qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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6,735 | [
"https://chemistry.stackexchange.com/questions/6735",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/2196/"
] | Physical chemistry is easy to study as I have to just understand the concepts (like in physics) and apply some equations for calculations. In organic chemistry, reaction mechanisms helpsin remembering a lot of reactions and also doing conversion problems help a lot.
But, in the case of inorganic chemistry it is very ... | In organic chemistry, everything is based around C, H, O and N. Therefore to understand reactivity (somehow), there is just limited number of options.
In contrast, inorganic chemistry deals with the rest of periodic table, and each of the elements has its special properties. But there are general trends as well, but a... | Let me tell you how I have managed to, with about 85-90% accuracy, been able to predict a large number of inorganic reactions. There are some prerequisites to do this. They are as follows:
<strong>1. The Periodic Table:</strong> You need to learn the stable oxidation states and configurations of ions. For instance, pr... | https://chemistry.stackexchange.com |
332,160 | [
"https://mathoverflow.net/questions/332160",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11145/"
] | Suppose <span class="math-container">$\mathcal L \subseteq \mathcal L’$</span> are first-order languages, <span class="math-container">$\kappa$</span> is a cardinal, and <span class="math-container">$T’$</span> is a theory in <span class="math-container">$\mathcal L’$</span> that is <span class="math-container">$\kappa... | The answer is no, one can lose categoricity in a reduct of a theory. Consider the following example.
Consider the theory <span class="math-container">$T$</span> describing a bijection between two disjoint infinite
predicates <span class="math-container">$f:A\to B$</span>. So a model consists of two disjoint parts, th... | One can also break countable categoricity when <span class="math-container">$|\mathcal{L}'|>{\aleph_0}$</span>. This example comes from an undergraduate course I took with Malliaris.
Let <span class="math-container">$\mathbb{P}$</span> be the collection of primes and let <span class="math-container">$\mathcal{P}(\... | https://mathoverflow.net |
100,783 | [
"https://physics.stackexchange.com/questions/100783",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/38242/"
] | So, I was playing hill climb racing and I noticed that if we move with high speeds towards a ramp going down we just jump it off. While lower speeds, help us to stay in contact with the ramp.
<img src="https://i.stack.imgur.com/DYQew.png" alt="enter image description here">
Sticks :
<img src="https://i.stack.imgur.co... | Consider centre of mass of cylinder to perform circular motion about that point :
$ \frac{Mv^2} R = Mgcos\theta - N$
$\frac 2 3 M((gR(1-cos\theta) + u^2) = Mgcos\theta -N$
$N=\frac 2 3 M((gR(1-cos\theta) + u^2) - Mgcos\theta$
<strong>Condition</strong> : $\frac 2 3 M((gR(1-cos\theta) + u^2) - Mgcos\theta \geqslant ... | Suppose the ramp wasn't there, then the trajectory of the object would the same as if it fell off a cliff:
<img src="https://i.stack.imgur.com/zLVs8.gif" alt="Cliff">
To get the equation of motion you simply note that the horizontal and vertical coordinates are given by (neglecting air resistance):
$$ x = ut $$
$$ ... | https://physics.stackexchange.com |
733,025 | [
"https://physics.stackexchange.com/questions/733025",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/348775/"
] | I am trying to understand the necessity of density matrices and the notion of "mixed states" in quantum mechanics (I read all the other posts about this, I promise).
As far as I understand, one could motivate these notions as follows:
Let <span class="math-container">$H_1$</span> and <span class="math-contain... | Imagine that Alice has a qubit in the state <span class="math-container">$$|\psi\rangle = \alpha |0\rangle + \beta|1\rangle.$$</span> She measures her qubit in the computational basis <span class="math-container">$\{|0\rangle, |1\rangle\}$</span>, obtaining the outcome <span class="math-container">$|0\rangle$</span> wi... | There are a lot of reasons. Here's one. We sometimes want to couple a small quantum system to a very <em>large</em> one, like a two-level atom interacting with the (quantized) electromagnetic field (perhaps in its vacuum state so that we are modeling spontaneous emission). The large system has <em>many</em> degrees ... | https://physics.stackexchange.com |
735,564 | [
"https://physics.stackexchange.com/questions/735564",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <blockquote>
A man holds in his hands two equal masses with outstretched arms, standing on the center of a platform that rotates with a certain angular velocity. If you drop both of the masses without moving your arms, what happens to the angular velocity of the man and the angular velocity of the masses?
</blockquote>... | <blockquote>
I read in a couple of papers that there won't be any field detected by such observer, but this is not demonstrated and sounds strange to me. The reasoning of these papers is that the electromagnetic tensor is invariant, so if it is zero in the inertial frame it will be zero also in the non-inertial one.
Bu... | After thinking a bit now I think there should be an electric field inside: electromagnetic tensor depends on the charge density, and this changes in the reference frame of the sphere due to the fictious force drive, so should not be invariant: hope I'm not saying blasphemies. Anyway, for a mechanical reasoning I should... | https://physics.stackexchange.com |
21,134 | [
"https://electronics.stackexchange.com/questions/21134",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5697/"
] | I am wondering since there are so many functions an ALU need to do, how might I start implementing one (a homework where I am supposed to implement a MIPS system with Logisim, using basic Gates, Flip-flops etc).
The part I am confused about is how can I implement an ALU which can do different functions like Add/Subtr... | While internally computing all the answers, and then using a mux to select among them will work, it certainly is not a minimal design.
Consider that you can bit-slice the problem; instead of a single block of logic with two 8 bit inputs, you could partition this as two 4-bit sections, as long as you can link them to ... | Yes, you need more control logic.
Your previous assignment was purely <em>arithmetical</em> (is that a word?), so you could use a single adder and massage the inputs using the control signals to create the functions you want
Your new functions are <em>logical</em>, so you need another block to perform logical operati... | https://electronics.stackexchange.com |
325,872 | [
"https://physics.stackexchange.com/questions/325872",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/152648/"
] | If I am riding a bike on top of a train will the speed of the bike relative to the train and the speed of the train relative to the ground be added?
For example: bike going 5mph train going 50mph. If I used a speedometer would I be going 55mph or 5mph?
| Your speedometer would read 5 mph as it measures your speed as apposed to the surface of the train. A traffic cop with a radar gun would measure the train at 50 mph and you at 55 mph relative to his stationary position. If the traffic cop was driving at 55 mph in the same direction as you he would measure your speed as... | The speedometer would read 5mph because it measures speed according to the ground it's on. If you were to lift your bike up off the ground and you rid it, the speedometer wouldn't say 0mph even though you aren't really moving.
| https://physics.stackexchange.com |
2,119,929 | [
"https://math.stackexchange.com/questions/2119929",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/338817/"
] | Whenever I try to learn about a relationship, I try to reason intuitively why a theorem or lemma should make sense. I know often times this is increasingly difficult to achieve. However, I have the following:
Let $ L: \mathbb{V} \to \mathbb{W} $ be a linear mapping. $L$ is one-to-one if and only if Ker($L$) = $\{\vec{... | I try to see it like this:
The kernel $K$ of a linear map $L:V \to W$ is a kind of universal fiber. The mathematical version of this is that the fiber $L^{-1}(w)$ of $w$ is $v + K$, for any $v$ with $L(v)=w$. So the fiber is essentially a translated version of the kernel.
To represent this pictorially, I imagine $K$... | If $f$ is not injective, there are $v\ne w$ such that $f(v)=f(w)$. By linearity, then, $f(v-w)=0$, so the kernel contains $v-w$. But this is nonzero because $v\ne w$.
I find this pretty intuitive. The key underlying fact is that <strong>a linear function applies in the same way to differences between vectors as to vec... | https://math.stackexchange.com |
40,255 | [
"https://chemistry.stackexchange.com/questions/40255",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/17011/"
] | If I react the following with Raney nickel and $\ce{H2}$,
$\hspace{65 mm}$<img src="https://i.stack.imgur.com/oXxFm.png" alt="alkene">
then I am getting a meso compound, as the $\ce{H-}$ anion will have anti addition, right? One $\ce{H}$ will attack on right $\ce{C}$ from bottom and the other on the left $\ce{C}$ fro... | The hydrogenation of alkenes using heterogenous catalysts such as Raney nickel is <em>syn</em>-stereospecific; i.e. both hydrogen atoms are added to the same face of the double bond.
Therefore, the hydrogenation of (2<em>E</em>)-(2,3-<sup>2</sup>H<sub>2</sub>)but-2-ene yields
(2<em>R</em>,3<em>R</em>)-(2,3-<sup>2<... | Good old paper drawing has blindsided you. Think of the $\ce{H2}$ as adding on top of the molecule as you have drawn it on paper. Not all the molecules know that they are supposed to land "right-side" up.
<img src="https://i.stack.imgur.com/4OHpb.png" width="500" height="300" alt="right sideup drawing">
Some will la... | https://chemistry.stackexchange.com |
822,542 | [
"https://math.stackexchange.com/questions/822542",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/147985/"
] | How to integrate: $\int_0^T\cos(T-s)\sin(s)ds$? I was trying to use $\cos(a+b)=\cos a\cos b-\sin a\sin b$ and substitute $\cos(s)=u \Rightarrow \sin(s)ds=du$ but it does't help.
| No. For example, suppose $\mu$ is Lebesgue measure on $\mathbb R$ and
$d\nu(x) = \exp(-x) d\mu(x)$. The indicator functions of intervals $[n,n+1]$
form a closed set in $L^1(\mu)$ (because any two have distance $2$), but converge to $0$ in $L^1(\nu)$.
| Let $\mu$ be Lebesgue mesure on $[0,1]$ and let $\nu$ be defined by $d\nu(x)=\sqrt{x}d\mu(x)$. Then $1/x \in L^{1}(\nu)$, but $1/x \notin L^{1}(\mu)$. $L^{1}(\mu)$ is not closed in $L^{1}(\nu)$, though $L^{1}(\mu)\subset L^{1}(\nu)$ and $L^{1}(\mu)$ is dense in $L^{1}(\nu)$. You have $\mu \ll \nu \ll \mu$, and both mea... | https://math.stackexchange.com |
95,951 | [
"https://physics.stackexchange.com/questions/95951",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/36559/"
] | Does increasing the amount of electric charge on a conductor cause an increase in its <em>electric potential</em> to a point at which it becomes maximum; where it can hold no more extra charge?
Is it true? How?
I read it from a book while studying <em>capacitance</em>.
Does this idea sound <em>foolish</em>?
| In principle, you can charge a conductor indefinitely.
But remember that in order to cause a flow of charges from a body (call it a 'source') to another (the conductor in question), the potential of the former has to be lower than the potential of the latter.
This potential difference causes a current to flow from t... | For all conductors we can define a constant called the Capacitance such that,
$$Q=CV$$ where $Q$ is the total charge on the conductor and $V$ is its potential.
