qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
100,326 | [
"https://math.stackexchange.com/questions/100326",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/15962/"
] | I have to prove some Propositional Logic assertions.
Given this one: $\alpha \models \beta \Leftrightarrow (\alpha \Rightarrow \beta)$ is valid
Where $\models$ is entailment
<strong>The answer is:</strong> $\alpha \Rightarrow \beta$ <strong>holds</strong> in those models where $\beta$ <strong>holds</strong> or wher... | You can think of the phrase "[insert something here] holds" as "[that same something] is [insert property here]". More concretely, "holds" in this context is a sort of expression that refers to some thing "holding true" or always having the property of being true.
So, when we say $\alpha \Rightarrow \beta$ holds, we m... | <blockquote>
Definition :
<span class="math-container">$\Gamma$</span> - set of one or more sentences
<span class="math-container">$S_1$</span> - conjunction of the elements of <span class="math-container">$\Gamma$</span>
<span class="math-container">$S_2$</span> - sentence
then : <span class="math-container">$\Gamma ... | https://math.stackexchange.com |
4,221,414 | [
"https://math.stackexchange.com/questions/4221414",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/156754/"
] | I'm reading a book in which Conway's game of life is mentioned: the author states that it can be proved that the growth rate cannot be exponential but it's at most quadratic.
Can someone suggest me some reference for a proof of this statement?
Thanks!
| If you have a finite configuration of living cells, it fits inside an <span class="math-container">$N \times N$</span> bounding box, for some large <span class="math-container">$N$</span>. Over the next <span class="math-container">$t$</span> generations, no matter what your finite configuration is doing, it cannot aff... | Consider two infinite Game of Life grids that are identical except for some bounded region (for instance one can be completely dead and one can have finitely many live cells). Then the region where they differ in the next generation can at most extend a single cell beyond the region where they currently differ. So a di... | https://math.stackexchange.com |
127,467 | [
"https://mathoverflow.net/questions/127467",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10980/"
] | I am looking for a theorem that guarantees the polynomial growth of a function $f$ defined by a Fourier integral, that is, when
$$f(x)=\int_{-\infty}^{\infty}F(y)e^{ixy}dy.$$
I am only interested in one-sided growth, say $x\rightarrow +\infty$. Further, in the case I have in mind, $f$ is almost everywhere continuous, a... | Since it came up in comments, I will give an answer about the group I believe was intended to be asked about. A monomial matrix is a matrix which has one non-zero entry in each row and one non-zero entry in each column. The monomial $n \times n$ matrices who non-zero entries are all $\pm 1$ form a group, which may be t... | See:
Leonov, Yu.G.; Yasyns'kyj, V.V.
On representation of multiple wreath products of groups ${\mathbb Z}_2$. Visn., Ser. Fiz.-Mat. Nauky, Kyiv. Univ. Im. Tarasa Shevchenka, No. 2, 14-17 (2007).
Summary from Zentralblatt: Representations of multiple wreath products of groups ${\mathbb Z}_2$ by unitriangular matrices ... | https://mathoverflow.net |
144,608 | [
"https://security.stackexchange.com/questions/144608",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/96843/"
] | If so, what are these OSes? Are they specially crafted? How difficult is it to apply this kind of program verification to the everyday OSes we use?
If not, why haven't people invented such OSes?
Package signature verification is quite common with today's package managers. What I'm asking about is signature verificati... | iOS and Android both validates the signature of every single piece of code before loading them into memory.
Windows UWP apps are also all checked for signature before being loaded as well.
<blockquote>
Package signature verification is quite common with today's package managers. What I'm asking about is signature v... | Why do not all OS verify signature of programs? Simply because in the early times, most programs were written and compiled locally, and still nowadays, some business applications are specifically built locally. A lot of high quality programs are distributed as source and <em>can</em> be compiled locally. It often make ... | https://security.stackexchange.com |
271,317 | [
"https://softwareengineering.stackexchange.com/questions/271317",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25276/"
] | I just began reading O'Reilly's <em>Learning Perl, 6th Edition</em> and was surprised when I came across this excerpt.
<pre><code>#!/usr/bin/perl
print "Hello, world!\n";
</code></pre>
<blockquote>
Let’s imagine that you’ve typed that into your text editor. (Don’t
worry yet about what the parts mean and how they ... | The advice in the book is perfectly valid -- at least for UNIX-like systems. The execution of the script is controlled by the <code>#!</code> line, not by the extension part of the file name. Using a special extension for Perl scripts exposes information that should not be important to anyone running the script.
Windo... | Doesn't matter
<pre><code>#!/usr/bin/perl
</code></pre>
tells the system what program to use to run the code.
if you changed that to
<pre><code>#!/usr/bin/bash
</code></pre>
or
<pre><code>#!/usr/bin/python
</code></pre>
you would use a different interpreter.
Having the extension is totally optional, and the ... | https://softwareengineering.stackexchange.com |
111,373 | [
"https://softwareengineering.stackexchange.com/questions/111373",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15455/"
] | When deciding upon how to design a software project with my colleagues, most suggestions tend to be for using specific frameworks "because it's popular in the job market" or "that's the framework that gets recruiters on the phone," and never what I'm looking for which is, "because it's a good fit for the project as it ... | I don't think frameworks are a cause of over-engineering. More often than not, frameworks remove boilerplate code and simplify the codebase that you are left to maintain.
I also agree with Thorbjorn's comment that it's a bad idea to expect an API for everything. Much better to have the runtime environment focus on the... | <blockquote>
Are frameworks the catalyst of many of the over engineered projects out there
</blockquote>
No.
<blockquote>
or is it something much more simple?
</blockquote>
Yes.
<blockquote>
If you'd encountered these issues in a software project, how have you dealt with it?
</blockquote>
Ignore it.
<blockq... | https://softwareengineering.stackexchange.com |
2,786,462 | [
"https://math.stackexchange.com/questions/2786462",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/488416/"
] | I stumbled upon this problem and I'm having hard time understanding the solution , mainly the part about the supremum of the function.
Study the uniform convergence of the following sequence of functions on the interval [$0,1$].
$$f_n(x)=
\begin{cases}
n^2x, & \text{$0\le x\le \frac{1}{n}$}\\
n^2(\frac{2}{n}-x), ... | <ul>
<li>For the first question the goal is to study point wise convergence. So $x$ is fixed and then $n$ goes to $+\infty$.</li>
</ul>
You have $\frac{1}{n}<x<\frac{2}{n}$ for only a finite number of $n$ so it does not matter when $n \to \infty$.
<ul>
<li>As uniform convergence implies point wise convergence, ... | For every fixed $x$, then, unless $x=0$, $x>\frac2n$ if $n$ is large enough. But then $f_n(x)=0$, and this proves that $\lim_{n\to\infty}f_n(x)=0$.
On the other hand, $\sup f_n\geqslant f_n\left(\frac1n\right)=n$. Therefore, your sequence is cannot converge uniformly to the null function (or to any bounded function... | https://math.stackexchange.com |
8,888 | [
"https://mechanics.stackexchange.com/questions/8888",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4123/"
] | I have a 2006 Nissan Xterra with about 106,000 miles on it. For some reason, the car doesn't always start. I will try to start the car, and I can hear it attempting to start but it never does. Additionally, it almost always starts on the second attempt, if I wait about 20 seconds with the key out of the ignition.
I ha... | Since you already replaced the battery, one of the next reasonable plans of attack would be to see how dirty the air filter is or see if any of the spark plugs have been fouled. If you find the spark plugs or air filter are old, see if replacing them helps your issue.
After those steps, I would also investigate the fu... | See what the spark plugs look like. Are they black and covered in soot/ Has oil leaked past the valve covers and soaked the plugs and wires/ are they wet and smell like gas? Spark plugs cans tell you a whole lot about your air/fuel mix and ignition.
Id make sure to check fuel pressure too. make sure pressure doesn't dr... | https://mechanics.stackexchange.com |
329,296 | [
"https://electronics.stackexchange.com/questions/329296",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/134956/"
] | For an electronic device the the MTBF requirement is 4500 hours per year for 10 years, what does this MTBF mean and how to convert it into hours?
| MTBF means mean time between failures, so on average every 4500 hours there is a failure. This is for the first 10 years. Since there are about 365.25 * 24 = 8766 hours per year, this means an average of 8766/4500 = 1.948 failures per year.
| The statement is rather ambiguous. I <i>think</i> it says what the MTBF is supposed to be after 10 years if you operate the device for 4500 hours per year. If so, that's a long-about way of saying the MTBF is supposed to be 45,000 hours. Perhaps this is supposed to give some indication of both elapsed time and runni... | https://electronics.stackexchange.com |
13,909 | [
"https://mathoverflow.net/questions/13909",
"https://mathoverflow.net",
"https://mathoverflow.net/users/828/"
] | I'm a bit confused by the double role which sheaves play in the theory of stacks.
On the one hand, sheaves on a site are the obvious generalization of a sheaf on a topological space. On the other hand a sheaf on a site is (or better its associated category fibered in sets is) a very particular stack itself, so a gener... | Let me see if I understand your example correctly: you are fixing $X$ and $Y$, families
of curves over $S$, and now you are considering the functor which maps an $S$-scheme $T$
to the set of $T$-isomorphisms $f^*X \to f^*Y$ (where $f$ is the map from $T$ to $S$).
If I have things straight, then this functor shouldn't ... | I'm not a geometer, but here's one way to think of it. Let M be a stack (in groupoids, say) and X an object, and consider just a single point p:X→M. Then $Hom_M(p,p)$ is a sheaf, which is the "isotropy group" of the stack M at the point p, i.e. the space of automorphisms of p in M. If you think of your stacks as lik... | https://mathoverflow.net |
237,470 | [
"https://dba.stackexchange.com/questions/237470",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/179876/"
] | In my scenario, I have two servers in each of them two SQL Server instances:
<ul>
<li>Server 1: Instance 1 and Instance 2</li>
<li>Server 2: Instance 1 and Instance 2</li>
</ul>
I created availability groups between the instances like this:
<ul>
<li>Instance 1 from Server 1 with Instance 1 from Server 2: Availabili... | The data in a CSV file is encoded one way; the table in MySQL is encoded another way. The difference could be 2x <em>either way</em>. That is, the 25GB csv file <em>might</em>, for example, expand to 50GB, then have trouble adding on the indexes.
When MySQL runs out of disk space, it waits for you to free some space... | You already have an improvement from more than 40 hours to 4 hours, and still complaining ? …
This increase of speed seems to be related to your changes in the configuration of MySQL, but it's unclear what you changed. Also is this configuration of MySQL the same as the configuration your coworker has?
If both confi... | https://dba.stackexchange.com |
60,112 | [
"https://stats.stackexchange.com/questions/60112",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/26160/"
] | One of the academic's at the university where I am studying has conducted research on organisational sustainability. He approached me to turn his research into software that can be used for consulting purposes.
The general idea is that the members of an organisation sign up and take the survey online. The survery has ... | With a multinomial logit model you impose the constraint that all the predicted probabilities add up to 1. When you use separate binary logit model you can no longer impose that constraint, they are estimated in seperate models after all. So that would be the main difference between these two models.
As you can see in... | You can try a "one vs. all" approach, where you train a as many binary classifiers as classes you have. For each classifier, the positive samples are the ones belonging to that class, and negative the rest, so that each logistic classifier gives you the conditional probability that a concrete sample belongs to that cla... | https://stats.stackexchange.com |
226,744 | [
"https://security.stackexchange.com/questions/226744",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/228295/"
] | I access internet at my workplace with an iPad that has workplace profile installed on it. This allows me to automatically connect to the company wifi, along with their own DNS settings. If I change these settings to a static address, would I be able to have a bit more privacy when I access the web, or will all my acti... | I think you are misunderstanding where and why CORS is used. It is not intended to prevent a script from calling out to an untrusted server (with an <code>Access-Control-Allow-Origin: *</code> header, for example), since that is often a valid use case. The default, restrictive policy doesn't even restrict whether data ... | Your understanding of CORS is lacking an important aspect: why it even exists. CORS doesn't make SOP obsolete at all. What CORS does is allow a site owner to, selectively, reduce the protections of SOP for their own site. You can't lower SOP for a third-party site via CORS (unless you can inject response headers), any ... | https://security.stackexchange.com |
549 | [
"https://mechanics.stackexchange.com/questions/549",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/305/"
] | I find myself having to apply the break pedal everytime I go down an inclination. It's not too steep but the car seems to gain speed faster and faster.
