qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
86,135 | [
"https://stats.stackexchange.com/questions/86135",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/27158/"
] | ...and how might we do this? If possible, I am curious if outliers in the Rayleigh distributed data would also remain outliers in the new Gaussian distributed data. Thanks.
| If you know the Rayleigh parameter, then the conversion to a standard normal is readily achieved by the probability integral transform followed by an inverse normal cdf. If $X\sim\text{Rayleigh}(\sigma)$, with cdf $F_\sigma(x)$, then $F_\sigma (X)$ is uniform, and $\Phi^{-1}(F_\sigma (X))$ is standard normal (where $\P... | If $R$ is a Rayleigh random variable and $\Theta \sim U[0,2\pi)$ is independent of $R$, then $X=R\cos \Theta$ and $Y=R \sin \Theta$ are independent
<strong>zero-mean</strong> normal random variables with identical variance
$\sigma^2 = \frac{1}{2}E[R^2]$. Thus, if you transform your data set as
$$\{r_1, r_2, \ldots, r... | https://stats.stackexchange.com |
84,003 | [
"https://electronics.stackexchange.com/questions/84003",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29606/"
] | If voltage is the same across each resistor in a parallel circuit, what's the point of resistors if there's 4 of them in a ciruit with 50volts, it won't affect the voltage.
I also noticed that when more resistance is added into a parallel circuit, it actually gets decreased instead of increasing. Please someone expla... | It could be one of three reasons:
<ul>
<li>Increasing power handling capabilities of a single resistor. If the footprint only allows for a certain size package (say, for height reasons), multiple resistors will spread the wattage out.</li>
<li>A pick & place machine is assembling the circuit, and its cheaper to p... | If you turned your bathroom tap on this is like putting a resistor across a voltage supply. Water flows and so does electric current. If you also turned your kitchen tap on more water flows and the same for current.
In other words the "resistance" to the pressure has lowered when you add parallel paths that the water... | https://electronics.stackexchange.com |
29,737 | [
"https://physics.stackexchange.com/questions/29737",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7951/"
] | A problem I am trying to work out is as follows:
A particle moves in a force field given by
$\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant.
I set it up as follows:
$\vec F = m {d^2\vec r \over dt^2}$
$\vec v = \int {\frac {\vec F}{m} }\ dt = \int {\frac {\... | If you want to prove that $\vec{L}=\vec{r}\times \vec{p}$ is constant with respect to time for a particle in a central force field $\vec F = \phi(r) \vec r$, just show that the angular momentum doesn't change with time, i.e. $\frac{d}{dt}\vec{L}=0$.
Using the product rule we get two terms:
$\frac{d}{dt}\vec{L}=\frac{... | Since $ F = \phi(r) \vec r $, you can find the torque around the origin.
Torque $ \tau = \vec F \times \vec r = \phi (r) \vec r \times \vec r$
But $\vec r \times \vec r$ is zero, so the torque around the origin is also zero.
Since torque is just rate of change of angular momentum $\frac{ d\vec L}{dt}$, the angular m... | https://physics.stackexchange.com |
168,296 | [
"https://physics.stackexchange.com/questions/168296",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/66165/"
] | Let's suppose I have a spacetime manifold $M$. Let $p$ be a point on my manifold. Now I move from $p$ to some other point $p'$. Presumably I should have moved some "distance" right? How can I speak of notions of space and time if I have no conception of distance?
But now consider light moving through spacetime. Suppo... | Let's separate out some definitions:
<strong>metric(1):</strong> Given a set $X$, a function $d : X \times X \to \mathbb{R}$ such that the following axioms hold for all $x,y,z \in X$:
<ul>
<li>$d(x,y) \geq 0$,</li>
<li>$d(x,y) = 0 \Leftrightarrow x = y$,</li>
<li>$d(x,y) = d(y,x)$, and</li>
<li>$d(x,z) \leq d(x,y) + ... | I think it might help to think about the spacetime interval $\text{d}s^2$ as a measure of movement in spacetime <em>relative to the speed of light</em>. Let's say that you want to move from a point $p=(0,0,0,0)$ to another point $p'=(t,x,0,0)$. The quantity $\text{d}s^2 = c^2\text{d}t^2-\text{d}x^2$ is then:
<ul>
<li>... | https://physics.stackexchange.com |
160,432 | [
"https://math.stackexchange.com/questions/160432",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/33515/"
] | What is the appropriate way to simplify such an expression.
i am unsure of how to use the series i know to apply to this situation
$$\sum_{L=0}^{M}s^{L}L^{2}$$
do i modify such a series as power series, or is there a more efficient series to use here?
thank you very much!!
| Try to make the inner expression look like a derivative:
$$
\begin{align}
\sum_{L=0}^M\left(Ls^{L-1}\right)sL & =s\sum_{L=0}^M\left(\partial_ss^L\right)L\\
& =s\partial_s\sum_{L=0}^Ms^LL\\
& =s\partial_s\sum_{L=0}^M\left(Ls^{L-1}\right)s\\
& =s\partial_s\left(s\sum_{L=0}^M\left(Ls^{L-1}\right)\right)\\
... | Write : $L^2=L(L-1)+L$ and use derivative. For $ L \geq 2$ :
$$L^2 s^L = s^2L(L-1)s^{L-2}+ s Ls^{L-1}= s^2(s^L)'' + s (s^L)'$$
We get :
$$\sum_{L=0}^M L^2s^L=0^2+1^2 s + s^2 \left(\sum_{L=2}^{M} s^L \right)''+s \left(\sum_{L=2}^{M} s^L \right)'$$
| https://math.stackexchange.com |
140,191 | [
"https://cs.stackexchange.com/questions/140191",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/129561/"
] | I have been reading Michael Sipser's <em>Introduction to the Theory of Computation</em>, and I have stumbled upon a paragraph in Chapter 8 (Theorem 8.9 on page 339 of the 3rd international edition) that I simply do not understand.
For context, TQBF is the language of all first-order logical formulas in prenex normal fo... | If you want to write <span class="math-container">$N$</span> words of output, it takes at least <span class="math-container">$N$</span> steps of computation to do that. So, if you need to produce an exponential-sized output, you'll need to spend exponential time to do it. For that reason, a polynomial-time reduction ... | The fact that the given reduction takes exponential space implies it must take exponential time and therefore is not polynomial.
Using Cook-Levin on a NP-complete problem does not produce an exponential-sized output; it produces a polynomial-time circuit. It constructs a circuit whose size is polynomial in the number ... | https://cs.stackexchange.com |
364,288 | [
"https://softwareengineering.stackexchange.com/questions/364288",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/69247/"
] | Can anyone point me to patterns for, or material on decentralised federated system design / federated data/service architectures?
To give some more background on the problem I'm looking to solve, here's the full context. I've had an idea floating around for a while to create a "reverse address book". i.e. Rather t... | Let's break down the problem:
<ul>
<li>You need some way to identify users</li>
<li>Given an identifier, you need to have some way to determine how to push/pull information</li>
</ul>
Additionally, you obviously need some kind of standard protocol and a way to manage access rights. Also, the user id should be somethi... | First @VladislavRastrusny is right.
This is not a pattern problem, a pattern is a general abstract way of solving an abstract known problem, that you then (try to) apply to a concrete case.
Here @JohnLBevan you seems more to have difficulties transforming an app/service/platform idea to "reality".
So to follo... | https://softwareengineering.stackexchange.com |
17,342 | [
"https://chemistry.stackexchange.com/questions/17342",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/8167/"
] | What are weak acids? My chemistry and biology classes skimmed over them briefly but nothing in depth. I understand that an acid is weak if it partially dissociates and breaks down into ionic compounds, but they never stated why.
So my question is why do weak acids break down in water? Do strong acids dissociate at all... | <blockquote>
What are weak acids?
</blockquote>
Examples of weak acids in <em>water solution</em> would be acetic acid (main component of vinegar) and ammonium ion (conjugate acid of ammonia).
<blockquote>
I understand that an acid is weak if it partial dissociates and breaks down into ionic compounds but they ... | There is nothing magic about weak acids. The dissociation reaction of an acid in water looks like this: $\ce{HA + H2O <=> A- + H3O+}$. There's an equilibrium constant <em>K</em> that's related to the free enthalpy $\Delta G$ in the usual manner:
$$\Delta G=-RT \cdot \ln K$$
A weak acid is simply an acid where ... | https://chemistry.stackexchange.com |
711,382 | [
"https://physics.stackexchange.com/questions/711382",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/259524/"
] | <blockquote>
Consider a system of bullet (of mass 5 kg) and block (of mass 20 kg). Initially the block is at rest and the bullet moves towards it at 30 m/s. After penetrating the block, the bullet comes out with speed 10 m/s. What is the velocity of block?
</blockquote>
<strong>My attempt</strong><br />
As there is no ... | <blockquote>
Why am I getting incorrect answer with the Work energy theorem?
</blockquote>
The collision is not elastic, therefore KE is not conserved, it is lower after the collision. The missing KE is converted to heat and sound and deformation of the block. It is precisely this missing KE that makes bullets deadly.
| Kinetic energy of the bullet-block system isn't a conserved quantity. i.e. not all of the kinetic energy lost by the bullet is transferred into kinetic energy of the block.
| https://physics.stackexchange.com |
148,081 | [
"https://softwareengineering.stackexchange.com/questions/148081",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/43136/"
] | When correcting bugs, it is encouraged where I work to first write a test that fails with the given bug, and then to fix the code until the test passes.
This follows TDD practices, and is supposed to be good practice, but I noticed it tends to produce cryptic tests that come really close to the implementation.
For ins... | Yes, in general you <em>should</em>. As with all guidelines, you'll need to use your best judgement when they run against other guidelines. For this scenario, the severity of the bug needs to be weighed against the work needed to implement the test and the quality of that test in being targeted to the business problem ... | I think the best practice - one I'm embarrassed to admit I don't often follow - is to create a system or integration test that demonstrates the problem observed in production, then research to find the unit(s) responsible for the problem, <em>and then write unit tests for those units that demonstrate the problem at the... | https://softwareengineering.stackexchange.com |
196,185 | [
"https://softwareengineering.stackexchange.com/questions/196185",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/89277/"
] | I've collected a bunch of interview questions like "Describe how you would design a photo album application", "Describe how you would design this particular feature of this particular website" (e.g. likes on Facebook, recommendation on Amazon, shopping cart, game of black jack). Then, what if there are millions of this... | The point of such questions is to assess whether you have real-world skills in writing a software application. You have learned some theory, but theoretical knowledge can only go so far. The only way to truly understand software development is by doing it.
There is no shortcut to this, because there are no stock an... | <blockquote>
It looks like this is either expecting a database schema or a bunch of
class definitions (or both?)
</blockquote>
I think you're too focused on details here. With that question, the recruiter is not expecting a complete description of all classes you would write (otherwise they would ask you to code i... | https://softwareengineering.stackexchange.com |
181,608 | [
"https://softwareengineering.stackexchange.com/questions/181608",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53348/"
] | Consider someone is writing a message (or a question at StackOverflow). The context is following:
<blockquote>
In my code, I have the following line:<br />
<code>int foo = Bar();</code>
However, the compiler <strong>returns</strong> an error:<br />
<em>line 42: Bar() is unknown function</em>
</blockquote>
I'm puzzled t... | "Compiler <em>reports</em> an error" sounds appropriate and is actually used in literature.
It does not necessarily "fail" or "return", because it can carry on and report more further errors, warnings or notes.
| I would go with
<blockquote>
Compile <strong>fails with</strong> the error "Fizzy buzzy Bizzy fuzzy"
</blockquote>
I would stay far away from throw, also print and return aren't particularly great but throw is a downright misnomer.
| https://softwareengineering.stackexchange.com |
8,381 | [
"https://scicomp.stackexchange.com/questions/8381",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/4912/"
] | Is there a way to understand what happens when a singular operator is discretized and inverted using the pseudoinverse (say using the SVD Moore-Penrose pseudoinverse)?
