g_2$</span> is not correct.
There are a few trivial counterexamples:
<ul>
<li>Setting <span class="math-container">$g_1 = g_2 = x$</span>, then <... | If <span class="math-container">$xyx^{-1}y=e$</span> then <span class="math-container">$y^{-1}x=xy$</span> (and also <span class="math-container">$yx=xy^{-1}$</span>), so every element of <span class="math-container">$G=\langle x,y\mid xyx^{-1}y\rangle$</span> can be represented by <span class="math-container">$x^my^n$... | https://math.stackexchange.com |
324,098 | [
"https://softwareengineering.stackexchange.com/questions/324098",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102569/"
] | Apllication structure:
Business layer
<pre class="lang-cs prettyprint-override"><code>public interface IOrderDataService
{
void Save(Order order);
}
public interface IOrderLineDataService
{
void Save(OrderLine orderLine);
}
public class OrderManager
{
private IOrderDataService _OrderDataService;
p... | If you truly want to keep all of it separate, you could create your own <code>TransactionScope</code> interface and use that in your <code>Create</code> Method.
The implementation of said interface then uses the <code>SqlTransactionScope</code> to do the "real" work.
| What you need is a Unit of Work for your Repositories. The Unit of Work would have an interface similar to
<pre><code>public interface IUnitOfWork
{
ITransaction Start();
void Commit();
void RollBack();
}
</code></pre>
then your save method on <code>IOrderDataService</code> and <code>IOrderLineDataServi... | https://softwareengineering.stackexchange.com |
3,879,372 | [
"https://math.stackexchange.com/questions/3879372",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Show that for all prime numbers <span class="math-container">$p$</span> greater than <span class="math-container">$3$</span>, <span class="math-container">$24$</span> divides <span class="math-container">$p^2-1$</span> evenly.
</blockquote>
Since <span class="math-container">$(p+1)(p-1) = p^2-1$</span> we ... | You've nearly answered your own question. The value of the derivative would be a complex number. Should that complex number be <span class="math-container">$+1$</span> or <span class="math-container">$-1\text{?}$</span> If you approach <span class="math-container">$z$</span> from one direction you get one number and fr... | <span class="math-container">$$\lim_{h\to0}\frac{\overline{z+h}-\overline z}{h}=\lim_{h\to0}\frac{\overline{h}}{h}$$</span> is already enough to show that the derivative exists everywhere or nowhere.
Then with real variables
<span class="math-container">$$\lim_{u\to0}\frac{\overline{u}}{u}=\lim_{u\to0}\frac{u}{u}=1,\\\... | https://math.stackexchange.com |
55,500 | [
"https://biology.stackexchange.com/questions/55500",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/21277/"
] | Why should you use an annealing temperature about 5°C below the Tm of your primers?
According to my current research, I think it has something to do with the other reactents in the PCR, but I am not sure.
| The annealing temperature of a primer is defined as the temperature in which 50% of the nucleotides of the primer are bound to the DNA. 50% annealing proportion will not yield an optimal PCT product. Thus, by lowering the temperature by around 5oC, the proportion of bound primer changes to more then 50% (perhaps around... | You want to have primers which bind under the conditions of the reaction only to your sequence of interest. If you go too far off the optimal annealing temperature (5°C below the Tm is indeed a relatively good choice in my experience), your will affect the PCR efficency and thus the yield of your reaction.
An annealin... | https://biology.stackexchange.com |
211,404 | [
"https://softwareengineering.stackexchange.com/questions/211404",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102136/"
] | I have a typical MVC based website, and I'd like to give some registered users the abillity to extract data from the database (in a variety of formats). The workflow is very simple:
<ul>
<li>User logs in,</li>
<li>User clicks export,</li>
<li>A file is generated,</li>
<li>User downloads the file.</li>
</ul>
I'm trying ... | You could serve the file via your PHP script, which checks if the user is authentificated.
E.g. pseudocode
<pre><code>if session.user is loggedIn
filename = url.filename
if filename belongs to session.user
fetchfile(filename)
else
"you are not authorized to download this file"
else
"pl... | Don't generate a file prior to authorizing request. This might be an expensive operation. First make sure that user has the necessary permissions and then generate files accordingly.
Since you are generating files on the fly, why store them? Can you not just serve files through response object and forget about them?
| https://softwareengineering.stackexchange.com |
2,862,702 | [
"https://math.stackexchange.com/questions/2862702",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/579536/"
] | Peter draws a ball from the bag, and then Angelina draws a ball. What is the probability that Angelina got a green ball?
So far I have this:<br>
Scenario A: 1st ball is not green, 2nd green: 7/12 * 5/11 = 35/132<br>
Scenario B: 1st ball is green, 2nd green: 5/12 * 4/11 = 20/132<br>
--> $$\frac{55}{132} = \frac{5}{12... | Your approach is fine, but it's worth realizing that unless you know something about the ball Peter has chosen, he may as well not have chosen at all, in which case Angelina simply has a $5/12$ chance of choosing a green ball.