In the other cars I have driven, this was not the case. cars would maintain their speed without much change even without holding the break pedal.
| This very much depends on the incline.
If it is a slight incline, I would expect that the vehicle would still accelerate, but probably not if you are going fast (Over 30 mph, say). If it's more than a 5 degree incline, then you could probably go highway speeds without touching the gas.
If you find yourself riding th... | At risk of sounding facetious, yes it is normal. It's due to gravity. The steeper the slope the greater the acceleration.
Exceptions include: some off road vehicles which use intelligent engine braking for downhill, but even they will only cope up to a certain slope angle, loss of grip.
| https://mechanics.stackexchange.com |
24,917 | [
"https://chemistry.stackexchange.com/questions/24917",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/8208/"
] | <blockquote>
Vinegar generally contains 5% acetic acid. We would expect the pH of vinegar to be approximately:<br>
<strong>a</strong>. 0<br>
<strong>b</strong>. 3<br>
<strong>c</strong>. 7<br>
<strong>d</strong>. 9<br>
<strong>e</strong>. 12
</blockquote>
I don't have the key for this question, so I just w... | You are not given a concentration, but a percentage value. Assuming its mass percent (wt%), you first have to calculate the actual concentration of the solution like this:
5% Acetic acid means in a $\pu{1 kg}$ solution, you can find $0.05 \times \pu{1000 g} = \pu{50 g}$ acetic acid. With a molar mass of $\pu{60.05 g/m... | Consider the choices. Since it's acetic <em>acid,</em> you can rule out any pH values that indicate a basic or neutral solution. Knowing that acetic acid is a weak acid and that vinegar is a fairly dilute solution, you can also rule out any pH values that would indicate either a strong acid or a highly concentrated sol... | https://chemistry.stackexchange.com |
91,503 | [
"https://electronics.stackexchange.com/questions/91503",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | <img src="https://i.stack.imgur.com/LKImd.jpg" alt="enter image description here">
A PC is connected to a data acquisition card which has single ended channels. One of the channels is outputting a constant DC voltage which can be controlled by a user via a program in the PC.
The output voltage is feeding a VFD. The ... | <blockquote>
What might be the reason then for this amplifier?
</blockquote>
The possible reason is that your motor controller (Variable frequency drive) is connected to AC mains power and may not have satisfactory protection to offer a signal that controls it. This might mean that the VFD can inject (unintentionall... | The VFD used a high voltage AC drive that does not share a common return or ground with the DAC, thus isoation is needed.
| https://electronics.stackexchange.com |
188,664 | [
"https://mathoverflow.net/questions/188664",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30395/"
] | We work in the set theory NBG (with local choice, but not global choice), because if there is global choice, every proper class is well-ordered, so that every proper class is bijective with the class On of ordinals and the class V universe, and we only have one level of bijective equivalent proper classes.
As it is kn... | The answer to question 2 is Negative. This is because, answering to my question "Injection of the proper class of ordinals into every proper class", J.D. Hamkins proved on 02/12/2014 the existence in NBG of a proper class W that does not inject into On.He also proved that On does not inject into W.
So that if A were to... | In a previous question Joel Hamkins linked to a model obtained by adding Cohen subsets to every regular cardinal. This model had the property that the universe could not be linearly ordered.
In particular, there was a class of pairs that witnessed that. Namely there was a class of pairs without a choice function. Cons... | https://mathoverflow.net |
12,729 | [
"https://quant.stackexchange.com/questions/12729",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/7788/"
] | Do quants need to know Accounting?
In my school's undergrad Quant program, we had Financial Accounting and Managerial Accounting, which were listed as prerequisites for our undergrad Finance subjects.
I am taking grad Quant now in the same school, and I have not seen Accounting ever turn up again except in Financial St... | Certain structural models of credit risk/default require some background in accounting, but not much. That these credit models are getting baked into the Basel regulations for CVA, CoCo bonds, and so on, makes it marginally more important to know. There's also an entire industry based on convertible bond and capital st... | Accounting is a vital skill if you end up in a managerial position, and unless your career goal is to always be a cog in someone else's clockwork, then you will eventually find yourself in a managerial/senior partnership position even through quant research. I still play a critical role in my firm's quant strategies te... | https://quant.stackexchange.com |
529,980 | [
"https://physics.stackexchange.com/questions/529980",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247621/"
] | Let velocities of two bodies <span class="math-container">$m_1$</span> and <span class="math-container">$m_2$</span> be <span class="math-container">$v_1$</span> and <span class="math-container">$v_2$</span> respectively. So can we write <strong>relative kinetic energy</strong> of <span class="math-container">$m_1$</sp... | Consider a rectangular Amperian loop of sides <span class="math-container">$\Delta w$</span>, <span class="math-container">$\Delta h$</span> (as per your right hand diagram), symmetrically placed with respect to the interface.
Faraday's law yields
<span class="math-container">$$ (E_{1t} - E_{2t})\Delta w + \frac{1}{2}... | The integral form of Maxwell's equation, i.e., Faraday's law, where the flux and <em>emf</em> are calculated over a surface <span class="math-container">${\mathcal S}$</span> and its boundary contour <span class="math-container">${\mathcal{L}=\partial \mathcal S}$</span>, resp., is <span class="math-container">$$\oint_... | https://physics.stackexchange.com |
283,450 | [
"https://stats.stackexchange.com/questions/283450",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/120828/"
] | Are there any problems with using Item Response Theory models such as the Graded Response Model when the number of measures is small? I don't know if there are any asymptotic results that would make a Graded Response Model undesirable with such a small number of measures.
| There are a number of issues, include convergence failures, biased parameter estimates, large standard errors, and difficulty in using the fitted model for predictive purposes (i.e., for scoring individuals by obtaining $\hat{\theta}$ estimates).
These are all technical issues, though more philosophically you can thi... | I would like to complement the above answer, by noting that estimation problems in 2PL Graded Response Model (GRM) may also depend on the issues of sample size and item response format. Note: there is no golden rule for 2PL GRM sample size, but some simulation studies (Reise & Yu, 1990) recommend that with a 5-cate... | https://stats.stackexchange.com |
14,989 | [
"https://dba.stackexchange.com/questions/14989",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7385/"
] | If I run the following code:
<pre><code>select PolicyNumber, MAX(decpageid) as decpageid, Risk
from StatRiskDecpages
where PolicyNumber = 'AR-0000301132-04'
group by PolicyNumber, Risk
</code></pre>
I get the following results:
<pre><code>PolicyNumber decpageid Risk
AR-0000301132-04 41 1
AR-000030... | I'd probably use
<pre><code>SELECT TOP (1) WITH TIES PolicyNumber,
decpageid,
Risk
FROM StatRiskDecpages
WHERE PolicyNumber = 'AR-0000301132-04'
ORDER BY decpageid DESC
</code></pre>
Assuming the covering index on <code>(PolicyNumber, decpageid) INCLUDE(Risk... | Here's how I refactored your query. <em>(first I'll post your query with your execution plan, and then follows is my new query and the corresponding query plan)</em>
<strong>Your Query</strong>
<pre><code>Select
t1.PolicyNumber,
t2.DecpageID,
t2.Risk
from
(
select
PolicyNumber,
MA... | https://dba.stackexchange.com |
37,780 | [
"https://security.stackexchange.com/questions/37780",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/5248/"
] | We're using a CMS that has a password reset function that works according to best practices out of the box.
<ul>
<li>Passwords are stored as salted hashes</li>
<li>Forgot Password works like this:
<ul>
<li>User enters either username or email address in textbox</li>
<li>System generates an email with a "reset passwo... | No, there should be absolutely no security risk with this approach.
Usernames are public information and should be treated as such.
<strong>EDIT</strong>
@Polynomial pointed out a key fact I left out. My advice doesn't apply if the username in question is some piece of sensitive information like a SS number.
| This isn't a significant security risk, though it does slightly increase attack surface. It's likely that the usability gain from allowing it greatly outweighs the minuscule risk.
However, it is useful to note that an attacker would gain two things if they were somehow able to intercept a lot of your reset emails:
<... | https://security.stackexchange.com |
14,622 | [
"https://physics.stackexchange.com/questions/14622",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/935/"
] | We sometimes play a game in my family whereby we trace the energy for a device back to it's source:
<ol>
<li>The Xbox got power from the wall.</li>
<li>The wall got power from the local transformer.</li>
<li>The transformer got power from the coal plant via the power lines.</li>
<li>The coal plant got power from the t... | Bonds - lots of bonds
Chemical reactions take in energy to break bonds and give off energy when they make bonds.
Big organic molecules like those in petrol have lots of weak carbon-carbon and carbon-hydrogen bonds which don't take a lot of energy to break.<br>
But when it burns the combustion products make lots of ve... | I will add an interesting flavor of physics to spice up Martin's excellent chemistry answer and which is in line with your original reasoning on how to trace energy content.
When chemical reactions take place and bonds form, break, and reshape, the atom nuclei don't change in any way. What happens is that the electron... | https://physics.stackexchange.com |
505,678 | [
"https://physics.stackexchange.com/questions/505678",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/201807/"
] | I've been trying to understand the conceptual idea and purpose of enthalpy for the past two days.
From what I've learned, enthalpy is defined as:
<span class="math-container">$$E = U + PV$$</span>
This leads me to my first question. Was this formula <em>created</em> or was it <em>derived</em>?
For example, the for... | <blockquote>
From what I've learned, enthalpy is defined as:
<span class="math-container">$$H = U + PV$$</span>
This leads me to my first question. Was this formula <em>created</em> or was
it <em>derived</em>?
</blockquote>
I have taken the liberty of changing <span class="math-container">$E$</span> to <... | Pressure does not <em>need</em> to be constant, but unless you are doing an experiment in a closed/pressurized (or depressurized) environment, the pressure at which a reaction occurs will be the ambient atmospheric pressure (which is effectively a constant). Moreover, if you are doing a reaction in an open vessel, the... | https://physics.stackexchange.com |
415,686 | [
"https://softwareengineering.stackexchange.com/questions/415686",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/374450/"
] | So I'm currently working on building a restful API. Let's keep it simple and say I have two endpoints, both GET:
<pre><code>/products
/products/{productId}
</code></pre>
The first returns a list of all products, the second returns a particular product.
The response for the first endpoint would likely look something thi... | For endpoints denoting a single resource, such as <code>/products/{productId}</code> it's best to return this resource, not a list. If it does not exist, a 404 error is appropriate.
If you'd access the resource using a query parameter <code>/products?id={productId}</code> you've got a different situation. In this case ... | You wouldn't return an empty list or null in a RESTful API -- you'd return a 404, which doesn't need a response body.
In a query or search (which /products is), I would expect to get a enumerable of some sort back. In a fetch (/products/{id}), I'd expect just the object itself.
| https://softwareengineering.stackexchange.com |
27,099 | [
"https://mathoverflow.net/questions/27099",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3710/"
] | There appear to be a number of rational canonical forms. The best thing about standards is how many there are to choose from. However, the standard I choose seems to have a centralizer that is difficult to describe.
