qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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|---|---|---|---|---|---|
317,639 | [
"https://physics.stackexchange.com/questions/317639",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/148085/"
] | My lessons about optics are long behind me, so I need to confirm a point:
<strong>Are IR and UV affected the same way as visible spectrum by a lens?</strong>
Let's say someone is able to perceive the full light spectrum. If he is looking through a pair of binoculars, does the effect apply to IR and UV as well?
Edit:... | So, work, which the energy expended is given by
$ \textbf{W} = \int \textbf{F} \cdot d\textbf{s} $
Where $\textbf{r}$ is the distance over which the force acts. Let's say that the force is applied directly in one direction and we have no other forces going on (i.e. no gravity). We can then drop the integral and the ... | Let $v$ be the final velocity, $a$ the acceleration and $t$ the time.<br>
Assuming the initial velocity is zero then the distance travelled $x =\frac 12 at^2=\frac 32 t^2$.<br>
The work done is force times distance $=3x=\frac 92t^2$.
| https://physics.stackexchange.com |
4,345 | [
"https://physics.stackexchange.com/questions/4345",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1700/"
] | So we have two particles (A and B) that are entangled.
From what I understand, entanglement isn't destroyed, it is only obscured by subsequent interactions with the environment.
Particle A goes zooming off into outer space.
10 years later, Particle B becomes incorporated into my brain.
The day after that, an alien ... | <blockquote>
From what I understand, entanglement isn't destroyed, it is only obscured by subsequent interactions with the environment.
</blockquote>
Depends on how you view it. There is an explanation of quantum measurement (called decoherence) in which this is true. I will not be using that explanation in this pos... | Even with quantum entanglement, quantum information still can't be transmitted faster than light. This is the no-signaling theorem.
| https://physics.stackexchange.com |
1,882,386 | [
"https://math.stackexchange.com/questions/1882386",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/300848/"
] | $$\lim_{x\to \infty} \frac{x^{\frac{3}{2}}\cdot \arctan(x)}{\sqrt{2x^3+4x^2+x}}\le \lim_{x\to \infty} \frac{x^{\frac{3}{2}}\cdot \arctan(x)}{\sqrt{2x^3}}=\lim_{x\to \infty} \frac{x^{\frac{3}{2}}\cdot \arctan(x)}{\sqrt{2}x^{\frac{3}{2}}}=\frac{\pi}{\sqrt{2}\cdot2}$$
So the limit of $\displaystyle\frac{x^{\frac{3}{2}}\c... | $$\displaystyle\lim_{x\to \infty} \frac{x^{\frac{3}{2}}\cdot \arctan(x)}{\sqrt{2x^3+4x^2+x}}=\lim_{x\to \infty} \frac{\arctan(x)}{\sqrt{2+4\frac{1}{x}+\frac{1}{x^2}}}=\frac{\pi}{\sqrt{2}\cdot2}$$
| Use equivalents:
<ul>
<li>$\arctan x\sim_{+\infty}\dfrac\pi 2$,</li>
<li>$\sqrt{2x^3+4x^2+}x\sim_{+\infty}\sqrt{2x^3}$,</li>
</ul>
hence $\; \dfrac{x^{\tfrac{3}{2}}\cdot \arctan(x)}{\sqrt{2x^3+4x^2+x}}\sim_{+\infty}\dfrac{\pi x^{\tfrac{3}{2}}}{2\sqrt{\mathstrut 2} x^{\tfrac{3}{2}}}=\dfrac{\pi\sqrt{\mathstrut2}}4$.
| https://math.stackexchange.com |
12,847 | [
"https://mathoverflow.net/questions/12847",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3509/"
] | Suppose a compact Lie group $G$ acts on a manifold $M$ with only one orbit type $G/H$ ($H$ denotes the stabiliser group). Then the manifold $M$ becomes a fibre bundle over the quotient manifold $X:=M/G$ with typical fibre $G/H$ and structure group $G$.<br>
On the one hand one could look at the cotangent bundle $T^* X$ ... | These two symplectic manifolds are canonically symplectomorphic.
Notice first, that the map $\mu$ vanishes on the sub-bundle of $T^* M$ of 1-forms vanishing on the fibers of the fibration $M\to X$. Let us call this sub-bundle by $T_h ^* M$ (h- for horizontal).
To construct the symplectomorphism notice that there is ... | In addition to Dmitri's answer: when you're doing reduction at non-zero momentum some interesting things happen: the symplectic reduced space $J^{-1}(\mu)/G_\mu$ then becomes a fiber bundle over $T^\ast X$ with typical fiber the co-adjoint orbit $\mathcal{O}_\mu$. In the case $\mu = 0$, this reduces to the case discus... | https://mathoverflow.net |
312,593 | [
"https://physics.stackexchange.com/questions/312593",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62743/"
] | The Hamiltonian for the quantum harmonic oscillator is
$$\hat{H}=-\dfrac{\hbar^2}{2m}\dfrac{\partial^2}{\partial x^2}+\dfrac{1}{2}m\omega^2 x^2$$
and one can try to factorise it by writing down what later on will turn out to be ladder operators of the eigenspectrum
$$\begin{align}\hat{A}&=\sqrt{\dfrac{m\omega}{2... | <ul>
<li>We know the explicit form of $A$ and $A^\dagger$ in terms of $p$ and $x$.</li>
<li>We know the expression of $H$ in terms of $p$ and $x$.</li>
</ul>
So just express $p$ and $x$ as a function of $A$ and $A^\dagger$, then plug the result in the formula for $H$. To do that, simply find $A + A^\dagger$ and $A - ... | How about this approach:
<ul>
<li>We know that position measurements $\hat{x}\left|n\right\rangle$ yield real numbers;</li>
<li>We know that momentum measurements $\hat{p}\left|n\right\rangle$ yield real numbers;</li>
<li>We know that energy measurements $\hat{H}\left|n\right\rangle$ are supposed to yield real numbers... | https://physics.stackexchange.com |
177,559 | [
"https://softwareengineering.stackexchange.com/questions/177559",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6770/"
] | I'm making a program that will post data to a database, and I've run into a pattern that I'm sure is familiar: A short table of most-likely (very strongly likely) fixed values that serve as an enum. So suppose the following table called <code>Status</code>:
<pre>
Status
Id Description
--------------
0 Unproce... | I would hard-code the enum within your program, as I suspect these different statuses affect your programs logic. If you have a new status, how is your program supposed to react to this new status?
Because the database is part of your application, I don't think it would make sense to affect one without consulting oth... | I would normally load this data into a static cache (usually in a HashMap or something like that) when the application starts up. It avoids having to recompile just because the enum has been modified in some way.
| https://softwareengineering.stackexchange.com |
493,906 | [
"https://electronics.stackexchange.com/questions/493906",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/189890/"
] | Let's says I have a gate driver and a MOSFET. I have made the decision to drive my FET using 5V. The gate driver peak current is 2A. Do I size my 5 volt power supply at 2A plus my other stuff? Do I need more or can I get away with less but at the price of, say, max permissible switching frequency?
| The PEAK driver current is 2A, not the continuous current. Your power supply needs to supply the continuous current to recharge the decoupling caps and the caps are what actually supplies the peak currents to the gate-source capacitance in the MOSFET since the power supply is too slow (or unavailable if it's a high-sid... | If use of a gate-driver requires peak-performance (minimum switching times, quickest possible charging of the FET gate, minimum of ringing), then you need to design a LOW INDUCTANCE power supply.
That means
(1) you use a Ground Plane under the gate-driver and under the FET;
(2) you have 0.1uF SMT from the gate-dr... | https://electronics.stackexchange.com |
163,317 | [
"https://mathoverflow.net/questions/163317",
"https://mathoverflow.net",
"https://mathoverflow.net/users/38889/"
] | Let S be a finite simple nonabelian group, w a word in a finite number of variables which is not a power of another word. Must there be a substitution of elements of S in w such that the resulting element is not 1?
Equivalently, let S be a finite simple group and F a free group on a finite number of variables. Let w b... | The answer is 'no' if you fix $S$ and consider all (primitive) words $w$ (see Derek Holt's answer). However, if you fix the word $w$, then $w$ takes a non-trivial value on $S$ (equivalently, $S$ is generated by values of the word $w$) for all but finitely many non-abelian finite simple groups $S$. This is due to the ... | Let $a$ and $b$ be in a free generating set of $F$ and $w = a^{|S|}b^{|S|}$.
| https://mathoverflow.net |
267,297 | [
"https://security.stackexchange.com/questions/267297",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | I have a web application created with Flask in python that uses asymmetric encryption using RSA, the private key is generated from the user's password and is only stored in a cookie on the user's device, so even I as the person who has access to database cannot decrypt the data. However, I would like the user to be abl... | <blockquote>
the private key is generated from the user's password
</blockquote>
That means you are doing it horribly wrong. The private key should be generated on the client, not on the server. It should be generated through picking two random and sufficiently large primes - nothing else.
<blockquote>
stored in a cook... | <blockquote>
I would like the user to be able to share their data via web application...
</blockquote>
One of the typical approaches is following.
<strong>Briefly</strong>
User A encrypts data with a symmetric key, uploads to the server and shares this key with user B using some secure way.
<strong>Details</strong>
<ul... | https://security.stackexchange.com |
498,346 | [
"https://stats.stackexchange.com/questions/498346",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/208291/"
] | Suppose <span class="math-container">$\boldsymbol X$</span> belongs to the exponential family,
<span class="math-container">$$ f_X\!\left(\,\mathbf{x} ; \boldsymbol \theta\,\right) = h(\mathbf{x}) \, \exp\!\Big(\,\boldsymbol\eta({\boldsymbol \theta}) \cdot \mathbf{T}(\mathbf{x}) - A({\boldsymbol \theta})\,\Big)$$</span... | To get <span class="math-container">$f_{T}\!\left(\,\mathbf{T} ; \boldsymbol\theta\right)$</span>, we take the full density and integrate <span class="math-container">$\mathbf{x}$</span> out:
<span class="math-container">\begin{align}f_{T}\!\left(\,\mathbf{T} ; \boldsymbol\theta\right) &= \int_{{\bf x} : {\bf T(x)... | In a discrete setting, when the sampling space <span class="math-container">$\mathfrak X^n$</span> (assuming an iid sample of size <span class="math-container">$n$</span> from an exponential family) is finite or countable, the conditional distribution of
<span class="math-container">$$\mathbb P(\mathbf X_n=\mathbf x_n;... | https://stats.stackexchange.com |
364,692 | [
"https://softwareengineering.stackexchange.com/questions/364692",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/285517/"
] | We are working on a large (legacy) distributed system with various applications, messaging (soap services, database dblinks, rest services)... We are lacking for documentation and a big view of this complex system. and we are searching a way to know if a certain update on a shared datatype could or not impact our syste... | Push the production stuff into the <code>master</code> branch of a new repo. Create a <code>develop</code> branch from that, and then merge the staging server into it. You may wind up with conflicts that need to be resolved. Once those are resolved, create another <code>feature_branch</code> from <code>develop</code> a... | It's a good idea to have the history. I would create the repository (or one for each product) from the most stable environment. Create branches or diffs for the others.
At a high level:
<ol>
<li>Create a new repo</li>
<li>From a production-based working copy: add all, commit, and push</li>
<li>Checkout master to a ne... | https://softwareengineering.stackexchange.com |
1,186,779 | [
"https://math.stackexchange.com/questions/1186779",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/204820/"
] | Good day, my family had a dinner discussion about polygons and how many sides a polygon has in relation to the angle measurement you'll get when you measure an "arc" encompassing a "side" of the polygon. Of course this is assuming that all sides are equal.