For example, if we discretize $(\nabla u, \nabla v) $ with a finite element method or something, the operator should usually be singular due to the f... | The Moore-Penrose pseudoinverse of a matrix has the property that
$x=A^{\dagger}b$
is a least squares solution, and that among all least squares solutions (if there's a nontrivial nullspace of $A$), $x$ will be the least squares solution that minimizes $\| x \|_{2}$.
When it comes to discretizing a PDE and solvin... | It depends on how you define your pseudoinverse. If you define it as the operator that produces the least-$L_2$-norm element, then you will get that $u=u_0+c$ that has the smallest norm $\|u_0+c\|_{L_2}$ where $u_0$ is an arbitrarily chosen solution and $c$ is a constant. In general, of course, $u$ will not have zero m... | https://scicomp.stackexchange.com |
687,406 | [
"https://physics.stackexchange.com/questions/687406",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266050/"
] | From the references I have dug in, it seems that no explanation for the cause of Meisner Effect exists besides the phenomenological london equation that says that the bulk energy is reduced with zero interior magnetic field.
Have I not looked at the right places or is it true that the phenomenological london equation i... | Imagine each grain of sand as a rock lying on the side of a mountain. There will be a certain 'critical' steepness of the mountain, above which the rock will start to roll.
Now apply this idea to the pile of sand. If the pile is <em>steeper</em> than the critical angle, then grains of sand will roll downhill and pile u... | I would give you some intuition behind this. When some sand falls on the ground, the sand is collected on the ground, and the 'heap' begins to rise. Now whatever sand falls, on already collected sand, on boundaries, they begin to fall and roll-off, and so a conical shape is eventually formed. Moreover, the lower portio... | https://physics.stackexchange.com |
481,233 | [
"https://physics.stackexchange.com/questions/481233",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214375/"
] | Currently trying to calculate the moment of inertia of a uniform sphere, radius R, I know the answer is <span class="math-container">$\frac{2}{5}MR^2$</span> but I keep getting <span class="math-container">$\frac{1}{5}MR^2$</span>
Setup:
Assume mass per unit volume <span class="math-container">$\rho$</span>
Centerin... | I don't understand how are you splitting the hemisphere into circular discs. your <span class="math-container">$dm$</span> must have same distance from the axis to zeroth order everywhere inside it. Disc does not.
If you want to split your sphere into discs, you need to compute the moment of inertia of a disc first (<s... | Each slice (disk) is offset by <span class="math-container">$x$</span> from the origin and has radius <span class="math-container">$r = \sqrt{R^2-x^2}$</span>. The contribution to MMOI of each disk is <span class="math-container">$$ {\rm d} I = \frac{\rho}{2} \pi r^4 {\rm d}x $$</span>
Why? Either do another integral ... | https://physics.stackexchange.com |
400,586 | [
"https://mathoverflow.net/questions/400586",
"https://mathoverflow.net",
"https://mathoverflow.net/users/146464/"
] | Let <span class="math-container">$\Sigma$</span> be a Riemann surface and let <span class="math-container">$n,d$</span> be two relatively prime integers. We can consider different moduli spaces related to those. On one hand we have:
-<span class="math-container">$M_{Dol}$</span> the moduli space of stable Higgs field ... | Yes, there is a description of the rank 1 de Rham moduli space, and you can find it for example in Goldman's notes: Higgs Bundles and Geometric Structures on Surfaces.
The deRham moduli space is given by an affine holomorphic bundle over the Jacobian with underlying holomorphic bundle the cotangent bundle, where the At... | The difference of two connections on a line bundle <span class="math-container">$L$</span> is an <span class="math-container">$\mathcal{O}_X$</span>-linear homomorphism <span class="math-container">$L\to L\otimes\Omega^1_X$</span>, i.e. an element of <span class="math-container">$H^0(X, \Omega^1_X)$</span>. Therefore t... | https://mathoverflow.net |
321,833 | [
"https://softwareengineering.stackexchange.com/questions/321833",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/232853/"
] | A question that gets asked a lot is "Why use low level languages if you can code in high level languages more easily (and often tersely)?". I think the answers are fairly straight forward here, being mainly efficiency concerns.
However, I pose "Why do we use high level languages in the first place?". Besides the fact ... | <blockquote>
"Besides the fact that a higher level language is easier to code in and therefore less error prone"
</blockquote>
I really think this is a good enough reason all by itself. If you have no compelling reason to work in a low level of abstraction (such as performance, knowledge in the team, etc), then ther... | <strong>Money.</strong> Cheaper developers, faster development speeds, and less bugs equal more money.
<strong>Portability.</strong> Many high level languages allow you to target different platforms out of the box. Low level languages like C require significant efforts run on multiple platforms.
<strong>Training.</s... | https://softwareengineering.stackexchange.com |
636,141 | [
"https://physics.stackexchange.com/questions/636141",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/299320/"
] | I don't really have strong backgrounds studying quantum physics, but I did learn special and general relativity, and I have now a question how to get the momentum of photon.
For my understanding, Einstein "predicted" energy and momentum of photon through his research on photoelectric effects (1905) and Compto... | The four-momentum of any particle must be tangent to its world line, including photons. Since <span class="math-container">$ds^2=0$</span> for a photon, its four-momentum must also satisfy <span class="math-container">$P\cdot P=0$</span> to ensure that it is tangent along the photon's world line.
We must also note that... | When the particle is going at the speed of light, its line interval <span class="math-container">$ds^2 = 0$</span>, but that does not mean that any relativistic invariant is zero.
Considering, as you did, the four-velocity <span class="math-container">$\underline{U}^2 = c^2$</span>. The four-momentum is defined by <spa... | https://physics.stackexchange.com |
25,986 | [
"https://physics.stackexchange.com/questions/25986",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | At my new job, it's soon going to be my turn for doing night/graveyard shifts for a fair amount of weeks. Perfect excuse to buy a decent beginners telescope to replace the 4.5" 15 y/o Meade that doesn't work anymore with a 10" Dobsonian reflector!
My girlfriend wants to join me (which I'm all for), and having grown up... | I have operated public observing nights at various universities for eight or ten years. These are the objects that have stood out for me.
<strong>Saturn</strong> and <strong>Jupiter</strong> are the "stars" of the night sky. Bar none. Spec. Tac. U. Lar. If you can look at Saturn with nothing between it and your eye be... | Turning a telescope on the Pleiades and Saturn are breath taking for the new (and not so new!) astronomer. If that doesn't elicit a response then its probably best to go somewhere warmer...
| https://physics.stackexchange.com |
1,185 | [
"https://quant.stackexchange.com/questions/1185",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/526/"
] | Assume a scalper/market maker who is operating on an exchange with $N$ stocks with different characteristics such as current market value, average bid-ask spread, average daily volume and historical volatility.
Due to constraints imposed on this market maker he can only engage in $n$ of the $N$ stocks on the exchange... | All things being equal, stocks with the highest bid-ask spread present the greatest opportunity for the market maker
The size of the opportunity (i.e. revenue expectation) can be represented as Volume * Bid-Ask Spread. Your algorithm should rank-order that revenue expectation
Stocks with high current market values w... | I don't know about an algorithm, but you probably want to pick the stocks that have the most ways to hedge, or the ones with the least idiosyncratic risk.
| https://quant.stackexchange.com |
44,936 | [
"https://electronics.stackexchange.com/questions/44936",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11177/"
] | I need to split one power cord from the wall socket to power three 20w lamps.
Should I use a parallel, or a serial connection?
Follow up question: In which ever case, where can I find some guidelines for how to proceed?
| As long as the 20W lamps are designed to operate at the wall socket voltage then you will want to wire the lamps in parallel connection.
Some guidelines.
<ul>
<li>Make sure you appreciate that messing with AC wall power can be dangerous.</li>
<li>Make sure the power cord is not plugged in when you are wiring the cir... | Parallel. If you place the lamps in series each will only get 1/3 of the mains voltage, and give less than 1/10th of the rated light level. (Theoretically 1/9th, because power is proportional to voltage squared, but at lower voltages the filament will be less hot, meaning emitting less light.
If you place the lamps in... | https://electronics.stackexchange.com |
6,903 | [
"https://quantumcomputing.stackexchange.com/questions/6903",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/5125/"
] | The Gottesman-Knill theore states (from Nielsen and Chuang)
<blockquote>
Suppose a quantum computation is performed which involves only the following elements: state preparations in the computational basis, Hadamard gates, phase gates, controlled-NOT gates, Pauli gates, and measurements of observables in the Pauli g... | To my mind, this theorem is not very well stated in this form, if taken out of context. Where it says "phase gates", this may be misleading. It means specifically just <span class="math-container">$S=\sqrt{Z}$</span> and not what I think of as a phase gate, which can have an arbitrary phase (but they have very specific... | Another way to think about this: To simulate what goes on in a quantum computer we have to do a lot of matrix math using <span class="math-container">$(2^N \times 2^N)$</span> matrices<span class="math-container">$^1$</span>, and the action of (most) of the clifford gates can be actually be accomplished by applying som... | https://quantumcomputing.stackexchange.com |
133,637 | [
"https://softwareengineering.stackexchange.com/questions/133637",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27417/"
] | So my team and I are quite new to Scrum and today moved from estimating in Ideal Hours to Story Points. All seems sound rationale, BUT with timeboxed activities. Here is the case, we have an extremelly complex User Story that needs a spike so to explore underlying technical unknowns. With Ideal Hours it would be easy: ... | Personal opinion here, but firstly I prefer to think in terms of complexity rather than story points. I think story points can mean different things to different people so there can be a point (no pun intended!) of confusion when talking about them and estimating based on them.
Secondly, I would not worry about estima... | Personal Opinion:
I don't think you should assign points to a spike. The reason for a spike is you cannot poker plan stories because of some unknowns.
Timebox it "outside" your sprint.
<ol>
<li>You realize you need a spike because you cannot estimate something in terms of story points</li>
<li>Try to find out what ... | https://softwareengineering.stackexchange.com |
1,373,418 | [
"https://math.stackexchange.com/questions/1373418",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/256790/"
] | Find equation of a line with gradient equal to $2$ which intersects the parabola $y = 6 − x − x^2$ at one point?
I tried using the equation of the line $y=2x+c$ and making it equal to $y= -x^2 - x +6$. Then finding $x$ using the quadratic formula. But I just can't find the $c$ value.
| Let's find point of intersection:
$$
2x+c=-x^2-x+6\Longrightarrow x^2+3x+(c-6)=0.
$$
These equation must have exactly one root; so,
$$
3^2=4\cdot1\cdot(c-6)\Longrightarrow c=\frac{33}{4}
$$
| The equation of such a line, which passes through the point $(x_0,y_0)$ is given by $$y-2x=y_0-2x_0$$
It intersects the parabola at only one point if the abscissae equation for the intersection (which is a quadratic equation):
$$6-x-x^2=2x+y_0-2x_0\iff x^2+3x+y_0-2x_0-6=0$$
has a double root, which amounts to saying it... | https://math.stackexchange.com |
174,879 | [
"https://security.stackexchange.com/questions/174879",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/162035/"
] | I'm planning a home backup setup, and I'm not sure if I really understand this quite right.
The idea is I'll set up a Linux server on the network that contains two drives. Drive1 will be network-accessible and used as a backup location for several other machines on the network as well as a general file share. Drive2 ... | Reasonably accurate. You might also let the Linux server <em>read</em> the files off the PCs, which have no write access to the Linux server (nor even know it's there. They're simply accessed routinely by <em>someone</em> reading all their data).
What you really want, though (because I saw this happen) is an emergency... | This is somehow assuming that your server is not going to be infected. I don't know how reliable that assumption is ; after all, there do exist ransomware infections for linux, but I don't know their different infection mechanisms. That said, I think you're reasonably safe.
The trick I use to protect against ransomw... | https://security.stackexchange.com |
23,688 | [
"https://quantumcomputing.stackexchange.com/questions/23688",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/18635/"
] | Niesen and Chuang, 2nd edition, page 107, Box 2.6, in its motivation for partial trace, says that if M is an observable on system A and <span class="math-container">$\tilde{M}$</span> is the corresponding observable on system AB, then it is physically reasonable that the average measurement outcomes computed for the tw... | It's easy to see that it's true for <span class="math-container">$\rho^{AB} = A \otimes B$</span> for any matrices <span class="math-container">$A,B$</span> (even when <span class="math-container">$\rho^{AB}$</span> is not a state, but just a matrix).