<blockquote>
1) Is there a reference that chooses a specific (hopefully pretty) rational canonical ... | For a start the accepted usage for "rational canonical form" in the literature
is for a diagonal sum $C(f_1)\oplus C(f_2)\oplus\cdots\oplus C(f_k)$ where
$C(f_i)$ is the companion matrix for a monic polynomial $f$ and
$f_1\mid f_2\mid\cdots\mid f_k$. That said, if I needed to find a centralizer
explcitly it isn't the c... | Here is part 1″ solved, but the answer is complex and too long for a comment or edit. Notation is similar but not identical to before:
Let f be a separable, irreducible polynomial of degree d. Let B be the block-Toeplitz matrix whose diagonal blocks are the companion matrix of f, whose first super-diagonal blocks ar... | https://mathoverflow.net |
261,340 | [
"https://physics.stackexchange.com/questions/261340",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/83398/"
] | When we first learn physics, it's often presented very 'discontinuously'. For example, pop quantum likes to talk about objects being "either" particles or waves, leading to a lot of confused questions about how things switch between the two. Once you learn about wavefunctions, the problem goes away; 'particle' and 'wav... | Any process that causes a physical quantity to become <em>truly</em> discontinuous in space and/or time by definition takes place over an <em>extremely</em> (in fact, infinitely) short time or length scale. From the usual uncertainty principles of quantum mechanics, these process would have huge energy or momentum, an... | Although you've indicated elsewhere that you don't like this example, I'm posting it in case others like it more:
Balance a pencil on its point, at an angle $\theta$ ranging from $0$ (flat on the table) to $\pi/2$ (perfectly vertical). Let $f(\theta)$ be the angle of the pencil when it reaches equilibrium. Then for ... | https://physics.stackexchange.com |
20,951 | [
"https://security.stackexchange.com/questions/20951",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/13659/"
] | I was looking at the tripartite structure of a virus, and it seems to check to see if a computer is infected before infecting it with the virus. Would this be an attempt to use files that are already present to infect, instead of transferring another copy of the virus onto the machine?
| The goal of most malware is to remain active as long as possible. The longer it can collect keystrokes, participate in DDoS attacks, redirect search results, send spam emails, shows popup ads, etc., the more profitable it is for the creator. To reach this goal, it has to be undetected.
If a piece of malware infects a ... | It's partially a business reason rather than a technical reason. I was once reading a blog post that was detailing a sales pitch, and it was heavily stressed by the person selling access to infected machines (for the purposes of spam relaying, stealing credit card info, DDoS, etc) that he wouldn't load multiple binarie... | https://security.stackexchange.com |
69,715 | [
"https://softwareengineering.stackexchange.com/questions/69715",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4385/"
] | David Allen's "Getting Things Done" method seems to be a very useful way of organizing tasks and getting those tasks done. Has anyone here used GTD in their day-to-day programming tasks, and if so, what's the best way to go about it?
| Well I use Onenote w/ skydrive (which syncs with my phone). I have a GTD notebook which has a page for <strong>Inbox, Next Actions, Waiting On, Ideas/Later</strong> which I use GTD style (Add everything to Inbox, then at some time empty the inbox to by doing it now, put it in Next Actions or later, or delegate it, in w... | <ol>
<li>Whatever you use to keep track of things, make sure it is available.</li>
<li>Get in the habit of entering things.</li>
<li>I prefer something with a reminder, so I don't have to worry about it. We have alarms so we can sleep and reminders to tell us something is up. No worries.</li>
<li>Triage tasks, identify... | https://softwareengineering.stackexchange.com |
269,347 | [
"https://softwareengineering.stackexchange.com/questions/269347",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/163691/"
] | <strong>Context</strong>
I'm designing a database which, simplified, should be able to handle users sending job requests to each other, and after that a job can be started, finished, and reviewed. The design should be scalable (think millions of users).
<strong>Approaches I've considered:</strong>
<em>Gargantuan tab... | Sounds like you have 3 major categories of data you are trying to store:
<ol>
<li>General job data (job id, job requester id, job receiver id etc)</li>
<li>State transitions (job started, job finished)</li>
<li>State-specific job data</li>
<li>(optional) job-related events (price changed, job receiver user reassigned ... | How about a hybrid of the two? A large table with a JobID and state (and perhaps other information common to all jobs and states), with other tables to manage the additional state information. That reduces (or eliminates) the duplication of data, but keeps things more manageable.
| https://softwareengineering.stackexchange.com |
25,336 | [
"https://dsp.stackexchange.com/questions/25336",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/16901/"
] | I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y[0]=0$.
By one approach I've read,
$$
\text{characteristic equation:}\quad z-0.4=0 \quad\therefore y_n[n]=A(0.4)^n \\
\\
y_f[n]=B... | The way to solve such problems is to use the unilateral $\mathcal{Z}$-transform, which allows you to take initial conditions into account. Note that the unilateral $\mathcal{Z}$-transform of $y[n-1]$ is
$$\mathcal{Z}\{y[n-1]\}(z)=z^{-1}Y(z)+y[-1]\tag{1}$$
where $Y(z)$ is the $\mathcal{Z}$-transform of $y[n]$. Using $... | As Matt L pointed out, your initial condition is wrong. y[0] is NOT 0, it's 4. This is obvious from the difference equation. Once you use y[0] = 4, both results come out to be the same.
| https://dsp.stackexchange.com |
635,284 | [
"https://physics.stackexchange.com/questions/635284",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/294912/"
] | I am practicing questions from the topic elasticity.
There was a question from the book I.E. Irodov, Q.no)1.291.
The question is as follows:
What internal pressure(in the absence of an external pressure) can be sustained by a glass spherical flask, the wall thickness <span class="math-container">$\Delta$</span>r = 1.0m... | Take a small element on the surface of the sphere <span class="math-container">${\rm d}A$</span> and perform static analysis by balancing the forces.
"Tensile" force is the the force exerted by the sphere to the surroundings as a result of deformation. A better term would be radial force, or even better it sh... | They are splitting the sphere into a hemisphere, and balancing forces normal to the flat split. The resultant force of pressure on the hemisphere is <span class="math-container">$\pi r^2 p$</span>. The tensile force on the glass is <span class="math-container">$2\pi r\Delta r\sigma$</span>, where <span class="math-co... | https://physics.stackexchange.com |
485,033 | [
"https://physics.stackexchange.com/questions/485033",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/143038/"
] | While doing some exercises on the variation of the metric tensor <span class="math-container">$g_{\mu\nu}$</span> and of its inverse <span class="math-container">$g^{\mu\nu}$</span>, I came across the following identity:
<span class="math-container">$$\begin{align} & \delta(g_{\mu\nu}g^{\mu\nu})=\delta g_{\mu\nu} ... | So here is what I gathered from other posts such as the one that @Qmechanic posted in the comments. In my expansion, one must not only consider <span class="math-container">$\delta \sqrt{-g}$</span> but also <span class="math-container">$\delta g^{\mu\nu}$</span> for the derivatives. The variation <span class="math-con... | I know you basically said this, but here is the answer. If you have a metric which is a sum of a background metric and a small perturbation,
<span class="math-container">$$
g_{\mu \nu} = \overline{g}_{\mu \nu} + h_{\mu \nu}
$$</span>
then the inverse metric is
<span class="math-container">$$
g^{\mu \nu} = \overline{g}^... | https://physics.stackexchange.com |
102,854 | [
"https://mathoverflow.net/questions/102854",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1682/"
] | If AD$_\mathbb{R}$ holds and $\kappa < \Theta$ then every tree $T$ on $\kappa$ is weakly homogeneous (Martin–Woodin, "Weakly homogeneous trees.") I recall hearing that the hypothesis can be weakened to "AD holds and there is a Suslin cardinal above $\kappa$." Is this correct? If so, does anyone know where a proof... | I hope it's okay to post an answer to my own question. I am essentially repeating Woodin's proof that he just showed me. Any errors were probably introduced by me.
Recall that under AD all measures on ordinals are countably complete and ordinal-definable.
By the coding of measures theorem of Kechris assuming AD and ... | You indeed don't need $AD_{\mathbb{R}}$ and $\kappa < \Theta$ and it is correct this can be weakened. The argument was improved by Woodin : Assume $AD$ and assume that $\kappa$ is less than the supremum of the Suslin cardinals if there is one (this assumption is necessary) then every tree on $\omega \times \kappa$ i... | https://mathoverflow.net |
24,817 | [
"https://dba.stackexchange.com/questions/24817",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4628/"
] | I'm migrating data from a schema where people and organisations are separate tables to one where people and organisations are all treated as contacts (they share a lot in common). Currently, the people table has about 90k records with 80k relationships to 10k organisations.
New model:
<pre><code>Contact Rel... | Since you invoked The One True Way... I'll invoke it. 1NF would insist on "no repeating groups," which is what cid_a and cid_b are... two columns of the same "stuff" (to use the technical term).
You should not have to look at data two different ways to get the correct answer.
<pre><code>contact relatio... | If you can guarantee that each person can only belong to a single organisation there is no reason why you could not add an extra column to store the organisation_id to your table. Then you could use a self join in the query to get the organisation per person.
If each person can belong to multiple organisations then y... | https://dba.stackexchange.com |
81,317 | [
"https://physics.stackexchange.com/questions/81317",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26794/"
] | I read what if we have acceleration given as a function of velocity we can calculate time as
$$t(v) = t_0 + \int_{v_0}^{v} \frac{dv}{a(v)}.$$
Why?
| You have $a(v) = \frac{dv}{dt}$. By separating the variables you get $dt= \frac{dv}{a(v)}$. Now you just integrate between $v_0$ and $v$ to obtain the equation you wrote.
| Really @Yola answered your question directly so I want to be a little more complete. I want to show how to deal with problems of $a(v)$ and $a(x)$.
<ol>
<li>Acceleration as a function of speed $$ t= t_0 + \int_{v_0}^v \frac{1}{a(v)}\,{\rm d} v
\\ x = x_0 + \int_{v_0}^v \frac{v}{a(v)}\,{\rm d}v $$</li>
<li>Acceleration... | https://physics.stackexchange.com |
58,060 | [
"https://dba.stackexchange.com/questions/58060",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8040/"
] | Here is some innodb table. It <code>insert,update,query</code> very frequently.
<code>tn</code> is product id
<code>col</code> is product sub id
<code>tindex</code> is product description.(store by each word)
<code>date</code> is product add date stored by <code>strototime('now')</code>
<pre><code>CREATE TABLE IF... | Some notes:
<ul>
<li>Why is there no <code>PRIMARY KEY</code> in the table?</li>
<li>Why <code>date</code> is of type <code>int</code> and not <code>date</code> or <code>datetime</code> or <code>timestamp</code>?</li>
<li>Why is it called <code>date</code> when it stores date and time?</li>
</ul>
Regarding the actual... | Use JOIN
<pre><code>SELECT *
FROM mytable a
JOIN
mytable b
ON b.tn = a.tn
AND b.col = a.col
WHERE b.tindex = 'waterproof'
AND a.tindex = 'anticorrosive'
ORDER BY a.DATE
LIMIT 10
</code></pre>
Also a composite <code>index(tn,col,tindex)</code> will help.
| https://dba.stackexchange.com |
166,510 | [
"https://softwareengineering.stackexchange.com/questions/166510",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66466/"
] | I'm designing a file handler interface:
<pre><code>public interface FileHandler
{
public void openFileHandler(String fileName);
public void closeFileHandler();
public String readLine();
public String [] parseLine(String line);
public String [] checkLine(String line[]);
public void incrementLi... | An interface specifies <strong>behavior</strong>, not specific implementation details.
You should specify the operations you want anything that implements your interface to support. One way of determining that is asking "How will consumers use my interface; what is the contract I am specifying?"
Leave the detail... | Interfaces should be designed by keeping in mind what outside objects will need to call on classes that implement the specific interface.
