qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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662,485 | [
"https://physics.stackexchange.com/questions/662485",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231892/"
] | I think I might be asking a stupid question and I might be corrected quite quickly on this, but I will ask it anyway.
<hr />
<strong>Question</strong>
Since quantum fields are everywhere in space and can create and annihilate particles at a given location, can these same quantum fields be considered as absolute observe... | I think it's best to answer this question first in the context of classical field theory.
In classical field theory on curved spacetimes, we don't usually consider field equations and observables which single out a preferred reference frame. (You <em>can</em> do this, but it's not very useful for doing gravity or elec... | Quantum fields are Lorentz invariants. The easiest example is the electromagnetic field: different frames observe the same field for its effects (movement of a charge for example). But the components of the Faraday tensor (<span class="math-container">$E_i$</span> and <span class="math-container">$B_i$</span>) are not ... | https://physics.stackexchange.com |
101,237 | [
"https://dba.stackexchange.com/questions/101237",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/66246/"
] | How to configure the property of DBPROP_COMMANDTIMEOUT ?
Can this property be configured in Database ?
Thanks.
| Install the Oracle Instant client - both the 32 and 64 bit versions find orasql12.dll and register it with <code>regsvr32 orasql12.dll</code> and <code>c:\windows\syswow64\regsvr32.exe orasql12.dll</code> for the 32 bit version. and add the oracle bin directory the the path environment variable
Make sure that you can ... | Checking "Allow Inprocess" in the Properties of the Driver "OraOLEDB.Oracle" in SSMS allowed the driver to work correctly with our OpenRowSet Query against the Remote Oracle Server.
| https://dba.stackexchange.com |
54,735 | [
"https://physics.stackexchange.com/questions/54735",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21255/"
] | For simplicity I'm considering only the sphere case.
In the Gauss' Law formulation we have some field $E$ introduced by charges $Q$ inside some sphere, then we compute flux and integrate, and we get result $Q/e_0$. Right.
But this formulation doesn't take into account any possible outer charges, because $E$ used in th... | The electric field used in Gauss's law is <em>not</em> just the electric field from the interior charge distribution. It <em>may</em> contain contributions from exterior sources. Usually, we do assume that there are no exterior sources, which is what allows us to impose symmetry considerations.
Why are we able to do... | First of all we use Gauss's law because it is a law of nature!
Second: Gauss's law (together with $\nabla\times\vec{E}=0$, which is only strictly valid in electrostatics) is equivalent to Coulomb's law for the electric field of a distribution of charges. You can prove one from the other.
Third: You a right about exte... | https://physics.stackexchange.com |
3,265,400 | [
"https://math.stackexchange.com/questions/3265400",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/403888/"
] | Using only elementary group theory.
<blockquote>
Let G be a group with an element <span class="math-container">$a$</span> of order <span class="math-container">$k$</span>. Let <span class="math-container">$p$</span> a prime which divides <span class="math-container">$k$</span>. If there is <span class="math-contain... | Since <span class="math-container">$p$</span> divides <span class="math-container">$k$</span> so <span class="math-container">$k=pq$</span> where <span class="math-container">$q<k$</span>. Since <span class="math-container">$x^p=a$</span> and <span class="math-container">$a$</span> has order <span class="math-contai... | Since <span class="math-container">$x^p=a$</span> and <span class="math-container">$a$</span> has order <span class="math-container">$k$</span>, we have the <span class="math-container">$k$</span> elements <span class="math-container">$1,x^p,x^{2p},\dots,x^{(k-1)p}$</span> are all distinct, and forms a subgroup of the ... | https://math.stackexchange.com |
75,627 | [
"https://dba.stackexchange.com/questions/75627",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/46757/"
] | As per the title, I'm struggling to find out if it's safe to delete the <code>innodb</code> schema that's created on a fresh Amazon RDS instance.
<pre><code>mysql> SHOW DATABASES;
+--------------------+
| Database |
+--------------------+
| information_schema |
| innodb | -- This was automatic... | There is a reason you cannot touch the innodb database.
This is where Amazon stores the system tablespace file <code>ibdata1</code>
If you run
<pre><code>SHOW GLOBAL VARIABLES LIKE 'innodb_data_home_dir';
</code></pre>
you might see something like this
<pre><code>/rdsdbdata/db/innodb
</code></pre>
It will point ... | Hmm, regardless of whether it's safe to delete the <code>innodb</code> schema or not, RDS won't let you do it anyway (tested on a temporary test instance):
<pre><code>DROP DATABASE `innodb`;
Error dropping database (can't rmdir './innodb/', errno: 17)
</code></pre>
| https://dba.stackexchange.com |
185,366 | [
"https://security.stackexchange.com/questions/185366",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/177528/"
] | In the context of SSL/TLS certificates, what is the difference between key encipherment and data encipherment? What are some examples that highlights the difference?
| Key encipherment means that the key in the certificate is used to encrypt another cryptographic key (which is not part of the application data). This is used within TLS in the RSA key exchange, where the pre-master secret (from which the symmetric encryption key is derived) is generated by the client, then encrypted wi... | Key encipherment is Use when a certificate will be used with a protocol that encrypts keys. An example is S/MIME enveloping, where a fast (symmetric) key is encrypted with the public key from the certificate. SSL protocol also performs key encipherment.
Data Encipherment is used when when the public key is used for en... | https://security.stackexchange.com |
2,072,253 | [
"https://math.stackexchange.com/questions/2072253",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/401982/"
] | I tried solving the question in the title as follows:
$$\lim_{x\to \infty} \frac{4x^2}{x-2} - 4x \to 4x - 4x \to 0$$
However, apparently that first step ($\to 4x - 4x$) was wrong, and I should first have brought the second $4x$ into the numerator.
My question is not how I need to solve the question, as I know that n... | As $x \to \infty$, $\frac{4x^2}{x-2}$ and $4x$ are asymptotically equivalent. However, the notion of asymptotic equivalence is of <em>relative</em> equivalence (in the sense that their ratios tend to $1$). We cannot deduce anything about the differences. The differences may be fixed (e.g. $x^2 \sim x^2 + 1$), tend to $... | What yo did was wrong for at least three reasons:
(1) Why would $\;\lim_{x\to\infty}\frac{4x^2}{x-2}=4x\;?$
(2) You can't take the limit when $\;x\to\text{whatever}\;$ and <em>still</em> remain with $\;x\;$ in the final expression
(3) You can't pass to the limit in only part of the expression, which is what ou did h... | https://math.stackexchange.com |
116,876 | [
"https://electronics.stackexchange.com/questions/116876",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29617/"
] | I have bought this board for working on Cortex-M0 series microcontrollers. its MCU is STM32F030F4P6. this is the board:
<img src="https://i.stack.imgur.com/069Pt.jpg" alt="board">
<img src="https://i.stack.imgur.com/ghCcu.jpg" alt="pcb">
and its schematic:
<img src="https://i.stack.imgur.com/6fdYC.jpg" alt="schemat... | +1 to waltx and special thanks to him and @BrianDrummond . I found the problem. add to the answer of both guys, the big problem was 'delay()' function. it made a big delay for Blink. I replaced one 'Delay(0x29020c0)' after toggle function and now it's works. Thanks again, guys.
| In the function "void MX_GPIO_Init(void)" pin 1 is being initialized.
In the loop, pin 0 is being toggled.
| https://electronics.stackexchange.com |
406,604 | [
"https://mathoverflow.net/questions/406604",
"https://mathoverflow.net",
"https://mathoverflow.net/users/422133/"
] | <strong>Let <span class="math-container">$\Omega$</span> be domain in <span class="math-container">$\mathbb{C}^n$</span>. Suppose we have taken two distinct points from <span class="math-container">$\Omega$</span>. Does there exist a domain <span class="math-container">$U$</span> in <span class="math-container">$\mathb... | The simplest blowup morphism <span class="math-container">$\mathrm{Bl}_0(\mathbb{A}^2) \to \mathbb{A}^2$</span> (with center at a point) is not flat.
EDIT. Here is an example with affine morphism. Let
<span class="math-container">$$
X = \{ x_1y_1 + x_2y_2 + x_3y_3 = 0 \} \subset \mathbb{A}^4_{x_1,x_2,x_3,x_4} \times \m... | First of all, the version that we would like people to read (and hopefully check for more mistakes, if any remain) is the Arxiv version of our paper. We worked on that for 4 years and with great care. Unfortunately, we were asked to reduce the length of our paper significantly as a precondition for publication, or that... | https://mathoverflow.net |
23,910 | [
"https://cs.stackexchange.com/questions/23910",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16876/"
] | Say I want to compute a covnex hull of given points on the plane. I would like to write an algorithm, that only compares the points and doesn't do any arithmetic operations. Wikipedia states, that:
<blockquote>
The standard $\Omega(n \log n)$ lower bound for sorting is proven in the decision tree model of computing,... | Consider the set of points $(0,0),(1,1.2),(0,2),(0.5,0.65)$ versus the set of points $(0,0),(1,1.2),(0,2),(0.5,0.55)$. The last point belongs to the convex hull only in the second set. However, if you compare any two ordinates in the two situations, you will get the same answer.
| For a slightly more general way of looking at this, what you want to do is equivalent to saying you can reconstruct the convex hull from the orderings induced by projections onto the coordinate axes.
To see you can't do this, just observe that for three points $a$, $b$, and $c$, knowing that $a < c < b$ in bot... | https://cs.stackexchange.com |
250,777 | [
"https://softwareengineering.stackexchange.com/questions/250777",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/96427/"
] | Is it a fair assumption to say that an overloaded constructor for a class can be thought of as a 'duck' for duck typing? Let's say that ClassA has an overloaded constructor, it would stand to reason that the different constructors are there for a reason -- the object is being used in a manner that indicates all of its... | <h2>No, It Isn't Duck Typing</h2>
I would argue that this is <strong>not</strong> an acceptable form of duck typing in a static language.
In a language that supports duck typing, one would expect to be able to define a function that accepts an object <code>foo</code> of unspecified type that defines a function (or pr... | No it isn't.
Objects of a particular class all support exactly the same set of messages no matter what constructor they were created with. Overloading constructors merely means that it isn't necessary to initialize <em>explicitly</em> all the fields that make up an object's state. For instance, an object might have co... | https://softwareengineering.stackexchange.com |
612,653 | [
"https://physics.stackexchange.com/questions/612653",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/288148/"
] | I just started learning about Hooke's Law and calculating the slope of a force vs. extension graph of a spring for the spring constant. If I conduct an experiment and the extension length of my spring isn't accurately proportional to the force on the spring, how should I go about plotting the graph, and how do I find t... | You are right that the traveler need not age much when voyaging from one star to another many lightyears away. If the distance plotted from Earth is <span class="math-container">$d$</span> in the measurements appropriate to the rest from of Earth or Sun, then the proper time accumulated by the traveler is
<span class="... | <blockquote>
Does special relativity imply that I can reach a star 100 light years away faster than in 100 years?
</blockquote>
The time that you experience in your spaceship on your way to the star could be more than or less than (or equal to) 100 years depending on how fast your spaceship travels.
The time that an ea... | https://physics.stackexchange.com |
97,227 | [
"https://softwareengineering.stackexchange.com/questions/97227",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32847/"
] | I've got a legacy PHP web application wherein almost each and every function makes references to $_POST variables - retrieving their values, AND <strong>setting them (or setting new POST variables)</strong> as a means to communicate with the calling code or other functions.
eg:
<pre><code>function addevent()
{
...
$a... | <blockquote>
As an old-school programmer, albeit a bit out of touch now, I find
this structure grotesquely unsettling - where data is passed
arbitrarily all over the place. What do others think?
