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 |
|---|---|---|---|---|---|
429,003 | [
"https://electronics.stackexchange.com/questions/429003",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/216569/"
] | I'm designing the CAN interface for a STM32F042C4T6 to be able to receive and send messages. I've tested my code and everything seems to work perfectly fine in loopback mode. However, when I hook up two STM32's together (with CAN transceivers on both ends as middle men) with one of them transmitting and the other recei... | I actually fixed the issue, thank you to Michel for trying to help me, the reason it wasn't working was because I didn't have the correct filter enabled because it seems the data sheet only that there are 14 filters to be enabled (incorrectly) but the header file specifies 28 correctly.
| I had the same problem as you, however, it seems you are not using HAL/CubeMX or do you? If so, make sure you have the latest version of the HAL library for the STM32F103C8T6 library, because a bug has been fixed that indeed it only worked in loopback mode. Update the HAL F1 library to 1.7 (or higher), where the CAN im... | https://electronics.stackexchange.com |
139,305 | [
"https://softwareengineering.stackexchange.com/questions/139305",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/33609/"
] | I'm currently working on an indie project, so I don't exactly have the luxury of throughout human testing or external code review — however, I don't see any difficult bugs in my current code (I fix them as I see them, and most of the time they're just wrong field names and such, things that you fix in a minute or two),... | LOC is probably one of the most abused metrics, and as a result is probably one of the more useless measures of code quality, and an even more useless measurement of programming effort.
Yes, that's a bold statement for me to make, and no, I can't point you to studies proving my point. However, I can state with hard ... | Not at all - some days you are fixing a hard to find bug and only change one line. Other days you're adding new code and write several thousand lines.
Daily LOC doesn't tell you anything except that the tasks for that day could be accomplished with 400 lines of code.
| https://softwareengineering.stackexchange.com |
518,218 | [
"https://electronics.stackexchange.com/questions/518218",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/261577/"
] | So digital circuits work by using two states either on or off , and i was wondering how two consecutive bits of zero(or one) be identified? is there like a timing circuit or anything like that?
| Perhaps the simplest to understand is a serial connection like RS232. It works as follows:
<ul>
<li>A bit rate is agreed. Typically this will be 9600 bits per second but can vary from 300 to 115000 or so.</li>
<li>A character length is agreed. Typically this is 7 or 8 bits.</li>
<li>The line default is agreed. This is ... | A basic AND or OR digital gate will respond to changes at its inputs as fast as its internal circuitry permits. If you want it to respond only at certain times, then, as you surmised, timing circuits are required. A simple example is a D flip-flop which has one data input and one clock input. The output can only change... | https://electronics.stackexchange.com |
183,344 | [
"https://physics.stackexchange.com/questions/183344",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24784/"
] | Suppose we have a mass <span class="math-container">$m$</span>. We can talk about two of its parameters: The net force applied on it <span class="math-container">$f(t)$</span> and its net acceleration <span class="math-container">$a(t)$</span>.<br>
I want to know whether there is any delay between <span class="math-co... | In the real world, you push the atoms in the back end of the object, which push the atoms in the next layer, etc. This means that the front end of the object won't start accelerating until $t = t_0 + \Delta x/c_s$, where $\Delta x$ is the length of the object and $c_s$ is the speed of sound in the material of the objec... | <blockquote>
Suppose before time t=t0 the net force was zero but at time t=t0 the force is non-zero. At what instant is the acceleration gonna be non-zero ? Is it gonna be at t=t0 too ?
</blockquote>
Remember that, if we're talking instantaneous measurements, your target can have a non-zero acceleration and still ha... | https://physics.stackexchange.com |
197,509 | [
"https://softwareengineering.stackexchange.com/questions/197509",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/67655/"
] | I have a class, called PolicyProvider, at present with the following (abridged) interface:
<pre><code>public interface IPolicyProvider
{
List<Policy> GetRenewalPolicies(Client client, int financialYear);
}
</code></pre>
The purpose is quite obvious - every year, the insurance renews for the client, and they... | Following <code>nulliusinverba</code>'s suggestion, I'm creating an answer out of my original comment.
I see it as a scenario for a factory pattern, with your core <code>PolicyFactory</code> (or provider) creating policies for any given client.
You could then in turn have a <code>PolicyFactoryFactory</code> class, a... | A standard approach to avoiding "if"s is to use subtyping and dynamic binding. All you need to do is to create subtype policies for each financial year.
| https://softwareengineering.stackexchange.com |
536,174 | [
"https://electronics.stackexchange.com/questions/536174",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/270552/"
] | Basic question about L293D, which I could not find a clear answer by searching the internet.
Still learning with my arduino project. The examples are good at describing how to use things and how to wire them all up. What is missing is why we use some of the components.
I see these are the benefits of using L239D:
<pre>... | <blockquote>
Is there any good reason to use L293D if I don't need to reverse the motor but only control motor speed?
</blockquote>
No, there is not. An N-FET low side switch and a catch diode is a much better solution.
Really there's no good reason to use an L293 even if you <em>do</em> need to control the motor dire... | Basically, H-bridge drivers like L293d make it easy for beginners to drive motors without going into in-depth knowledge and numerical calculations as such. The L293d is a 2 motor driver, used widely in hobby projects even if the direction is not a concern. The PWM pin of Arduino UNO(or similar microcontroller ) is not ... | https://electronics.stackexchange.com |
496,494 | [
"https://stats.stackexchange.com/questions/496494",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/302766/"
] | I have been studying markov chains for my Introductory Stochastic Processes exam, but i am struggling with the following problem:
<strong>Question</strong>: Consider a matrix with state space <span class="math-container">$S=\{1,2,3\}$</span> and the following one step transition matrix:
<span class="math-container">$$P... | I think it's normal to see changes wrt parity because if in any of the previous states you hit <span class="math-container">$3$</span>, you'll stay there, and otherwise, you'll end up alternating between 1 and 2. So, for example, for <span class="math-container">$n=1$</span>, it's impossible to be in state <span class=... | Gunes gives the answer by reasoning (which is probably what you should do for this exam).
A more general and straightforward method (but which requires more computation time) is the following:
You decompose the begin state as a sum of eigenvectors. Then you describe the evolution in terms of the evolution of those eige... | https://stats.stackexchange.com |
107,425 | [
"https://math.stackexchange.com/questions/107425",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11801/"
] | Problem 1:
If $n$ people are seated in a random manner in a row containing $2n$ seats, what is the probability that no two people will occupy adjacent seats?
I know that the probability that $n$ people are seated in $2n$ rows is ${2n\choose n}$
I also know that the answer to this problem is $n+1\over {2n\choose n}$
... | ad 1: $2n\choose n$ is the number of ways to seat $n$ people without regarding their identities. Now, how many of these will have no two people adjacent? You could occupy all odd seats, leaving the even ones free. Note that this will also leave seat $2n$ free, although this is not necessary in order to "keep the distan... | For problem 2, why not consider the smaller problem where there are only two states? Small enough that you can write down all the possibilities and see what the answer is, and then compare to the formulas you are asking about.
| https://math.stackexchange.com |
18,706 | [
"https://scicomp.stackexchange.com/questions/18706",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/14353/"
] | I'm looking for a way to compute the coordinates of the intersection of two lines.
Each lines are defined with a point and a normal vector.
<img src="https://i.stack.imgur.com/9FDHl.png" alt="Graphic representation">
We can assume than the normal vectors are not zero and that the lines are not parallel (this has bee... | I might as well add this since you haven't gotten an answer that deals with the format you have for the lines (i.e. point and normal vector). In your case, you can write the equation of each line as
$$
(\vec{x}_0-\vec{x})\cdot\vec{n}=0
$$
where $\vec{x}_0$ is a point on the line. This gives
$$
(A_x-x)u_x+(A_y-y)u_y=0
$... | To elaborate a bit, start with the ray/parametric form of the first line (0):
$\vec r_0(t) = \vec p_0 + t \cdot \vec q_0$
.. where $\vec p_0$ is some origin point known to be on the line (like your point $\vec A$), and $\vec q_0$ is the known unit vector along the line (the tangent, orthogonal to your normal $\vec u$... | https://scicomp.stackexchange.com |
377,926 | [
"https://physics.stackexchange.com/questions/377926",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/173002/"
] | I'm working through a chapter about forces and I was wondering about the definition of gravitational force of which things of mass are brought together. When thinking about the solar-system this "feels" some kind of intuitive to imagine the gravitational idea. But it makes me curious if this would also work in a smalle... | I presume that you want to build a tiny <strong>working scale model</strong>, keeping all distances in the same proportions, and keeping the rotation periods the same.
The same equations would apply for the model as for the real Solar System. The force of gravitational attraction provides the centripetal force keeping... | Some things would change, others would not. To answer this, you need to think about how things change with size. Do they change as $r^3$, $r^2$, $r$, ...?
Suppose you made a model where everything was $1/10^\mathrm{th}$ as big. The Sun and Earth were $1/10^\mathrm{th}$ their diameters, and $1/10^\mathrm{th}$ as far ap... | https://physics.stackexchange.com |
665,180 | [
"https://physics.stackexchange.com/questions/665180",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/181053/"
] | I studied the Higgs mechanism a couple of times now and one question that always comes to my mind is the imaginary part of the mass in the Higgs potential.
The Higgs potential can be written as <span class="math-container">$$V = -\mu^2 \lvert\phi\rvert^2 + \lambda \lvert \phi \rvert^4$$</span> where the <span class="ma... | The equation states that the transverse applied force at one point in the string is equal to the transverse force at that point expressed in terms of the string tension. It is not stating that there is no net force on a <em>portion</em> of string. If it did say the latter, then it really would contradict the string bei... | I think your mistake is that you consider that the force exerted by the string on the outside is a force acting on the string.
At the left end, the only force acting on the string is the external force <span class="math-container">$F$</span>. And by Newton's third law, this force <span class="math-container">$F$</span>... | https://physics.stackexchange.com |
401,741 | [
"https://physics.stackexchange.com/questions/401741",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/69147/"
] | The action for an EM field that interacts with a set of point particles is
$$
S_{mf} = -\sum_i \frac{e_i}{c} \intop A_k dx^k \tag{27.3}
$$
(ref - Landau & Lifshitz, eq. 27.3.)
In the book mentioned it is said that
<blockquote>
"In each term of this sum. $A_k$ is the potential of the field at that point of ... | Here you may be confused by the short-hand being used. In English, "$A_k$ is the potential of the field at that point of spacetime at which the corresponding particle is located". In mathematics,
$$A_k\equiv A_k(x_i(\tau)),~~~~~~~~~~k=0,1,2,3.\tag{1}$$
where $x_i(\tau)$ is the spacetime trajectory of the $i^\text{th}$... | FWIW, The $i$th summand in the interaction term (27.3) is a 1-dimensional contour integral over the $i$th particle worldline. It is e.g. not a 4-dimensional integral over the entire spacetime.
| https://physics.stackexchange.com |
158,147 | [
"https://electronics.stackexchange.com/questions/158147",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/69155/"
] | I am making a coil gun. I have just ordered some 330uF 200v 105c Radial Electrolytic Capacitor.
I will be using the charging circuit from a disposable camera. I know that two of the same caps in series have double the voltage rating but half the capacitance. I haven't received my caps or camera, but my question is if... | Yes, you can do that.