This is just what the class should be able to do from the outside. For everything else you can use abstract classes with protected methods (so you will have the same commodity to fo... | https://softwareengineering.stackexchange.com |
339,476 | [
"https://physics.stackexchange.com/questions/339476",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/135191/"
] | Why does the potential difference between the plates of a capacitor decrease when a dielectric is inserted in it? How is this possible if the capacitor is connected to a DC power supply?
Also, does a dielectric actually 'touch' the plates of the capacitor or is it kept in the middle?
| If the capacitor is isolated then the charge on the capacitor $Q$ is constant.
Adding a dielectric increases the capacitance, $\dfrac {(\epsilon \uparrow )A}{d} \Rightarrow C\uparrow$, and this in turn decreases the (electric potential) energy stored in the capacitor $\dfrac 1 2 \dfrac{Q^2}{C \uparrow} \Rightarrow ... | The voltage will only reduce if the capacitor is isolated. This is because the dielectric increases the capacitance. When the capacitor's terminals are not connected to anything, the charge cannot change, and hence the voltage will drop due to the capacitor equation $V=Q/C$.
On the other hand, if the capacitor is conn... | https://physics.stackexchange.com |
116,383 | [
"https://mathoverflow.net/questions/116383",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6666/"
] | EDIT The question was based on an error, as it turns out. In fact my example is a category (and therefore a groupoid), by Eric Wofsey's argument. I can't remember why I thought it wasn't, and I feel a little silly, but I am very glad that it is.
In the nerve of a small category an $n$-simplex is determined by $n+1$ o... | It's called a groupoid. Given an object $A$, call the degenerate edge from $A$ to itself the identity map at $A$. Given an edge $f:A\to B$, let $f^{-1}:B\to A$ denote the unique edge that fills in a 2-simplex whose other two edges are $f$ and the identity. Given $f:A\to B$ and $g:B\to C$, define $gf$ to be the uniqu... | For related ideas, (rather than being strictly an answer), have a look at 'simplicial T-complex' as explored by some of Ronnie Brown's students is related. The nerve of a groupoid is one. I would also suggest that a strict Segal space is going to give you another related notion. The idea of $T$-complex is that it is a... | https://mathoverflow.net |
698,711 | [
"https://physics.stackexchange.com/questions/698711",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/311743/"
] | For the thin film deposition of some metal A onto another metal B, I understand it is possible for a bit of metal a to diffuse into grain boundaries of metal B. How are these diffused atoms of metal A bonded to metal B and does that constitute an alloy locally? In the case of Al and Nb, Al can diffuse a bit into Nb, bu... | Any amount of <span class="math-container">$Al$</span> on a <span class="math-container">$Nb$</span> matrix is an alloy <span class="math-container">$NbAl$</span> by definition.
But if you are asking about a compound like <span class="math-container">$Nb_3Al$</span>, it requires a minimum amount of <span class="math-c... | It is indeed true that elements that diffuse along grain boundaries can react with other elements in the bulk to form alloys that are <em>segregated</em> at the grain boundaries. This effect is commonly used to stabilize grain boundaries in metal alloys and thereby make them more resistant to deformation.
For example, ... | https://physics.stackexchange.com |
361,197 | [
"https://stats.stackexchange.com/questions/361197",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/124272/"
] | I need to generate samples from a pdf given by $\frac{f_Z(z)\cdot 1_{Z \in B}}{P(Z \in B)}$ where $Z \in \mathbb{R}^d$ is a normal random vector with independent components. $Z \in B$ is a set that is hard to characterize and may be defined implicitly. However, it can be assumed that it is a closed set with no holes.
... | Yes, you do have to save the old state a second time, or however many times you reject a proposal.
As you say, Metropolis-Hastings is a Markov chain Monte Carlo (MCMC) method. Given some distribution of interest $\pi$ (in your case $\pi(z)\propto f(z)\mathbf{1}_{z\in B}$), you simulate a Markov chain that is designed ... | Usually when you are doing MCMC sampling you generate a list of sampled values from the algorithm. If the proposed state is rejected then you set $X_t = X_{t-1}$, where $X_{t-1}$ is the current state of the MCMC algorithm. Alternately, you could have 2 (associated) lists first one w/the values and the second one with t... | https://stats.stackexchange.com |
262,662 | [
"https://physics.stackexchange.com/questions/262662",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86936/"
] | <blockquote>
Monochromatic light passes through a double-slit arrangement. The intensity of the monochromatic light passing through one of the slits of the double-slit arrangement is reduced. State, and explain, the effect of this change on the appearance of the bright fringes and of the dark fringes.
</blockquote>
... | Suppose the amplitude of the wave from slit $1$ arriving at a point is $A_1$ and the amplitude of the wave from slit $2$ arriving at the same point is $A_2$ and let $A_2>A_1$.
The relative phase between the waves from the two slits arriving at that point depends on the path difference between the slits and the poin... | I'm not sure if my understanding is correct, but i hope this would help!
When it comes to destructive interference, usually we would be given a situation where two coherent waves move in opposite direction. However, the resultant displacement only becomes zero when both have the same amplitude.
As an illustration, ... | https://physics.stackexchange.com |
97,511 | [
"https://dba.stackexchange.com/questions/97511",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/63128/"
] | I was tried ogr2ogr command like this.
<pre><code>ogr2ogr -f "ESRI Shapefile" "C:\temp\sqlexport.shp" "MSSQL:server=[RemoteServerIp];database=[dbname];User Id=[user];Password=[password];trust_connection=yes;" -sql "SELECT [geometrycolumn].STAsBinary() FROM [tableName] WHERE [indexColumn] = 1;" -overwrite
</code></pre>... | This is probably done by your log rotation software. On my Ubuntu machine its defined in <code>/etc/logrotate.d/mysql-server</code>.
<code>logrotate</code> is run daily by a cron job. Take a look in <code>/etc/crontab</code>. In my case I have the following:
<code>
25 6 * * * root test -x /usr/sbin/anacron ||... | Never. It just grows and grows. All the more reason to fix the slow queries.
(Or you could do something to delete the file. Of course it will come back.)
| https://dba.stackexchange.com |
504,151 | [
"https://physics.stackexchange.com/questions/504151",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/243042/"
] | From what I know of gravitational fields and our earth gravity always repel objects and any mass. But I was wandering if there were forces that can oppose the earth gravitational force.
| The gravitational force is attractive in nature so it always attracts. The Earths gravity also attracts other object towards it. Gravity is directly proportional to the masses of the objects. So, anything that has more mass than the earth has more gravitational field and hence stronger force of gravity.
As for the fo... | Any body more massive than earth generates a more powerful gravitation field. This includes the sun, Jupiter, Saturn, other large planets, and other stars.
There is nothing we know of that repels the gravitation field. The magnetic field and electric field can be repulsive but not necessarily to massive bodies.
| https://physics.stackexchange.com |
60,989 | [
"https://electronics.stackexchange.com/questions/60989",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9079/"
] | I've never done a 4 layer board and am not familiar with the process of manufacture for them. Will the external layers isolate inner layers from water if say, I will be putting the board into water for long periods (months) of time?
| No. Ordinary PCB technology does not protect against moisture ingress over the long term - that's actually a very, very difficult problem to solve where joints between different materials exist.
| The material most commonly used is FR-4 which is a composite material composed of woven fiberglass cloth with an epoxy resin binder that is flame resistant. Because it's a woven cloth, the water can still go through the edges.
| https://electronics.stackexchange.com |
28,619 | [
"https://dba.stackexchange.com/questions/28619",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/15055/"
] | I am not able to understand how to achieve a hierarchy accessing 3 tables. That is, I have Table1, Table2 and Table3 where:
<pre><code>Table1 (ID_table1, name_c, size)
Table2 (ID_table2, ID_table1, name_l, size)
Table3 (ID_table3, ID_table1, ID_table2, name_d, size)
</code></pre>
How do I make a hierarchy with all ... | I've never tried anything like that, but what if you UNION your three tables into one, and then do a "one-table hierarchical query" on the result of that?
<pre><code>WTIH alltabs as
(Select 'T1' as src, Table1.ID, NULL AS ID_table1, NULL as ID_table2, Table1.name, Table1.size
from Table1
union
Select '... | Similar to Frusterated's answer<sup>+1</sup>, but with a few different assumptions.
<pre><code>drop table table1;
drop table table2;
drop table table3;
create table table1 (ID Number(3), Name Varchar2(10), SizeX number(3));
create table table2 (ID Number(3), ID_table1 Number(3), Name Varchar2(10), SizeX number(3));
c... | https://dba.stackexchange.com |
349,785 | [
"https://mathoverflow.net/questions/349785",
"https://mathoverflow.net",
"https://mathoverflow.net/users/480516/"
] | I have just been told about this result, available as Exercise 2.5.10 in Ram. M. Murty's book, "Problems in Analytic Number Theory (2nd edition)". It says:
Let <span class="math-container">$\alpha>0$</span>. Suppose <span class="math-container">$a_n \ll n^{\alpha}$</span> and <span class="math-container">$A(x) \ll ... | It seems there is a typo in the application of the hyperbola method. Since <span class="math-container">$b_n=\sum_{d\mid n}a_d$</span>, we have
<span class="math-container">\begin{align}
\sum_{n\le x}b_n &=\sum_{n\le x}\sum_{de=n}a_d=\sum_{de\le x}a_d\\
&=\sum_{\substack{de\le x\\ d\le y}}a_d+\sum_{\substack{d... | The computation of the powers is wrong and the result stated in the book is incorrect and it should be <span class="math-container">$cx+ O(x^{(1+\delta-\delta^2)/(2-\delta)})+O(x^{\frac{(1-\delta)(1+\alpha)}{2-\delta}})$</span>
If <span class="math-container">$y=x^{(1-\delta)/(2-\delta)}$</span>, <span class="math-con... | https://mathoverflow.net |
378,677 | [
"https://softwareengineering.stackexchange.com/questions/378677",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/163655/"
] | When I am working in ASP.Net MVC or WebApi, I often find myself creating Views or return data structures that include 'List<>'s of objects. Meaning that I have a list of data objects that I want to return as part of a view.
I know that best practice is that the property for the List should be a IEnumerable interfac... | Personally I'd do something like this
<pre><code>public class AllProfilesViewModel
{
public AllProfilesViewModel(IEnumerable<FullUserProfile> allProfiles)
{
_allProfilesList.AddRange(allProfiles);
}
private List<FullUserProfile> _allProfilesList = new List<FullUserProfile>();... | First off:
<blockquote>
I know that best practice is that the property for the List should be a IEnumerable interface.
</blockquote>
Not necessarily. <code>IEnumerable</code> is a read-only, sequential-access-only collection interface. There are many cases in which that's exactly what you need, but plenty of othe... | https://softwareengineering.stackexchange.com |
434,318 | [
"https://softwareengineering.stackexchange.com/questions/434318",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/384487/"
] | I would like to display something on my desktop by tapping a button on my mobile app.
For example, there is a "show cat" button on my mobile app. When I tap that button, a new window should be opened and display a cat picture on my desktop.
The scenario is a bit similar to Zoom. The desktop application is idl... | Be aware that to be able to send an information, the sender needs to know the target.
Normally the client knows the server. But the server has no clue about the clients until they try to connect.<br />
Therefore you first have to establish a connection to the server, THEN the server can send data to the client.
In gene... | The client can simply connect to the server, identify itself, and leave the connection open without doing anything special. When something happens, the server can send some data to the client.
Nothing more complicated is needed. Except - don't forget to use TLS.
<hr />
Because almost everyone uses NAT at the moment, yo... | https://softwareengineering.stackexchange.com |
467,017 | [
"https://electronics.stackexchange.com/questions/467017",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/155534/"
] | What happens when a ceramic bypass capacitor fails? I am picking out parts and is wondering is it worth the extra few cents for rated capacitors?
Since generally most IC can function without a bypass, if a bypass cap fails there should be no problem, right? Or when a ceramic bypass fails does it form a short circuit?
| Surface Mount Multi-Layer Ceramic Capacitors (MLCC) primarily fail in the cracking regime.