Any matrix (not only states) is a linear combination of such product... | If you're tracing over two systems, <span class="math-container">$A$</span> and <span class="math-container">$B$</span>, you can split this into two steps
<span class="math-container">$$
\text{Tr}(Q_{AB})=\text{Tr}\left(\text{Tr}_B(Q_{AB})\right)
$$</span>
(To see this, let the basis you use for taking the first trace ... | https://quantumcomputing.stackexchange.com |
329,741 | [
"https://physics.stackexchange.com/questions/329741",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/149663/"
] | Newton's first law can be derived from his second law. Then why did he put forth the first law, when it's already contained in second law?
My teacher was saying that first law is valid for an inertial reference frame, while second law is also valid for non-inertial reference frame. Is that correct? (I don't think so, ... | The height $h(t)$ of the body as a function of time is $$h(t)=-\frac{1}{2}gt^2+vt$$ with $v$ the initial speed. At $t_1$ and $t_2$, the body will be at the same height. It means that $$h(t_1)=h(t_2)$$ or, equivalently $$-\frac{1}{2}gt_1^2+vt_1=-\frac{1}{2}gt_2^2+vt_2 \\\Downarrow \\v(t_1-t_2)=\frac{1}{2}g(t_1^2-t_2^2) ... | In other way :
Average Velocity between two points at the different height:
$V_(av)$ = $\frac{V_1 +V_2}{2}$
=$\frac{gt_1 +gt_2}{2}$
=$\frac{g(t_1+t_2)}{2}$
| https://physics.stackexchange.com |
25,496 | [
"https://dba.stackexchange.com/questions/25496",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/13201/"
] | In SQL SERVER 2008 I'm thinking about a query such as:
<pre><code>SELECT ...
FROM ...
WHERE ...
AND @a=1
UNION
SELECT ...
FROM ...
WHERE ...
AND @a=2
</code></pre>
Given that <code>@a</code> is clearly the same value, and therefore either the first <code>SELECT</code> returns results or the second <code>SELECT</c... | With respect to your question
<blockquote>
will the query optimizer identify one of the queries as false and not
run it?
</blockquote>
You'd need to check the execution plans. An example below where it doesn't.
<pre><code>DECLARE @P INT =1
SET STATISTICS IO ON;
SELECT name
FROM sys.objects
WHERE type='P' AND @... | SQL Server optimizer is closed source, so we cannot see what exactly is going on under the hood. Of course, there are tons of documentation, and just as surely there are lots of cases when this thing does not behave exactly as documented.
In my experience, all documentation from all vendors tends to get out of sync qu... | https://dba.stackexchange.com |
32,264 | [
"https://chemistry.stackexchange.com/questions/32264",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/16660/"
] | Some webpages describe the contact process as this (I left out $\ce{SO2}$, $\ce{SO3}$ production):
$\ce{SO3 + H2SO4 -> H2S2O7}$
After this, it is controllable to add water to the oleum therefore making liquid sulfuric acid. However, some other sites describe this:
$\ce{SO3 + H2O -> H2SO4}$
I am confused abo... | I think you should not focus on the ligand to define chelation. You should instead focus on the complex that is formed. In fact, the very same multidentate ligand may participate in binding in more than one way:
<ul>
<li>by forming more than one bond with the same central atom, therefore forming a chelated complex;</l... | This is what my textbook says:
<blockquote>
All polydentate ligands are the example of chelating ligands.
However, it must be noted that <span class="math-container">$\ce{NH2NH2}$</span> and <span class="math-container">$\ce{N(CH2CH2)N}$</span> cannot act as chelating ligands due to the formation of a three membered ri... | https://chemistry.stackexchange.com |
4,116 | [
"https://computergraphics.stackexchange.com/questions/4116",
"https://computergraphics.stackexchange.com",
"https://computergraphics.stackexchange.com/users/4981/"
] | In general, I understand the creation of viewing transformation matrix, but I have my doubts.
For example, let's say that a world coordinate (called $A$) has a center at $(1,1,1)$, and the view reference point (VRP) (called $B$) has a center at $(3,3,2)$.
Each vertex of the world must be "mapped" to $B$. The axes of ... | If there is no divergence (i.e. all threads in a wave take the same branch) newer GPU's can skip all the work within the if-branch. If there's divergence, then code in both branches is executed, but thread execution mask basically defines which threads execute code in which branch (code in non-executed branches for thr... | <h1>Old Hardware</h1>
Some older cards didn't used to jump instructions in warps, so this was indeed an issue. If you have a conditional with these cards, the inside logic of the conditional would still be evaluated even if the block wasn't entered by any of the pixels, vertices, etc. There's little you can do in this ... | https://computergraphics.stackexchange.com |
25,102 | [
"https://math.stackexchange.com/questions/25102",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1069/"
] | In Leibniz notation, the 2nd derivative is written as
$$\dfrac{\mathrm d^2y}{\mathrm dx^2}\ ?$$
Why is the location of the $2$ in different places in the $\mathrm dy/\mathrm dx$ terms?
| Somewhat mundanely,
$$ \frac{d}{dx}\left(\frac{d}{dx}(y)\right) = \frac{d}{dx}\left(\frac{dy}{dx}\right) = \frac{d\,dy}{dx\,dx} = \frac{d^2 y}{dx^2} $$
| Purely symbolically, if we accept that $dy = f'(x)\,dx$, and treat $dx$ as a constant, then $$d^2y = d(dy) = d(f'(x)\,dx) = dx\,d(f'(x)) = dx\,f''(x)\,dx = f''(x)\,(dx)^2,$$
so dividing yields:
$$\frac{d^2y}{(dx)^2} = \frac{d^2y}{dx^2} = f''(x).$$
As to where this notation actually comes from, though: My guess is that... | https://math.stackexchange.com |
1,101,072 | [
"https://math.stackexchange.com/questions/1101072",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/195130/"
] | Why $$\lim_{x\rightarrow1} \frac{ e^{ \frac{1}{\pi} \ln x } -1} {\frac{1}{\pi} \ln x }=1$$
I do not get it at all... I do not want explanation that would involve use of l'hospital rule
| If you know that $\lim_{x \to 0}\left(1 + x\right)^{1/x} = e$
Put $\ln y = \dfrac{1}{\pi}\ln x$. The limit becomes $$\lim\limits_{y\to 1}\dfrac{y-1}{\ln y}$$
$z=y-1$
$$\lim\limits_{z\to 0}\dfrac{z}{\ln (z+1)}$$
Also you can obtain
$$\lim_{z \to 0}\frac{\ln(1 + z)}{z} = \lim_{z \to 0}\frac{1}{z}\ln(1 + z) = \lim_{z ... | <strong>Hint:</strong>
Take $z = \frac{1}{\pi}\text{log}(x)$ and use the definition of derivative.
| https://math.stackexchange.com |
369,133 | [
"https://mathoverflow.net/questions/369133",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41619/"
] | A Banach space <span class="math-container">$X$</span> is said to be Grothendieck if the weak and the weak* convergence of sequences in <span class="math-container">$X^{*}$</span> coincide. I have the following two questions.
Question 1. A Banach space <span class="math-container">$X$</span> is Grothendieck if and only... | I find the following criterion useful: A sequence <span class="math-container">$(x_n)$</span> is Cauchy iff for all subsequences <span class="math-container">$(x_{n_{k+1}}-x_{n_k})$</span> tends to <span class="math-container">$0$</span>. This works for the norm topology, the weak topology and the weak<span class="math... | Q1 is already answered by Prof. Dirk Werner above. I simply list a number of equivalent conditions that seems to be related, but not the same as the Grothendieck property.
The following are indeed equivalent:
<ol>
<li>every weak*-null sequence in <span class="math-container">$X^{\ast}$</span> has a weakly Cauchy subseq... | https://mathoverflow.net |
338,989 | [
"https://physics.stackexchange.com/questions/338989",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/157316/"
] | In the topic of pure A.C. Circuits, we have $I = V/\omega L$ and $I = V/\omega C$.
I know that $\omega C$ & $\omega L$ does the work of Resistor, but what does it mean and what do we mean by saying that $I$ is inversely proportional to $\omega$ and $C/L$?
Edit: I want to know the behaviour of I with $\omega$ and L... | <h1>Basics in AC circuits</h1>
Since we are using AC circuits, we have inputs which can be described as:
$$I_{in} = A\sin(\omega t + \phi)$$
And:
$$V_{in} = B\sin(\omega t + \phi)$$
Note that all sinusoid input signals can be written like this! (If the signal is not a pure sinusoid, we can use Fourier decompositio... | Could you elaborate further? I'll try and answer though:
These laws are equivalent to Ohm's law. It was observed that voltage and current ratio was constant in certain points, depending only on the material in which the current flows. We just extended that law to A.C. system and found these ratios had these values.
| https://physics.stackexchange.com |
679,151 | [
"https://math.stackexchange.com/questions/679151",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/128641/"
] | I was wondering if $\infty^0=1$. Some people have told me that there is no answer; it is undefined. Others have told me that the answer is $1$, using the rule $a^0=1, \ a\neq 0$. If it is truly undefined, then why is it undefined? Please answer, thanks!
| $\infty^0=\infty^{^\frac1\infty}=\sqrt[\infty]\infty$ . Now, $\sqrt[n]x$ is the quantity which, when multiplied <em>n</em> times with itself, gives <em>x</em>. So: which quantity, multiplied an infinite number of times with itself, yield infinity as a result ? Obviously, <strong>any</strong> real number $>1$ has thi... | Since $\infty$ is not a real number, the expression $\infty^0$ is not interpreted like $3^0$, but rather as the following:
<blockquote>
We are given two sequences of real numbers, $a_n$ and $b_n$, such that $\lim a_n=0$ and $\lim b_n=\infty$, and now we calculate the limit of the exponentiation, $\lim b_n^{a_n}$.
</... | https://math.stackexchange.com |
222,447 | [
"https://electronics.stackexchange.com/questions/222447",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/103443/"
] | I am working on a PCB layout in which I have a 40cm long traces (bus of 4 traces). This traces will support between 50mA to 100mA and 5V. I want to minimize possible antenna effects that may occur due its length.
Could you provide me any tip on how to avoid this effect (width of trace affects?)? Or at least methods of... | It's unclear from your question if you're more concerned with your traces generating EMI/RFI (creating interferance & possibly failing FCC compliance), receiving interference (causing unwanted/undefined circuit behavior), or inter-trace interference (one trace's signal interferes with its neighbors).
Fortunately h... | Using a groundplane is a good idea. The solid copper layer limits the loop area to the length of the track x layer distance. This minimizes the inductance of the loop. You could also use two groundplanes, one above and one below the tracks in question making it more like a full screen. You could also alternate send and... | https://electronics.stackexchange.com |
76,785 | [
"https://dsp.stackexchange.com/questions/76785",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/58770/"
] | Are these terms just parallel words? If not, why is it that when one reads about the first then one is very likely to come across the second? In such case, what would be a nice example to explain the possible connection between the words?
| The word <em>discrete</em> is used to define a signal that is not continuous, but is composed of a sequence of values.
The word <em>digital</em> is used to define a discrete signal whose values have been quantized and can be stored... digitally.
You can have a discrete signal that is not digital, for example the signal... | There is continuous time, and discrete time. With a continuous time signal, between any two points in time you can find signal, which may be different than either of the two points. With discrete time, there are values between certain points in time, and nothing between adjacent values. "Digital" is simply an... | https://dsp.stackexchange.com |
930,476 | [
"https://math.stackexchange.com/questions/930476",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/170831/"
] | 1) Determine how many ways Brian, Katie, and Charlie can split a 50 dollar dinner bill such that Brian and Katie each pay an odd number of dollars and Charlie pays at least 5 dollars .
2) Determine how many ways I can distribute 80 candies to 3 kids, such that:
The first kid receives an arbitrary number of candies (... | By using the substitution:
$$u = qx + c$$
$$du = qdx, dx = \frac{du}{q}$$
You are incorrect in your derivation.