<em>So yes,increasing the charge on a conductor increases its potential.</em>
However,as the charge on the conductor increases,so does the electric field nea... | https://physics.stackexchange.com |
477,364 | [
"https://physics.stackexchange.com/questions/477364",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208833/"
] | For example, the proton beams in the LHC collider have 7 TeV energy. Does this mean that the individual protons in the beam have 7 TeV energy or that the energy of all the protons in the beam add up to 7 TeV?
| In the LHC, each individual collision has a center-of-mass energy of roughly 14 TeV. Since the collisions are symmetric (two protons with equal energy, moving in opposite directions, collide), we can say that <strong>each individual proton</strong> has roughly* 7 TeV of energy.
As you can probably tell, adding up the ... | Collision experiments are done to create particles that can not be studied under normal circumstances. Energy and momentum conservation as well as the famous Einstein equation <span class="math-container">$E=mc^2$</span> tell us that a heavier particle can not just "pop out of thin air". But if we let two particles wit... | https://physics.stackexchange.com |
118,875 | [
"https://chemistry.stackexchange.com/questions/118875",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/80063/"
] | Our instructor told us that prior to the equivalence point, the <span class="math-container">$\mathrm{pH}$</span> of a solution is dependent on the HH equation. However, when I tried practicing for polyprotic acid titration, I came upon this problem that does not make any sense at all. When I'm using the HH equation, t... | The key approximation made in deriving the Henderson-Hasselbalch equation is that the equilibrium constant can be written as <span class="math-container">$$K=\frac{c_{H^+}c_{A^-}}{c_{HA}}$$</span>
that is, we assume activity coefficients are unity. If you take the base-10 logarithm of this equation and rearrange terms ... | For the derivation of the Hendersson-Hasselbalch equation, it is assumed that both hydronium and hydroxide ions are minor species, i.e. there concentration is low compared to that of the buffer species.
In your exercise, the hydronium ion concentration (according to your calculation) is about 0.03 M or higher. With a ... | https://chemistry.stackexchange.com |
1,838,584 | [
"https://math.stackexchange.com/questions/1838584",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/272986/"
] | <blockquote>
Let <span class="math-container">$A = \begin{bmatrix}1&-5&3&-3&-4&-2\\0&0&1&1&0&-5\\0&0&0&0&1&-3\\0&0&0&0&0&0\end{bmatrix}$</span>
Describe all solutions of <span class="math-container">$Ax = 0$</span>
<span class="math-contain... | Notice that there are no pivot columns for columns $2,4,6$, i.e. the columns do not have a leading $1$.
Thus, we let the following corresponding components of the vector $\vec{x}$ be free: $x_2=r,x_4=s,x_6=t$ where $r,s,t\in \mathbb{R}$.
We know solve for $x_1,x_3,x_5$ in terms of these free variables.
\begin{align}... | From the already row-reduced matrix you can see that $x_2,x_4,x_6$ are free variables because the columns are missing leading $1$'s.
<br/>From row $3$, you can get $x_5-3x_6=0$, so $x_5=3x_6$<br/>
From row $2$, $x_3+x_4-5x_6=0$, $x_3=-x_4+5x_6$
From row $1$, $x_1-5x_2+3x_3-3x_4-4x_5-2x_6=0$, $x_1=5x_2-3x_3+3x_4+4x_5+2x... | https://math.stackexchange.com |
303,873 | [
"https://physics.stackexchange.com/questions/303873",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/141502/"
] | I am currently reading <em>A Universe from Nothing</em>, by Lawrence M. Krauss, and I have come across a concept that I found confusing:
<blockquote>
Now, if gravity is an attractive force, then it should be slowing the expansion of the universe. This means the galaxy we see moving away from us at $500$ kilometers/s... | If I'm following your question, you're misunderstanding acceleration or, more accurately, deceleration and velocity.
Before the discovery of dark energy the observation was that the universe was flying apart in a uniform manor, where the further away galaxies were the faster they were moving away, which implies, if yo... | UserLTK's answer is correct but Id like to expand on it. It is not simply expanding out and decelerating or accelerating. The speed at which galaxies are flying away from each other increases as their distance increases, and that is an important and not obvious factor.
We know this because as the galaxies get further... | https://physics.stackexchange.com |
136,724 | [
"https://physics.stackexchange.com/questions/136724",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59626/"
] | As the title asks: How close can you get to lava before burning?
I know that it depends on an number of factors; speed of lava flow, wind direction/strength, type(?) of lava flow (related to speed, in part, I think?). I'm guessing it also depends on the person and what they're wearing.
I'd be looking for an actual di... | The factors that most matter when you are near lava:
<ol>
<li>The fractional solid angle of lava as subtended at the observer ("how much lava do you see")</li>
<li>The temperature of the lava</li>
<li>The reflectivity of the clothing you are wearing</li>
<li>Any effect of air flow (wind blowing towards lava or away fr... | I got close enough to slowly flowing lava to stick a rock hammer in it, but you had to pull back quickly -- it felt like a bonfire. It was tolerable 8 feet away. The lava was about 6 inches thick, oozed less than an inch per second and showed orange-red on an advancing toe that was only about six inches in diameter. ... | https://physics.stackexchange.com |
384 | [
"https://datascience.stackexchange.com/questions/384",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/97/"
] | I have a binary classification problem:
<ul>
<li>Approximately 1000 samples in training set</li>
<li>10 attributes, including binary, numeric and categorical</li>
</ul>
Which algorithm is the best choice for this type of problem?
By default I'm going to start with SVM (preliminary having nominal attributes values co... | It's hard to say without knowing a little more about your dataset, and how separable your dataset is based on your feature vector, but I would probably suggest using extreme random forest over standard random forests because of your relatively small sample set.
Extreme random forests are pretty similar to standard ran... | For low parameters, pretty limited sample size, and a binary classifier logistic regression should be plenty powerful enough. You can use a more advanced algorithm but it's probably overkill.
| https://datascience.stackexchange.com |
540,485 | [
"https://physics.stackexchange.com/questions/540485",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/184767/"
] | How can photons have different energies if they have the same rest mass (zero) and same speed (speed of light)?
| Some areas of physics are counter-intuitive. For them, your everyday experience is a poor guide to how the universe really works. This is one of those areas.
Photons have no mass. They all have the same speed. Yet they have energy and momentum, and it isn't the same for all photons.
If you are used to <span class="ma... | The only difference between the two is the energy they have.
<span class="math-container">$$
E=\frac{hc}{\lambda}
$$</span>
As you can see from the equation above, different energies means different wavelengths. Different wavelengths means different colors.
It is important to know that even though photons are always... | https://physics.stackexchange.com |
203,930 | [
"https://softwareengineering.stackexchange.com/questions/203930",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/81495/"
] | I've been working in the software industry for a few years now. I've seen Waterfall in practice, and I've seen several projects attempt Agile with varying degrees of success... which got me thinking.
What are the bare-minimum requirements for an Agile startup to be successful? I'm thinking in terms of tools, practic... | <h2>Tools</h2>
You definitely will need <strong>source control</strong>. Preferably one that includes a web interface so that every day you can start off by seeing what people have checked in recently.
You will need a <strong>team space</strong> where your developers, QA, and product owners can work together to deliv... | While I won't argue with any of the suggestion @BryanOakley has already put forth, I would like to point out that in the end, the tools don't really matter. What matters is the people you have working on the project.
Each member of the team needs, first and foremost, to be a good communicator. They need to be able t... | https://softwareengineering.stackexchange.com |
5,627 | [
"https://physics.stackexchange.com/questions/5627",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/139/"
] | In the center of our milky way, it is assumed that a black hole exists with a mass of $\approx 4\times 10^6$ times our sun's mass. How much light bending (in degrees) would arise for stars that are in perspective near the position of this black hole in the sky?
Could the mass of a black holes become so great that it a... | The general theory of gravitational lensing shows that a light ray which approaches within a radius $r~>>~2GM/c^2$ will be deflected approximately by an angle $\theta~=~GM/rc^2$. In a more general setting the deflection of light is given by the Einstein angular radius
$$
\theta_E~=~\sqrt{\frac{4GM}{c^2}\frac{d_{... | Famously, stars near the sun are deflected 1.75 arc seconds, as predicted by Einstein.<br>
I calculate that stars on the other side of the galaxy whose light passed very near the galaxy center would be coincidentally be deflected by about the same amount.<br>
If you observe in the submillimeter band you could see it... | https://physics.stackexchange.com |
39,677 | [
"https://physics.stackexchange.com/questions/39677",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/13000/"
] | Can you explain me what are the differences between the four following subjects?
<ul>
<li>analytical mechanics</li>
<li>rational mechanics</li>
<li>classical mechanics</li>
<li>theoretical mechanics</li>
</ul>
| My understanding of the usage of these terms is obviously not perfect, but I can still try. I have to admit beforehand that I have never encountered the term ‘rational mechanics’, maybe someone more knowledgeable can expand on this.
<h1>Theoretical Mechanics</h1>
This is a term used to differentiate between experimen... | Analytical mechanics is a branch of classical mechanics that is not vectorial mechanics (original Newton's work). Analytical mechanics uses two scalar properties of motion, the kinetic and potential energies, instead of vector forces, to analyse the motion. Analytical mechanics includes Lagrangian mechanics, Hamiltonia... | https://physics.stackexchange.com |
40,076 | [
"https://scicomp.stackexchange.com/questions/40076",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/38499/"
] | Question is mostly related to literature or suggestions.
Given a semi infinite domain: <span class="math-container">$x=[0; +\infty);y=[0; +\infty)$</span>. Willing to transform it to computational domain of: <span class="math-container">$[0,1]\times[0,1]$</span>.
I did find the <span class="math-container">$(-\infty, +... | The LU decomposition will give you what you want with only <span class="math-container">$\tfrac{2}{3}n^3 + \mathcal{O}(n^2)$</span> FLOPs. The linear system is solved by solving two triangular systems. The determinant is the product of the determinants of L and U, which, in turn, are the products of the diagonal elem... | If your matrix <span class="math-container">$A$</span> is close to the identity I guess that you could try the following approximation
<span class="math-container">\begin{align}
\log(\det(I + \epsilon B)) &= \log\det(I + \epsilon_0 B)
+ (\epsilon - \epsilon_0)\operatorname{tr}(B (I + \epsilon_0 B)^{-1}) - (\epsilon... | https://scicomp.stackexchange.com |
158,307 | [
"https://stats.stackexchange.com/questions/158307",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/80499/"
] | I am new to machine learning so I am trying to find some literature but I'm not even sure what to Google for. My data is of the following form:
<pre><code>User A performs Action P
User B performs Action Q
User C performs Action R
...
User C performs Action X
User A performs Action Y
User B performs Action Z
...