That is the ultimate failure mode of a capacitor is with a body crack.
MLCC are made of very fine intermeshing metalic layers embedded in a ceramic substrate
A large portion of these failures result in short circuits (low i... | Ceramic capacitors can fail in a couple of ways.
They can be mechanically damaged - too much physical stress (pressure on the part or the board is bent a little too much) can cause a crack. The capacitor will then develop short circuits between layers. It acts more like a resistor in that case. If you are really un... | https://electronics.stackexchange.com |
510,183 | [
"https://math.stackexchange.com/questions/510183",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/85300/"
] | I thought this exercise would be fairly easy, but it seems i can't find a proper approach to it.
I have to prove that $f(x) = (1-x-x^2-x^3-x^4-x^5-x^6)^{-1}$ is the function that generates the number of forms we can get a number $n$ as the sum of the values given rolling a dice -as many times as is needed-.
My first ... | You should recognize that $r=|z|$. In this case, using $2\cos{\theta} = e^{i \theta}+e^{-i \theta}$, you get that $z=\left ( 1+e^{i \theta}\right)^2$. The image of this under $w=z^2$ is $w=\left ( 1+e^{i \theta}\right)^4$, and the polar curve that results is, as expected, $r = (2+2 \cos{\theta})^2$.
| Resulting curve will loop twice around the origin therefore you cannot express your curve as function $r=g(\theta)$. You got the answer right that
$$
w(\theta)=4(1+\cos\theta)^2 e^{2i \theta}, \ \theta \in [0,2\pi)
$$
You should look at this as parametric equation, so as $w : [0,2\pi)\rightarrow \mathbb{R}^2$
$$
w(\th... | https://math.stackexchange.com |
1,584,290 | [
"https://math.stackexchange.com/questions/1584290",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/291945/"
] | <blockquote>
Find $\Im((\cos 12^\circ +i \sin 12^\circ +\cos 48^\circ+i\sin 48
^\circ )^6)$.
</blockquote>
I've solved this problem but I think I've taken the long way to do this, so I am asking if there's some slick way to solve this.
<strong>That's how I solved it</strong>:<br>
I've applied the identity $\cos 48... | You were close. The argument of the expression is equivalent to
$$
\left(\mathrm{e}^{i\frac{\pi}{15}}+\mathrm{e}^{i\frac{4\pi}{15}}\right)^6 = \mathrm{e}^{i\frac{2\pi}{5}}\left(1+\mathrm{e}^{i\frac{\pi}{5}}\right)^6
$$
then you can extract $\mathrm{e}^{i\pi/10}$ to find
$$
\mathrm{e}^{i\frac{2\pi}{5}+i\frac{6\pi}{10}}\... | Let me try.
$$2^6\cos^6 18(\cos 30 + i\sin 30 )^6 = 64\cos^6 18 (\cos 180 + i^6\sin 180) = -64\cos^6 18.$$
| https://math.stackexchange.com |
29,028 | [
"https://datascience.stackexchange.com/questions/29028",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/46805/"
] | I have train and test data in two separate files.
OneHotEncoder gives different number of features for Train and Test Data based on the different values they have. But the classifier requires that the number of features for test and train data should be equal, how can I solve this problem?
| One hot encoding is a way of converting output label for 3 categories like 2 into [0, 1, 0] or 3 into [0, 0, 1].
If you are using scikit learn to convert the value into one hot encoder then in training time you should use
<pre class="lang-py prettyprint-override"><code>enc = OneHotEncoder()
enc.fit(x_train)
</code><... | One hot encoding is only a symptom. The cause of the problem is that your factor valible has not the same leveles in the test and train data.
Here you should distinct. Is it only a problem of sampling? You created your test data as (say) 20% sample of the original data. Some levels with small cardinalty could fail to ... | https://datascience.stackexchange.com |
102,643 | [
"https://stats.stackexchange.com/questions/102643",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/47992/"
] | I am in the process of describing my research design for my dissertation and ran into a roadblock. In my design, I am converting 20 y/n responses from 190 participants to two dichotomous groups: 1). Chance level and 2). Above chance level.
If chance level is 50% or 10 responses correct/incorrect, how do I determine wh... | Here's one possibility:
If you assume the answers are like independent coin-flips, you can work out the probability of getting any number correct. For example if the answers were 50-50 coin flips the change of getting at least 15 correct is about 2%. You might say "well, that's pretty unlikely, let's say that 15 or m... | @Glen_b offered one solution. It is correct for each individual, and that's fine. But you have 190 individuals. By chance, some of them will be above chance level and some below. For example, here is a <code>R</code> code for a single case of 190 people flipping 20 coins.
<pre><code>set.seed(19291010)
choices <- r... | https://stats.stackexchange.com |
22,129 | [
"https://electronics.stackexchange.com/questions/22129",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5984/"
] | I rent a house in the SF Bay Area. The house is not exactly new, but it's in good condition; hopefully the AC installation is the same. Most AC outlets are without grounding; but fortunately, there are two outlets in the backyard that do have ground connectors.
I am thinking to build a kiln to fuse and slump glass. Th... | As others have said, 72A can't be drawn from a regular outlet and will need special wiring. Legally, this wiring will need to be done by a licensed electrician, and of course will require the landlord's approval.
As to whether the grid feed can support that, that is something you should be able to ask the electric co... | Here in Belgium a house has a main automatic switch (before the fuse cabinet) approved by the electricity utility. The switch's rating is the maximum you can draw for the whole house. For my apartment that's 40A (at 230V).<br>
I guess in California things will be more or less the same. I wouldn't worry about the wiring... | https://electronics.stackexchange.com |
2,305,656 | [
"https://math.stackexchange.com/questions/2305656",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/206637/"
] | I solved this problem on my own, months ago, but the solution seems to me completely forgotten, a little help on it would be appreciated:
Suppose $\alpha= \alpha(t)$ on an interval $I$ is a smooth (of class C$^1$) parametric representation of the curve $C$, and for any $t \in I$ we have $\space\space\frac{d}{dt}\alpha... | I think you mean $a=b$.
Thus, $2a>c$ or $\frac{a}{c}>\frac{1}{2}$ and
$$k=\frac{r}{R}=\frac{\frac{2S}{a+b+c}}{\frac{abc}{4S}}=\frac{16S^2}{2abc(a+b+c)}=$$
$$=\frac{(a+b-c)(a+c-b)(b+c-a)}{2abc}=\frac{(2a-c)c^2}{2a^2c}=\frac{\frac{2a}{c}-1}{\frac{2a^2}{c^2}}.$$
Hence,
$$\frac{2ka^2}{c^2}-\frac{2a}{c}+1=0,$$
which g... | We know that $r=4R\sin{(\dfrac{A}{2})} \sin{(\dfrac{B}{2})} \sin{(\dfrac{C}{2})}.$ where A, B and C are the angles of the triangles.
And $\dfrac{a}{c}=\tan{A}$, where A is the equal angles or base angles which can be proofed using sine rule.
Now $\frac{r}{R}=k=8\sin{(\dfrac{A}{2})}\cos{(\dfrac{A}{2})}$,
$\therefore k... | https://math.stackexchange.com |
351,349 | [
"https://math.stackexchange.com/questions/351349",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/68213/"
] | <blockquote>
Let $z$ be a primitive $n$-th root of unity. Prove that for any $m\in\mathbb{Z}$, if $\gcd(m,n)=1$, then $z^m$ is a promitive $n$-th root of unity. Verify each condition in the definition.
</blockquote>
| Hint:
$$(z^m)^k=1\iff z^{mk}=1\iff n\mid mk\implies n\mid k\;,\;\text{since}\;(m,n)=1\ldots$$
| Suppose that $z^m$ is not primitive $n$-th root of unity then there's $k<n$ such that
$z^{mk}=1$, so $n|mk$ and with the fact $(m,n)=1$ we find by Euclid's lemma that $n|k$.Absurd
| https://math.stackexchange.com |
256,680 | [
"https://physics.stackexchange.com/questions/256680",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/112636/"
] | UV radiation isn't visible to the human eye, so how come we can see it as a purple/violet light from a UV lamp? Is it just because the lamps aren't perfect and end up emitting some light at a higher frequency? Or do they add some purple light intentionally? Or is there some more complex mechanism going on?
| Yeah, I would guess that the alternate heating/cooling of the wax in the sun pushes it up the side of the glass. Presumably the surface tension between the wax and the glass is quite strong and holds the wax up once it's been pushed up. Subsequent cycles cause wax to "backfill" the wax that's been pushed up.
It woul... | Candle wax expands considerably when hot and molten. So while burning the candle the level in the glass rises.
But when the candle is extinguished the outer region (nearest the glass) cools down quicker (candle wax doesn't conduct heat very well) and solidifies first, becoming immobile. The molten remainder then shrin... | https://physics.stackexchange.com |
412,824 | [
"https://physics.stackexchange.com/questions/412824",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/196898/"
] | If work done by a <strong>constant</strong> conservative force where work is independent of path taken is:
$W=\vec{F}\cdot \Delta\vec{x}$ where $\vec{x}$ is displacement
Then work done by a <strong>constant</strong> non-conservative force where work is dependent of path taken is:
$W=\vec{F}\cdot \Delta d$ where $d... | In the case of conservative force, the path does not matter. In the case of non-conservative force, it does. By definition:
$$W=\int_C \vec{F} \cdot \mathrm{d} \vec{s}$$
Where $C$ is the path, let's say, from $A$ to $B$. In the case of conservative force, there exists a potential for the force, and the work done is sim... | Work is <em>defined</em> as
$$ W = \int_{r_i}^{r_f} \mathbf{F} \cdot d\mathbf{r} $$
regardless of whether $\mathbf{F}$ is conservative or nonconservative.
<hr>
However, you ask about the case of a constant conservative force. A conservative force is one such that
<ul>
<li>It can be written as the gradient of a po... | https://physics.stackexchange.com |
96,588 | [
"https://stats.stackexchange.com/questions/96588",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/44417/"
] | The only thing I understood about fuzzy neurons is that the neuron's activation function is replaced with some operation used in fuzzy. Other than that, I didn't understand much from science paper I found. Also, it is hard to just Google it because of it's name, which results in listing some fuzzy or ANN or hybrid syst... | fuzzy means it has a probabilistic state.
fuzzy neurons would not just be 0 or 1 activated neurons, but will have a distribution of states.
it is a very generic term, and there is no specific answer to give.
| Let me take a stab at this. The term "fuzzy neuron" is in a sense a fuzzy set in and of itself, given that it has a broad definition encompassing a panoply of different types of neurons, which have different types of "fuzz" added to different internal components. The easiest way to explain it is as a Cartesian product ... | https://stats.stackexchange.com |
3,018,721 | [
"https://math.stackexchange.com/questions/3018721",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/621010/"
] | So I need to take the Laplace transform of the following function:
<span class="math-container">$$
Eqn. 1: \\\frac{1}{2}\mathcal{L}{\{t^2 \ddot y\}}
$$</span>
I've found that
<span class="math-container">$$
Eqn. 2:\\
\mathcal{L}{\{t^{n} f(t)\}} = (-1)^{n}F^{n}(s) \,\,\, \text{for}\, n\, =\, 1,\, 2,\, 3, ...
$$</spa... | <span class="math-container">$$
\mathcal{L}(t f(t)) = \int_0^{\infty} t e^{-st}f(t) dt = -\frac{d}{ds}\int_0^{\infty}e^{-st}f(t) dt = (-1)\frac{d}{ds}F(s)
$$</span>
so
<span class="math-container">$$
\mathcal{L}(t^n f(t)) = (-1)^n\frac{d^n}{ds^n}F(s)
$$</span>
then
<span class="math-container">$$
\mathcal{L}(t^n f'... | No, just as the integral of <span class="math-container">$f(x)g(x)$</span> is not the product of the integrals of <span class="math-container">$f(x)$</span> and <span class="math-container">$g(x)$</span>.
