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 |
|---|---|---|---|---|---|
141,236 | [
"https://mathoverflow.net/questions/141236",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5984/"
] | Let $e$ be an index of an oracle Turing machine program and $k$ be some natural number. Let us say that a subset of $\mathbb N$ is <em>arithmetic</em> if it is definable in the model $\langle \mathbb N,+,\cdot,<,0,1\rangle$. Now suppose that there is a non-arithmetic oracle $A$ such that $\Psi_e^A(k)\uparrow$. Is it... | Consider an oracle Turing machine $M$ which enumerates its oracle $A=\{n_0<n_1<n_2<\dots\}$ by querying every $n\in\omega$ in increasing fashion, and whenever it hits a new element $n_k\in A$, it halts unless all the following conditions are met:
<ul>
<li>$n_k$ is the Gödel number of a finite set $T_k$ of ari... | To give a more recursion-theoretic answer, the stronger statement in which "arithmetic" is replaced by "hyperarithmetic" also holds. Take a recursive subtree $T$ of the finite increasing sequences of natural numbers such that $T$ has infinite paths but has no infinite hyperarithmetic path. Consider the oracle Turing ... | https://mathoverflow.net |
462,686 | [
"https://physics.stackexchange.com/questions/462686",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65337/"
] | By the Leibniz rule, I expected it to be
<span class="math-container">$$\delta \Gamma^\sigma_{\mu\nu} = \frac 12 (\delta g)^{\sigma\lambda}(g_{\mu\lambda,\nu}+g_{\nu\lambda,\mu}-g_{\mu\nu,\lambda}) + \frac 12 g^{\sigma\lambda}(\partial_\nu (\delta g)_{\mu\lambda}+\partial_\mu (\delta g)_{\nu\lambda}-\partial_\lambda (... | <ul>
<li>The difference between two connections is a tensor, so <span class="math-container">$\delta\Gamma$</span> is a tensor.</li>
<li>Evaluate your variational formula in Riemannian normal coordinates at some arbitrary point <span class="math-container">$x_0$</span>. Since the metric derivatives are zero at that poi... | <span class="math-container">$ \Gamma^{a}_{bc} = \cfrac{1}{2}g^{ad}(\partial_{b}g_{dc} + \partial_{c}g_{bd} - \partial_{d}g_{bc}) \Rightarrow $</span><br />
<span class="math-container">$ δ\Gamma^{a}_{bc} = \cfrac{1}{2}δg^{ad}(\partial_{b}g_{dc} + \partial_{c}g_{bd} - \partial_{d}g_{bc}) + \cfrac{1}{2}g^{ad}(\partial... | https://physics.stackexchange.com |
271,026 | [
"https://softwareengineering.stackexchange.com/questions/271026",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/108340/"
] | I have a ServiceCallContext object that must be passed in as the first parameter of any service call. I would like to put a User object on the context object but I know I can't force the caller to send back the User object they received from the service and I can't prevent them from filling that in with any information... | Lets assume you are testing a class "interval", representing intervals of natural numbers:
<pre><code> var interval= new Interval(1,100);
</code></pre>
Now your first two tests are "green":
<pre><code>AssertIsTrue(interval.Contains(100))
AssertIsFalse(interval.Contains(101))
</code></pre>
and you are confident the ... | <blockquote>
In boundary analysis testing, some authors suggest testing MIN-1, MIN, MIN+1 (and the same for MAX) ... I do not see the point
</blockquote>
The point is that your code is <em>expected</em> to fail for values outside the permitted range and that's what you're testing with these "extra" cases.<br>
Not ev... | https://softwareengineering.stackexchange.com |
11,393 | [
"https://mechanics.stackexchange.com/questions/11393",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/6487/"
] | I have a 2008 Suzuki Intruder (VL250) that is really struggling to run in the cold weather. It stalls and dies, loses power while riding, and dies while waiting at the lights. When I warm it up, even with the choke on full and the idle high, it still chokes and dies after a few minutes. I have to keep the revs up and c... | It is a carburetor problem, but only because the fuel and air mixture is too lean. In cold environment there is more oxygen in the air, which increases the amount of "air" in the air-fuel mixture. This is further proven by the fact you have to accelerate to keep the bike alive - by accelerating you use parts of the car... | I think you need a new stator. Your problem sounds like there are loose connections or there may be reason that the bike is not charging properly. I think you start checking all the basics first and check the battery to make sure it is good. Check the volts on your battery with voltmeter.
| https://mechanics.stackexchange.com |
28,576 | [
"https://cs.stackexchange.com/questions/28576",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/15659/"
] | I'm more concerned with just finding big oh since that can be used to find big omega. I am also told I cannot use limits to find the answer.
I'm given:
$3+9+27+\dots+3^n$. My first assumption is that $3^n = \Theta(3^n)$. The method we're supposed to use goes something like this:
$3+9+27+\dots+3^n<3^n+3^n+\dots+3^n... | First, your assumption, <code>I'm more concerned with just finding big oh, since that can be used to find big omega</code> is a bit dangerous. You could indeed easily find a $O()$ upper bound for your sum, $S(n)=3^1+3^2+3^3+\cdots+3^n$ by observing that each term is less than $3^n$ so you could have
$$
3^1+3^2+\cdots+... | Hint: use the formula for the sum of a geometric series.
Note that, when you write $3^n + \dots + 3^n$, you have $n$ terms so that sum evaluates to $n3^n\notin\Theta(3^n)$.
| https://cs.stackexchange.com |
60,860 | [
"https://physics.stackexchange.com/questions/60860",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22381/"
] | why cosmic background radiation is not ether? I mean it's everywhere and it' a radiation then we can measure Doppler effect by moving with a velocity.
| The luminiferous aether was, by definition, a hypothesized medium that was <em>needed</em> for electromagnetic waves to propagate through space. The cosmic microwave background isn't needed for photons to move; indeed, they move through space even if one removes (shields) the cosmic microwave radiation. So that's why C... | There are a couple of misconceptions here. The CMB radiation is thought to be the (historical) light left over after the big bang. Due to space expansion, it has been red-shifted towards the microwave region of spectrum. While on the other hand, ether is the medium required for light to travel when it was thought as a ... | https://physics.stackexchange.com |
46,827 | [
"https://electronics.stackexchange.com/questions/46827",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10190/"
] | My friend, who is interested in jet engines and welding is getting is working on a jet car, or something along that lines. I am just working on the electronics because I like the circuit building and like to understand how that works. I am wondering how controlling motors or relays or solenoids with a remote controller... | Nowadays, you don't just broadcast each signal on a different frequency. You send a digital stream that includes instructions for whatever you want to control. For example, a number proceeded by a 1 byte might control valve 1, a 2 byte valve 2, etc. You have to figure radio messages will occasionally get garbled or ... | There are basically three stages to this:
<ul>
<li>The analogue side of radio transmission and recieving: the basics of producing a signal at a particular frequency, and tuning into it.</li>
<li>Modulation: the basic types are AM and FM. When used to carry digital signals, these become ASK and FSK. Mobile phones and w... | https://electronics.stackexchange.com |
80,501 | [
"https://mathoverflow.net/questions/80501",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19149/"
] | Let $X_t$ be a sequence of i.i.d. random variables with mean $\mu$. Then the law of large numbers states that
$$\lim_{T \to \infty} \frac1T \sum_{t=1}^T X_t = \mu \quad a.s.$$
Now suppose that (in a game theoretic context) an agent can choose at every instant of time if she wants to observe $X_t$ or not. I want to pr... | Using John's notation, and assuming $\{X_{\sigma(i)}\}$ are independent, then $X=(X_1,X_2,\ldots)$ has the same distribution as $X_\sigma=(X_{\sigma(1)},X_{\sigma(2)},\ldots)$. Let $f(X)=\limsup_{n\rightarrow\infty}(X_1+\cdots+X_n)/n$. Then $f(X_\sigma)=\limsup_{t\rightarrow\infty}Y_t/N_t$, and $\mathbb P[f(X_\sigma)=\... | Wrong solution. See James' below. I'll just add that to show independence for say $X_{\sigma(1)},X_{\sigma(2)}$, $E(E(f(X_{\sigma(1)}) g(X_{\sigma(2)})|X_{\sigma(1)})) = E( f(X_{\sigma(1)}) E(g(X_{\sigma(2)}| X_{\sigma(1)}))$. It would suffice to show $E(g(X_{\sigma(2)})|X_\sigma(1)) = E(g(X_1))$. This can be done by c... | https://mathoverflow.net |
497,930 | [
"https://electronics.stackexchange.com/questions/497930",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/251662/"
] | I am wanting to measure the energy consumption of running some intensive blocks of code on Android, but I am very shakey with my electricity knowledge, so I am unsure what measurements I should be looking for.
In the Android settings,they give power consumption in mAh. An academic paper I am looking at gives energy co... | Amp hours can be multiplied with the battery voltage to get the Watt hours, for a lithium battery in a phone this can generally be assumed to be 3.6V as this is the average voltage for most lithium batteries over there discharge curve, so on average your code will draw that much watt hours.
As this is a constant, you ... | Energy consumption measures <em>energy</em>. Full stop – if the paper measures anything else than energy, it's mislabeling it.
Energy has the SI-derived unit J (joule), which is 1 J = 1 W·s; the rest is trivial conversion of units. I don't know what to explain about that – having a clear understanding of what power is... | https://electronics.stackexchange.com |
311,099 | [
"https://physics.stackexchange.com/questions/311099",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/118807/"
] | In the derivation of the equilibrium concentration of vacancies by statistical mechanics method, I was stumped by this procedure (marked by "?").
$\textbf{Physical Model}:$
1.Solid viewed as a collection of $N$ atomic sites;
2.Each site may or may not be occupied, and assume now that $N_o$ sites are occupied and $N_... | <blockquote>
Why we don't consider the internal energy of the whole system rather than the vacancies?
</blockquote>
Every atom being exactly at a crystalline site represents the minimum energy configuration. (Aside: This configuration only happens at absolute zero temperature.) What this energy is is irrelevant; it'... | Calculate the ratio of the number of vacancies in equilibrium at 27 C in aluminum to that produced at 527 C. The energy of the formation of vacancies in aluminum is 68 kJ/mol
| https://physics.stackexchange.com |
5,326 | [
"https://chemistry.stackexchange.com/questions/5326",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1617/"
] | <blockquote>
Which ions do not react with each other in solution?
A. <span class="math-container">$Ba^{2+},SO_4^{2-},NO_3^-$</span>
B. <span class="math-container">$Cu^{2+},SO_4^{2-},OH^-$</span>
C. <span class="math-container">$Ag^+,Cl^-,H^+$</span>
D. <span class="math-container">$K^+,Fe^{3+},Br^-$</span>
</blockquot... | I believe the question is slightly misleading, non of the ions <em>react</em> however some do <em>precipitate</em>.
BaSO<sub>4</sub>, Cu(OH)<sub>2</sub> , and AgCl will precipitate in A, B, and C respectively.
| The question (and its choices) are bogus. One can make species (and solutions) of all of these combinations of cations with anions.
| https://chemistry.stackexchange.com |
235,127 | [
"https://stats.stackexchange.com/questions/235127",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/131164/"
] | I have a dataset with a dependent and an independent variable. Both are not a time series. I have 120 observations. The correlation coefficient is 0.43
After this calculation, I have added a column for both variables with the average for every 12 observations, resulting in 2 new columns with 108 observations (pairs). ... | Let's have a look at two vectors, the first being
<pre><code> 2 6 2 6 2 6 2 6 2 6 2 6
</code></pre>
and the second vector being
<pre><code> 6 2 6 2 6 2 6 2 6 2 6 2
</code></pre>
Calculating the Pearson correlation you'll get
<pre><code>cor(a,b)
[1] -1
</code></pre>
However if you take the average of succes... | Averaging can be attractive or convenient. It can also be a source of deception, at worst deceit, so tread carefully even when there is a clear rationale for averaging.