</blockquote>
I, too, find this structure grotesquely unsettling. Those functions should be atomic, independent of ext... | <blockquote>
As an old-school programmer, albeit a bit out of touch now, I find
this structure grotesquely unsettling - where data is passed
arbitrarily all over the place. What do others think? Is the above
approach acceptable now?
</blockquote>
No, the above approach is completely not acceptable now. If anyt... | https://softwareengineering.stackexchange.com |
66,103 | [
"https://mathoverflow.net/questions/66103",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15392/"
] | Is there a known example of a countable discrete group G whose full group C*-algebra C*(G) is not quasidiagonal?
Let us recall that a separable C*-algebra A is quasidiagonal if it admits a faithful
*-representation $\pi:A \to L(H)$ on a separable Hilbert space with the property
that there is an increasing sequence $(... | I don't know much about the subject, but isn't this an example? There is a discrete property (T) group $G$ without nontrivial finite dimensional representations [2, Remark in the last page]. Then, its max C*-algebra contains a non-QD algebra as its direct summand, namely $C^*(G)(1-z)$ for the Kazhdan projection $z$ ... | Over the last week, I was discussing this question with Narutaka Ozawa. I could come up with a proof that quasi-diagonal, torsion generated Kazhdan groups must have a finite quotient. Here, a group is called quasi-diagonal, if it admits a faithful quasi-diagonal unitary representation. In particular, some Tarski monste... | https://mathoverflow.net |
844,752 | [
"https://math.stackexchange.com/questions/844752",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/157279/"
] | I am having a hard time figuring out how to evaluate this integral from a book that I am reading.
Here's the background info but I doubt it's highly relevant to the problem at hand:
$X$ is a real valued, weakly stationary random field defined on $\mathbb{R}^2$ with mean 0, variance 1, and correlation function
$r(\tau... | It <em>usually</em> makes more sense to do the substitution $r^2 = x^2+y^2$, since this corresponds to polar coordinates. Why? Because it is easy to visualize and to get the inverse transformation,
\begin{aligned}
x & = r\cos\theta\\
y & = r\sin\theta,
\end{aligned}
in case you would ever need it (e.g. for inte... | You are just using polar coordinates: $x=r \cos \theta$, $y=r\sin \theta$, so that $x^2+y^2 \to 0$ becomes $r^2 \to 0$, i.e. $r \to 0$.
| https://math.stackexchange.com |
127,763 | [
"https://softwareengineering.stackexchange.com/questions/127763",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I started my programming career with BASIC, during 9th grade. I learned a bit of BASIC by writing simple programs to add, subtract and to print. Then I went to the university and took Computer Information and Systems Engineering. In the first year I was taught C, and I have good command over it.
Next I learned C++ in... | We're all just learning bits of programming languages. I would only consider the language <em>implementers</em> to be those who are a 10 out of 10 in the knowledge of a language.
Learning multiple languages, and paradigms, is the only way to develop a "taste" for what you like and don't like. If you only learned one... | If you're still in university, it shouldn't matter yet that you don't feel you've covered everything in any of the languages you know. Understanding the common fundamental theories <em>behind</em> these languages is much more important. Once you understand the basics, you can learn the details of other languages when y... | https://softwareengineering.stackexchange.com |
194,201 | [
"https://physics.stackexchange.com/questions/194201",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59052/"
] | Is it possible with radioactive decay as pure radiation of neutrinos and antineutrinos? From a theoretical point of view?
I'm not asking for processes since I'm convinced there are no known processes resulting in pure neutrino radiation, that is decay without any other radiation than of neutrinos and antineutrinos.
| All processes involving neutrinos are weak mediated because neutrinos have zero electromagnetic and color charge.
At tree level, all processes involving a $\nu + \bar\nu$ final state without other debris involve a time-like $Z^0$ (except neutrino NC scattering) which implies the annihilation of a particle/antiparticle... | I'm speculating here, basically looking at two considerations.
Considering you used the term "radioactive decay" I'm going to look at this from a gross nuclear viewpoint rather than a particle/subnuclear viewpoint.
If a nucleus is in it ground state, it would have no mode to lose energy without changing Z. So, in thi... | https://physics.stackexchange.com |
289,925 | [
"https://electronics.stackexchange.com/questions/289925",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/139307/"
] | In the UK, if that makes any difference, I was wiring a motor and then I wondered (and kinda needed to know), how does a plug socket know how much power to put out? because all the input ampages on all the plugs sad different things but can all be plugged into the same socket.
How does this madness work?!? XD
| The rating of a plug is the maximum current it can provide. The rating of equipment is the current it will actually demand. The plug provides a fixed voltage, and the equipment (the load) decides how much current to draw at that voltage.
If the load tries to draw more current than the plug can handle, then in theory... | As Olin mentioned the socket does not technically put out power, it supplies amps (current) at a fixed voltage. The load determines how much current, which translates to power, is needed and used.
If your load is too high for the fuse in the plug, or ultimately the breaker or fuse in the fuse-box, you will blow a fuse... | https://electronics.stackexchange.com |
119,328 | [
"https://physics.stackexchange.com/questions/119328",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/50476/"
] | This may have a quick answer, but it has been on my mind so here it goes: why, if according to special relativity, do photons obey the rules of causality, if they are inherently timeless. According to special relativity, wouldn't a particle travelling at light speed experience no time, and therefore, why would it be ex... | Consider a photon that is emitted and then absorbed. For any "timely" observer (that is, anyone that sees the time flowing) will see the emission of the photon to happen before the absorption, and everyone will agree on which one comes first. So, whatever happens when and where the photon was emitted, cannot affect the... | In order to help the answer to this question, I would recommend the distinction between two things: You are referring to <strong>photons, that is lightlike movements</strong>. If you "remove" this lightlike movement (and the photons) from your consideration, there will remain <strong>two events</strong>: one event of e... | https://physics.stackexchange.com |
179,348 | [
"https://math.stackexchange.com/questions/179348",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/33774/"
] | I know you could find the number of even numbers (since they are a multiple of two). For example the number of even numbers between $11$ and $30$ will be
$$n= \frac{28-12}{2} + 1 = 9 $$
I wanted to know is there a similar way to find the number of odd numbers b/w two extremes?
| You can use the exact formula. What is number of odd numbers between $11$ and $30$?
$$n = (29-13)/2 + 1 = 16/2 + 1 = 9$$
Let's list them out to make sure $: 13, 15, 17, 19, 21, 23, 25, 27, 29.$ There are $9$ of them, so that is correct.
By the way, your formula was calculated wrong. $$n = (28-12)/2 + 1 = 16/2 + 1 = 8... | Method 1:
If you can find the number of numbers, and you can find the number of even numbers, ....
Method 2:
The number of odd numbers between 11 and 30 is the same as the number of even numbers between 12 and 31.
| https://math.stackexchange.com |
551,710 | [
"https://physics.stackexchange.com/questions/551710",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/248774/"
] | If I apply Coulomb's Law, I get that the field is defined in all space for volumetric densities. For linear and surface charges, the field is undefined where the charges are (division by <span class="math-container">$0$</span>).
Why wouldn't <span class="math-container">$ \mathbf{E}=\vec{0} $</span> inside an infinite... | <blockquote>
For linear and surface charges, the field is undefined where the charges are (division by <span class="math-container">$0$</span>).
</blockquote>
This is so only for linear charge distribution. For surface charge distribution, electric field can be defined everywhere (unless the distribution on the surf... | There is no "inside" for a plane or line, they are as thick as a point, therefore zero width. Secondly, infinite distributions would demand infinite energy to put together, they serve as idealizations for other problems or situations but intuition is not to be followed (no way of imagining real infinite quantities). Th... | https://physics.stackexchange.com |
58,204 | [
"https://stats.stackexchange.com/questions/58204",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/21361/"
] | I am trying to classify a data set with 2 boolean values.
I have two classifiers that may/may not be independent. The first one is 65% accurate, and the second one is 60% accurate.
Can I combine the two somehow to get a better classifier? Or will the second one just weaken my prediction?
| Some kind of ensembling technique rather, which combines the two. The whole idea behind them are to combine weak classifiers into one powerful classifier.
Edit: Boosting is used in combination with an ensembler to increase prediction power/accuracy.
| As you only have two classifiers there only few options that come to my mind:
<ul>
<li>min/max value</li>
<li>Logical operators: AND, OR, XOR, NOR and the like.</li>
</ul>
However my suggestion is twofold:
<ul>
<li>First, I will focus not on the decision but on the score associated to that decision. If you use score... | https://stats.stackexchange.com |
48,523 | [
"https://stats.stackexchange.com/questions/48523",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20081/"
] | Is it fair to say that observational studies are the 'bread and butter' of epidemiological studies?
By epidemiological studies I mean studies looking for an association between an environmental factor and a disease.
| Yes.
Well, "Yes, but..."
Observational studies are the 'bread and butter' of epidemiology, as generally speaking if we can manage to assign you an exposure we're talking about clinical trials, and those generally aren't considered "Epidemiology", but this:
"By epidemiological studies I mean studies looking for an a... | Yes. Epidemiological studies look at the environmental factors which people happen to live with; they don't assign people to live with certain environmental factors, which would have serious ethical problems ("We're going to assign you to live in a home with high radon concentrations... sorry, but it's for science!").
... | https://stats.stackexchange.com |
177,353 | [
"https://security.stackexchange.com/questions/177353",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/60797/"
] | I've been trying to understand the risk of an unprotected BIOS being the victim of an UEFI attack using Meltdown and what the risks are compared to the bug being unpatched in the OS.
What is required in order to insert UEFI malware? Is this possible from within the OS, to load code up into UEFI or does it require a ph... | There is no relation between Meltdown and UEFI attacks.
Meltdown allows to read kernel memory by using a a cache side-channel used during speculative execution. It does not write anything into privileged memory, or processor microcode.
| Previous answer is wrong in-part. Yes there is no direct correlation between Meltdown and UEFI attacks (yet) being seen in practice or in theory. But based on the fact that meltdown allows you to read kernel protected memory, the possibility to read any data in memory by incorrectly training the branch predictions.
S... | https://security.stackexchange.com |
31,905 | [
"https://mathoverflow.net/questions/31905",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2678/"
] | Let the Chern-Simons lagrangian for a group $G$ be,
$$L= k \epsilon^{\mu \nu \rho} Tr[A_\mu \partial _ \nu A_\rho + \frac{2}{3} A_\mu A_\nu A_\rho]$$
Then it is claimed that on "infinitesimal" variation of the gauge field ("connection") the lagrangian changes by,
$$\delta L = k \epsilon^{\mu \nu \rho} Tr[\delta A_\mu... | The secret to understanding the Chern-Simons functional over a 3-manifold is to realise that it's a 4-dimensional functional in disguise.
If $X$ is a closed, oriented 4-manifold, and $P \to X$ a principal $SU(n)$-bundle, one has the Chern-Weil formula for the second Chern number,
$$ c_2(P)[X] = \frac{1}{8 \pi^2} \int_... | I'll address your first question, in some computational detail; although I cannot do better than the answers which have already been given in terms of what is conceptually going on.
Let $G$ be a 1-connected Lie group with Lie algebra $\mathfrak{g}$. We assume that the group admits a bi-invariant metric or, equivalent... | https://mathoverflow.net |
3,448,370 | [
"https://math.stackexchange.com/questions/3448370",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/560409/"
] | This problem is from the pre-final round for the 2018 year of the competition
IYMC.