The correct form is a convoluton
<span class="math-container">$$\mathcal{L}{\{f_{1}(t)f_{2}(t)\}} = \frac 1{2\... | https://math.stackexchange.com |
93,322 | [
"https://security.stackexchange.com/questions/93322",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/70088/"
] | I first thought all these terms were synonyms, but I sometimes see those terms used in the same document. For instance, on MSDN:
<blockquote>
data origin authentication, which enables the recipient to verify that
messages have not been tampered with in transit (data integrity) and
that they originate from the ex... | <strong>Integrity</strong> is about making sure that some piece of data has not been altered from some "reference version". <strong>Authenticity</strong> is a special case of integrity, where the "reference version" is defined as "whatever it was when it was under control of a specific entity". <strong>Authentication</... | Looks like there is a good answer already, but let me elaborate on availability versus authentication in the CIA triad. What the "A" stands for changes with context.
Authentication is used if we talk about hardware-based embedded security. When we discuss the crypto primitive functions of a secure element or a full TP... | https://security.stackexchange.com |
295,263 | [
"https://stats.stackexchange.com/questions/295263",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/171794/"
] | I created an n-gram language model on the Penn Treebank using the following command:
<pre><code>ngram-count -text $trainfile -order 5 -lm $temp/templm.ptb -gt3min 1 -gt4min 1 -kndiscount -interpolate -unk
</code></pre>
This code snippet was taken from Mikolov's rnnlm toolkit.
I tried to check if the created ngram LM ... | This depends on whether your data is normally distributed or not, and if the relationship is dependent or independent. In data with normal distribution the t-test is preferred, but for non-normal distributions the Wilcoxon–Mann–Whitney is fine. Also, Wilcoxon–Mann–Whitney is for independent samples; the Wilcoxon signed... | The Wilcoxon-Mann-Whitney makes no distributional assumptions and so could always be applied. It has the advantage of providing exceptionally good robustness; for instance, if there were to be a few extremely bad points in your data (e.g., individuals with 10000+ diseases) these wouldn't heavily influence the Wilcoxon-... | https://stats.stackexchange.com |
297,133 | [
"https://physics.stackexchange.com/questions/297133",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84967/"
] | Let $\psi(x)$ be the field of the electron. Its Fourier transformed two-point function reads
$$
\langle\psi\bar\psi\rangle=\frac{1}{\not p-m-\Sigma(\not p)}.
$$
If we calculate $\Sigma(\not p)$, we observe that it depends on the gauge parameter $\xi$, which in principle is not a problem because $\Sigma(\not p)$ is not... | The propagator $S(p)$ is the Fourier transform of the two-point function
$S(x,y)=\langle\psi(x)\bar\psi(y)\rangle$,
$$
S(p) = \int \frac{d^p}{(2\pi)^4} \, \exp(-ip\cdot(x-y)) \, S(x,y)\, .
$$
Note that because of Lorentz invariance $S(x,y)$ does not depend on $x+y$. Clearly, the two-point function is non-local and n... | As an alternative to Thomas answer, we note that if we write the transformation law explicitly, we get
$$
\langle\psi(x)\bar\psi(y)\rangle\to \langle\psi(x)\mathrm e^{i\alpha({\color{red}x})}\mathrm e^{-i\alpha({\color{red}y})}\bar\psi(y)\rangle=\mathrm e^{i(\alpha(x)-\alpha(y))}\langle\psi(x)\bar\psi(y)\rangle
$$
We ... | https://physics.stackexchange.com |
604,265 | [
"https://electronics.stackexchange.com/questions/604265",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/301747/"
] | I have a neon sign transformer that converts 120 V to 12 kV which is the rated voltage. Using the 1:100 ratio would it be safe to have the input voltage be 140 V converted to 14 kV when the specified input voltage is 120 V? I am working with 60 mA. Is it also safe to connect the NST to a variac?
| It possibly <em>might</em> work, but more information is needed to answer that question.
<ol>
<li>How close to saturation is the transformer? It's unlikely the manufacturer added more silicon steel than needed, so it is probably close to saturation at 120 VAC. In that case, the extra voltage goes into heating the trans... | <strong>Would there be any safety issues if the input voltage on the primary coil is bigger than what the rated voltage is?</strong>
Depends. Is the possibility of the transformer catching fire a safety issue? Just asking.
Sigh. <em>Of course</em> there is a safety issue. Whenever you operate a device beyond its rating... | https://electronics.stackexchange.com |
9,235 | [
"https://dsp.stackexchange.com/questions/9235",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/3183/"
] | I recently realized that FFT's aren't perfect. Meaning if I take a signal and then take it's FFT, and then do an inverse FFT, the resulting output isn't exactly the same as the input. Here's an image to show you what I mean :<img src="https://i.stack.imgur.com/2iuVj.jpg" alt="FFT doesn't always work">
I think the ... | The differences you see are due to numerical errors in floating point format. All operations needed to perform an FFT and an inverse FFT can only be done with finite precision and you've shown the result of this finite accuracy in your lower right plot.
| In general a number can't be represented exactly in digital form. An error is introduced. If you are in Matlab you can write eps at the command, it gives you a number.
<blockquote>
EPS, with no arguments, is the distance from 1.0 to the next larger
double
precision number, that is EPS = 2^(-52).
</blockquot... | https://dsp.stackexchange.com |
311,953 | [
"https://physics.stackexchange.com/questions/311953",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98822/"
] | If a planet with an atmosphere and a flat surface is always directed with the same side to the sun (or star), how does the (nonstatic) thermodynamic equilibrium look like?
Has eventually an equilibrium developed in which there is a constant heat transfer through the planet from the sunlit side to the dark side?
And ... | In this specific case, the hamiltonian separates into the three dimensions separately. Writing $\mathbf r_j=\sum_kx_k^{(j)}\hat{\mathbf e}_k$, your hamiltonian reads
$$
H=\sum_k\left[\frac{(p_k^{(1)})^2+(p_k^{(2)})^2}{2m} + \frac12m\omega^2\left((x_k^{(1)})^2+(x_k^{(2)})^2\right)-\frac14\lambda m\omega^2(x_k^{(1)}-x_k^... | Hamiltonian of the k-th HO can be separated into two parts
$H_k = H_k^{(1)}+H_k^{(2)}$
Where,
$$H_k^{(1)} = \frac{(p_k^{(1)})^2}{2m}+\frac12m\omega^2(y_k^{(1)})^2$$
and
$$H_k^{(2)} = \frac{(p_k^{(2)})^2}{2m}+\frac12m\omega^2(1-\lambda)(y_k^{(2)})^2$$
With the substitutions
$$Y_k^{(1)}= \sqrt\frac{m\omega}{2\hbar}y_k^... | https://physics.stackexchange.com |
246,686 | [
"https://softwareengineering.stackexchange.com/questions/246686",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30483/"
] | We have decided to build separate applications for user authentication and user management. The reason is that the the former is a "this just needs to always work, and do so instantly" style service, and the latter includes a much-larger user-interface component with many requirements and features.
Unfortunately, whi... | Long story short: all in one.
If you consider one of these as "master" and the other as an augmented replica, that updates are replicated one way only, and you can survive large latencies in synchronisation (and I'll let you define "large") then two separate DBs will work. For anything else I'd suggest a single DB.
... | I used to work on a similar application, but the anticipated situation in my application would be very different from the way this site, facebook, twitter, or your application would work.
This is just in case, this can somewhat give you some insight.
I put both authentication data and business data in the same SQL dat... | https://softwareengineering.stackexchange.com |
163,903 | [
"https://electronics.stackexchange.com/questions/163903",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/57254/"
] | While writing a time critical piece of code for an Attiny13, I figured I could use the rising edge of an input as a trigger to read in some <strong><em>self clocking data</em></strong>. However, the number of clock cycles needed to go into the interrupt routine differs depending on the instruction being executed at the... | One option would be to have two triggers, the first causes the code to jump into a loop waiting for the signal to go low and then back high. As soon as the signal has gone back high, then start clocking the data.
Something like:
<pre><code>while(PINREG & (1<<PORTBIT)); //wait for low
while(!(PINREG & (1... | Maybe you can flag readiness to accept an interrupt from within your code. This then clocks a D type flip flop and if the D input was set (meaning a pending interrupt) then the output from the D type becomes the "new" interrupt edge. It all depends on your ability to flag readiness.
| https://electronics.stackexchange.com |
433,170 | [
"https://physics.stackexchange.com/questions/433170",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/113085/"
] | When we write down the lagrangian of a general <span class="math-container">$U(1)$</span> scalar field theory we generally write
<span class="math-container">$$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi^* - \frac{m^2}{2}\phi \phi^* - V(|\phi|^2)$$</span>
I.e., we don't write terms linear in <span cl... | The whole philosophy of perturbative QFT is that you assume the field's fluctuations about its energy- or action-minimizing value are small, so that you can Taylor expand the potential energy (and other quantities) about zero field. A Taylor expansion can't result in a <span class="math-container">$|\phi|$</span> term ... | Unless you make assumptions on <span class="math-container">$V$</span>, any expression in <span class="math-container">$|\phi|$</span> is of the form <span class="math-container">$V(|\phi|^2)$</span>. If you do make assumptions on the shape of <span class="math-container">$V$</span>, it is probably because you want it ... | https://physics.stackexchange.com |
128,215 | [
"https://chemistry.stackexchange.com/questions/128215",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/87257/"
] | I want to remove water hardness using Ion exchange resin filter. Does anyone tried this method I want to know if this method really lowers the hardness. What is the best method of regenerating resin filter? How much water it uses for regenerating process?
| Yes - the process works
If you are just looking to remove hard water salts (divalent, trivalent) the sodium chloride regenerable resin ("softener" resin) works fine and you can regenerate and put the waste to sewer.
If you want to remove all metals, then you'll need to acid regenerate and neutralise the wash before ... | The ion exchange resin works pretty well. It removes the hardness. This is the standard method for producing demineralized water in practice. If you want to regenerate the used resin, you treat it with concentrated hydrochloric acid, and then wash it with plenty of water until the water is not acidic any more when gett... | https://chemistry.stackexchange.com |
351,697 | [
"https://stats.stackexchange.com/questions/351697",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/188211/"
] | Sometimes a time serie may need to be differenced to be made stationary. However I don't understand how second order differencing can help to make it stationary when first-order differencing is not enough.
Could you give an intuitive explanation for second order differencing and the cases where is it needed?
| Second-order differencing is the discrete analogy to the second-derivative. For a discrete time-series, the second-order difference represents the <strong>curvature</strong> of the series at a given point in time. If the second-order difference is positive then the time-series is curving upward at that time, and if i... | Two thoughts:
<em>Recursion</em>. After you first-order difference, what do you have? Another time series which is, under the right conditions, closer to stationary. If it's not close enough, you now have a time series that's not stationary and you want to move it closer to stationary, so you take a first-order differ... | https://stats.stackexchange.com |
365,321 | [
"https://electronics.stackexchange.com/questions/365321",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/125197/"
] | This is a very beginner question. And below is an arbitrary made up example:
Imagine you established communication with a USB device through your PC's USB COM port.
The USB device is measuring the voltage through it's analog input and then converting it to digital by its ADC. And through its port sending the 10-bit s... | <blockquote>
Imagine you established communication with a USB device through your PC's USB COM port.
...
I set the baud rates and the rest by using HyperTerminal and connect to the port, I can see 4 voltage readings per second as incoming lines.