Here is a situation it which it is not a good idea. Consider that by careful definition of groups you (usually) could reduce your data to two summary... | https://stats.stackexchange.com |
332,960 | [
"https://math.stackexchange.com/questions/332960",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/8122/"
] | Is it possible to write this in closed form:
$$\sum_{k=0}^{n} k\binom{n}{k}\log\left(\vphantom{\Huge A}\binom{n}{k}\right)$$
Can you get something like $$n2^{n-1}\log(2^{n-1})$$
| <strong>Warning!</strong>
I couldn't find a closed form. An approximation is described below.
<hr>
You may start by symmetrizing the summand to get
$$\sum_{k=0}^{n} k\binom{n}{k}\log\binom{n}{k}={n\over 2}\sum_{k=0}^{n} \binom{n}{k}\log\binom{n}{k}.\tag1$$
The terms in the sum on the right hand side of (1) are sy... | If $f(n)$ is your sum, then $e^{f(n)}$ becomes an integer product, say $p(n)$, formed by multiplying each binomial coefficient $\binom{n}{k}$ to the power $k \cdot \binom{n}{k}.$ That is,
$$p(n)=e^{f(n)}=\prod_{k=0}^n \binom{n}{k}^{k \binom{n}{k}}.$$
The first few terms are
$$p(1)=1,\ p(2)=2^2,\ p(3)=3^9,\ p(4)=2^{44}3... | https://math.stackexchange.com |
46,831 | [
"https://dsp.stackexchange.com/questions/46831",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/33600/"
] | I have two scalars $x$ and $y$ that vary with time $t$ such that
\begin{align}
\frac{dx}{dt} &= ay + b + dx\\
\frac{dy}{dt} &= cx
\end{align}
but $a, b, c$ are unknown.
If $d$ is too small, the system will be underdamped (and oscillate badly), but if $d$ is too large, the system is overdamped, and doesn't co... | First, combine your two variable set of first order differential equations into a single variable second order one.
$$ \frac{d^2y}{dt^2} = c \frac{dx}{dt} = acy + bc $$
$$ \frac{d^2y}{dt^2} - acy = bc $$
Solve:
$$ y(t) = C_1 e^{\sqrt{ac} \cdot t} + C_2 e^{-\sqrt{ac} \cdot t} - \frac{b}{a} $$
$$ x(t) = \int{ ( ay(t... | An empirical approach:
I'm adding a new answer as it is completely different in nature.
It seems you have a system you are studying where you can vary one parameter (or more?) to control the dampening rate, and you are looking for the best setting, i.e. finding the critical dampening. This is where the roots of the ... | https://dsp.stackexchange.com |
332,365 | [
"https://softwareengineering.stackexchange.com/questions/332365",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/248027/"
] | I am working on a piece of server software that is licensed under the AGPL. I would like to require that all clients to it be released under a free license (GPL preferable, but I'm open to other licenses).
Is there a way to do this? Is there a standard way to do this?
| The short answer is no, especially not if you expect others to build the clients.
If you are building this server software with the intention of others building clients, they are communicating at arms length with each other, and are therefore seperate works and so the requirements of the AGPL do not apply to the clien... | Per the discussion in the comments of the question, I think the only recourse is to make a requirement in the Terms of Service for accessing the server.
The license of the server can't impose additional restrictions on the client as they are another separate piece of software. Even if it could, the AGPL provides for ... | https://softwareengineering.stackexchange.com |
368,579 | [
"https://stats.stackexchange.com/questions/368579",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | A car hire firm has three cars, which it hires out on a daily basis. Number of cars demanded per day follows a poisson distribution with mean 2.1
a) Find the probability that all cars are in use on any one day.
b) Find the probability that all cars are in use on exactly three days of a five day week.
What I tried:
... | Let <span class="math-container">$X\sim Pois(\lambda = 2.1)$</span> be a Poisson random variable with mean <span class="math-container">$\lambda = 2.1$</span>.
a) Let <span class="math-container">$A$</span> be the event all cars are hired in one day. Your mistake is only calculating the probability that <span class="m... | Because, in (a), you need to calculate <span class="math-container">$P(X\geq 3)$</span>, which is 0.35 nearly. If the number of requests coming is greater than 3, you still give your three cars. You don't have to have three requests exactly. For (b), you continue with classical binomial.
| https://stats.stackexchange.com |
277,766 | [
"https://mathoverflow.net/questions/277766",
"https://mathoverflow.net",
"https://mathoverflow.net/users/84871/"
] | I have three equations:
${m \choose 2} + nk = {x \choose 2}$
${n \choose 2} + mk = {y \choose 2}$
$x + y = m + n + k$
$m, n, k, x, y$ are natural numbers. I want to deduce from this 3 equations either $x = y$ or $m = n$. From where I got these equations makes me sure that this is only possible if $x = y$ and $m = ... | The first two equalities imply $x>m$ and $y>n$ so one can substitute $x=m+X$, $y=n+Y$ and $k=X+Y$, with still $X,Y \in \mathbb N$:
${X \choose 2}=nX+nY-mX\tag{1}$
${Y \choose 2}=mX+mY-nY\tag{2}$
From (1) follows: $\quad m=n+n\frac{Y}{X}-\frac{1}{X}{X \choose 2}$,
then eliminate $m$ from (2): $\quad {Y \choose... | Rewrite the system of equations.
$$\left\{\begin{aligned}&m(m-t)+2n(x+y-m-n)=x(x-t)\\&n(n-t)+2m(x+y-m-n)=y(y-t)\end{aligned}\right.$$
The solution of this system can be written as.
$$n=(-8a^3+12ba^2-6ab^2+2b^3)p+(4a^2-5ab+b^2)s$$
$$m=(8a^3+2ba^2-ab^2)p+(4a^2-5ab+b^2)s$$
$$t=(-8a^3+12ba^2-6ab^2+2b^3)p+(12a^... | https://mathoverflow.net |
137,443 | [
"https://softwareengineering.stackexchange.com/questions/137443",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I'm a PHP developer with familiarity with Rails and a focus on MVC development. My company is moving more and more to SharePoint and I feel I need to learn to build application within the SharePoint system.
I have some brief introduction to C# but that's about it. I've used some SharePoint Designer and the web interfa... | First: there are multiple implementations of Lisp, each of which may have different evaluation models. I believe SICP mostly uses Scheme.
Exercise 1.6 does <em>not</em> imply that Scheme uses normal order -- it's about a special form (<code>if</code>). For special forms, the evaluation can be neither of applicative... | <blockquote>
because normal-order evaluation becomes much more complicated to deal
with when we leave the realm of procedures that can be modeled by
substitution.
</blockquote>
To put this differently, consider
<pre><code>let x = (print "ha", print "ho") in x
</code></pre>
The question is, does this print a) n... | https://softwareengineering.stackexchange.com |
250,570 | [
"https://softwareengineering.stackexchange.com/questions/250570",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/99672/"
] | In a project that I have started working on, the database has a lot of <code>FooDefinition</code> tables which act like an enum. It's a C# project using Entity Framework although that is not central to the question.
The entities have an ID, a string Name field and an int Type field that is converted to an enum. For ex... | There are several issues that need to be resolved.
<strong>Categories</strong>
The usual use of categories is to identify classes or groups of records. If you create reports, having the values kept in a category table makes it easy for report generators or external data warehouses to properly categorize items.
<stro... | I see three reasons
1) As jimwise says, they can be changed without recompiling.
If they are actually used as enum values in application (do something if it equals that), only usefull thing to change without recommpiling is their name.
2) they CAN contain more than name and id, but two cannot have same id unlike C# s... | https://softwareengineering.stackexchange.com |
120,781 | [
"https://softwareengineering.stackexchange.com/questions/120781",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2568/"
] | I have been working on a integration that has posed an interesting user interface conundrum that I would like suggestions for.
The user interface is displayed within a third party product. The state of the interface is supplied by calls to a service I have written. There can be small delays between the actual state ch... | Just for the purposes of posterity, I'll share the solution.
<h1>Race Condition</h1>
The problem here is that the polling mechanism occurs every <em>n</em> milliseconds, and a request may be in-flight when a user clicks, causing a race condition.
Happy path (button is enabled, then disables and stays that way):
<ul... | Immediately show <em>some</em> feedback: change the visual state of the button, display an animated throbber.
If the app logic allows, disable the button once it has been pressed, enable it back when the answer arrives.
Once the answer has arrived, show the <em>real</em> feedback: update the controls, remove the thr... | https://softwareengineering.stackexchange.com |
2,430 | [
"https://physics.stackexchange.com/questions/2430",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/871/"
] | I've always heard that watering plants if the temperature goes a few degrees below freezing will help prevent them from freezing, but I've never quite understood the physics behind it. Can you guys help me to understand this a bit better? Thanks!
| If the temperature is not much below freezing, the rate of heat transfer from your plants (and particularly from the earth around their roots) is low, if there is a lot of water present, the high heat of fusion means that it will take a long time to actually freeze much of it. So maybe the plant makes it through the ni... | While this may be true, a better option is actually to spray your plants with water. When water freezes, it releases heat (a little counterintuitive, I know, but that's why you have to put water in a cold place to freeze it - you have to take away heat). So, if your plants have a thin layer of water on them that freeze... | https://physics.stackexchange.com |
4,492 | [
"https://physics.stackexchange.com/questions/4492",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1729/"
] | We have learned that Torque is equal to a force that is perpendicular to a radius (displacement); however, I just cannot grasp one of the study questions we received:
<blockquote>
A hammer thrower accelerates the
hammer (mass = 7.30 kg) from rest
within four full turns (revolutions)
and releases it at a speed of 30.0
... | You know the tangential and centripetal acceleration so it's good to use these directions as base. And you know that the direction of the force is the same as the acceleration. Meaning, you have the direction of the force in the plane the hammer is rotating $\vec{v} = (-600, 11.94)$. In this same plane you know the dir... | For linear acceleration you know you find distance by<br>
Distance = 0.5 x acceleration x time^2
That would solve your problem for the linear case. Try looking around for something similar in the rotational case. There are a bunch of ways of doing the problem even starting with my hint.
| https://physics.stackexchange.com |
134,953 | [
"https://electronics.stackexchange.com/questions/134953",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/31312/"
] | I have a 555 timer set up in a standard monostable oscillator configuration. Nothing fancy, no modifications whatsoever. I'm driving it with about 12V. If I trigger the 555 with the ground directly, everything works as planned. However. if I connect the collector of a transistor to pin 2, the emitter of that transistor... | <blockquote>
The overheating only happens with 12V, which I'm getting from a hobby
power supply normally used for a train. My meter reads ~11.5V on the
supply.
</blockquote>
I have a suspicion that the sort of power supply used for a model tranin may be un-smoothed rectified DC. You meter reads 11.5 VDC but the ... | I'm with Andy on this one. To fix it, I'd recommend a 5V regulator powering the 555 circuit. You could replace the 12v train supply with a regulated supply, but once you start running trains on the track you'll find significant spikes and noise which might also damage the CMOS 555.
Use a 7805 or similar linear regulat... | https://electronics.stackexchange.com |
61,499 | [
"https://dba.stackexchange.com/questions/61499",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2502/"
] | Can I have data guard system like:
Primary: 11.2.0.1
Standby: 11.2.0.3
In logical standby ?
In physical standby versions(releases) must be the same?
| The physical standby database must be physically the same as the primary database and this means the versions must be identical.
A logical standby database can be any version, depending on how it is implemented. With 3rd party tools you can go from v10 to v12 and back. The restrictions here are on the data types that ... | Physical:
"Differences between the primary server(s) and the standby server(s) are always supported as long as the Oracle software installed on all servers is of the same Oracle Platform as defined above, is certified to run on each server, and is the <strong>same Oracle Database Release and Patch Set</strong>."