</code... | By fitting an lm object you obtain all the necessary components to do this. Mathematically you have estimates:
$$\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right) ^{-1} \left( \mathbf{X}^T y \right) $$
and and estimate:
$$\mbox{vcov}\left(\hat{\beta} \right) = \hat{\sigma}^2 \left( \mathbf{X}^T\mathbf{X} \right) ... | we have
$$
\hat{\beta}\pm t_{\alpha/2,n-2} \sqrt{\frac{MSE}{\sum(x_i-\bar{x})^2}}
$$
then
<pre><code> l=lm(y~x)
MSE=mean ( (l$residuals)^2)
SSX=sum ( (x-mean(x))^2 )
U= l$coefficients + qt(1-alpha/2,n-2) * sqrt(MSE/SSX)
L= l$coefficients - qt(1-alpha/2,n-2) * sqrt(MSE/SSX)
</code></pre>
| https://stats.stackexchange.com |
2,081,415 | [
"https://math.stackexchange.com/questions/2081415",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/81560/"
] | Suppose I have two positive numbers $x, y$.
Obviously $$q=\dfrac{x}{x+y} \in (0, 1)$$
since $x + y > x$, implying $\dfrac{x+y}{x} > 1$ and thus $\dfrac{x}{x+y} < 1$. This is bounded below by $0$ is because a quotient of positive numbers is positive (or maybe there's some other reason, but this is irrelevant f... | Hint :-
Case 1. When $y>x\implies \frac{x}{x+y}<\frac{x}{x+x}=\frac{1}{2}$.
Similarly the other case follows.
| <strong>Hint</strong>
$$\frac{x}{x+y} +\frac{y}{x+y} =1 \\
\frac{x}{x+y} > \frac{y}{x+y} \Leftrightarrow x >y$$
| https://math.stackexchange.com |
460,843 | [
"https://physics.stackexchange.com/questions/460843",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86573/"
] | We know that the set of fundamental and derived physical units can be structured as a vector space over the rational numbers. In the International System of Units the dimension of this space is <span class="math-container">$7$</span> ( the seven foundamental units form a basis). This number has some special physical s... | This number of “independent dimensions” is physically meaningless and just a historical convention. For example, we don’t <em>have</em> to treat distance and time as independent dimensions. We could decide to measure both in seconds, where “1 second of distance” is the distance light travels in vacuum in one second. Ph... | There is no special significance to the number 7 of SI units. They are indeed a matter of practical convenience.
For example, we could easily live in physics without the unit ‘mol’, but it was added to the SI units, because it is convenient in chemistry.
Another example: We could introduce entropy as a dimensionless... | https://physics.stackexchange.com |
18,151 | [
"https://stats.stackexchange.com/questions/18151",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7300/"
] | I have a situation in which I have $n$ observations, each with $p$ independent variables and $q$ dependent variables. I would like to build a model or series of models to obtain predictions of the $q$ dependent variables for a new observation.
One way is to build multiple models, each one predicting a single dependent... | You need to check for correlations amongst your dependent variables (<em>edit: @BilalBarakat's answer is right, the residuals are what's important here</em>). If all or some are independent, you can run separate analyses on each. If they are not independent, or whichever ones aren't, you could run a multivariate anal... | To contradict @gung's first paragraph (sorry!), you should actually check for correlations among the <em>residuals</em> in your multiple models, rather than for correlations among the dependent variables as such. The fact that the latter are correlated by itself tells you nothing about whether your estimates will impro... | https://stats.stackexchange.com |
518,129 | [
"https://physics.stackexchange.com/questions/518129",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246879/"
] | Why in many, if not all, references that discuss the time dependent perturbation theory, they start the discussion with the interaction (Dirac) picture, although, what we need is only solving the time dependent Schrodinger equation?
<strong>In another way:</strong>
Why these references do not start with the time depe... | <blockquote>
<strong>My question</strong> How could an infinitesimally thin bridge be fully responsible for the expansion of the (possibly enormous) gulf between left and right sides? ...let’s ask what happens if the metal is on top of a frictionless surface and the metal is not fixed to anything.
</blockquote>
When yo... | As the bridge is getting thinner, if the centers of mass of the two rectangles are held in place, the bridge will want to expand in length, but it will be constrained by the rectangles. So compressive stress will develop in the bridge. (If the bridge were free to expand, the rectangles would move apart.) For a very ... | https://physics.stackexchange.com |
103,106 | [
"https://physics.stackexchange.com/questions/103106",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28118/"
] | The current $i$ can be defined as:
$$i = \int \vec{J} \dot{}d\vec{A} $$
where $\vec{J}$ is the current density and $d\vec{A}$ is the area vector.
Is it possible for:
$$i = \int \vec{J} \dot{}d\vec{A} \neq J\times A $$
where $A$ is the area?
My book gives the example of when the current is not parallel to the are... | (The others did already a good job I think but I will still give it a shot. ^^)
"@dmckee But by definition the "rain" density is the "amount" of rain that passes through it per unit area. So regardless of the angle of the frame, the net rain that passes through it would be rain density * area. The fact that holding th... | <blockquote>
If 3 electrons passes through a circle per second, wouldn't the
current be 3e/s regardless of whether they pass at 45 degrees or 90,
since they pass regardless?
</blockquote>
It would. But here we know that there is a stream of electrons going at a certain speed $v$ having a cross sectional area $A$... | https://physics.stackexchange.com |
169,075 | [
"https://electronics.stackexchange.com/questions/169075",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | As far as I understood there is two type of hand shaking. Hardware and software.
For hardware handshaking other pins of RS232 connectors used.
Does that mean of we us a USB converter we cannot employ hardware flow control?
| You can if the converter supports the additional RS-232 signals. Whether a converter supports them is at the discretion of the designer of the converter.
| Some usb to serial cables provide full rs232 pin out and -12v to +12v voltage. Others just provide TX and RX at TTL voltage levels. And there are ones all in between.
The IC that drives these modules often have the other signal pins, including the hardware handshaking pins, but don't break them out of the connector.
... | https://electronics.stackexchange.com |
83,509 | [
"https://stats.stackexchange.com/questions/83509",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31466/"
] | As far i understand the difference between <code>Risk factor</code> and <code>Prognostic factor</code> is :
Risk factor is the <code>cause</code> of a condition whereas Prognostic factor influences the outcome
who has the condition, like resectability of tumour for lung cancer.
Is that the case ?
Would you explain t... | You are correct in that these terms are usually used in different settings.<br>
(1) A risk factor is associated with the outcome of interest (causality is almost never assumed). Usually a disease.<br>
(2) A prognostic factor is associated with the outcome of interest. Usually morbidity or mortality.
Thus smoking... | A risk factor is typically a variable thought to be related to the incidence of an outcome. Anylyses of risk factors usually center on trying to make reasonable causal inferences, to facilitate subsequent preventive efforts.
A prognostic factor is typically a variable thought to be related to how a disease progresses... | https://stats.stackexchange.com |
3,334,819 | [
"https://math.stackexchange.com/questions/3334819",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/663440/"
] | For example, if <span class="math-container">$x$</span> is an element of <span class="math-container">$S$</span>, such that <span class="math-container">$x$</span> is a natural number greater than <span class="math-container">$5$</span>, the possible values of <span class="math-container">$x$</span> are many, but does ... | In the statement, "Let <span class="math-container">$S = \{n\in\Bbb N~:~n\geq 5\}$</span> and let <span class="math-container">$x\in S$</span>" then <span class="math-container">$x$</span> is an arbitrary single element of <span class="math-container">$S$</span>. An element may only be one value at any given time. Al... | Yes. It's something like the idea of common nouns in normal language use. Such nouns as man, country, plant, etc., refer to any one of a class of objects. Thus, they're like the variables of mathematics.
| https://math.stackexchange.com |
16,988 | [
"https://mechanics.stackexchange.com/questions/16988",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7004/"
] | My 2 month old bike is a 200CC Bajaj Pulsar (made in india) with only 2000kms on the odometer.
I have ridden it carefully. I touched 100km/h accidentally on a drag race with my friend, just one time, but mostly ride between 50-70km/h. I recently completed a +500km trip over bad terrain.
<b>Problems</b>
<ul>
<li>The h... | I am supposing its a Bajaj Pulsar 200NS.
<ul>
<li>problem 1: Your front Fork Oil Seal is broken(a good way to check is to notice any oil leaks near your forks) , This will cause issue with the suspension travel thus the issue.Secondly since you mentioned you did travel over bad terrain there is a slight chance of you... | <h1>Possible Issues</h1>
<ol>
<li>Low probability - The oil in the forks is too high of a weight. 'Thicker' higher weight oil would make the forks seem very stiff. As your motorcycle is relatively new and more than likely came with forks assembled from the factory, this is probably not the case.
</li>
<li>Compression... | https://mechanics.stackexchange.com |
301,961 | [
"https://physics.stackexchange.com/questions/301961",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/113839/"
] | When drag force ($bV$) equals to object's weight (mg) then upward and downward force becomes equal. As a result the object comes to rest. If this is true, how is a body moving with constant velocity?
| You have the incorrect (but very common) misconception that objects that experience balanced forces will come to rest. This is just not the case. Objects that experience balanced forces continue at a constant velocity.
The root of this misconception is usually the idea that forces cause motion. That is not the case. F... | When opposing forces are equal the object does come to arrest. Just try standing on a scale. As for a car traveling down the highway it matches the wind and road resistance with more throttle until an equilibrium is reached at whatever speed you desire.
| https://physics.stackexchange.com |
11,351 | [
"https://stats.stackexchange.com/questions/11351",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/4496/"
] | This is pretty hard for me to describe, but I'll try to make my problem understandable. So first you have to know that I've done a very simple linear regression so far. Before I estimated the coefficient, I watched the distribution of my $y$. It is heavy left skewed. After I estimated the model, I was quite sure to obs... | To answer your question, let's take a very simple example. The simple regression model is given by $y_i = \beta_0 + \beta_1 x_i + \epsilon_i$, where $\epsilon_i \sim N(0,\sigma^2)$. Now suppose that $x_i$ is dichotomous. If $\beta_1$ is not equal to zero, then the distribution of $y_i$ will not be normal, but actually ... | With reference to the excellent answer from @Wolfgang, here are the plots from his R code:
<img src="https://i.stack.imgur.com/ZDmIj.png" alt="enter image description here">
| https://stats.stackexchange.com |
11,117 | [
"https://bioinformatics.stackexchange.com/questions/11117",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/4595/"
] | I have a data frame like this
<pre><code>> head(a[1:2,1:4])
Tumor_Sample_Barcode Chromosome Position End_Position
1: A1 chr4 90169866 90169866
2: A1 chr11 60235747 60235747
> dim(a)
[1] 753655 134
>
> unique(a$Tumor_Sample_Barcode)
[1] "A1" ... | I think you are looking for <code>gsub</code> function:
<pre class="lang-r prettyprint-override"><code>a$Tumor_Sample_Barcode <- gsub("A","res",a$Tumor_Sample_Barcode)
</code></pre>
If you prefer, you can use the <code>str_replace_all</code> function from <code>stringr</code> package. But it tooks a little bit mor... | Other options:
<ul>
<li>Drop 1st character and prefix with <code>"res"</code></li>
<li>We get 5x speed up if we set <code>fixed = TRUE</code> for <em>gsub</em>. </li>
</ul>
<pre><code>microbenchmark::microbenchmark(
# dc37 answer
gsub("A","res", dt<span class="math-container">$Barcode),
stringr::str_replace_a... | https://bioinformatics.stackexchange.com |
2,946,265 | [
"https://math.stackexchange.com/questions/2946265",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <strong>question:</strong>
For <span class="math-container">$a,b,c,d \in \mathbb{R^+}$</span> with <span class="math-container">$a+b+c+d = 4$</span>, Prove <span class="math-container">$\displaystyle \sum\dfrac{a}{b(b+1)}\geq \dfrac{8}{(a+c)(b+d)}$</span>
<strong>my attempt:</strong>
<span class="math-container">$f(... | You are almost there. Taking from where you left off, observe that <span class="math-container">$x=ab+bc+cd+da = (a+c)(b+d)$</span>. Thus you need to go one step further to establish <span class="math-container">$\dfrac{64}{x(x+4)} \ge \dfrac{8}{x}$</span>,and this is clear from AM-GM inequality .