Where this point really becomes worth understanding is if, for example, not only Peter, but ... | Angela's draw is actually independent from the order she draws the ball whether she is first, second, ..., or twelfth (surprisingly enough). So, the probability of her drawing a green ball is actually $\dfrac{5}{12}$. To give you a better explanation, suppose there are $k$ green balls and $n$ total balls. Then, the pro... | https://math.stackexchange.com |
212,458 | [
"https://softwareengineering.stackexchange.com/questions/212458",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/103127/"
] | I'm a Java programmer, but I want to program in Jython. I've never coded in Python before, but have been looking through some tutorials and I'm fairly confident I can grasp it.
My question is clarity over Jython. I understand with Jython you have the joys of writing Python code with the added bonus of accessing Java ... | If you have Active Directory, you can test for membership in an Active Directory Group:
<pre><code>public bool IsInADGroup(string ADGroupName)
{
bool result = false;
List<string> myGroups = new List<string>();
using (PrincipalContext pc = new PrincipalContext(ContextType.Domain... | <strong>The manager is right about the password getting out</strong>. Its not a matter of if, but when.
Since Active Directory isn't an option for some users, you could create a <em>signed</em> text file with a list of windows login names that are allowed super user access. <em>This assumes that people are not sharing... | https://softwareengineering.stackexchange.com |
41,938 | [
"https://dba.stackexchange.com/questions/41938",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/23634/"
] | I am on OS X 10.8.3, I've install PostgreSQL from macports, but I've realized that I have not enough space on my system drive for the DB I am about to populate with data.
Is there a way to create new database on another drive/partition (not the system one, where postgres is installed)?
How can I do that?
| Create the new database, then create a tablespace on your external drive:
<pre><code>CREATE TABLESPACE mytablespace LOCATION '/Volumes/externaldisk/pg';
</code></pre>
Then alter the database so that the new tablespace is the default location for it:
<pre><code>ALTER DATABASE MYDB TABLESPACE mytablespace;
</code></pr... | I very strongly recommend that you do <em>not</em> put a tablespace on an external removable drive. If the tablespaces disappears (ie: drive unplugged) you risk <em>severe database corruption</em> that will be difficult to recover from. You'll likely find permissions management a challenge, too.
You should generally <... | https://dba.stackexchange.com |
134,091 | [
"https://electronics.stackexchange.com/questions/134091",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/27067/"
] | Or is there any issues I should be wary of? I need at least 7A on a 12V line, but I've found that a computer PSUs are significantly cheaper.
| Yes.
There's not much more to say than that ;)
Getting them to turn on though can be a bit tricky. Some may require a load on the 5V before they will allow you to turn them on (a simple resistor will do), some may require the load on the 12V (in which case you're fine), and some don't care either way.
To switch a... | Well you may find some other surplus options, but otherwise, as long as the output amp rating of the PS is enough for what you need, it may work. I'll caution you though that I've observed very poor regulation on everything but the lower voltage (5V, 3.3V, 2.2V) outputs, which MUST be very precise. The 12V outputs are ... | https://electronics.stackexchange.com |
469,224 | [
"https://physics.stackexchange.com/questions/469224",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/171413/"
] | I was just wondering something ridiculously simple; does an electric field penetrate through glass? Say I have a proton or charged cotton pulp ball inside a Pyrex glass container and apply an electric field on the outside, through the whole thing, do the particles 'feel' the field and will they be drawn to either of th... | OK I think I know what is going on. It's all about primes. Consider an active spacetime transformation:
<blockquote>
<span class="math-container">$$ x^{\mu} \mapsto x'^{\mu}(x) \, ,$$</span>
<span class="math-container">$$g_{\mu \nu} (x) \mapsto g'_{\mu \nu} (x') = g_{\alpha \beta} (x) \frac{\partial x^{\alpha}}{\parti... | I'm a mathematician, not a physicist, so I learned all of these ideas with different notation, but I think I understand what might be confusing you.
Conformal transformations are indeed a special kind of diffeomorphism, and a rotation (say in the plane with the usual metric) is indeed conformal, so the two formulas yo... | https://physics.stackexchange.com |
194,752 | [
"https://math.stackexchange.com/questions/194752",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/40155/"
] | Yes, this is a homework problem. And no, I'm not asking for the answer to this.
I just want to understand how to tackle this type of problem. What are the steps towards finding the solutions? My class is not much help and I am lost!
Any help is appreciated!
| Here's an extremely short Haskell GHCi session:
<pre><code>Prelude> [ x | x <- [0..34], (6 * x) `mod` 35 == 14 ]
[14]
</code></pre>
Therefore, $x = 14$. Why? Note that $6 \times 14 = 84 = (2 \times 35) + 14$.
| In this case, we note that $6$ is a unit in $\textbf{Z}/35 \textbf{Z}$ since $\gcd(6,35)=1$. So multiplying both sides of your equation by the inverse of $6$ mod $35$ (which happens to be $6$, we see that we obtain a unique solution, $x = 14*6 = 14 \mod 35$.