Logi... | https://dba.stackexchange.com |
274,871 | [
"https://stats.stackexchange.com/questions/274871",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/119747/"
] | "A simple linear regression model was fitted with an intercept equal to -17 and slope equal to 2.37. Calculate the value of the residual when X = 11 and the observed value of Y at that value of X is 12. Use 2 decimal places. "
Got this question from a lecturer in an exam and nobody got it emailed her after and she sai... | The lecturer states that the observed value of Y is 12 (when X is 11).
| From the question we can see that the modeled relationship between Y and X is:
$Y = a + bX +u$, where a is the intercept, b is the slope coefficient, and u is the error.
This equation was estimated and the predicted values are:
$\hat{Y} = -17 + 2.37*X$
Residuals = $Y - \hat{Y}$
In this case:
Residual = 12 - (-17 ... | https://stats.stackexchange.com |
21,724 | [
"https://stats.stackexchange.com/questions/21724",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6446/"
] | I'm reviewing a conference paper (not a stats conference). The authors have done some funny things with their methodology. The experiment setup has 4 treatments, each applied to the same 30 subjects. This is repeated in 10 different circumstances.
ANOVA is used to determine whether the choice of treatment has any effe... | Whether you should combine 10 different ANOVA's into a single ANOVA depends on what the scientific question is. Remember there are assumptions that go into ANOVA models, one is equal variances, if the 10 different conditions lead to widely different variances then combining them into a single analysis may violate the ... | <ol>
<li>Yes, they should do multiple testing correction for trying to show the differences in 10 different conditions. This is assuming that they tried 10 conditions, with the starting hypothesis that some of them may show a difference. If the starting (a priori) hypothesis of their experiments was that this one parti... | https://stats.stackexchange.com |
29,982 | [
"https://mathoverflow.net/questions/29982",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2559/"
] | Let $n\geq 2$ be a positive integer. For the purposes of this definition, let a <em>colored graph</em> be a finite undirected graph in which each edge is colored with one of $n$ colors so that no vertex is incident with two edges of the same color. (Without loss of generality, we suppose that every vertex is incident ... | If you wanted this for directed graphs, I would say this:
As Andy Putman suggests, look at Stallings Inventiones paper "The topology of finite graphs."
A directed graph colored with $n$ colors admits an obvious map to a colored oriented wedge of $n$ circles, $X$ say.
Given two directed colored graphs, the fiber prod... | If these were digraphs with one outgoing edge of each color at each vertex rather than undirected graphs with one incident edge of each color at each vertex, then this construction would be the Cartesian product of deterministic finite automata. It's useful for showing that regular languages are closed under union and ... | https://mathoverflow.net |
592,736 | [
"https://physics.stackexchange.com/questions/592736",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/279346/"
] | here is my question:
Im trying to find the matrix elements of the momentum operator <span class="math-container">$\hat{P}$</span> in the position basis <span class="math-container">$|x\rangle$</span>:
<span class="math-container">$$\langle x|\hat{P}|x'\rangle := \langle x|\hat{P}\int dp|p\rangle \langle p|x'\rangle=\la... | I'm proceeding the same way as you did:
<span class="math-container">$$\hat{p}|x'\rangle=\int\hat{p}|p\rangle\langle p|x'\rangle dp=\int p|p\rangle\frac{1}{\sqrt{2\pi}}e^{-ipx'}dp$$</span>
<span class="math-container">$$\langle x|\hat{p}|x'\rangle=\int p\langle x|p\rangle\frac{1}{\sqrt{2\pi}}e^{-ipx'}dp=\frac{1}{2\pi}\... | This is a well-known result, though I don't believe it's usually introduced in most introductory level quantum mechanics texts like Griffiths or Shankar. To answer your questions:
<ol>
<li>Yes, <span class="math-container">$(1)$</span> is equal to <span class="math-container">$(2)$</span>, though you should know that ... | https://physics.stackexchange.com |
73,226 | [
"https://mechanics.stackexchange.com/questions/73226",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/54058/"
] | New driver here. I drive ford fiesta 2019, petrol, car is around half year old, 5k km.
Sometimes when I need to maneuver slowly in 1st gear or reverse (for example in a parking lot or a very slowly moving traffic jam), and I try to set my clutch to a biting point, it starts doing this weird noise (I think around 440 H... | Most manual petrol cars don't really have sufficient torque at idle to move on clutch alone, and what you describe sounds about normal for a car that's about to stall (if the clutch were raised further without applying more throttle). Some can creep on the clutch alone but it's a fine line to walk - and you won't move ... | If you are not confident yet in using a clutch, it may be beneficial for you to ride with a friend or family member that you trust and has excellent driving skills and carefully observe how they manipulate clutching. Riding through town up and down hills and braking should be paid special attention to.
| https://mechanics.stackexchange.com |
99,144 | [
"https://softwareengineering.stackexchange.com/questions/99144",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/73/"
] | How does one do unit testing for multiple environments that behave differently?
Here is my problem. I have a PHP class for which I'd like to create unit tests. The class provides shortcuts for manipulating folders. On Linux, you can set the folder permissions without a problem, on Windows, you can't at all.
Knowing ... | In this case, I would make it conditional on the OS and make it clear in the test's name that it's only intended to run on Linux.
I'm not familiar with PHP's unit testing frameworks, but if I were doing this in Python, I'd set up the test to be skipped when running in Windows, since <code>unittest</code> supports con... | Create unit tests for both! You need to know that it is working code!
PHP has a great unit testing tool known as PHPUnit, which offers a few ways of doing this. My recommendation would be to group the tests that are OS-specific with that OS name.
<pre><code>/**
* @group linux
*/
class LinuxTest extends PHPUnit_Fr... | https://softwareengineering.stackexchange.com |
197,375 | [
"https://electronics.stackexchange.com/questions/197375",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/89646/"
] | Trying to figure out how to design this with decent precision but having trouble getting this started. I've worked with 555's before but not for precise counting that can be modified in steps.
I'm trying to come up with a 5 volt system that accurately pulses an output of +5v that is measured and displayed in pulses p... | If you want to implement something without using any programmable parts beyond a custom-frequency oscillator, it should be possible to build a circuit that takes a 3-digit BCD frequency and outputs a signal with that many beats per minute using an oscillator plus five off-the-shelf chips.
Feed a 1,092,267Hz oscillator ... | This could easily be done with a microcontroller. 240 BPM is 4Hz. By using a microcontroller with timer peripherals it would be easy to get accuracy in the +/-0.01% range.
Suggest a microcontroller such as PIC or AVR or MSP430 with a small display, buttons. An LCD display could be used to save power, and there are mi... | https://electronics.stackexchange.com |
96,050 | [
"https://dba.stackexchange.com/questions/96050",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/61971/"
] | I have a server that someone has setup which are acting as a master on both database. Since they have been configured as both master on the same database, changes one on end has caused all sorts of issues on the other.
On one of the master is displaying two databases in the replication-do-db when I do show master stat... | The DMV <code>sys.dm_exec_sessions</code> has column <code>host_name</code> which is the computer at the client end of the connection. You can join that to your posted query through the <code>session_id</code>.
| I have a query for this. It will provide you login,hostname(server), start time,session_id with query text.
<pre><code>select
r.session_id,
r.start_time,
s.login_name,
c.client_net_address,
s.host_name,
s.program_name,
st.text
from sys.dm_exec_requests r
inner join sys.dm_exec_sessions s
on r.session_id = s.session_id... | https://dba.stackexchange.com |
552,059 | [
"https://electronics.stackexchange.com/questions/552059",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/278707/"
] | I am a beginner at this. I know that energy cannot be created nor destroyed. I know you can't use 3 kVA inverter to run a 5 kVA dynamo (assuming I want it that way). Why then is 2400 W (12 V x 2 x 100 A) able to power some 5 kVA (4000 W with 0.8 power factor) inverters? Is there anything I don't understand?
| Most batteries are able to supply far more output current than the "nominal" value you find in data sheets. In fact some will supply nearly "infinite" current until they destroy themselves.
As far are your 100A batteries supplying enough input to an inverter to generate 5KVA there are two possibili... | The 100 Ampere Hour rating on the battery is a capacity specification, not a maximum current specification. In order to run an inverter that puts out 240 VAC at 16 Amps, you need to pull about 340 Amps on the 24 Volt side. This actually isn't unreasonable but only for a short period of time. In a case like that, you'll... | https://electronics.stackexchange.com |
378,151 | [
"https://softwareengineering.stackexchange.com/questions/378151",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54071/"
] | Scenario: I fork a project and submit a PR on Feature A, and then another on Feature B. I want to continue working with both features while I'm waiting for the PRs to be merged (theoretically they might never be if the upstream is abandoned).
<strong>Updated Requirement:</strong> I’ll have to push the changes to my f... | There is no particularly good approach to solve this. When the upstream project merges, squashes, or rebases your features A and B, they are creating new commits that are not part of any branch that you can work on right now. Therefore, if you continue work on top of your features, you will have to merge or rebase in t... | Create your 'continue working' branch (whatever that's going to be called), and cherry-pick the other PR changes in. (You could merge, but it'll get messy if you later need to address review comments in those PR branches.)
<pre><code>---- upstream/master
\_ origin/pr-a
\_ origin/pr-b
\___ origin/continu... | https://softwareengineering.stackexchange.com |
119,206 | [
"https://security.stackexchange.com/questions/119206",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/106257/"
] | While at school I stumbled upon a folder that holds a program that can control the schools computers, such as shutting them down, logging everybody off, controlling what files they can access.
How should I approach my School Board / School about the problem? Because I do want to report it to them.
At the start of the... | In that order, the first hit solves it:
<ol>
<li>If your school has a bug bounty program, report it there</li>
<li>If your school has a sysadmin, report it there</li>
<li>If your school has an IT board, report it there</li>
<li>If your school has an IT teacher, report it there</li>
<li>Report it to the principal.</li>... | OP has probably made a decision by know, but for future readers, I'd add my opinion. Since you mentioned a "school board" I am assuming this is a high school, and I am assuming they don't have a bug bounty program either. In order of preference.
<ol>
<li>If you know who, report it to the actual IT person who maintains... | https://security.stackexchange.com |
631,044 | [
"https://electronics.stackexchange.com/questions/631044",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/319804/"
] | I'm writing a driver for a QMC5883L triple-axis magnetometer and in the datasheet it specifies "Full Scale" as a configurable parameter which can either be 2G or 8G. I've seen this on other datasheets as well.
What is the unit "G" and what does full scale actually mean in the context of a magnetomet... | Since it is a magnetometer, one would expect G to stand for Gauss, a unit of magnetic field strength. The sensor can be configured so that either an external field of 2 Gauss or 8 Gauss corresponds to the maximum output of the sensor. This enables the user to have a tradeoff between the maximum field strength that can... | Full scale is simply the maximum range the sensor can measure. Its configurable so that you can either get a bigger range of output , or a more sensitive one. If you only want to measure accelerations below 2G , the 2G full scale will give you better resolution, but will clip above 2G.
| https://electronics.stackexchange.com |
47,795 | [
"https://dba.stackexchange.com/questions/47795",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/26882/"
] | Here's the deal, I'm in charge of creating a website that will host small web apps. This apps will be photo contests, creatives sentences and other similar gibberish. The deal is, since apps we'll be constantly changing and some new ones will come up what's the best way to save the config specs for each one? Should I c... | First of all, the way you are wanting to do it won't really work. You can't have one login and multiple users on a single database. If you try you get the following error:
<pre><code>Msg 15063, Level 16, State 1, Line 1
The login already has an account under a different user name.