<blockquote>
Find a function <span class="math-container">$θ(n)$</span> with following behaviour:
<span class="math-container">$$θ(n) = \begin{cases}
0 \text{ if } n \text{ is composed} \\
n \text{ if } n \text{ is prime}
\end{case... | <span class="math-container">$$\theta(n)=n(\pi(n)-\pi(n-1))$$</span>
| For a function using "known" functions
<span class="math-container">$$n(1-|\text{sgn}(\sigma_0(n)-2)|).$$</span>
<span class="math-container">$\text{sgn}$</span> is the sign function
<span class="math-container">$\sigma_0$</span> is the number of divisors function
| https://math.stackexchange.com |
292,165 | [
"https://physics.stackexchange.com/questions/292165",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/106703/"
] | Under consideration is a classical mechanical system.
At first I would like to ask for a simple example of non-monogenic systems, e.g. something where a single or a few mass points are considered (e.g. atoms).
Secondly, do non-monogenic systems exist whose potential is not time dependent?
Thirdly, can non-monogeni... | Monogenic systems are systems where the generalised potential, $U(q,\dot{q},t)$ can be expressed as a function of position, velocity and time (and nothing else). The components of generalised force are given by:
$$Q_j=-\frac{\partial U(q,\dot{q},t)}{\partial q_j}+\frac{d}{dt}(\frac{\partial U(q,\dot{q},t)}{\partial \do... | In the mean time I can answer my third question.
A classical system is conservative by definition if and only if $ \vec{F} = -\nabla \Phi.$
A classical system is monogenic by definition if and only if $\mathcal{F}_i= - \frac{\partial \mathcal{V}}{\partial q_i}+\frac{d}{dt}\left(\frac{\partial \mathcal{V}}{\partial \... | https://physics.stackexchange.com |
310,629 | [
"https://stats.stackexchange.com/questions/310629",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/182749/"
] | Of my dataset $X$ I want to calculate the likelihood using my GMM model (for BIC). Mathematically it seems to make sense that as the samples are independant $P(X) = P(X_1)P(X_2)..$, so I would get the likelihood by taking the product of the likelihoods per sample.<br>
But it doesn't seem intuitively correct that the mo... | <blockquote>
But it doesn't seem intuitively correct that the more samples I have the less likely my model.
</blockquote>
I think your intuition has it the wrong way around. You're not computing how likely <em>your model</em> is - you're computing how likely the data are, GIVEN your model. You do this by multiplying... | <blockquote>
it doesn't seem intuitively correct that the more samples I have the less likely my model
</blockquote>
Maximum likelihood is used to find parameters of the model, so it isn't really a problem.
<blockquote>
seems to make more sense (to me) to average the likelihoods per sample.
</blockquote>
You're ... | https://stats.stackexchange.com |
384,947 | [
"https://physics.stackexchange.com/questions/384947",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/149232/"
] | If a conductor of varying cross sectional area is connected across a battery, does the current $I$ or the current density $J$ remain constant throughout the conductor? Why?
Thanks.
| It's the current density $J$ that changes.
Current is defined as an amount of charge per seconds, $I=Q/T$, i.e. a number of electrons flowing through the wire every second. Once your conductor is connected to the battery, the battery emf forces a current $I=V/R$ through the conductor. This current only depends on $V$... | The current $I$ remains constant irrespective of the wire cross section. This follows from the conservation of charge. Thus, when the cross section area $A$ changes along the wire, the product of current density $J$ and area $A$ always stays the same $$I=J A$$
| https://physics.stackexchange.com |
52,893 | [
"https://softwareengineering.stackexchange.com/questions/52893",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18741/"
] | I'm writing a small research paper which involves software development methodologiess. I was looking into all the available methodology's and I was wondering, from all methodologies, are there any that have provided the foundations for the others?
For an example, looking at the following methodologies:<br>
Agile, Pro... | The names in your list are not all methodologies and they scale on different levels :
<ul>
<li>Iterative is a characteristic, a trait shared by several methods and techniques. Scrum is an iterative methodology, TDD is an iterative technique.</li>
<li>I see Agile as a methodology superset that remains at a conceptual/p... | There are Three:
<ol>
<li>none (aka cowboy coding)</li>
<li>waterfall</li>
<li>rapid application development (RAD or spiral)</li>
</ol>
the rest are variants and combinations of these
note that the artifacts from waterfall (inception, requirements, functional spec, design spec, testing spec, quality control spec, et... | https://softwareengineering.stackexchange.com |
1,763 | [
"https://engineering.stackexchange.com/questions/1763",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/613/"
] | I am constructing an autonomous, unmanned boat for voyages of several months. Traditional autopilots use a linear actuator to move the tiller but require several adjustments per minute. They will consume a lot of electricity and probably wear out mid-voyage. We are looking at wind-vane designs to steer the boat. Win... | I am going to suggest that you use a worm-drive linear actuator. This will allow you to have a linear movement that does your adjustment and then holds that adjustment when power is removed.
If you can't use a linear actuator, you might have to build something yourself. Regardless of how you do is, I'd still suggest... | One problem with the windvane pictured above is that it might require continous 360 degrees rotation around its mounting vertical axis, e.g. the case boat navigates in circles and/or wind direction rotates 360 degrees.
Otherwise the boat loses the advantage of having a wingsail being able to continously rotate in eith... | https://engineering.stackexchange.com |
229,925 | [
"https://softwareengineering.stackexchange.com/questions/229925",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51334/"
] | I'm writing a linear algebra library (long story short, it's a school assignment) that involves matrices, vectors, etc. In the process of creating this library, I'm going to be creating functions that perform mathematical operations on objects. For example, transpose matrix, invert matrix, normalize vector, etc.
I w... | This is just a matter of style and taste. I have seen different linear algebra libraries, either
<ul>
<li>written in an OOP style using member functions</li>
<li>written in a non-OOP style using only free functions</li>
<li>providing an API with both</li>
</ul>
and all of them were working. At least, your API should ... | <blockquote>
Avoid membership fees: Where possible, prefer making functions
nonmember nonfriends.
Nonmember nonfriend functions improve encapsulation by minimizing
dependencies: The body of the function cannot come to depend on the
nonpublic members of the class (see Item 11). They also break apart
monol... | https://softwareengineering.stackexchange.com |
425,398 | [
"https://softwareengineering.stackexchange.com/questions/425398",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/350205/"
] | We have a battery manager implementation which uses a fuel gauge driver and a charger driver. Currently both of these drivers are hard-references to the fuel gauge and charger driver we currently support.
Now for new projects, another fuel gauge and another charger have been selected. We would like to keep the logic of... | Both options 1 and 3 I have seen being used in C code bases.
Option 2 has the disadvantage that there might be a timing issue. For example, the Battery Manager could try to retrieve a Charger from the central repository before the corresponding driver has registered itself. Or the driver might be absent completely. Han... | Drivers like this are often implemented as shared libraries (<code>.so</code> or <code>.DLL</code>) with agreed-upon interfaces. They serve to "abstract away" how the device actually works. Then, all of these libraries are managed by a single layer of software – your so-called "Battery Manager" – ... | https://softwareengineering.stackexchange.com |
442,838 | [
"https://physics.stackexchange.com/questions/442838",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/213903/"
] | I'm reading a paper that claims that for thermal states both entropies are equal up to the Boltzmann-Faktor.
'for states in thermal equilibrium, i.e. states of the form ... it is known that the thermodynamic entropy equals the Von Neumann entropy. '
I've been trying to find out more about this but to no avail :/
Ca... | The von Neumann entropy reads <span class="math-container">$$ S(\rho)= -\mathrm{Tr}( \rho \log \rho),$$</span> where <span class="math-container">$\rho$</span> represents the state for which you want to compute the entropy. For thermal states we have that <span class="math-container">$$ \rho = \frac{e^{-\beta H}}{Z},$$... | For quantum states the von Neumann entropy quantifies the informational entropy. If a quantum system is weakly coupled to a bath at equilibrium we may associate a canonical ensemble and Gibbs entropy to it.
In this circumstance, the von Neumann entropy is equal to the Gibbs entropy giving an explicit connection between... | https://physics.stackexchange.com |
334,331 | [
"https://physics.stackexchange.com/questions/334331",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/156156/"
] | I am interested in getting the overall intensity (which is defined as $I\equiv \,<S>$) with 2 or more beams of coherent and monochromatic plane waves at the same frequency. I understand that Poynting vector is not linear so I will have to construct the new $\vec{E}$ and $\vec{B}$ fields separately and then constr... | Of course it does.
It helps a little bit to compare the ideal gas to a model that <em>does</em> take note of the size of the molecules and the forces the exert on one another. The van der Waals gas has explicit parameters for both behaviors. Compare the equations of state for these two models
\begin{align}
Pv &= k... | Mathematically one can represent an "ideal" electric dipole or magnetic dipole, which is equivalent. You can have a point size while still maintaining a moment (electrical, magnetic, inertial)
| https://physics.stackexchange.com |
48,807 | [
"https://stats.stackexchange.com/questions/48807",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1329/"
] | Nate Silver in his excellent "The Noise and the Signal" warned that we are much in awe of Big Data. But, that Big Data predictions in many fields have been disastrous (financial markets and economics just to name a few fields). With more data, you get more spurious correlations, more false positives, and erroneous an... | This isn't the whole answer, but an important consideration is which part of your data is big.
Consider the following example. I'm doing some analysis on physical measurements of human beings. For each volunteer I measure the distance between the eyes, then length of each digit, the length of the shins, etc. And I re... | Another thing to consider is how people work with big data (as opposed to 'small' data). Big data usually requires multiple pre-processing steps before it is fed into analysis. And sometimes it is not clear what to test for exactly in these data sets to begin with. Both facts combined allow for considerable wiggle room... | https://stats.stackexchange.com |
2,598,625 | [
"https://math.stackexchange.com/questions/2598625",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/5209/"
] | For a topological space $X$, the Hurewicz Theorem relates the homology groups of $X$ with its homotopy groups. However, for non-simply connected spaces the Hurewicz theorem doesn't say much. I'd like to know if there are other theorems relating the homology and homotopy groups of a topological space even if the relatio... | So, because of your calculation, the matrix for $f $ wrt the given basis is $\Biggr(\begin {matrix} 1&0&-1\\0&1&-1\\-1&-1&2\end {matrix}\Biggr ) $. ..
Now, $imf $ is the span of the columns, which is the span of the first two columns (the third is obviously a linear combination of the first... | We know that $\dim(E)=\dim(\operatorname{im}(f))+\dim(\ker(f))$ which is true for any endomorphism on a finite dimensional vectorspace.<br>
Now you already know what $\ker(f)$ is, if you look closely, since $f(e_1)$ and $f(e_2)$ are linearly independent. An easy calculation shows that $\operatorname{im}(f)\cap\ker(f)=\... | https://math.stackexchange.com |
83,399 | [
"https://chemistry.stackexchange.com/questions/83399",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/48420/"
] | Polar solvents love polar solutes to be dissolved in it and non polar with non polar. Often said as <em>like dissolves like</em>.
Okay, polar loving polar can be understood with help of the facts: same polar nature, same kind of interactions etc.
But how will you explain the application of this rule with organic or n... | The reason behind this is the <em>hydrophobic effect.</em> Everyone has seen it if they pour a spoonful of vegetable oil into a pot of water, e.g. to cook pasta. As long as nothing is disturbing the vegetable oil, it will collect itself together in one big bubble rather than form many small bubbles.
Polar solvents wil... | I would be quite dubious in ascribing much validity to answers which use the word "unpolar", since that word indicates either a lack of familiarity with chemical terminology or a lack of respect for it.<br>
The way I consider solvation (for two pure chemical compounds) is that in their pure state the interactions are b... | https://chemistry.stackexchange.com |
330,580 | [
"https://softwareengineering.stackexchange.com/questions/330580",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/83295/"
] | Whenever I learn about a high-level language I want to learn about, part of me says, "I should probably learn the lower-level language it's built upon to really master it". For example,
<pre><code>Ruby => C
Closure => Java
Elixir => Erlang
</code></pre>
My experience with Ruby and C makes me think that I... | This may seem like a cop-out, but honestly....do both, if you can.