</blockquote>
Many USB devices that appear to PC software as "COM p... | 1) No, the data are not being averaged. The path from the ADC to Hyperterminal goes through a number of buffers, and data can not get through at the rate you are actually sampling at. There is a buffer in your sending device's UART hardware, and data is being written into that when it's free, while the ADC is continual... | https://electronics.stackexchange.com |
33,088 | [
"https://mathoverflow.net/questions/33088",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7699/"
] | How is entropy of a general probability measure defined?
| The Entropy of a function $f$ with respect to a measure $\mu$ is
$$ Ent_{\mu}(f)=\int f \log f d\mu - \int f d\mu \log(\int f d\mu ) $$
The entropy of a probability distribution $P$ with respect to $\mu$ is given by $ Ent(\frac{dP }{d\mu })$. I a not aware of a general definition that would not implie a reference (h... | Entropy is not defined for a single probability measure!
Entropy is a relative thing, you define between two measure $\mu$ and $\nu$. Then the entropy is defined by
$$
\mathcal{E}(\mu,\nu) = \begin{cases} - \int w(x) \log(w(x)) d\nu(x),& d \mu = w d\nu; \\\ -\infty, & otherwise.\end{cases},
$$
I might have me... | https://mathoverflow.net |
7,801 | [
"https://cs.stackexchange.com/questions/7801",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/2069/"
] | I wonder if there is a simple example of sets $A$ and $B$ such that $A$ is Turing-reductible to $B$ but not many-to-one reductible to $B$.
| For example sets $H = \{x \, | $ Turing machine with index $x$ halts on input $x\}$ and $\overline{H} = \{x \, | $ Turing machine with index $x$ doesn't halt on input $x\}$.
Because if $\overline{H} \leq_m H$, then $\overline{H}$ would be recursively enumerable and therefore $H$ would be recursive, which is contradict... | The key distinction (or at least one important one) is that Turing reductions are <em>oracle</em> based, whereas many-one reductions require a <em>total computable function</em> (i.e. you need to be able to map all inputs to something). With this in mind we can get a pretty clear example:
Consider the set of Turing ma... | https://cs.stackexchange.com |
231,054 | [
"https://softwareengineering.stackexchange.com/questions/231054",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/121368/"
] | I want to work on a very simple compiler for a very simple language. The compiler will compile the code to some basic bytecode. Later, a virtual machine program will run the bytecode, and execute the program.
I have several questions about what bytecode actually is:
<ul>
<li>Does bytecode have to be of binary form, a... | <ul>
<li>there is no need to go binary, you can write out text and interpret that directly. Most VMs will use octet-based binary for efficiency.</li>
<li>that is entirely up to the designer. however usually the common instructions (adding 2 numbers, GOTOs,...) will be shorter than the uncommon ones (calling a function,... | What you are doing, effectively, is designing new computer instructions, along with a new computer (your virtual machine) implemented as a program.
Generally, instructions (which is what byte-codes are) have an initial part that the interpreter examines to work out what is coming next. For example, as you have suggest... | https://softwareengineering.stackexchange.com |
118,880 | [
"https://mathoverflow.net/questions/118880",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8916/"
] | Suppose $X_i, \; i=1,2,3...,n$ are each Gaussian, then it is not in general true that the set is jointly Gaussian (a multivariate Gaussian).
Does a similar statement hold if the variates are <em>pairwise</em> Gaussian? i.e. if we have that $X_i, X_j$ are a bivariate Gaussian for all $i, j$, then it is not in general t... | Let $X_i$, $i=1\ldots3$, be iid standard normal random variables. Let $Y = |X_3|$ if
$X_1 X_2 > 0$ and $-|X_3|$ if $X_1 X_2 \le 0$. Then $X_1, X_2, Y$ are normal and pairwise
independent, but they are not jointly normal since $X_1 X_2 Y \ge 0$.
| Another, more general class of examples follows through the construction in "Families of m-Variate distributrions with given margins and m(m-1)/2 Bivariate dependence paramters" by H. Joe 96: The uniform and bivariate margins can be Gaussian, the higher level copulas can be arbitrary.
| https://mathoverflow.net |
24,231 | [
"https://chemistry.stackexchange.com/questions/24231",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/10212/"
] | I understand the fact that ionic compounds are good conductors of electricity in molten state. But why aren't they good conductors in solid state. Cannot ions vibrate about their mean position and transfer electricity in the same way as they transfer heat?
| Electric charge is transferred by physically moving charged particles around. In the case of an electric current moving through a wire (for example), the electrons are moving.
In an ionic compound, the ions are locked in place. They can move around a little bit, but there is not much translational motion - the ions st... | Ionic compounds do not conduct electricity in solid state because electron motion results in electricity being conducted but in solid state the constitutive particles are strongly bonded or in fixed positions; thus, they can't move from one part to another. In molten state, the ionic compound is split into ions, and io... | https://chemistry.stackexchange.com |
73,683 | [
"https://chemistry.stackexchange.com/questions/73683",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/17271/"
] | I realize as balloons go higher, the atmospheric pressure decreases, doing less to counteract the force of the gas particles pushing against the inner walls of the balloon. But at the same time, doesn't the outside temperature decrease, causing the gas particles in the balloon to lose energy and have less impactful col... | I didn't know that balloons expanded during the fly because of thermodynamics, and I didn't know how high they can fly, but a rapid search tells that a partially unfilled regular balloon can fly until an altitude of around $\pu{25 km}$.
Now, $\pu{25 km}$ means that it reaches the first part of the stratosphere, with t... | You are exactly correct that it is a matter of atmospheric pressure decreasing at a rate great enough to overcome the contraction due to decrease in temperature. On a nice, clear, dry 25°C day at sea level, atmospheric pressure decreases by about 12% per km, where the air temperature decreases by about 3% per km.
This... | https://chemistry.stackexchange.com |
50,247 | [
"https://electronics.stackexchange.com/questions/50247",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16557/"
] | I've two short questions regarding circuits with a transistors or diodes:
1) The following circuit with two diodes: Does it produce an electrical short for B=1 (5V) and for B=0 there is V[out]=1? Is this correct?
<img src="https://i.stack.imgur.com/okiNK.jpg" alt="enter image description here">
2) Does the following... | <blockquote>
Does it produce an electrical short for B=1 (5V)
</blockquote>
I'm afraid this is an example of muddled thinking about short circuits.
For clarity's sake, assume the diodes are ideal, then, the input B <em>can never be greater than zero volts</em>; B will <em>never</em> = 1.
The input B is a short cir... | Think of a diode as a current controlled switch. if no forward current, then leakage might be effectively >10 Mohm near zero current. If it is a small signal diode using silicon, consider it has a 0.6V drop with an internal series resistance such as 100ohms. The Vf at rated current will indicate how much Rs exists in ... | https://electronics.stackexchange.com |
259,714 | [
"https://mathoverflow.net/questions/259714",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Let $\text{Part}(X)$ denote the collection of all partitions of $X$. For $A, B\in \text{Part}(X)$ we set $A\leq B$ if $A$ refines $B$, that is for all $a\in A$ there is $b\in B$ such that $a\subseteq b$. This relation defines a lattice structure on $\text{Part}(X)$.
Is there a distributive lattice $L$ such that for no... | In the paper
Ore, Oystein,
Theory of equivalence relations,
Duke Math. J. 9, (1942), 573–627
it is proved that $\textrm{Part}(X)$ is simple. (This is very easy to prove.)
So the only nontrivial quotient of $\textrm{Part}(X)$ is $\textrm{Part}(X)$ itself, which is not distributive when $|X|>2$. Therefore the ans... | Yes. Since $\text{Part}(X)$ has a least element and a greatest element, just let $L$ not have that, e.g., let $L$ be the ordering of the integers.
| https://mathoverflow.net |
361,005 | [
"https://mathoverflow.net/questions/361005",
"https://mathoverflow.net",
"https://mathoverflow.net/users/43158/"
] | Given a smooth, non-vanishing vector field on a compact manifold, when does the 1-dimensional foliation given by its integral curves admit a transverse invariant measure?
I've seen examples of higher-dimensional foliations not admitting transverse invariant measures, but I'd imagine the same question is much easier to... | I think that the best reference for this question is still the (relatively) old paper by Plante <em>Foliations with measure preserving holonomy</em> Ann. of Math. (2) 102 (1975), no. 2, 327–361, although it is a bit of an overkill for one-dimensional foliations. For instance, by Theorem 4.1 holonomy invariant measures ... | As R W says, the answer is in Plante's paper, but the special case of <span class="math-container">$1$</span>-dimensional foliations is actually simple, and well-known: let <span class="math-container">$M$</span> be the manifold, <span class="math-container">$*\in M$</span> be a basepoint, <span class="math-container">... | https://mathoverflow.net |
4,032,570 | [
"https://math.stackexchange.com/questions/4032570",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/826066/"
] | Given <span class="math-container">$x_1 = 1$</span>, it is clear that <span class="math-container">$x_n \ge 1$</span> for any <span class="math-container">$n \in \Bbb{N}$</span>. I know that {<span class="math-container">$x_n$</span>} is obviously increasing and limit as <span class="math-container">$n \to \infty$</spa... | For boundedness from above just note that
<span class="math-container">$$x_n \leq 4\Rightarrow x_{n+1} = 1+\sqrt{x_n} \leq 1+\sqrt 4 =3 \leq 4$$</span>
Now, the claim follows immediately by induction.
| From the recurrence , we can deduce that
<span class="math-container">$$x_2 = 2$$</span>
<span class="math-container">$$x_3 = 1 + \sqrt{2} $$</span>
<span class="math-container">$$ x_4 = 1 + \sqrt{1+\sqrt{2}} $$</span>
<span class="math-container">$$ x_5 = 1 + \sqrt{1+\sqrt{1+\sqrt{2}}} $$</span>
You can continue . Let... | https://math.stackexchange.com |
562,639 | [
"https://physics.stackexchange.com/questions/562639",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/268603/"
] | I'm trying to reconcile how photons do and don't have mass, and the distinction seems to come from the frame of reference. As far as I understand, if you were to somehow stop a photon relative to an observer so that it was at rest, you wouldn't be able to measure its mass, probably for multiple paradoxical reasons, alt... | Photons don't have rest mass because if they did, then they would have an infinite amount of energy. For all particles with mass, it requires an infinite amount of energy to accelerate it to the speed of light. This can be seen from the formula for the energy of a particle, which is of the form <span class="math-contai... | <blockquote>
if you were to somehow stop a photon relative to an observer so that it was at rest
</blockquote>
You <strong>cannot</strong> stop a photon. In special relativity, it's not even possible to consider a situation in which you <em>could</em> stop a photon. A reference frame in which a photon is at rest <stron... | https://physics.stackexchange.com |
17,109 | [
"https://chemistry.stackexchange.com/questions/17109",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1677/"
] | Wikipedia states that waxes can be dissolved by non-polar organic solvents.
I failed to dissolve candle wax in both acetone and ethanol, which are the only organic solvents I have at home.
I have some clothes with wax stuck on them. How can I dissolve the wax and drive it away without damaging my clothing?
| Ethanol and acetone are not non-polar organic solvents. Each one has a slight dipole moment; due to the difference of electronegativity between $\ce{H}$ and $\ce{O}$ in ethanol and between $\ce{C}$ and $\ce{O}$ in acetone. Wax is composed of heavy, long-chain alkanes. And as "Like dissolves like" try to dissolve yo... | Being a chemist, I know that paraffin would require a lipophilic solvent as pointed out by others. It occurred to me that ordinary vegetable oil is a cheap and of course innocuous lipophilic substance. I spilled about 2 oz molten candle wax on a marble surface and after it solidified removed a good portion by scraping ... | https://chemistry.stackexchange.com |
215,974 | [
"https://electronics.stackexchange.com/questions/215974",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/97507/"
] | I need to increment a stopwatch at 10hz using timer1 on a PIC16F628. The external clock is 1Mhz, supplied by a packaged oscillator (EPSON sg8002db). With no prescaler, the value to set the timer to (I think) should be:
clock ticks in 1 second: 1000000
timer ticks in 1 second: 250000 (clock/4)
timer ticks in 1/10th o... | Instead of using the 16-bit timer 1, which requires you to reload the value in code, use the 8-bit timer 2, which has a preset register PR2. Load PR2 with 250, with a prescaler value of 1:1. It will then interrupt every 1 ms and reload it self automatically so no latency problems.