In general, if you look at an equation of the form $ax = b \... | https://math.stackexchange.com |
462,745 | [
"https://electronics.stackexchange.com/questions/462745",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/234014/"
] | I was studying about currents in an injected semiconductor (by illumination) from <em>Integrated Electronics</em> by Millman and Halkias. They consider the diffusion hole current in an injected n-type open-circuit uniformly doped semiconductor, assuming that hole concentration is negligible compared to electron concent... | Shrinking with heat makes no sense if its not a closed shape since it would pull apart since the heat activates both the shrinking and the adhesive.
If you are after rigidity and toughness then "silicone self adhesive tape", "self amalgamating tape", "self-fusing tape" (or some other name along those lands) will becom... | "Heat shrink tape" absolutely does exist. Just do a search using that phrase, and you'll find many vendors.
| https://electronics.stackexchange.com |
63,902 | [
"https://mathoverflow.net/questions/63902",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14878/"
] | I'm sure you all are familiar with Theorem 5.3 from Sipser's TOC book:
S = "On input (M,w) where M is a TM and w is a string:
1. Construct the code of TM M2 as follows:
M2 = "On input x:
(a) If x = 0n1n for some n ≥ 0, accept.
(b) If x = 0n1n, run M on w and if M accepts w, then accept."
2. Run R on (M2).
3. If R acce... | First of all, the undecidability of REGULAR_TM follows immediately from Rice's theorem.
For a direct proof, Sipser gives a reduction from the language A_TM. He constructs a decider R for A_TM out of a decider for REGULAR_TM, as follows.
R inputs the pair , where M is a TM and w is a string.
It constructs the TM M2, w... | We know that the language A_TM is undecidable. Let us just suppose that REGULAR_TM is decidable. If I can build a decider for A_TM, using a decider for REGULAR_TM, it is clear that REGULAR_TM is not decidable. This is how to build a decider for A_TM, M_A using a decider for REGULAR_TM, M_R:
M_A = On input , run M_R on... | https://mathoverflow.net |
599,441 | [
"https://electronics.stackexchange.com/questions/599441",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/245875/"
] | A CT (current transformer) is installed to measure the line current for digital measurement and protection devices. In many cases, the CT is installed in open weather or on poles, making it vulnerable to lightning.
The voltage across the burden resistor of the CT is amplified and measured through a microcontroller to d... | By convention, unless otherwise indicated, <code>34 Vac</code> means <code>the RMS voltage of the AC voltage is 34 V</code> or simply <code>34 Vrms</code>. If you mean the peak value of the AC voltage then you should say <code>34 Vpk</code> because the peak is not an AC <em>(i.e. peak does not change with time -- it's ... | <blockquote>
I have a 24Vdc battery that I have connected to an inverter to. Using the Vrms to Vac equation(ie multiplying by sqrt(2)) I would find the peak value of the Vac.
</blockquote>
What Vac?
<blockquote>
So it would be 34.0 Vac.
</blockquote>
You seem to have assumed a 24 VAC RMS here, and converted it to 34 V ... | https://electronics.stackexchange.com |
93,481 | [
"https://physics.stackexchange.com/questions/93481",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/37283/"
] | The relativistic Lagrangian is given by
$$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi $$
I need to derive, $\displaystyle \frac{d\vec p}{dt} = q \left( \vec E + \frac 1 c (\vec u \times \vec B)\right)$. Everything (in my note) is fine until there is one expression which I don... | This is not correct: "Since the relativistic Lagrangian is transitionally invariant, there is no dependence on coordinates so the last term is zero." In fact,
$$
\frac{\partial L}{\partial {\bf r}} = q\nabla\left[ \frac{1}{c} \left({\bf u} \cdot {\bf A}\right) - \phi \right] = q\left\{\frac{1}{c} \left[\left({\bf u} \c... | <blockquote>
Minkowski metric: $\text{diag}(+1,~+1,~+1,~-1)$
</blockquote>
How about deriving from Lagrangian using 4-vector?
The Lagrangian is
\begin{eqnarray}
L = -\frac{1}{\gamma} mc^2 + Q \dot{x}_{\nu} A^\nu,
\qquad\left( \gamma = \frac{1}{\sqrt{1-(v/c)^2}} = \frac{c}{\sqrt{-\dot{x}_{\mu}\dot{x}^{\mu}}}\rig... | https://physics.stackexchange.com |
23,846 | [
"https://electronics.stackexchange.com/questions/23846",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4245/"
] | Given an inductor of an unknown (though magnitude-estimatable) value, and a resistor of precisely known resistance, how can one calculate the inductance of the inductor?
Tools I have at my disposal:
<ul>
<li>Oscilloscope (both digital and analogue)</li>
<li>Signal generator (can make any waveform up to around 20KHz)<... | We've actually thought about how to do this from a microcontroller to make a cheap L/C/R meter. It needs to be cheap and small because we plan to make a business card that has a useful circuit on it.