Higher-level languages are very good for teaching high-level concepts; you can accomplish a lot, very quickly, and learn good practices and design patterns. Learning a high-level language can teach you to look at problems in a big-picture way, and brea... | <strong>Generally!?</strong>
It probably depends. The biggest motivator I see for preferring one end of the spectrum over the other, for self directed study, is <em>interest.</em>
Trudging through <code>c</code> and writing console apps will be of little interest to someone who ultimately wants to write web applicat... | https://softwareengineering.stackexchange.com |
438,564 | [
"https://softwareengineering.stackexchange.com/questions/438564",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/147568/"
] | I'm working with a basic REST API, through user interaction on the UI, the JSON object is built up, including Arrays and a POST is sent to an endpoint using this object as the request body. For example:
<pre><code>"data": {
"id": "424",
"types": [ "01", "0... | The size of a posted JSON array is unlikely to be the thing that causes issues by itself, because reading and parsing of json objects, regardless of size, in almost any language is essentially a solved problem with very very well tested implementations
You may run into issues, however, if the size of the array you rece... | Don't set limits without it being forced.
Check what happens with 10,000 items in the array. If your app crashes, fix the crash and try again. If it becomes slow - just because YOU think there should be only five items, your users might find a use for an array with hundreds of items. Disabling that for no good reason i... | https://softwareengineering.stackexchange.com |
201,997 | [
"https://physics.stackexchange.com/questions/201997",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7348/"
] | I'm doing some self studying of introductory physics, and was working a question from a textbook that has several parts. The first few parts asked me to show that the magnetic field of an infinite current carrying cylinder has the form $\vec{B} = f(r)\begin{bmatrix}0 & z & -y\end{bmatrix}$ if we choose the x ax... | What exactly does $\Delta_{r_e}$ mean ?
Your wave function isn't a field in space, it is a field on configuration space, i.e. it assigns complex numbers to a configuration. If your electron is at $(x_e,y_e,z_e)$ and your proton is at $(x_p,y_p,z_p)$ then the configuration is the point $(x_e,y_e,z_e,x_p,y_p,z_p)$ in ... | The index of the Laplacian tells you which of the coordinates it acts on, that is, if you write $r = (r_x,r_y,r_z)^T$ and $R = (R_x,R_y,R_z)^T$ as Cartesian coordinates, then
\begin{align} \Delta_r & := \frac{\partial^2}{\partial {r_x}^2} + \frac{\partial^2}{\partial {r_y}^2} + \frac{\partial^2}{\partial {r_z}^2} \... | https://physics.stackexchange.com |
593,421 | [
"https://physics.stackexchange.com/questions/593421",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249491/"
] | I was thinking of a problem that most of the lecture notes go over when introducing special relativity to the students.
Consider a spaceship with Alice inside it. Let's say the spaceship is traveling at a speed of <span class="math-container">$0.7c$</span>. Alice then shines a laser light and tries to calculate the tim... | We have 2 equations for Lorentz tranformation, considering both observers in the same position and time when the light is emmited.
<span class="math-container">$x_b = \gamma(x_a - vt_a)$</span><br />
<span class="math-container">$t_b = \gamma(t_a - (v/c^2)x_a)$</span>
For Alice: <span class="math-container">$x = ct$</s... | Do all your calculations in the frame of your choice and then transform them to the other frame.
In this case, the easy frame to work in is Alice's. Take frames based at the event <span class="math-container">$A$</span> where Alice releases the lightbeam. So <span class="math-container">$A$</span> is given by <span c... | https://physics.stackexchange.com |
430,559 | [
"https://electronics.stackexchange.com/questions/430559",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/190132/"
] | Does the CMSIS SysTick_Handler() have to be placed in the main file (i.e. same file where it is configured)?
If not, how would I go about placing it elsewhere? Is it just a matter of defining the function in another .cpp file, and including "LPC17xx.h"?
| You can put it anywhere, as long as it has the right linkage spec the linker will take care of it for you.
You don't need any header included, just <code>extern "C" void SysTick_Handler(){ ... }</code> in an implementation file.
| It does not. I have it in a separate .cpp file dedicated to SysTick code. It's not even declared in the .h file associated with that .cpp file. The compiler will search it out, wherever it is. This is true for all the interrupt handler function names.
| https://electronics.stackexchange.com |
568,542 | [
"https://physics.stackexchange.com/questions/568542",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/141502/"
] | I am currently studying the textbook <em>The Quantum Theory of Light</em>, third edition, by R. Loudon. In the introduction, the author says the following:
<blockquote>
In the customary photon description of quantum-optical interference experiments, it is never the photons themselves that interfere, one with another, b... | The confusion seem to be purely one of semantics. Different people associate slightly different concepts with the term "photon."
Take for instance the famous statement of Paul Dirac: "Each photon then interferes only with itself. Interference between different photons never occurs." Compare this wit... | You are confused, and I understand, because the text you are referring to, is a little bit misworded.
"In the customary photon description of quantum-optical interference experiments, it is never the photons themselves that interfere, one with another, but rather the probability amplitudes that describe their prop... | https://physics.stackexchange.com |
229,833 | [
"https://mathoverflow.net/questions/229833",
"https://mathoverflow.net",
"https://mathoverflow.net/users/43681/"
] | Let $\beta\mathbb N$ is the set of ultrafilters on $\mathbb N$ and $\mathscr F\in\beta\mathbb N$. Assume that $l_{\mathscr F}\in\big(\ell^\infty(\mathbb N)\big)^{\!*}$ is the functional which assigns to a bounded sequence $\{a_n\}_{n\in\mathbb N}\subset\mathbb C$ its limit, with respect to the ultrafilter $\mathscr F$.... | Identify $\mathbb{N}$ with $\mathbb{Q}\cap[0,1]$ via a bijection, and consider the subspace $C([0,1])\subset\ell^\infty(\mathbb{N})$ of sequences which extend to a continuous function on $[0,1]$. When we restrict each $l_{\mathscr{F}}$ to $C([0,1])$, we get evaluation at some point of $[0,1]$ (namely, the limit of $\m... | Eric Wofsey's answer is very nice and simple. Nevertheless this might be interesting. Very old results of Kakutani [Concrete Representation of Abstract (M)-Spaces, Ann. of Math. 42 (1941)] show that for every compact space $K$ the bidual of $C(K)$ is isomorphic to $C(Z)$ for some compact space $Z$ containing $K$. If $X... | https://mathoverflow.net |
13,961 | [
"https://dsp.stackexchange.com/questions/13961",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/4673/"
] | In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation techniques, such as maximum likelihood, will only be useful when your SNR is so low that you can't run a basic peak searc... | The FFT is really a bank of matched filters - each FFT bin corresponds to the output of a matched filter. The criterion for a matched filter is to maximize the SNR at the output of the filter - Note SNR at the output is measured differently than at the input.
While the FFT can be used for frequency estimation, it isn'... | I doubt that there is such a rule because your assumption- the negative of computational work more than offsets the benefits of lower error probabilities- assumes that computations are expensive and errors are not. The "costs" of computational work and errors depends entirely on the application.
| https://dsp.stackexchange.com |
277,426 | [
"https://mathoverflow.net/questions/277426",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3621/"
] | How does one show that for a given packing body $B$ (a finite set of integers) there is a periodic packing of the integers by disjoint translates of $B$ that achieves as its density the supremum of the set of densities achieved by all periodic packings?
I know (via a compactness argument) that the supremum is achieved... | Once you have it for some packing (and the standard mumbo-jumbo about achieving (as true density) the supremum of upper densities over all packings, periodic or not), the (upper) density of certain not too long intervals $A---A$ ($A$ here is some not too short packing pattern) is positive (because every sufficiently lo... | The difference between this and higher dimensions is that the evolving boundary is finite.
I think I could make this explanation tighter, but maybe this will be clear enough: I will describe a particular finite directed graph $G.$ A packing corresponds to a certain walk in $G$ and, if it makes the (or an) optimum cho... | https://mathoverflow.net |
21,575 | [
"https://stats.stackexchange.com/questions/21575",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/4544/"
] | I have multivariate time series data of the EURUSD financial vehicle. In this data each variable represents a different metric. There are ~200,000 rows and ~20 variables.
There are no NULL values for any variable at any row. All data is numerical.
Alongside this data, at each time point I have the univariate data "Pro... | The traditional approach to this sort of problem is:
<ul>
<li>if you have a theoretical reason for a relationship between your explanatory variables and your response (profit), then base a model on that, and test it rigorously...</li>
<li>if you don't, then look at the 20 plots with each of your variables on the horiz... | The best way to find most 'significant' parameters in such problems is Principal Component Analysis. Alternatively, finding the correlation matrix of your data will do the job too. Using principal component analysis, you can basically identify the parameters with most variance which are often of most interest. Once, yo... | https://stats.stackexchange.com |
466,291 | [
"https://electronics.stackexchange.com/questions/466291",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/202241/"
] | Do I need to derate a wire if it is stranded? Or will a #12 wire have the same ampacity whether or not it is stranded? Is this affected at all by AC versus DC?
| Gauge is defined by cross-sectional area, not outside dimension, so the stranded #12 wire has the same per-length resistance as the solid #12 wire. Ampacity is more complicated (it depends on type of insulation, what other wires are nearby, and other details), but whether it's solid or stranded again does not matter (o... | By the term 'derate', you must mean to reduce a manufacturer's specified ratings to compensate for some aspect of its application.
The wire manufacturer's specifications will give you the current carrying capability, be it stranded wire or solid core. You do not have to derate the values in that specification - the ma... | https://electronics.stackexchange.com |
1,130,994 | [
"https://math.stackexchange.com/questions/1130994",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/59174/"
] | Does a function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f'(x) > f(x) > 0$ exist?
Intuitively, I think it can't exist.
I've tried finding the answer using the definition of derivative:
<ol>
<li>I know that if $\lim_{x \rightarrow k} f(x)$ exists and is finite, then $\lim_{x \rightarrow k} f(x) = \lim_... | <strong>expanded from David's comment</strong>
$f' > f$ means $f'/f > 1$ so $(\log f)' > 1$. Why not take $\log f > x$, say $\log f = 2x$, or $f = e^{2x}$.
Thus $f' > f > 0$ since $2e^{2x} > e^{2x} > 0$.