| By Holder
<span class="math-container">$$\sum_{cyc}\frac{a}{b(b+1)}\sum_{cyc}ab\sum_{cyc}a(b+1)\geq(a+b+c+d)^3.$$</span>
Thus, since <span class="math-container">$(a+c)(b+d)=\sum\limits_{cyc}ab$</span>,it's enough to prove that
<span class="math-container">$$(a+b+c+d)^3\geq8\sum_{cyc}(ab+a)$$</span> or
<span class="mat... | https://math.stackexchange.com |
505,533 | [
"https://electronics.stackexchange.com/questions/505533",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/137321/"
] | How can I find direction of the main beam of an antenna if antenna has radiation intensity as following?
<span class="math-container">$$U=[\dfrac{sin(5\pi cos\theta)}{10sin(\pi cos(\theta/2))}]^2$$</span>
Where
<span class="math-container">$$0<\theta<\pi$$</span>
My first trial is to find the places where derivat... | <blockquote>
<em>But the results also give places of the nulls. So, how should I
distinguish themain beam between the all nulls (zeros) and sidelobe
peaks (local maximas)?</em>
</blockquote>
Use your favourite spreadsheet and produce a graph then you get all your information together. The formula is not hard to use in ... | By evaluating U at the local extrema you found, as well as the endpoints of the domain, and picking the one with the highest value. No fancy tricks.
| https://electronics.stackexchange.com |
275,333 | [
"https://electronics.stackexchange.com/questions/275333",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/103063/"
] | I have a big 500 F 2.7 V capacitor, and a module of six 120 F 2.7 V capacitors. If I calculated the capacitance correctly, the module has 20F total capacity.
If I calculate the energy stored in them by E = 0.5 * C * V^2, I get:
<ul>
<li>For the module: E = 0.5 * 20 * 16.2^2 = 2624 J</li>
<li>For the big cap: E = 0.5 ... | Your calculations are consistent, though your measurements of capacity look a bit low.
The 20F, 16.2v capacitor stores 20*16.2 = 324 Coulombs, 324 Ampere seconds, or about 0.09 ampere hours. As you correctly calculate, 2624 Joules.
The 500F, 2.7v capacitor stores 500*2.7 = 1350 Coulombs, 1350 ampere seconds, 0.375 am... | Your confusion comes from trying to compare two basically different variables.
mAh is and indication of a reservoir's energy capacity only either at a constant voltage or, if the voltage falls during discharge, at some mean value.
Using simplistic calculations of mAh x max voltage or mAh x mean voltage the energy i... | https://electronics.stackexchange.com |
2,903,908 | [
"https://math.stackexchange.com/questions/2903908",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/283072/"
] | If the function is defined as
$$
f(x) =
\begin{cases}
|x|^\phi, & x \text{ is rational} \\
0, & x \text{ is irrational}
\end{cases}
$$
where $ \phi > 0 $. For what values of $ \phi > 0 $ is the function $ f $ differentiable at $ x = 0 $?
I suspect this occurs when $ \phi > 1 $ (is this correct?) a... | Well, note that if $f$ is to be differentiable at $x= 0$, then the limit $\lim_{h \to 0} \frac{f(h)}{h}$ is to exist, since the differential quotient at the point $x = 0$ is $\frac{f(0+h) - f(0)}h = \frac{f(h)}h$.
Now, the point is that if $\lim_{h \to 0} \frac{f(h)}{h}$ is to exist, then it better be equal to zero, s... | First off, it must be continuous therefore $\phi\ge 0$. Clearly $\phi=0$ is one answer. If $\phi >0$ and the function is differentiable in $0$ the following limit $$\lim_{h\to 0}\dfrac{f(h)-f(0)}{h}=\lim_{h\to 0}\dfrac{f(h)}{h}$$must exists and equals some real value $l$. If so, we have $$\lim_{h\to 0}\dfrac{f(h)}{h... | https://math.stackexchange.com |
471,404 | [
"https://math.stackexchange.com/questions/471404",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/79250/"
] | Clearly I suppose to put the condition $n > 1$ in use. So my proof must went wrong.. Could someone help me take a look at it? Thanks!
<blockquote>
Suppose $X$ is a smooth, compact, connected $n$-manifold without boundary which admits an immersion to $S^n$. Show that if $n > 1$, then this immersion is a diffeom... | What you have is in fact a "local embedding" instead of a global embedding. You need to be slightly careful since different books may use different definition of "embedding" and "immersion". But anyway, now you have an immersion $f$ which is <em>locally</em> a diffeomorphism
$$M\overset{f}{\to} S^n$$
For a <em>local... | Acturally, it should also be noted that the dimension of <span class="math-container">$M$</span> plays a critical rule, since the claim <span class="math-container">$f$</span> is open is a consequence of the invariance of domain. The problem can be split into a few well-known results:
(1) Let <span class="math-containe... | https://math.stackexchange.com |
40,334 | [
"https://mathoverflow.net/questions/40334",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8430/"
] | Recently, while playing around with infinite-divisibility, i arrived at the following metric:
$$d(x,y) := \sqrt{\log\left(\frac{x+y}{2\sqrt{xy}}\right)},$$
defined for positive reals $x$ and $y$. Proving that $d$ is a metric is trivial, except for the triangle-inequality. However, we can bypass a direct proof by appe... | Take the coordinate transformation from $\mathbb{R}$ to $\mathbb{R}_+$ by the exponential map. Then $(x+y) / \sqrt{xy} = e^{a-b} + e^{b-a}$ where $x = e^{2a}$ and $y = e^{2b}$. So we re-write
$$ d(e^{2a}, e^{2b}) = \sqrt{\log \cosh (a-b) } $$
So it suffices to consider the function $q(x) = \sqrt{ \log \cosh x}$, whic... | This is just the $L^2(\frac{dt}{t})$ distance between $e^{-xt}$ and $e^{-yt}$ (Frullani integrals) up to some positive factor. I'm not sure whether you'll call this "elementary" though.
| https://mathoverflow.net |
5,282 | [
"https://mathoverflow.net/questions/5282",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1646/"
] | Given <span class="math-container">$n$</span> i.i.d. variables <span class="math-container">$X_1$</span> to <span class="math-container">$X_n$</span> with an unknown probability distribution, the sample average is an unbiased estimator for the mean of the distribution. Is there some non-trivial probability distribution... | No. The minimum as always smaller than or equal to the arithmetic mean, and is strictly smaller with positive probability (i.e., when not all the $X_i$ have the same value). Hence its expected value is strictly smaller than that of the mean.
| Not unless n=1 (sorry couldn't resist). Not sure why you're asking this but there do exist f(n,min(X_i)) that work for given distributions. (That is funtions of n and min(X_i) that work). So given only the <em>mean</em> (edit meant min here) and a parametric form of a distribution you can get an unbiassed estimate of t... | https://mathoverflow.net |
273,461 | [
"https://physics.stackexchange.com/questions/273461",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52647/"
] | Why do we have standard voltage $110/220~\mathrm{V}$?
I mean electricity delivery savings (or wastage when heating the to thin cable) by switching to higher voltage would be enormous more power delivered using same lines. I am sure that some smart people have considered it before, <strong>is it because of safety or t... | Distributing power at low voltage would indeed be uneconomical. Everyone knows this, and it is common to transmit AC power over high tension lines at 200 - 300 kV, in order to minimize joule heating in the several miles of conductor running to your house. This voltage is transformed to 240V very close to your house, so... | Safety is the reason why it is done so. Higher (than $110\mathrm{V}/220\mathrm{V}$) potential difference between a human body and a circuit will result in a very, very severe electrical shock. Of course, power loss can be quite minimised by increasing the voltage, but that will be at the cost of lives of all living spe... | https://physics.stackexchange.com |
175,811 | [
"https://math.stackexchange.com/questions/175811",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/5798/"
] | Let $A$ be a subring of a commutative unital ring $B$.
Can you tell me if my proof of the following claim is correct?
Claim: $B \otimes_A A[X] \cong B[X]$
Proof:
It's enough to show that $B[X]$ satisfies the universal property of $B \otimes_A A[X]$, that is if $N$ is any $R$-module and $b^\prime: B \times A[X] \to... | You have a problem in that $p(x)\in B[x]$ may not be in $A[x]$, so defining the map by setting
$p(x)\mapsto b'((1,p(x))$ is not valid.
A more direct route might be to use the map you have from $B\otimes _AA[x]\to B[x]$ and provide an inverse; for example, the map that sends $bx^k$ to $b\otimes x^k$.
| By the universal property of $(B \otimes_A A[x],b)$ there exists a unique linear map $l: B \otimes A[x] \to B[x]$ such that for the map $b^\prime : B \times A[x], (b_0, p(x) ) \mapsto b_0 p(x)$ we have $l \circ b = b^\prime$.
We claim that $l$ has a two-sided inverse: define $\varphi: B[x] \to B \otimes A[x]$, $\sum ... | https://math.stackexchange.com |
302,865 | [
"https://mathoverflow.net/questions/302865",
"https://mathoverflow.net",
"https://mathoverflow.net/users/28104/"
] | Given a prime number $p$ and a primitive root $a$ modulo $p$, let
$\sigma_{a,p}$ denote the permutation of the set $\{1, \dots, p-1\}$ which
maps $b$ to $a^b$ modulo $p$.
<strong>Question:</strong> Let $p$ be fixed. Does the following hold?:
<ul>
<li>If $p$ is congruent to $1$ modulo $4$, then for precisely half of ... | Your second guess is also correct.
At first, we write down the sign of the permutation $\sigma_a$ as the product $\prod_{1\leqslant i<j\leqslant p-1}\frac{a^j-a^i}{j-i}$ modulo $p$. The denominator equals $(p-2)!(p-3)!\dots 1!$, and denoting $p=2m+1$ ($m$ is odd) we write it as $m!\prod_{j=1}^{m-1} j!(p-1-j)!=m!\p... | Let $\varphi$ be an automorphism of the multiplicative group $\mathbb{F}_p^*$. Then
$$x\sigma_{a,p}\varphi = (a^x)\varphi = (a\varphi)^x = x\sigma_{a\varphi, p}.$$
So the permutations $\sigma_{a,p}$ form a coset of the group of automorphisms of the cyclic group $\mathbb{F}_p^* \cong C_{p-1}$.