In this case, we'll get 120 degrees for a triangle, 90 degree... | A polygon is never a circle, no matter how many sides it has.
| You and your family are effectively exploring the notion of limits from calculus in a geometric context. Think of this problem in terms of real numbers for a second. If we start at 1 and add $\frac{1}{2}$, and then add $\frac{1}{4}$, and then add $\frac{1}{8}$, etc., how many times would we need to add these terms befo... | https://math.stackexchange.com |
2,291 | [
"https://astronomy.stackexchange.com/questions/2291",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/1495/"
] | I know that tidal forces are pushing Jupiter farther from the Sun, but I couldn't find exactly the yearly amount. In a few billion years would this effect (and subsequent decrease in gravity pull) allow the formation of a new planet from the asteroid belt or would Jupiter take the asteroids with it farther away?
| The only light you would see, would be from the stars outside the black hole. Any light that is generated inside the event horizon would be refracted towards the singularity. You wouldn't see the object in front of you since the light would not reach your eye.
| As said above, you'd see the light coming into the black hole but you mught also see a dim light from Hawking radiation.
| https://astronomy.stackexchange.com |
248,497 | [
"https://security.stackexchange.com/questions/248497",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/252768/"
] | We host our web application on a VPS, I maintain LAMP environment there to fulfill our client needs (I work on relatively small SaaS service provider), I also set up a script to backup the system regularly at night.
Our company had just upgraded all of our Linux VPS to specification of 5gb ram, 5 vcpu, 100gb ssd, etc.,... | No, this is not normal at all.
If you need to give them access, create a new account for them that exists only for as long as they need access. Only give them as much access as they need.
But they should have resource monitoring from the VPS side and shouldn't need local access to the server.
| It's not that surprising in this particular case. If you have an <strong>unmanaged</strong> VPS then they are not supposed to have credentials. If it were preinstalled they could have created an account for themselves, but they chose not to (and if they did, the customer should be made aware of this).
You may have inst... | https://security.stackexchange.com |
199,444 | [
"https://dba.stackexchange.com/questions/199444",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8244/"
] | Many user forms contain an option for "Other - Add Comment" where the user can provide an item not found in the given list.
In other words, the developer sets the list of items. The user must either select an item or type a value.
Examples:
<ul>
<li>How did you hear about us? {Web, TV, Friend, Radio, other}</li>
<li... | To replicate this kind of code, without creating a function:
<pre><code>CREATE FUNCTION dbo.add1(@x int)
RETURNS int
AS
BEGIN
RETURN (SELECT @x + 1);
END
GO
SELECT dbo.add1(v.Value1), dbo.add1(v.Value2)
FROM (VALUES(1,2),(3,4)) AS v(Value1, Value2);
</code></pre>
You can use <code>CROSS APPLY</code>:
<pre><code>S... | I'm putting further work in an answer instead of cluttering up the actual question..
I was able to make progress thanks to <code>Aaron Bertrand's</code> answer, so I've marked that as the answer.<br>
People reading this question should look at that first to get more context.
It turns out that if only one column is ... | https://dba.stackexchange.com |
22,487 | [
"https://mechanics.stackexchange.com/questions/22487",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/12959/"
] | What is this supposed to be connected to? It is screwed into the cabin wall. It seems to be a ground cable of some sort.
<img src="https://i.stack.imgur.com/Pa9dE.jpg" alt="Disconnected Cable">
Also is this hose supposed to be just open like that? This is from the passenger side coming out of the cabin.
<img src="ht... | Yes to both. The top picture is just a ground to the body from wherever it starts at. You'll find many of them around the car and under the bonnet (hood). Trying to find where it started will be a chore, but shouldn't be too difficult. It's probably on the engine very near by. Use the length of it to search around. You... | The ground wire was attached to the end of the intake manifold. The shiny aluminum part in the center right side of the picture. Repair is needed. The A/C evaporator drain is to be left open.
| https://mechanics.stackexchange.com |
162,652 | [
"https://electronics.stackexchange.com/questions/162652",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/44227/"
] | I am trying to run through a sequence of memory and display it on the command window. Here is the code:
<pre><code>int addr[10]; //Address addr is 32 bit
for{int i=0 ; i<10 ; i++}
{
int *p = &addr[i]; //Pointing to the 32 bit addresses from 0 to 9
cout<<p<<endl; //... | Since <code>i</code> is declared as <code>int</code> it will take 4 bytes to store each value of <code>i</code>. Since each address corresponds to a single byte, it will take 4 locations to store an <code>int</code>.
In your case,
It will take memory range <code>002AF948 - 002AF94B</code> to store 0 (<code>0x0000000... | Four bytes are 32 bit since one byte is (normally) 8 bit.
In the past there have been some exotic exceptions to the 8 bit per byte rule but I don't think that they exist any longer.
| https://electronics.stackexchange.com |
320,784 | [
"https://physics.stackexchange.com/questions/320784",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/120609/"
] | I am starting to study physics in detail and as I read about physical quantities, I was puzzled why <em>mol</em> (amount of substance) is taken as a physical quantity.
A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents the amount of substance by telling the... | The mole definitely isn't a fundamental physical quantity. It's just a shorthand for Avogadro's number, to make really big numbers more tractable. It's purely there for convenience, there's nothing fundamentally physically significant about it.
| Mols are a units of quantity. Technically, you can have a two cars, or a mole of cars, two forks, or a mole of forks, two baby rabbits, or a mole of baby rabbits. But since one mole is such a large number, it is only really useful for things that you have lot of, like molecules. In that case, though, it is very useful,... | https://physics.stackexchange.com |
103,385 | [
"https://softwareengineering.stackexchange.com/questions/103385",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23377/"
] | I work with a code base that is over 500K lines of code. It is in serious need of refactoring. There have been refactoring efforts identified that will take longer than the normal two week sprint. These can't be broken up into smaller tasks as I have seen suggested in other answers on this site. The product needs to wo... | If you have the luxury of delaying the refactoring, I suggest focusing coming iterations on adding unit test and automated integration tests to the point where you can comfortably refactor the codebase, and then refactor in a single sprint.
| My suggestion:
<ol>
<li>Create a branch</li>
<li>Merge daily from trunk to your branch and resolve conflicts.</li>
<li>Work until it's done. Your branch may be outside core development for several sprints.</li>
<li>Merge back to trunk.</li>
</ol>
There's no getting around the fact that it will probably get ugly. I do... | https://softwareengineering.stackexchange.com |
268,883 | [
"https://mathoverflow.net/questions/268883",
"https://mathoverflow.net",
"https://mathoverflow.net/users/103376/"
] | Let $f:\mathbb{R} \to \mathbb{R}$ be a smooth function with bounded derivative. Define the Nemytskii map $F:H^1(\Omega) \to H^1(\Omega)$ by $F(u)(x) := f(u(x))$. Here $\Omega$ is a bounded smooth domain.
There exists work where we can deduce continuity and differentiability of $F$ under some assumptions on $f$.
What... | This is not much different from Robert Israel's answer, but here goes:
Let $A(t)=\begin{pmatrix}0&1\\1&t\end{pmatrix}$ and write $A^n(t)=\begin{pmatrix}c_n&b_n\\b_n&a_n\end{pmatrix}$. Then,
$$\begin{pmatrix}c_{n+1}&b_{n+1}\\ b_{n+1}&a_{n+1}\end{pmatrix}=A^{n+1}=\begin{pmatrix}c_n&b_n\\b_n&... | Your matrix (call it $A(t)$) has characteristic polynomial $\lambda^2 - t \lambda - 1$, so it satisfies $A(t)^2 - t A(t) - I = 0$ and thus
$A(t)^{n+2} = t A(t)^{n+1} + A(t)^n$. For $n \ge 2$ I get
$$ A^n = \pmatrix{i^{n-2} U_{n-2}(-it/2) & i^{n-1} U_{n-1}(-it/2)\cr
i^{n-1} U_{n-1}(-it/2) & i^n U_{n}(-it... | https://mathoverflow.net |
904,659 | [
"https://math.stackexchange.com/questions/904659",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/105951/"
] | Stuck on the simplest case in my foray into fields...
I know there is a really similar question out there, but I can't find any contradiction with the field axioms if 1 + 1 = 1 instead of 0.
Can someone explicitly show me the logic behind why 1 + 1 = 0 over the binary field and not 1 or 2?
| Well 2=0 in the binary field. Also, a field is an (abelian) group under addition so it satisfies cancellation: $a+b = a+c \Leftrightarrow b =c$. Since $0$ is stipulated to be the additive identity we have
$$1 + 1 = 1 = 1+0 \Leftrightarrow 1= 0$$
But we know $1 \neq 0$ , so $1 + 1 \neq 1$ in any field. This is a gener... | What's the additive inverse of $1$ if $1+1=1$?
The field axioms unambiguously decide what $+$ and $\cdot$ are for $\mathbb{F}_2$, and the above counter-question should give you an idea why.
| https://math.stackexchange.com |
21,843 | [
"https://softwareengineering.stackexchange.com/questions/21843",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8648/"
] | Not talking about the recent Java/Oracle debacle here, but something I've been wondering recently.
When I first started programming, Java was the big thing client-side, however these days you hardly ever see a Java applet whereas Flash and Javascript are ubiquitous.
Where did Java go wrong? Did Sun decide to concentr... | <ul>
<li>Firewalls would sometimes block java applets, so developers couldn't be sure if they were going to work or not.</li>
<li>They required a browser plug-in, which led many developers to favour javascript over java applets, so that they didn't require the user to download and install a plug-in. The Macromedia Fla... | I believe streaming video was the "killer app" for Flash. Although video had been tried before in Java applets, the frame rate wasn't very high and it required users to install the relatively heavyweight JRE.
Along came Flash with its small install size and (eventually) high video frame rate. It helped that browser ve... | https://softwareengineering.stackexchange.com |
3,409,706 | [
"https://math.stackexchange.com/questions/3409706",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/716605/"
] | So far the complementary solution (that is the solution to the associated homogeneous equation) has only been in the form: <span class="math-container">$$y(t)=c_1e^{at}+c_2e^{bt}$$</span> Where <span class="math-container">$a$</span> and <span class="math-container">$b$</span> are obtained from solving the characterist... | How do you solve for <span class="math-container">$a$</span> and <span class="math-container">$b$</span>? You solve <span class="math-container">$$4x^2+1=0$$</span> which has solutions <span class="math-container">$$x=\pm\frac i2$$</span> with <span class="math-container">$i=\sqrt{-1}$</span>. So the complimentary solu... | You are asking for solutions to <span class="math-container">$$ 4y''+y=0$$</span>
The characteristic polynomial <span class="math-container">$$4\lambda ^2+1=0$$</span> has roots of <span class="math-container">$$\pm i/2$$</span> therefore solutions are <span class="math-container">$$e^{\pm i x/2}=\cos x/2 \pm i \sin x... | https://math.stackexchange.com |
88,433 | [
"https://mathoverflow.net/questions/88433",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16326/"
] | Let $(M,g^{TM})$ a Riemannian manifold of dimension $n$ and $\Delta$ the Laplace–Beltrami operator. I would like to find a reference (analytic or probabilistic) for the following classic result.
<blockquote>
If $p_t(x,y)$ is the kernel of the semigroup $e^{t\Delta}$, then there exist $C,c>0$, such that
$$p_{t}(... | A probabilistic proof is given in the book: "Stochastic Analysis on Manifolds" by E. Hsu.
See Theorem 5.3.4, which also gives the lower bound.
| I'm pretty sure this can be found in Davies, <em>Heat kernels and spectral theory</em>. I'll check when I get to my office in an hour or so.
| https://mathoverflow.net |
148,047 | [
"https://physics.stackexchange.com/questions/148047",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4075/"
] | I'm trying to understand the derivation of the Riemann curvature tensor as given in Foster and Nightingale's <em>A Short Course In General Relativity,</em> p. 102. They start by giving the covariant derivative of a covariant vector field $\lambda_{a}$:
$$\lambda_{a;b}=\partial_{b}\lambda_{a}-\Gamma_{ab}^{d}\lambda_{d... | The covariant derivative for a general tensor of the form $T^{a_1\dots a_n}_{b_1 \dots b_n}$ is given by,
$$\nabla_c T^{a_1\dots a_n}_{b_1 \dots b_n} = \partial_c T^{a_1\dots a_n}_{b_1 \dots b_n} + \Gamma^{a_1}_{cd}T^{d\dots a_n}_{b_1 \dots b_n} + \dots - \Gamma^d_{c b_1}T^{a_1\dots a_n}_{d \dots b_n} - \dots$$
Takin... | A covariant derivative of a tensor is itself a tensor. Actually, when we say something is covariant (or invariant under coordinate transformation), we mean that thing is a tensor. So, in this case $\nabla_\mu V^\nu\equiv T_\mu{}^\nu$. Now calculate $\nabla_\alpha T_\mu{}^\nu$ easily.
\begin{equation}
\nabla_\alpha T_\... | https://physics.stackexchange.com |
40,024 | [
"https://chemistry.stackexchange.com/questions/40024",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/22456/"
] | I am new to chemistry. Could someone explain me how to calculate the charges on anions and cations. I've heard about some crossing method (the left subscript becomes the right superscript and the right subscript becomes the left super script.)