<strong>added:</strong> Is there a sub-exponential solution?<br>
From $(\log f)'>1$... | There are multiple mistakes in your proof (i.e. dividing by $f(x)$ is not necessarily okay, since it is not necessarily positive). The most major is that you treat the variable in the limit as if it were not "bound". That is, if you have something like
$$\lim_{h\rightarrow 0^+}1>0$$
which is true, you can't necessar... | https://math.stackexchange.com |
2,816,407 | [
"https://math.stackexchange.com/questions/2816407",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/569172/"
] | Let $\mathbf{A}$ be a $k\times k$ invertible matrix, let $\mathbf{x}$ be a $k\times 1$ vector and let $\mathbf{1}$ be a $k\times 1$ vector of ones. For a generic $k\times 1$ vector $\mathbf{z}$, let the function $\exp\left(\cdot\right)$ be defined as follows:
$\exp\left(\mathbf{z}\right)=\exp\left(\left[\begin{array}... | OK, I'll give you a counterexample that your quest is impossible for a 2x2 matrix, for simplicity; that is, you assume there is a potential <em>φ</em> (pardon the physicsese...), s.t.<br>
$$\frac{d}{d\mathbf{x}} \phi =\exp\left(\mathbf{Ax}\right) \qquad \Longrightarrow \\
\frac{d}{d x _1} \phi =\exp\left(A_{11}x_1+A_{1... | Define two new variables and their differentials
$$\eqalign{
y &= Ax &\implies dy=A\,dx \cr
e &= \exp(y) &\implies de = {\rm Diag}(e)\,dy = E\,dy \cr
}$$
Now finding the differential and gradient of your function is straightforward
$$\eqalign{
\phi &= 1:A^{-1}e \cr
d\phi
&= 1:A^{-1}de \cr
&a... | https://math.stackexchange.com |
563,455 | [
"https://stats.stackexchange.com/questions/563455",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/348495/"
] | I have data with columns "y" and "n", which for this example can be "y" count of heads out of "n" coin flips. There are "i" rows ie "i" different coins:
<span class="math-container">$$
P(y_{i} \mid p_{i}, n_{i}) = \binom{n_{i}}{y_{i}}\: p_{i}^{y_{i}} \: (1-p_... | There is no essential difference between the two approaches. If we define your unknown parameters as <span class="math-container">$\theta$</span> (<span class="math-container">$\mu_1,\mu_2,\sigma^2_1,\sigma^2_2$</span>), then in your first approach you calculate the <em><strong>conditional</strong></em> probability:
<s... | <blockquote>
<span class="math-container">$PS \equiv Pr(X_1 > X_2) \tag{1}$</span>
</blockquote>
is a statement about two random variables. You describe approach 2 by saying
<blockquote>
[...] Conditional on the data (not the parameters), <span class="math-container">$X$</span>'s have a known distribution. [...]
</b... | https://stats.stackexchange.com |
16,065 | [
"https://cs.stackexchange.com/questions/16065",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/4341/"
] | When using A* (or any other best path finding algorithm), we say that the heuristic used should be <strong>admissible</strong>, that is, it should never overestimate the actual solution path's length (or moves).
How does an admissible heuristic ensure an optimal solution? I am preferably looking for an intuitive expla... | While Anton's answer is absolutely perfect let me try to provide an alternative answer: being admissible means that the heuristic does not overestimate the effort to reach the goal, i.e., $h(n) \leq h^*(n)$ for all $n$ in the state space (in the 8-puzzle, this means just for any permutation of the tiles and the goal yo... | If the heuristic function is not admissible, than we can have an estimation that is bigger than the actual path cost from some node to a goal node. If this higher path cost estimation is on the least cost path (that we are searching for), the algorithm will not explore it and it may find another (not least cost) path t... | https://cs.stackexchange.com |
222,001 | [
"https://softwareengineering.stackexchange.com/questions/222001",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/76790/"
] | I have an exercise in Python as follows:
<ul>
<li>a polynomial is given as a tuple of coefficients such that the powers are determined by the indexes, e.g.: (9,7,5) means 9 + 7*x + 5*x^2</li>
<li>write a function to compute its value for given x</li>
</ul>
Since I am into functional programming lately, I wrote
<pre>... | Horner's method is probably more computationally efficient as @delnan points out, but I would call this pretty readable in Python for the exponentiation solution:
<pre><code>def eval_poly(poly, x):
return sum( [a * x**i for i,a in enumerate(poly)] )
</code></pre>
| Many functional languages have mapi implementations that allow to you have an index weaved through a map. Combine that with a sum and you have the following in F#:
<pre><code>let compute coefficients x =
coefficients
|> Seq.mapi (fun i c -> c * Math.Pow(x, (float)i))
|> Seq.sum
</code></... | https://softwareengineering.stackexchange.com |
72,992 | [
"https://dsp.stackexchange.com/questions/72992",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/55501/"
] | I want to know how I could get from the first line to the second. I've been trying to figure it out for a while with no luck. Thank you in advance!
<span class="math-container">\begin{align}
H\left(e^{j0.5\pi}\right) &= \frac{1 - e^{-j0.5\pi}}{1 - 0.25e^{-j\pi}}\\
&=1.13e^{j\frac{\pi}{4}}
\end{align}</span>
| There's a tendency when doing "pure" DSP to call a filter "noncausal" because you started by designing it to be symmetric around t = 0, but then you're running it with a bunch of delay, or because you're running filtfilt on the data (where you scan the filter forward, and then backward), or some oth... | <blockquote>
Is there a way to make this filter non-causal?
</blockquote>
Remember that non-causal filters aren't possible to interpret in <em>any</em> case, because "non-causal" literally means there's output caused by input that comes <em>later</em>.
Just because you can buffer something if latency doesn't ... | https://dsp.stackexchange.com |
90,149 | [
"https://stats.stackexchange.com/questions/90149",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17046/"
] | I achieved a strong linear relationship between my $X$ and $Y$ variable after doubly transforming the response. The model was
$Y\sim X$
but I transformed it to
$\sqrt{\frac{Y}{X}}\sim \sqrt{X}$
improving $R^2$ from .19 to .76.
Clearly I did some decent surgery on this relationship. Can anyone discuss the pitfalls ... | You can't really compare $R^2$ before and after, because the underlying variability in $Y$ is different. So you literally can take <em>no comfort whatever</em> from the change in $R^2$. That tells you nothing of value in comparing the two models.
The two models are different in several ways, so they mean different thi... | There's a bigger problem than the ones identified by @Glen_b .
<pre><code>set.seed(123)
x <- rnorm(100, 20, 2)
y <- rnorm(100, 20, 2)
dv <- (y/x)^.5
iv <- x^.5
m1 <- lm(dv~iv)
summary(m1)
</code></pre>
And I get an $R^2$ of 0.49 and a P-value that is $5.5 \times 10^{-16}$.
You have $X$ on both sides ... | https://stats.stackexchange.com |
558,435 | [
"https://physics.stackexchange.com/questions/558435",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/248484/"
] | I want to know if capacitors connected in DC circuits having any combination of capacitors and resistors ever reach a steady state(no current flows through the capacitor) If that is the case then how can we prove it for the general case ?
| It kind of depends on what you mean by a DC circuit. If it involves e.g. a DC voltage source that is instantaneously connected to an LC combination of an inductor and a capacitor with zero-resistance wires, then no, a steady DC state is never reached -- but presumably that's not what you meant.
If, instead, you have a ... | There are examples of circuits consisting of DC (constant) sources, resistors and capacitors that do no have a DC steady state solution. A simple example (with ideal circuit elements) is a series RC circuit driven by a (non-zero) constant current source. The capacitor current is then constant.
| https://physics.stackexchange.com |
44,321 | [
"https://mechanics.stackexchange.com/questions/44321",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/11443/"
] | I realise that can't be answered without me saying how serious the corrosion is. The context is that I'm looking at a 2004 Ford Focus on eBay and the MOT history on the DVLA web site reports an advisory at the last MOT six months ago:
<blockquote>
O/S REAR INNER SILL IS RUSTY
</blockquote>
None of the previous MOTs... | The sills are a vital structural part of a unibody chassis, they provide strength and rigidity which is important in the event of an accident, this is why it's been flagged up in the MOT.
Without a photo, its hard to tell how bad it is, but even with a photo, what you can see is normally the tip of the iceberg. Upload... | The inner sills are a vital structural part of the vehicle much more so than the outer sills which are the lower parts of the body below your doors usually from where the front wing/door meet right back to your rear wheel arch.
If it's an advisory then it hasn't rotted or rusted through the sill which is an instant f... | https://mechanics.stackexchange.com |
50,196 | [
"https://mathoverflow.net/questions/50196",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8224/"
] | <strong>Background/motivation:</strong> A model for the <strong>classical</strong> propositional calculus is a boolean function <em>b(S)</em> which assigns 1 or 0 to each (modal-free) sentence <em>S</em> according to the usual rules. I'm looking at models for propositional <strong>modal</strong> logic, where a modal m... | You've shown that there are $2^c$ models $B$ but only $c$ corresponding functions $f$, so indeed many $B$'s must yield the same $f$. Since you say you don't see how it's possible for even two $B$'s to yield the same $f$, here's an example. Consider the countably many sentences $S$ such that neither $S$ nor its negati... | Of course, this is all assuming the original language (before augmentation by modal operators) was countable. It could be that we have a language with 2^c, or 2^2^c, or whatever, propositional atoms, which would of course drastically change the answer.
By the way, the most general possible semantics is to simply trea... | https://mathoverflow.net |
158,918 | [
"https://security.stackexchange.com/questions/158918",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/2075/"
] | I'm studying for the CISSP and am getting hung up on some terminology. Specifically, I'm confused on the difference between <strong>access aggregation</strong> and <strong>authorization creep</strong>.
In both cases, it seems to me that an individual users are gaining more access to more systems. Is access aggregati... | <strong>Aggregation</strong> is a condition of many systems and security designs and isn't an inherent problem. But it's something that the admins have to be aware of to prevent <strong>creep</strong>.
<strong>Creep</strong> happens unintentionally and can result in violations in authorised access as a result of <str... | Not sure if this is correct specifically for CISSP, but where I work the terms mean the following:
<strong>Access Aggregation</strong>
Users gaining more access across more systems, this might be intentional as a result of something like the implementation of single sign on capabilities or unintentional where they are... | https://security.stackexchange.com |
130,584 | [
"https://dba.stackexchange.com/questions/130584",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/68592/"
] | We have a Stored Procedure with many linked-server queries. When executing it displays a Warning:
<blockquote>
Warning: Null value is eliminated by an aggregate or other SET
operation.
</blockquote>
To suppress this, I tried :
<blockquote>
SET ANSI_WARNINGS OFF
</blockquote>
But that threw this error :
<blo... | Nevermind, found a workaround. The code was as such:
<pre><code>select name, count(*) from employees group by name
select * from RemoteServer..departments
</code></pre>
I modified it to :
<pre><code>SET ANSI_WARNINGS OFF
select name, count(*) from employees group by name
SET ANSI_WARNINGS ON
select * from Remote... | This should remove your warning.
<pre><code>select name, count(employeeId) from employees group by name
select * from RemoteServer..departments
</code></pre>
| https://dba.stackexchange.com |
122,900 | [
"https://chemistry.stackexchange.com/questions/122900",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/85137/"
] | What is the gas that if formed when a reactive metal is placed in a salt solution of a less reactive metal? Theoretically, it should just be a simple displacement.
I know that this question has been asked on a different page, but there Hydrogen formation was the accepted answer, which I don't think is the case (see obs... | When you dip magnesium ribbon into a copper sulfate solution, theoretically (and realistically) you do get a simple replacement reaction. Then reality sets in: you have a metallic anode (magnesium) with little cathodes (copper) all over it. At that point, the magnesium just overreacts. Well, it reacts faster.