To be on the safe side of things I suggest an addition:
Put two 50KOhm to 100kOhm resistors in parallel to the capacitors. These resistors make sure that:
<ul>
<li>The voltage level at the junction between the capacitors is close to 1/2 of the total voltage. </li>
</ul>
With ideal capacitors... | Yes, if you make two series strings of two 200v 330uF capacitors and connect them in parallel then you will have a capacitor bank rated for 400v and a capacitance of 330uF. However, you're not going to get much energy from that. Let's assume you charge up the capacitors with the maximum 400v. Your energy will only be <... | https://electronics.stackexchange.com |
1,739,433 | [
"https://math.stackexchange.com/questions/1739433",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/255098/"
] | Prove that $\frac{2\sec\theta +3\tan\theta+5\sin\theta-7\cos\theta+5}{2\tan\theta +3\sec\theta+5\cos\theta+7\sin\theta+8}=\frac{1-\cos\theta}{\sin\theta}$<br><br>
<hr>
$$\frac{2\sec\theta +3\tan\theta+5\sin\theta-7\cos\theta+5}{2\tan\theta +3\sec\theta+5\cos\theta+7\sin\theta+8}=\frac{\frac{2}{\cos\theta} +\frac{3\si... | Let $\cos\theta=c,\sin\theta=s$. Then,
$$\begin{align}&s(2+3s+5sc-7c^2+5c)-(1-c)(2s+3+5c^2+7cs+8c)\\&=5c^3+5cs^2-5c+3c^2+3s^2-3\\&=5c(c^2+s^2-1)+3(c^2+s^2-1)\\&=0\end{align}$$
from which the claim follows.
| Let's simplify our notation by writing $c=\cos\theta$ and $s=\sin\theta$. First note that $$\frac{1-\cos\theta}{\sin\theta}=\frac{\sin\theta}{1+\cos\theta}.$$ So, for arbitrary $a$ and $b$, not both zero, we can write either fraction as $$\frac{a(1-c)+bs}{as+b(1+c)}.$$It's not hard to spot that setting $a=5c$ and $b=3+... | https://math.stackexchange.com |
537,734 | [
"https://math.stackexchange.com/questions/537734",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/98069/"
] | I'm studying probability and having trouble in understanding the following calculation
<img src="https://i.stack.imgur.com/4KRxB.png" alt="enter image description here">
How to get from left to the right on the first line, with the condition that m could only be even numbers? Any hint would be appreciated, thanks~~
| We write the same thing, with different symbols. We have
$$(x+y)^k =\binom{n}{0}x^0y^k+\binom{k}{1}xy^{k-1}+\binom{k}{2}x^2y^{k-2}+\binom{k}{3}x^3y^{n-3}+\cdots.$$
Also,
$$(x-y)^k =\binom{n}{0}x^0y^k-\binom{k}{1}xy^{k-1}+\binom{k}{2}x^2y^{k-2}-\binom{k}{3}x^3y^{k-3}+\cdots.$$
Add, and observe the cancellation. We get
... | Go from right to left, instead. Note that
\begin{align*}
\left[\left(1 - \frac{1}{n}\right) - \frac{1}{n}\right]^k &= \sum_m {k \choose m} \left(1 - \frac{1}{n}\right)^{k - m} \left(-\frac{1}{n}\right)^{m} \\
&= \sum_m {k \choose m} \left(1 - \frac{1}{n}\right)^{k - m} (-1)^m \left(\frac{1}{n}\right)^m
\end{al... | https://math.stackexchange.com |
230,018 | [
"https://electronics.stackexchange.com/questions/230018",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/107793/"
] | Sorry if this is the wrong place, but hopefully someone here can help me
OK so the way I have been taught is that turning off the lights doesn't really actually save electricity due to the fact that all electricity is is electric fields pushing electrons. So when you shut off a light and stop the electron flow, the el... | Think of electricity as a handy on-demand way of moving work done in the generating plant into your home's lights and appliances.
If you turn off the switch, you break the circuit, and your lights no longer request this work of the generators. That means they consume a little less fuel, and in the aggregate if a lot ... | What turning the light off means is that you don't consume power in your home (so you don't get billed for it), so the power never gets generated at the power station, and fuel never gets burnt there to make it (which the power company then don't get billed for).
That's what 'saves' means in this context. Most people ... | https://electronics.stackexchange.com |
2,915,160 | [
"https://math.stackexchange.com/questions/2915160",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/429985/"
] | So given the curve $\frac{ax-b}{x^2-1}$ has a turning point at (3,1), find values a and b
Just wondering if there are any elegant ways to solve this problem??
| The fact that the function has a 'turning point' at $(3,1)$ implies that the derivative of your function at $x=3$ is $0$. That is,
<blockquote>
$\dfrac{d}{dx}\bigg(\dfrac{ax-b}{x^2-1}\bigg)_{x=3}=0$, here you will need to use the quotient rule of differentiation.
</blockquote>
Find the derivative, plug in $3$ for $... | You have two unknown, namely $a$ and $b$ in $$ \frac{ax-b}{x^2-1}$$ and you also have two conditions which help you find the unknowns.
First of all $(3,1)$ is on your graph, and secondly your derivative at $x=3$ must be zero.
Two equations and two unknowns.
Can you take over from here?
I found $a=6$ and $b=10$
| https://math.stackexchange.com |
376,042 | [
"https://electronics.stackexchange.com/questions/376042",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/185032/"
] | Is it possible to use the stored energy while the capacitor is being charged? In other words, use a capacitor almost as a <em>conductor</em>?
My gut says the answer is probably no (and my own experiments so far seems to be justifying my hunch) but if so, I'm very curious on what's actually happening inside the capaci... | No, the charge on a capacitor is increasing (charging), decreasing (discharging) or remaining the same. There are no other possible states (assuming an ideal capacitor with no leakage).
When the capacitor is charging or discharging, there is a potential difference between the two terminals and apparent current flow.
... | No a passive part is either an insulator (dielectric) or a conductor with very weak character flaws of the other. We may ignore inductance and active parts.
When doing what you think it may be alternating pulse charging and then slow discharge in order to reduce voltage fluctuations or if near DC only getting the ... | https://electronics.stackexchange.com |
166,297 | [
"https://mathoverflow.net/questions/166297",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36862/"
] | Weil's bound for Kloosterman sums states that for $(a,b)\not=(0,0)$,
$$
|K(a,b;q)|:=\left|\sum_{x\in\mathbb{F}_q^*}\chi(ax+bx^{-1})\right|\leq 2\sqrt{q},
$$
where $\chi$ is a non-trivial additive character on $\mathbb{F}_q$ (the field with $q$ elements).
My question is, is it known to be false that $\sqrt{q}$ can be r... | Going a bit beyond $61$, I find that the first counterexample to $|K(a,b;q)| < 2 \sqrt{q-1}$ with prime $q$ has $(q,ab) = (139,38)$, when $K(a,b;q) = -23.51308393\ldots = -2 \sqrt{138.216\ldots}\,$, and there are no further prime counterexamples up to $10^3$.
[<em>added later</em>] Extending the search overnight re... | This is a supplement to Noam Elkies' answer. I claim that the Weil bound is never attained for $q=p$ prime. Assume that the bound is attained, then $K(a,b,p)=\pm 2\sqrt{p}$, so $\sqrt{p}$ lies in the cyclotomic field $\mathbb{Q}(\zeta_p)$. Then $\mathbb{Q}(\sqrt{p})$ is a subfield of $\mathbb{Q}(\zeta_p)$, so $2$ is un... | https://mathoverflow.net |
6,279 | [
"https://cs.stackexchange.com/questions/6279",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/3146/"
] | <blockquote>
If $L$ is a regular language, prove that the language
$L_1 = \{ uv \mid u \in L, |v| =2 \}$
is also regular.
</blockquote>
My idea: $L$ can be represented as a DFA and then you could add 2 consecutive transitions from every final state for the letters of $v$, creating a new NFA diagram. Is that corr... | Your idea is correct.
You should take the following path to formally write it up/prove it. First assume that $L$ is accepted by some DEA $M=(Q,\Sigma,\delta,q_0,F)$ then define a new NEA $M'=(Q',\Sigma,\delta',q'_0,F')$ based on $M$. Just express you ideas formally, for example start with
<ul>
<li>$Q'=Q\cup\{q_\text... | If <span class="math-container">$A$</span> is the alphabet, <span class="math-container">$L_1 = LAA$</span>. Now <span class="math-container">$A$</span> is finite and thus regular. Thus if <span class="math-container">$L$</span> is regular, then <span class="math-container">$L_1$</span> is the product of three regular ... | https://cs.stackexchange.com |
27,643 | [
"https://physics.stackexchange.com/questions/27643",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/184/"
] | For a countable sequence of positive numbers $S=\{\lambda_i\}_{i\in N}$ is there a construction producing a Hamiltonian with spectrum $S$ (or at least having the same eigenvalues for $i\leq s$ for some $s$)?
Here by 'Hamiltonian' I understand a polynomial of $p_i$ and $q_i$ (or equivalently - $a_i$ and $a_i^\dagger$) ... | It seems there is a simply way to do this for polynomials with finite degree $d$. Since $a^\dagger a$ is the number operator, we can take $a^\dagger a = N$, where $N$ is the number of excitations corresponding to a particular level. Then if the Hamiltonian has the general form $H = \sum_{k=0}^d c_k (a^\dagger a)^k$, th... | It was already mentioned in a comment above about a topic in physics.SE, that it may be related with inverse scattering problem. I only may add, that there is precise method of construction of Shroedinger operator $p^2 + V(q)$ with arbitrary finite spectrum for one-dimensional case. It is very well developed due to app... | https://physics.stackexchange.com |
327,125 | [
"https://physics.stackexchange.com/questions/327125",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/147769/"
] | I came across the following question in a graduate exam it looks trivial nevertheless it is conceptual and I do not know how to connect the concept of potential and frequency to get one of the answers given.
A simple harmonic oscillator has a potential energy $V=\frac{1}{2} kx^2$. An additional potential term $V = ax$ ... | Since another has given an explicit answer, I will simply add the following.
Recall that the force is
$$F = -\frac{dV}{dx} = -(kx + a)$$
Thus there is a <em>constant</em> force of $-a$ in addition to the restoring force $-kx$.
Think of, for example, the case of a mass suspended by a spring from the ceiling. Gravi... | Write the new potential
$$
V'=\frac{1}{2}k(x-x_0)^2+C
$$
where $C$ is a constant.
Expanding $V'$:
$$
V'=\textstyle\frac{1}{2}kx^2-kx_0x+\frac{1}{2}kx_0^2+C
$$
and choose $x_0=-a/k$ such that $-kx_0=a$. This yields
$$
\textstyle\frac{1}{2}kx^2+ax+\frac{1}{2}kx_0^2+C
$$
and you can now find $C$ to remove the $\frac{1}{... | https://physics.stackexchange.com |
234,518 | [
"https://mathoverflow.net/questions/234518",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50438/"
] | Any help with this problem would be appreciated. Thanks
Suppose $(M^3,g)$ is a smooth compact Riemannian manifold with smooth boundary and $\gamma$ is a simple smooth orientable curve in $M$. Does there exist a <strong>global</strong> smooth function $f:M \to \mathbb{R}$ such that $df(X)|_{\gamma} \neq 0$ along $\gamm... | <strong>Edit.</strong> Surely $f$ has at least two critical points if $M$ is closed, so we cannot have $|df|_g\ne 0$ everywhere in that case. This arguments fails if we assume that each component of $M$ has a nonempty boundary. To the contrary, now one can assume that $f$ is generic (after a $C^1$-small perturbation, w... | $f$ will decrease or increase along $\gamma$, so $\gamma$ cannot be closed. But if $\gamma$ is embedded and not closed, then a suitable diffeomorphism will take $\gamma$ into a coordinate ball, so some $f$ exists near $\gamma$. But globally, even with boundary, we might have no function without critical points. Edit: a... | https://mathoverflow.net |
1,797,403 | [
"https://math.stackexchange.com/questions/1797403",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/203407/"
] | Let $(a,b)$ be an open interval of real numbers and let $c \in (a,b)$. Describe an open interval $I$ centered at $c$ such that $I \subseteq (a,b)$.
Here is the proposed solution to the problem:
Let $\epsilon >0$ be the radius of an interval I centered at a point $c \in (a,b)$ such that $a < c-\epsilon$ and $c+\... | His answer is wrong in that he stated "let $\epsilon $ be the radius of an interval centered at c" implying such an interval exists. Then he claims "such that" giving conditions assuming what is to be proven.