Example: $\ce{Rb2S -> 2Rb+ + S^2-}$
But what about:
$\ce{K2MnO4}$ and $... | Some basic knowledge of the atoms in the periodic table is necessary to extract the ionic charges. In the case of $\ce{K2MnO4}$, for example, we know that the potassium ion is positive, and that the manganate ion is negative. We see that the compound is neutral: has zero net charge. So how can we place charges to get t... | Elements like K, Li, Cs and Rb can only have +1 charge on them (Due to very high second ionization energy). Also, they can't have negative charge due to their low electron gain enthalpy (they are metals and are electropositive in nature). Also, Oxygen can only have -2 (in oxides, eg: H2O), -1 (in peroxides, eg: H2O2) a... | https://chemistry.stackexchange.com |
559,131 | [
"https://physics.stackexchange.com/questions/559131",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101452/"
] | I have an incoherent light source that is of unknown size, and I was wondering about the possible methods to measure its size. The issue is that I am expecting it to be very small (few micrometers), and if I try to use a pinhole camera much smaller than the source size I will not gain enough light to actually resolve t... | You are working in a spectral range for which finding lenses will be a problem, so we'll reject the idea of using a lens.
Making a small pinhole comparable to the wavelength will be difficult or expensive, but you're right that the spot of light that makes it through the pinhole would be the convolution of the source w... | Here is an off the wall thought. Some glues are set with UV light. Are there any that work with xrays? Cover the source with a thin film of glue. Expose it enough to set it. Pry the glue off and look at it under a microscope.
Or the other way around. Cover the source with something that is damaged by xrays. Pry it off ... | https://physics.stackexchange.com |
125,736 | [
"https://softwareengineering.stackexchange.com/questions/125736",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/41085/"
] | I haven't read about this anywhere, but here are my thoughts: programming is inherently intellectually hard. I remember reading in Code Complete something that stuck with me: the author pushing and working on something long hours only to spend the rest of the week fixing it.
This is something managers don't understand... | First off, I'd suggest that other that organizing <em>when</em> items need to be delivered, project managers should stay out of the business of telling the development team <em>when</em> to perform certain activities. The team should be able to figure out for themselves when they need to do what, based on the <em>pri... | I don't think there is a "good time" and a "bad time" for a specific type of task throughout the day for anybody that you could apply universally. For example I'm not much of a morning person but sometimes I wake up in the early morning and remote in because something's just clicked and I realised exactly what needed t... | https://softwareengineering.stackexchange.com |
43,846 | [
"https://mathoverflow.net/questions/43846",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2081/"
] | My question is how should one think of p-adic L functions? I know they have been constructed classically by interpolating values of complex L-functions. Recently I have seen people think about them in terms of Euler systems. But we know only a few Euler systems and there are lot of p-adic L functions.
In case of ellipt... | There are three way to obtain $p$-adic L-functions. The big dream is that one can do all of them for a large class of $p$-adic Galois representations $V$. To study them one starts best to look at the cases $\mathbb{Q}(1)$ for the classical Kubota-Leopoldt $p$-adic $L$-functions or the Tate-module of an elliptic curve e... | It's a sensible question, for this reason: the (classical, complex) L-functions are defined in such a way that you can write them down, as Dirichlet series, at least in a right half-plane. What corresponds for p-adic L-functions? Essentially there isn't anything that matches. You can sit in many lectures on p-adic L-fu... | https://mathoverflow.net |
1,347,158 | [
"https://math.stackexchange.com/questions/1347158",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/223097/"
] | <blockquote>
i)Suppose that $x$ and $y$ are real numbers. Prove that if $x\neq 0$,
then if $y=\frac{3x^2+2y}{x^2+2}$ then $y=3$
ii)Suppose that $x$ and $y$ are real numbers. Prove that if
$x^2y=2x+y$, then if $y\neq 0$ then $x\neq 0$
</blockquote>
What I did is
i)Suppose that $y\neq3\Rightarrow \frac{3x^2+... | <strong>i)</strong> Given $$y=\frac{3x^2+2y}{x^2+2}$$
cross multiplying we have,
$$y(x^2+2)=3x^2+2y$$
$$\implies yx^2+2y=3x^2+2y$$
canceling $2y$ in both side we have,
$$yx^2=3x^2$$
Since $x\neq 0 \implies x^2\neq0$ So dividing both side by x^2, we have
$$y=3$$
<strong>ii)</strong> On contrary suppose that $x=0$ the... | For ii), a better starting approach is to assume that $y=0$ and $x \neq 0$. You are trying to find a contradiction.
Then for the left hand side you would have:
$$ x^2 y = x^2 (0) = 0$$
On the right hand side:
$$ 2x + y = 2x + 0 = 2x \neq 0 \text{$\qquad$ by assumption that $x \neq 0$}$$
| https://math.stackexchange.com |
61,810 | [
"https://dba.stackexchange.com/questions/61810",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36227/"
] | Where DB backups are not available, our support team has been trained to restore using the following steps:
<ol>
<li>Get a copy of the MDF/LDF from a file system backup.</li>
<li>Stop the instance.</li>
<li>Overwrite the existing MDF/LDF files.</li>
<li>Restart the instance.</li>
</ol>
This is without a detach. The M... | It should be OK. after all, that's what the entire goal of recovery is, to survive any abrupt interrupt. Instance shutdown is actually quite a graceful shutdown, will properly close all DBs (should be no pending xact to rollback on recovery).
But the gist of it is that you're using a sledgehammer to break an egg shell... | This is a terrible way to take a backup. Why aren't they using, uh, <strong>backups</strong>? Not just because they don't require that you take down the entire instance.
If you just stop the instance, there isn't really a guarantee that the MDF/LDF files will be detached gracefully. So just because you are able to cop... | https://dba.stackexchange.com |
169,935 | [
"https://electronics.stackexchange.com/questions/169935",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/71109/"
] | I'm trying to test ULN2803 with Led MATRIX.
But with different Logic it is giving no change on the output and making the LED lit up.
Why is this so<img src="https://i.stack.imgur.com/enonL.png" alt="enter image description here">
| It's a simulation model misbehavior, you should add pull up resistors to the outputs (for the simulation only) to correct it.
<img src="https://i.stack.imgur.com/V3Rv1.jpg" alt="enter image description here">
The shown schematic is valid for simulation only, the pullup network is not needed in the real circuit.<br>
... | Try connecting pin 9 to 0V: -
<img src="https://i.stack.imgur.com/wfwFl.jpg" alt="enter image description here">
You don't appear to have a pin 9 on your model?
Current limit resistors are needed for each LED segment although this is only a simulation.
| https://electronics.stackexchange.com |
5,193 | [
"https://dba.stackexchange.com/questions/5193",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1012/"
] | Does anybody know of a way to alter a time zone on a SQL database?
Is there any tool that could find the objects using the date and time?
| The easiest way I have used to see if any objects are using a particular command (e.g. those that use a local time zone, such as <code>GETDATE()</code> and <code>CURRENT_TIMESTAMP</code>) is <code>syscomments</code>. The <code>text</code> column of this table in SQL 2000 has the actual command that makes up the object.... | Assuming SQL Server
<ul>
<li>getdate gives local server time</li>
<li>getutcdate gives utc / gmt</li>
</ul>
There is no timezone setting or changes possible inside SQL Server
| https://dba.stackexchange.com |
117,572 | [
"https://softwareengineering.stackexchange.com/questions/117572",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3139/"
] | I am contributing to a library that is licensed under the MIT license.
In the license and in each class file it has a comment at the top saying:
<blockquote>
Copyright (c) 2011 Joe Bloggs <joe.bloggs@example.com>
</blockquote>
I assume that he owns the copyright to the file, and can change the license of tha... | I'm not a lawyer, but the answer is yes. Copyright holder is the person or entity that can claim right to having created a piece work, or to whom such right has been transferred. The MIT license is not about transferring copyright, but about granting legal right to use the (copyrighted) work as stated in the license. I... | Yes, you can.
<blockquote>
I assume that he owns the copyright to the file, and can change the license of that file as he sees fit.
</blockquote>
He cannot change the terms of existing licenses nor can he prevent new licensees from being issued (by others, but to <em>his</em> code) under different terms. The MIT l... | https://softwareengineering.stackexchange.com |
209,793 | [
"https://mathoverflow.net/questions/209793",
"https://mathoverflow.net",
"https://mathoverflow.net/users/75226/"
] | I just ran across the following expression and would like to know if anyone can identify it:
$\sum\limits_{n=1}^\infty \frac{(-1)^n}{n!}\frac{d^n f(x)}{dx^n}\frac{d^n g(y)}{dy^n}$.
It almost looks like a shift operator,
$T^tf(x)=f(x+t)=e^{t\frac{d}{dx}}f(x)$,
but is a bit more complicated.
| To my understanding the situation is roughly like this. Let $\mathcal{C}$ be an $\infty$-category admiting small limits and colimits and let $f: X \to Y$ be a map of spaces whose homotopy fiber is $n$-truncated for some $n$. One can then define what it means for $f$ to be $\mathcal{C}$-ambidextrious. When $f$ is $\math... | I hope someone more knowledgable about this replies. But it seems to me the nlab comment is pointing to the remarks after equation (3.9) in [FHLT]:
<blockquote>
To guarantee that this formula describes a well-defined functor
from $Fam_n(C)$ to $C$, we need to make certain assumptions on $C$: namely,
that it... | https://mathoverflow.net |
455,461 | [
"https://physics.stackexchange.com/questions/455461",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99217/"
] | Let <span class="math-container">$A,B$</span> be two non commuting observables, then we do know that
<span class="math-container">$\langle (\Delta A)^2 \rangle \cdot \langle (\Delta B)^2 \rangle \geq \frac{|[A,B]|^2}{ 4}.$</span> Also, we do know that, when the system is in an eigenfunction state of <span class="math... | Your claim that the r.h.s. is zero is simply incorrect. The general Robertson-Schrödinger uncertainty relation is
<span class="math-container">$$ \sigma_A(\psi)\sigma_B(\psi) \geq \langle \frac{1}{2}[A,B]\rangle_\psi,$$</span>
where <span class="math-container">$\sigma_A(\psi)$</span> is the standard deviation of <span... | To see this, you have to be a Little more mathematical precise. Consider the commutator
<span class="math-container">$[A,B]=AB-BA$</span>.
Take the norm <span class="math-container">$||...||_n$</span> (with natural number <span class="math-container">$n$</span> as a parameter) defined by <span class="math-container">... | https://physics.stackexchange.com |
220,461 | [
"https://stats.stackexchange.com/questions/220461",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/119895/"
] | From a car, I get a value every second for accelerator pedal, from 0 to 100%. When you don't touch it, it reports 0%, and when you kick it to the max, that is 100%.
I want to calculate how much change there is in this value. It will be one of many indicators of how you drive (how aggressively).
The best I have so f... | Average absolute value from one reading to the next is potentially a very good measure of volatility. You might consider whether a 1 second interval is optimal, vs. computing successive changes after averaging over, say, 3s intervals. Other useful summaries might include the maximum acceleration over a long time peri... | There are two analogous areas in which you may be able to find pre-existing formulae.