</code></pre>
What you really shou... | Yes, you may use an AD Windows Group as a LOGIN to the server and then map the <em>individual</em> AD Windows Logins to database USERs <em>in the approriate databases</em>. Since the Windows Group LOGIN only adds rights to access the SQL Server and any databases with the guest user enabled (master, msdb, tempdb) then... | https://dba.stackexchange.com |
438,069 | [
"https://softwareengineering.stackexchange.com/questions/438069",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/408555/"
] | I've got a class that is a facade class (encapsulates complex-ish behaviour for reusability). It has a function called <code>manage</code> (the class is called Manager):
<pre><code>function manage()
{
$entityBuilder = 'Some builder';
$someData = 'Some data';
foreach ($someData as $someDatum) {
if (!... | Logging would only break the SRP if the manager class would implement the log mechanics by itself. But adding some event mechanics to send notifications to a callback does not, for example
<pre><code> $notify = // initialize this member variable by a function, passed to the constructor
// ...
foreach ($someData as $s... | First, I'd just like to say, returning a list of statuses could potentially be a nice solution (I think functional-oriented people would prefer that), but of course, it may or may not be easy to implement, depending on what's going on in the rest of your system.
But if you want to go the decorator route, you could deco... | https://softwareengineering.stackexchange.com |
27,985 | [
"https://cs.stackexchange.com/questions/27985",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/17999/"
] | I understand what a B-Tree is (I already implemented a B-Tree in Java with insert and delete methods that preserve the invariant).
However I do not understand exactly how it is used for example for file systems or databases.
<ol>
<li>How do you choose the keys in these 2 scenarios? And what is the data? </li>
<li>Are... | A B-Tree is a type of dictionary, no more and no less. It can be used to implement a set (e.g. see the interface for <code>java.util.Set</code> for the sort of operations we're talking about), but is most commonly used to implement a map (ditto for <code>java.util.Map</code>). So let's just look at maps for a moment.
... | If you do proper research all you'r doubts will be clear. Let me try
<blockquote>
how it is used for example for file systems or databases.
</blockquote>
Take an example of a library books, And you want to search a specific book and you have kept all the books randomly how much time will it. If you use B-trees then... | https://cs.stackexchange.com |
1,764,199 | [
"https://math.stackexchange.com/questions/1764199",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/288116/"
] | What would be the value of the limit $\lim _{x\to \infty} (\frac{3x +1}{3x-1})^{4x}$?
My initial idea was to divide by x in the numerator and denominator. However that would only solve the inner problem. How can the power be manipulated to evaluate the limit?
| $$\left(\frac{3x +1}{3x-1}\right)^{4x}=\left[\frac{\left(1+\frac{1}{3x}\right)^{3x}}{\left(1-\frac{1}{3x}\right)^{3x}}\right]^\frac{4}{3}\to\left[\frac{e}{e^{-1}}\right]^{\frac{4}{3}}=e^\frac{8}{3}$$
| HINT:
$$\dfrac{3x+1}{3x-1}=1+\dfrac2{3x-1}$$
Use $$\lim_{n\to\infty}\left(1+\dfrac1n\right)^n=e$$
$$\lim_{x\to\infty}\left(\frac{3x +1}{3x-1}\right)^{4x}=\left[\lim_{x\to\infty}\left(1+\dfrac2{3x-1}\right)^{\dfrac{3x-1}2}\right]^{\lim_{x\to\infty}\dfrac{2\cdot4x}{3x-1}}=?$$
| https://math.stackexchange.com |
161,713 | [
"https://mathoverflow.net/questions/161713",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11145/"
] | I'm not sure if this is research level, so feel free to vote to migrate.
Suppose we have a complete boolean algebra $A$, with a <em>dense</em>, $\sigma$-complete subalgebra $B$, and a $\sigma$-complete homomorphism $h : B \to C$, where $C$ is complete. Does $h$ have a $\sigma$-complete extension $h' : A \to C$?
EDIT... | Finally, I found that a stronger result is known:
<strong>Theorem.</strong> For any integer $d \geq 1$ and $\delta \in [0,1]$, let
$$C_{d,\delta} = \frac{\Gamma(\tfrac{d}{2})(1-\delta^2)^{(d-1)/2}}{2\sqrt{\pi}\,\Gamma(\tfrac{d+1}{2})}.$$
Then for all $v_1, \ldots, v_n \in \mathbb{R}^d$ there exists $u \in \mathbb{R}^d... | Your constants are optimal, by the same arrangement: large number of unit vectors uniformly distributed over the sphere. Clearly, an optimal S consists of all vectors from a half space, say $x_1>0$. Then
$$
C_d \le \frac{1}{S_{d-1}} \int_{S_{d-1}^+} x_1\, d\omega_{d-1}(x)
$$
($S_d$=surface area of the $d$-sphere), a... | https://mathoverflow.net |
23,305 | [
"https://dba.stackexchange.com/questions/23305",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11212/"
] | I have been monitoring file growth via the data collector in sql server 2008 r2 for two weeks. The database is growing consistently at around 35(MB)/Day. The DB has not yet hit the initial size of 2 GB.
The DB files auto growth is set to 5MB and I would like to try a different approach, so I am looking for suggestions... | You should be aiming to auto-grow as little as possible. Seven times a day is excruciating, even with instant file initialization.
Don't do a Shrink Database. Ever. Shrinkfile, maybe, but only after an extraordinary event. Shrinking it just to grow again is an exercise in futility and should actually be called auto-fr... | Auto growth is something that you should try to avoid if possible. The issue is you have no control over when the growth can happen and your system can take a serious hit while it does so.
Set your file size to something sensible for a month or so and monitor your growth rate from there work out how much space you es... | https://dba.stackexchange.com |
234,902 | [
"https://physics.stackexchange.com/questions/234902",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/90074/"
] | If we place a ball at a certain height it falls and the process is irreversible. Is there any entropy change associated with the falling of ball? If so why?
| Actually, the process you described is not irreversible. What has happened is that potential energy has been converted to kinetic energy. It is possible to reverse the process by using a roller coaster kind of arrangement where the ball is redirected to go up a hill. In the end, its kinetic energy is converted back ... | <blockquote>
If we place a ball at a certain height it falls and the process is irreversible.
</blockquote>
The process you described is irreversible. A object, falling towards a source of gravity, does not experience any force and by this does not accelerate. That seems to be paradoxical. To see that this is right ... | https://physics.stackexchange.com |
1,261 | [
"https://stats.stackexchange.com/questions/1261",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/287/"
] | Suppose I have a table of counts that look like this
<pre><code> A B C
Success 1261 230 3514
Failure 381 161 4012
</code></pre>
I have a hypothesis that there is some probability $p$ such that $P(Success_A) = p^i$, $P(Success_B) = p^j$ and $P(Success_C) = p^k$.
Is there some way to produce e... | Following up on my comment, this question would be very simple if i, j, and k were not restricted to be integers. The reason is as follows: pA, pB, and pC denote the observed probability of success in the three groups. Then let p=pA, i=1, j=log(pB)/log(pA), and k=log(pC)/log(pA). These will easily satisfy the required... | You could write the likelihood function like so:
$L(p,i,j,k|-) \propto (p^i)^{1261} (1-p^i)^{381} (p^j)^{230} (1-p^j)^{161} (p^k)^{3514} (1-p^k)^{4012}$
Maximize the above likelihood function to estimate your parameters. Constructing confidence intervals and hypothesis testing should be straight forward once you have... | https://stats.stackexchange.com |
188,641 | [
"https://security.stackexchange.com/questions/188641",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/55103/"
] | I just received an email from Citi saying "We've locked your access for 24 hours due to multiple failed login attempts." and "If you didn’t attempt these logins, we recommend that you reset your password immediately."
Ignoring the humor of being told to change my password immediately when my access to the password res... | If the password was randomly chosen, then there's no reason to do so.
There might be a reason if someone is trying targeted password at you. ie: if they know you like horses, you are born on 1990, and you're from Alabama, then they might be trying all combinations of these words. Changing your password then <em>could<... | If your password is strong enough and random (can withstand dictionary type of attack) you don't need to worry about it.
But the fact is attacker knows your <strong>user name</strong> (that's why the login attempts were tagged under you) and trying to guess the password.
In this case, consider changing the account u... | https://security.stackexchange.com |
391,222 | [
"https://physics.stackexchange.com/questions/391222",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45664/"
] | Given the wave equation
$$u_{xx}(x,t)=\frac {1}{c^2}u_{tt}(x,t) $$
with initial conditions:
IC1: $$u(x,0)= f(x)$$
IC2: $$u_{t}(x,0)= g(x)$$
Why isn't $g(x)$ always equal to $f_t(x)$?<br>
For example, if $t=0$ is the time that a snapshot is taken of a freely traveling wave it seems to me that it must be true that... | Note that f(x) and g(x) are functions of x alone [not "x and t"].<BR>
f(x) is what the string looks like on a photo [taken at t=0]...<BR>
and you don't have access to other snapshots.<BR>
That is, "f" doesn't have information on how the string is moving.<BR>
<BR>
g(x) is what the velocity profile would look like at t=... | consider a wave on a rope, if you choose to define the height of a point on this wave at x, there will be two possible conditions for this wave. The two conditions are that the point may move either up or down, so you need to define the velocity in order to know the motion of the wave.
| https://physics.stackexchange.com |
158,452 | [
"https://electronics.stackexchange.com/questions/158452",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29522/"
] | I have bought a bunch of LEDs from the rummage table of my local electronics store. Now, I don't have a fact sheet, neither I do know the vendor and / or the article number.
How do I find out about the desired voltage and current of the LEDs (without doing it trial-and-error)?
| Short answer: you can't. But you can do some smart non destructive trial and error.
First of all you need to at least know what current/voltage you are expecting: are they power leds, are they small 3mm leds, are they smd or not, what color are they? Try to find a datasheet of a led you think is similar.
Let's assume... | A lot of common LEDs have very similar specs. For example, if I picked up a jellybean red LED, my first guess at its specs would be \$V_F = 2.0 V\$, \$I_F = 20mA\$. If you're just using these as a hobbyist, numbers like those should be close enough to make them light up on a breadboard. You probably don't need to get c... | https://electronics.stackexchange.com |
35,978 | [
"https://physics.stackexchange.com/questions/35978",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9920/"
] | I want to demonstrate what force $F$ you would have to exert on an inclined plane of angle $t$, mass $M$ to prevent a block on top of it with mass $m$ from sliding up or down the ramp. I worked out an answer, but I figure it must be wrong because it doesn't factor the mass $M$ of the inclined plane into the force need... | I'm not sure I entirely understand the question. This is what I think you're asking; please ignore the rest of this answer if I've misunderstood you.
If the plane is stationary (and I assume there is no friction) then a block on the plane will feel a force down the plane of $mg \space \sin\theta$, so it will accelerat... | The block and wedge have the same horizontal acceleration $a$ so use horizontal and vertical axes.
FBD of $m$:
Y dir: $N \cos(t) - mg= 0$
X-dir: $N \sin(t)= ma$
Solving $a=g \tan (t)$
FBD of M:
$F-N \sin(t)=Ma$
$$F-ma=Ma$$
$$F=(M+m)a$$
$$F=(M+m)g \tan(t)$$
| https://physics.stackexchange.com |
1,575,419 | [
"https://math.stackexchange.com/questions/1575419",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/206726/"
] | <blockquote>
Let <span class="math-container">$S^1=\{z \in \Bbb C : |z|=1\}$</span>. Let <span class="math-container">$f$</span> be any continuous function from <span class="math-container">$S^1 \to \Bbb R$</span>. Then:
A. <span class="math-container">$f$</span> is bounded
B. <span class="math-container">$f$</span> is... | C is wrong as $f$ might be constant.
| C is true if $f$ is nontrivial, for then $f[S^1]$ is a nontrivial connected subset of $\mathbb R$.
| https://math.stackexchange.com |
565,801 | [
"https://electronics.stackexchange.com/questions/565801",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/61597/"
] | Required to use a DB9 connector to pass DC to unit requiring 12V/5A supply. An easy way to do that is using a DB-9 to Terminal Block adapter. But most DB-9 to TB adapters I see have 3 A or less current rating per pin. How can use such adapter to make it pass a 12V/5A stably?
| There are some DB9 connectors with 5A rated pins. Most are 3A rated pins (or higher) Assuming you design for the lower standard your options are use a higher voltage and use a switching regulator to bring it down to the Voltage/Amperage needed, or... use multiple pins. For 5A on a 3A contact, you'll need 4 pins, 2 V+ a... | Seeing that 5A is already relatively high a current to pass it trough a d-sub pin, I'd recommend at least not putting a large terminal block at the connector. Instead, I'd get a connector with solder lugs, and solder in appropriately sized cabling. That inherently solves the issue.