BUT
It <em>could</em> have worked as this:
"Intervals centered a $c $ of every possible radii exist (by sim... | Easy route: Let $c \in (a,b)$ and take $\epsilon = \frac{1}{2} \cdot \textrm{min}\{|c-a|,|c-b|\}$. Then just define $I = (c-\epsilon, c+\epsilon)$.
| https://math.stackexchange.com |
494,205 | [
"https://physics.stackexchange.com/questions/494205",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/175286/"
] | By Euler rotation Equation, torque
<span class="math-container">$$\tau (t)=I \omega '(t) + \omega(t) \times I \omega(t)$$</span>
where <span class="math-container">$I$</span> is the inertia tensor in rotating frame and is constant;
<span class="math-container">$\omega(t)$</span> is the Angular velocity in the rotating... | The Euler rotation equation,
<span class="math-container">$$
\vec{\tau} = \mathbf{I} \dot{\vec{\omega}} + \vec{\omega} \times \left(\mathbf{I} \vec{\omega} \right),
$$</span>
implicitly refers to the description of the motion in a rotating reference frame, namely the reference frame rotating with the rigid body. In su... | Your second equation is a formula which is obtained for a certain reference frame.
On the other hand, your first one is relating two different frames.
| https://physics.stackexchange.com |
128,105 | [
"https://softwareengineering.stackexchange.com/questions/128105",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44271/"
] | I have been doing some research on developing on the Android platform and found that the only way to develop an app using C++ is using the NDK. I also came to know that the NDK has limited support to C/C++, with C++ having even lesser support than C.
Here's the problem. I need to develop using C++ as I'm not very famil... | I think you'll be better off just learning Java as you learn to make Android apps. The stuff you know of C++ won't really get in your way of understanding Java.
I know it seems hard to learn a new language AND a new platform all in one go, but if you try to do it in C++, you have have an third problem: understanding ... | Your problem is that you don't know Java, but I promise you if you're proficient with C++ , its only a matter of a few months, you can master Java too.You say you're only 18 and you don't have experience with many languages, YES this is the time, dive into Java, you'll never regret.
| https://softwareengineering.stackexchange.com |
516,419 | [
"https://physics.stackexchange.com/questions/516419",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/238167/"
] | My physics textbook states that in measuring the time period of a pendulum it is advised to measure the time between consecutive passage though the mean position in the same direction. This results in better accuracy than measuring time between consecutive passage through an extreme position.
Why is one method of find... | To measure the time period it is useful to use a fiducial (reference) mark which in this case could be a vertical line drawn on a piece of card and placed “behind” the pendulum bob/string.
It is assumed that the time for a number of complete oscillations will be measured to enable one to find a more accurate value o... | The issue with measuring at the ends is that the pendulum “dwells” at the end point as it turns around, so that there is a greater spread of time for which it looks “at the extreme point” than for which it looks “at the midpoint”.
This spread of time introduces error, whether you are triggering a stopwatch by hand or ... | https://physics.stackexchange.com |
63,506 | [
"https://dba.stackexchange.com/questions/63506",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36985/"
] | I have one table of services. I need to merge two SELECT queries. Both have different where clauses. For example
<pre><code>SELECT
U_REGN as 'Region',
COUNT(callID) as 'OpenServices',
SUM(CASE WHEN descrption LIKE '%DFC%' THEN 1 ELSE 0 END) 'DFC'
FROM OSCL
WHERE
([status] = - 3)
GROUP BY
U_REGN
ORDE... | Treat your two current queries' resultsets as tables and join them:
<pre><code>select
FirstSet.Region,
FirstSet.OpenServices,
FirstSet.DFC,
SecondSet.ClosedYesterday
from
(
SELECT U_REGN as 'Region', COUNT(callID) as 'OpenServices',
SUM(CASE WHEN descrption LIKE '%DFC%' THEN 1 ELSE 0 END) 'DFC... | Building off Michael's suggestion:
<pre><code>SELECT
U_REGN AS 'Region',
SUM(CASE WHEN [status] = -3 THEN 1 ELSE 0 END) AS 'OpenServices',
SUM(CASE WHEN [status] = -3 AND [description] LIKE '%DFC%' THEN 1 ELSE 0 END) AS 'DFC',
SUM(CASE WHEN DATEDIFF(day, closeDate, GETDATE()) = 1 THEN 1 ELSE 0 END) AS ... | https://dba.stackexchange.com |
293,172 | [
"https://math.stackexchange.com/questions/293172",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/17962/"
] | Let $A$ be an $n\times n$ matrix over $\mathbb{C}$.
First I don't understand why $AA^*$ can be diagnosable over $\mathbb{C}$.
And why $i+1$ can't be eigenvalue of $AA^*$?
Hope question is clear enough and I don't have any spelling mistake and used right expressions.
| $\textbf{Hint:}$ Any hermitian matrix is diagonalizable. Prove, by definition, that $AA^*$ is a hermitian.
| Any Hermitian matrix is diagonalizable. All eigenvalues of a Hermitian matrix are real. These two facts (that you probably learnt) solve the question: Show your matrix is Hermitian and note that $1+i$ is not real.
| https://math.stackexchange.com |
43,470 | [
"https://quant.stackexchange.com/questions/43470",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/38329/"
] | I am trying to understand intuitively the difference between two different measures of realized variance of a basket of assets.
The first measure I am aware of is when you take the realized variance to be the sum of squared log returns of the basket. I.e.
<span class="math-container">$\sigma_B^2 = \sum_{i=1}^T{r_i}^... | The firs is at portfolio level while the second is from estimated from the constituents. Mathematically they should be the same assume the mean return is zero for your first formula. But in reality they may not in certain context like ETF, because of the trading cost and trading mechanism, there might be a gap between ... | If the correlation estimate <span class="math-container">$\rho_{ij}$</span> is calculated using the same period <span class="math-container">$[1,T]$</span> then 2 expressions are identical. They just differ in the order in which you are performing the 2 summations (one in time direction and the other in the cross-secti... | https://quant.stackexchange.com |
251,130 | [
"https://electronics.stackexchange.com/questions/251130",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38392/"
] | I'm trying to set the lock bits on my ATMega328p-pu, using an Arduino UNO as an ISP.
this is what happens:
<pre><code>>avrdude -c arduino -p m328p -P COM4 -b 19200 -U lock:w:0xFC:m
avrdude: AVR device initialized and ready to accept instructions
Reading | ################################################## | 100%... | I asked if you could provide an existing schematic for your pre-existing board that you are adapting in some way, I guess. It would really help to see what you already have, in order to better understand why you want to avoid adding a base resistor and to better understand how to offer an effective answer to you. You'v... | <blockquote>
Seems in doing this the voltage at the collector of the NPN would be 5v-2.8v = 2.2v due to voltage dropped across the LED.
</blockquote>
The forward voltage of the LED is only 2.8 V when there is a current flowing through the LED. If the current through the LED is lower than the normal operating value, ... | https://electronics.stackexchange.com |
125,524 | [
"https://mathoverflow.net/questions/125524",
"https://mathoverflow.net",
"https://mathoverflow.net/users/32505/"
] | Suppose $G$ is a connected Lie group whose radical is $R$. It is known that the solvable group $R$ can always be decomposed as $R=UT$ where $U$ is a simply-connected normal subgroup of $R$ and $T$ is a compact abelian subgroup of $R$ with $U\cap T = 1_G$. We know that $R$ is a normal subgroup of $G$.
<strong>Questio... | There is a complete classification of groups with all Sylow-subgroups being cyclic. In fact one can weaken this: we say that a group <span class="math-container">$G$</span> is <strong>almost Sylow-cyclic</strong> if every Sylow subgroup of <span class="math-container">$G$</span> has a cyclic subgroup of index at most <... | Take $p$ and $q$ two prime numbers with $q$ dividing $p-1$. Then there is a nonabelian semi-direct product $C_p \rtimes C_q$ which seems to be what you want, if i understand the question well. Here $C_n$ is the cyclic group of order $n$, and note that $p-1$ is the order of the automorphism group of $C_p$, when $p$ is a... | https://mathoverflow.net |
512,583 | [
"https://electronics.stackexchange.com/questions/512583",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/76283/"
] | In Square D's marketing copy for their plug on neutral load centers, they have a photo for demonstrating "cleaner wiring" in which the hot and neutral wires are twisted inside the panel before reaching the breaker. I agree it looks neater, but it got me thinking and I know just enough about electricity to be ... | There is no electrical reason for the twist; it merely serves to keep the two wires physically associated with each other once the Romex jacket is removed. It both "looks neater" and is easier to do subsequent work on.
There is no increased capacitance (the distance between the wires doesn't change), except f... | If you locate a sensitive audio system behind the wall of the panel, the twisting may matter.
I'm not sure the heavy gauge 1cm diameter incoming wires can be twisted at 1 twist per inch. However, even at 1 twist per 6", the flux cancellation at moderate distances away (6" or further) will become a bunch of dB... | https://electronics.stackexchange.com |
67,048 | [
"https://electronics.stackexchange.com/questions/67048",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18442/"
] | I am building a temporary Arduino project, and I need to order an adapter online. I am concerned that, if my adapter has lots of noise, it will affect the Arduino. Since this is temporary, I am going to buy a dirt cheap adapter to save money, but will it be "smooth"? I don't care if it breaks; two of them are much chea... | As far as I can recall, the Arduino doesn't clean up noise in the power supply. Some boards have smoothing capacitors, and other boards have <em>nothing</em>. This means that you'll have to put a smoothing capacitor in between your adapter and your Arduino to avoid accidentally resetting it.
| The 5V node is pretty raw with only a small amount of decoupling.
The Vin and Barrel jack are connected to a regulator with significant decoupling capacitors. The regulator will filter out relatively slow changes to the input voltage while the decoupling capacitors will clean up higher frequency content.
| https://electronics.stackexchange.com |
241,427 | [
"https://electronics.stackexchange.com/questions/241427",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/114234/"
] | This is a fundamental circuit question. Suppose two nodes of a circuit are always kept at the same voltage by some unknown mechanism. If I now connect these two nodes with a wire, would it introduce any changes to the operation of the circuit?
For example, in an <em>ideal</em> op-amp, the two input terminals have equa... | <strong>For the question in the first paragraph</strong>
A clarification to my earlier statement. You have to be careful how you explain things. If you assume that "two nodes are <strong>always</strong> kept at the same voltage by some unknown force", then the problem is simply, no it will not have an effect - because... | The stable non-saturated solution to an op-amp circuit satisfies equality of voltage across the inputs, but it also satisfies other requirements such as near-zero current into the inputs.
If you add a wire, you replace the restriction with a much weaker one -- that the currents at both inputs are equal and opposite. ... | https://electronics.stackexchange.com |
1,353,602 | [
"https://math.stackexchange.com/questions/1353602",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/224404/"
] | Any ideas?
$$ \lim_{x \to 0^+} \frac{\ln (x)+e^{\frac{-1}{x}}}{ \frac{1}{x^2} + x\sin \left(\frac{-1}{x^2} \right)}$$
L'Hopital didn't really help, maybe taylor?
Thanks
| An idea
$$0\xleftarrow[0^+\leftarrow x]{}\frac{\log x}{\frac1{x^2}+1}\le\frac{\log x+e^{-1/x}}{\frac1{x^2}+x\sin\left(-\frac1{x^2}\right)}\le\frac{\log x+1}{\frac1{x^2}-1}\xrightarrow[x\to0^+]{}0$$
The right-hand and left-hand limits follow from applying l'Hospital, say:
$$(*)\stackrel{l'H}=\lim_{x\to0^+}\frac{\frac... | <strong>hint</strong>: the answer is $0$. Just look at the first term of both the numerator and denominator and it equals to: $\dfrac{\ln x}{\dfrac{1}{x^2}}$, and use L'hospitale here because the other terms go to $0$.
| https://math.stackexchange.com |
195,297 | [
"https://physics.stackexchange.com/questions/195297",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86230/"
] | The escape velocity of different planets and stars vary. If they vary, the velocities of bodies escaping from the respective stars or planets should also vary.