Water level measurements over time: it seems you are truly seeking a measurement similar to the most common water level over a given time period. Farming and geological sites will have loads of equations related to that for you to c... | https://stats.stackexchange.com |
5,312 | [
"https://math.stackexchange.com/questions/5312",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1960/"
] | Suppose we have a $3\times 3\times 3$ cube of cubes (i. e. $27$ cubes) and consider the graph whose vertices are the cubes, and let an edge connect two iff they have touching faces. I'm quite sure there is no Hamilton path that starts at the middle cube and ends in a corner cube, though I'm not sure how to prove it wi... | If you give 3D coordinates to the cube nodes $(x,y,z)$. Two nodes are adjacent iff they differ by exactly $1$ in exactly one of the coordinates.
Consider $x+y+z$. The parity(whether it is even or odd) of this flips each time you move to an adjacent node.
The parity of the center cube and the corner cube are different... | Here is a more general framework for problems of this kind.
A bipartite graph is one for which the vertices can be divided into two sets so that any edges only join vertices which are not in the same same one of these two sets. Bipartite graphs can be vertex colored with two colors and any circuits they have must have... | https://math.stackexchange.com |
50,387 | [
"https://softwareengineering.stackexchange.com/questions/50387",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18030/"
] | From my experience of working on several Java based projects, I've seen tons of codes which we call 'dirty'. The unconventional class/method/field naming, wrong way of handling of exceptions, unnecessarily heavy loops and recursion etc. But the code gives the intended results.
Though I hate to see dirty code, it's ti... | It's worth it, and it should be done by the whole team. "When it stinks, change it" works for babies & code (thanks, Kent Beck).
Some have said that for a little, short-term project, it's not worth doing. I don't agree. In the first place, we rarely know just how short-term a project is going to be, but in the ... | I tell my students that this is the order I expect that code be written about (what I care about most to least):
<ol>
<li>Documentation - if I don't know what it is supposed to do how will I know if it is doing it properly or not?</li>
<li>Formatting and conventions - if I cannot read it how will I know what it is att... | https://softwareengineering.stackexchange.com |
7,235 | [
"https://chemistry.stackexchange.com/questions/7235",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/43/"
] | Question is rather self-explanatory. Came up during a lecture without a concrete answer.
I understand that the differences in emission wavelengths is due to relaxation to the lowest energy level of S1, but <strong>why do fluorescent molecules necessarily overlap in their excitation and emission spectra?</strong>
| The problem you are having with the formula is based on a misunderstanding about how far you can take molecular and structural formulae.
For compounds that form distinct molecules it is often worth writing the molecular formula in a way that helps you understand the structure of the molecule. But this is a convenienc... | Every $\boxed{^{14}\textrm{Si}}$ atom is surrounded by <strong>4</strong> $\boxed{^8\textrm{O}}$ atoms. On the other hand, every $\boxed{^8\textrm{O}}$ atom is surrounded by <strong>2</strong> $\boxed{^{14}\textrm{Si}}$ atoms.
Suppose that the number of $\textrm{Si-O}$ bonds is $n$, then the number of $\boxed{^{1... | https://chemistry.stackexchange.com |
4,551 | [
"https://mechanics.stackexchange.com/questions/4551",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/546/"
] | I noticed the other day that a component (breather valve) was not fitted properly (the clip that held the valve cover breather in place was sitting between the O-ring and the lip, instead of fastening the component to the top of the engine) and since have been trying to learn more about the PCV system in my car.
When ... | Whether or not it's right for your car, I can't say as I don't know anything about Audis. However, it's normal for there to be some (not a lot) oil in the intake of the cars I'm familiar with.
| I'm curious to what you found by blowing into the valve. I recently replaced the crankcase vent tube which attaches to this valve. Upon disassembly, I cleaned out the oil gunk from the valve, but was able to blow into every hole with no issue. I'm assuming there should be some sort of diaphram in there, but not so o... | https://mechanics.stackexchange.com |
238,922 | [
"https://mathoverflow.net/questions/238922",
"https://mathoverflow.net",
"https://mathoverflow.net/users/76102/"
] | In his famous book 'Introduction to Analytic and Probabilistic Number Theory', Gérald Tenenbaum established the following result (Theorem III.3.5):
Let $g$ be a positive multiplicative function and let $A$ and $B$ be two constants such that for all $y\geq 1,$
$$\sum_{p\leq y} g(p) \log{p} \leq Ay \quad \textrm{ and }... | In the French edition, it is said that the considered constant does not exceed $4(1+9\lambda_{1}+\lambda_{1}\lambda_{2}/(2-\lambda_{2})^2)$ where $\lambda_{1}>0$, $0\leq \lambda_{2}<2$ are such that $g(p^\nu)\leq\lambda_{1}\lambda_{2}^{\nu-1}$.
| You can also find a very clean explicit version of Tenenbaum's inequality as Proposition 2.10 in www.dms.umontreal.ca/~andrew/PDF/Pretentious010611.pdf . The proof is short enough that you should be able to re-produce it as a Lemma (including of course the appropriate references).
| https://mathoverflow.net |
138,028 | [
"https://dba.stackexchange.com/questions/138028",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/26426/"
] | I have a history table which has an 'ID' and 'TIMESTAMP' column as such
<pre><code>CREATE TABLE hist (
HIST_ID INTEGER,
HIST_TIMESTAMP TIMESTAMP,
ID INTEGER, -- this is the id of the table that is being tracked
--OTHER COLS
);
</code></pre>
I also have an index on this table as such
<pre><code>CREATE INDEX h... | Index usage is obviously possible, but optional.
<pre><code>CREATE TABLE hist (
HIST_ID INTEGER,
HIST_TIMESTAMP TIMESTAMP,
ID INTEGER -- this is the id of the table that is being tracked
--OTHER COLS
);
CREATE INDEX hist_ix ON hist (ID, HIST_TIMESTAMP);
explain plan for SELECT ID, MAX(HIST_TIMESTAMP) FROM hi... | Your index is a composite index on both hist_id AND hist_timestamp. Since hist_id is the leading portion of that index, the index can't be used when your WHERE predicate is on just the trailing hist_timestamp portion.
| https://dba.stackexchange.com |
175,936 | [
"https://mathoverflow.net/questions/175936",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30186/"
] | Sorry if this sounds like a silly reference request, but I wasn't able to track down any. I'm looking for proof, via forcing, that axiom of choice can fail in a model of $ZF$. All of papers I found where either proving something more sophisticated or, if it was some introductory paper/book, it showed that $\neg CH$ is ... | This is difficult to prove using forcing, for one simple reason.
If $M\models\sf ZFC$, and $G$ is an $M$-generic filter (for some forcing notion), then $M[G]\models\sf ZFC$.
In other words, the only way to use forcing to have a model where the axiom of choice fails, is if the ground model was such that the axiom of c... | As Asaf wrote, the usual construction of models of $\neg AC$ consists of forcing followed by passing to an inner model. There is, however, an alternative construction that might be closer to what you're looking for. One can begin with a model of ZFC and first construct a model of ZFCA, a modification of ZFC that allow... | https://mathoverflow.net |
64,442 | [
"https://physics.stackexchange.com/questions/64442",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21904/"
] | The first law says that the change in internal energy is equal to the work done on the system (W) minus the work done by the system (Q). However, can $Q$ be any kind of work, such as mechanical work? For example, does a string heat up if it is attached to a block and a tension is applied to move the block? And what abo... | The work in the first law is exactly the usual work $W=\int Fdx\rightarrow\int PdV$. For point particles, this is enough to completely specify the behavior of the system using Newton's first law, or energy methods. However, for macroscopic objects, the motion of the internal components (in thermodynamics these would be... | $Q$ is heat and $W$ is work. $Q$ is considered positive when it is added to the system and work is considered positive when work is done by the system. Also remember that $Q$ and $W$ are energies in transit I.e energies associated when system moves from one state of equilibrium to another state of equilibrium. One cann... | https://physics.stackexchange.com |
221,953 | [
"https://security.stackexchange.com/questions/221953",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/221732/"
] | How secure is a 4 digit numbers only captcha?
How many tries will take to be able to bruteforce that captcha?
| GOG is not a pirate or cracking group. Removing DRM is a good thing for anyone owning an original product.
They officially re-sell games and their modifications of the games make the more compatible with latest operating systems. Removing the DRM is not the only thing they do.
I do not like the fact that they add var... | A digital signature is as trustworthy as the company signing. Therefore, the fact that an executable is signed means nothing. Anyone can set up a fake company and create a signature for that company. This fake company can then use their own signature to spread malware.
However, GOG is generally seen as trustworthy an... | https://security.stackexchange.com |
103,282 | [
"https://security.stackexchange.com/questions/103282",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/89792/"
] | I run my own mail server and would like to use different addresses on the same domain. If I were to sign mails from those addresses, I'd have to generate new PGP keys for each and every one of them. This could become unmanageable very quickly.
As I understand it, DKIM signatures prevent the mail from being tampered ... | First, DKIM only gives you the assurance that:
<blockquote>
a DNS administrator was involved in the process of signing this message.
</blockquote>
That DKIM signature is intended for a reputation to be built with a "selector". A selector (signing key) is issued:
<ul>
<li>per user</li>
<li>per groups of users</l... | PGP offers end-to-end encryption, your e-mail client signs the message, and the receiver's e-mail client verifies it. With DKIM, your mail server signs the message. The difference is that the message could be altered in transit while your client submits the message to the server. You can remove that risk by submitti... | https://security.stackexchange.com |
158,443 | [
"https://stats.stackexchange.com/questions/158443",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/45720/"
] | Can anyone explain the link between bias-variance tradeoff and precision-recall tradeoff. Are they effectively the same thing?
| Well there are parallels between the two, for the mean squared error case, the error of the model is due to its bias and its variance.
$MSE(W) = Bias^2(W) + Var(W)$
where, $Bias(W) = E[W] - \theta$, if $\theta$ is the true parameter.
If the model is able to fit the training dataset very well it would have a low b... | In general precision-recall tradeoff is seen as a discrimination threshold for what we consider positive. A more strict/picky/pessimistic threshold will lead to higher precision (at the cost of ignoring possible positive cases). A more lax/optimistic threshold will lead to higher recall (at the cost of false alarms).
B... | https://stats.stackexchange.com |
441,581 | [
"https://softwareengineering.stackexchange.com/questions/441581",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/413443/"
] | I am currently working on a web product where we have a testing strategy that includes end-to-end testing.
Our tech lead is of the opinion that each e2e test should only validate a single feature. For example, we would have a test for creating an account, a separate test for logging in and an other separate test for up... | This isn't something where there will be a law that says "you can't use facebook for hosting", that will be left up to the contract between facebook and you, i.e. their terms of use.
You might well find that for a small volume of images that you currently want to store, you <em>can</em> do exactly this. It wo... | It's an interesting idea, not for the commercials but for potential anonymous distributed storage.
The problem of course is you would run afoul of the Terms and Conditions of any site you used and presumably have your accounts periodically banned and data deleted.
To deal with that you would have to automate account cr... | https://softwareengineering.stackexchange.com |
114,330 | [
"https://physics.stackexchange.com/questions/114330",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/47211/"
] | Note: This is for a physics project, so please don't just give me the answer...
Say we have a cup that is 3/4 full with water. We place that cup (with the water in it) upside down on a smooth table. Why doesn't the water fall out?
This is my understanding... The cup on the table has created an air tight seal that do... | Consider a couple of cases:
If the glass was completely full, no air, there is nothing inside the glass to balance the air pressure outside (the water can only exert its own vapour pressure, which at room temperature is much less than typical ambient air pressures). So, the air outside the glass keeps everything in pl... | I would imagine this has to do with surface tension. If the space between the table and the glass is small enough, you get the same effect that makes water not able to escape a small hole (the force due to the surface tension is higher than that due to the pressure).
I guess a good experiment to test if this may be th... | https://physics.stackexchange.com |
518,201 | [
"https://physics.stackexchange.com/questions/518201",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/238016/"
] | I came upon this question recently while studying about buoyancy. It goes like this:
<blockquote>
If an iron block is covered with ice and floats in a tub of water, what will be the change to the water level when the ice melts and the iron submerges completely?