Anyway, the answer is probably different from doing this manually with a signal generator and scope or automatically w... | One option would be to form a series RL circuit and apply a sinusoidal voltage, \$v_i\$, of a given frequency, \$f\$. Then measure the phase difference between the input and output voltage. From the voltage divider equation \$\frac{v_{o}}{v_{i}}=\frac{j\omega L}{R+j\omega L}\$ the phase difference is equal to \$90^{\ci... | https://electronics.stackexchange.com |
103,783 | [
"https://mathoverflow.net/questions/103783",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19142/"
] | What is the "no small subgroups" argument for $GL(n,\mathbb R)$? That is, how do we show that in $GL(n,\mathbb R)$ there exists a neighborhood of the identity which contains no subgroup other than the trivial one? I had some scribbling (for the $n=2$ case) but could not arrive at a clean proof.
| Here is Asaf's agrument expanded a bit. It has the advantage of working for all Lie groups simultaneously.
Given a Lie group $G$ with Lie algebra $\mathfrak{g}$, consider the exponential map $\exp:\mathfrak{g}\rightarrow G$. It is known that it is a diffeomorphism on a small enough open set $U\subseteq\mathfrak{g}$... | It suffices to show that the powers of some non-identity element $g \in \text{GL}_n(\mathbb{R})$ near the identity "escape from the identity." If $g$ has an eigenvalue not equal to $1$ then this follows by examining eigenvalues (we should take a neighborhood of the identity containing only elements with eigenvalues ver... | https://mathoverflow.net |
16,105 | [
"https://mathoverflow.net/questions/16105",
"https://mathoverflow.net",
"https://mathoverflow.net/users/492/"
] | The answer to this question should be obvious, but I can't seem to figure it out. Suppose we have a surface $F$, and a representation $\rho : \pi_1(F)\to SU(n)$. We can define the homology with local coefficients $H_*(F,\rho)$ straightforwardly as the homology of the twisted complex $$C_*(F,\rho):=C_*(\widetilde{F};\ma... | For me it is easier to work with cohomology (just for psychological reasons). Also, I will distinguish the representation $\rho$ from the local system $V$ with fibres ${\mathbb C}^2$ that it gives rise to. So where you would write $H^1(F,\rho)$ I will write $H^1(F,V)$.
I will let $\overline{V}$ denote the complex c... | What you say is right, and makes sense on any even dimensional manifold. Computing it can be tricky: a useful approach is to use a regular cell complex and the dual complex, then on the chain level the intersection form is given by the identity matrix (see the first couple pages of Milnor's "a duality theorem for Reide... | https://mathoverflow.net |
91,813 | [
"https://softwareengineering.stackexchange.com/questions/91813",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30611/"
] | Some say that DBaaS (database as a service) -- aka cloud database -- is not suitable for Business Intelligence (BI), analytics (OLAP) or archiving.
Is this true? More generally, when DBaaS is the most effective technical choice?
| "Explicit is better than implicit" is only one of the maxims in Python's design philosophy. "Simple is better than complex" is there too. And, although it's not in the Zen of Python, "We're all consenting adults here" is another.
That second rule is perhaps the most important here. When I design a class, I have some i... | The Python convention is to use an underscore prefix for protected/private members.
This convention, when followed, is effectively same as access modifiers, except 1) you'll see directly from the member's <em>name</em> whether it's public or not, and 2) you <em>can</em> break "encapsulation" if you really want to (thi... | https://softwareengineering.stackexchange.com |
240,856 | [
"https://softwareengineering.stackexchange.com/questions/240856",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/45335/"
] | "Code review" (aka "peer review") seems like a really great idea, so my team started practicing it.
For a little while it worked well, but then a co-worker merged a branch in, and asked for a review of the code. When I went to review her code, the Github diff page was about 420k pixels in height. Given that my scree... | This is actually one of the benefits of introducing code reviews in your organization: getting people to make small, incremental changes. Just wait until the guy that made that huge commit has to review a similarly sized commit of yours.
Other, more constructive ways of getting to the same result without starting a "... | A working solution is to put a soft upper limit on how large merges you accept, but changes have to be reviewed as some point.
If you don't have much experience with source code reviews yet, you could start out recording metrics of the reviews (too):
<ul>
<li>Merge/commit size</li>
<li>Issues resolved</li>
<li>Errors... | https://softwareengineering.stackexchange.com |
47,942 | [
"https://stats.stackexchange.com/questions/47942",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11821/"
] | I am trying to build a logistic regression model where I have a dependent variable $y$ and independent variables $x_1$, $x_2$... $x_n$. $y$ can take only two values - 0 or 1.
My original modelling dataset has 100,000 observations - which I have divided into two samples - a training sample with 80,000 observations and ... | You haven't overfit your model, what you've done is demonstrate (again) that stepwise, forward and backward methods don't work well for this type of task. (Although it was good that you used a training and test set, this let you see that these methods can find things that aren't there).