Therefore, we can substitute this:
$$\int\frac{dx}{qx +c} = \int\frac{\frac{du}{q}}{u} = \int\frac{du}{qu} = \frac{1}{q}\int\frac{du}{u} = \frac{1}{q}\ln |u| = \frac{\ln|qx + c|}{q} + C_1$$
Comment if ... | <span class="math-container">$$\int\frac{dx}{qx+c}=\frac{\ln\left| qx+c \right|}{q}+C$$</span>
| https://math.stackexchange.com |
416,386 | [
"https://softwareengineering.stackexchange.com/questions/416386",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/375683/"
] | I’m still really new to learning to program. Just learning the syntax for a few programming languages at the moment.
The courses I viewed for C# and Java touched only very briefly on getters & setters and it still didn’t make an awful lot of sense to me. So I researched them further and found that the whole subject... | <blockquote>
I’m still really new to learning to program. Just learning the syntax for a few programming languages at the moment.
</blockquote>
And that is actually the problem here - you approach this way too much from a syntactical point of view. What you need to learn first is solving problems with programs. When th... | Getters and setters make accessing fields into their own methods. When you're in Java you have to do this up front or when you decide to do it later you change the interface. In C# they have lovely properties so your clients won't care when you decide to make your public fields private.
These let you detect when someth... | https://softwareengineering.stackexchange.com |
68,462 | [
"https://cs.stackexchange.com/questions/68462",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/64399/"
] | To my knowledge, lots of languages can be classified as undecidable after applying Rice's theorem, for example {"M" | L(M) is regular}.
But what I am not sure is, how to determine if a language is enumerable after applying Rice's theorem? I reckon we can examine that whether the M halt on some specific input, i.e. tes... | You can use the fact that if $L$ is undecidable and $\overline{L}$ is enumerable then $L$ is not enumerable (since if both $L$ and $\overline{L}$ are enumerable, then $L$ is decidable). In order to determine whether an undecidable language is enumerable or not, you can try to construct an enumerator for the language or... | In addition to Yuval's approach You can also read about monotonic and non-monotic properties of languages as well. This statement usually an extension to Rice theorem says :
“Every non-monotone semantic property
of Turing machines is unrecognizable”
| https://cs.stackexchange.com |
145,302 | [
"https://electronics.stackexchange.com/questions/145302",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22979/"
] | Is it because the CPU increases its hertz as necessary?
And when a CPU cycle has to enter a register, does the extra distance in its path measurably affect the speed of that specific cycle? And will it delay the start of the next cycle?
| There are two effects that influence the amount of power a chip needs. The static power (transistor leakage) and dynamic power. The static power depends on the technology used to build the chip. Therefore even at 0Hz clock the chip draws current. The dynamic power is what you're interested in.
The reason for consuming... | <em>And when a CPU cycle has to enter a register, does the extra distance in its path measurably affect the speed of that specific cycle?</em>
This doesn't make sense, but the answer to the question I think you mean is no; the CPU doesn't know it's own propagation delay. The propagation delay is fixed at design time b... | https://electronics.stackexchange.com |
292,067 | [
"https://physics.stackexchange.com/questions/292067",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95688/"
] | We've been learning about the derivation for moment of inertia as:
$$\int r^2 dm$$
However, for me, this looks like it's a bit backwards. As a first year calc student, I see the differential in the integration as almost being the "independent" variable and the function inside as being the "dependent" variable (when w... | Suppose you have a single point mass $m$ at a distance $r$, then the moment of inertia is of course just:
$$ I = mr^2 $$
But suppose now our mass is an extended object not a point mass, so the above equation doesn't apply. We could get an approximation for $I$ by splitting the mass up into $n$ smaller masses $m_i$ wi... | The integral in the question is an acceptable definition; when we write,
$$I = \int dm \, r^2$$
we mean here that $r$ is the distance a point of the object is from the axis of rotation, as a function of mass. An equivalent definition of $I$ would be,
$$I = \int_V dV \, \rho \, r^2$$
where again $r$ is the distance ... | https://physics.stackexchange.com |
16,336 | [
"https://security.stackexchange.com/questions/16336",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10634/"
] | I was thinking last night after reading an article about pen testing and security audits, why would you get a list of all the passwords for the company you are auditing and put them through a piece of software to analyse ?
| You wouldn't get a list of all the passwords. Any company that could or would produce such a thing would fail any reasonable security audit.
You might get a list of all the password hashes which could then be run through a tool that attempts to determine what the password is. The ease with which the password hashes ... | To test for potentially weak passwords that can be cracked easily by a malicious attacker.
This could give an indication of the state of the password policy of the particular company, which might be an issue in certain circumstances.
If there are plenty of weak passwords found, the pen tester could suggest to the co... | https://security.stackexchange.com |
9,850 | [
"https://electronics.stackexchange.com/questions/9850",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2924/"
] | What purpose does the IO shield on computers serve? I have been reading a lot of articles (mostly forums) on the internet and can't seem to find a definitive answer.
| I/O shield:
<img src="https://i.stack.imgur.com/k4GrD.jpg" alt="enter image description here">
1) Shield to keep electro-magnetic radiation inside of the case
2) Dust Cover / Air circulation director: The fan in the power supply shall draw air throughout the entire case and not just along the short way from the I/... | For posterity's sake, I'll add something new, here. I'm finding this thread in 2017 after typing the question into Google.
Before now, I've read a few POVs stating that the IO shield isn't necessary at all. In fact, I went to a parts shop recently after losing mine assuming it was an absolute requirement. I was set to... | https://electronics.stackexchange.com |
111,425 | [
"https://softwareengineering.stackexchange.com/questions/111425",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/37397/"
] | I am developing a web application as well as the API the web application uses. I'm trying to determine whether it is better to log events (to determine the path that leads to an error as well as to determine whether the site has been compromised) in a database or simply by writing to a file.
On the one hand, I don't ... | If logging to the DB, where would you log db failures, like the DB being unavailable?
Yes, if logging to the file system, the file system could become unavailable, but my guess is that you then would have other things to worry about...
In a server application (not a web server, but one under heavy load anyway), we lo... | Only if most of your team members don't know how to handle text file in command line can you justify the use of a db based log. For concerns you have listed:
<ol>
<li>Performance: for appending information row by row, I think no db does it faster than a text file.</li>
<li>Easy query: how are you so sure db is better ... | https://softwareengineering.stackexchange.com |
116,924 | [
"https://mathoverflow.net/questions/116924",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25869/"
] | Given a group $G$ and $G$-modules $M,N$ with $M$ $\mathbb{Z}$-free then it's well known that
$$Ext_{\mathbb{Z}G}^i(M,N) \cong H^i(G,Hom(M,N))$$
for all $i \ge 0$ (a reference is Brown, Cohomology of Groups, Proposition 2.2).
But what happens if $M$ is not $\mathbb{Z}$-free ? Is it still possible to express $Ext_{\ma... | There is a long exact sequence
<blockquote>
$$0 \to H^1(G,Hom(M,N)) \to Ext_{\mathbb{Z}G}^1(M,N) \to \cdots $$
$$\begin{array}{lll}
\cdots & \to & H^i(G,Hom(M,N)) \to Ext_{\mathbb{Z}G}^i(M,N) \newline
& \to & H^{i-1}(G,Ext_{\mathbb{Z}}^1(M,N))\to H^{i+1}(G,Hom(M,N)) \to \cdots
\end{array}$$
</blo... | As you've probalby noticed, we can't just take group cohoology. If $G$ is trivial, we are just taking exts in the category of abelian groups, which are nontrivial, but the group cohomology is trivial.
The spectral sequence idea is completely correct. The functor $Hom_{\mathbb ZG}(M,-)$ is the composition of the functo... | https://mathoverflow.net |
191,968 | [
"https://dba.stackexchange.com/questions/191968",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1822/"
] | We are trying to find out why a (pretty complicated) statement has an extremely high variance in runtime. Sometimes it just takes "minutes" (around 40-50) and sometimes it does not finish even after 12 hours.
My usual approach to problems like that is to check if the statement is monitored and if it is, get t... | You can create separate tables, like user table and contact table:
<ul>
<li>user table
<pre><code>uID
---
2
</code></pre></li>
<li>contact table
<pre><code>Contact | uID
1221 | 2
1223 | 2
</code></pre></li>
</ul>
| As suggested above, the best way is to have two tables - one for user and the other for contact.
From your example it appears as if you have nothing more than an id for the user. If that is the case, and if you know for a fact the maximum number of contacts a user has (let’s say 3), then you can use a single table wi... | https://dba.stackexchange.com |
524,107 | [
"https://physics.stackexchange.com/questions/524107",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251344/"
] | The lagrangian of the Real Scalar Field <span class="math-container">$\phi$</span> is given by
<span class="math-container">\begin{equation}
\mathcal{L} = \frac{1}{2}\eta^{\mu \nu} \partial _\mu \phi \partial _{\nu} \phi - \frac{1}{2} m^2 \phi^2
\end{equation}</span>
<span class="math-container">\begin{equation}
\eta^... | As you say, when building a Lagrangian for a theory, we almost always wish it to be a Lorentz scalar. Obviously, we can take any power of the scalar field, <span class="math-container">$\phi$</span>, that is, we can have terms of the form,
<span class="math-container">$$\mathcal L = \dots + \sum_{n\geq 0} c_n \phi^n +... | The Euler-Lagrange equation following from this lagrangian is the Klein-Gordon equation, which is the field theoretical equivalent of the special relativistic energy-mass-momentum equation.
| https://physics.stackexchange.com |
39,266 | [
"https://stats.stackexchange.com/questions/39266",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5339/"
] | I'm wondering if there are any sorts of standard distributions on subsets of integers $\{1, 2, ..., J\}$. Equivalently, we could express this as a distribution on a $J$ length vector of binary outcomes, e.g. if $J = 5$ then $\{1, 3, 5\}$ corresponds to the vector $(1, 0, 1, 0, 1)$.
Ideally what I'm looking for is some... | <strong>You might favor location families based on Hamming distance</strong>, due to their richness, flexibility, and computational tractability.
<hr>
<h3>Notation and definitions</h3>
Recall that in a free finite-dimensional module $V$ with basis $\left(\mathbf{e}_1, \mathbf{e}_2, \ldots, \mathbf{e}_J\right)$, the ... | A sample from a k-determinantal point process models a distribution over subsets that encourages diversity, such that similar items are less likely to occur together in the sample. Refer to K-determinantal point process sampling by Alex Kulesza, Ben Taskar.
| https://stats.stackexchange.com |
389,793 | [
"https://physics.stackexchange.com/questions/389793",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/186746/"
] | For a medical experiment I am doing, I need an equation to find the angle at which someone will lean before falling. I am not mathematically inclined in terms of advanced stuff, I am more so of a trigonometry person.
I assume factors that will be needed are BMI, including height and weight, but that is really all I ha... | $T^\mu{}_\nu$ and $T_\nu{}^\mu$ are both maps from a vector and a dual vector to $\mathbb R$, true. But they aren't necessarily the <em>same</em> map as each other.