The size ... | The bubbles are still hydrogen. Transition metal salts are generally much weaker acids than whatever you put your magnesium ribbon into for your hydrogen control. So you get less gas for the candle flame to react with when you use the transition metal salt, which I am sure you saw. That the decreased amount of gas s... | https://chemistry.stackexchange.com |
591,146 | [
"https://physics.stackexchange.com/questions/591146",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | In a pressure cooker, when T increases -P increases which means that the K.E of molecules increases. But According to equation PV/Tinc so T inc P inc and V dec. If they less volume I.e gas molecules does it means they occupy less space in the cooker.Does that mean that molecules don’t reach or go to some areas of cooke... | One way to describe the behavior of a gas is by an equation of state that relates the measurable properties of a gas. One of these is
<span class="math-container">$$\frac{PV}{T} = \textrm{constant}.$$</span>
Equivalently, this can also be written as
<span class="math-container">$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_... | <span class="math-container">$\frac{PV}{T}$</span> does not mean that the volume has to decrease in this situation. There are other situations where it means volume has to decrease, but not this one. The rule, as Mark H pointed out, is that <span class="math-container">$\frac{PV}{T}$</span> must not change. So if th... | https://physics.stackexchange.com |
923,765 | [
"https://math.stackexchange.com/questions/923765",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/174556/"
] | i want to prove it with mathematical induction :
first i am tried with n=0
then it is divisible by zero then i move to next step change all n with K then i get this product :
$$P(K)=K^3+2K = 3m$$
<em>Note: $3k$ because we multiply any no. with $3$ is divisible by $3$</em>
now , next step i am increase $+1$ in $k$ s... | For the induction step:
$(n+1)^3+2(n+1)=n^3+2n+3n+3n^2+3=n^3+2n+3(n+n^2+1)$
$n^3+2n$ is divisible by 3 (by assumption) and the last addend is obviusly divisible by 3
<strong>Remark:</strong> If you want to show a statement for all $n\geq k$ then you prove the statement in the first step for k, not for $0$. (In our ... | $$\left((n+1)^3+2(n+1)\right)-\left(n^3+2n\right) = 3(n^2+n+1)$$
is always a multiple of three, hence if $3\mid (n^3+2n)$, then $3\mid ((n+1)^3+2(n+1)).$
| https://math.stackexchange.com |
638,748 | [
"https://electronics.stackexchange.com/questions/638748",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/323236/"
] | So my question is simple, we know that its good practice to use flyback diodes in solenoid valves and relays, but do pumps and motors also need them as they also have coils?
| Flyback diodes are also needed for DC motors and pumps.
For AC motors we also need snubbers to limit the voltage transient but usually made of resistor in series with a capacitor.
| AC circuitry has the benefit of short half-cycles
of power, separated by zero crossings. So, an arc
on switch contacts is usually short and nondestructive.
Diode clamps are common for suppressing
arcing with DC excited coils.
Several other treatments are possible: old house switches
were long-span snap action (increa... | https://electronics.stackexchange.com |
620,122 | [
"https://electronics.stackexchange.com/questions/620122",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/193922/"
] | If a 12 volt battery is exposed to 12 volts for a long time would it overcharge the battery and harm it, or would the battery be unaffected, and not charge at all since there is no "additional" voltage over the battery's rated volts?
Edited to provide further context:
The battery chemistry I'm referencing is ... | Lead acid can be float charged indefinitely at the recommended voltage; typically 13.4V. Check your battery datasheet for exact numbers.
Note you will need a current-limited and slightly voltage-adjustable "12V" supply to do this. Current limiting is required to prevent overtemp or failure when connecting a... | Given that your battery is a nominal 12V lead acid battery, it will be fine.
Under ideal conditions the battery would maintain a constant charge of 12V and no current would flow into or out of the battery. (This assumes that current can flow into your 12V supply as well as outta of it.).
In reality, as temperatures cha... | https://electronics.stackexchange.com |
224,200 | [
"https://physics.stackexchange.com/questions/224200",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/89669/"
] | Is it true that if a conducting object is not grounded, the nearby charge will induce equal and opposite charges in the conducting object?
It is mentioned on Wikipedia (electrostatic induction) but it is also mentioned that charges will appear such that the total electric field inside the conductor becomes zero.
M... | 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 |
24,242 | [
"https://stats.stackexchange.com/questions/24242",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7534/"
] | Using R, I have fitted a linear model for a single response variable from a mix of continuous and discrete predictors. This is uber-basic, but I'm having trouble grasping how a coefficient for a discrete factor works.
<strong>Concept:</strong> Obviously, the coefficient of the continuous variable 'x' is applied in th... | <strong>This is not a problem specific to R.</strong> R uses a conventional display of coefficients.
When you read such regression output (in a paper, textbook, or from statistical software), you need to know which variables are "continuous" and which are "categorical":
<ul>
<li>The "continuous" ones are explicitly ... | You can check your "contrasts" are the default by <code>options()</code> and looking for:
<pre><code>$contrasts
unordered ordered
"contr.treatment" "contr.poly"
</code></pre>
If your unordered contrasts are set as <code>contr.treatment</code> (as they should be unless you've changed them), t... | https://stats.stackexchange.com |
83,647 | [
"https://stats.stackexchange.com/questions/83647",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/38117/"
] | <blockquote>
Given is that all the assumptions for a linear regression $y_i=x_i'\beta + \epsilon_i$ hold for $i=1,\dots, n$. For the (n+1)st observation we can write: $y_{n+1}=x'_{n+1} \beta + \nu + \epsilon_{n+1} $Then prove that the Least Squares Estimator (LSE) for $\beta$ for the full sample is $b \ (=(X'X)^{-1}X... | The regression specification here is actually
$$y_i =\beta_1x_i + \nu\cdot I_{\{i=n+1\}} +\epsilon_i, \;\;i=1,...,n+1$$
which leads us to the OLS estimator
$$\begin{pmatrix}
\hat \beta_1\\
\hat v
\end{pmatrix} =
\frac{1}{\sum\limits_{i=1}^{n+1} x_i^2 - x_{n+1}^2} \begin{pmatrix} 1 & -x_{n+1} \\ -x_{n+1} & ... | @Alecos, I think I kind of understand your hint now, so here is my attempt (too long for the comments).
Edit made after comments:
For simplicity assume that $\beta=\begin{pmatrix} \beta_1 \end{pmatrix}$. Let $\alpha=\begin{pmatrix} \beta_1\\ \nu \end{pmatrix}$. Also, let $Z=\begin{pmatrix} X & e_{n+1} \end{pmatri... | https://stats.stackexchange.com |
30,581 | [
"https://mathoverflow.net/questions/30581",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7328/"
] | Fix a prime number $p$. Suppose that I have a valuation $v_p: \mathbb{Q} \to \mathbb{Q}$ on the rationals $\mathbb{Q}$. That is, $v_p( p^n(\frac{a}{b})) = p^{-n}$ where each of $a,b$ is not divisible by $p$.
How can I extend $v_p$ to $v$ on the reals $\mathbb{R}$ such that $v|_\mathbb{Q} = v_p$? I am looking for an e... | As you point out, it follows on general grounds that there is an extension of $v_p$ to a valuation on ${\mathbb R}$ (in fact, there are uncountably many such extensions), but it is impossible to give an "explicit" description. Indeed, not only will any such extension by discontinuous with respect to the usual Euclidea... | You can extend $v_p$ to $\overline{\mathbb{Q}}_p$ in a unique way, and then the general theory of fields tells you that $\overline{\mathbb{Q}}_p$ is isomorphic to $\mathbb{C}$ which gives you the extension you want. The fields $\overline{\mathbb{Q}}_p$ and $\mathbb{C}$ are isomorphic because they are both algebraically... | https://mathoverflow.net |
163,946 | [
"https://softwareengineering.stackexchange.com/questions/163946",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/63589/"
] | I have no code here, as this is more of a design question (I assume this is still the best place to ask it).
I have a very simple server in java which stores a mapping between certain values and UUID which are to be used by many systems across multiple platforms. It accepts a connection from a client and creates a ... | A general way these references are broken is via interfaces. Instead of the parent class having a reference to the mapper, have it hold a reference to IWhateverParentNeedsFromMapper. Instead of the mapper having a reference to the parent, have it hold a reference to IWhateverMapperNeedsFromParent.
Often, thinking ab... | It isn't a bad design. Back pointers are a commonly used mechanism. There's already a dependency between the classes, so you're not creating a coupling where none existing. You could make it an abstract coupling by introducing interfaces, IF you choose to, but that violates YAGNI. Incidentally, note that the java impor... | https://softwareengineering.stackexchange.com |
65,966 | [
"https://electronics.stackexchange.com/questions/65966",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22727/"
] | So many people have asked questions related to mine already, but mine is not quite out there. So my question is I have a 3.7V Lithium Ion battery and I need to power Arduino Uno, which requires a minimum of 7V. I found some voltage doubling circuits, either they are using an external component(like mosfets, etc) or the... | As noted by others, there is no simple way to boost a DC voltage, without an IC.
First, a short note on how the Arduino works. The Uno can use a Vin barrel jack that goes to a NCP1117 5v regulator, that needs at least 7v In for proper regulation. It can also use the VIN header pin for the same regulator. Or it can be ... | There is something called a <i>charge pump</i> that can boost a voltage, but at 150 mA out that is not applicable here. The capacitors required would need to be quite large and would need to tolerate significant ripple current. While that is all theoretically possible, it is not a practical solution.
What you want i... | https://electronics.stackexchange.com |
411,341 | [
"https://electronics.stackexchange.com/questions/411341",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/206810/"
] | I've built the scheme below in circuit simulator and it didn't work because of "wire loop" mistake. Why it's wrong? Why it's wrong physically?
The simulator is falstad.com/circuit
<img src="https://i.stack.imgur.com/lOCJK.jpg" alt="enter image description here">
| <blockquote>
Two parallel wires with no resistance - why it's wrong?
</blockquote>
This is wrong because there are no wires with no resistance. When trying to resolve Kirchhoff equations for this loop (or whatever their algorithm is), the simulator would run into division by zero exception. To avoid program crash, i... | Falstad wants to be able to animate the circuit, showing how much current flows in each wire.
In this circuit, that isn't possible, so it is indicating this as an error.
| https://electronics.stackexchange.com |
173,584 | [
"https://electronics.stackexchange.com/questions/173584",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/77871/"
] | I think I blew a capacitor (heard a pop sound) inside a UPS when I plugged in a 29 watt LED light bulb. It still works, but now the UPS is really slow to switch back to AC power after a brownout.
Model: Tripp Lite SMART750USB
| The LED lamp probably has a switching power supply with a capacitor and bridge rectifier. This would account for a brief arc and pop when screwed in since the capacitor could draw many amperes if it makes contact near the peak of the AC line.
Since UPS units are designed to work with massive switching power supplies ... | An LED lamp, or any lamp for that matter, shouldn't have any effect on the UPS itself. The output is generally magnetically (transformer) isolated from the switching electronics of the UPS.
Are you absolutely certain you didn't short the output somehow when plugging your lamp in?
| https://electronics.stackexchange.com |
368,237 | [
"https://softwareengineering.stackexchange.com/questions/368237",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/300830/"
] | Following Hevery's advice to inject collaborators into constructor rather than new'ing things within constructor body, how gracefully do this when a collaborator needs a back reference to its owner, without using an evil 'init' method (another violation of Hevery's best practices for testable code).
E.g.
<pre><code>... | I think this is a case where you just need to <code>new</code> it up: create the instance in the constructor. If the two things can't exist without each other, and you don't need to utilize polymorphism, then there is no sense in passing the dependency in.
Otherwise you need to break the circular dependency between Mo... | You can inject a factory instead of a instance:
<pre><code>export class Model {
constructor(HistoryFactory factory) {
this._history = factory.createHistory(this);
...
}
...
}
</code></pre>
But I guess Misko would advise you to get rid of the circular dependency.
| https://softwareengineering.stackexchange.com |
89,593 | [
"https://security.stackexchange.com/questions/89593",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/31625/"
] | Title says it all really.
I realise I can Google this, but the top links don't cover all the new features I am aware of, so people will benefit from a canonical answer here.
| Windows 10 contains many new features and many existing features from previous versions of Windows that have been expanded on or improved such as Windows Defender, Windows Firewall and Bitlocker.