</blockquote>
According to me the the water level shou... | No, you cannot write that particles are allowed to surpass the speed of light but with a vanishing probability. The fundamental reason is that statistical mechanics for classical particles is constructed in phase space <span class="math-container">$(\vec r,\vec p)$</span> Therefore, in special relativity, the partition... | The Maxwell-Jüttner distribution describes the distribution in a relativistic gas:
<span class="math-container">$$ f(\gamma) = \frac{\gamma^2\beta}{\theta K_2(1/\theta)}e^{-\gamma/\theta}$$</span>
with
<span class="math-container">$$ \theta = \frac{kT}{mc^2}$$</span>
The Boltzmann factor is defined in terms of ene... | https://physics.stackexchange.com |
274,057 | [
"https://stats.stackexchange.com/questions/274057",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/157531/"
] | As far as I know in K-fold cross validation the samples are split into k sets and at round k-1 of these are used for the training of the model and the last one is used for testing the model and estimating the error of the model. Totally k measurements are done and finally is made the mean of the errors.
So, if my desc... | Leave-one-out fits the model with k-1 observations and classifies the remaining observation left out. It differs from your description because this process is repeated another k-1 times with a different observation left out. You can learn about this from the original paper by Lachenbruch and Mickey in 1968. In my ans... | In loocv method we divide the dataset as one data point for test data while all the remaining data points as our train data. We then validate our model by using this n-1 train data against 1 test data. We perform n iterations like this with 1 test data being forwarded and remaining n-1 data being our new train data. Th... | https://stats.stackexchange.com |
441,603 | [
"https://softwareengineering.stackexchange.com/questions/441603",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/421687/"
] | I have an intuition, that I'd like to read what others have talked about. To me, it seems fairly intuitive that when you have a function which is called multiple times with the same arguments, it would be better to create an abstraction which doesn't require arguments, to avoid duplication. So for example, if I have:
<... | <blockquote>
What I'm wondering is if there are good theoretical treatments of this question by scholars, (or even a good popular article will do as well), since I couldn't find anything.
</blockquote>
Not really. However, you will read often that the fewer arguments the better. Zero-argument functions are ideal. This ... | It doesn't really make a difference in the number of mental entities, as the parts of the function name in composite names such as <code>getFooBarErrorMessage</code> also constitute mental entities. You just moved them from the parameter list where the reader could quickly see that this is just the plain old <code>getE... | https://softwareengineering.stackexchange.com |
9,879 | [
"https://mathoverflow.net/questions/9879",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3578/"
] | I've started using TikZ for a paper I'm writing and am worrying that a journal might not accept the paper with inline TikZ. I had to update my PGF installation for all the examples to work and I'm not even sure that my collaborator will have an updated version...
So here are the questions.
-Do people know if journals... | There is a method for doing this in the back of the TIkZ manual; you can put special commmands around a TikZ picture do have it make a separate PDF which you then include as usual graphics. I'll admit, though, that I've had poor luck using it. I'd rather just give an earful to any journal who doesn't like TikZ.
| It is not exactly answering either of your two questions, but here is another work-around. I had problems putting papers on the arxiv which used pgf/tikz because the version of pgf/tikz they used at the arxiv was not as up to date as my version. The admin at the arxiv told me to do the following. LaTeX your file wit... | https://mathoverflow.net |
130,711 | [
"https://softwareengineering.stackexchange.com/questions/130711",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/20717/"
] | Consider these two examples:
<h3>Passing an object to a constructor</h3>
<pre><code>class ExampleA
{
private $config;
public function __construct($config)
{
$this->config = $config;
}
}
$config = new Config;
$exampleA = new ExampleA($config);
</code></pre>
<h3>Instantiating a class</h3>
<pre><code>c... | I think the first one will give you the ability to create a <code>config</code> object elsewhere and pass it to <code>ExampleA</code>. If you need Dependency Injection, this can be a good thing because you can ensure that all intances share the same object.
On the other hand, maybe your <code>ExampleA</code> <em>requi... | Do not forget about testability!
Usually if the behavior of <code>Example</code> class depends on the config you want to be able to test it without saving/modifying the internal state of the class instance (i.e. you would want to have simple tests for happy path and for wrong config without modifying the property/meme... | https://softwareengineering.stackexchange.com |
589,869 | [
"https://physics.stackexchange.com/questions/589869",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/278243/"
] | The product of annihilation operator with zero ground state of a harmonic oscillator is zero since energy cannot be negative or less than zero. I understand this explanation but what is the intuitive explanation of its conjugate operator i.e creation operator when operating on bra is also zero ?
I understand this part,... | The statement that <span class="math-container">$a|0\rangle=0$</span> is exactly the same as the statement <span class="math-container">$\langle 0|a^\dagger=0$</span>. This is one of these things that is easier to see in the mathematicians notation. In their notation, the inner product between two vectors <span class="... | I'm not aware of any "intuitive" physical reason why this must be, whatever that may mean. This is a straight mathematical application of the standard results (<span class="math-container">$\hat A$</span> and <span class="math-container">$\hat B$</span> are operators): <span class="math-container">$$(AB)^\dag... | https://physics.stackexchange.com |
76,898 | [
"https://stats.stackexchange.com/questions/76898",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28740/"
] | This should be a very elementary question, yet I cannot figure out where I am going wrong.
The matrix below contains data on the colour distributions of balls in two urns. I am looking for a formal method that can tell me whether the contents of the two come from the same population distribution.
<pre><code>freqs = c... | You correctly performed a $\chi^2$-test of independence, so the only problem is in the formulation of its hypotheses and the interpretation of the test result:
The $\chi^2$-test of independence tests the null hypothesis "The two color distributions are <em>equal</em>" versus the working hypothesis of any difference. T... | Suppose Y | X = 0 and Y | X = 1 are two multinomial distributions indicated by X. Then:
P(Y = y| X = x) = P(Y = y) implies independence, it also implies:
P(Y = y| X = 0) = P(Y = y| X = 1) and vice versa.
i.e., test of independence equivalent to test of same distribution
| https://stats.stackexchange.com |
7,788 | [
"https://dsp.stackexchange.com/questions/7788",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/3666/"
] | I've just stepped into the FFT's world since the last weeks, therefore I still don't have an clear overall idea of how to setup the frequency array.
In case of <code>even</code> number <code>N</code>, I usually do (with respect to the Nyquist cut-off frequency)
$f=\left(-N/2\,:\, N/2-1\right)*f_{s}$
but how does it ... | Short answer: yes, I think so.
Long answer: The FFT is just a fast implementation of the DFT. The frequency spacing of an N-point DFT operation is $\frac{f_s}{N}$. Samples of the DFT where $\omega \ge \pi$ correspond to the negative frequencies. If N is odd, then $\frac{N-1}{2} \cdot \frac{2\pi}{N}$ is less than $... | Posted for anyone who may find this useful...
I created a picture that shows DFT frequency bin spacing for odd and even cases of N where N is the number of samples. FFTs usually operate on an even number of samples (the algorithm works by repeatedly breaking the problem into halves), so only the even case applies. T... | https://dsp.stackexchange.com |
653,751 | [
"https://electronics.stackexchange.com/questions/653751",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/332721/"
] | Over time, I lost all four rubber feet that were under my laptop (Asus UX530U) and I want to replace them. The original ones used to stick to the laptop by having a little rubber pin plugged into the aluminum case through a hole, and also being glued to it. The original rubbers aren't available anymore, so I bought oth... | Use double-sided polyimide ("Kapton" is one brand) tape, rather than liquid glue which can be hard to control and messy to remove. Polyimide tape is designed for use around sensitive electronics. It's even available in small disc shapes, but it will be easier to obtain as a 1/2" wide roll which you can c... | It’s a valid concern, but there really aren’t any glues that - when used on the exterior of the laptop’s case - would affect the electronics inside.
One potentially iffy glue would be the vinegar-smelling silicone polymer. The acetic acid produced while it cures can corrode electronics. But: 1) it’s not a great glue fo... | https://electronics.stackexchange.com |
92,415 | [
"https://chemistry.stackexchange.com/questions/92415",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/59919/"
] | There is something I don't understand about a particular application of the Le Chatelier principle. The following system is in equilibrium: $$\ce{CH3COOH + H2O <=> H3O+ + CH3COO-}$$ If I add some $\ce{H3O+}$ the reaction will shift left. Now if I keep adding $\ce{H3O+}$, it will keep shifting left until the $\ce{... | <strong>tl;dr</strong>
<blockquote>
What wasn't clear to me that the second reaction is going to be that of a salt dissolving reaction that is dissolved completely as is claimed in the video.
</blockquote>
Remember the rule: "All ionic salts and strong acids/bases are 100% dissociated in aqueous solution"
<hr>
<b... | The solution which is $0.15$ M in $\ce{NH_3}$ and $\ce{0.35 M}$ in $\ce{NH_4NO_3}$, acts as nothing but a <strong>basic buffer</strong> solution. <br/>Applying the Henderson-Haselbach equation for basic buffers, $$\ce{pOH = pK_b + log({[salt]/[base]})}$$ Here the salt ( which is actually the salt formed by the base aft... | https://chemistry.stackexchange.com |
370,662 | [
"https://math.stackexchange.com/questions/370662",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/72616/"
] | We know that the formula for computing a geometric series is:<span class="math-container">$$\sum_{i=1}^{\infty}{a_0r^{i-1}} = \frac{a_0}{1-r}$$</span>
Out of curiosity, I would like ask: Is there any ways the formula can be derived other than the following two ways?
<hr />
Method 1 (The way I found on my own):
<span cl... | If by derive, you mean go from the summation to the fraction representation, you probably identified the best ways of doing it. However, here's one non-rigorous way to get the result going the other way, i.e., starting with the fraction
$$
\frac{a_0}{1-r}
$$
Some have observed that you can write the Taylor series fo... | <span class="math-container">$a+ar+a(r^{2})...=s$</span>
<span class="math-container">$a+rs=s$</span>
<span class="math-container">$a+rs-s=0$</span>
<span class="math-container">$a+(r-1)s=0$</span>
<span class="math-container">$-a=(r-1)s$</span>
<span class="math-container">$\frac{-a}{r-1}=s$</span>
<span class="math-c... | https://math.stackexchange.com |
24,358 | [
"https://electronics.stackexchange.com/questions/24358",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6694/"
] | I want to run a parallel algorithm I will implement in Verilog/VHDL and use a FPGA to run it.
I have some questions:
<ol>
<li>How can I make an http request to servers using an FPGA - should I use a computer and transfer the data to registers?</li>
<li>What are the parameters in an FPGA which indicate the number of r... | As far as microcontroller eval boards ready to use out of the gate, there is the arduino family of course. but also consider the msp430 launchpad for $4.30. good instruction set and similar in performance to the avr with a lean toward low power/cost. For $20 you can get the stm32f4 discovery (not to be confused with... | The Arduino is a great introduction to programming a microcontroller.
There is a big difference between writing software for a PC and writing firmware for a microcontroller.
The Arduino would be a good starting point for getting your head around interfacing with peripherals etc without having to get bogged down in de... | https://electronics.stackexchange.com |
135,029 | [
"https://electronics.stackexchange.com/questions/135029",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52466/"
] | I want to build my own switching power supply. I already know how to make a 10 Ampere Linear supply, and I'm wondering if I should bother. What do I have to learn to do a switching supply? What makes a switching supply better if they both end up giving me DC?
What I don't get is the "inefficiency" argument. Maybe lin... | The answer to which one you use depends on the application, and the efficiency needs.
For example, you're asked to make a phone charging dock. The dock is powered via a 12 V wallwart, and powers the phone with 5V of power at 500mA. Using a linear regulator, 3.5W is dissipated.That's quite a bit of waste, but you're co... | As DoxyLover pointed out, it's not just a matter of "getting hot". The efficiency of a linear regulator is Vout / Vin, which is <em>really</em> bad when there's a large difference between input and output. Consider a modern desktop CPU running at 0.9V for an extreme example.