Mathematically, you can see this by considering the difference explicitly:
$$ T^\mu{}_\nu-T_\nu{}^\mu $$
You can use the metric to raise/lower one of th... | The difference is $(T^{\mu\rho}-T^{\rho\mu})g_{\rho\nu}$.
| https://physics.stackexchange.com |
3,616,538 | [
"https://math.stackexchange.com/questions/3616538",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/573505/"
] | Assume <span class="math-container">$f:E \rightarrow \mathbb{R}^m$</span> and <span class="math-container">$g:E \rightarrow \mathbb{R}$</span>, and <span class="math-container">$E \in \mathbb{R}^n$</span> is open. Assume <span class="math-container">$x \in E$</span>, and <span class="math-container">$f$</span> and <spa... | The derivative of <span class="math-container">$f$</span> at <span class="math-container">$x_0$</span> is a linear map <span class="math-container">$A$</span> such that <span class="math-container">$f(x) - f(x_0) - A(x-x_0) = o(x-x_0)$</span> as <span class="math-container">$x \to x_0$</span>. That linear map is what w... | To sort this out more carefully, let's consider the derivative at a point <span class="math-container">$x$</span> in the direction <span class="math-container">$v\in\Bbb R^n$</span>. Then <span class="math-container">$g(x)\big(f'(x)v\big)$</span> is the product of a scalar with a vector in <span class="math-container">... | https://math.stackexchange.com |
33,768 | [
"https://softwareengineering.stackexchange.com/questions/33768",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12411/"
] | I've been contemplating how to balance testable design using dependency injection with providing simple fixed public API. My dilemma is: people would want to do something like <code>var server = new Server(){ ... }</code> and not have to worry about creating the many dependencies and graph of dependencies that a <code>... | Dependency injection is a powerful pattern when used well, but all too often its practitioners become dependent on some external framework. The resulting API is quite painful for those of us who don't want to loosely tie our app together with XML duct tape. Don't forget about Plain Old Objects (POO).
First consider ... | How about providing a subclass which provides the "public api"
<pre><code>class StandardServer : Server
{
public StandardServer():
this( depends1, depends2, depends3)
{
}
}
</code></pre>
The user can<code>new StandardServer()</code>and be on their way. They can also use the Server base class if th... | https://softwareengineering.stackexchange.com |
29,570 | [
"https://datascience.stackexchange.com/questions/29570",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/49517/"
] | I am trying to develop a NN for a very simple classification model with keras/tensorflow:
Ex:
<ul>
<li>input: "Do" => class output: "Dog"</li>
<li>input: "Ca" => class output: "Cat"</li>
<li>input: "Mo" => class output: "Mouse"</li>
</ul>
I train the model with many "Do", "Ca", etc. (as dictionary), indexing the inp... | I will add my 2 cents at the end of this answer. However, this is how it can be done using a neural network. Firstly, yes, you should expect to need more data to train even a simple neural network because their are more parameters that need tuning. Think of them like little faucets that you need to tune in order to get... | For every problem there is proportional solution.
I understand that you want to build your classifier inside an image recognition algorithm.
You may need a NN for the image (lots of inputs + lots of possibilities) but not for the whole system.
What is usually done for this kind of problematic is to build a "pipe"... | https://datascience.stackexchange.com |
71,808 | [
"https://mathoverflow.net/questions/71808",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16876/"
] | Given a morphism $f$ of Schemes $X \to Y$ and two sheaves $\mathcal F$, $\mathcal G$ of modules on $Y$,
is it right that the tensor product of $\mathcal F$ and $\mathcal G$ as modules commutes with the inverse image (not the module pullback but only the inverse image $f^{-1}$)
construction? Here I mean one time tensor ... | $\newcommand{mc}{\mathcal}$
I guess that the problem lies in all the sheafifications so let me explain how to get rid of them in some small independent steps which are of some interest on their own.
I denote by $\cdot^\#$ the sheafification.
The following two statements follow without difficulty by checking that the ob... | The tensor product $F \otimes G$ of sheaves of modules has the following universal property:
$\hom(F \otimes G,H) = \text{bilin}(F \times G,H)$
Here, the right hand side is the set of bilinear sheaf homomorphisms $F \times G \to H$. You should keep this in mind instead of the explicit construction involving sheafific... | https://mathoverflow.net |
2,776 | [
"https://mathoverflow.net/questions/2776",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1178/"
] | If ℝ<sup>#</sup> exists then why is cof(θ<sup>L(ℝ)</sup>) = ω? Also I have the same question for the L(V<sub>λ+1</sub>) generalization (if it's actually a different proof; I presume it isn't), i.e. if θ is defined as the sup of the surjections in L(V<sub>λ+1</sub>) of V<sub>&... | This is because the pieces of the sharp singularize Theta. Let s_n be the sequence of the first n cardinals above continuum and let a_n be the nth cardinal above continuum. Then the theory of reals with a parameter s_n in L_{a_n+1}(R) is a set of reals A_n. They are Wadge cofinal in Theta, another words the sequence i... | Scott, the best way to think of sharps is via mice. Think of x^# as a mouse over x with one measure which is iterable. R^# is a mouse over R with one measure which is iterable. Things become very easy ones you make the move from sharps as reals or sets of reals or etc to sharps as mice.
| https://mathoverflow.net |
4,566,288 | [
"https://math.stackexchange.com/questions/4566288",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1072855/"
] | I know according to some textbooks, rings do not have to contain <span class="math-container">$1$</span>. But if I define rings to have <span class="math-container">$1$</span>, are all ring homomorphisms unital? Here's my attempt to prove this:
Let <span class="math-container">$\phi:R\rightarrow S$</span> be a ring hom... | u could only deduce that <span class="math-container">$\phi(x) (1-\phi(1))=0$</span> for every <span class="math-container">$x\in R$</span>(there is no cancellation for multplication in general) , if <span class="math-container">$S$</span> is an integral domain and <span class="math-container">$\phi$</span> isn't the z... | Here is a concrete example of what can go wrong.
Consider the ring <span class="math-container">$\mathbf Z/(6)$</span>. Its subset <span class="math-container">$\{0, 3 \bmod 6\}$</span> is a "subset with ring structure" since <span class="math-container">$3+3 = 0$</span> and <span class="math-container">$(3)... | https://math.stackexchange.com |
58,009 | [
"https://mathoverflow.net/questions/58009",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2234/"
] | Let $f: X \to Y$ be a morphism of varieties such that its fibres are isomorphic to $\mathbb{A}^n$. Since the definition of a vector bundle stipulates that $f$ be locally the projection $U \times \mathbb{A}^n \to U$, it is likely that there exist morphisms that are not locally of that form, but I can't come up with an e... | In Jack's example the fiber is not scheme-theoretically $\mathbb A^1$. You can get a counterexample by taking $Y$ to be a nodal curve, $Y'$ its the normalization, with one of the two points in the inverse image of the node removed, and $X = Y' \times \mathbb A^1$.
If we assume that the map is smooth, this becomes quit... | EDIT: See the comments for why this isn't a good example. Angelo gives a similar example that actually works.
Suppose that $Y=C$ is a cuspidal curve, and let $\tilde C\to C$ be the normalization. Put $X = \mathbb{A}^1\times \tilde C$, and let $X\to Y$ be the obvious map. The fibers are all $\mathbb{A}^1$'s, but ov... | https://mathoverflow.net |
190,416 | [
"https://stats.stackexchange.com/questions/190416",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/93121/"
] | Consider the linear regression model: $$y_{it}=x_{it}\beta+\epsilon_{it}$$
where $x$
is single regressor. The conditional mean of any specific observation is:$$E[y_{it}|x_{it}]=x_{it}\beta$$
under the conditional mean independence assumption.
The conditional variance, howevever, is where I am confused. On one ha... | The title of your question "<strong>Conditional</strong> variance in OLS regression" gives a clue. The first expression
$$\text{Var}(y_{it})=\beta^{2}\sigma_{x}^{2}+\sigma_{\epsilon}^{2}$$
gives the <em>unconditional</em> variance ($x$ is not "conditioned away" and remains in the expression) while the second one
... | But your final equation cannot be right if you are not treating the predictors as fixed. For
$$y_i = \beta x_i + \epsilon_i$$
recalling that
$$E\left(Y \right) = E\left[ E \left(Y|X \right) \right]$$
we have
$$E(y_i) =E\left( E\left(\beta x_i + \epsilon_i|x_i \right) \right) = \beta \mu_x$$
and so
\begin{alig... | https://stats.stackexchange.com |
273,081 | [
"https://electronics.stackexchange.com/questions/273081",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/131903/"
] | I want to make a voltage divider using a potentiometer.
Will the value of the potetiometer affect anything or not? I mean, if I use 10k or 1k or even 100 ohm, what's the difference?
And also if I use the voltage divider as a power source, why its a bad idea?
| When you use a transformer to transfer electrical power from a source to a load, we call that a "power" transformer. The adjective is added to help understand the function of the particular transformer. For exemple, they also are "audio" transformer", "data" transformer, "gate driver" transformer, "isolation" transform... | Welding transformers need to be <em>soft</em>, which means they have a reasonably high voltage as long there is no current flowing, and a pretty low voltage at high nominal current. That is because you want to break any insulating layers on the metal you weld while not suppling excess current which would melt holes in ... | https://electronics.stackexchange.com |
186,515 | [
"https://math.stackexchange.com/questions/186515",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/19125/"
] | Let $P$ be a $d$-dimensional convex polytope.
$P$ is contained in $[0,1]^d$ and all vertices have only integral coefficients.
Given a set of facets of $P$, how to check that this set is maximal. i.e. that it is the set of all facets of $P$?
<strong>[update]</strong> I don't know yet if this is valid, but here's a sim... | I assume you have the polytope $P$ of dimension $d$ specified by a set of points, and a set of facets $\mathcal{F}$ where each facet is a subset of $P$ spanning a $d-1$-dimensional polygon. I'm not assuming that $P\subset\{0,1\}^d$: it could be in some $d$-dimensional subspace of $\mathbb{R}^D$ or $\{0,1\}^D$ for some ... | Assuming the $D-1$-faces do not have common interior points. Otherwise, you'll need to do some polytope subtraction before applying this method.
Since it is a convex polytope, its centroid is guaranteed to be within it. For each $D-1$-face, you can project all the vertices and $D-2$-edges onto a hollow unit $D-1$-sphe... | https://math.stackexchange.com |
4,475,026 | [
"https://math.stackexchange.com/questions/4475026",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1013744/"
] | I am trying to solve:
<span class="math-container">$\int_{\gamma} \frac{e^{2 \pi z}}{(z+i)^3}dz$</span>, <span class="math-container">$\gamma(t)=2e^{it}, t \in [0,2 \pi]$</span> by using the Cauchy Integration Formula.
My Calculations:
I did define <span class="math-container">$f(z):=z\frac{e^{2 \pi z}}{(z+i)^3}$</span... | <span class="math-container">$\frac {e^{2\pi z}} {(z+i)^{3}}=\frac {e^{2\pi (z+i)}} {(z+i)^{3}}$</span> and expanding the exponential we see that the coefficient of <span class="math-container">$\frac 1 {z+i}$</span> is <span class="math-container">$\frac {(2\pi)^{2}} {2!}$</span>. This the residue at <span class="mat... | Let <span class="math-container">$f(z) := \mathrm{e}^{2\pi z}$</span>.
Using Cauchy integral formula
<span class="math-container">$$f^{(n)}(a) = \frac{n!}{2\pi\mathrm{i}}\int_{\gamma}\frac{f(z)}{(z - a)^{n+1}}\,\mathrm{d} z,$$</span>
we have
<span class="math-container">$$\int_{\gamma}\frac{\mathrm{e}^{2\pi z}}{(z + \m... | https://math.stackexchange.com |
66,019 | [
"https://mathoverflow.net/questions/66019",
"https://mathoverflow.net",
"https://mathoverflow.net/users/37021/"
] | I have a feeling that this may be a very easy question for some people on MO, but it isn't for me.
Take a finite pointed set $X$, with $*$ the base-point. Build a cosimplicial set which in degree $n \ge 1$ is $X^n$ (the cartesian product of $n$ copies of $X$), and in degree $0$ is $\{ * \}$; the cofaces are:
$d^0(x_1... | If I've understood well your construction, the complex $\hom_k(A,k)$ is the Hochschild complex of the cochain $k$-algebra $C^\star(X,k)$ of the (discrete) space $X$ with coefficients in the $C^\star(X,k)$-module $k$. The $C^\star(X,k)$-module structure on $k$ is given via the augmentation $C^\star(X,k)\rightarrow k$ in... | No matter what cosimplicial set $X^\bullet$ is used, the complex will always have $H^n=0$ for $n>0$. This follows from the fact that if elements $x,y\in X^n$ are not in the image of any of the face maps $d^j:X^{n-1}\to X^n$ then the equation $d^ix=d^jy$ implies $x=y$ and $i=j$. (This suggests that there is no intere... | https://mathoverflow.net |
50,632 | [
"https://stats.stackexchange.com/questions/50632",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/21154/"
] | First of all, I apologize since this question has probably been asked many times and is easily answered. However, as a statistics amateur I simply couldn't figure out what keywords are relevant to my question.