No matter what you do, you won't be a... | https://electronics.stackexchange.com |
234,564 | [
"https://electronics.stackexchange.com/questions/234564",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | When I see some teardowns of single phase induction motors on the internet, I see their capacitors look like:
<img src="https://i.stack.imgur.com/ICBLt.jpg" alt="enter image description here">
<img src="https://i.stack.imgur.com/DU7Eg.jpg" alt="[2]">
Why are they that big in size compared to other caps, even though ... | Motor capacitors are not plain electrolytics, because the voltage across them reverses at the mains frequency.
The larger value ones are start capacitors - usually bipolar electrolytic, and rated to the peak mains voltage - but not for continuous operation. They are usually disconnected by a centrifugal switch in the... | In my experience the physical size of a capacitor is proportional to the capacitance times its voltage. Double the voltage, double the size.
In practical terms, voltage is higher still.
<ul>
<li>AC voltage is RMS (sinewave peaks are somewhat higher than the stated voltage). </li>
<li>When a motor is disconnecte... | https://electronics.stackexchange.com |
43,027 | [
"https://mathoverflow.net/questions/43027",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9102/"
] | Given a complete graph of n vertices (no three of which are no collinear) in the plane and straight edges, what is the maximal possible number of "incidental intersections" of edges, i.e., number of non-vertices at which two distinct edges intersect each other, not counting multiplicity?
This is a question that I pose... | Assuming straight line segment edges, any 4 vertices determine 6 edges with at most one non-vertex intersection, so you can't have more than $n$-choose-4. You will have $n$-choose-4 if no vertex is interior to any triangle of vertices, which is to say if all $n$ vertices lie on the boundary.
| This problem (although phrased slightly differently) is #1.3.5 in Loren C. Larson's "Problem Solving Through Problems."
The rephrase of this is, "On a circle, n points are selected and the chords joining them in pairs are drawn. Assuming no three of the chords are concurrent (except at the endpoints), how many points... | https://mathoverflow.net |
97,039 | [
"https://softwareengineering.stackexchange.com/questions/97039",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30794/"
] | I've just started getting to grips with event driven programming and I'm finding delegates and events to be very useful. Since starting to see the potential I've began using them all the time to solve problems such as updating displays between controls and calling stored procedures following updates etc.
I'm starting ... | For me the distinction between using an event and calling a method is for proper separation of concern.
When you call a method, the caller know what method is being called. When you raise an event, the raiser doesn't know who's listening (if anyone at all).
A button control is an excellent example of when an event... | I would say the simplest rule is:
<ul>
<li>If you know exactly which other method(s) of which other object(s) need(s) to be executed, and there is no need to alter this at runtime, then use a direct call. Helps with readability.</li>
<li>If you cannot know in advance who would want to receive the information provided ... | https://softwareengineering.stackexchange.com |
335,873 | [
"https://softwareengineering.stackexchange.com/questions/335873",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/244472/"
] | In C, When do we say that a variable is undefined ? When it is not present in the complete code or in a function scope ?
| There's declared, defined, and initialized; these terms can be applied to both functions and variables.
<hr>
Declared means that some declaration is in scope. For example, within some function's code, some block may contain a variable declaration, e.g. <code>{ extern int a, b (); }</code>. Without at least a declar... | A variable is undefined when an attempt is made to access or assign it before it is declared.
This:
<pre><code>int c;
</code></pre>
is a declaration.
This:
<pre><code>c = 4;
</code></pre>
is an assignment.
If you do <code>c = 4</code> before <code>int c</code>, that will cause an "undefined variable" error.
Y... | https://softwareengineering.stackexchange.com |
690,060 | [
"https://physics.stackexchange.com/questions/690060",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/312234/"
] | Consider a particle travelling at 0.9c through a 9-light-second long tube which erects a wall at exactly 10 seconds to block off the particle. For a stationary (relative to the tube) observer, he sees that it takes the particle exactly 10 seconds to traverse through the tube, so he sees the particle getting blocked by ... | As Dale said, you forgot the relativity of simultaneity, which caused you to misapply the concept of time dilation.
If we stick with the coordinates suggested by JEB, the particle enters the tube at t=t'=0. In the frame of the tube, t=0 is also the time when the construction of the wall started at the other end. But in... | <blockquote>
This is an obvious paradox, which part of my reasoning was flawed?
</blockquote>
You forgot the relativity of simultaneity. This is the resolution of most of the SR paradoxes.
Although the wall construction is indeed time dilated in the particle’s frame, the construction started much earlier. Sufficiently ... | https://physics.stackexchange.com |
44,417 | [
"https://mathoverflow.net/questions/44417",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2386/"
] | Let $\mathbb Z^2$ denote the two-dimensional integer lattice with norm of $i=(i_1,i_2)$ given by $\|i\|=|i_1|+|i_2|$.
For each $x\in\mathbb Z^2$, we assign a uniform random variable, $\sigma_x$ taking values on the set $\{-1,1\}$.
Fix $\omega\in\{-1,0,1\}^{\mathbb{Z}^2}$ and $\beta>0$. For each finite $\Lambda\su... | Concerning questions 1 and 2, if I understand it correctly (i.e., you're simply looking at the finite-range ferromagnetic Ising model with free, resp + or -, b.c.), then the sequences actually converge and the limits are translation invariant. This follows from monotonicity in the volume (GKS for free, GKS of FKG for +... | At very large\beta I think the big review of Dobrushin-Shlosman
The problem of translation invariance of Gibbs states at low temperatures
RL Dobrushin… - Sov. Sci. Rev., Sect. C, Math. Phys. Rev., 1985
gives results for general 2d models.
The fact that you won't get anything with Dobrushin boundary conditions foll... | https://mathoverflow.net |
111,010 | [
"https://stats.stackexchange.com/questions/111010",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/53356/"
] | I have read enough threads on QQplots here to understand that a QQplot can be more informative than other normality tests. However, I am inexperienced with interpreting QQplots. I googled a lot; I found a lot of graphs of non-normal QQplots, but no clear rules on how to interpret them, other than what it seems to be co... | Note that the Shapiro-Wilk is a powerful test of normality.
The best approach is really to have a good idea of how sensitive any procedure you want to use is to various kinds of non-normality (how badly non-normal does it have to be in that way for it to affect your inference more than you can accept).
An informal appr... | Without contradicting any of the excellent answers here, I have one rule of thumb which is often (but not always) decisive. (A passing comment in the answer by @Dante seems pertinent too.)
It sometimes seems too obvious to state, but here you are.
<strong>I am happy to call a distribution non-normal if I think I c... | https://stats.stackexchange.com |
465,410 | [
"https://physics.stackexchange.com/questions/465410",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/224981/"
] | I have a question regarding conservation of energy in regards to two different scenarios:
In the first case I was told that a ball with an initial velocity, V, was launched at an angle, <span class="math-container">$\theta$</span> and to solve for the max height in terms of <span class="math-container">$h$</span>.
S... | From a comment:
<blockquote>
I'm curious as to why the final kinetic energy of the projectile motion depends on the angle but the final kinetic energy of a ball being launched up a slope is 0, and doesn't depend on the angle (at max height for both)
</blockquote>
I think this comment shows a misunderstanding that n... | The difference is that the motion of the projectile is constrained by one force - its weight acting vertically downwards and there is no horizontal forc,e whereas the object moving up the ramp is constrained by two forces - its weight acting vertically downwards and the normal reaction force due to the ramp which has a... | https://physics.stackexchange.com |
513,330 | [
"https://physics.stackexchange.com/questions/513330",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228212/"
] | I have a question regarding the interpretation of the Wightman quantum field in mathematical quantum field theory.
A quantum field <span class="math-container">$\phi$</span> is a operator-valued distribution. This means that <span class="math-container">$\phi$</span> is a linear function
<span class="math-container"... | The smearing (test-) function is not a relic of the mathematical description, but a key ingredient of the theory. To quote from the fathers Wightman and Streater (<em>PCT, Statistics, and all That</em>):
<blockquote>
It was recognized early in the analysis of field measurements for
the electromagnetic field in qu... | I like to think of it this way: We can only measure something with finite spatial resolution and for a finite time. So any experiment only measures an average over a small spacetime region. This is basically<br>
<span class="math-container">$$
\phi(f)=\int \phi(x)f(x) d^4x
$$</span>
for some compactly supported smoo... | https://physics.stackexchange.com |
260,565 | [
"https://softwareengineering.stackexchange.com/questions/260565",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/153680/"
] | Here is a simplified requirement:
<blockquote>
<strong>User creates a <code>Question</code> with multiple <code>Answer</code>s. <code>Question</code> must have at least one <code>Answer</code>.</strong>
Clarification: think <code>Question</code> and <code>Answer</code> as in a <em>test</em>: there is one questi... | <h2>Updated. Clarifications taken into account.</h2>
Looks like this is a multiple choice domain, which usually has the following requirements
<ol>
<li>a question must have at least two choices so that you could choose among</li>
<li>there must be at least one correct choice</li>
<li>there should not be a choice with... | In case where requirements are so simple, that multiple possible solutions exist, then KISS principle should be followed. In your case, that would be option E.
There is also case of creating code that expresses something, that it should not. For example tying creation of Answers to Question (A and B) or giving Answer ... | https://softwareengineering.stackexchange.com |
56,745 | [
"https://cs.stackexchange.com/questions/56745",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/50350/"
] | Will $L = \{a^* b^*\}$ be classified as a regular language?
I am confused because I know that $L = \{a^n b^n\}$ is not regular. What difference does the kleene star make?
| A language is regular, by definition, if it is accepted by some DFA. (This is at least one common definition.) Can you think of a DFA accepting the language?
A well-known result (that is proved in many textbooks) states that the language of a regular expression is regular. Since $a^* b^*$ is a regular expression, its ... | $\{a^* b^*\}$ is a regular language, since it's generated by a regular expression.
The key difference between $L_* = \{a^* b^*\}$ and $L_= = \{a^n b^n\}$ is that $L_=$ requires counting the $a$'s and $b$'s to check whether there's the same number of them, whereas $L_*$ doesn't require any counting. Counting requires u... | https://cs.stackexchange.com |
572,232 | [
"https://physics.stackexchange.com/questions/572232",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/271937/"
] | I watched Interstellar and I got really confused around different time thing. How can it be possible at all that time is different at different places in the universe?
Please explain.
| The spacetime metric of a spatially-flat Friedmann universe — like ours seems to be, on the largest scales — is
<span class="math-container">$$ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2)$$</span>
where the function <span class="math-container">$a(t)$</span> is the Friedmann scale factor describing the expansion of space as a fun... | I think the essential problem lies in the difference between the mathematical meaning of <em>curvature</em>, and the way in which we actually describe a manifold, or a curved space (or spacetime).
Although we describe the universe as having spacetime curvature (which is mathematically true), <em>curvature</em> refers t... | https://physics.stackexchange.com |
331,551 | [
"https://electronics.stackexchange.com/questions/331551",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/162522/"
] | I know this question may be <strong>very</strong> stupid, but it comes from a true beginner, and a Google search came up inconclusive.
When porting high or low the input pins on an integrated circuit (particularly CMOS), are the input current sinked or sourced ? To me it makes sense that they would be sinked, but I am... | It depends on the technology.