Model selection is a big topic ... | It can mean too many things, it may mean your data miss critical observations, it may mean that the problem you are facing is not as solvable as you thought (e.g. trying to fit a nonlinear determinstic model to some iid data stream), and yes, sure, for the case you demonstrated, it can also mean your model is over-, o... | https://stats.stackexchange.com |
196,889 | [
"https://physics.stackexchange.com/questions/196889",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46450/"
] | When discussing events at the quantum level, we deal in probabilities and not absolutes. Articles I've read on particle physics state that a particle has a probability of being created in a collision. What determines this probability?
Assuming we have the energy and other criteria met, which would allow us to create r... | This is actually an open question.
So far what we are able to state from theoretical considerations are restrictions in terms of the conservation laws that we have observed. These tells you for example that the whole momentum in a reaction is conserved, an the mass-energy, or some quantum numbers. And this already co... | Once one specifies a quantum field theory, typically in the form of a Lagrangian density, one can calculate the probabilities of various outcomes in collisions.
A quantum field theory is a theory based on fields that obeys quantum mechanics and special relativity. The so-called Standard Model is perhaps the most famou... | https://physics.stackexchange.com |
38,912 | [
"https://chemistry.stackexchange.com/questions/38912",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/21414/"
] | In addition polymerisation, a double bond in the monomer is broken and a long chain of polymers is formed. How is this bond broken (where is the energy input) and how is the long chain formed?
(something to do with free bonds?)
| During radical polymerization, we use molecules called initiators $I$ for forming free radicals. The molecules of initiators contain at least one fragile bond that can easily dissociate upon heating, and yield free radicals.
$$I\rightarrow2A^.$$
The as-formed radicals have enough energy to attack the monomer molecule... | Addition polymerisation is usually classed as chain growth. Whilst free radicals are usual and the mechanism is by homolytic fission, cationic and anionic initiation are both valid where propagation is by heterolytic fission. For example, the polymerisation of cyanoacrylate to give superglue is usually initiated by tra... | https://chemistry.stackexchange.com |
436,011 | [
"https://physics.stackexchange.com/questions/436011",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206197/"
] | It’s getting cold where I live and I sleep with multiple blankets. I am wondering whether it generally matters how I might use blankets to keep something warm; if I put blanket <span class="math-container">$A$</span> on top of blanket <span class="math-container">$B$</span>, will it better insulate something than if I... | Such a system is actually quite complex, and as any backpacker would know, what keeps you warm is the amount of dead air within the layers. Dead air is non-circulating air. If we ignore the dead air between the layers and only consider the blankets themselves, I would say it's the same. However once you consider dead a... | each blanket layer represents a resistance to the conduction of heat. the heat flow resistance of a stack of blankets is then the sum of the resistances of each individual layer within the stack because to flow all the way through the entire stack, a parcel of heat must traverse each layer in it.
The ordering of that... | https://physics.stackexchange.com |
568,793 | [
"https://physics.stackexchange.com/questions/568793",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236734/"
] | I was recently doing a question on a spring block system and I was just suddenly weirded out by the fact that regardless of how much momentum or energy the block starts with (indirectly how much the spring is compressed), the time period is independent of it. Why does this happen intuitively?
Reason why I think that ti... | It follows from the spring's force law: <span class="math-container">$F = kx$</span>, or <span class="math-container">$a = (k/m)x$</span>. The important point is acceleration is proportional to distance from the center.
You are aware that one solution to the equation is <span class="math-container">$x = A_1sin(t/T)$</s... | <blockquote>
I mean, if you compress a spring more like push it more in, then it would have more distance to travel and hence need more time
</blockquote>
Intuitively you can think like this : If you compress a spring greater , and then release it the force on the block by spring is greater. Hence it's acceleration(avg... | https://physics.stackexchange.com |
150,412 | [
"https://cs.stackexchange.com/questions/150412",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/149579/"
] | So I have a recursive algorithm which sums up the numbers from 1 to n <strong>plus one</strong> (hence the return 1):
<pre><code>public static int S(int n) {
if(n < 0) {
return 1;
}
else {
return n + S(n-1);
}
}
</code></pre>
This algorithm has a time complexity of O(n).