Now when $p-1=m=2u$ wi... | https://mathoverflow.net |
101,124 | [
"https://electronics.stackexchange.com/questions/101124",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37488/"
] | Transmitted data in CDMA mobile is encoded with a random code. Receiver requires this random code to decode data from the received signal.
From where the receiver will get this random code?
| The code is statistically random but it is not secret. In fact, it's chosen to not conflict with another code on the same frequency. Both ends know the code--it's part of the notion of "channel number". This code sequence stuff is common and you will find the same thing in GPS, and even modems. Sometimes it is call... | The unique code is not truly random, it is a psuedorandom bit sequence generated by a linear-feedback shift register (LFSR) or something similar. The method of generating the code is predetermined and known to both the transmitter and the receiver.
| https://electronics.stackexchange.com |
26,628 | [
"https://chemistry.stackexchange.com/questions/26628",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/4093/"
] | <blockquote>
The following reaction is not a complete reaction. Determine if the change is an oxidation, a reduction, or neither:
$$\ce{CrO4^{-2} -> Cr2O7^{-2}}$$
</blockquote>
I know that the answer to this problem is neither, but I don't have any idea as to how that answer is reached. <strong>Could anyone... | Find the oxidation numbers of the substances in each compound.
You should find the oxidation number of Cr in each compound to be +6, and the oxidation number of O to be -2. Since there is no change in the oxidation numbers, <strong>this reaction is neither an oxidation or reduction.</strong>
| As pointed out in the comments and the other answer, it is neither an oxidation, nor a reduction.
Q: So, what is it?
A: It is a <strong>condensation</strong>: two molecules of an <strong>ortho acid</strong> combine under loss of one molecule of water to yield a <strong>diacid</strong> (<strong>pyro acid</strong>).
T... | https://chemistry.stackexchange.com |
376,657 | [
"https://physics.stackexchange.com/questions/376657",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/146004/"
] | In my electricity course, I am having trouble understanding the difference in between $U=QV$ and $U=\frac{QV}2$ when talking about energy stored in a system.
My idea was that when the potential is created by the charges arriving to the system, we would use $U=\frac{QV}2$, as the charges themselves are building the sys... | You use $U=QV$ when V is being supplied by charges other than the one in your formula (we call these "external"). When you're talking about the the amount of energy stored in charges and the voltage is supplied by the same charges your asking about, then you use $U=\frac{QV}{2}$.
In either case, the correct formula is... | As you said, if you have for example a particle of charge $q$ in an <strong>external</strong> electric potential $V$, then its energy is given by
$$E=qV$$
On the other hand, take a capacitor for example. The charge $Q$ that accumulates and the voltage across it $V$ satisfy the relation
$$Q=CV$$
where $C$ is the cap... | https://physics.stackexchange.com |
77,801 | [
"https://softwareengineering.stackexchange.com/questions/77801",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25109/"
] | We have a large (1200+ hours) website that has <strong>a lot</strong> of technical debt. This is mainly caused by the following (usual) reasons.
<ol>
<li>Multiple programmers who come and go during development.</li>
<li>Change of specifications during development.</li>
<li>Numerous added functionalities added (in a sh... | I'll play devil's advocate, having seen far too often how this turns out: You can't cope with it. I guarantee you're the only one who actually sees a real problem with the system as it is, or else you wouldn't have to ask how to cope with it because the company culture would be one to stamp out bugs and fix the code ... | I suggest you add some CI-based testing, primarly on the areas that break most frequently. That will help you increase quality as work is being done on the project.
It's also becomes more apparent which areas/functionality break more often and thus it's easier to decide which parts need refactoring, or at least increa... | https://softwareengineering.stackexchange.com |
386,131 | [
"https://softwareengineering.stackexchange.com/questions/386131",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/33996/"
] | Java and C# provide memory safety by checking array bounds and pointer dereferences.
What mechanisms could be implemented into a programming language to prevent the possibility of race conditions and deadlocks?
| Races occur when you have simultaneous aliasing of an object and, at least, one of the aliases is mutating.
So, to prevent races, you need to make one or more of these conditions untrue.
Various approaches tackle various aspects. Functional programming stresses immutability which removes the mutability. Locking/atomi... | <blockquote>
Java and C# provide memory safety by checking array bounds and pointer dereferences.
</blockquote>
It's important to first think about how C# and Java do this. They do so by converting what is <em>undefined</em> behaviour in C or C++ into defined behaviour: <em>crash the program</em>. Null dereferences ... | https://softwareengineering.stackexchange.com |
302,399 | [
"https://mathoverflow.net/questions/302399",
"https://mathoverflow.net",
"https://mathoverflow.net/users/54552/"
] | Consider the class of functions
$$X:=\{f\in \mathcal{C}_0^{\infty}(\mathbb{R})\;s.t.\;f\equiv 1 \mbox{ in a neighbourhood of}\;\;x=0\}$$
<strong>Is it true that, for every $\varepsilon > 0$, I can find $f\in X$ such that $\|f\|_{H^{1/2}(\mathbb{R})}<\varepsilon$?</strong>
For $s\in[0,1/2)$, it is easy to show... | It is well known and easy to verify that (Exercise 14 p. 309 in [1])
$$
\log\Big|\log\sqrt{x^2+y^2}\Big|\in H^1(B^2(0,e^{-1}))
$$
so the trace of this function on the $x$-axis belongs to the trace space
$$
f(x)=\log\Big|\log|x|\Big|\in H^{1/2}((-e^{-1},e^{-1})).
$$
Let
$$
f_t(x)=\begin{cases} 0 & \text{if } f(x)\le... | I now think this is indeed possible, and here's a sketch of my current ideas: I want to use the formula
$$
\|f\|_{H^{1/2}}^2 \simeq \|f\|_2^2 + \int\!\!\int \left( \frac{f(y)-f(x)}{y-x} \right)^2 \, dxdy
$$
to compute the $H^{1/2}$ norms. I'll focus on our function on $x<0$, and I'll let it increase from $0$ to $1$ ... | https://mathoverflow.net |
16,142 | [
"https://stats.stackexchange.com/questions/16142",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6537/"
] | I conducted a survey asking people of various income groups about their annual expenditure under various consumption brackets such as food, clothing, housing etc. I then calculated the amount spent by people of different income brackets in these categories as a percentage of their total income. Now, to plot this data a... | This is a typical linear programming problem, where both objective and constraints are linear. R has many functions to solve this, for example optim() or package BB. However your decision variables are binary and N is probably big. So you may want to try to solve the dual problem, instead of solving the primal directly... | This is too complicated for a specific R function. Here is a suggestion for an algorithm which may sometimes work:
You should start by calculating $E_{n,f}$, the expected profit for each customer for each offer.
Then find the most profitable offer per customer, and rank the customers by profitability. If at least $b... | https://stats.stackexchange.com |
275,355 | [
"https://dba.stackexchange.com/questions/275355",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/164886/"
] | I have this select query
<pre><code> SELECT
info.[OFNumber]
--Get sum of item quantity from the same category (all quantity before production) PS_ProjectInfo table
,SUM(Case WHEN info.[FK_PSCategory]=2 then ((info.Length * info.[Quantity] )/1000)Else 0 end ) as 'm'
-- Get sum of item quantity from the sam... | <pre><code>SELECT
info.[OFNumber]
--Get sum of item quantity from the same category (all quantity before production) PS_ProjectInfo table
,SUM(Case WHEN info.[FK_PSCategory]=2 then ((info.Length * info.[Quantity] )/1000)Else 0 end ) as 'm'
-- Get sum of item quantity from the same category (Only quantity produced) ... | This is how I did it
<pre><code> SELECT
info.[OFNumber]
--Get sum of item quantity from the same category (all quantity before production) PS_ProjectInfo table
,(SELECT SUM(CASE WHEN (PS_ProjectInfo.[FK_PSCategory]=2 )THEN CAST(((CAST(PS_ProjectInfo.Length AS float) * PS_ProjectInfo.[Quantity])/1000)AS dec... | https://dba.stackexchange.com |
14,028 | [
"https://physics.stackexchange.com/questions/14028",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5058/"
] | I often hear people say that so-and-so [some famous physicist] can <strong><em>see</em></strong> the solution without calculation. What exactly does this mean? Is it an intuition? But how does one have intuition when it comes to say QM? How might one develop such an intuition?
| There is nothing spectacular about "seeing" the solution, everyone does it. The reason they tell you this is to try to get you to do it. The famous physicists become famous because they see it for a new problem, where no-one else saw it before, and an important problem. Please, do it too. The purpose is to learn someth... | I will share with you a story from a famous physicist, Feynman, related by him at a workshop back in the 80s.
<blockquote>
During the, I think it was called the Manhattan project, when they were scrambling to create the A bomb, all physicists were employed in doing the laborious cross section calculations, integrals w... | https://physics.stackexchange.com |
99,421 | [
"https://mathoverflow.net/questions/99421",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23900/"
] | Several sources state that the computational or time complexity of square rooting is the same as that of multiplication (or division). See for example:
<ul>
<li>Jean-Michel Muller, "Elementary Functions: Algorithms and Implementation" (Birkhäuser, Boston, USA, 2006, 2nd edn.) on p.93 where the Newton-Raphson method is... | First, note that the asymptotic complexity of arithmetic operations stated in the common literature concerns operations on numbers with arbitrary precision, and the running time is expressed as a function of the desired number of digits. From the standpoint of asymptotic complexity it makes no sense to ask for operatio... | The Newton-Raphson algorithm uses, for computation of $A^{1/p}$, the sequence $u_0=A$, $u_{n+1}=u_n-\frac {u_n^p-A}{pu_n^{p-1}}$, whose speed of convergence , always quadratic, is essentially independent of $p$ (and $A$). So, mostly, it asks for $\ln p$ multiplications and 1 division at each step.
| https://mathoverflow.net |
627,528 | [
"https://electronics.stackexchange.com/questions/627528",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/110826/"
] | I have a PCBA that uses an IP5306 chip to charge the battery and it is described as a "Fully-Integrated Power Bank System-On-Chip with 2.1 A charger, 2.4 A discharger".
I need to use a 750-800 mAh Li-po battery for the application. My question is, what C rating for the 800 mAh lipo battery is needed to suppor... | <strong>The <span class="math-container">\$C_r\$</span> charge rate is simply the inverse of 1 hour time to full charge or discharge</strong> (when new ?). So 1C is a 1hour and 10C is 0.1 h.
I don't know the standard value for defining this rating but I expect it is at a reduced capacity like 80% or 90% and/or a safe t... | The C rating is how fast your battery can be discharged or charged. The rating is often different for charging than discharging.