Standard TTL sources current when pulled low. CMOS can have pull-ups or pull downs that will source or sink current respectively.
Also, be aware that with CMOS devices there is also input capacitance. That means while switching they sink on high edges and source on falling edges. As suc... | Input pins are usually high impedance.
In other words they act as if floating. However some ICs have internal pullup or pulldown resistors on some pins to bias the pin high or low.
| https://electronics.stackexchange.com |
647,026 | [
"https://physics.stackexchange.com/questions/647026",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246877/"
] | Is it safe to say that imaginary part of wavefunction (one that "located" in a Complex plane around it's real component) - <strong>always</strong> represents some physical entity, that cannot be simultaneously known as precise as whatever is represented by real part?
Say, if "real" component is posi... | The real and imaginary components of a wavefunction can be interchanged by multiplying the entire wavefunction by a global phase <span class="math-container">$i$</span>. Therefore, they cannot have different physical meaning from each other. The only physical information lies in the relative phases between components o... | It seems you've been bit by the idea that "imaginary numbers" are somehow "not real", as in "fictitious", because of their name. This name is just a historical artifact; it has <em>no</em> philosophical implication from a modern mathematical point of view. Imaginary/complex numbers are jus... | https://physics.stackexchange.com |
28,914 | [
"https://quantumcomputing.stackexchange.com/questions/28914",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/15947/"
] | In the case of the No-cloning theorem, it is argued that a unitary <span class="math-container">$U$</span> that is capable of performing coping does not exist. Specifically, for any two unknown states <span class="math-container">$|\psi_1\rangle$</span> and <span class="math-container">$|\psi_2\rangle$</span> the calcu... | The cloning strategy certainly gives one potential way to disprove existence of a solution. If you're really just looking for a unitary transformation, it's extremely effective - essentially, you're saying that unitaries are linear, but you're proving that you require a non-linear transformation. But it's not the only ... | Given any two states <span class="math-container">$|\psi\rangle$</span> and <span class="math-container">$|\theta\rangle$</span>, there always exists a unitary mapping that takes <span class="math-container">$\psi$</span> to <span class="math-container">$\theta$</span>.
There is in fact a stronger result.
Given any two... | https://quantumcomputing.stackexchange.com |
1,729 | [
"https://stats.stackexchange.com/questions/1729",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/913/"
] | I am trying to format the output from pairwise.t.test into LaTeX, but have not found a way of doing this. Has anyone got any suggestions?
<strong>EDIT:</strong> As this is a one-time only report where I do need to customize the variable names, and row-/column headings, I was hoping to avoid using Sweave.
| Does this help?
<pre><code>> library(xtable)
> attach(airquality)
> res <- pairwise.t.test(Ozone, Month)
> xtable(res$p.value, caption=res$method)
% latex table generated in R 2.9.2 by xtable 1.5-6 package
% Mon Aug 16 04:24:21 2010
\begin{table}[ht]
\begin{center}
\begin{tabular}{rrrrr}
\hline
&... | One way that you can do the above task without using Sweave is as follows:
<ol>
<li>Write a <strong>custom export function</strong> from R that takes the pairwise.t.test object and outputs latex code.</li>
<li>Use <code>\input{...}</code> in your LaTeX document to <strong>input</strong> this file into your LaTeX docu... | https://stats.stackexchange.com |
375,539 | [
"https://mathoverflow.net/questions/375539",
"https://mathoverflow.net",
"https://mathoverflow.net/users/168099/"
] | let <span class="math-container">$X,Y$</span> be smooth schemes (or rigid spaces etc..) over a base <span class="math-container">$S$</span>, let <span class="math-container">$f:Y \rightarrow X$</span> be a <span class="math-container">$S$</span>-morphisn and let <span class="math-container">$\mathcal{F}$</span> be a lo... | Recall that you have a map <span class="math-container">$f^* \colon f^{-1} \Omega_X \to \Omega_Y$</span> (pull-back of differentials). Consider the composition <span class="math-container">$$ \nabla' \colon f^{-1} E \xrightarrow{f^{-1} \nabla} f^{-1} E\otimes_{f^{-1} \mathcal{O}_X} f^{-1}\Omega_X \xrightarrow{{\rm id}\... | Another option is to proceed as follows : show that there exists a unique connection <span class="math-container">$f^*\nabla$</span> on <span class="math-container">$f^*\mathcal F$</span> verifying :
<span class="math-container">$$ (f^*\nabla)(f^*s) = f^*(\nabla(s))$$</span>
where on the right-hand side you use the ca... | https://mathoverflow.net |
207,201 | [
"https://physics.stackexchange.com/questions/207201",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60857/"
] | The boiling point of a liquid is defined as
<blockquote>
The temperature at which the vapor pressure of the liquid is equal to the external atmospheric pressure.
</blockquote>
That being the case, why, in a pot of boiling water, does the water have a pretty stable liquid-air interface? Why are bubbles seen as comin... | Boiling is clearly not a surface phenomenon. But vaporising is.
Boiling happens at all the points inside the liquid whereas when vaporising only the molecules at the surface escape into the space above.
And it is true that a liquid boils when its saturated vapour pressure equals external (room) pressure. But it is n... | The quoted definition may sound confusing because of the use of "vapour pressure", which is not necessarily related to the liquid-air surface. This can be made clearer by a different example:
Suppose you have a water container at room temperature and you heat only a small volume at the centre of the container (by usin... | https://physics.stackexchange.com |
43,897 | [
"https://quant.stackexchange.com/questions/43897",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/31825/"
] | I am trying to understand asset price volatility.
Many of the news articles I read link how stock market volatility is linked to asset price volatility?
To give an example, in Mike Mackenzie's (Financial Times), February 4th article,
<blockquote>
Volatility in the US equity market has retreated to its lowest lev... | To be clear, journalistic assessments of the kind above refer to "IMPLIED volatility", ie the expected and priced level of future vol from options, that is effectively a measure of investor sentiment (as opposed to an observable economic reality).
This matters in so far as observations about the REALISED (as ... | Equity market volatility reflects the confidence/certainty about economic future. When it's a low volatility environment, it reflects the underlying psychology of participants (e.g. not a lot of tug of war between the bull and the bear, not much uncertainty of the direction of the economy.). It also reflects relatively... | https://quant.stackexchange.com |
233,831 | [
"https://electronics.stackexchange.com/questions/233831",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/108684/"
] | I am new to electronics so I hope this question is acceptable. I have been playing around with an Arduino. I have use the USB output from a computer as a power source. I also have a 9V battery. I am a bit concerned about creating a short somewhere and damaging the computer or the battery. I am guessing that this is wha... | To answer your question, yes, those 1 Amp 250 Volt fuse will work fine in small projects, as the Voltage is a maximum. A 1 Amp 250V fast fuse should blow even at lower voltages. <strong>The important number here would be the Current rating</strong>.
For example, my multimeter has a 500 mA 250 Volt fast fuse, with a re... | Look up 'Pico Fuses' on the web. They are small PC mount fuses, in a package that looks like a 1/4 watt resistor. They are rated for 50 to 125 volts max, with currents as low as 1/20th of an amp to 5 amps. These are fast-blow uses, so be sure to use them in places where the in-rush current is low. Digi-Key and Mouser s... | https://electronics.stackexchange.com |
27,332 | [
"https://stats.stackexchange.com/questions/27332",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10785/"
] | I am using R, I searched on Google and learnt that <code>kpss.test()</code>, <code>PP.test()</code>, and <code>adf.test()</code> are used to know about stationarity of time series.
But I am not a statistician, who can interpret their results
<pre><code>> PP.test(x)
Phillips-Perron Unit Root Test
data: x
Di... | Testing if a series is stationary versus non-stationary requires that you consider a sequence of alternative hypotheses . One for each listable Gaussian Assumption. One has to understand that the Gaussian Assumptions are all about the error process and have nothing to do with the observed series under evaluation. As co... | Stationarity means that the marginal distribution of the process does not change with time. A weaker forms states that the mean and the variance stay the same over time. So anything that violates it will be deemed non-stationary, for whatever silly reasons. For instance, a deterministic $y_t = \sin t$ is non-stationa... | https://stats.stackexchange.com |
95,496 | [
"https://stats.stackexchange.com/questions/95496",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/30676/"
] | What effect does data averaging have on the variogram? To be specific, please see a simple example:
<pre><code>#Simulate a pure random walk data set, call this *PROCESS A*
n <- 1000 #number of data points
t <- 1:n #time
y <- cumsum(rnorm(n)) #data points
# Averaging at every 2 lags, call this *PROCESS B*
t2... | It is difficult to say what you mean by "(2) is not [confirmed]," so let's begin by describing what is going on.
The code begins by generating realizations of $n$ independent standard normal variates $X_t,$ $t=1,2,\ldots, n$, and computing their cumulative sum $Y_t = \sum_{s=1}^t X_t$. Therefore the variogram of $Y$ ... | The variogram is a function of the correlation function, inter alia. The correlation function is affected by data averaging. Check out the Slutsky-Yule effect. This is an old result in time series analysis to the effect that if you do a moving average on white noise, you induce autocorrelations into the transformed ser... | https://stats.stackexchange.com |
532,591 | [
"https://physics.stackexchange.com/questions/532591",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Is it possible to derive the wave functions of all particles in the standard model?
Would this be through the Schrödinger equation?
| <blockquote>
Is it possible to derive the wave functions of all particles in the standard model?
</blockquote>
A wavefunction isn't a property that is unique for each particle type. The same type of particle can have different wavefunctions, and different particles can have the same wavefunction (or at least have th... | The seventeen particles in the Standard Model are the quanta of seventeen fundamental quantum fields: six for quarks, six for leptons, four for gauge bosons, and one for a scalar boson (the famous Higgs). Other than spacetime, which is where these fields “live”, today’s model of reality has only seventeen things to und... | https://physics.stackexchange.com |
148,931 | [
"https://security.stackexchange.com/questions/148931",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/92643/"
] | A company I worked with has what seems to me to be a bit of an odd security policy, for working remotely all people need to connect through a corporate VPN to reach the internal networks. The process though is slightly different for contractors and regular employees. Contractors need to use a number generated from an... | That is a common usage. The interesting part in a physical device, is that when you no longer work with a contractor, you ask him to give you back the device and you are sure that he will no longer be able to connect to your system.
Employees are assumed to be more reliable, so a software way is enough. The security i... | It looks like full-time employees, being better vetted (since a large portion of the vetting is usually up to the vendor for contractors) are given a "more convenient" way to access the VPN, since the tokens are generated on the laptop. Contractors would need one more "something you have" factor (of 2 factor auth fame)... | https://security.stackexchange.com |
596,026 | [
"https://physics.stackexchange.com/questions/596026",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266148/"
] | I have a basic question about how to make the comparison of different measurements. For example, suppose I have measured the focal length of a convergent lens using three different methods, <span class="math-container">$A$</span> and <span class="math-container">$B$</span> and <span class="math-container">$C$</span>, a... | One way to express whether a pair of measurements are consistent with each other is to look at the difference of the quantities with its associated uncertainty. So, for example, you could define <span class="math-container">$\delta_{AB} \equiv f_A - f_B = 0.0004$</span> m. Assuming that the errors in <span class="mat... | If you perform multiple (pair-wise) hypothesis tests, the so called <span class="math-container">$\alpha$</span> risk (type I error) increases. Therefore, better method is to use an ANOVA or a <span class="math-container">$\chi^2$</span> goodness of fit test to compare all results at once. Only if we find a significant... | https://physics.stackexchange.com |
170,871 | [
"https://softwareengineering.stackexchange.com/questions/170871",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/59738/"
] | I recently created a .net web app that used over 200 custom validators on one page. I wrote code for both <code>ClientValidationFunction</code> and <code>OnServerValidate</code> which results in a ton of repetitive code.