Another advantage of switching regulators ... | https://electronics.stackexchange.com |
282,138 | [
"https://physics.stackexchange.com/questions/282138",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/130934/"
] | Quantum mechanical effect such as quantum mechanical tunneling, quantum mechanical confinement, quantum entanglement, or any other quantum mechanical effect to which I may not be aware, what is the largest scale that we have seen/verified these effects to have taken place at? Is it at the sub-atomic scale, at the atomi... | Quantum effects such as a wave like behavior are relevant until a measurment of the vector state occurs. At a complex molecular scale the particles are constantly measured by each other and the wave function collapses. Therefore the quantum effects remain at atomic scales and below.
| Super-Conductivity and Super-Fluidity are macroscopic quantum phenomena.
| https://physics.stackexchange.com |
4,354,207 | [
"https://math.stackexchange.com/questions/4354207",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/971434/"
] | I'm stuck on a problem about <span class="math-container">$\sum_{n=1}^\infty \frac{1}{(n^{\frac{2}{\beta}}(n^{2\beta}+1))^{\frac{1}{5}}}$</span>. I need to find for which values of <span class="math-container">$\beta$</span> this series converge (the correct answer is <span class="math-container">$0 < \beta < \f... | Clearly, the series diverges for <span class="math-container">$\beta < 0$</span> since as <span class="math-container">$n \to \infty$</span>, we have
<span class="math-container">$$a_n =\frac{1}{[n^{\frac{2}{\beta}}(n^{2\beta} +1)]^{\frac{1}{5}}}= \frac{n ^{\frac{2}{5|\beta|}}}{(n^{-2|\beta|}+1)^{\frac{1}{5}}}\to +\... | Notice that :
<span class="math-container">$$\frac{1}{(n^{\frac{2}{\beta}}(n^{2\beta}+1))^{\frac{1}{5}}} \sim \frac{1}{n^{\frac{2}{5 \beta} + \frac{2\beta}{5}}}$$</span>
We deduce that the series :
<span class="math-container">$$\sum \frac{1}{(n^{\frac{2}{\beta}}(n^{2\beta}+1))^{\frac{1}{5}}}$$</span>
converges if, and... | https://math.stackexchange.com |
2,305,652 | [
"https://math.stackexchange.com/questions/2305652",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Why does free groups need to be infinite? I couldn't see a proof of this, the book just said it is "obvious" which got me frustrated. Could someone at least give me an intitutive reason behind free groups being infinite?
Also, are the trivial subgroups of free groups are free groups? If so, why?
Why are abelian group... | I think you mean $a=b$.
Thus, $2a>c$ or $\frac{a}{c}>\frac{1}{2}$ and
$$k=\frac{r}{R}=\frac{\frac{2S}{a+b+c}}{\frac{abc}{4S}}=\frac{16S^2}{2abc(a+b+c)}=$$
$$=\frac{(a+b-c)(a+c-b)(b+c-a)}{2abc}=\frac{(2a-c)c^2}{2a^2c}=\frac{\frac{2a}{c}-1}{\frac{2a^2}{c^2}}.$$
Hence,
$$\frac{2ka^2}{c^2}-\frac{2a}{c}+1=0,$$
which g... | We know that $r=4R\sin{(\dfrac{A}{2})} \sin{(\dfrac{B}{2})} \sin{(\dfrac{C}{2})}.$ where A, B and C are the angles of the triangles.
And $\dfrac{a}{c}=\tan{A}$, where A is the equal angles or base angles which can be proofed using sine rule.
Now $\frac{r}{R}=k=8\sin{(\dfrac{A}{2})}\cos{(\dfrac{A}{2})}$,
$\therefore k... | https://math.stackexchange.com |
406,653 | [
"https://stats.stackexchange.com/questions/406653",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/45971/"
] | I'm trying to figure out what <span class="math-container">$E[X - E[X | Y] |Y]$</span> equals to. Assuming that <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> are continuous random variables, I thought that
<span class="math-container">$E[X - E[X | Y] |Y] = E[X |Y] - E[E[X|Y]|Y] = ... | Since <span class="math-container">$\mathbb{E}[X|Y]$</span> is a function of <span class="math-container">$Y$</span> (but not <span class="math-container">$X$</span>), it is constant when taken conditional on <span class="math-container">$Y$</span>. Hence, you have:
<span class="math-container">$$\begin{equation} \be... | Firstly, apply linearity of expectation:
<span class="math-container">$$E[X-E[X|Y]|Y]=E[X|Y]-E[E[X|Y]|Y]$$</span>
The first term needs no further modification, while he second term can be simplified. <span class="math-container">$E[X|Y]$</span> is a function of <span class="math-container">$Y$</span>, and <span class="... | https://stats.stackexchange.com |
87,819 | [
"https://mathoverflow.net/questions/87819",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36814/"
] | Dear MOs,
Let $\mathcal{D}(R):=C_c^\infty(R)$ be the smooth functions with compact support. Its dual space is the space $\mathcal{D}'(R)$ of distributions. This space $\mathcal{D}(R)$ has its weak *-topology induced by $\mathcal{D}(R)$, which makes it into a locally convex space (See Rudin Functional Analysis P.160). ... | Well, that depends on what topology you want to put on the space of distributions. The weak$^*$ is probably not really the one you would like to take. Instead, the strong dual might be more useful. The seminorms of this topology are given by
$$p_B(\varphi) = \sup_{f \in B} |\varphi(f)|$$ where $B \subseteq \mathcal{D}(... | Check Francois Treves' book (now available in Dover)
<blockquote>
Topological Vector Spaces, Distributions and Kernels
</blockquote>
| https://mathoverflow.net |
51,073 | [
"https://dsp.stackexchange.com/questions/51073",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/35433/"
] | Basic Signal Operations Performed on dependent variables-- The periodicity of the signal is varied by modifying the horizontal axis values, while the amplitude or the strength remains constant. These are:-
Time scaling of signals
Reflection of signals
Time-shifting of signals.
<strong>Is there a specific preferred ... | If you consider <strong>LTI</strong> filtering as the operations, then the order does not matter. The <strong>delay</strong> is an LTI filtering, as well as <strong>magnitude scaling</strong>, so their orders do not matter.
On the other hand, operations like <strong>time scaling</strong> or <strong>time reversal</stro... | Time scaling, reflection, and time-shifting can each be expressed as a mapping of time $t,$ here unitless:
$$t \mapsto f(t)$$
<strong><em>Time scaling</em></strong> by factor $c$ can be defined by:
$$f_\text{scale}(t;c) = ct,\quad c\in\mathbb{R}^+$$
<strong><em>Reflection</em></strong> can be defined by:
$$f_\text... | https://dsp.stackexchange.com |
50,034 | [
"https://softwareengineering.stackexchange.com/questions/50034",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7536/"
] | Ok, I "<em>almost</em>" lost a job offer because I "<strong><em>didn't have enough experience as an enterprise software engineer</em></strong>".
I've been a programmer for over 16 years, and the last 12-14 professionally, at companies big and small.
So this made me think of this question: What's the difference betwee... | Rick. I think big companies inheritently don't like Jack's of All Trades. You say you do everything. In a small company, we want people who can do everything. Those people are more valuable because they can wear multiple hats.
In an enterprise environment, there is clear job separation. They don't want people who... | When you say "enterprise engineer" thats usually mean big software, lot of different services and networks. When you developing enterprise soft you should have in mind big picture, not only local service.
Software engineer is more general, who can work with many types of projects including enterprise.
IMHO enterprise e... | https://softwareengineering.stackexchange.com |
329,149 | [
"https://electronics.stackexchange.com/questions/329149",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17526/"
] | The transmitters for hobby projects working on 433/868/915 MHz (RFM69) require an antenna connected to the board. The board is battery powered, without metallic chassis and overall much smaller than the wavelength (i.e. 20x20 mm board vs 700 mm or 345 mm wavelength).
I can choose between full, half- and quarter-wave. ... | <h3>Quarter vs. half-wave</h3>
A quarter-wave antenna, in the sense of "a wire or rod 1/4 wavelength long", is not a complete antenna; it is half of one. The other half is whatever is connected to the other terminal of your transmitter output — probably its ground, i.e. the ground plane or chassis (if any) of your boa... | Coiled vs straight does not matter that much for this kind of application. What is a lot more important is the correct feed point impedance. A 1/4 antenna has about 30R impedance, which means you will need an impedance converter to get good coupling into the antenna. I would suggest to use a 5/8 antenna, which has appr... | https://electronics.stackexchange.com |
40,756 | [
"https://stats.stackexchange.com/questions/40756",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | Assume that $c_{ij}(W)$ is a simple function of a random variable W. (This comes is Dynamic Programming where we are currently at node i and we want to go to node j in the shortest path problem and W is the random variable denoting the time that we wish to minimize)
What does the following expression mean?
$$\mathbb{E... | You have a random variable $W$ and simple functions $c_{ij}$, for, say, $i=1,\dots,I$, and $j=1,\dots,J$.
Each $c_{ij}(W)$ is also a random variable (easy to prove), and
$$
Y_i = \min_{1\leq j\leq J} c_{ij}(W) = \min \, \{ c_{i1}(W), \dots, c_{iJ}(W) \}
$$
is a random variable for each $i=1,\dots,I$ (easy to prove)... | The expression would return a column vector. The value at position $i$ in the vector is the index for the node $j^*$ which minimizes the W function with respect to that particular node $i$, by comparing the W values for all possible $j$. In other words, if we are sitting on node $i$ and want to know on average which no... | https://stats.stackexchange.com |
727,614 | [
"https://physics.stackexchange.com/questions/727614",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/345421/"
] | I have three questions about applicability of ME from nerdy physicists:
<ol>
<li>Is Multipole-Expansion a general mathematical decomposition tool? or it is only applicable in physics? (physics = gravity, electrostatic, electromagnetic, radiation, ...).
</li>
<li>if it is a general mathematical tool, could we apply it t... | <ol>
<li>Multipole expansion is a series expansion for functions of two angles. The basis of the series is made of spherical harmonics <span class="math-container">$~Y^{m}_{l}( \theta , \varphi ) ~$</span>.
It has nothing to do with clustering.</li>
</ol>
<span class="math-container">$$f( \theta , \varphi )= \sum_{m=0}... | <ol>
<li>ME is used in Physics as a way for approximating the influence of a cluster of "neighboring systems" to points far from them, but it could be as a general mathematical method for approximating sum of functions, decaying as the the independent variables increase</li>
<li>I guess so, as far as the assu... | https://physics.stackexchange.com |
2,872,669 | [
"https://math.stackexchange.com/questions/2872669",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/464054/"
] | Find the least value of the expression
$x^2+2xy+2y^2+4y+7$
I am not able to solve this equation though i am able to differentiate it.
| I like dxiv's factorization approach.
For a more routine method, solve
$$\frac{\partial f}{\partial x}=2x+2y=0$$
$$\frac{\partial f}{\partial y}=2x+4y+4=0$$
where the equations by equating the derivative to zero.
Remember to check the Hessian is positive definite a well.
| Given $x^2+2y^2+2xy+4y+7$$$x^2+2y^2+2xy+4y+7$$$$x^2+y^2+2xy+y^2+4y+7$$$$x^2+y^2+2xy+y^2+4y+4+3$$$$(x+y)^2+(y+2)^2+3$$Minimum of square of any number is $0$. So, minima will be at $x=2,y=-2$
Therefore, $(2+(-2))^2+(-2+2)^2+3=3$
Therefore, the least value of the expression $x^2+2y^2+2xy+4y+7$ is $3$
| https://math.stackexchange.com |
67,308 | [
"https://mathoverflow.net/questions/67308",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15056/"
] | While analysing the average runtime of an algorithm, I came across the following identity, and would like to know if anybody knows of any references for it?