Let’s say your 750-800mAh battery is actually 800mAh to keep things easy. Therefore 1C is 800, 2C is 1600mAh etc.
Since your charger is charging at 2.1 or 2100mAh that is ALMOST 3C or 2400.... | https://electronics.stackexchange.com |
2,523,132 | [
"https://math.stackexchange.com/questions/2523132",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/383757/"
] | This problem was recently posed to me that I prove it.
<span class="math-container">$\vdash (A \land B ) \iff \neg(\neg A \lor \neg B) $</span>
We are only allowed to use derivation rules. It is obviously just the statement of DeMorgan's law. Somehow we have to use biconditional introduction, but when I assume <span... | Well, that's a pretty nasty proof ... especially the first half. I doubt you're going to learn any logical reasoning from it, but hey!
$\def\fitch#1#2{\begin{array}{|l}#1 \\ \hline #2\end{array}}$
$\fitch{}{
\fitch{1. A \land B \quad A}{
\fitch{2. \neg A \lor \neg B \quad A}{
\fitch{3. \neg A \quad \quad A}{
\fitch... | I dont know why anyone would like or need to use biconditional introduction to do this. It seems like a very far workaround. Here is a sketch of what you need to do in order to get you going.
When proving $\neg (\neg A \vee \neg B)$ from $A \wedge B$, assume $\neg A\vee \neg B$ and try to arrive at a contradictions. T... | https://math.stackexchange.com |
3,181 | [
"https://dba.stackexchange.com/questions/3181",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/746/"
] | After I pulled these datas what I wanted from a SQL Server Database,I can't update on row.I'm receiving the following the error.
<img src="https://i.stack.imgur.com/HCcid.png" alt="enter image description here">
<img src="https://i.stack.imgur.com/Ja2YW.png" alt="enter image description here">
| I suppose that you have used the "Edit top x Rows" feature of Management Studio and wanted to update one row. In case that specific row was already deleted by another user/session then you'll receive the upper error.
I think it's better not use the Management Studio's results grid to update data, but use SQL commands.... | The benefit of using SQL commands is that you can also use different isolation levels to preserve the data you are viewing.
| https://dba.stackexchange.com |
250,844 | [
"https://softwareengineering.stackexchange.com/questions/250844",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/121368/"
] | I'm looking for a book to learn how to implement interpreters for programming languages. Thing is there are much more 'compiler books' than 'interpreter books'. So my question is: can I read a book that teaches how to build compilers, to learn how to build interpreters (at a very beginner level)? Is this a good idea? I... | Absolutely - an interpreter is just a "one line at a time" compiler. It performs much the same task, that of taking some form of human-understandable source code and turning it into something a computer processor can understand. A compiler will do this for entire source file(s), whereas an interpreter will do this on a... | <blockquote>
Is a book that teaches how to build compilers good for learning to implement interpreters?
</blockquote>
Yes - A good book on compilers will cover a wide range of topics, many of which are directly relevant to interpreters / interpreted languages. For example:
<ul>
<li>lexical analysis</li>
<li>parsin... | https://softwareengineering.stackexchange.com |
8,240 | [
"https://datascience.stackexchange.com/questions/8240",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/12321/"
] | I have many different strings of text. These strings of text are labels for particular things. But these labels are sloppy, sometimes one label is used for many different things. For example:
"Brown foxes edition 1999 series 1-6 EDI"
"Light [old] seasons 1,2,3,4 other gibberish"
I would like to answer the question: ... | So there are many ways to denote a series. How are you going to parse the series down to determine the values if you don't know the format?
Determining if the label has a series does not get you to the specific numbers in the series.
2,3,5,7 parses out to 4 numbers
Is 6 in 1996? I assume that is one number and... | I think your question is badly formulated, but if I understand it you are trying to separate numbers that are "good" numbers (here the number of the tv show season) from "bad" numbers (for example if the text contained the year "1996" and you were looking for "6", or a 6 in any other context).
Naive Bayes might do the... | https://datascience.stackexchange.com |
76,070 | [
"https://security.stackexchange.com/questions/76070",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/63500/"
] | Can someone give a clear definition of a Salami Attack? In the book Security in Computing (4th Edition) by Charles P. Pfleeger.
It is stated as a attack to data integrity and I quote the passage:
<strong>Data Integrity</strong>
<blockquote>
Stealing, buying, finding, or hearing data requires no computer sophistica... | Nope, I don't think @munkeyoto has got the right idea.
The following passage is from Bruce Schneier's Secret And Lies.
<blockquote>
There’s the so-called salami attack of stealing the fractions of
pennies, one slice at a time, from everyone’s interest-bearing
accounts; this is a beautiful example of something t... | <strong><em>Salami attack</em></strong> is when small attacks add up to one major attack that can go undetected due to the nature of this type of cyber crime. It also known as salami slicing/penny shaving where the attacker uses an online database to seize the information of customers, that is bank/credit card details,... | https://security.stackexchange.com |
21,753 | [
"https://physics.stackexchange.com/questions/21753",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4107/"
] | What is the explanation between equality of proton and electron charges (up to a sign)? This is connected to the gauge invariance and renormalization of charge is connected to the renormalization of photon field, but is this explanation enough? Do we have some experimental evidence that quarks have 2/3 and -1/3 charges... | Because a proton can decay to a positron. It is an experimental fact that the proton and positron charges are very close. To conclude that they are exactly equal requires an argument. If a proton could theoretically decay to a positron and neutral stuff, this is enough.
In QED, charge quantization is equivalent to the... | On the level of QED and above, the equality of the charges has no theoretical explanation. But it is extremely well established experimentally, as even small deviations would add up to huge amounts of electricity in bulk matter.
On the level of the standard model, the value of the charges of the up and down quark come... | https://physics.stackexchange.com |
542,928 | [
"https://electronics.stackexchange.com/questions/542928",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/274024/"
] | I am currently trying to learn how to program in VHDL with the goal of implementing an LDPC decoder in hardware. My understanding is that log-likelihood ratios (LLRs) serve as inputs to the decoder.
Is there an efficient way of reading from RAM if, for example, I have 1) 8-bit LLRs stored in a block of RAM that is 16 a... | A circuit that can identify a particular set bit in a vector in a fixed amount of time is called a "priority encoder". The general concept is that you use the priority encoder to find the first set bit in your vector, use its number to address your memory, and then you clear that bit in the vector so that the... | You can accelerate this as much as you want with more hardware. One way would be to create a circuit to count the number of zeros on the left, and use this as input to a barrel shifter to left shift the bit vector. You would accumulate the total number of shifts as the address that you want to look up. Barrel shift... | https://electronics.stackexchange.com |
266,230 | [
"https://physics.stackexchange.com/questions/266230",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/122739/"
] | I know some physics calculations require alot of computing to solve.
Are there currently systems where it is more logical to do an experiment to "let the universe simulate the experiment for us" and measure the outcome instead of calculating it out of time/resource concerns?
Note i do not mean the complexity of the e... | Virtually all experiments (at least in condensed matter physics) fall under this category. Unlike in high energy, where we're actually testing fundamental physical theories, at the energy scales of condensed matter, we are quite confident that in principle, the many-body nonrelativistic Schrodinger equation runs the w... | A very well-known example is atomic weapons. It is <em>much</em> easier to build a device and test it than it is to simulate it: it took a very long time before simulations of existing designs and small variations on them became convincing enough that people had any faith in them at all, and I believe that we can real... | https://physics.stackexchange.com |
1,921,191 | [
"https://math.stackexchange.com/questions/1921191",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/354073/"
] | Prove that:
<blockquote>
$$\cos^3{A} + \cos^3{(120°+A)} + \cos^3{(240°+A)}=\frac {3}{4} \cos{3A}$$
</blockquote>
My Approach:
$$\mathrm{R.H.S.}=\frac {3}{4} \cos{3A}$$
$$=\frac {3}{4} (4 \cos^3{A}-3\cos{A})$$
$$=\frac {12\cos^3{A} - 9\cos{A}}{4}$$
Now, please help me to continue from here.
| There's also another more algebraic way. You can easily show (by expansion) that if $$a+b+c=0$$ then $$a^3+b^3+c^3=3abc$$
Since, in your problem, for every $A$ $$\cos{A}+\cos{(A+2\pi/3)}+\cos{(A-2\pi/3)}=0$$ Then you can use the above identity
$$\cos^3{A}+\cos^3{(A+2\pi/3)}+\cos^3{(A-2\pi/3)}=3\cos{A}\cos{(A+2\pi/3)}\c... | You can use this particular formula: $$\cos{x}\cos{y}=\frac{1}{2}\left(\cos(x+y)+\cos(x-y)\right)$$
twice and simplify $\cos^3{A}$, $\cos^3{(A+2\pi/3)}$, and $\cos^3{(A-2\pi/3)}$ in this way:
$$\begin{aligned} \cos^3{A}&=\cos{A}\left(\cos{A}\cos{A}\right) \\
&=\frac{1}{2}\cos{A}\left(1+\cos{2A} \right) \\
&... | https://math.stackexchange.com |
28,986 | [
"https://mathoverflow.net/questions/28986",
"https://mathoverflow.net",
"https://mathoverflow.net/users/93724/"
] | Okay, we know that
$$ \frac{sin(x)}{x} = \prod_{n=1}^{\infty} \Big(1-\frac{x^2}{n^2\cdot\pi^2}\Big) $$ .
Is there some known (trigonometric(?)) function that is equal to the following infinite product?
$$ \prod_{n=1}^{\infty} \Big(1-\frac{x}{n\cdot\pi}\Big) $$
I'd be happy as well if someone could provide me wit... | It's a <strong>divergent</strong> infinite product. You might as well ask for the sum of
$$\sum_{n=1}^\infty\frac{x}{n\pi}.$$
You can "cure" the divergence by multipliying each term by a suitable factor, so
for instance
$$f(x)=\prod_{n=1}^\infty e^{x/n\pi}\left(1-\frac{x}{n\pi}\right)$$
does converge (as the $n$-th ter... | I would suggest the development of the Gamma function
$$1/\Gamma(z) = z e^{\gamma z}\ \Pi_{n=1}^\infty\ (1+{z\over n})\ e^{-{z\over n}}$$
| https://mathoverflow.net |
174,860 | [
"https://softwareengineering.stackexchange.com/questions/174860",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/69764/"
] | Is an ID field is always needed in database tables?
In my case I have a user with <code>firstName</code>, <code>lastName</code> and <code>email</code> fields. <code>email</code> is unique and not null, so it could be used as an ID, right? So in that case, could/should I try to remove the ID?
Also I want to have anoth... | Virtually every table needs a primary key. I would strongly argue that every table needs a primary key but I'm willing to make the occasional exception.
Whether the primary key of a table should be a "natural" primary key-- some column or columns that are part of the business data that are naturally unique-- or wheth... | <blockquote>
email is unique and not null, so it could be used as an index, right?