Is it possibl... | The sum <span class="math-container">$1+2+3+\cdots+n$</span> is equal to <span class="math-container">$n(n+1)/2$</span>; hence, the following function would return the same output:
<pre><code>Function S(n):
if n < 0, then return 1
Else return n(n+1)/2 + 1
</code></pre>
It takes time <span class="math-contain... | Yes. The method was invented by Carl Friedrich Gauss, aged 6. It’s simple. Add the first and the last number. Add the second and the second-to-last number. Then the third and third to last. And so on. Find the pattern.
| https://cs.stackexchange.com |
412,647 | [
"https://softwareengineering.stackexchange.com/questions/412647",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/250257/"
] | I used to work for a software development company, and there they had following way of solving bugs and the according testing:
<ul>
<li>The bug ticket is analysed by the developer.</li>
<li>The developer solves the bug.</li>
<li>The developer describes the testing procedure.</li>
<li>QA (Quality Assurance) automates th... | Tricky. When you have a bug and need to fix it, you proceed through the following steps:
<ol>
<li>QA describes desired behaviour and actual (different) behaviour.</li>
<li>If the behaviour is not always different, QA or developer finds a way to reproduce it - if you can't reproduce the bug, then you can't really say yo... | The answer to your question depends entirely on the way each company runs their business, how much money they're willing to devote to QA efforts, the kind of software being written, and other factors. There is no "correct way."
Your method adds substantial overhead, requiring close coordination between the Q... | https://softwareengineering.stackexchange.com |
95,396 | [
"https://electronics.stackexchange.com/questions/95396",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10190/"
] | I have heard of using the ground for communication with extremely low frequency waves. They said 100 watts gives you a km and 1000 watts gives you 10 km. How can I go about pumping the waves into the ground, and what would be a good frequency to operate?
| The Popular Electronics article I remembered described a short distance communications system made by pumping the AUDIO from an AUDIO PA into the ground through two ground connections about 20 feet apart. To achieve an approximate match into the earth, they used an audio output transformer turned around backwards.
Th... | It's really not so easy to do that. You can't just pump energy into the ground; you have to have an antenna of some sort to transmit with. And for very low frequency, you need an antenna that is very, very long. Hundreds of meters to kilometers. And it's not going to be very efficient, either, so you're going to ne... | https://electronics.stackexchange.com |
394,383 | [
"https://softwareengineering.stackexchange.com/questions/394383",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/340479/"
] | I would like to get your code thought and views on using conditional vs logical testing.
<strong>For example:</strong>
To test the conditions of truthness of all of the following variables, their currect status is as follows:
<pre><code>a= True
b= True
c= True
d= True
e= True
</code></pre>
One could use as test... | <blockquote>
<pre><code>If a Then If b Then If c Then If d Then If e Then x = "Passed" Else x = "Failed"
</code></pre>
</blockquote>
That is some horrendous code right there, and it doesn't do what you think it does either: the 3 "methods" you're showing are NOT equivalent. If we expand #3...
<pre><code>If a Then
... | I feel I must insist on readable, flexible, debugable code.
<pre><code>If a = False Then Return "Failed"
If b = False Then Return "Failed"
If c = False Then Return "Failed"
If d = False Then Return "Failed"
Return "Passed"
</code></pre>
Or more simply
<pre><code>Debug.Assert a
Debug.Assert b
Debug.Assert c
Debug.As... | https://softwareengineering.stackexchange.com |
193,378 | [
"https://physics.stackexchange.com/questions/193378",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/73586/"
] | One of my Textbook's Multiple Choice Question is-
A Thick plane mirror shows a number of images of the filament of an electric bulb. Of these, the brightest image is the-
<ol>
<li>First</li>
<li>Second</li>
<li>Last</li>
<li>Fourth</li>
</ol>
First of all I fail to understand How can a single plane mirror forms som... | The mirror described in the problem sounds like one used in a bathroom: a slab of glass with a silver coating on the back (see diagram below). This means that the first reflection is off the front of the mirror, which is a reflection off glass. The second reflection will be off the silver backing. Silver is much more r... | This is because it suffers a strong reflection at the silvered surface.
| https://physics.stackexchange.com |
70,569 | [
"https://stats.stackexchange.com/questions/70569",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/18528/"
] | I'm reading a book on data-analysis and in my book I have the following picture of 3-dimensional data and its scatter plot:
<img src="https://i.stack.imgur.com/JStuY.png" alt="3D data and scatter plot">
Could anyone help me understand how is the scatter plot interpreted? It confuses me at the moment...in other words... | 3D-scatterplots are sometimes a bit confusing, especially if you can't rotate the plot around. However, the scatterplot matrix supports the interpretation, at least here, rather nicely, even if it is missing the colors.
As a.desantos already pointed out, the individual scatterplots in the second image are projections ... | I think there are missing colours on the second image. They are the projections on the different planes $x_1,x_2,x_3$.
| https://stats.stackexchange.com |
60,238 | [
"https://stats.stackexchange.com/questions/60238",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/26220/"
] | I'm trying to get intuition for each of the main functions in actuarial science (specifically for the Cox Proportional Hazards Model). Here's what I have so far:
<ul>
<li>$f(x)$: starting at the start time, the probability distribution of when you will die.</li>
<li>$F(x)$: just the cumulative distribution. At time ... | Combining proportions dying as you do is not giving you cumulative hazard. Hazard rate in continuous time is a conditional probability that during a very short interval an event will happen:
$$h(t) = \lim_{\Delta t \rightarrow 0} \frac {P(t<T \le t + \Delta t | T >t)} {\Delta t}$$
Cumulative hazard is integrat... | I'd <sub><sup>HAZARD</sup></sub> a guess that it's noteworthy owing to its use in diagnostic plots:
(1) In the Cox proportional hazards model <span class="math-container">$h(x)=\mathrm{e}^{\beta^\mathrm{T} z}h_0(x)$</span>, where <span class="math-container">$\beta$</span> and <span class="math-container">$z$</span> ar... | https://stats.stackexchange.com |
384,762 | [
"https://electronics.stackexchange.com/questions/384762",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/193564/"
] | First time poster:
I want to learn about opamps. I am just a college graduate with no practical experience.