For $i \in \mathbb{N}$, let $\bar{s}(i)$ denote the square-free part of $i$, eg., $\bar{s}(12) = 3$ (and $\bar{s}(1)=1$). Then
$$
\lim_{n \rightarrow \infty} \fr... | The question asked for a reference, not a proof. A reference is Karl Greger, Square divisors and square-free numbers, Mathematics Magazine 51, No. 4 (Sept. 1978), 211-219. I make no claim that the result was unknown before Greger's paper.
| If my understanding is correct, for "squarefree part" can be "squarefree kernel" in other cases, the generating Dirichlet series is
$${\zeta(2s)\zeta(s-1)\over\zeta(2s-2)}=\prod_p\biggl(1+{p\over p^s}+{1\over p^{2s}}+{p\over p^{3s}}+\cdots\biggr)=\sum_n{\bar s(n)\over n^s}$$
alternating $1$ and $p$ as the coefficients,... | https://mathoverflow.net |
32,519 | [
"https://chemistry.stackexchange.com/questions/32519",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/6925/"
] | $K_p$ is defined as $\Pi_j(\frac{P_j}{P^{\Theta}})^{\nu j}$ where $P_j$ is the partial pressure of component j and $\nu$ is the stoichiometric coefficient. I have a couple of questions already. Firstly, $K_p$ is meant to be dimensionless so therefore, $\frac{P_j}{P^{\Theta}}$ must be dimensionless. However, surely $P_j... | <blockquote>
However, surely $P_j$ alone is dimensionless as it's a partial pressure defined by dividing a pressure by a pressure - leaving no units. How does that work? Or am I wrong by assuming that a partial pressure has no units?
</blockquote>
You are wrong to assume that partial pressure has no units. Partial ... | The standard change in free energy, which is used to determine the equilibrium constant Kp is based on the pure reactants at 1 atm going to pure products at 1 atm. Therefore, the partial pressure must be expressed in atm in order to be consistent with Kp. This essentially normalizes the partial pressure by 1 atm.
| https://chemistry.stackexchange.com |
507,538 | [
"https://physics.stackexchange.com/questions/507538",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84158/"
] | <ol>
<li>Imagine a hypothetical action:
<span class="math-container">$$S=\int \left(\frac{\partial}{\partial t}\phi(x,t)\right)^2 d^3x dt$$</span>
Now we have a symmetry of the action: <span class="math-container">$$\phi(x,t)\rightarrow \phi(x,t)+\chi(x).$$</span>
At time <span class="math-container">$t$</span>, <span ... | Re. "Is this what happens to real sounds waves as they attenuate"
Yes: a pulse tends to become less oscillatory as it propagates through a medium that attenuates as a function of frequency and also gets stretched out in time. An FIR filter should be a good model of this.
For example if you convolve a single cycle of ... | No, a filter is not a good model for the attenuation of sound.
The attenuation with distance in free air is due the the <span class="math-container">$r^{-2}$</span> dependence of power. That factor affects all frequencies in the same way. There is also no dispersion, the velocity of sound does not depend on frequency.... | https://physics.stackexchange.com |
2,598,500 | [
"https://math.stackexchange.com/questions/2598500",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/519985/"
] | I'm stuck on this problem:
<blockquote>
If<br>
$$a\sin^2x + b\cos^2x = c$$
$$b\sin^2y + a\cos^2y = d$$
$$a\tan x=b\tan y$$<br>
then prove that<br>
$$\frac{a^2}{b^2} = \frac{(d-a)(c-a)}{(b-c)(b-d)}$$
</blockquote>
| $${{a^2}\over{b^2}}={{\tan^2y}\over{\tan^2x}}={{\sin^2y\cos^2x}\over{\cos^2y\sin^2x}}$$
also
$$\cos^2x={{c-a}\over{b-a}}$$
$$\sin^2x={{c-b}\over{a-b}}$$
$$\cos^2y={{d-b}\over{a-b}}$$
$$\sin^2y={{d-a}\over{b-a}}$$
Therefore the result can easily be derived.
$${{a^2}\over{b^2}}={{(d-a)(c-a)(a-b)(a-b)}\over{(b-a)(b-a)(c... | I think it's wrong.
Try $a=b=c=d=x=y=1.$
| https://math.stackexchange.com |
3,328,644 | [
"https://math.stackexchange.com/questions/3328644",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/694852/"
] | Let <span class="math-container">$P$</span> denote the plane given by the point-normal equation: <span class="math-container">$0 = (1,2,−1)·((x,y,z)−(1,1,1))$</span>
How do I find the points <span class="math-container">$(x, y, z)$</span> that lie on the plane <span class="math-container">$P$</span>?
| You must write better your equation:
<span class="math-container">$0 = (1,2,−1)·((x,y,z)−(1,1,1))$</span>
Implies
<span class="math-container">$0=(1,2,-1)(x-1,y-1,z-1)$</span>
So
<span class="math-container">$(x-1)+2(y-1)-z+1=0$</span>
Then
<span class="math-container">$x+2y-z=2$</span>
<span class="math-conta... | The points on the plane satisfy the given equation. I think this is just an exercise in using the dot product. Recall that for vectors <span class="math-container">$a,b,c,$</span> we have that <span class="math-container">$$a\cdot(b+c)=a\cdot b + a\cdot c,$$</span> so that your equation simplifies to <span class="math-... | https://math.stackexchange.com |
512,334 | [
"https://physics.stackexchange.com/questions/512334",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246668/"
] | Pardon my really rusty school physics knowledge.
I heard martial artists talking about the physics of board breaking and one of the things which they mentioned is formula "F=ma". They were talking that the more mass you have and faster you punch the more force you will apply to board and it will break.
However, there... | <span class="math-container">$\partial^\mu$</span> is not <span class="math-container">$\partial/\partial x_\lambda$</span>. There is no such thing as <span class="math-container">$x_\lambda$</span>. Instead <span class="math-container">$\partial^\mu \equiv g^{\mu\nu}\partial_\nu$</span>. In curvilinear coordintes <s... | Your identity is false. Here is a simple counter example in 2D switching between cartesian and polar coordinates: <span class="math-container">$(x^1,x^2)=(x,y)$</span> and <span class="math-container">$(\tilde{x}^1,\tilde{x}^2)=(r,\theta)$</span>.
A simple calculation yields
<span class="math-container">$$
\frac{\part... | https://physics.stackexchange.com |
54,536 | [
"https://mechanics.stackexchange.com/questions/54536",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/37832/"
] | How can I disable the tire pressure monitoring system on my 2009 Mazda 3 so that it doesn't warn me upon starting the car and doesn't maintain a yellow warning light on the dash if it can't detect the wireless sensors?
| In the United States, it is illegal to work on someone's vehicle, render TPMS non-functional, and return it to the customer. As such, no shop or dealer will ever do this for you.
It's perfectly legal for you to do it yourself.
Now that that's out of the way...
Some vehicles can have the TPMS disabled by physically r... | Replace any dead sensors and relearn the sensors. If you want to take the cheap route, remove your cluster and put black electrical tape over the light.
| https://mechanics.stackexchange.com |
10,126 | [
"https://mathoverflow.net/questions/10126",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2805/"
] | Let $G$ be a finite group and $\chi$ be an irreducible character of
$G$ (characteristic zero algebraically closed base field). If $H$ is
the kernel of $\chi$ then the irreducible representations of $G/H$
are exactly all the irreducible constituents of all tensor powers
$\chi^n$.
<ol>
<li>Do you know any reference for ... | I am not quite sure about the reference :( I always thought of this fact as follows.
Matrix elements of tensor powers of a representation U are all possible monomials in matrix elements of U, so the space of all their linear combinations are values of all possible polynomials in the matrix elements of U. Now, by defin... | The easiest proof I know of this result for finite groups is due to H. Blichfeldt ( I believe),
and I think it is easier than Brauer's proof, which was itself easier than the power series
type proof which maybe first appeared in W. Burnside's book. I am not sure about a textbook reference for it, though. It is certainl... | https://mathoverflow.net |
3,858,264 | [
"https://math.stackexchange.com/questions/3858264",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Let <span class="math-container">$(X,d)$</span> be a metric space and <span class="math-container">$A$</span> a non-empty subset of it. Show that the set <span class="math-container">$$U= \{x\in X \vert d(x,A) >0 \}$$</span> is open in <span class="math-container">$X$</span>.
</blockquote>
Let <span cla... | In order to use separation of variables, we can propose a solution of the form
<span class="math-container">$$
\omega(t,\eta)=()ℎ(\eta)+\frac{}{A}
$$</span>
where <span class="math-container">$g,h$</span> are two unknown functions, that we want to find out. Then we have:
<span class="math-container">$$
\frac{\partial\o... | Using the Fourier transform
<span class="math-container">$$
\hat{f}(t,\xi) = \int_{-\infty}^{\infty} f(t,\eta) \, e^{-i\xi\eta} \, d\eta.
$$</span>
we get
<span class="math-container">$$
A\partial_t\hat{f}(t,\xi) = -B\xi^2\,\hat{f}(t,\xi) + C\,2\pi\,\delta(\xi).
$$</span>
The homogeneous equation,
<span class="math-con... | https://math.stackexchange.com |
478,813 | [
"https://physics.stackexchange.com/questions/478813",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/93387/"
] | I'm confused with this definition of displacement currents within capacitors via Wikipedia:
<blockquote>
However it is not an electric current of moving charges, but a
time-varying electric field.
</blockquote>
It's a time-varying electric field, but there isn't any actual flow of current, while at the same time.... | The effect you are describing was discovered theoretically by considering a though experiment (at least that is how many texts present it). Ampere's law relates the line integral of the B field around a loop to the number of currents that pass through any surface bound by the loop. The mathematical theorem is Stokes'... | In the absence of current the Maxwell equation reads <span class="math-container">$\partial \vec E = \vec \nabla \times \vec B /c^2$</span>. This equation means that both sides denote the very same thing. It does not mean that E induces B or vice versa.
| https://physics.stackexchange.com |
488,839 | [
"https://physics.stackexchange.com/questions/488839",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/153577/"
] | Suppose we have a large area where the net electric field is zero.<br>
We place a charge <strong><em>q</em></strong> somewhere in this area.<br>
How long will it it take for another positive charge <strong><em>q'</em></strong> standing at
a distance <strong><em>d</em></strong> from <strong>q</strong> to feel the effec... | At the present time of physics models of nature , we expect that Lorentz transformations are exact and are the way the world is working. They have been tested in innumerable particle experiments, cosmological observations are consistent and there has been no experimental falsification.
Thus as far as our theories go,... | Your assumption is correct.
You may be asking this because in the Coulomb gauge the Coulomb potential obeys the Poisson equation, which predicts instantaneous propagation of the potential. However the electric field is equal to <span class="math-container">$\vec \nabla V$</span> only if the charges are truly static.... | https://physics.stackexchange.com |
23,148 | [
"https://dba.stackexchange.com/questions/23148",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11360/"
] | Is there a way to mirror databases in MySQL? In SQL Server, you have the ability to link 2 databases in a master to master relationship. One DB will accept transactions and the transactions will be committed on both DBs at the same time. Is there a a similar concept in MySQL?
| I think the other answer missed the point of the question; which is that in SQL Server mirroring, a transaction that commits to both servers A and B are committed at the same time (in atomicity). If the transaction fails on one server, it fails on both. It doesn't seem like there is a similar feature on MySQL
| its called MySQL Replication:
Replication enables data from one MySQL database server (the master) to be replicated to one or more MySQL database servers (the slaves). Replication is asynchronous by default - slaves need not to connected permanently to receive updates from the master. This means that updates can occur... | https://dba.stackexchange.com |
46,775 | [
"https://chemistry.stackexchange.com/questions/46775",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/22232/"
] | For my school lab, I'm determining the solubility of carbon dioxide at different temperatures. I will determine the amount of dissolved carbon dioxide by titrating carbonated water with sodium hydroxide. I'm confused as to how I can determine the pH at equivalence point (for indicator)? I don't know the concentration o... | The two pKa values for carbonic acid are given as 6.37 and 10.25, so you may want to pick the midpoint between these (pH 8.31) as your equivalence point. At that pH, a tiny amount of base will change the pH a lot, so the amount of base needed should not depend strongly on the exact value you select for the equivalence ... | The pH would be basic at the equivalence point. This makes the standard phenolphthalein an even more ideal choice. It goes from clear to purple at around a pH of 8.
| https://chemistry.stackexchange.com |
691,732 | [
"https://physics.stackexchange.com/questions/691732",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/326808/"
] | Let's assume i have a wave function <span class="math-container">$$\psi = N(x+y+z)e^{-r^2/a^2} $$</span> with <span class="math-container">$N$</span> and <span class="math-container">$a$</span> some constants. This function can be written as a sum of the spherical harmonix <span class="math-container">$Y_{1,0}$</span>,... | The angular momentum operator is
<span class="math-container">$$L_z = I \otimes \left(-i\hbar \frac{\partial}{\partial \phi}\right)\:.$$</span>
The tensor product refers there to the decomposition
<span class="math-container">$$L^2(\mathbb{R}^3, d^3x)= L^2([0, +\infty), r^2 dr) \otimes L^2(S^2, \sin\theta d\theta d\phi... | Your expression
<span class="math-container">$$P=|\langle1,1|\psi\rangle|^2$$</span>
is inconsistent, because the ket on the right side has an
<span class="math-container">$r$</span>-dependency, and the bra on the left side has not.