Suppose you have 100 merchants and 100 products. Each merchant sells a certain range of products, ranging fro... | Let me expand on alternative solution proposed by @curious_cat.
$P_{ij}$ is the matrix of pitches
$L_{ij}$ is the matrix of sells
$S_{ij} = L_{ij}/P_{ij}$ is the matrix of success rates (elementwise division where it exists and 0 elsewhere)
As @curious_cat suggested, you want to approximate $S_{ij}$ by the outer ... | This type of problem is typically referred to in econometrics and marketing research as a "choice modeling" problem. Texts dealing with such problems include:
Louviere, J., D. A. Hensher, et al. (2000). Stated Choice Methods: Analysis and Application. Cambridge, Cambridge University Press.
Train, K. E. (2009). Discret... | https://stats.stackexchange.com |
532,014 | [
"https://physics.stackexchange.com/questions/532014",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247868/"
] | If I had to give a guess based on limited understanding, I would expect it to be something to do with the resulting object no longer obeying tensor transformation properties.
However, if that is the case I have one further question. If I contract the indices of a (2,0)-tensor I obtain a scalar, which is (by definition... | Let's consider a simple <em>explicit</em> example of how contracting two upper Lorentz indices or two lower indices doesn't produce a Lorentz invariant.
A particle has energy and momentum. The particle can be observed in two different inertial frames which might be moving relative to one another. In one frame the ener... | Under coordinate transformations, vectors transform with the Jacobi matrix, whereas covectors transform with its inverse. If you contract an upper and a lower index, these operations cancel, and the result will be invariant under coordinate transformations.
In contrast, summing over two indices in the same position ge... | https://physics.stackexchange.com |
31,983 | [
"https://quant.stackexchange.com/questions/31983",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/25995/"
] | I am trying to get multiple indicator values such as RSI and EMA for equities using the package tidyquant in R. I tried the example from the vignette which is:
<pre><code>tq_get("AAPL", get = "stock.prices")%>% tq_transform_xy_(x_fun = 'close', transform_fun = 'periodReturn',period = 'weekly') %>% tq_mutate(x_f... | I'll be using <code>tidyquant</code> version 0.3.0 to answer this question, which changes from <code>x_fun</code> to <code>ohlc_fun</code> in <code>tq_mutate</code> and <code>tq_transform</code> and adds the new <code>col_rename</code> argument to solve situations like yours with non-intuitive column names.
<strong>Pa... | Answer to 1):
<pre><code>library(tidyquant)
tq_get("AAPL", get = "stock.prices")%>%
tq_transform_xy_(x = 'close', transform_fun = 'periodReturn',period = 'weekly')
</code></pre>
this gives you
<pre><code> A tibble: 525 × 2
date weekly.returns
<dttm> <dbl>
</code></pre>
App... | https://quant.stackexchange.com |
317,971 | [
"https://math.stackexchange.com/questions/317971",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/37248/"
] | I'm trying to find the indefinite integral of
$$f(x) = \begin{cases} \sin x & x<\pi/4 \\ \cos x & x\ge \pi/4 \\ \end{cases}$$
In all of $\Bbb R$. It seems continuous at $\frac{\pi}4$ and everywhere else, so it should have a definite integral. I intuitively think of something like:
$$F(x) = \begin{cases} -\... | The best and fastest route to find the antiderivatives is the one taken by Andre Nicolas. This answer shows how to go from where the OP stopped.
Yes, that's a problem.
You first need to adjust the constants so that your antiderivative be continuous at $\pi/4$, hence on $\mathbb{R}$.
Equate the right and the left li... | After we have found <strong>one</strong> antiderivative, getting them all is mechanical. Let $f(x)$ be our function. Since $f$ is continuous everywhere, one antiderivative $F(x)$ is given by
$$F(x)=\int_a^x f(t)\,dt,$$
where $a$ is a constant. Now we are finished.
But if we want an explicit formula, pick any $a$ you... | https://math.stackexchange.com |
380,639 | [
"https://mathoverflow.net/questions/380639",
"https://mathoverflow.net",
"https://mathoverflow.net/users/128887/"
] | Let <span class="math-container">$G$</span> be a finitely presented group. It is clear that if the profinite completion <span class="math-container">$\widehat{G} $</span> of <span class="math-container">$G$</span> is finite, then any finite dimensional complex linear representation <span class="math-container">$\rho: G... | Yes, there exists such a finitely presented group.
Let <span class="math-container">$\Gamma$</span> be a cocompact arithmetic lattice in a product of <span class="math-container">$\ge 2$</span> rank 1 groups simple groups (with trivial center) over locally compact fields of finite characteristic. So <span class="math-c... | Yes if you weaken to finitely generated. Take an infinite finitely generated torsion group that is residually finite like the Grigorchuk group. By a theorem is Schur any finitely generated torsion linear group is finite. I am not sure of the general case.
| https://mathoverflow.net |
496,212 | [
"https://physics.stackexchange.com/questions/496212",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236248/"
] | I have seen multiple questions which talk about a tank with a partition in the middle and different ideal gases on either side at some different value of pressure,volume and temperature and then they say that when the partition is removed find final temperature of the mixture of gases....what has been told to me is tha... | In engineering, we regard an ideal gas as a substance which exhibits the limiting behavior of a real gas in the region of low gas density. As such, it displays the following key characteristics:
<ol>
<li>Its equation of state is Pv=RT, where v is the molar volume</li>
<li>Its molar internal energy u is a function onl... | Your teachers are correct that we normally talk about the change in internal energy of an ideal gas according to
<span class="math-container">$$\Delta U=nC_{v}\Delta T$$</span>
It’s true you generally can't determine the absolute value of internal energy because of the many contributions (kinetic plus potential) to i... | https://physics.stackexchange.com |
154,331 | [
"https://mathoverflow.net/questions/154331",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13356/"
] | Though the Atiyah-Singer index theorem holds for pseudodifferential operators, all the applications of the index theorem I know of only need it for Dirac-type operators. I know that pseudodifferential operators play a major role in the K-theoretic <em>proof</em> of the index theorem, but it seems to me that they are of... | Boundary problems for elliptic differential equations are often studied by reducing to equations on the boundary. These equations are, as a rule, pseudo-differential but not differential. If the boundary problem is elliptic then the pseudo-differential operator is elliptic, thus Fredholm, and its index is of interest f... | Index theory is fundamentally about a homomorphism
$$K_n(M) \to \mathbb{Z}$$
from the top degree K-homology of $M$ (even dimensional) to the integers called the <em>analytic index map</em>. It is called this because every graded self-adjoint elliptic (pseudo)differential operator on $M$ determines a class in $K_n(M)$ ... | https://mathoverflow.net |
554,272 | [
"https://electronics.stackexchange.com/questions/554272",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/279723/"
] | I know that in a battery:
The anode is where oxidation takes place (the anode losses electrons).
The cathode is where reduction takes place (the cathode gains electrons).
But I am confused why is the anode called anode if it is providing electrons instead of attracting them?
Why do we say Cathode is negative and Anode ... | It's not usual to talk about anode and cathode of a battery (or cell) in electroncs, it's more a chemistry thing.
In chemistry the anode is the terminal that is producing external electron current and the cathode is consuming an equal current.
<blockquote>
I know that in a battery: The anode is where oxidation takes pl... | They (electrons) flow from cathode to anode. What’s got you confused is that electron flow is the opposite of <em>conventional current</em> flow, which pre-dates electron theory by about 100 years or so. (Ben Franklin vs. JJ Thomson.)
The math still works out either way as long as you’re consistent.
Inside the battery ... | https://electronics.stackexchange.com |
258,729 | [
"https://softwareengineering.stackexchange.com/questions/258729",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/151751/"
] | How can I put in the design constraint into a user story?
The system to be developed will generate a invoice when a payment is made, and will send the invoice to <em>xMail</em> (an emailing tool) which will then email the invoice to the customer.
How should I put the information where the system will send the invoice... | Consider what the key steps of the process are and when the value to the customer is derived. Try and capture that in the user story. Then use your acceptance criteria to flush out the requirements further. There is nothing wrong with putting a constraint in a story; not everything can/needs to be negotiable.
Examp... | User stories are great for capturing functional requirements, but they don't work that well for design constraints and non-functional requirements.<br>
For design constraints and non-functional requirements, a more traditional formulation still works best.
As user stories tend to get more attention, it is a good idea ... | https://softwareengineering.stackexchange.com |
431,556 | [
"https://mathoverflow.net/questions/431556",
"https://mathoverflow.net",
"https://mathoverflow.net/users/121665/"
] | I can prove the following result.
<blockquote>
<strong>Theorem 1.</strong> Let <span class="math-container">$f_n:\mathbb{R}^n\to \mathbb{R}$</span> be a sequence of convex functions
that converges almost everywhere to a function <span class="math-container">$f:\mathbb{R}^n\to\mathbb{R}$</span>.
Then <span class="math-... | It follows from Theorem 10.8 in
R. Tyrrell Rockafellar. Convex analysis. Princeton Mathematical Series, No.
28. Princeton University Press, Princeton, N.J., 1970.
This theorem essentially says the following: if <span class="math-container">$f_n$</span> are convex functions on an open domain <span class="math-container"... | I hope it's OK to post with a proof rather than a reference; when I started writing I thought this would be shorter...
<strong>Lemma.</strong> Let <span class="math-container">$(f_n \mid n \geq 1)$</span> be a sequence of convex functions <span class="math-container">$f_n: \mathbf{R}^d \to \mathbf{R}$</span>, assumed t... | https://mathoverflow.net |
278,358 | [
"https://softwareengineering.stackexchange.com/questions/278358",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/173510/"
] | I am building a website but I am wondering can I call the initial set of pages a framework?
Say I have a project to build a website for a school. Before I start implementing the requirements I have to build a basic structure which includes initial homepage, navbar etc. just basic set-up pages and structure.
The websi... | Framework has come to mean something like angular.js or .NET, so it would perhaps be misleading to use that word. (Only because of current trends in programming culture, though; it's perfectly reasonable usage otherwise.)
You could refer to your initial set of files as a <strong>scaffolding,</strong> or as <strong>moc... | As with any naming question it's hard to say that anything is incorrect, but it would definitely be misleading and/or confusing to use the term "framework" for this. The term "framework" normally refers to something like ASP.NET which provides necessary features like session management, but doesn't impose any particula... | https://softwareengineering.stackexchange.com |
136,668 | [
"https://cs.stackexchange.com/questions/136668",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/-1/"
] | <blockquote>
Given an array <span class="math-container">$A[1..n]$</span>. <span class="math-container">$A$</span> is mixed of two sorted arrays <span class="math-container">$B$</span> and
<span class="math-container">$C$</span> of equal sizes, such that <span class="math-container">$B$</span> is in the ascending order... | Let <span class="math-container">$a$</span> is the first element of <span class="math-container">$A$</span>. Let <span class="math-container">$A$</span> is composed of array <span class="math-container">$B = (b_{1},\dotsc,b_{n})$</span> and array <span class="math-container">$C = (c_{1},\dotsc,c_{n})$</span>.
Now, we w... | Here is the natural intuitive way to sort the array. The idea is to keep track of <em>two</em> inserting positions.
<ol start="0">
<li>(Data structure) A node contains a value, a pointer to its previous node, which can be null, and a pointer to its next node, which can be null.
</li>
<li>Initialize a two-way linked lis... | https://cs.stackexchange.com |
18,187 | [
"https://stats.stackexchange.com/questions/18187",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5837/"
] | I would like to run a 1000 simulations of $X-Y$ where $X$ is the average of 100 random observations with mean of 69.5 and SD 2.9 and $Y$ is the average of 100 random observations with mean of 63.9 and SD 2.7.