What I know:
A few basic high level applications such as
Hysteresis,
Voltage follower,
Inverting and non inverting configuration,
Various Filters, and
Oscialltors
All these we studied (and some lab exper... | My two cents here
<blockquote>
Is it possible for a 5V power supply to have very low internal
resistance such that a device that operates at 5V turns down its
resistance in attempt to draw 5A from the power supply , but instead
accidentally draws greater than > 5A due to the power supply having
very low inte... | A power supply that is capable of delivering more current at its rated voltage will not harm a load that draws less current. Generally the load will draw what it will and as long as that current is within the capability of the power supply things are going to be just fine.
If you did have a load that varied its curren... | https://electronics.stackexchange.com |
24,384 | [
"https://cs.stackexchange.com/questions/24384",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/17318/"
] | I have this recurrence $p(n) = 2p(n-2) + n$, and I have guessed that the solution is $O(n^2)$, however, when I do the following calculations, I cannot get the inequality to hold
$p(n-2) \leq c(n-2)^2$ (induction hypothesis)
$2c(n-2)^2 + n \leq cn^2$ (substitution)
$cn^2-8c + n \leq cn^2$
Can anyone see where I go w... | Okay, really sorry. I got confused with maximal and max flow in the graph. Obviously, the maximal is what is at most the capacity, and max flow is how much at most can flow though this network. The answer to the former is of course 9, where at the latter is 7.
In this case the max flow from s to t through 1 is 4 and ... | Max flow isn't 9 it is 7. 4 from s to 1 and 3 from s to 2.It cannot have more than that.You can see that it is also equal to min-cut.
| https://cs.stackexchange.com |
23,320 | [
"https://cs.stackexchange.com/questions/23320",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16358/"
] | Consider the problem:
<blockquote>
Given an undirected graph and two of its vertices, is there a path between them?
</blockquote>
I often read that this problem can be solved in linear time in the number of vertices! I am not sure why this claim holds.
Can this really be done in linear time (not amortized) withou... | It is not possible to decide $s$-$t$ connectivity in $O(n)$, in the adjacency matrix model. In fact, here is an $\Omega(n^2)$ lower bound. Let $|S| = |T| = n/2$ be a partition of the vertex set, and choose some $s \in S$ and $t \in T$. Consider the graph in which $S$ and $T$ are both cliques. In this graph $t$ is not r... | Your sources are sloppy or you misinterpret something. In general, deciding reachability requires time $\Omega(n+m)$ (assuming adjacency lists). This is linear in the <em>input size</em> (which is in $\Theta(m)$), however, so saying that reachability is solvable in linear time [in input size, which is the default] is c... | https://cs.stackexchange.com |
387,763 | [
"https://softwareengineering.stackexchange.com/questions/387763",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/318324/"
] | I want to place validation in one layer for the reason of simple code maintenance. I was thinking of entity validation, cause this protects directly database. Am I right, or should I add validation also on dto level? I would be happy, if someone share his experience on the topic.
| Without knowing what you mean by DTO or Entity, I'm going to make some assumptions, and then I can answer.
<ul>
<li>DTO — An object that represents data passed to the server from the client</li>
<li>Entity — A business logic class mapped to a persistent data store</li>
</ul>
Entities should perform valida... | Each layer should have own validations. For example, <strong>Business Logic Layer(BLL)</strong> and <strong>Data Access Layer(DAL)</strong> should have own validations.
Beyond this, assume that you call the <strong>BLL</strong> via network. Then, you can check some input validations or something else before send reque... | https://softwareengineering.stackexchange.com |
4,299,050 | [
"https://math.stackexchange.com/questions/4299050",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/778190/"
] | <blockquote>
Let <span class="math-container">$a$</span> and <span class="math-container">$b$</span> be self-adjoint elements in a <span class="math-container">$C^{\ast}$</span>-algebra <span class="math-container">$A$</span> with <span class="math-container">$-b \leq a \leq b.$</span> Then show that <span class="math-... | Let <span class="math-container">$e$</span>, <span class="math-container">$r$</span> and <span class="math-container">$\sigma$</span> denote the unit, the spectral radius, and the spectrum, respectively. For each selfadjoint elements <span class="math-container">$c \in A$</span> we have <span class="math-container">$r(... | Here are two more ways of proving the argument.