So you need to be careful how to formulate the inner product.
You can factorize your wa... | https://physics.stackexchange.com |
168,946 | [
"https://security.stackexchange.com/questions/168946",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/74850/"
] | I would like to understand much about Microsoft Security Essentials or another antivirus which build in or developed by Microsoft. I'm planning to set up the network for my company and use Microsoft Plattform for operating that structures But I don't understand much about Antivirus or another Security which can help to... | I suggest you contact some local security provider and consult with them about securing your network and desktops. You can use Windows Defender to protect computers from malware and Microsoft System Center to configure it globally. In my opinion, the solution from Kaspersky Lab (their security center and endpoints) wil... | Please research Microsoft Security Essentials and how it has held up in credible evaluations in security effectiveness compared to third party solutions. Although its effectiveness has improved the past few years, it never ranks among the top when compared to solutions from companies focused on providing security solut... | https://security.stackexchange.com |
64,056 | [
"https://softwareengineering.stackexchange.com/questions/64056",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13020/"
] | As a programmer, I enjoy embarking on small personal projects and I have a load of open source scripts that I host on github. I am very much a <strong>programmer</strong> and not a <strong>designer</strong>. However, it is inevitable that sometimes I am forced to <em>design</em>. These are usually cases where there ... | There are tons of webdesign blogs out there. I would recommend:
<ul>
<li>Smashing Magazine</li>
<li>Webdesigner Depot</li>
<li>A List Apart</li>
<li>Webdesigner Wall</li>
<li>CSS-Tricks</li>
</ul>
Website design ends up incorporating a wide set of skills: user experience, typography, colour selection, image editing,... | <ol>
<li>Stumbleupon search - It's my favorite way of finding interesting articles about web design and design techniques. You can search for design lists or just styling techniques and get a wide variety of interesting websites.</li>
<li>CSS Zen Garden / Browsing theme repositories - I like to see what others have don... | https://softwareengineering.stackexchange.com |
169,130 | [
"https://electronics.stackexchange.com/questions/169130",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/74878/"
] | I have a FUTEK CSG110 amplifier, conditioning a signal provided from a load cell, providing a -3V to 3V signal. I can change this range to my liking, however I will be stuck with a +- voltage representing the compression and tension of the load cell.
I want to use the ADC of the Teensy 3.1 to measure this voltage, by... | Yes, you can do this with a <i>resistor divider</i>. We usually think of a resistor divider as multiplying a voltage by some value less than 1, meaning scaling relative to ground. However, a resistor divider can be set up to scale relative to any particular voltage.
In your case, you can scale the voltage about the ... | You can do this with two or three resistors- one to the reference for your ADC and one to the input, and perhaps one to ground.
However, it's important to realize that the result (and your ADC accuracy, both zero and span in this case) will depend on the accuracy and stability of that reference. If the reference drif... | https://electronics.stackexchange.com |
163,348 | [
"https://softwareengineering.stackexchange.com/questions/163348",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35276/"
] | I'm curious about this because I recall before learning any functional languages, I thought them all horribly, awfully, terribly unreadable. Now that I know Haskell and f#, I find it takes a little longer to read less code, but that little code does far more than an equivalent amount would in an imperative language, so... | Code readability is very <strong>subjective</strong>. Because of this, different people would consider the same code readable or unreadable.
An assignment, <code>x = x + 1</code> sounds weird to a mathematician, because an assignment looks misleadingly similar to a comparison.
A simple OOP design pattern would be tot... | <strong>Short answer:</strong>
One of the elements which make people say that functional programming code is difficult to read is that it gives preference to a more compact syntax.
<strong>Long answer:</strong>
Functional programming itself cannot be readable or unreadable, since it's a paradigm, not a style of writ... | https://softwareengineering.stackexchange.com |
86,257 | [
"https://electronics.stackexchange.com/questions/86257",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8494/"
] | I have a 3.3V UART (two pins) plus a direction selector pin (also 3.3V.) I need to talk to and listen on a single duplex serial bus at 5V with 20 mA drive strength. The signaling rate is 3 Mbit/s, although switching directions is allowed to take 4 microseconds.
An automatic bidirectional translator like TXB0102 is not ... | The 74HCT125 is fine. Power it with 5V and it will read your 3V3 Tx and enable signal just fine because \$V_{IH}\$ is only 1.6V (2V worst case). For the 3V3 Rx use a resistive voltage divider for 'level translation' from the 74HCT125.
| You need one driver ('125) for each direction of the bus:
<ul>
<li>One with the input connected to the 5V bus, and the output connected to the 3.3V IC. For this, you could use a 74AHC125, or a 74LVC125, powered from 3.3V, as these tolerate the 5V input. 74HC125 is not okay, as it does not tolerate input above its V<su... | https://electronics.stackexchange.com |
81,415 | [
"https://softwareengineering.stackexchange.com/questions/81415",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/26933/"
] | The title sums up my question, but to elaborate basically what I want to understand is why the Android designers want apps that need to work with shared data to use a Content Provider rather than just accessing the SQLite database directly?
The only reason I can think of is security because certain files can by access... | It is above all a way of insulating data consumers and data providers. You develop your own content provider or extend an existing one if you want to make some of your data public or at least available to other application.
True this can server to control accesses from a security point of view but it also allows you ... | The <code>ContentProvider</code> also abstracts out all of the inter-process communication that is required in order to communicate with other third-party applications. Having to write this code yourself would be a <em>huge</em> pain.
| https://softwareengineering.stackexchange.com |
371,061 | [
"https://softwareengineering.stackexchange.com/questions/371061",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/305957/"
] | I was just going through a food delivery application's preferences file where I found that it had a boolean to check if the user has one of its rival's app installed or not. Is it ethical to do so on their part?
| It really depends on what they do with that information. If they purely use it to have a statistic "X% of our users also have the app from competitor Y installed" then I don't see anything wrong with it.
If they use it to skew the competition, e.g. by offering such users special discounts, I would counsider it unethic... | It seems that the security of the operating system is broken. An app should not be able to find out what other applications are running on your device.
| https://softwareengineering.stackexchange.com |
24,859 | [
"https://security.stackexchange.com/questions/24859",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/16685/"
] | This is probably a stupid question/vaguely defined, but I need to ask it anyway.
I want to put a public key for mail exchange on my website, such that even very powerful adversary with power to intercept and fiddle with traffic on both sides and DNS couldn't read e-mails mailed to me.
What I mean is that:
<ul>
<li>t... | You are right that an adversary that could intercept all your traffic could put a system in place that would act as a MiTM between all your email recipients and yourself, creating a separate public/private keypair for each recipient and keeping you in the dark on it. There isn't any way you can defend against that tota... | You need to find a third party that both you and the sender trust, and have them host your public key. Then you don't have to run your own hardware, as the trusted third-party's hardware is deemed to be secure.
| https://security.stackexchange.com |
343,653 | [
"https://electronics.stackexchange.com/questions/343653",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/138702/"
] | I currently have a system consisting of two PCB connected via a 5 cm cable.
Each PCB has a microcontroller, the two microcontrollers are communicating via SPI at 1Mbps Data rate.
Now the system will go into EMC and EMI testing, and i never dealt with a system were i should consider both the sourcing and receiving end... | Radiation will depend mainly on two things.
<strong>The rise and fall time of your signals</strong> You can control this with something as simple as a series resistor at the driver output, or with a filter. The series resistor essentially creates an RC filter where the capacitance is provided by the load. If you're no... | There is an EMC 'outgoing' radiation test (my term). All EMC signals emitted from your product should lay below a certain value. The value depends on the radiated frequency.<br>To prevent radiating you can using shielding (using a shielded cable). Another way is make that your signals do not have 'sharp' edges. The fir... | https://electronics.stackexchange.com |
114,584 | [
"https://softwareengineering.stackexchange.com/questions/114584",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/33723/"
] | Is it perhaps time for enterprise systems to be developed to strict enforced standards? Many books list optional 'standards' and best practices, but these are purely suggested practices. Still, every time I look at the code for an enterprise system I have not been a part of, I spend a lot of time trying to work out the... | Standards sound all fine and dandy, but what happens when a customer has performance needs or a different business model that are impossible to achieve without a unique architecture? Each customer has to make an informed choice about the advantages and disadvantages of different solutions. Developer Lock-In is just one... | The main issue with Standard Architectural models are they that only work on standard systems. The problem with real world enterprise environments are that they are ALWAYS different.
In turn, the standards would end up being so vague that you might as well be better off without any.
| https://softwareengineering.stackexchange.com |
63,807 | [
"https://electronics.stackexchange.com/questions/63807",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | I recently built an audio amplifier based on the LM386. When I touch one of the input signals with my finger, I can hear a buzzing sound on the output. I checked with the oscilloscope, and there appears to be some kind of voltage signal on my hand with respect to the amplifier's ground. What is this voltage? By what th... | Your body becomes connected to the circuit. Probably, capacitively coupled through an equivalent of about 100pF. Then, several things can happen:
<ul>
<li>Extra capacitance makes your amplifier oscillate.</li>
<li>Your body acts picks up 50/60Hz interference from power lines (aka "60Hz hum") and introduces it into y... | Your body is acting as an antenna, or more accurately, the secondary winding of a transformer. A tiny AC voltage/current is being induced in your body from the electromagnetic field produced by the mains electricity power lines all around. When you touch the input line of an amplifier, the tiny voltage/current is ampli... | https://electronics.stackexchange.com |
145,755 | [
"https://math.stackexchange.com/questions/145755",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/30856/"
] | <blockquote>
$A$ and $B$ are two square matrices then show that $R(AB) = R(A)$ iff $\mathrm{rank} (AB) = \mathrm{rank} (A)$, and $N(AB) = N(B)$ iff $\mathrm{rank} (AB) = \mathrm{rank} (B)$.
</blockquote>
Here is my attempt:
Clearly $R(A)\supset R(AB)$, now can we say that these two subspaces are identical iff they... | Note that $R(AB)\subseteq R(A)$ always holds: if $x$ is any vector, then $AB(x) = A(Bx)\in R(A)$.
Thus, if $\mathrm{rank}(AB)=\mathrm{rank}(A)$, then that means that $\dim(R(AB))=\dim(R(A))$; since $R(AB)\subseteq R(A)$, equality of dimensions suffices to conclude that $R(AB)=R(A)$, because we are in finite dimension.... | The key issue here is that any basis for a (finite dimensional) subspace $S$ must have exactly $\dim S$ elements.
You are given that $R(AB)\subset R(A)$. Let $\{v_1,...,v_r\}$ be a basis for $R(AB)$ (where $r=\dim R(AB)$, of course). Then for some $b_i$, we have $v_i = AB b_i = A (B b_i)$. Then we have $\{v_1,...,v_r\... | https://math.stackexchange.com |
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