Like, if I want a ball to reach 10 meter height, I should throw with different velocities on earth compared to some other planet. As light (say, a photon) cros... | As far as we can tell, the local speed of light in vacuum is indeed constant.
Photons don't slow down or speed up as they fall into or rise out of a gravity well. However, just as a massive object's kinetic energy changes as the object falls into or rises out of a gravity well, photons also gain or lose energy. In the... | <strong>No</strong>, in perfect vacuum, photons do not slow down. Although, gravity of massive objects like stars or planets can bend the trajectory of photon (the Theory of General Relativity) like a lense.
If you are referring to the fact that Black Hole is black because no photons can escape its massive gravitationa... | https://physics.stackexchange.com |
3,102,210 | [
"https://math.stackexchange.com/questions/3102210",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/446637/"
] | I'm trying to solve the following problem:
<blockquote>
Let <span class="math-container">$v_0$</span> be a vertex in a graph <span class="math-container">$G$</span>, and <span class="math-container">$D_0 := \{v_0\}$</span>.
<ol>
<li>For <span class="math-container">$n = 1, 2 \dots$</span> inductively define
... | You are mixing closed and open neighbourhood. I think when they are stating <span class="math-container">$D_n=N(D_0\cup\ldots\cup D_{n-1})$</span>, they are implying the <strong>open neighbourhood</strong>
The open neighbourhood <span class="math-container">$N(S)$</span> of some set of vertices <span class="math-conta... | It depends on how you define the neighbourhood, but it seems that here it is defined so that <span class="math-container">$N(V')$</span> comprises the vertices adjacent to some vertex in <span class="math-container">$V'$</span>, excluding vertices in <span class="math-container">$V'$</span>.
So in that case, <span cla... | https://math.stackexchange.com |
655,449 | [
"https://electronics.stackexchange.com/questions/655449",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/243146/"
] | AFAIK, Igs of MOSFET/JFET is around 0.
That means that in MOSFET/JFET almost no current flows from gate to drain.
Modern FET input stage:
<img src="https://i.imgur.com/kylCSCZ.png" alt="" />
I read some op-amp datasheets, those op-amps have FET inputs, but they still have a max. value for the input current.
For example... | Those are absolute maximum ratings.
And it does not mean that current goes through the FET gate, but protection circuitry, such as clamping diodes to VCC and GND.
If you exceed the maximum allowed voltage, the protection diode starts to conduct current to clamp the voltage, and that limit comes from internal wiring inc... | The max. limit of input current and voltage stated in the datasheet has to do with the reliability and safe operating area for the MOS input stage.
If the user forces more than the state current (meaning, that current has no other way to go than the gate/ESD input circuitry of the input stage), the manufacturer cannot ... | https://electronics.stackexchange.com |
29,630 | [
"https://chemistry.stackexchange.com/questions/29630",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7697/"
] | The thermodynamic definition of entropy is expressed as
$$dS = \frac{dq_{rev}}{T}$$
I understand that it depends on amount of heat transferred because heat transfer can be understood as the degree of dispersion of energy but what does the temperature dependence actually mean?
| An analogy that I like is one paraphrased from Peter Atkins' great book "The Laws of Thermodynamics - a VSI":
<blockquote>
Imagine two rather different places in terms of noise - a silent
library and a busy train station. Imagine that the temperature is the amount of noise at the given place - a measure of the "s... | What this equation is saying essentially is that the level of disorder can be modeled as the number of configurations if you have a number of particles and a number of quanta of energy. It's like having three cups and three balls; all the balls can occupy one cup or one ball can occupy one cup and two can occupy anothe... | https://chemistry.stackexchange.com |
1,370 | [
"https://mechanics.stackexchange.com/questions/1370",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/39/"
] | Considering a turbo car. The specific model is a Dodge Caliber SRT 2008, but I'd prefer a more generic answer.
How can one prevent the car from boosting while still having a car that can be driven around (on vacuum)?
The process should be reversible to make the car boost again. Ideally, this could be done at will wit... | You can't prevent the turbo from spooling up without physically removing it from the car. Depending on how the boost is controlled (ie, if there is a manual or electronic boost controller involved, too, or if it's just standard boost control by the ECU) you might be able to turn down the maximum boost to the pressure c... | Any boost controller (manual or electronic) would allow you to turn down the boost. I have a DiabloSport unit and I can go way down almost to the point where the car is atmospheric (max. boost under 3 psi). When ready to restore it, flash back the original tune map.
| https://mechanics.stackexchange.com |
408,213 | [
"https://physics.stackexchange.com/questions/408213",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/196742/"
] | It requires concept from Newton's laws of motion and circular motion. While solving for net force on a body on an inclined plane , we always resolve mg (weight) parallel and perpendicular to the plane but in the banking of road concept, we resolve normal reaction. Why don't we simply resolve weight and then equate it w... | As a general rule, resolve force vectors into components that are parallel to and perpendicular to the acceleration of the object. In the case of a vehicle driving around a banked curve the acceleration is horizontal, towards the center so it's the normal force (and friction if any) that you would resolve into compone... | What you solve for depends on the coordinate system you choose.
<ul>
<li>Choose a tilted coordinate system along the incline, and you must resolve the weight into components (because it is not parallel to any axis) but not the normal force (which is parallel to the y-axis).</li>
<li>Choose a horizontal/vertical coordi... | https://physics.stackexchange.com |
90,232 | [
"https://softwareengineering.stackexchange.com/questions/90232",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27876/"
] | I'm working on a software project where so far I'm the sole developer. As of right now the code is unlicensed, but the copyright of whatever I've written belongs to me (this is true at least in North America AFAIK).
Before I release the software to the public, I'm going to license its distribution, probably under some... | A lot of your confusion will go away if you keep in mind that <strong>copyright</strong> and <strong>licensing</strong> are two completely separate things.
<strong>Copyright</strong> is owned by the original author. (Unless it was produced under a "work for hire" contract, in which case it is owned by the employer. T... | FYI if you are employed as a programmer in the USA, then depending on your state of residence, your employee contract, what your employer does, and what the software you wrote does, it may or may not belong to your employer. Even if you wrote it in your own time, on your own computer.
Check your employment contract, ... | https://softwareengineering.stackexchange.com |
80,888 | [
"https://dsp.stackexchange.com/questions/80888",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/60483/"
] | Cheers, I am trying to find the fourier transform of the signum function, which is
<span class="math-container">$$ \operatorname{sgn}(t) \triangleq \begin{cases}
1 \qquad & t>0 \\
0 \qquad & t=0 \\
-1 \qquad & t<0 \\
\end{cases} $$</span>
I rewrite this as:
<span class="math-container">$$\operatorname... | By taking the derivative you loose all information about the DC value of the original signal. Any signal
<span class="math-container">$$x(t) = 2\cdot u(t)- a$$</span>
has the same derivative, regardless of what <span class="math-container">$a$</span> is. So you do have to calculate the DC value by hand, which is simply... | As you've shown via differentiation, the Fourier transform of all piecewise constant signals that have a jump discontinuity of height <span class="math-container">$2$</span> at <span class="math-container">$t=0$</span> is
<span class="math-container">$$X(j\omega)=\frac{2}{j\omega}+c\delta(\omega)\tag{1}$$</span>
where ... | https://dsp.stackexchange.com |
19,128 | [
"https://bioinformatics.stackexchange.com/questions/19128",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/3766/"
] | I have a data frame <code>df</code>. The below table only represent top 8 rows of the data frame. There are multiple combination of <code>LIBRARY_NAME</code> and <code>ANCHOR_NAME</code>
<pre><code>BARCODE ANCHOR_NAME LIBRARY_NAME ANCHOR_CONC Synergy HSA Bliss
14482 5-Fluorouracil Cisplatin 2.5 ... | The difficulty in answering the question is:
<ul>
<li>The absence of "Y" in the "Gene of interest" tree</li>
<li>The sampling bias in the number of taxa mostly between the "genome tree" and the "gene of interest" and "16S" tree</li>
<li>The "genome" tree is un... | It seems like you've got the right approach, in trying out a few different genes and looking for consistency. As you say, different genes can have different selective pressures, which influences how much they change in relation to the whole genome background.
Certainly don't put too much trust in a single gene, and esp... | https://bioinformatics.stackexchange.com |
413,052 | [
"https://electronics.stackexchange.com/questions/413052",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/200117/"
] | How can I measure FOM(figure of merit) of an operational amplifier? There are so many parameters, how can I decide which formula to use while calculating FOM?
| A Figure of Merit severely depends on the situation. In commercial applications I can only see limited use for it, but for R&D purposes it does have its advantages.
The idea is that you try to isolate anything that is not dependent on factors common to all amplifiers. For example, in CMOS design, driving a 1pF cap... | First, you define what your Figure of Merit (FOM) means.
I've sometimes (but not often) done this when comparing op-amps for a new application. Once I needed to make a low distortion video driver into 50 ohms, and had the choice of one beefy opamp, or several smaller ones in parallel. I defined an FOM as the output cu... | https://electronics.stackexchange.com |
453,560 | [
"https://physics.stackexchange.com/questions/453560",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/112257/"
] | I was doing a problem regarding field theory. I am given the following lagrangian density: <span class="math-container">$$\mathcal{L}=\frac{1}{2}\partial_\mu\phi_i\partial^\mu\phi_i-\frac{m^2}{2}\phi_i\phi_i$$</span> for three scalar fields. I want to determine the equations of motion for the field <span class="math-co... | As mentioned in the comments by WarreG and user2723984, since the full expression of the two in terms of the metric tensor is
<span class="math-container">$$
\partial_\nu \partial^\nu=\partial_\nu g^{\mu\nu}\partial_\mu=\partial^\mu\partial_\mu,
$$</span>
the two equations are identical.
| I would say the answer to your question is: it depends on the metric. Yes, because if your metric is Minkowski and Cartesian then <span class="math-container">$$\partial_{\mu}\partial^{\mu} = \partial_{\mu}\left(g^{\mu\nu}\partial_{\nu}\right)=\underbrace{\left(\partial_{\mu}g^{\mu\nu}\right)}_{0}\partial_{\nu}+g^{\mu\... | https://physics.stackexchange.com |
6,762 | [
"https://mathoverflow.net/questions/6762",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2008/"
] | X is a Noetherian scheme, F is an injective object in the category of quasi-coherent sheaves on X. U is an open subset of X. Why F's restriction on U is still an injective object in the category of quasi-coherent sheaves on U?
| The restriction-by-zero type arguments can actually be made to work, with some effort and an extra hypothesis. Suppose $X$ is <em>locally Noetherian</em>, $j: U \to X$ the inclusion of an open subscheme.
Let $Mod(X)$ and $QCoh(X)$ be the categories of $O_X$-modules, and quasi-coherent $O_X$-modules, respectively.
Th... | This is false is general. In particular, if $X = SpecA$ is affine, this would imply that given an injective $A$-module $M$ and $f \in A$, one would have $M_f$ is injective over $A_f$; this is FALSE in general (see, for example, "Localization of Injective Modules" by Everett C. Dade (it's in Journal of Algebra ~ April 1... | https://mathoverflow.net |
1,021,879 | [
"https://math.stackexchange.com/questions/1021879",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/187799/"
] | How can I prove this inequality $$\sqrt[n]{x^n+\sqrt[n]{(2x)^n+\sqrt[n]{(3x)^n+\cdots}}}< \left(x+\frac{1}{n-1}\right)$$ if $n$ and $x$ are positive integer number $$x>=1$$ $$n>1$$
| $a_n = \left( 1 +\dfrac{1}{n} \right)^n $ converges to $e$
| How about $a_n$ = the decimal expansion of $\sqrt{2}$ up to the $n$-th place
A formal definition could be $$a_n = \lfloor 10^n\sqrt{2} \rfloor 10^{-n} $$
| https://math.stackexchange.com |
130,109 | [
"https://electronics.stackexchange.com/questions/130109",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37643/"
] | Consider the equation
$$
E = -L\,\dfrac{di}{dt}
$$
The negative sign in the above equation indicates that the induced emf opposes the battery's emf.