Windows 10 also includes the following new features:
<h3>Device Guard</h3>
When enabled, Device Guard checks to ensure that ... | I am aware of the following features:
<strong>Windows Hello</strong> - A new authentication system, which will replace passwords with a combination of biometrics and public key crypto. This will eliminate "pass the hash" attacks. Private keys will be stored on the TPM. Biometric authentication to the local device can ... | https://security.stackexchange.com |
189,732 | [
"https://dba.stackexchange.com/questions/189732",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/133732/"
] | Users can be either student or teachers, and are able to do different things depending on which role they are. Can I just use <code>role</code> with a 0 or 1? I usually see lookup tables which map a user to a role to permissions and whatnot, but would that be overkill for this scenario?
<pre><code>user
---
id 1
n... | With lock hints, a reader can take an U or X lock, so in that case yes. But otherwise no.
Even in SERIALIZABLE isolation level, readers don't take locks that would block other readers.
| SELECT queries take shared locks on the rows they retrieve. Shared locks may conflict exclusive locks from update/delete/insert statements. Two SELECT statements are not going to deadlock, but a SELECT can deadlock with an UPDATE.
| https://dba.stackexchange.com |
375,489 | [
"https://softwareengineering.stackexchange.com/questions/375489",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/310929/"
] | My team is going to be using Visual Studio Team Services for an upcoming project. The Agile tools let me organize User Stories and Tasks hierarchically like this:
Epic > Feature > User Story > Task/Bug
Let's say that I am designing a Student Org (club) management system for high school students and advisers. Student... | <blockquote>
I shouldn't write a "Generate UI and DB" Task for each User Story. That's too much redundancy. But I don't know how to write a "Generate UI and DB" task that must be completed before any of the User Stories can be started.
</blockquote>
<em>You don't</em>.
You write your user stories as high-level user... | Given that you are entering each sprint with a prioritised list of stories, and each story is broken down into separate technical tasks, all the developers should be working on tasks for the highest priority story before starting work on the second highest priority story. Because of this, by the time you start work on ... | https://softwareengineering.stackexchange.com |
2,165,874 | [
"https://math.stackexchange.com/questions/2165874",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I never got a chance to take complex analysis in college so I decided to study it on my own. In the beginning of the books they start by proving some properties of complex numbers however I noticed that most of the proofs involve (usually implicitly) the assumption that $i/i = 1$ It is not obvious to me that this shoul... | You should ask yourself the following: what does "division" mean, anyway? I would say this: once you know how multiplication works, the quotient $a/b$ <strong>means</strong> the number $x$ for which $bx = a$. For example, I would say that
$$
20/4 = 5
$$
because $x = 5$ is the unique solution to
$$
4x = 20
$$
Now: wha... | The notation $x/y$ is just another way of writing $xy^{-1}$. By definition, $yy^{-1}=y^{-1}y=1$. So $i/i=ii^{-1}=1$.
This all follows from the definition of inverses and the notation we use for them. There is nothing to prove, really.
| https://math.stackexchange.com |
637,462 | [
"https://physics.stackexchange.com/questions/637462",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/272285/"
] | In Sean M Carroll's <em>Introduction to General Relativity: Spacetime and Geometry</em>, after deriving the Tolman-Oppenheimer-Volkoff equation on page 233, Chapter 5, he says:
"<em>To get a closed system of equations, we need one more relation: the equation of state.</em>"
What does 'closed system of equatio... | "Closed system of equations" means the number of unknown variables is equal to the number of equations supplied with boundary and initial conditions sufficient to unambiguously find the searched variables.
In case of "the equation of state", it is often a solution (an expression rather than a differ... | In this context, a system of equations is said to be <em>closed</em> when it constrains fully the dynamics of the system. Heuristically, it means that there are as many equations as there are independent degrees of freedom.
For example, the Maxwell equations :
<span class="math-container">$$\begin{array}{ccc}
\nabla \... | https://physics.stackexchange.com |
21,073 | [
"https://security.stackexchange.com/questions/21073",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/4556/"
] | I'm interested in searching for botnets out in the wild. Besides Google dorking for a phrase or code used on the control panel backend for web based interfaces. What other ways are there to search for a botnet?
| Set up a honeypot, let it get infected with some malware and log where this malware connects to.
Pros:
<ul>
<li>You might discover some interesting botnets.</li>
<li>You'll uncover more than google will. I guess that their control pages are not indexed!</li>
</ul>
Cons:
<ul>
<li>You need to get a machine infected w... | You might wanna try to look into Dionaea (http://dionaea.carnivore.it/) as it will help emulate as vulnerable machine to copy the malware sample from already infected machine.
It will also capture machine IP attacking your dionaea honeypot and be surprise how much attack you'll get once your honeypot listen to public ... | https://security.stackexchange.com |
73,593 | [
"https://physics.stackexchange.com/questions/73593",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Only because
<ol>
<li>Rep is unitary, so saves positive-definite norm (for possibility density),</li>
<li>Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and</li>
<li>It is the representation of the global group of relativistic symmetry, </li>
</ol>
yes?
| First, note that in physics, we consider unitary representations $U$ of the Poincare group acting on the Hilbert space $\mathcal H$ of the theory because we are interested in a precise formulation of the concept of Poincare transformations acting on the quantum mechanical states of the theory as symmetries (since the l... | The irreducible representations of the Poincaré group are labeled by mass $m$ and the spin $s$ [this corresponds to Casimir invariants $m^2$ and $m^2s(s+1))$, so it corresponds naturally to $1$-particle relativist states.
The states corresponding to a representation $m, s$ are labelled $|p,\lambda \rangle$, with $p^... | https://physics.stackexchange.com |
517,349 | [
"https://physics.stackexchange.com/questions/517349",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/100527/"
] | I have done all of the work to this problem, but I am having trouble conceptualizing the answer(s) I am arriving at.
<blockquote>
A block is placed on an inclined plane at an angle of <span class="math-container">$30^\circ$</span> to the horizontal. A horizontal pushing force of 6N prevents the block sliding down th... | There are actually an infinite number of solutions. You have just been assuming there is no static friction, or that static friction is equal to its maximum magnitude<span class="math-container">$^*$</span>. But really all we have for the static friction magnitude is
<span class="math-container">$$0\leq F_\text{fric}\... | In the way you interpreted the problem, you will not only find 3 solutions, but an infinite number of them. This is because the friction can take any value between 0 and <span class="math-container">$\mu N$</span> in both directions.
The way I interpret the problem though, is that the force is the minimal force neces... | https://physics.stackexchange.com |
222,343 | [
"https://physics.stackexchange.com/questions/222343",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44487/"
] | Using the integral $$A=\frac{\mu_0}{4 \pi} \int \frac{I \vec{dl}}{r}$$ for calculating magnetic vector potential of an infinite wire we get $$A = \left(\frac{\mu_0 I}{4 \pi}\right) \ln(\sec \theta + \tan \theta)$$ which diverges when the limits are from $-\pi$ to $\pi$. We can get around this by solving $B=\nabla \time... | The reason that the formula fails is because you have computed the integral wrong. The coulomb gauge does work, it by definition MUST.
The equation for A is
<span class="math-container">$\nabla(\nabla \cdot \vec{A}) - \nabla^2 \vec{A} = -\mu_0 \vec{J}$</span>
In the coulomb gauge <span class="math-container">$\nabla \c... | Ok, so lets start with the basics, the answer we are expecting is given by:
$$\vec B= \frac{\mu_0I}{2\pi r} \hat e_\theta$$
Which is from Ampere's law.
From this we can kind of backwards engineer, to show that:
$$\vec A=-\frac{\mu_0I}{2\pi} \ln(r) \hat e_z$$
would work as the potential.
The reason I don't think your... | https://physics.stackexchange.com |
36,267 | [
"https://dba.stackexchange.com/questions/36267",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/20624/"
] | We have a fairly simple table structure, but with a LOT of fields per table (talking 40+). This data is initially produced in plain-text, user-readable tables, but then it is translated into higher-performance, easier to query tables before being installed for use in production.
What we do is, wherever possible and r... | As others have pointed out, this is a Really Bad Idea. Still, if you insist, the SQL is not hugely complicated:
<pre><code>CREATE TABLE RawData
(
PartNumber VARCHAR(30) NOT NULL PRIMARY KEY,
Manufacturer VARCHAR(30) NOT NULL,
Data1 VARCHAR(30),
Data2 VARCHAR(30),
Data3 VARCHAR(30)
)
CREATE TABLE Translatio... | Not many people like them, but I would suggest you use a cursor in a stored procedure to loop though the fields and normalise them into the target table (silly ETL process).
You could probably do better having had separate lookup tables for each type of field, but it depends on you scenario.
| https://dba.stackexchange.com |
1,257,313 | [
"https://math.stackexchange.com/questions/1257313",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/196850/"
] | Assume you have a die in your hand. Each time you throw it, you look to see what value you would get. If the value is greater than 4, roll the die again. Otherwise you stop.
Let X be the number of times you toss the die before coming to a halt. For instance, if you get $5 → 6 → 1 → stop$, the corresponding value of $... | About point a), I would say that $p_x(n)=\left( \frac 23 \right)\left( \frac 13 \right)^{n-1}$, since to stop at the $n$-th toss you need to get 5 or 6 in the first $n-1$ tosses, and 1,2,3,4 in the last.
Thus also the following calculation for $E(X)$ changes:
$$E(X)=\sum_{n=1}^{\infty}n\left( \frac 23 \right)\left( \f... | Say that a roll of 1-4 is "good".
The simple solution for (b) is: a single roll produces a 1–4 with probability $\frac23$. Therefore each roll produces $\frac 23$ good results on average.
Since expectations are additive, the expected number of good rolls in $n$ rolls is $\frac 23n $.
How many rolls do we need for th... | https://math.stackexchange.com |
1,534,871 | [
"https://math.stackexchange.com/questions/1534871",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/279189/"
] | $$\lim_{x \to \pi/2} \frac{\sqrt[4]{ \sin x} - \sqrt[3]{ \sin x}}{\cos^2x}$$
I have an idea of replacing $\sin x$ to $n$ when $n \to 1$ but wolfram says that answer is $\frac{\pi}{48} $ so my suggestion is it's had to use trigonometry simplifications which I do not know so well.
Assuming that L'Hopital is forbidden ... | Let $\sin x=n^{12}$ then your problem becomes:
$$\lim_{n\rightarrow1}\frac{n^3-n^4}{1-n^{24}}$$
$$=\lim_{n\rightarrow1}\frac{n^3(1-n)}{(1-n)\sum_{i=0}^{23}n^i}$$
$$=\lim_{n\rightarrow1}\frac{n^3}{\sum_{i=0}^{23}n^i}$$
$$=\frac{1}{24}$$
| Ian Miller's answer is the nicest and most efficient solution to the problem.
Just for your curiosity, I shall give you another one using Taylor series since you will use them a lot during your studies.
First, changing variable $x=\frac \pi 2+y$ $$\frac{\sqrt[4]{ \sin (x)} - \sqrt[3]{ \sin (x)}}{\cos^2(x)}=\frac{\sqr... | https://math.stackexchange.com |
42,598 | [
"https://engineering.stackexchange.com/questions/42598",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/32676/"
] | Recently I was thinking about home improvement, and one idea that is haunting me is that I could use some kind of refrigerator for gaming consoles and laptops.
The obvious benefit is that it maintains a constant low temperature. Also, the doors usually can be closed firmly and it won't let dust come inside, so there is... | We do. It's just an up-sized (i.e. more powerful) version of a refrigerator known as an air conditioning unit.
Essentially all server rooms and most spaces where PCs are located (speaking for the U.S., at least) are air conditioned. Server rooms almost universally have dedicated HVAC systems and they will indeed be des... | A refrigerator is basically a heat pump designed to achieve a temperature close to 0 °C. There are a couple of problems here:
<ol>
<li>Most refrigerators are way too weak to effectively tackle the heat output of modern PCs. It will not magically make your PC 6 °C - instead the PC will de-cool all your groceries.