The inside your interrupt, just inc... | instead of resetting timer 1 just update the alarm to be 0.1s further in the future
| https://electronics.stackexchange.com |
100,950 | [
"https://electronics.stackexchange.com/questions/100950",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37803/"
] | When I am done with a circuit and want to build another, should I remove power from the Arduino or can I just remove the unnecessary parts and start plugging in the necessary parts?
| It is best to remove power while re-wiring a circuit, so, yes, disconnect the USB cable, and any other sources of power.
While disconnecting and re-connecting things, you may introduce short circuits, or put the circuit in undesirable states (eg disconnecting power to a chip while leaving power on its I/O pins, thus p... | If you do not remove power during changing your circuit elements on the Arduino, you might have risk of putting a positive in a negative and negative in a positive, or do other type issues:
<ol>
<li>Short Ciruiting</li>
<li>Over Powering the Arduino board from a wrong Vcc power source</li>
<li>Causing a circuit to go ... | https://electronics.stackexchange.com |
373,933 | [
"https://softwareengineering.stackexchange.com/questions/373933",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/310162/"
] | I'm having trouble understanding how to provide an API to 3rd parties in order to allow extensions for desktop applications. I understand that if I'm using a compiled language (e.g. C++), I can load dynamic libraries as extensions at runtime, provided they link against my library and provide a well-defined API that the... | I work on an API for a video editing application. We have separate SDKs (and hence APIs) for different types of extensions. There's one set of APIs for image/video processing. There's another set of APIs for importing video of different formats into the application. There's another set of APIs for exploring the documen... | A plugin API is very much like a (fully) abstract base class. It might even be expressed as an abstract base class. You require the plugin export functions of a given name and signature. Your application then calls these functions
<pre><code>extern void Frobnicate(Frobber frob);
extern Bazzer MakeBazzer();
</code></pr... | https://softwareengineering.stackexchange.com |
392,780 | [
"https://physics.stackexchange.com/questions/392780",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | If entropy must increase for any real process and natural processes move from order to disorder then the early universe must have been "highly ordered". However, when I think of the extremely dense and hot singularity known as the big bang the word ordered doesn't come to mind. Can anyone help me make sense of this?
| While the matter/energy contents of the universe started in a very high entropy state, the spacetime was apparently very smooth and hence low entropy. As the universe expanded not only did the bound on entropy increase (as J.G. points out) but it also allowed clumping of matter that increased the spacetime entropy but ... | As the universe has expanded, its maximum allowable entropy has grown in proportion to its squared radius. Entropy has grown, but relative to size it has fallen, making the universe more ordered.
| https://physics.stackexchange.com |
465,700 | [
"https://physics.stackexchange.com/questions/465700",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/225113/"
] | If you had two identical video cameras and started recording synchronized atomic clocks recording at the same speed and you put one on the spaceship and sent it out traveling at 99% of the speed of light for a while and left the other one on earth both recording the whole time, when the spaceship returned and you playe... | <blockquote>
Why do we assume the reflected and transmitted waves are sinusoidal
</blockquote>
This has no <em>a priori</em> justification - it is simply a useful Ansatz, and it gets all of its validity <em>a posteriori</em> when we use this Ansatz to build useful solutions of the Maxwell equations.
In other words,... | The waves are not necessarily sinusoidal but can always be written as a linear expansion of these. The amplitude/phase version, not the squared, Fresnel equations are then applied to each component. Note that the frequency is not affected by the medium. Also momentum parallel to the interface cannot change, as this wou... | https://physics.stackexchange.com |
90,032 | [
"https://cs.stackexchange.com/questions/90032",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/84399/"
] | I know that the answer is no but I'm not sure why. Here's where I started. We know that all data with length $n$ Bits and minimum $1$ Bit can be compressed, either lossless or lossy. But how do I continue? Why is it impossible to compress all the data without loss?
| There are $2^n$ bitstrings of length $n$, but only $2^n-1$ bitstrings of length smaller than $n$. Hence there is no one-to-one mapping which maps every bitstring of length $n$ to a bitstring of strictly smaller length. In other words, for any (lossless) compression scheme there will always be a string which it doesn't ... | Each string of bits can also be a number.
Then we add pigeonholes. For each possible original message create a pigeon. For a message up to $n$ bits that is $\sum^n_{i=1} {2^i}=2^{n+1}-2$ pigeons.
Now create a pigeonhole for each possible compressed message. If you <em>have</em> to compress (compressed message always... | https://cs.stackexchange.com |
191,262 | [
"https://mathoverflow.net/questions/191262",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7206/"
] | In the early 20th century there was a lot of fuss over the axiom of choice implying that there are Lebesgue non-measurable sets of reals. In his book about The Axiom of Choice, Gregory Moore points to the following paper:
<blockquote>
Sierpinski, W. <strong>"L’axiome de M. Zermelo et son rôle dans la théorie des ens... | Here's Sierpinski's argument: Let $h:[\mathbb{R}]^{\omega} \to \mathbb{R}$ be any injection. Define $f:\mathbb{R} \to \mathbb{R}$ by $f(x) = h(E_x)$ where $E_x$ is the set of all reals which are at a rational distance from $x$. Note that $x - y$ is rational iff $f(x) = f(y)$. Towards a contradiction, suppose $f$ is Leb... | A reprint of the mentioned paper can be found in: W. Sierpinski, Oeuvres choisies Tome II, PWN--Editions Sci. Pologne, Warszawa, 1975,
pp. 208-255
| https://mathoverflow.net |
103,182 | [
"https://mathoverflow.net/questions/103182",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20356/"
] | An acyclic category (also called loopfree category or scwol (small category without loops)) is a small category where only identity morphisms have inverses, and any morphism from an object to itself is the identity.
Every poset P can be regarded as an acyclic category by identifying the set of objects with the element... | One thing that has come up a little bit in my work and I believe also e.g. in work of Dmitry Feichtner-Kozlov is such an extension of the widely used fact (popularized by Gian-Carlo Rota) that the Moebius function $\mu_P(x,y) $ of a poset $P$ may be interpreted as the reduced Euler characteristic of a simplicial comple... | This is not a generalization of posets, but an illustration of how they come up unexpectedly.
There is a notion of subdivision of a (small) category, and the second subdivision of any
category is a poset. This was folklore in the early 1960's. It plays a role in Thomason's
Quillen equivalence between the category of... | https://mathoverflow.net |
120,150 | [
"https://cs.stackexchange.com/questions/120150",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/115048/"
] | I am trying to figure out a formal grammar for the above language. This language describes palindromes, so it is context-free, if I am not wrong. I came up with a context-sensitive grammar, but I can not find a context-free one. Any ideas?
| The languages of all palindromes is context-free.
That does not implies that any language that contains only palindromes is context-free. For example, many language over the unary alphabet <span class="math-container">$\{a\}$</span> are not context-free. In fact, they can even be non-context-sensitive or undecidable.... | How about <span class="math-container">$\{a^{\Sigma(n)} \colon n \ge 1\}$</span>, where <span class="math-container">$\Sigma$</span> is Radó's noncomputablr busy-beaver function?
| https://cs.stackexchange.com |
908,305 | [
"https://math.stackexchange.com/questions/908305",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/116309/"
] | How can one build a subset $A\subset [0,1]\times[0,1]$ containing at the most one point from each horizontal and each vertical section and whose boundary (frontier) is $[0,1]\times[0,1]$?
I don't know how to build this set. I know that if $A$ contains points in each quarter of the square it's enough.
| Let $\alpha, \beta$ be two irrationals such that $\alpha/\beta$ is also irrational. What can one say about the set
$$A=\{(n\alpha \mod 1,n\beta\mod 1):n\in \Bbb Z\}?$$
<em>Edit:</em> probably I should give some more hints:
<ol>
<li>The fact $A$ contains at most one point in each vertical/horizontal stripe follows by ... | You can also do this by constructing a function $f: [0, 1] \rightarrow [0, 1]$ such that $f$ is identity on irrationals, $f$ restricted to rationals is a bijection and the graph of $f$ is dense in the unit square. Just list a countable basis $\{B_n : n \geq 1\}$ and indutively ensure that the graph of $f$ picks a point... | https://math.stackexchange.com |
634,491 | [
"https://physics.stackexchange.com/questions/634491",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/149630/"
] | In machine vision, you can use linear lasers as sheets of light to infer an object's 3D position or shape. (AFAIK it's just a laser beam stretched in one direction using optics.) Those are usually Class 3 or lower, and they're almost always based on laser diodes. Some of those lasers have a power regulation input. By c... | What source are you using in this derivation? Wikipedia, for example, uses the same notation as you, <span class="math-container">$e^{i\pi/4}\begin{pmatrix}1&0\\0&-i\end{pmatrix}$</span>, for the fast-axis vertical case and <span class="math-container">$e^{-i\pi/4}\begin{pmatrix}1&0\\0&i\end{pmatrix}$</... | Your rotated matrix and the wiki one are indeed equal, but you dropped a minus sign on the phase term outside of the wiki matrix. Otherwise if you factor an i out of your rotated matrix they appear to be the same.
| https://physics.stackexchange.com |
118,651 | [
"https://security.stackexchange.com/questions/118651",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/83600/"
] | There is a huge number of articles advising to enable two-factor authentication on sensitive cloud services. I understand the benefits for my accounts' security, but doesn't it defeat the purpose of cloud backups ?
For example, if both my phone and my laptop get stolen (not far-fetched), I just lost my two-factor auth... | If your concern is avoiding losing all of your physical assets (laptop, phone, etc...) you could simply encrypt your files using any software you like and then upload redundant copies to two or more storage services which you think are the most stable and secure. That said naturally you would want to choose a great enc... | I suppose you have a copy of the key of your home. And I suppose you have already given such a copy to someone you trust (wife/husband, parents, etc.). I know that there is a slight difference between a physical lock and a file in the cloud: if you loose you key, you could try to break the lock/the door, while if you a... | https://security.stackexchange.com |
87,789 | [
"https://mechanics.stackexchange.com/questions/87789",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/67709/"
] | I've been told that if you use the 2-man method for bleeding brakes (one man at the bleed valve with a PVC tube over the nipple, one pumping pedal) you can damage the seals as "the brake shaft goes further than it's intended". They went on to say you should never press the brake pedal all the way down to the ... | In my opinion the 2 man method is the best. There is validity to the "shaft" concern. The shaft would be the master cylinder piston. It has a normal use area. If you press the pedal all the way down you are using the cylinder in an area that can cause friction possibly causing it to become stuck. The remedy f... | I've never heard this and have used the "two man method" many times before acquiring a vacuum bleeder.
I suppose it's possible, somehow, to damage things but I don't see how routine bleeding could do so.
| https://mechanics.stackexchange.com |
101,067 | [
"https://mathoverflow.net/questions/101067",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10400/"
] | Let $G$ be a reductive group over a local non-archimedean field $F$.
Can every irreducible supercuspidal representation of $G(F)$ be realized as the induction from an open subgroup, which is compact modulo the center?
| It is known for GL(N) and SL(N) (Bushnell and Kutzko), for classical groups when the residue characteristic is not $2$ and when no quaternionic algebra is involved (Stevens), for GL(N) of a division algebra (Stevens and Sécherre), for a general reductive group when the residue characteristic of $F$ is large enough (Ki... | It is perhaps worth noting that all the proofs Broussous mentions are along the lines of: Construct some types that induce irr scs and then show that all irr scs are thus obtained. In other words they are explict constructions. But that is stronger than the original question asked. One might hope that there would be a ... | https://mathoverflow.net |
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