If we're talking about a purely inductive circuit, the induced emf is equal and opposite to applied emf. Isn't it just like two identical batteries in opposition?
... | <blockquote>
If the value of resistance tends to zero, the induced emf becomes
equal and opposite to applied emf resulting in no net current.
</blockquote>
No, not remotely so. You're caught in the trap of thinking that an equal and opposite induced emf to the applied emf implies zero current but that does not lo... | If you attach a fixed source of voltage V across an inductor L, the current increases at a rate di/dt = L/V.
If there is resistance, it levels off asymptotically towards V/R. If there is no resistance, it increases (for fixed V) linearly until something breaks.
This is how superconducting coils are charged. A sourc... | https://electronics.stackexchange.com |
47,779 | [
"https://dba.stackexchange.com/questions/47779",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/26869/"
] | We want to use Windows Authentification on SQL Server 2008 within Active Directory.
Is it possible to use an AD Group as a LOGIN to the server, but then to map the actual AD USER to a database user?
The idea is to have one AD group which has the basic login access, but then to fine-granulate roles and access rights t... | First of all, the way you are wanting to do it won't really work. You can't have one login and multiple users on a single database. If you try you get the following error:
<pre><code>Msg 15063, Level 16, State 1, Line 1
The login already has an account under a different user name.
</code></pre>
What you really shou... | Yes, you may use an AD Windows Group as a LOGIN to the server and then map the <em>individual</em> AD Windows Logins to database USERs <em>in the approriate databases</em>. Since the Windows Group LOGIN only adds rights to access the SQL Server and any databases with the guest user enabled (master, msdb, tempdb) then... | https://dba.stackexchange.com |
96,961 | [
"https://security.stackexchange.com/questions/96961",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/61255/"
] | I was resetting my password on a website and the website emailed me a new password in plain text rather than giving me a reset link to change the password myself. I logged back in and changed the password to something else.
I'm wondering - Does this email indicates that these passwords are stored in plain text or with... | No, this does not indicate whether they are <strong>storing</strong> your password in plain text or with reversible encryption. They <em>might</em> be, but this still leaves other possibilities open. All you know for certain is that they created a new password and emailed that new password to you. That password may wel... | Not necessarily, I don't see an immediate correlation between the two.
What is probably happening is that the application got your plain text password from the POST request and sent it to you as a reminder. It is likely that they are not retaining the plain text version and that they are keeping its hash instead.
If,... | https://security.stackexchange.com |
496,204 | [
"https://physics.stackexchange.com/questions/496204",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/193422/"
] | Let's assume I have a one dimensional harmonic oscillator. The eigenvalue of the oscillator would be <span class="math-container">$E= (n+ \frac{1}{2}) \hbar \omega$</span>.
Now I have two electrons (their spins are identical, I mean either both are spin up or spin down) and I want to find the ground spin state of th... | This depends on the statistics of your particles and with electrons (fermions) the total (i.e. spin plus spatial parts) wave function must be antisymmetric. Since the spectrum is <span class="math-container">$(n_1+n_2+1)\hbar\omega$</span>, the lowest energy state is one where <span class="math-container">$n_1=n_2=0$<... | First note the spectrum. The energy actually is <span class="math-container">$(n_{1}+n_{2}+1)\hbar\omega$</span>. So, the ground state actually is <span class="math-container">$(0,0)$</span>, and there are two degenerate first excited states <span class="math-container">$(1,0)$</span> and <span class="math-container">$... | https://physics.stackexchange.com |
207,367 | [
"https://mathoverflow.net/questions/207367",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $X\subset\mathbb{P}^4$ be an hypersurface of degree six given by the Pfaffian of a $6\times 6$ matrix $M$ whose entries are quadratic forms in the homogeneous coordinates of $\mathbb{P}^4$. I am interested in the singular locus of $X$.
Is it true that $Sing(X)$ is the curve defined by the $4\times 4$ sub-Pfaffians... | As Sasha proved the general Pfaffian is smooth. On the other hand the special Pfaffian $X$ you wrote is an irreducible hypersurface of degree $6$ in $\mathbb{P}^4$ singular along a smooth curve $C$ of degree $20$ and genus $26$. Indeed $X$ has ordinary double points along $C$.
Your Pfaffian is indeed birational to the... | Let me add a bit more details to abx comment. Consider the projectivization $P^{14}$ of the space of all $6 \times 6$ skew-symmetric matrices. It contains the Pfaffian cubic hypersurface, which parameterizes matrices of rank 4, and its singular locus is the locus of matrices of rank 2, i.e. $Gr(2,6)$. Indeed, its codim... | https://mathoverflow.net |
9,481 | [
"https://softwareengineering.stackexchange.com/questions/9481",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4459/"
] | Why does Software Engineering not have union representation like other professional occupations, such as teaching? Are there any unions for software developers that exist and are successful?
| Unions are useful when one person can pretty much do the same job as anybody else with little or no training. By allowing employees to negotiate as a whole, you don't run the risk of employers simply finding the person who'll work the cheapest and driving wages down. (At least, that's the theory.)
For professional fie... | Interesting question.
We produce a product - code - but we're not like typical unionized laborers. We're also not professionals like doctors and lawyers and accountants. (Can you imagine some hospital administrator demanding that a surgeon work overtime on Saturday - with no extra pay - to push a few more patients thr... | https://softwareengineering.stackexchange.com |
2,693,522 | [
"https://math.stackexchange.com/questions/2693522",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/262230/"
] | If $\alpha,\beta \in(0,\frac{\pi}{2})$ and $\alpha+\beta=\sigma$(constant),then prove that maximum value of $\cos\alpha \cos\beta$ occurs when $\alpha=\beta=\frac{\sigma}{2}$<br><br>
<hr>
$\cos\alpha \cos\beta=\frac{\cos(\alpha+\beta)+\cos(\alpha-\beta)}{2}$<br>
As $\cos x$ is a concave function,so by Jensen inequali... | Hint:
As $\alpha+\beta=\sigma$(constant), $\cos(\alpha+\beta)=\cos(\sigma)=$(constant)
So, we need to maximize $\cos(\alpha-\beta)$
| $$\cos\alpha \cos \beta =\frac{\cos(\alpha + \beta )+\cos(\alpha -\beta)}{2}=\frac {\cos\sigma +\cos (\sigma-2\beta)}{2}$$
Hence, it is maximized when $\beta =\sigma/2$ so that $\cos(\sigma -2\beta )=1$
| https://math.stackexchange.com |
52,164 | [
"https://engineering.stackexchange.com/questions/52164",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/38976/"
] | I wonder if an automobile CVT could ditch the secondary set of pulleys by having the chain/belt drive the output shaft directly. Gear ratios would result from movement of the drive-pulley set only. Is that possible?
| Well the answer is different depending on what 1.30% <span class="math-container">$CO_2$</span> is. Is it by mass or by volume? I would think the most likely is volume, but with out knowing I'll just do both.
<hr />
<h2>Volume</h2>
Our volume of <span class="math-container">$CO_2$</span> would be:
<span class="math-con... | As a proofing method you can use the input of fuel to estimate the mass of CO2 produced.
First get the percentage mass of carbon in woodchips (around 50% according to a quick bit of searching)
Then multiply the mass of woodchips burned by that percentage and by
<span class="math-container">$$\frac{molar\ mass\ CO2}{mol... | https://engineering.stackexchange.com |
2,136,302 | [
"https://math.stackexchange.com/questions/2136302",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/414663/"
] | I read somewhere that:
$$\int_{0}^{t} \delta(\tau-a) \ d\tau = \begin{equation}
u(t-a)=%
\begin{cases}
0 &\text{if $t < a$} \\
1 &\text{if $t \geq a$}.
\end{cases}
\end{equation}$$
How is that so?
| Raw explanation.
In a distributional sense, the Dirac Delta is the derivative of the Heaviside theta:
$$\frac{d}{dx} \theta(x) = \delta(x)$$
But as I said, it's a distributional derivative, so take that writing with gloves.
Hence, the distributional integral of the Dirac Delta is the Theta.
<strong>Distributional ... | In a, somewhat, more visual sense:
You know, that heavyside defined his fuction to be 1 after a certrain point and zero before.
Similiarly, the Dirac-Distribution ist very, very small (infinitly small) in width, but so incredibly high, that the area under the function is $1$.
If you now using the "Integration in Are... | https://math.stackexchange.com |
557,540 | [
"https://physics.stackexchange.com/questions/557540",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266740/"
] | Will connecting, 6x1.5v(non recharge) cells (in series) to a 9v battery(non recharge) through parallel combination, increase circuits capacity while keeping the voltage same?
If yes, then will this be true if the 9v battery was rechargeable?
| In theory you should be able to supply the same load with the same voltage (or a little higher) for longer than with a single battery. However it is bad practice to connect batteries in parallel. Even if they have the same nominal e.m.f. (9 V in your case), the emf's won't <em>stay</em> exactly equal and the difference... | So long as the batteries are of the same type, it should. The 9v battery will consist of 6 cells in series.
| https://physics.stackexchange.com |
40,834 | [
"https://dsp.stackexchange.com/questions/40834",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/28423/"
] | So we that a complex sinusoid of the form $e^{j\omega_0n}$ is periodic over $N=2\pi/\omega_0$ <strong>only</strong> if $\omega_0$ is a rational multiple of $\pi$, otherwise the exponential is <em>not</em> periodic. <strong>(see EDIT!)</strong>
Then we got to the DTFT, specifically the synthesis equation:
$$x[n]=\fra... | The reason the DTFT has values at frequencies that result in discrete aperiodic sinusoids is because we are interested in representing <em>all</em> possible discrete time signals including (linear combinations of) discrete aperiodic sinusoids. Let's say that we have a signal $x[n] = e^{j \omega_0 n}$ where $\omega_0$ i... | $e^{j\omega n}$ in the synthesis equation
$$\displaystyle x[n]=\frac{1}{2\pi}\int_{2\pi}X\left(e^{j\omega}\right)e^{j\omega n}d\omega$$
is <em>NOT</em> discrete since $\omega$ is the independent variable. Hence, it is periodic over $[0, 2\pi]$ for any $n$. Expand it by Euler's formula for better understanding.
Same ... | https://dsp.stackexchange.com |
2,978,010 | [
"https://math.stackexchange.com/questions/2978010",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/609130/"
] | <span class="math-container">$z \in \mathbb{U}$</span>, let <span class="math-container">$x= |z-1|$</span>, show that :<span class="math-container">$|z^2-z+1|=|x^2-1|$</span>
I tried from both sides but nothing worked for me, any ideas ?
| Well, <span class="math-container">$x^2=(z-1)(\bar{z}-1)=z\bar{z}-z-\bar{z}+1$</span>. Since <span class="math-container">$\bar{z}=\dfrac{1}{z}$</span> for <span class="math-container">$z\in\mathbb{U}$</span>, we get
<span class="math-container">$$x^2-1=\frac{z-z^2-1}{z}=-\frac{z^2-z+1}{z}\,.$$</span>
That is,
<span c... | Hint: With <span class="math-container">$$z=x+iy$$</span> we get
<span class="math-container">$$|x^2-y^2+2xyi-x-iy+1|=|(x-1)^2+y^2-1|$$</span>
Can you proceed?
| https://math.stackexchange.com |
10,329 | [
"https://cs.stackexchange.com/questions/10329",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7172/"
] | Here is the question:
Show that $L = \{0^m1^n : m > 1, n > 1, n < m \}$ is not regular.