</li>
... | https://engineering.stackexchange.com |
442,211 | [
"https://physics.stackexchange.com/questions/442211",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/181022/"
] | I've come across the term potential of mean force (PMF) in polymer physics, colloidal physics etc., but have not come across a complete definition.
As far as I understand, the PMF determines the equilibrium distribution of some degree of freedom of interest (call it x) in a (usually large) system with all other degree... | I'll start by assuming a canonical ensemble, but the ideas apply equally well to other ensembles. Suppose you can measure the probability distribution function of a degree of freedom, i.e. a coordinate <span class="math-container">$x$</span>. Call this <span class="math-container">$\mathcal{P}(x)$</span>. Formally it i... | LonelyProf gave a nice general description of the potential of mean force, but to get a basic feel for what it "is", I think it's helpful to look at the simple case of a system of <span class="math-container">$N$</span> point particles in thermal equilibrium with temperature <span class="math-container">$T$</span>. Tha... | https://physics.stackexchange.com |
621,806 | [
"https://physics.stackexchange.com/questions/621806",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/168151/"
] | I am trying to solve a problem in which I have to prove that for a particle with mass <span class="math-container">$m$</span> in a potential <span class="math-container">$U=A|x|^n$</span>, has a period of oscillation given by
<span class="math-container">$$\tau =\frac{2}{n} \sqrt\frac{2\pi m}{E} \left ( \frac{E}{A}\rig... | Assume the total energy of the particle is <span class="math-container">$E$</span>, a conservative quantity:
<span class="math-container">$$
E = \frac{1}{2}m v^2 + A|x|^n.
$$</span>
We can obtain the velocity as function of position:
<span class="math-container">$$
v = \pm \sqrt{\frac{2(E-A|x|^n)}{m}}
$$</span>
Fot... | I think that you can obtain analytical solution for the period <span class="math-container">$~T$</span>
follow the solution from @ytlu
with A and m equal 1 and omit the abs() function
the energy E is:
<span class="math-container">$$E=\frac{1}{2}\,v^2+x^n$$</span>
with:
<span class="math-container">$$E_0(v=0~,x=x_0)=E... | https://physics.stackexchange.com |
660,229 | [
"https://physics.stackexchange.com/questions/660229",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300272/"
] | If a body falls hitting an edge parallel to itself, is it the normal force that causes this rotation, if so how does one calculate this force as the body doesn't come to a complete stop it barely even causes acceleration in the linear sense?
| You are talking about a situation like so
<img src="https://i.stack.imgur.com/HYtVv.png" alt="fig1" />
The force that causes the rotation is the contact force with the edge, which exerts a torque about the center of mass.
Over a short period of time <span class="math-container">$\Delta t$</span> this force will modify ... | maybe it will help you to understand if you imagine that the body is stationary and the edge is moving upward and striking the body.
So imagine a baseball bat striking a stationary Frisbee near the edge of the Frisbee. The Frisbee will be given two components of motion.
<ol>
<li>Translation of the Frisbee will be caus... | https://physics.stackexchange.com |
307,461 | [
"https://mathoverflow.net/questions/307461",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41669/"
] | Let $A$ be a matrix and $x$ a fixed vector. How can we determine whether or not there exists a permutation matrix $P$ such that $APx=0$? Does this problem reduce to anything well-understood?
| Let's see if I can convince everyone that this problem is NP-complete.
First: it is in NP because a permutation $P$ can be guessed and checked in polynomial time.
I'll restate the problem: Given a vector $x$ and a vector space $V$ (the null-space of $A$), is there a permutation of $x$ that lies in $V$?
I'll take th... | This can be formulated and solved as a Mixed Integer Linear Programming (MILP) feasibility problem. Such NP-hard problems are routinely solved in practice, even to fairly large scale, despite being "intractable". For <span class="math-container">$P$</span> being <span class="math-container">$n$</span> by <span class="m... | https://mathoverflow.net |
84,824 | [
"https://security.stackexchange.com/questions/84824",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/71164/"
] | I would like to ask about the differences between Software Testing and Web Application Penetration Testing.
I am aware of usage different tools in both disciplines Software Testing (JIRA/Selenium) and Web App Pentesting (BurpSuite, SQLMap, etc.).
Also I would like to know if these two disciplines cross over and a Sof... | I'll put a slight different spin on the second part of your question concerning discipline cross-over, since I have experience doing these in my career.
A good <strong>Penetration Tester</strong> has a hacker mindset. They work to defeat what security protections have been put in-place, by whatever creative means ava... | I would say you should view relationships between these 3 types of activities like that: penetration testing is a subtype of security testing which is in turn is a subtype of software testing. Security testing deals with very specific types of defects: security defects; ones that could result in compromised system, rui... | https://security.stackexchange.com |
145,135 | [
"https://physics.stackexchange.com/questions/145135",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | As written in <strong>Principles of Physics</strong> by Halliday, Resnick and Walker:
<blockquote>
The electric field is a <em>vector field</em>; it consists of a distribution of vectors,one for each point in the region around a charged object. In principle, we can define the electric field at some point near the ch... | The presence of the test particle may influence the distribution of charge in the charged object. The electric field measured the above way then depends on the quantity of charge in the test particle and is different from what it is when the test particle is removed.
If the charge of the test particle is much lower th... | The definition of Electric Field is:
<blockquote>
The electric field at a point is defined as the limit of the ratio between the force on a test charge placed at that point to the test charge <strong>as the test charge approaches to zero</strong>.
</blockquote>
So in the definition, we have seen that the placed t... | https://physics.stackexchange.com |
2,283,981 | [
"https://math.stackexchange.com/questions/2283981",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/407608/"
] | When presented with an equation, say, $y=5x^3+7x^2+4x+9$, you can write on the second line, $\frac{dy}{dx}=15x^2+14x+4$. Similarly, $f(x)=5x^3+7x^2+4x+9$ and $f'(x)=15x^2+14x+4$. But is there a way to write "the derivative of $5x^3+7x^2+4x+9$ is $15x^2+14x+4$" in just one line?
What should l write, $\frac{dy}{d5x^3+7... | You would denote the derivative of $5x^3+7x^2+4x+9$ as
$$\frac{d}{dx}(5x^3+7x^2+4x+9)$$
That is the only notation I've ever seen unless the expression is expressed as a function.
| A common choice of notation is $D_{x}(5x^3 + 7x^2 + 4x + 9)$. The subscript indicates the variable with respect to which one is differentiating.
| https://math.stackexchange.com |
89,767 | [
"https://cs.stackexchange.com/questions/89767",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/63996/"
] | In the book, <em>Operating System Concepts, 9th Edition</em>, there is this paragraph that I don't quite wrap my head around.
<blockquote>
Swapping is constrained by other factors as well. If we want to swap a
process, we must be sure that it is completely idle. Of particular
concern is any pending I/O. A proces... | One scenario that can explain this more obviously is as follow: Suppose that a process wanted to read a disk block to a buffer in its address space (An I/O buffer is just a portion of the processe's memory. eg. <code>char[1024]</code>). The process will make a system call to ask the OS to issue an I/O to read the corre... | Your OS book seems to be a bit of an antique.
Here’s where you need to be careful: You can’t remove the _ address space_ for an application. But with a 64 bit OS, you have tons of address space at practically no cost. And you need active I/O buffers to stay in memory where you are, which is also no problem whatsoever... | https://cs.stackexchange.com |
1,517,514 | [
"https://math.stackexchange.com/questions/1517514",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/203149/"
] | I do know that $\left\|Lx-Ly\right\|=\left\|L(x-y)\right\|\le\left\|L\right\|\left\|x-y\right\|$ and then function is Lipschitz, but doesn't it require $||L|| $? I've been reading many sources and it wasn't unequivocal that $||L||$ must be finite. It would really help me if you could shed some light on it.
| Compute! (I assume that $\|\cdot\|$ is Euclidean norm.) Suppose $\|x\|\le 1$. Then $\|Lx\|^2=\sum_i(\sum_j L_{ij}x_j)^2$. By Cauchy-Schwarz, $(\sum_j L_{ij}x_j)^2\le \sum_j L_{ij}^2\cdot\sum_k x_k^2\le \sum_j L_{ij}^2.$ Therefore $\|L\|\le\sqrt{\sum_i \sum_j L_{ij}^2}<\infty$.
| Hint:
Let $\dim X<\infty$ and let $\|.\|$ be the given norm on $X.$ Let $T:X\rightarrow Y$ be a linear operator. Define, for $x\in X,$
$$\|x\|_1=\|x\|+\|T(x)\|. $$
Then $\|.\|_1$ defines another norm on $X$ which is equivalent to the given norm $\|.\|.$ Then, $\exists\,c>0$ such that $\|T(x)\|\leq \|x\|+\|T(x)... | https://math.stackexchange.com |
152,011 | [
"https://electronics.stackexchange.com/questions/152011",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/50637/"
] | Upon using an 'RF to DC converter', DC power management is needed. There is a dilemma in the approach as there are a number available.
From the storage capacitor, there is the 'Switched-mode power supply' or more specifically a 'boost converter' that would output the configured power.
Alternatively, there is a 'DC-DC... | A charge pump uses capacitors to do the boosting of the input from the lower to the higher voltage. They usually provide an unregulated output voltage which is the double of the input voltage. This means, that for most applications you need a voltage regulator behind the charge pump to get a well regulated voltage.
A ... | The difference is the part that stores energy during conversion. A boost converter uses an inductor, while a charge pump uses a capacitor.
A charge pump is more common for very low power requirements in the ballpark of mA, and voltage doubling/tripling. Within this limitations, it is often preferred over boost convert... | https://electronics.stackexchange.com |
246,961 | [
"https://mathoverflow.net/questions/246961",
"https://mathoverflow.net",
"https://mathoverflow.net/users/46931/"
] | The grassmannian space $G(n,m)$ may be identified with the quotient space $O(n)/(O(m)\times O(n-m)$. As such, it is endowed with a natural invariant probability measure which I call "Haar measure on $G(n,m)$". Let $\gamma_{n,m}$ be this measure. Let us endow $G(n,m)$ with the usual metric $d(V,W)=\|P_V-P_W\|$, where $P... | Yes, this is true. The answer by Ben Webster gives the idea, but for completion let me give you a list of easy facts that combined together answer the question.
<ol>
<li>The inequalities you seek are correct for any Riemannian manifold with bounds on the curvature (upper/lower bounds for corresponding sides of the ine... | The Haar measure is the volume induced by the unique (up to scalar) $O(n)$ invariant Riemannian metric on $G(n,m)$, and any volume induced by a Riemannian metric has this property (since the metric looks flatter and flatter as you zoom in).
<strong>EDIT</strong>: Uri's comment below points out that a Riemannian metric... | https://mathoverflow.net |
126,101 | [
"https://physics.stackexchange.com/questions/126101",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46758/"
] | So I'm reading a text on electricity and it talks about using the integral to compute the total charge of a collection of points, which I mostly understand. But then we get to finding the electric field due to a charged collection of points and I find things that don't make sense to me. For instance, for an infinite ... | <blockquote>
for an infinite sheet of constant charge, the text says that the electric field is constant on any one side of the sheet. But that seems intuitively wrong to me, since I would think the field should be stronger the closer a point is to the sheet.
</blockquote>
There's a geometric scaling argument at han... | It's definitely strains one's intuition. But think about this: if you are in the vicinity of an infinite sheet of charge, how can you determine whether you are close to it or you are far away? I can tell if I'm close to or far from a sphere by comparing my distance to the sphere with the radius. If I'm close the s... | https://physics.stackexchange.com |
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