I did the following:
<pre><code>x <- rnorm(100, 69.5, 2.9)
y <- rnorm(100, 63.9, 2.7)
</code></pre>
... | Let's go for the one-line solution:
<pre><code>replicate(1000, mean(rnorm(100, 69.5, 2.9)) - mean(rnorm(100, 63.9, 2.7)))
</code></pre>
| To say something about the math of it rather than the programming: it would be useful to think about whether you can actually avoid the repeated simulations altogether in this case by using elementary properties of the Gaussian normal distribution. In this toy example it doesn't matter, but in general it's vastly more ... | https://stats.stackexchange.com |
62,026 | [
"https://electronics.stackexchange.com/questions/62026",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8793/"
] | I've recently found, in some old stuff, a circuit board from an toy, specifically a target for a light gun (if you light up the photoresistor in the middle of the target with the light from the "gun", it generates a sequence of pretty lights).
What baffled me is that the traces look like this:
<img src="https://i.sta... | This is a classic example of the early days of wave soldering w/o solder mask. It looks like a phenolic pierce and blank style board too so a very low cost. Obviously solder was not considered a cost item nor something to be minimized. It did have the additional effect of reducing trace resistance. Do keep in mind ... | This is due to the process used to make the board. No soldermask was used, so the solder stuck to all parts of all copper traces. There is really nothing wrong with that. It all comes down to cost. Apparently for this board, at that time, with the available processes to that manufacturer, at that volume, this was t... | https://electronics.stackexchange.com |
15,953 | [
"https://quant.stackexchange.com/questions/15953",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/2264/"
] | Consider an americal Call option on an underlying paying dividends. Then it is often argued that it is only optimal to exercise right before the dividend is paid out, otherwise one will not exercise.
Now what if the dividend is continuous -can one then always see exercise?
Furthermore, is a reasonable assumption t... | When dividends are continuous, they are essentially negative interest rates, so you should price options w.r.t. new interest rate $\hat r := r-d$ where $r$ is the original interest rate and $d$ is the continuous dividend yield. If $\hat r>0$ then the price of the call is still a submartingale, so early exercise is n... | in the continuous case, you can regard the dividend rate as the interest on a foreign bank account if we invest it so the number of shares grows at the rate $d.$ So we can think it as a call option on a foreign exchange rates. Now calls and puts are the same thing in foreign exchange just by changing viewpoint. So the ... | https://quant.stackexchange.com |
4,271,940 | [
"https://math.stackexchange.com/questions/4271940",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/797790/"
] | I was looking at an old algebra exam, and one of the problems were to determine if there exists a permutation <span class="math-container">$$a\in A_{10}: a\tau a^{-1}=\sigma$$</span>
where <span class="math-container">$\sigma=(1\space7)(5\space6\space9)(\space2\space3\space4\space8\space 10),
\tau=(1\space2)(3\space4\s... | Yes, such an <span class="math-container">$a$</span> must exist. Since <span class="math-container">$\sigma$</span> and <span class="math-container">$\tau$</span> have the same cycle structure, <span class="math-container">$\exists b \in S_{10}~(b \tau b^{-1} = \sigma)$</span>. If <span class="math-container">$b$</sp... | Here is one such even permutation,
<span class="math-container">$$\sigma =(126489537)$$</span>
You line up the cycles structures, and then it is a question of whether to use <span class="math-container">$(12)$</span> or <span class="math-container">$(21)$</span>, the latter gives an odd cycle.
| https://math.stackexchange.com |
34,332 | [
"https://stats.stackexchange.com/questions/34332",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13309/"
] | I have an ecological experiment for which I need to analyze bird count data. Here is the set up:
2 treatments (open/control), 3 regions. Not quite a full 3x2 factorial because in 2 regions there are 3 plots (250m x 250m) for both open & control (6 plots). For “reference” region there are just 3 plots (more similar... | Software: R is certainly a good choice. I use python for this sort of thing; I write my own objective/gradient function(s) and use one of the scipy optimizers, like L-BFGS. But, R is better if you aren't a strong programmer.
Caveat: I'm a machine learning guy, not a statistician, so please consider my answer to be o... | If you choose a negative bionomial, then the package <code>glmmADMB</code> in R is the package for you. It is fantastic! It works just like a <code>lmer</code> model (where you can have fixed, random effects and nested components if you choose, along with the negative bionomial distribution/family.
Best of luck.
Here... | https://stats.stackexchange.com |
396,105 | [
"https://softwareengineering.stackexchange.com/questions/396105",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/343548/"
] | My research team and I are using Git to manage our various scripts and notes/publications for our on-going projects, and I'm wondering about what is considered best practice for the situation we are in.
Until now, the scripts we were using were fairly small and did not require too much computing power. We were usually... | Data and logic do not need to be separated to satisfy SRP. In fact, I do not think you should be doing that, not even for functional programming. Yet, will get to that.
About your code, at method level you are not breaking SRP. However, at class level you are. Let us speak in reasons to change...
You could have to ch... | From OOP and C# perspective the example code doesn't violate SRP. Data and basic operations over it belong together, that's what classes are. The idea to separate data and logic should be applied on higher level in large applications, e.g. business logic should be separate from data persistence.
One can make other rem... | https://softwareengineering.stackexchange.com |
3,062 | [
"https://electronics.stackexchange.com/questions/3062",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/142/"
] | Usually you either combine capacitors in parallel because you want to increase the total capacitance while fitting the components in a certain shape/position, or you just combine capacitors by buying a single capacitor of a larger value.
Combining capacitors in series reduces the total capacitance, and isn't very comm... | I have only seen it done to increase voltage. On some power supply front-ends (AC/DC conversion) with a voltage doubler the capacitors are in parallel at low voltage
and in series at high voltage. This works out well since for a constant power out
the current is double at the lower voltage.
As you mention balancing re... | In an automotive application I've seen two ceramic capacitors in series to increase safety against shorts. In the extreme case a short could start a fire, and I heard that had happened at least once.
| https://electronics.stackexchange.com |
3,712,625 | [
"https://math.stackexchange.com/questions/3712625",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/325808/"
] | Let <span class="math-container">$$H(t) = \begin{cases} 1 & t\gt0 \\ 0 & t\lt 0\end{cases}$$</span> I'm trying to find Fourier transform of <span class="math-container">$H(t).$</span> So we have <span class="math-container">$$\mathcal{F}\{H(t)\} = \int_{-\infty}^{+\infty}H(t)e^{-j\omega t}dt = \int_{0}^{+\inft... | I will denote the Fourier transform of <span class="math-container">$f$</span> by <span class="math-container">$\widehat{f}$</span>, and I recall that by definition
<span class="math-container">$$
\langle P(\tfrac{1}{x}),\varphi\rangle = \lim_{\varepsilon\to 0} \int_{|x|>\varepsilon}\frac{\varphi(x)}{x}\,\mathrm{d} ... | <span class="math-container">$\def\sign{\operatorname{sign}}$</span>
Let's start with the <span class="math-container">$\sign$</span> function:
<span class="math-container">$$
\sign(x) = \begin{cases}
-1, & (x<0) \\
1, & (x>0) \\
\end{cases}
$$</span>
Note that <span class="math-container">$\sign' = 2\del... | https://math.stackexchange.com |
83,028 | [
"https://physics.stackexchange.com/questions/83028",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23783/"
] | I'm getting a bit confused when finding components of vectors and forces.
In problems for vectors, I've always known that if you want to get the components of a vector, you would use the following:
<img src="https://i.stack.imgur.com/UWNQM.png" alt="enter image description here">
<hr>
Recently we've started working... | It depends how you define the angle. In this diagram you define the angle with respect to the horizontal and take the x-axis along the slope. So the x-component of of gravitational force comes out to be $m_2gsin\theta$. If you define the angle $\theta$ with respect to the vertical, then you would see $m_2gcos\theta$ as... | <img src="https://i.stack.imgur.com/KUnct.gif" alt="enter image description here">
The formula for horizontal or vertical will depend on the angle given. In the diagram:
-The horizontal component can be found using the two angles:
Using angle A:
<pre><code> CosA = adjacent/hypotoneuse= b/c
... | https://physics.stackexchange.com |
116,303 | [
"https://softwareengineering.stackexchange.com/questions/116303",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/39433/"
] | I want to compare the performance of two search trees of integers (an AVL tree and a RedBlack tree). How should I design/engineer the tests to accomplish this? For example, let's consider the <em>insert</em> operation; what steps should I follow in order to state that on average this operation is faster in the RB case?... | It highly depends on what you plan to do with the data structure. If you will end up filling it with a certain structured input, then you should also test it that way.
If you don't know anything about your future inputs and want to measure average performance, then remember that complexity theory calculates average pe... | Be careful with terminology. Data structures don't have performance; algorithms do. It's true that some data structures are designed specifically to enable their corresponding algorithms, but it's still a good idea to keep the distinction in mind.
For example, you asked about comparing "optimized" AVL to "straightforw... | https://softwareengineering.stackexchange.com |
334,488 | [
"https://softwareengineering.stackexchange.com/questions/334488",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/189386/"
] | Several teams at my company practice a code review workflow I've never seen before. I am trying to understand the thinking behind it, with the idea that there's value in making the whole company consistent. (I contribute to multiple codebases and have been tripped up by the differences in the past.)
<ol>
<li>Code auth... | In the first case, it's usually a courtesy. In most organizations, merges kick off a series of automated tests which must be dealt with promptly if they fail. Especially if there was a significant delay between when a pull request was submitted and when it was reviewed, it's polite to allow it to be merged on the aut... | Having the initial author merge their own pull request is my preferred workflow in small teams. In addition to technical advantages already mentioned (in terms of resolving merge conflicts, for example), I think it adds value on a cultural level: It builds a sense of ownership.
I specified <em>initial</em> author for ... | https://softwareengineering.stackexchange.com |
368,063 | [
"https://softwareengineering.stackexchange.com/questions/368063",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/172464/"
] | Today my college presented to me an argument about not use some primitives that I never heard before. I would like to see what you guys think about it.
We have a class in our project like:
<pre><code>class Order {
private long id;
private String name;
// more fields
}
</code></pre>
We have a builder for... | If you need a representation for "not set", then <code>Long</code> is a good choice, with <code>null</code> standing for "not set". If that isn't needed, don't waste time and space with the unnecessary boxing and unboxing between <code>long</code> and <code>Long</code>.
However you decide to represent "not set", clien... | There's nothing wrong with saying that all valid IDs / handles are positive. That has the advantage that a default-initialized ID / handle will indicate "not set" / "not existant" without any overhead. And it will be quite natural to support it in APIs, exchange- and output-formats without writing any extra-code for ha... | https://softwareengineering.stackexchange.com |
1,034,346 | [
"https://math.stackexchange.com/questions/1034346",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/180341/"
] | Let $A={\rm span}\{\cos^2x,\sin^2x\}$ be a subspace of the set of functions $C[0,\pi]$, for each of the following functions in $C[0,\pi]$, determine whether or not it is in $A$.
<ol>
<li>$f(x)=1$</li>
<li>$g(x)=3+\cos 2x$</li>
<li>$h(x)=x^2$</li>
</ol>
I'm just confused regarding the path to take, Am I supposed to wr... | You can check if $\{f(x), \cos^2x,\sin^2x\}$ is linearly dependent or not, same for $g$ and $h$. The first one is almost trivial. For the second one, remember that $\cos(2x) = \cos^2x - \sin^2x$. For the third one, you can use the Wronksian test: if $$W[f_1,f_2,f_3](x)=\begin{vmatrix} f_1(x) & f_2(x) & f_3(x) \... | Yes, you are either supposed to write each $f(x)$ as a linear combination of $\cos^2x$ and $\sin^2x,$ or show that it cannot be done. (Actually, based on the phrasing, you may only be required to <em>decide</em> whether or not it can be done, but being able to justify your claims never hurts.)
| https://math.stackexchange.com |
1,243,890 | [
"https://math.stackexchange.com/questions/1243890",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/44669/"
] | Martin Braun - Differential equations and their applications Chapter 2.1 p.137
<blockquote>
Let <span class="math-container">$y_1,y_2$</span> be solutions of Bessel's equation <span class="math-container">$$t^2y'' + ty' + (t^2-n^2)y=0$$</span> on the interval <span class="math-container">$(0,\infty)$</span> with <sp... | The Wronskian $W$ of an equation of the form
$$ y'' + py'+qy=0 $$
satisfies
$$ W'= -pW. $$
In your case, you have
$$ p(t)=\frac{1}{t}, $$
so you have
$$ W(t) = W(1) \exp{\left( -\int_1^t ds/s \right)} = W(1) e^{-\log{t}} = \frac{W(1)}{t}, $$
and $W(1)=1$, as you note, so $W(t)=1/t$.
| <strong>Hint:</strong> Start with the equation of evolution of the Wronskian of an ode written in the form $y^{\prime\prime}(t)=p(t)y'(t)+q(t)y(t)$
$$W'(t)=p(t)W(t)=-\frac{1}{t}W(t)$$
That can be obtained by just deriving
$$W(t)=\begin{vmatrix} y_1(t) & y_2(t)\\
y'_1(t) & y'_2(t)
\end{vmatrix}$$
and keep in... | https://math.stackexchange.com |
118,227 | [
"https://electronics.stackexchange.com/questions/118227",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/46074/"
] | I've been working my darnedest over the past few weeks learning more and more about amplifiers, BJTs and various topologies. As I go through Art of Electronics, I try out everything mentioned in at the very least (P)Spice.