First, if you consider <span class="math-container">$A$</span> represented as <span class="math-container">$A\subset B(H)$</span>, then the inequalities <span class="math-container">$-b\leq a\leq b$</span> give you
<span class="math-container">$$
|\langle a\xi,\xi\rangle|... | https://math.stackexchange.com |
26,275 | [
"https://stats.stackexchange.com/questions/26275",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6103/"
] | I'm testing the cointegration of two time series of stock prices using adfTest from fUnitRoots, but first I need to check if the series are I(1).
How can I check if a time series is I(1)?
| It's true that we live in politically correct times; for the most part, in my honest opinion, that's probably a good thing, but it certainly does get out of hand sometimes. Nonetheless, I have great difficulty envisioning any real-world scenario in which you will get in trouble for having put males or females on top i... | In a stacked barplot, put the largest category (the one with the greater number of occurrences) on bottom. The criterion here is readability.
In horizontal bars (the <em>bars</em> are horizontal), put the largest category on top. Again, the criterion is readability.
In histograms (vertical bars), use alphabetical ord... | https://stats.stackexchange.com |
161,303 | [
"https://physics.stackexchange.com/questions/161303",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56924/"
] | I've read that in the de Broglie–Bohm interpretation of QM, the particle directed by its wavefunction has a trajectory (meaning both position and velocity) and that these are the only properties possessed by the particle. Other properties, like spin and mass, are attributed to the wavefunction
But if a Bohmian particl... | In pilot wave theory, there is a wave and a particle. In truth, both are in configuration space, the wave is a function like $\Psi(\vec{r}_1, \vec{r}_2,\vec{r}_3, \dots, \vec{r}_n,t)$ (a function of time and configuration space) and the particle too, is really just a dynamically changing position in configuration spac... | No, it's not the Bohmian particle 1 that interacts with another Bohmian particle, 2. It's the wave-packet 1 interacting with the wave-packet 2. In the book of D. Dürr "<em>Bohmian Mechanics</em>" one can find a section on the scattering theory.
But I believe that for your question suits more the section 15.1.2, "<em>... | https://physics.stackexchange.com |
148,959 | [
"https://softwareengineering.stackexchange.com/questions/148959",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/45762/"
] | In Java, there are multiple languages that compile to Java bytecode and can run on the JVM -- Clojure, Groovy, and Scala being the main ones I can remember off the top of my head.
However, Python also turns into bytecode (.pyc files) before being run by the Python interpreter. I might just be ignorant, but why aren't... | Simple - last time I checked, Python had no formal specification, including its bytecode. CPython is the spec, and bytecode portability is IIRC not required. Thus, it's a moving, undocumented target designed for a specific language.
| There are multiple JVM languages because there were talented people who wanted to write code that would work with existing Java code, <em>but they didn't want to write Java</em>.
Apparently there are no programmers who want to work with existing Python code, but hate Python enough to port another language to the Pyt... | https://softwareengineering.stackexchange.com |
21,925 | [
"https://electronics.stackexchange.com/questions/21925",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6459/"
] | I am looking for a ultra low voltage 2 ch stereo analog switch.
I have two headphone audio sources that I need to switch between.
It is very important that the chip can run of a 1.2v rechargeable cell (900 mAh) and use very low current.
I have been looking in digikey, intersil and maxim but all I can find are using a ... | Your options basically fall into two broad catagories: Some sort of semiconductor device, like an opamp or analog CMOS switch, or some sort of mechanical switch (a.k.a. relay).
The problem with using a semiconductor device is that you really want your power rail to be higher than the audio. For a headphone that woul... | A latching relay might be an interesting solution, though you might have to rewind the coil yourself.
| https://electronics.stackexchange.com |
134,581 | [
"https://physics.stackexchange.com/questions/134581",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/14494/"
] | I'm trying to overcome some misunderstanding that I have in Noether's theorem.
There is formula in David Gross's Lectures on QFT for Noether's theorem:
$$J^\mu_\alpha=\mathcal{L}X^\mu_\alpha+\Pi^\mu_i\left[\Psi_{i\alpha}-\partial_\nu\phi_i X^i_\alpha\right]$$
$J^\mu_\alpha$ - conserved vector current, $\Pi^\mu_i$-c... | I think this calculation is the answer for your question:
$$\sum_{\alpha,\mu}\frac 1 2 \omega_{\alpha \mu} \left(x^\mu \partial^\alpha-x^\alpha \partial^\mu \right)=\frac 1 2 \sum_{\alpha<\mu}\omega_{\alpha \mu} \left(x^\mu \partial^\alpha-x^\alpha \partial^\mu \right)+\frac 1 2 \sum_{\mu<\alpha}\omega_{\alpha ... | This is one of the few times when using the Einstein convention isn't helpful: recall that in Noether's theorem you need to sum over the <em>independent</em> parameters of your transformation, which is usually trivial but, for Lorentz transformations, you need to be careful because of the antisymmetry of $\omega_{\mu\n... | https://physics.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.