My sql statements are parameterized, I have functions that pull data from input fields and valida... | You do need them as the client can decide to allow javascript in their browsers. You also should consider those people who want to break your software. There are plenty of tools out there that can manufacture posts and submit them to your website without having used your front end.
Client side validation is nice for t... | If I was going to skip doing validation, I'd be much more likely to do it on the client than on the server.
The problem with skipping it anywhere is that someone may open up a security hole by assuming validation is being done when it's not.
| https://softwareengineering.stackexchange.com |
86,422 | [
"https://mathoverflow.net/questions/86422",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2720/"
] | In his notes in Algebraic Number theory, J S Milne gives the following as an example of an unramified Abelian extension :
$ K = \mathbb Q (\sqrt{-5})$ having a quadratic extension $L = \mathbb Q (\sqrt{-1}, \sqrt{-5})$.
Then, $L/K$ has discriminant a unit, so it ramifies.
My question is, considering the simple exte... | You are slipping up because $i$ does not generate the ring of integers of $L$ as an $\mathcal{O}_K$-algebra: we have $\mathcal{O}_K = \mathbb{Z}[\sqrt{-5}]$, but $\mathcal{O}_L = \mathbb{Z}\left[i, \frac{1 + \sqrt{5}}{2}\right] \ne \mathbb{Z}[i, \sqrt{-5}]$. Hence the discriminant of $L/K$ is not the same as the discri... | A quick way of seeing what's going on is using the fact that
$L = K(i) = K(\sqrt{5})$; the fact that the different above (say of $L/{\mathbb Q}(i)$ divides the different below (e.g. of ${\mathbb Q}(\sqrt{5})/{\mathbb Q}$) shows (take norms) that the discriminant of $L/K$ divides both $-4$ and $5$, hence is trivial. Thi... | https://mathoverflow.net |
109,326 | [
"https://cs.stackexchange.com/questions/109326",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/51700/"
] | I read this sentence in a book:
<blockquote>
In VLIW architecture, the compiler/and or assembly writer chooses instructions that can be executed in parallel.
</blockquote>
What is the difference between assembly writer and compiler? Would an assembly writer also mean the same as assembler?
| The "assembly writer" in that book is a human software developer who writes code in assembler language.
| <blockquote>
In VLIW architecture, the compiler/and or assembly writer chooses instructions that can be executed in parallel
</blockquote>
The meaning of this sentence is that in VLIW architecture, assembler (machine) code defines which instruction will be executed in parallel, so it's fixed at the time assembly co... | https://cs.stackexchange.com |
100,269 | [
"https://physics.stackexchange.com/questions/100269",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1625/"
] | As a kid I was bemused at why soundboards worked. A small sound could be demonstrably amplified simply by attaching the source to a surface that is rigid and not too thick. How could the volume increase so much given that there was no extra energy added?
As an adult I kind-of-think I know, but there are still many nag... | You are right that a soundboard adds no energy to the system. However, it does allow the existing energy to be converted to sound better. The greater area of the soundboard causes more air to be pushed than the string alone can, even though the displacement amplitude of the soundboard is less than the string.
This e... | The comments above that say the sound is louder because the soundboard itself begins to vibrate are correct. This is called resonance. It sounds louder because the motion of the board is mechanically more efficient at converting the energy of the system into sound waves than the string alone. The board is an effective ... | https://physics.stackexchange.com |
139,704 | [
"https://softwareengineering.stackexchange.com/questions/139704",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/49731/"
] | I am basically asking this question to see if I am being unreasonable. My current employer has locked down the machines of all developers so that we do not have access to the root or c: drive. For example, I cannot write a directory under C:. I also cannot install any software which touches the registry. Is this an... | It depends a lot on your work environment. In bigger firms, it may be unfeasible for everyone to get their custom configuration, and your employer may do this to simplify assistance.
Where I work, I changed the OS the day I arrived, and have always been mantaining my computer since.
| This is not unusual as the default position for many large companies. The attitude is quite understandable as there may be many thousands of machines connected to a "secure" company network and the consequences of having a rogue machine can be severe.
You may be able to negotiate an exemption for your machine if yo... | https://softwareengineering.stackexchange.com |
76,941 | [
"https://electronics.stackexchange.com/questions/76941",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/26702/"
] | I am not an electronic person and found this site in a my quest for the perfect calculator. I use both a phone and calculator for calculations and find the back and forth to cause me to make errors due to the keypad reversal. Where would I go to find a simple handheld calculator (+,_,*./,% and =) with a keypad that l... | I think it's best not to over engineer anything here. Just use a voltage divider. Arduino uses 5V, MSP uses 3.3V. So... 5V*20k/(10k+20k) = 3.3V. However, MSP is powered at 3.3V...so use something like 5V*10k/(10k+10k) = 2.5V. What this means is that you need to connect the Arduino's Tx line to voltage divider to MSP's ... | The maximum voltage that can be applied at any pin on the MSP430 is only 0V3 above Vcc; trying to feed it 5V could be damaging it. Additionally, 3V3 is <em>just</em> below the typical threshold for a high input for 5V CMOS (3V5). You should consider using a voltage convertor on both pins in order to reduce possible iss... | https://electronics.stackexchange.com |
8,849 | [
"https://astronomy.stackexchange.com/questions/8849",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/2873/"
] | It is amazing that Kepler determined his three laws by looking at data, without a calculator and using only pen and paper. It is conceivable how he proved his laws described the data after he had already conjectured them, but what I do not understand is how he guessed them in the first place.
I will focus in particul... | Kepler's third law is trivial (in my opinion) compared to his first law. I am quite impressed that he was able to deduce that the orbits were ellipses. To get that, he had to go back and forth plotting Mars' direction from Earth and Earth's direction from Mars. He knew the length of both planets' years, so observations... | Kepler's account of how the third law came to be is as follows (Caspar p.286; emphasis mine):
<blockquote>
On the 8th of March of this year 1618, if exact information about the time is desired, it appeared in my head. But I was unlucky when I inserted it into the calculation, and rejected it as false. Finally, on Ma... | https://astronomy.stackexchange.com |
119,314 | [
"https://physics.stackexchange.com/questions/119314",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46239/"
] | <blockquote>
Displacement of an object is related to time $x=at+bt^2-ct^3$ where a, b and c are constant motion.Then the velocity of an object when it's acceleration is zero is given by
<ol>
<li>$a+\frac{b^2}{c}$</li>
<li>$a+\frac{b^2}{2c}$</li>
<li>$a+\frac{b^2}{3c}$</li>
<li>$a+\frac{b^2}{4c}$</li>
<... | $$v=\frac{dx}{dt}=a+2bt-3ct^2$$
$$acc=\frac{dv}{dt}=2b-6ct=0$$
This gives
$$t=b/3c$$
Put this in $v$ to get the answer
$$v=a+\frac{b^2}{3c}$$
| Think about it this way, when the acceleration is zero, the velocity is constant. Thus:
$$\frac{dv}{dt} = 0$$
Find $t$ in terms of $b$ and $c$
After doing so, substitue them into the equation you found for velocity, and it will give you the answer. I got:
$$a + \frac{b^2}{3c}$$
| https://physics.stackexchange.com |
436,911 | [
"https://softwareengineering.stackexchange.com/questions/436911",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/229710/"
] | <code>List<T>.Enumerator</code> “snapshots” list version upon creation by <code>_version = list._version;</code>. This allows <em>enumerator</em> to halt enumeration when <code>List<T></code> changed during it.
This behavior likely originates from need to move what is hidden under <code>foreach</code> state... | As I see the case, there was no best one options for authors than to exploit control flow constructs in <code>List<T></code> methods in order to preserve common contract of <strong>foreaching</strong>.
I mean mostly that not everyone needs help in ensuring something is valid/complete and that nobody ever said tha... | <blockquote>
So if there is change to List, there is in fact no threat to enumeration.
</blockquote>
Yes there is. You might repeat an element, or skip it. Just because the index refers to <em>an element</em> doesn't mean the enumerator is valid.
What you've shown is that if you carefully craft a situation, you can tri... | https://softwareengineering.stackexchange.com |
108,413 | [
"https://physics.stackexchange.com/questions/108413",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44557/"
] | <blockquote>
A disk of radius 0.10 m is oriented with its normal unit vector $\hat{n}$ at 30$^{\circ}$ to a uniform electric field $\vec{E}$ of magnitude 2000 N/C. What is the electric flux through the disk?
</blockquote>
I know that electric flux is given by the following equation:
$$
\Phi_E = \oint_{S} \vec{E}\cd... | It is, in fact, a double integral! The first notation used
$$\varPhi_E = \oint_S \vec{E} \cdot \mathrm{d}\vec{A} = \oint_S \vec{E} \cdot \hat{n} \ \mathrm{d}A$$
is simply a more compact notation. It's much easier to write $\mathrm{d} \vec{A}$ instead of, say, $r \ \mathrm{d}r \ \mathrm{d}\theta$ all the time. Further... | It is just a more compact notation. It is implied by the integration element $dA$ that you are integrating over the surface.
| https://physics.stackexchange.com |
24,330 | [
"https://stats.stackexchange.com/questions/24330",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7411/"
] | I'm playing with a randomForest and have found that generally increasing the sampSize leads to better performance. Is there a rule / formula / etc that suggests what the optimal sampSize should be or is it a trial and error thing? I guess another way of phrasing it; what are my risks of too small of a sampSize or too... | In general, the sample size for a random forest acts as a control on the "degree of randomness" involved, and thus as a way of adjusting the bias-variance tradeoff. Increasing the sample size results in a "less random" forest, and so has a tendency to overfit. Decreasing the sample size increases the variation in the i... | I ran 4500 random forests over night with some random parameter-settings:
Regression problem <code>Ysignal = x1^2+sin(x2*pi) + x3 * x4 + x5</code>
where any <code>x</code> are sampled independent from a normal distribution, sd=1, mean=1
<pre><code>Ytotal = Ysignal + Yerror
</code></pre>
where <code>Yerror = rnorm(n.... | https://stats.stackexchange.com |
78,341 | [
"https://physics.stackexchange.com/questions/78341",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20884/"
] | Suppose a thermally insulated container is filled with atmospheric air until the pressure reaches 5000 psi. This could represent the filling of a diving cylinder, before thermal dissipation becomes significant.
Initially, then, some mass of air has atmospheric temperature $T_1$ and $p_1$. When forced in to the tank ... | You're trying to ask a question about real life (would the tank melt) with a model that approximates away the very thing that you need (adiabatic). With the assumptions you have made, you are in fact using the correct equations.
The adiabatic assumption is only valid if it is thermally insulated which is not the case ... | Your calculation looks correct to me (although 5000 psi is a little high for a typical diving cylinder). But this calculation gives the final temperature of <em>the air inside the cylinder</em>. If -- after rapid compression -- we wrap insulation around the cylinder and allow the cylinder and the gas to reach equilibri... | https://physics.stackexchange.com |
130,920 | [
"https://mathoverflow.net/questions/130920",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23600/"
] | I am looking for a mathematical field that deal with this concept, I don't have a very formal definition of this and I'll have to count on these naive definitions I provided:
<blockquote>
<ol>
<li>It's about the idea of an adaptative live system;</li>
<li>The system evolves with time cycles;</li>
<li>This syst... | I think you are looking for dynamical systems theory.
In particular (especially discrete) cases you might be interested in automata theory, modal logic and game theory. But your “definition” sounds more like a general notion from dynamical systems theory.
Mathematical biology and modeling are “just” applications.
| It also sound a bit like neural networks;
these are "trained" (adapted) to yield certain output for certain input.
Maybe you will also be interested in Markov processes, (which can also be trained to give certain output for some given input).
Both these concepts are related to something called genetic programming,
wh... | https://mathoverflow.net |
29,614 | [
"https://softwareengineering.stackexchange.com/questions/29614",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3664/"
] | Programming always required to learn new concepts, paradigms, features and technologies and I always have been failed at first attempt to understand new concept what i encounter. I start to blame and humiliate myself without remember before how i understood new concept which i hadn't understand it before.