I am not sure what superscripts mean in this situation? Does it mean something like this:
$0^5 = 00000$ or $1^7 = 1111111$.
| Yes, <code>0^n</code> or $0^n$ denotes the string obtained by concatenating $n$ copies of the symbol $0$.
| Yes, superscripts mean exactly what you think they do. For your other question (how to use superscripts in SO), there are two ways: use html tags like sup, or use $...$ math.
| https://cs.stackexchange.com |
212,400 | [
"https://security.stackexchange.com/questions/212400",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/210795/"
] | If I have discovered an XSS vulnerability, is there another way of gaining access to an account without session hijacking? Mainly because on most of the sites I test, the HttpOnly and Secure flags are set on the session ID, so I can't access it through javascript (<code>document.cookie</code>). I know I could do some f... | If you have XSS, you can perform any action on the website the user can. This can include changing the email address, adding a new user, or granting access to some resource. Whether any of these actions compromise the account depends on the web application.
For example, consider an XSS payload that changes the email a... | There are definitely more ways of hijacking a session of a victim. Think about
<ul>
<li>Session Fixation</li>
<li>Session Poisoning</li>
<li>Cross-Site-Request-Forgery</li>
<li>Cookie replay attacks</li>
<li>Man in the Middle</li>
</ul>
<blockquote>
Session Fixation
</blockquote>
At Session Fixation you are able ... | https://security.stackexchange.com |
361,173 | [
"https://stats.stackexchange.com/questions/361173",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/164151/"
] | I have a CNN image classification problem with imbalanced classes. I could balance the dataset using data augmentation (Replication, mirror, etc.) on the minority classes. Also, imbalance could be handled using a weighted loss function that gives more importance to the minority classes. Is any of these methods preferre... | I've tried both minority (random) oversampling and class weighting to solve the problem of imbalance in the past and none proved to be better than the other (which is logical). The reason why I'd suggest class weights is that it has a much <strong>less training time</strong> than the over-sampling, as the number of exa... | You could try with a combination or Oversampling + Undersampling (i.e. replication and removal or certain "less useful" data points; applying SMOTE(and or any of its variants) + bagging...). You could also apply an ImageGenerator to increase your sample size while balancing the classes.
| https://stats.stackexchange.com |
88,356 | [
"https://mathoverflow.net/questions/88356",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19205/"
] | Let $X$ a variety. Say $X=\operatorname{Spec} A$.
Consider two ideals of $A$, say $I$ and $J$, with equal radical ; and consider the blow-ups of X with centre $I$ and $J$, say $Y_I$ and $Y_J$. <strong>How can I decide if the blow-up map $Y_I \to X$ factors through $Y_J$ ?</strong>
For example, if $X = \operatorname{S... | There are <em>two</em> conditions I can think of.
<ol>
<li>Perhaps $I = J \cdot J'$ for some other ideal $J'$. Indeed, blowing up a product of ideals is the same as blowing up one ideal (say $J$) and then blowing up the total transform of the other (say $J'$).</li>
<li>The other is requiring that $I = \overline{J}$, ... | The universal property of the blowup $\pi:Bl_I X\to X$ of an ideal $I$ in $X$ is that the sheaf of ideals $\pi^{-1}I\cdot O_{Bl_I X}$ is invertible. So, if you want to find out whether $Bl_I$ factors through $Bl_J$ you just have to check whether $\pi^{-1}J\cdot O_{Bl_I X}$ is invertible.
| https://mathoverflow.net |
680,531 | [
"https://physics.stackexchange.com/questions/680531",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167872/"
] | <strong>Problem:</strong>
<span class="math-container">$1 mol$</span> helium gas is kept at <span class="math-container">$2\times10^5Pa$</span> pressure and <span class="math-container">$600K$</span> temperature in a heat-insulating cylinder on top of which a frictionless piston is attached. Then the cylinder's pressur... | When there is a changing magnetic field inside the coil, Faradays law states that there is an induced emf
This Emf causes electrons to accelerate, producing a current
Amperes law( along with the negative in faradays law, )states that this current produces a magnentic field that wants oppose the change that causes it. ... | The opposition to the movement of the magnet is due to the induced current in the coil circuit.<br />
The larger the induced current the larger the opposition to the movement of the magnet.<br />
A factor which controls the magnitude of the induced current is the resistance of the coil circuit.<br />
The statement that... | https://physics.stackexchange.com |
193,410 | [
"https://physics.stackexchange.com/questions/193410",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/80827/"
] | I simply can not find material containing facts about the $n$-th root of the NOT gate and it's realization in Q.M. and also in C.M.. Does anyone have material?
A comparison of the $n$-th root NOT gate in Q.M. and C.M. would be nice!
| This topic seems to me as functions of operators, so I'll explain this issue and will use "n-th root NOT gate" as example.
Any function you apply on the operator - is applied on it's eigenvalues. If the operator is diagonal - all the eigenvalues are on the diagonal and applying the function is simply apply it to any e... | I'm guessing that by $n^{\text{th}}$ root you mean some gate which if you pass a signal through $n$ of them the output will be identical to the output of the gate you want to "root".
For odd $n$ it's pretty obvious that the classical NOT gate is it's own $n^{\text{th}}$ root. In that an odd number of NOT gates one a... | https://physics.stackexchange.com |
19,851 | [
"https://softwareengineering.stackexchange.com/questions/19851",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | This is happening in every team.
For some reasons, conflicts arise in the team and they affect the overall motivation and productivity.
What is your recommended approach to solve that common problem?
<em>Examples</em>:
<ul>
<li>one part of the team wants to implement dependency injection, the other part think it's ... | I have had a team of 10 people for two years without a conflict(touch wood) I could be lucky or may be doing something right. The best way to handle conflict is never to let one exist for a longer time. There are several core values that you can preach.
<ol>
<li>Team Spirit</li>
<li>Fairness in everything (compensati... | Have a third-party unbiased mediator sit down with both conflicted parties and have them talk it out.
It helps if the mediator is someone the problem-havers are comfortable talking around, but that they still respect and will not talk overtop of
| https://softwareengineering.stackexchange.com |
339,523 | [
"https://physics.stackexchange.com/questions/339523",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/155247/"
] | We would have a potential rise but where is potential drop? Considering wire to be having negligible resistance.
| <blockquote>
Since the total current is conserved at a junction in a parallel
circuit, the current in the branch with the fixed resistor should
increase.
</blockquote>
Your conclusion would be correct <em>only</em> if the current through the source were held constant, e.g., the source is a <em>current</em> sourc... | The potential difference across the fixed resistor remains constant from Kirchhoff's second law, hence the same current passes through the fixed resistor. However, increasing the resistance of the varistor decreases the current in the circuit. This is because the potential difference across each branch is equal to the ... | https://physics.stackexchange.com |
438,167 | [
"https://physics.stackexchange.com/questions/438167",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/165075/"
] | Feynman diagrams are drawn on Space-time graphs. So is it possible for any particle path in that diagram to have a slope smaller than 45° or greater than 135°, i.e. can they travel faster than light? Does the slope or or velocity of the particles have any effect on the outcome of the diagram?
Virtual particles (photons... | Incoming/outgoing particles with mass must travel at less than the speed of light. Incoming/outgoing massless particles must travel at the speed of light. The “virtual particles” inside the diagram can “travel” at any speed, but since they don’t really behave like particles this doesn’t matter.
Feynman diagrams aren’t... | Feynman diagrams are not drawn on space time, that is a common misconception. It helps to think of them as being drawn on space time, but the reality is a bit different.
Feynman diagrams are nothing more than abstract diagrammatic pictures representing various terms in the expression for the transition amplitude betwe... | https://physics.stackexchange.com |
8,196 | [
"https://mechanics.stackexchange.com/questions/8196",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4192/"
] | How does varying wheelbase during automobile design affect the properties of the vehicle that is going to be built (both two-wheelers and four-wheelers)? I know that greater wheelbase means less maneuverability (or maybe it's the other way around). Based on what factors will the wheelbase be finalized and manufactured?... | There are two concepts to understand (which I think you might already get to an extent). As the wheel base length grows, stability is gained, but you lose maneuverability. You also risk the greater chance of the vehicle becoming high-centered (ground rubbing the center of the vehicle) when traversing bumps in the road ... | The first and most important criteria is what the intended use of the vehicle will be and where it will be operated.
Two British Prime Ministers being very tall, Jim and Ted, my department 'stretched' vehicles for them to have extra leg room in the back of the vehicle. When a British University was going on an field t... | https://mechanics.stackexchange.com |
3,720,202 | [
"https://math.stackexchange.com/questions/3720202",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/797345/"
] | So here is the Question :-
A Dyck <span class="math-container">$n$</span>-path is a lattice path of n upsteps <span class="math-container">$(x,y)$</span> <span class="math-container">$\rightarrow$</span> <span class="math-container">$(x + 1,y + 1)$</span> and <span class="math-container">$n$</span>
downsteps <span clas... | Let <span class="math-container">$A$</span> be the set of all <span class="math-container">$(n-1)$</span> paths and <span class="math-container">$B$</span> the set of all <span class="math-container">$n$</span>-paths without even-length downramps. Define <span class="math-container">$u$</span>: <span class="math-contai... | The answer provided by Maths-Lover is actually incorrect.
The injection <span class="math-container">$u: A \to B$</span> is fine, however its inverse is incorrect.
Consider the inverse <span class="math-container">$L$</span> acting on the two Dyck paths represented by the binary strings <span class="math-container">$p_... | https://math.stackexchange.com |
440,241 | [
"https://physics.stackexchange.com/questions/440241",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/171182/"
] | Let's say we have a state <span class="math-container">$ \phi=\sum_i c_i \phi_i $</span> where the <span class="math-container">$ \phi_i $</span> denote energy eigen vectors with non degenerate eigen values.
Now if a measurement of the energy is done this state collapses to one of the eigen states at time <span class... | I agree with Pieter, especially when he refers to QED, writing
<blockquote>
Feynman explains this (in his little book QED, I recommend to read
that) with electrons having dials that turn around. Or one could
represent phase as color.
</blockquote>
It must be remarked however that Feynman was a strong opponent o... | They do not mean that the particle itself moves up and down in a wavelike way. What is meant by wave/particle behavior or duality is something more subtle; something that many very smart people have spent their lifetimes working on and which my answer will treat in a simplified way which I hope you can grasp.
For obj... | https://physics.stackexchange.com |
419,012 | [
"https://stats.stackexchange.com/questions/419012",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/78538/"
] | Is there a standard way of applying Gaussian processes to regression problems with categorical input? Are they standard kernels that one should apply to this problem?
| The answer to this question relies on philosophy and it relates to whether <span class="math-container">$Y$</span> is deterministic, or whether there is an element of randomness.
It's fine if you want to believe for a particular problem that there is some set of covariates that would allow you to perfectly predict, s... | Your regression is modeling a conditional expected value of some response distribution. Therefore, your observed value is the expected value of the response distribution, plus some variation from the error term.
<span class="math-container">$$E[y\vert X] = \hat{y} = f(X)$$</span>
| https://stats.stackexchange.com |
125,844 | [
"https://dba.stackexchange.com/questions/125844",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/70410/"
] | I have a two node RAC database running in OEL 7 server. If there is a need to change the IP addresses of the already running server to a new one, will that hamper the functioning of the database?
What changes on the database front would I need to incorporate to implement this?
Is it even possible in the first place ... | You can write a function to call from <code>SELECT</code> statement. Below is function definition. Parameter @FYear stands for financial year.