I've run into a conundrum. When I make a class-B output stage, as the following:
<img src="https... | There are two problems:
1) The first stage can only work properly at base voltages below zero. When the collector-base junction is reverse-biased, i.e. in normal operation mode, the the total voltage drop on R67 and R62 equals that on R56 (there is a small difference, which we can ignore here). This value can't be mo... | If you want a VAS stage, you need to make one. As it stands, the collector of Q20 is not a voltage output, it's a current sink. Try adding a 1k resistor from +12 to the collector of Q2.
You also now have a DC offset, but that's what biasing is for.
| https://electronics.stackexchange.com |
646,089 | [
"https://physics.stackexchange.com/questions/646089",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41836/"
] | I was told that the radiation intensity from a particular X-ray machine falls in half every 4 feet. I think this should tell us something about the angle of the beam from the machine. I use trigonometry to restate the assertion as follows:
Radiation is emitted at some angle <em>θ</em> producing a cone whose diameter ... | <blockquote>
the radiation intensity from a particular X-ray machine falls in half every <span class="math-container">$4$</span> feet
</blockquote>
This is the important part. After <span class="math-container">$4$</span> feet you have half the original intensity. After <span class="math-container">$4$</span> more feet... | The inverse square law works from a radius point. If you consider 4 foot to be the initial radius then two times the radius would not be Half the radiation, it would be 1/4 the radiation. Three times the radius would be 1/9 the radiation and four times the radius would be 1/16.
| https://physics.stackexchange.com |
24,150 | [
"https://stats.stackexchange.com/questions/24150",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | If you use 10-fold cross validation to derive the error in, say, a C4.5 algorithm, then you are essentially building 10 separate trees on 90% of the data to test on 10% - 10 times. Which one of the 10 trees is representative? Won't they all be different?
For example - how does WEKA give me a C4.5 tree and a cross-vali... | Typically, you use the 10 cross-validated trees to estimate "out-of-sample" error, and then fit an 11th and final tree on the full dataset.
In theory, the error of the 11th tree on out-of-sample data should be similar to the out-of-sample error you estimated from the 10 cross-validated trees.
| Yes, they will all be different, unless something surprising happens. The cross-validation is used to derive the error given the combination of algorithm choice and parameterization of that algorithm as applied to your problem; in this case, C4.5 as an algorithm and whatever parameterization you used for it. Its obje... | https://stats.stackexchange.com |
8,458 | [
"https://ai.stackexchange.com/questions/8458",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/19049/"
] | This is a question about pattern recognition and feature extraction.
I am familiar with Hough transforms, the Fast Radial Transform and variants (e.g., GFRS), but these highlight circles, spheres, etc.
I need an image filter that will highlight the centroid of a series of spokes radiating from it, such as the center ... | The Hough Transform extended to orthogonal ellipses uses this model, accumulating on <span class="math-container">$\theta$</span> for all <span class="math-container">$\{x, y\}$</span> with parameter matrix
<span class="math-container">\begin{Bmatrix}
c_x & c_y \\
r_x & r_y
\end{Bmatrix}</span>
where
<span... | First step would be getting the object out of the scene. This bit is not trivial in your case, however, there are many methods to choose from. I suggest reading about watershed threshold algorithm.
Second part is easier. Once you have a single segmented object at hand, perform noise removal. Next step is to extract th... | https://ai.stackexchange.com |
112,501 | [
"https://electronics.stackexchange.com/questions/112501",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9308/"
] | I've purchased bulk cheap DC motors for a robot problem. But I don't know their ratings.
Is there a way for me to find out?
For instance, I would like to know their max DC voltage input using basic tool like a multimeter.
| Motors are rated by manufacturers based on the class of insulation they have. Different insulation classes have different allowable maximum temperatures (or, alternatively, temperature rises over 40 C ambient temperature). A standard method of measuring temperature rise in an DC motor armature is to measure resistanc... | A multimeter won't tell you this and realistically nothing will other than either the maker's details (not available) or trial and error. Trial and error means testing each one and finding out how much torque and speed it can generate and how hot it might get. You need to make an estimate of how hot you dare run the mo... | https://electronics.stackexchange.com |
77,229 | [
"https://mathoverflow.net/questions/77229",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5572/"
] | Let $V$ be a real affine variety in $\mathbb R^n$, i.e. the zero set of a real polynomial $p(x_1,\dots,x_n)$. Consider the following three definitions of the dimension of $V$, $dim(V)$.
<blockquote>
<em><strong>Definition 1</em></strong>: if $I$ is the ideal of
polynomials vanishing on $V$, then
$dim(V)$ is the ... | They are all equivalent, including definition 1, to the Krull dimension of $S/I$, where $S=\mathbb{R}[x_1,\ldots,x_n]$ is the polynomial ring $I$ lives in. This is very good news for people like me who want to apply algebraic geometry to statistics, where numbers are mostly real.
Here's how it goes:
Definition 1 is... | At least for definitions 2 and 3 : ${\rm dim}_2 (V) \leq {\rm dim}_3 (V)$ since a semialgebraic map is peicewise a homeomorphism.
| https://mathoverflow.net |
5,526 | [
"https://dba.stackexchange.com/questions/5526",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/746/"
] | I'm using Microsoft SQL Server 2008.My question is:How to drop multiple tables with common prefix in one query?
something like that table names:
<pre><code>LG_001_01_STLINE,
LG_001_02_STFICHE
</code></pre>
| You can build up a string using the catalog views, e.g.:
<pre><code>DECLARE @sql NVARCHAR(MAX) = N'';
SELECT @sql += '
DROP TABLE '
+ QUOTENAME(s.name)
+ '.' + QUOTENAME(t.name) + ';'
FROM sys.tables AS t
INNER JOIN sys.schemas AS s
ON t.[schema_id] = s.[schema_id]
WHERE t.name LIKE 'LG_001%... | I ran this query then pasted the results back into query window to drop all the tables:
<pre><code>SELECT 'DROP TABLE ' + NAME from sys.tables
ORDER BY NAME
</code></pre>
If you want to delete all tables but keep those with names that started with A, B, C or D:
<pre><code>SELECT 'DROP TABLE ' + NAME from sys.tables
... | https://dba.stackexchange.com |
599,204 | [
"https://electronics.stackexchange.com/questions/599204",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/257152/"
] | I want to implement a circuit that generates a random 4 bit using a synchronous counter.
Is it satisfactory to achieve a "somehow" random generator by using a parallel 4-bit counter with the help of the clock speed?
For example, a button is pressed within 5 seconds to display a random number. Within 5 seconds... | You can indeed use a free-running counter for this purpose.
The randomness is generated by the length of time the user pushes the button, so if the clock rate is significantly faster than the users response time (let's say 10kHz+), then you should get a decent "random" number, with little ability for the user... | There are some ambiguities in your question, but the principle you suggest is sound. Taking the criterion used in athletics, human reaction time is more than 100ms thus a counter running at 100Hz and sampled by human action produces an unpredictable result. Translating this into design criteria, if you run your counter... | https://electronics.stackexchange.com |
111,232 | [
"https://cs.stackexchange.com/questions/111232",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/106317/"
] | How can i show that the following long language is not context free using the pumping lemma?
<span class="math-container">$L=\left\{abc^{i_1}bc^{i_2}...bc^{i_{2m}}def^{j_1}ef^{j_2}..ef^{j_{2n}}ghq^{k_1}hq^{k_2}...hq^{k_o}\right\}$</span>
Such that:
<span class="math-container">$m,n,o \geq 1;$</span>
<span class="m... | Start with a long enough string <span class="math-container">$w$</span> in <span class="math-container">$L$</span> in which <span class="math-container">$m=p+2,n=p+1,o=p$</span> and
<ul>
<li><span class="math-container">$i_1,...,i_{2m}=0$</span></li>
<li><span class="math-container">$j_1,...,j_{2n}=0$</span></li>
<li>... | Let us check the first part, <span class="math-container">$L=\left\{abc^{i_1}bc^{i_2}...bc^{i_{2m}}def^{j_1}ef^{j_2}..ef^{j_{2n}}ghq^{k_1}hq^{k_2}...hq^{k_o}\right\}$</span> where <span class="math-container">$m>n>o>0$</span>, <span class="math-container">$i_1,i_2,...,i_{2m} \geq 0$</span>, <span class="math-c... | https://cs.stackexchange.com |
242,447 | [
"https://stats.stackexchange.com/questions/242447",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/64954/"
] | The R function <code>mvrnorm</code> from the <code>MASS</code> package generates random numbers from a multivariate normal distribution. It expects a covariance matrix as an input, but I want to give it a correlation matrix. Is this statistically valid?
My understanding is that correlation is just a standardized form... | A correlation matrix is a covariance matrix (of standardized variables) so you <em>can</em> do it (a correlation matrix is a valid covariance matrix* after all) -- the question is whether you end up with what you need.
You'll get multivariate normals with unit variance, with the population correlation matrix you suppl... | No you cannot do this, those two things are not the same thing. There is no way, in general, you can go from correlation to covariance without knowing the individual variances. As pointed out in the comment below, the correlation will equal the covariance if all the variances are indeed $=1$.
The formula for the cor... | https://stats.stackexchange.com |
730,442 | [
"https://physics.stackexchange.com/questions/730442",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/307917/"
] | The concept is that time is another dimension, complementary to those we can observe and measure directly. For those three, I can take a ruler and measure how many millimeters one point in space is far from another. If time is another dimension, and if I had the ability to observe that dimension as I observe the othe... | Putting aside the fact that time and space <strong>are</strong> different, and that while they are unified as part of a single Lorentzian manifold there <strong>are</strong> important differences between "timelike" directions and "spacelike" directions, the conversion factor you're looking for is th... | Special relativity is derived from the observation that the speed of light <span class="math-container">$c$</span> is the same in all inertial frames and doesn't depend on the direction. This means that in a time interval <span class="math-container">$\mathrm{d}t$</span> light will always travel a distance <span class... | https://physics.stackexchange.com |
22,312 | [
"https://chemistry.stackexchange.com/questions/22312",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5084/"
] | What's the mechanism of cross-linkage for a typical household 2-party epoxy mix? I was working with some epoxy the other day and I was instructed to mix equal parts of epoxy and epoxy hardener. Stoichiometry at its finest.
The hardener contained "polymercaptans amines" according to the label. Google told me that a me... | Here is the Walsh diagram depicting all the valence molecular orbitals (a diagram showing how individual molecular orbitals change in energy due to bending around the central atom). Oxygen has 6 valence electrons, so ozone has 18 electrons in total. If we start on the right where ozone would be linear, we can see that ... | Your guess about electronic repulsion is right: the repulsion between the lone pairs of electrons on the Oxygen atoms leads to intense repulsion at such close ranges leading to instability. In comparison to this resonance is a far far more stable configuration.
Strain at the joints in the cyclic structure does its pa... | https://chemistry.stackexchange.com |
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