</blockquote>
Right. It would be the <em>natural</em> key of the table. You don't need to a surrogate key, but having to join on this field is wasteful and could be slower than using an int surrogate key.
<blockquote>
So the relati... | https://softwareengineering.stackexchange.com |
23,232 | [
"https://cs.stackexchange.com/questions/23232",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16275/"
] | In a programming book that I'm currently reading it's stated that
$$\sum\limits_{i=1}^{n}i^2$$ is $O(n^3)$. My understanding was that $i\times i$ is a primitive operation and the complexity would be $O(n)$. What am I missing?
| The expression
$$ \sum_{i=1}^n i^2 $$
is not an algorithm. It is just a number. In fact, what the book really means is the <em>function</em>
$$ n \mapsto \sum_{i=1}^n i^2. $$
Since
$$ \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6} = \frac{2n^3+3n^2+n}{6}, $$
we see that this sum is indeed $O(n^3)$, in fact, even $\Theta(n^3... | As an addendum to the other fine answer, you don't actually need to calculate what the exact value of the summation is:
$$\sum_{i=0}^{n} i^2 \le \sum_{i=0}^n n^2 = (n+1) n^2 = O(n^3)$$
It's a very coarse upper bound, but that's good enough.
As an exercise, show that the sum is $\Omega(n^3)$ using a similar argument.... | https://cs.stackexchange.com |
479,859 | [
"https://physics.stackexchange.com/questions/479859",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231898/"
] | In SR, I understand you can use 4 momentum conservation, but what are the special cases where you can use 3 momentum/energy conservation?
An example I have seen is with
<span class="math-container">$$P_1=(M_1, 0) \\ P_2=(M_2,0) \\ P_3=\left(\sqrt{(m_3^2+p^2)},p\right) \\ P_4 =(|p|,-p)$$</span>
where <span class="math... | The fact that the four-momentum vector <span class="math-container">$p^\mu=(E,p_x,p_y,p_z)$</span> is conserved,
<span class="math-container">$$p^\mu_\text{after}=p^\mu_\text{before},$$</span>
simply means that <span class="math-container">$E$</span> is conserved, <span class="math-container">$p_x$</span> is conserve... | Four-momentum is conserved as a four-vector, i.e. each component is conserved. Two inertial observers, moving relative to each other, observing the same particle, would see the particle to have different 3-momentum and different energy, but both would agree that the three-momenum and the energy (of the particle) does n... | https://physics.stackexchange.com |
394,879 | [
"https://stats.stackexchange.com/questions/394879",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/180790/"
] | I have ran an A/B test and using chi-square test of independence, results shows that group A improves on group B by less than 5% (statistically significant) YAY!!! Unfortunately, after few checks I have noticed that there were some collection errors and I had to remove some rows from the experiment. This accounts for ... | Typically, the regression assumptions are:
1) mean error of zero
2) conditional homoskedasticity
3) error independence
4) normality of the error distribution
I've done some econometrics course work so I am aware how the Gauss-Markov items mention things a bit differently and add two assumptions.
Technically, absence... | When you have approximate colinearity:
<ul>
<li>small changes in the data can lead to big changes in the parameter estimates and</li>
<li>the parameter estimates will have huge standard errors</li>
</ul>
Indeed, Belsely shows examples where a change in the 3rd significant figures of the data makes parameters that wer... | https://stats.stackexchange.com |
60,832 | [
"https://datascience.stackexchange.com/questions/60832",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/82846/"
] | I have a dataset with locations and a timestamp of a subject. For each location and timestamp I determined by comparing the location to the home address if the subject was at home or not (0/1) and added this value to the dataset.
Now, I want to train a model to learn based on the timestamp when it is most likely that ... | This is an ideal case for feature engineering!
I did this same case for myself using the google takeaway data to predict whether I am at home or at work.
Instead of just using time I extracted the following features:
<ol>
<li>Work Day --> 1 / 0</li>
<li>Day of the Week</li>
<li>Month</li>
<li>Year</li>
<li>Time</li>... | Choose any classifier you like and which fits your requirements...would be the "easy" answer :D
Your problem sounds as if you could go for an easy algorithm for classification up to complicated ones depending on which additional features you want to use. From the top of my head seasonal features could be interesting: ... | https://datascience.stackexchange.com |
230,737 | [
"https://security.stackexchange.com/questions/230737",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/233428/"
] | Is it possible to create a new root CA (just for myself) and use it to sign a set of existing intermediate CAs which I'd like to trust? If so, which tool can be used to accomplish this? The private keys of the intermediates are not in my possession.
| I have reconsidered my initial response and I think this is technically possible, although unsure as to what it would be useful for.
Certificate signing requests (CSRs) don't have any secret information so conceptually you could create CSRs using the information in your intermediate certs including their public keys. ... | This is a thrown-together ad-hoc 'tool' and can definitely be improved, but:
<pre><code>$ for f in chain.[01] dstx3; do echo $f:; openssl x509 <$f -noout -subject -dates -issuer -fingerprint; done
chain.0:
subject= /CN=*.stackexchange.com
notBefore=Mar 3 14:52:01 2020 GMT
notAfter=Jun 1 14:52:01 2020 GMT
issuer= ... | https://security.stackexchange.com |
188,669 | [
"https://dba.stackexchange.com/questions/188669",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136784/"
] | I would like to change my stored procedure so it is no longer utilizing a cursor to function. How could I write this stored procedure better?
I am using a cursor to compile dynamic SQL to query servers that I am creating from a list to track transaction log backup history.
<pre><code>ALTER PROC [dbo].[spLogBackup]
A... | For this type of operation you need the cursor. There are solutions out there to simplify your code but they also use cursors under the covers.
However, if you just want to simplify your stored procedure you can do that. I would create a stored procedure that accepts a string of dynamic sql (pre formatted) and then ... | Cursors are often condemned, and often rightly so. SQL tends to work best when processing what some have called "bags" of data; cursors lend themselves to row-by-row processing. If you can re-write something that's currently using row-by-row processing in SQL so it is all being handled by a single run of a query, it's ... | https://dba.stackexchange.com |
28,265 | [
"https://mechanics.stackexchange.com/questions/28265",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2748/"
] | <strong>Mini Cooper S (2003)</strong>
I've been noticing recently that it's been taking two attempts to get my car to turn over. I twist the key to the third position and nothing. I then try again and it works.
This morning, however, it took about 20 attempts. I got out, locked it, unlocked it etc, all the same.
The... | I thought I best provide what the "issue" was, but I read online that putting the handbrake on and "rocking" the car from the back may fix the issue due to something being seized in the cold weather.
I thought it was probably rubbish but gave it a go. Whether by fluke or not, I never had the problem again for the next... | If you don't get a click at all, then I'd think that the signal isn't getting to the starter motor, so either an immobiliser problem as you suggest, or a problem with the switch as per JPhi's comment.
If you can get at the starter, you might be able to attach a multimeter probe to the signal wire (the smaller of the ... | https://mechanics.stackexchange.com |
19,697 | [
"https://chemistry.stackexchange.com/questions/19697",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/9878/"
] | $\mathrm{Z=33,\ Z=37,\ Z=9,\ Z=31}$
Since we shouldn't look at the periodic table, I found their groups and periods, what should I do next?
| We have these elements:(just for ease, I'm naming them, you can just avoid it)
<blockquote>
$$
\begin{array}\\
Z=33&\text{Arsenic}&\ce{As}\\
Z=37&\text{Rubidium}&\ce{Rb}\\
Z=9&\text{Fluorine}&\ce{F}\\
Z=31&\text{Galium}&\ce{Ga}
\end{array}
$$
</blockquote>
Now, let's see the period... | I try this question before. First you find out the electron configuration and the group and period for each substances
(I will name each substances for clearing confusion A=33, B=37, C=9, D=31)
Electron arrangement
A= 2.8.8.15 (Group 4, Period 15)
B= 2.8.8.18.1 (Group 5, Period 1)
C= 2.7 (Group 2, Period 17)
D= 2.8.8.1... | https://chemistry.stackexchange.com |
381,675 | [
"https://physics.stackexchange.com/questions/381675",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/89027/"
] | Let's say I took a thermometer and affixed it to the end of a poll. Then I went halfway across a bridge and held the other end of the poll and dipped the thermometer into the middle of a river and just held it there. Then I sent my friend upstream a bit and he walked halfway across a bridge up there and dropped one o... | generally NOT true. Chemically speaking, higher temperature combustion of a fuel in oxygen tends to go more thoroughly to completion compared to lower temperature combustion.
However, higher temperature combustion tends to produce more oxides of nitrogen, which are considered pollutants.
Therefore, minimization of p... | Combustion of hydrocarbons in presence of air (mixture of Oxygen and Nitrogen) at high temperature (and pressure) will lead to the production of nitrous oxides, which are a group of <em>pollutants</em>. As you lower the combustion temperature by some means, even though the nitrous emissions would decrease, the fossil f... | https://physics.stackexchange.com |
11,523 | [
"https://softwareengineering.stackexchange.com/questions/11523",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3382/"
] | I often have to explain technical things and technical decisions to my <em>extremely</em> non technical manager and I'm pretty awful at it. What are good ways to essential dumb things down for the rest of the world who don't have a passion for programming?
Example questions I've been asked:
<ul>
<li>Why are you using... | I tend to use analogies. Take whatever the topic is, and think of something completely non-technical that they would understand, and explain it to them that way.
Best example I can think of offhand is if I need to explain object orientation, I'll explain it using a deck of cards. Or, when I was trying to explain the id... | <h2>Things I Use</h2>
<sup>to great and not so great effect.</sup>
<ul>
<li><strong>Analogies:</strong> When explaining a situation or a process it really works well if you can put it into terms that they will understand. </li>
<li><strong>Generic terms:</strong> Instead of saying <em>HTML tags</em> you could say <em... | https://softwareengineering.stackexchange.com |
11,505 | [
"https://mathoverflow.net/questions/11505",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3183/"
] | Does there exist a partial order, nontrivial for forcing, that is countably closed, but whose separative quotient is not countably closed? Supposing the answer is yes, then is there a partial order, nontrivial for forcing, that is countably closed, but is not forcing equivalent to any countably closed separative partia... | Stevo Todorcevic answered this question for me at the MAMLS conference in honor of Richard Laver last weekend in Boulder, CO. Apparently, the answer is that examples of forcings that are closed, whose separative quotients are not closed, come up frequently, with one particular example being forcings involving semi-sele... | I don't have a definite answer for either question, but here are some facts that may be useful (mostly for the second one) though you may be aware of them already.