<pre><code>CREATE FUNCTION [dbo].[FiscalDayNum](@currentDate Date,@FYear Int)
Returns smallint
AS
Begin
DECLARE @Q4days Int
IF (@FYear % 400 ) = 0 OR ((@FYear % 4 ) = 0 AND (@F... | The sequence number of a day in a year that begins on april 1 can be calculated this way:
<pre><code>SELECT 1+
DATEDIFF(day,
DATEFROMPARTS(
DATEPART(year, DATEADD(month, -3, [Date])),
4,
1),
[Date]) AS FYdayNumber
FROM tableWithDates;
</code></p... | https://dba.stackexchange.com |
444,504 | [
"https://physics.stackexchange.com/questions/444504",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214721/"
] | <span class="math-container">$$mgh = \frac{mc^2}{\sqrt{1-(v/c)^2}}-mc^2.$$</span>
In dimensional analysis do we just ignore the square root? Or do we solve what’s inside first then we do the square root? Do we say <span class="math-container">$(v/c)^2$</span> is 1 as dimensions cancel? Then say each term now has the ... | Since <span class="math-container">$v/c$</span> is dimensionless, the function <span class="math-container">$1/\sqrt{1-v^2/c^2}$</span> is dimensionless and dimensional analysis gets no information from this factor. It's not so much that you ignore this factor, but just it plays no role in dimensional analysis, just l... | Since:
<span class="math-container">$$ \beta = \frac v c $$</span>
and
<span class="math-container">$$ \gamma = \frac 1 {\sqrt{1-(\frac v c)^2}} $$</span>
are both dimensionless, that are not amenable to dimensional analysis.
In fact, their lack of dimension makes them great "scale factors" telling you how relativ... | https://physics.stackexchange.com |
55,637 | [
"https://physics.stackexchange.com/questions/55637",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6848/"
] | Say we have a constraint system with second-class constraints $\chi_N(q,p)=0$. To define Dirac brackets we need the Poisson brackets of these constraints: $C_{NM}=\{\chi_N(q,p),\chi_M(q,p)\}_P$ . Is the matrix $C_{NM}$ independent of $q,p$?
The motivation of the question is that when I tried to verify Dirac brackets ... | Here is a brief analysis of the problem which involves:
<strong>i) Momentum and the concept of impulse</strong>
<strong>ii) Analysis of a force into two components</strong>
<strong>iii) Moment of a force</strong>
<strong>iv) Moment of inertia and the parallel axis theorem</strong>
For the sake of simplicity let us... | Here are the applicable laws (Newton-Euler equations)
$$ \sum \vec{F} = m \,\vec{a}_G $$
$$ \sum \vec{M}_G = I \dot{\vec{\omega}} + \vec{\omega}\times I \omega $$
where the total torque applied is $\vec M_G = \vec{r}_G \times \vec{F} $ and $\vec{r}_G$ is the vector of the point of force $\vec{F}$ application relati... | https://physics.stackexchange.com |
284,814 | [
"https://physics.stackexchange.com/questions/284814",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/83184/"
] | Consider a mother and her child are in a elevator going down from the 100th floor to the first floor traveling at say 5MPH (or whatever speed). If the mother decides to pick up the child in her arms while going down, would she need to apply more lifting force or less? How about the opposite - going from first to the 10... | The baby and its mother are in a lift moving at a constant speed. So the baby itself (and its mother) are also moving at a constant speed. This means that their acceleration is zero (because the velocity is constant). Because $\vec{F\,} = m\cdot \vec{a\,}$, and $\vec{a\,}=0$, so the net force on the baby ($\vec{F\,}_{\... | Ask yourself this question: what would be different to your question, if anything, if you were the one in the elevator, and the mother and child were in the hallway outside? Does it matter which of you is moving, to determine the force the mother needs? It's obvious that it doesn't matter your motion, so this questio... | https://physics.stackexchange.com |
216,320 | [
"https://mathoverflow.net/questions/216320",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78726/"
] | Let $0< \alpha <1$ and $q>1.$
Consider the (alternating) series: $$
\sum_{k=1}^\infty
(-1)^k \frac{q^k (q^k-1)^\alpha}{(q^k-1)\dots (q-1)}.$$
Denote its sum by $f(q,\alpha).$
Prove (or disprove) that $f(q,\alpha)\neq 0$ for all
$\alpha\in(0,1)$ and all $q> 1.$
Computer computation confirms that ther... | I have no doubt that you have figured this exercise out by now but let me post the solution just for the fun of it.
Denote <span class="math-container">$U_k=\prod_{m=1}^k\frac 1{q^m-1}$</span> with the usual convention <span class="math-container">$U_0=1$</span>.
We have <span class="math-container">$\prod_{k\ge 1}(1... | Mathematica claims that your sum at $q=2, \alpha=1/2$ is $-0.519219,$ and in fact this is the minimal value when $1<q<2$ and $1/2<\alpha < 1.$ It seems to indicate that the sum at $a=1, q=2$ IS equal to zero (but that is the max over the same region). However, what is even better, is that the sum at $a=3/2,... | https://mathoverflow.net |
408,311 | [
"https://softwareengineering.stackexchange.com/questions/408311",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I've joined a small software development team to work on an existing code base. While I am tasking myself with learning the required programming languages and actually reading the code, I'm wondering if there are things software engineers would recommend I do in order to efficiently get up to speed on working with an u... | It depends on your strengths.
<ul>
<li>Some people learn best through tinkering. Taking the code, compiling it, poking at it somewhere, looking at the result, repeat as necessary.</li>
<li>Some people learn best through mapping. They find the entrypoint, then start following the flow to important bits of code, gettin... | Some common techniques you may find useful include:
<ul>
<li>Run the application with a debugger attached and step through the core parts of the code that way. This way, you can see a slow motion view of data flowing through the application as it runs. This should help better understand which parts of the code are res... | https://softwareengineering.stackexchange.com |
152,610 | [
"https://cs.stackexchange.com/questions/152610",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/122013/"
] | I have a list of apps the user has installed, a history of all previously opened apps, and a series of characters that the user has input.
The user is shown a list of apps filtered taking into account the input, the specific function should be given, but the app the user wants must never be filtered out. The list of ap... | <strong>An <span class="math-container">$O(n\log n)$</span> solution:</strong>
Sort the second list. For every element of the first, let <span class="math-container">$e$</span>, find the two elements just smaller and just larger than <span class="math-container">$-e$</span>, by dichotomic search. Then keep the smallest... | A solution that will often take not much more than n operations (but no guarantee):
<ol>
<li>In constant time find the range of both arrays, like -7 .. 6 and -2 .. 9 in the example.</li>
<li>Calculate the number of sums (16 in this case).</li>
<li>Make a guess for the smallest absolute difference say 2 in this case.</l... | https://cs.stackexchange.com |
24,955 | [
"https://physics.stackexchange.com/questions/24955",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8061/"
] | As the title suggests, I know collision of galaxies happens. Questions are
<ol>
<li>Why do they collide (obviously because of gravity, but in what conditions)?</li>
<li>Aftermath of the collision?</li>
<li>If there is a super massive blackhole in the center of the galaxies, what happen to them?</li>
</ol>
| Galaxies collide due to gravatational entanglement, same as more solid objects, as well as simple trajectory bringing them close enough to interact. Andromeda and the Milky Way are likely to collide, or possibly graze close enough for some interaction, sometime in the 2-5 billion year range (opinions vary), so we're go... | It takes millions of years for galaxies to collide so even though they're mainly gas and dust they have a weak force of attraction. Also as you mentioned in your question they have a super massive black hole in the middle that pulls them together and drags the rest of the galaxy with them.
It's also incredibly unlikel... | https://physics.stackexchange.com |
30,192 | [
"https://quant.stackexchange.com/questions/30192",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/11723/"
] | Often when I am reading about options pricing (and/or options greeks) the square root of time continually comes up. What the mathematical justification for why this keeps on turning up?
| For any process with independent increments, by the very fact of statistical independence the variance of $x_{t3}-x_{t1}$ is going to be the sum of the variances of $x_{t2}-x_{t1}$ and $x_{t3}-x_{t2}$ for $t1\leq t2 \leq t3$. Many processes have independent increments, including ABM, GBM, Poisson, etc. Then if you add... | The reason is that in many common models including geometric Brownian motion, the variance of the logarithmic returns is proportional to time. Thus, their standard deviation/volatility is proportional to the square root of time.
Consider for example the class of Levy models where $X$ is is the logarithmic stock price ... | https://quant.stackexchange.com |
107,939 | [
"https://dba.stackexchange.com/questions/107939",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/70964/"
] | I have a cursor defined as:
<pre><code>DECLARE idCursor CURSOR
FOR SELECT DISTINCT [id], [data]
FROM #tempTable
</code></pre>
And I have a variable defined as:
<pre><code>DECLARE @currentId TABLE (
[id] int,
[data] char(1)
... | No, you can't fetch scalar values from a cursor row into a table variable. You would have to declare the variables, fetch into them, and then insert:
<pre><code>FETCH NEXT FROM idCursor INTO @id, @data;
INSERT @currentId([id],[data]) SELECT @id, @data;
</code></pre>
However, perhaps it's the case that you don't need ... | Simple example using cursor:
<pre><code>DECLARE @CustomerID as INT;
declare @msg varchar(max)
DECLARE @BusinessCursor as CURSOR;
SET @BusinessCursor = CURSOR FOR
SELECT CustomerID FROM Customer WHERE CustomerID IN ('3908745','3911122','3911128','3911421')
OPEN @BusinessCursor;
FETCH NEXT FROM @BusinessCursor INT... | https://dba.stackexchange.com |
2,075,122 | [
"https://math.stackexchange.com/questions/2075122",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/360589/"
] | While going through many proofs in graph theory, I noticed that for proof of statement like
<blockquote>
a if and only if b
</blockquote>
we need to prove
$a \rightarrow b$ and $b \rightarrow a$.
We know
$$ a\rightarrow b ={a}'+b$$
and
$$b\rightarrow a ={b}'+a $$
also
$${a}'\rightarrow {b}'=a''+b'=... | You are correct. Proving the contrapositive is equivalent.
| Another way to see it:
If you prove the following two statements:<br>
$\begin{align}
a &\implies b \\
\text{not }a &\implies \text{not }b
\end{align}$
... you have shown that $a$ and $b$ are either both true or both false; the two statements are in lockstep. $a \mathord\iff b$.
| https://math.stackexchange.com |
51,562 | [
"https://engineering.stackexchange.com/questions/51562",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/36689/"
] | The snow load duration factor is 1.15 times the standard 10-year sustained maximum load rating as long as the accumulated time under this load is not more than 2 months. Does this mean that
<ol>
<li>a. the snow load being at the duration factor of 1.15 for 2 months continuously (experimental
case) is at the same level ... | The problem is you deciding to push the limit in one area and the owners will have to know that and maintain all the supports for the roof that entire 100 or 1000 years. Not likey, and it isn't collapse that is the outcome, it's FAILURE. One small part failing that isn't visible starts the process and then a portion of... | Timber structures are somewhat unique in that their strength and serviceability characteristics are adversely affected by the duration of time that the structure will carry a specific load. Normal load duration is ten years. This doesn’t mean that the specific load will be applied for ten consecutive years. Load durati... | https://engineering.stackexchange.com |
192,001 | [
"https://mathoverflow.net/questions/192001",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6094/"
] | I have a need to find a polynomial of minimal degree that connects
two points and stays within a given
"corridor," by which I mean an $x$-monotone polygon.
Here is an example:
<hr />
<img src="https://i.stack.imgur.com/Sqgf6.jpg" alt="Interp">
<hr />
The point $s=(0,3)$ needs t... | A much more efficient approach can be based on semidefinite programming feasibility testing. Namely, it is well-known that global nonnegativity of a
degree $2d$ polynomial $g(x)$ is equivalent to existence of a decomposition of $g$ into a sum of squares of polynomials, which in turn is equivalent to existence of a post... | The ellipsoid method applies to this problem: once you fix a degree, the space of polynomials threading through your corridor is a convex set. Given any polynomial, if there is a point on the graph which lies outside the corridor then that point provides a linear inequality (i.e. hyperplane) separating your polynomial ... | https://mathoverflow.net |
79,305 | [
"https://physics.stackexchange.com/questions/79305",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20281/"
] | This is a strange question I would like to have some explanation accompanied with:
We have an ice block, with in it a lead block. This entire block is put into a glass of water, resulting in a rise of water level until the edge of the glass. The block stays floating on the surface.