I can hardly... | Personally, everything is an analogy away. And if I don't understand something, it's probably because I haven't been shown the right concept to bridge me over to the Land of Understand. I usually keep scouring around for different tutorials and eventually one of them will take a different turn than the previous tutoria... | If you don't understand a problem, there is an easier problem that you don't understand.
Find that problem, and solve it. Then try your original problem again, and see if you are ready for it.
| https://softwareengineering.stackexchange.com |
281,406 | [
"https://physics.stackexchange.com/questions/281406",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/115426/"
] | If we consider a simple pulley system with two masses hanging on each end of a MASSLESS and INEXTENSIBLE string around a MASSLESS and FRICTIONLESS pulley, how then can one reason that the tension at each end of the string must be the same?
My own reasoning:
MASSLESS ROPE means that for any segment of the rope with te... | What we mean by a frictionless pulley is that the friction in the bearings of the pulley is negligible, and the pulley is free to rotate without any resistance. We don't mean that the friction between the string and the pulley surface is negligible. In fact, we assume that there is enough static friction between the ... | In general case such system moves with acceleration...
If rope is extensible we cannot assume that the magnitudes of accelerations of the two masses are the same( they will NOT move "jointly"). If the pulley has a mass then tensions on left and right of the pulley must differ to ensure the pulley's rotational accelera... | https://physics.stackexchange.com |
407,839 | [
"https://physics.stackexchange.com/questions/407839",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/187165/"
] | So I kept searching for answers or reasons as to why the sun can generate nuclear fusion at 15 million degrees C when I research that nuclear fusion is achieved at 100 million degrees.
Is it because the conditions of conducting nuclear fusion differ from one another?
| What you've just stumbled upon is the same puzzle that stumped many astrophysicists in the early 20th century. The "100 million degrees" figure you quote is indeed the temperature at which a significant portion of the plasma can undergo fusion reactions by overcoming the classical Coulomb barrier. But we know the Sun's... | Fusion can, in theory, occur at any temperature - even room temperature! It's just that the probability in that case is exponentially tiny (as in like <em>mystically small</em> meaning $10^{1000}$ or greater odds against; the kind of numbers that the ancients used to speculate about in wonder and awe, and not realistic... | https://physics.stackexchange.com |
1,065,495 | [
"https://math.stackexchange.com/questions/1065495",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/200566/"
] | I know that in $\Bbb Z[x]/\langle x^2 - 1\rangle$ the trivial idempotents are $0,1$ and the other idempotents are those elements in $\Bbb Z[x]$ that have the remainder $0$ or $1$ when divided by $x^2 - 1$. I end up with $x + 1$ and $x$ being the other idempotents.
I have no idea about $\Bbb Q[x]$, since now you can h... | By the Chinese Remainder Theorem, $$\mathbb{Q}[x]/(x^2-1) = \mathbb{Q}[x]/((x+1)(x-1)) \to \mathbb{Q}[x]/(x+1) \times \mathbb{Q}[x]/(x-1) \cong \mathbb{Q} \times \mathbb{Q}$$ is an isomorphism. The proof is constructive and therefore includes the construction of the isomorphism as well as its inverse. Have a look at t... | A “direct” proof. Not that Martin's is bad, to the contrary it's very nice.
The ring $\mathbb{Q}[x]/\langle x^2-1\rangle$ can be described as the set of expressions
$$
a+br
$$
with $a,b\in\mathbb{Q}$, where $r\notin\mathbb{Q}$ satisfies $r^2=1$. Moreover $a+br=a'+b'r$ if and only if $a=a'$ and $b=b'$. Then
$$
(a+br)^2... | https://math.stackexchange.com |
586,942 | [
"https://physics.stackexchange.com/questions/586942",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/250725/"
] | In Weinberg's QFT Page 109, he defines the "in" and "out" states as
<blockquote>
the 'in' and 'out' states* <span class="math-container">$\Psi_{\alpha}^{+}$</span> and <span class="math-container">$\Psi_{x}^{-}$</span> will be found to contain the particles described by the label <span class="math-c... | I think I got the point.
In Heisenberg's picture, the state-vectors do not change according to the Schodinger's equation governing the time evolution of the state. Since different pictures are defined in how operators and state vectors are changing with <span class="math-container">$\textbf{time evolution equation}$</s... | <blockquote>
a state-vector <span class="math-container">$\Psi$</span> describes the whole spacetime history of a system of particles.
</blockquote>
Think of <span class="math-container">$\Psi$</span> heuristically as corresponding to the worldlines of a system of particles. (Obviously there are no actual worldlines, b... | https://physics.stackexchange.com |
2,741,818 | [
"https://math.stackexchange.com/questions/2741818",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/494405/"
] | I have the two recursively-defined following sequences:
$u_0 = a$, $v_0 = b > a$, $u_{n+1} = \sqrt{u_nv_n}$, $v_{n+1} = \frac{u_n+v_n}2$.
I want to show that $u_n$ is increasing and $v_n$ is decreasing.
I was thinking that I should show it recursively. First starting off with $u_n$, we can say that $u_{1} = \sqrt... | <strong>Hint</strong>:
First observe that for any $n$, one has $u_n<v_n$ (use the <em>AM-GM inequality</em>).
Supposing $b>a>0$, you easily prove $0<u_n<v_n$. So all you have to prove is
<ol>
<li>$\dfrac{u_{n+1}}{u_n}>1$,</li>
<li>$\dfrac{v_{n+1}}{v_n}<1$.</li>
</ol>
| Your inductive hypothesis is $\color{red}{v_n > u_n}$ then
\begin{eqnarray*}
u_{n+1}=\sqrt{u_n \color{red}{v_n}} > \sqrt{u_n \color{red}{u_n}} =u_n
\end{eqnarray*}
and
\begin{eqnarray*}
v_{n+1}=\frac{\color{red}{u_n} +v_n}{2} < \frac{\color{red}{v_n}+ v_n}{2} =v_n.
\end{eqnarray*}
Finally by AM-GM $v_{n+1} &... | https://math.stackexchange.com |
70,421 | [
"https://dsp.stackexchange.com/questions/70421",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/50860/"
] | With many very similar frames of video that have been compressed with an unavoidably lossy encoding and available now as jpeg stills, are there available good mathematical techniques for recovering detail by considering multiple frames? Certain areas of the image are of great interest and the artifacts there change fr... | The method to improve resolution by few frames is called Multi Image Super Resolution (As opposed to Single Image Super Resolution).
For compression artifacts you can look for JPEG Deblocking algorithms.
| As video compression implicitly tries to track scene motion and express the residual approximately in a compact (and visually pleasing manner), I think that applying general multi frame super reolution is unlikely to give good results unless your video stream is encoded using only i-frames (eg motion jpeg, where tempor... | https://dsp.stackexchange.com |
69,036 | [
"https://mechanics.stackexchange.com/questions/69036",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/50453/"
] | I replaced my <1 year old car battery with a new one during troubleshooting, but the actual problem I had was the alternator. So now I have 1 new car battery and 1 used but good battery (and I can’t return the new one). Can I keep my old battery in my car as a backup? How long will it last? Can I just charge it some... | Hit Craigslist and sell the <strong>new one</strong> as exactly what it is: a <1 week old new battery, with exactly the story you just gave us. You should have takers at 2/3 the price of a new one. You'll need the receipt to prove it.
Put the 1-year-old battery back in the car, you will get at least 3 more year... | <b>Sell it on the second hand battery market!</b>
I'm pretty sure you can find some online site where you can buy and sell used second hand items.
The reason I'm promoting selling it is that:
<ul>
<li>Lead-acid batteries self-discharge</li>
<li>Lead-acid batteries don't like extended discharge for long amounts of ti... | https://mechanics.stackexchange.com |
111,621 | [
"https://physics.stackexchange.com/questions/111621",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46030/"
] | I understand that Cooper pair in low-temperature superconductivity are formed by electron-phonon interaction. Normally one then assumes that electrons of opposite momentum and spin are paired. This is what i dont understand. In my understanding two electrons with opposite momentum should seperate and thus not feel an a... | It is indeed a counterintuitive fact. Let us go slowly through the argument.
You start with a degenerate gaz of fermions. They are piled-up in the momentum space, up to the so-called Fermi level. It means that the last electrons entering the game have the Fermi energy, which is pretty huge ($\sim 10\;000$ Kelvin). Al... | As best I recall (what, me look in Wikipedia? :-) ), The point is that superconductivity and superfluids only can occur for boson-ic particles (thanks, Pauli!). By pairing off electrons, or even $He^3$ atoms, the paired items behave as though they are bosons, thus allowing state degeneracy and all that.
| https://physics.stackexchange.com |
54,499 | [
"https://physics.stackexchange.com/questions/54499",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9070/"
] | I'm reading Sternberg's Group Theory and Physics. I have a question about chapter 1.2 Homeomorphisms.
<hr>
Background:
A Lorentz Metric is defined as $||{\bf x}||^2=x_0^2-x_1^2-x_2^2-x_3^2$
And a Lorentz Transformation $B$ as one which satisfies $||B{\bf x}||^2=||{\bf x}||^2$
Identify ${\bf x}$ with $x=x_0I+x_1\si... | The space of vectors $(0,x_1,x_2,x_3)^T$ may also be defined as the space of 4-vectors $\vec v$ that satisfy $\vec v\cdot \vec e_0 = 0$. The inner product is Lorentzian. If all vector $\vec u$ are transformed to $C\vec u$, then this space of vectors is – by definition – transformed to the space of vectors that obey
$$ ... | If $C$ doesn't change the time component then it is just a spatial rotation!
To show this mathematically we can use $\boldsymbol{e}_{0}$ to construct a projection operator that projects down to the space orthogonal to $\boldsymbol{e}_{0}$:
$$ \Pi = \mathbb{I} - \boldsymbol{e}_{0} \otimes \boldsymbol{e}_{0} $$
Then t... | https://physics.stackexchange.com |
172,500 | [
"https://mathoverflow.net/questions/172500",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31446/"
] | During my work with order preserving homeomorphisms, I got interested in the double arrow space and, subsequently, in the lexicographic square.
I would really like to find examples of spaces like these two.
Specifically, I am looking for a space $X$ with the following properties:
<ol>
<li>$X$ is a compact linearly or... | One of my favorite spaces has this property: the <em>extended long ray</em>.
First, the long ray itself: this is just the space $L$ gotten by pasting together $\omega_1$-many copies of $[0, 1)$ in the natural way. Formally, $L$ is the lexicographic order on $\omega_1\times[0, 1)$, with both viewed as linear spaces in ... | The linear orders which are compact in the order topology are precisely the complete totally ordered sets $X$. By complete I mean that every subset of $X$ has a least upper bound including $\emptyset$ and $X$. If $R\subseteq X$ has no least upper bound, then let $S$ be the set of all upper bounds of $R$. Then $\bigcup_... | https://mathoverflow.net |
186,723 | [
"https://electronics.stackexchange.com/questions/186723",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40815/"
] | Consider the two (equivalent) formulas for the noise power spectra of a ohmic resistor:
$$W_u(f)=4kT\cdot R~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)$$
and
$$W_i(f)=4kT\cdot G~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)$$
with the Boltzmann constant \$k\$, the temperature \$T\$, the resistance \$R\$ and the conductance \$G... | After a couple of talks the following might answer the question:
As stated above it holds that
$$W_i(f)=4kT\cdot G=\frac{4kT}{R}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)$$
with the Boltzmann constant \$k\$ and temperature \$T\$. Increasing \$R\$ does indeed lower the current noise by \$1/R\$. You cannot measure current no... | I think you're comparing two different physical situations. (1) is for voltage across an open-circuit resistor, (2) is for current through a shorted resistor.
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