What will happen with the water leve... | OK, please comment on my final judgement on this question:
The Ice with lead in it will sink deeper than normal, so when all the ice will melt, it will not replace all the lost water. The lead is there from the beginning on, taking in the volume of the ice, so it will principally stay there. When all the ice is molten... | Let's deal first with a pure ice cube.
A 100 gram ice-cube (pure water) is floating in a glass of pure water, filled to the very top. By buoyancy laws the ice-cube must be displacing exactly 100 grams of pure water from the glass. The volume of the ice-cube that is below the water level is the volume of 100 grams of... | https://physics.stackexchange.com |
381,976 | [
"https://softwareengineering.stackexchange.com/questions/381976",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/45576/"
] | Suppose I have a loop (in Python syntax):
<pre><code>xml = "<x>...</x>"
for i in arr:
j = f(x) # some complex computation
obj = Class(i, j)
xml = obj.run(xml)
</code></pre>
Does it make sense to use dependency injection for <code>Class</code> in this situation? If yes, what is the proper way ... | Likely, you really don't need any dependency injection here. But if you do, then simply injecting via a function parameter is the simplest way to go in Python. Remember: in Python, all variables incl. class names are resolved at run time, so you can pass class objects around as ordinary variables. For example:
<pre><c... | It definitely makes sense (think unit tests, among other reasons). The counterargument would be exposing the dependency can expose implementation details. Exposure can be mitigated by providing a sensible default (set default field values within constructors, or default arguments to methods/functions, depending on lang... | https://softwareengineering.stackexchange.com |
76,524 | [
"https://mechanics.stackexchange.com/questions/76524",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/46687/"
] | I am building a 450-500 hp honda civic with a d16y8 head, i purchased brand new valves , and i was wondering how do I get these valves to seat and seal the chamber for combustion? Is lapping the valves effective enough to ensure the head will hold compression or do I have to go the extra mile and get some precision ma... | If you lap them in and get a proper seal then machining is not needed.
If the new valves are supplied without the final surfaces angled correctly i.e. as a “blank”, then they need machining.
| Since it is high performance, I would let a reputable automotive machine shop do a 3 angle valve job. Better flow and performance and everything gets checked, including checking for cracks in the aluminum head. Have it surfaced for a good head gasket seal also.
Find a machine shop that has experience in performance wo... | https://mechanics.stackexchange.com |
518,493 | [
"https://physics.stackexchange.com/questions/518493",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/105078/"
] | So I was calulating the matrix element of an interaction and arrived at the following contraction
<span class="math-container">$$\gamma^\mu_{ab}\gamma_{\mu\,cd}$$</span>
With <span class="math-container">$a,b,c,d$</span> spinor indices that are never contracted with each other through other matrices. I know that in <... | To derive an expression for <span class="math-container">$\sum_\mu\gamma^\mu_{ab}\gamma_{\mu\ cd}$</span>, note that this is equivalent to requesting an expression for
<span class="math-container">$$
\sum_\mu\text{trace}(X\gamma^\mu Y\gamma_\mu)
$$</span>
for aribtrary matrices <span class="math-container">$X$</span>... | Let's expand on @Chiral Anomaly's answer via taking a look at a concrete example.
In 2D, one would have the traceless property:
<span class="math-container">$$
\sum_\mu\gamma^\mu\gamma^\sigma\gamma_\mu = 0
$$</span>
which can be verified easily, e.g.
<span class="math-container">$$
\sum_\mu\gamma^\mu\gamma^0\gamma_\mu... | https://physics.stackexchange.com |
65,406 | [
"https://mechanics.stackexchange.com/questions/65406",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/34172/"
] | The tire shop balanced my tires at 41 psi, when my recommended psi is 30. I have since lowered it to specification, but would this throw off the balance?
| No. Balance is caused by even weight distributed around a tire.
If there is more weight in one spot the tire will "wobble" when spun.
Inflating a tire more may alter the diameter, but the weight of the tyre itself is still in the same relative place.
| It won't affect wheel balance, but high tyre pressures will give you a much harder ride, so any bumps & stones etc.. even smaller ones may well be felt through the steering wheel and come across as vibration. Lower the tyre pressures to the correct specs, if you still feel that there is a balance issue just have th... | https://mechanics.stackexchange.com |
1,121,010 | [
"https://math.stackexchange.com/questions/1121010",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/142968/"
] | Given that $P(F)$ is the set containing all polynomials with coefficients from field $F$, I am given the following:
$W_1$ is the set of all polynomials $f(x)$ in $P(F)$ such that for:
$$f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$$
$a_i=0$ if $i$ is even. Similarly, $W_2$ is the set of all polynomials $g(x)$ in $P(F)$ ... | Make sure you understand the definition of $\oplus$; $W_1\oplus W_2$ is very different from $W_1 \cup W_2$! For example, $\mathbb R^2$ is the direct sum of the $x$-axis $=$Span$\left\{\begin{pmatrix}1 \\ 0\end{pmatrix}\right\}$ and the $y$-axis, but it certainly isn't the union of the axes.
| You just have to separate the even powers from the odd powers, as in this example:
$$a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5=(a_1x+a_3x^3+a_5x^5)+(a_2x^2+a_4x^4).$$
| https://math.stackexchange.com |
130,805 | [
"https://mathoverflow.net/questions/130805",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24309/"
] | Consider the <span class="math-container">$\mathbb Z$</span>-module <span class="math-container">$\mathcal Z$</span> obtained as the set of sequences of integers <span class="math-container">$\mathbb Z ^ \mathbb N$</span> modulo the relation that two sequences are deemed equivalent when their difference is <span class... | This abelian group, which can also be described as the quotient of the direct product $\prod_{\mathbb N}\mathbb Z$ by the direct sum $\sum_{\mathbb N}\mathbb Z$, is isomorphic to the direct sum of the following two pieces. The first piece is a torsion-free, divisible abelian group (so you can view it as a vector space... | Do you mean by "the difference is stationary to 0" that the sequences are eventually equal,
i.e., equal from some point on?
This structure has been looked at quite a bit in the guise of a quotient of
$\mathbb N^{\mathbb N}$.<br>
This structure obviously does not have the algebraic structure you are looking for,
but t... | https://mathoverflow.net |
29,969 | [
"https://dba.stackexchange.com/questions/29969",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/15955/"
] | I'm trying to execute this script from Management Studio:
<pre><code>GRANT ALTER ON ROLE::[AdaptTemplate] TO [AdaptAdmin] AS [AdminSapr]
</code></pre>
Execution fails with this message:
<blockquote>
Msg 15151, Level 16, State 1, Line 1 Cannot find the role
'AdaptTemplate', because it does not exist or you do not... | This is happening because the principal in the AS clause needs to have the permission with the "GRANT OPTION". Running this will allow you to run your original code:
<pre><code>GRANT ALTER ON ROLE::[AdaptTemplate] TO [AdminSapr] WITH GRANT OPTION
</code></pre>
My reading of Books Online made me think that what you'r... | I have the same issues. It was mentionned to use the with grant options but correct me if I'm wrong but if you add with grant options you also permit that users to grant others permissions when it might not be what you want.
| https://dba.stackexchange.com |
1,963,194 | [
"https://math.stackexchange.com/questions/1963194",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/319190/"
] | An interviewer is given a list of people she can interview. If the interviewer needs
to interview 6 people, and if each person (independently) agrees to be interviewed
with probability 3/4, what is the probability that her list of people will enable her
to obtain her necessary number of interviews if the list consists ... | The interviewer doesn't want 6 successes, she wants <em>at least</em> 6 successes. The key is:
<blockquote>
her to obtain her necessary number of interviews
</blockquote>
If she has 7 interviews, that's fine. If she has 8 that's fine too, etc.
| In the Bernoulli distribution: X~Bernoulli(10,3/4), P(X=6) gives the probability that EXACTLY 6 people accept to be interviewed. Since you want the probability of her obtaining at least 6 people, the answer is:
P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10), as stated.
| https://math.stackexchange.com |
138,736 | [
"https://electronics.stackexchange.com/questions/138736",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/58373/"
] | Why do resistors in series add-up? Is there any visualization equivalent of that? I have in mind electrons as cars driving on the highway, now a resistor could be a narrow spot (R1) where cars are moving slower, if I will "add" another congestion point R2 (resistor), after the first one, the cars that had already past... | Your car analogy is almost there, but not quite.
Instead of a single length of road, imagine instead a racetrack.
That racetrack is packed with cars, end to end, wall to wall. No space between them.
Now there are some narrow points on the racetrack. Each narrow point is a resistor. Each car is an electron.
The ca... | The cars analogy doesn't model what's going on.
A better analogy is water in a pipe. Let's say you have a pump (like voltage source) that keeps a constant pressure from one end of a pipe to the other. With just a section of open pipe, the flow rate (like electric current) will be quite high.
Now imagine installing ... | https://electronics.stackexchange.com |
2,684 | [
"https://stats.stackexchange.com/questions/2684",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1290/"
] | I am using g*power to calculate the a priori power for a 2 group repeated measures anova with a continuous dependent variable with 3 time points. I think that higher values for the "correlation among rep measures" should indicate a better test (i.e., high test-retest correltaion) and thus yield better power and a lowe... | Higher correlation within subject gets you more power when the test being done is a differencing, equivalent to a paired t-test. The standard deviation used in calculating effect size is multiplied by $\sqrt{1-\rho}$. The standard deviation for difference scores (for a one-sample test) is $SD\sqrt{2-2\rho}$. This al... | <ul>
<li>All else being equal, bigger correlations in a repeated measures design means more power</li>
<li>A larger correlation means that more of the variance in the dependent variable is explained by systematic effects of cases/individuals</li>
<li>Prior research or previous datasets are useful for estimating the cor... | https://stats.stackexchange.com |
366,393 | [
"https://softwareengineering.stackexchange.com/questions/366393",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/296906/"
] | Among other things, the CQRS has a rule that each of the methods has one responsibility. So we can't have this in the model:
<pre><code>public class Store {
public Item getOrCreateItem(int id)
{
//logic
}
//....
}
</code></pre>
and this in the controller:
<pre><code>Store store = new Store(... | Oh for crying out loud.
The controller has no business knowing what your implementation of <code>getThingy()</code> has behind it. Whether <code>getThingy()</code> creates or passes out a cached copy is none of it's business. The only reason this implementation detail leaked out of the store and into the controller w... | Typically, one would have a Service which would provide this sort of functionality. The Controller would call something like StoreService.EnsureItemExists(1).
The model should probably not do much either - most of the business logic should reside in the service.
| https://softwareengineering.stackexchange.com |
3,384,022 | [
"https://math.stackexchange.com/questions/3384022",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/122510/"
] | If I have a compact connected set in <span class="math-container">$\Bbb R^2$</span>, and I'm examining the boundary points of this set. Is it true that around every cusp/corner on the boundary, there's an open interval where the boundary is smooth? This seems intuitive to me, but I don't know if it's true.
I.e.: is it... | If <span class="math-container">$x\in E$</span> then <span class="math-container">$x\in E_1$</span> but for every <span class="math-container">$k$</span> we have <span class="math-container">$x\notin E_k-E_{k+1}=G_k$</span> hence <span class="math-container">$x\notin\bigcup_{k=1}^{\infty}G_k$</span>.
So if <span clas... | Well you can see that <span class="math-container">$G_k\cap E=\emptyset$</span> since <span class="math-container">$E\subseteq E_{k+1}$</span> and <span class="math-container">$G_k\cap E_{k+1}=\emptyset$</span> for all <span class="math-container">$k$</span>. Thus <span class="math-container">$\bigcup G_k\cap E=\emptys... | https://math.stackexchange.com |
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