If $P$ is countably closed then the complete Boolean algebra $RO(P)$ is strategically closed. So, by a result of Boban Velickovic (<em>Playful Boolean Alge... | https://mathoverflow.net |
356,017 | [
"https://physics.stackexchange.com/questions/356017",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/148983/"
] | I've been doing some reading, and even though many people say different things, i think i'm pretty confident in saying that we <em>can't</em> treat differentials as fractions. In some scenarios it works out (chain rule), but in others it will not. Leibniz notation <em>is</em> still notation. It's just very suggestive o... | Yes.
\begin{align}
\mathbf{F} & = m\mathbf{a} \equiv m \ddot{\mathbf{x}} & \mathrm{definition}\\
\int \mathbf{F}\cdot \operatorname{d}\mathbf{x} & = m \int\ddot{\mathbf{x}}\cdot \operatorname{d}\mathbf{x} & \mathrm{path\ integrate\ both\ sides} \\
\int \mathbf{F}\cdot \operatorname{d}\mathbf{x} &... | What you are missing is the change of variable $s\mapsto s(t)$:
$$\int_0^l a(s)ds = \int_0^T a(s(t))\dot{s}(t)dt$$
where I prefer to use dots for the differentiation with respect to time as this is more classic a notation in physics. And $s(T)=l$. From there, this is trivial as $a(s(t))$ is the acceleration at time $... | https://physics.stackexchange.com |
9,690 | [
"https://mechanics.stackexchange.com/questions/9690",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4775/"
] | The car is a 2005 Mini Cooper. The bolts that hold the exhaust mounts in place have rusted and snapped on both sides:
<img src="https://i.stack.imgur.com/MU104.jpg" alt="enter image description here">
<img src="https://i.stack.imgur.com/XUJmK.jpg" alt="enter image description here">
I've taken up the floor of the bo... | The solution was to simply drill out the old bolts.
<img src="https://i.stack.imgur.com/k3mXE.jpg" alt="enter image description here">
<img src="https://i.stack.imgur.com/U1qyZ.jpg" alt="enter image description here">
| I had the same it was easy. I differed in just using a 3mm and then 7.5mm drill bit, the stud (screw) is M8. So it just fell out during drilling.
<ol>
<li>Strike center of circle with punch to guide drill</li>
<li>Drill straight, cutting fluid helps, HSS drill or better (HSS is ok it is soft)</li>
<li>Use an M8 tapp... | https://mechanics.stackexchange.com |
461,254 | [
"https://electronics.stackexchange.com/questions/461254",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/216344/"
] | I have a hardware algorithm that compares two operands, each (keyBits) bits long, and returns a logical one if the first operand is less than the second, and returns a logical zero otherwise. This algorithm works for any integer value of (keyBits) greater than one. So can I write my algorithm with the following Verilog... | Has nothing to do with cpus, memory, etc. For PCIe you are either a root complex or an endpoint. As wikipedia points out and as would other places (many good resources out there) there is one root complex and the rest are endpoints. All point to point connections (through bridges as needed) to the root complex. Onc... | The "root complex" is a logical construct that consists of the CPU, system memory, and PCIe root ports. So all CPU<->memory operations take place within the root complex. And that also means that components within the root complex have to direct accesses to addresses that correspond to the PCIe bus out over PCIe r... | https://electronics.stackexchange.com |
4,599 | [
"https://robotics.stackexchange.com/questions/4599",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/2155/"
] | In EKF-SLAM (based-feature map) once the robot senses a new landmark, it is augmented to state vector. As a result, the size of the state vector and the covariance matrix are expanded. My question is about the uncertainty of the new landmark and its correlation with other pairs of the covariance matrix. How should I as... | You can use the Jacobians of the inverse observation model to initialize the new row/column of the covariance matrix.
Suppose your observation model is $g(\mathbf{x})$, which maps your state $\mathbf{x}$ to a predicted observation $\hat{\mathbf{z}}$. The inverse observation model $g^{-1}(\mathbf{x}, \tilde{\mathbf{z}... | I don't have experience with SLAM specifically, but I do have a lot of EKF experience so here's my input.
Stick with your second approach. It is normal for the error to approach a non-zero steady-state value. This number can be calculated analytically for nominal cases, but I don't remember the math right now and woul... | https://robotics.stackexchange.com |
61,224 | [
"https://chemistry.stackexchange.com/questions/61224",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/33749/"
] | Here's what I have to balance:
<blockquote>
Solid <strong>aluminum bicarbonate</strong> and <strong>hydrochloric acid</strong> combine to form an <strong>aluminum chloride solution</strong> and <strong>carbonic acid</strong>.
</blockquote>
Or in an equation form:
$$\ce{\text{__ } Al(HCO3)3 + \text{__ } HCl -&g... | The properly balanced equation is:
$\ce{\text{}Al(HCO_3)_3 + \text{3 }HCl \bond{->} \text{ }AlCl3 + \text{3 }H_{2}CO_{3} } $
| <blockquote>
<em>My question is... what would be the reactants and products in this chemical equation?</em>
</blockquote>
You give the equation, you just need to balance it.
<blockquote>
<em>Would HCO3 as a whole compound be a reactant itself?</em>
</blockquote>
No, $\ce{HCO3^-}$ is an anion.
| https://chemistry.stackexchange.com |
25,866 | [
"https://mathoverflow.net/questions/25866",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6206/"
] | A maybe trivial question about fiber bundles (I'm not an expert, and I didn't find quickly an answer looking here and there). Suppose you are given fiber bundle $p\colon E\to M$, where
$E,M$ are smooth manifolds and $p$ is smoothly locally trivial. Also suppose that the fiber $F$ of the bundle is smoothly contractible.... | The answer is: Yes (at least for finite dimensional manifolds).
In fact you only need that the fiber is contractible not smoothly contractible. Take any continuous section $s_0 \colon B \to E$. cover $B$ by open sets $U_i$ such that the bundle is trivializable over each $U_i$, also make sure that the closure of each $... | Yes. This follows from smooth paracompactness of $M$. Basically, you choose local trivialisations over a suitable cover and then on the intersections you smoothly interpolate between the different choices. By choosing your cover carefully, at each stage you are interpolating between a finite number of choices so the... | https://mathoverflow.net |
63,508 | [
"https://dba.stackexchange.com/questions/63508",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/26768/"
] | While running DBCC CHECKDB I got this error
<blockquote>
Msg 8921, Level 16, State 1, Line 1 Check terminated. A failure was
detected while collecting facts. Possibly tempdb out of space or a
system table is inconsistent. Check previous errors.
</blockquote>
After that a coworker showed me this error, while e... | <code>DBCC CHECKDB</code> makes extensive use of tempdb. It relies on a mechanism similar to snapshot isolation to make sure it always sees a transactionally consistent image of the database, independent what else might be going on.
The error you receive is most likely due to the fact that there is not enough room on ... | I had run CheckDB against a 32GB db, and got this error. There were plenty space on the HD. So I increased the size of the tempdb log file to 8MB from 1MB, and closed some applications.
Reran CheckDB, and it worked.
| https://dba.stackexchange.com |
333,070 | [
"https://physics.stackexchange.com/questions/333070",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70392/"
] | I am reading 'The Oxford Solid State Basics' by S.H.Simon in which on page 92 defines an acoustic mode as:
<blockquote>
... any mode that has linear dispersion as $k\rightarrow 0$.
</blockquote>
Whilst on page 94 he defines it as:
<blockquote>
... one mode will be acoustic (goes to zero energy at $k=0$).
</block... | No, one does not imply the other, and I disagree with the first definition.
For example, the dispersion relation of the ZA mode in graphene goes to zero like $x^2$, so energy goes to zero as $k \to 0$ but does not do so linearly.
The 'A' in 'ZA' stands for acoustic, so that's an example of a nonlinear acoustic mode.
... | The vibrational modes that have linear dispersion close to $k=0$ are acoustic modes where the slope of the dispersion curve is the speed of sound in the material (different for different directions of $k$).
The frequencies of optical modes do not go to zero at $k=0$. I would guess the dispersion to be quadratic.
| https://physics.stackexchange.com |
876 | [
"https://mechanics.stackexchange.com/questions/876",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/341/"
] | I want to add some fluid additive (Lucas) to my transmission, but I don't want to overfill it. The dipstick has add, warm, and hot for measuring. So how hot is the hot level? My temperature gauge only gets up one third of the way going 70 on the freeway, and the fluid only gets up around the bottom of "HOT". Can I ... | You can add more fluid, but it's best to do it slowly. Your transmission has a lot of gears and tunnels and holes for transmission fluid to go, and it's important to get the fluid down in there in order to get an accurate reading on the dipstick.
After adding fluid, take another ride out on the freeway for a few minut... | Hot is when the transmission and engine is fully up to temperature. So, 15 minutes of driving or so.
| https://mechanics.stackexchange.com |
3,433,815 | [
"https://math.stackexchange.com/questions/3433815",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/66964/"
] | Let <span class="math-container">$m>1$</span> and <span class="math-container">$p_2,\cdots,p_k$</span> are all odd prime numbers less than <span class="math-container">$2m$</span>.
<span class="math-container">$q,a_2,\cdots,a_k$</span> are arbitrarily selected integers(I mean no matter how you choose these numbers)... | To end this question, someone find a counterexample for <span class="math-container">$m=70$</span>, where
<span class="math-container">$$q\equiv -\lbrace 1,2,1,8,1,9,5,6,10,11,3,2,22,1,33,21,1,23,18,20,4,18,21,19,35,38,44,45,51,54,56,59,69 \rbrace \\ \mod {\lbrace 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71... | OP asks about every possible choice of <span class="math-container">$q$</span>. Counterexamples are to be found for low values of <span class="math-container">$q$</span>, such as sequences <span class="math-container">$2,3,\dots,2m+1$</span> and <span class="math-container">$3,4,\dots,2m+2$</span>, where every member o... | https://math.stackexchange.com |
231,887 | [
"https://dba.stackexchange.com/questions/231887",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136766/"
] | I have configured log shipping at multiple database server with monitored server(separate server) and all of them are running fine without any issues.
One particular server has 7 database and the log shipping copy job fails once in a while for all databases, when I checked the error message, every time error remains ... | <blockquote>
I have been told that for data files backup operate at extent level and for log file, backup operates at page level.
</blockquote>
I would say this statement is not completely correct. Both data file and log file backup would operate at page level. For differential backup it scans through differential b... | Don't worry about extents and pages.
A Full backup contains all the data pages. The pages are not written to the backup at a single point-in-time. So a Full also contains the log records needed to redo/undo the changes from the earliest page to latest transaction committed during the backup.
A differential backup o... | https://dba.stackexchange.com |
66,427 | [
"https://quant.stackexchange.com/questions/66427",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/58736/"
] | I'm looking for fundamental data on US public companies. If anyone could recommend paid or free sources of the fundamentals in <em><strong>original, non-standardized</strong></em> form that would be great. I tried scraping the XBRL files from the SEC but its way too complicated.
| Management fees are commonly charged on the asset base, in this case, the 10MM. There might be exceptions to this rule, but they are rare. FOr mutual funds, management fees are typically charged on a daily basis, say 2%/260 (260 being the proxy for the number of trading days in a year) of the prevailing net asset value... | From a managed fund operation perspective, the 2% charge is on how much funds one investor controls not the total FUM of the fund.
| https://quant.stackexchange.com |
53,626 | [
"https://cs.stackexchange.com/questions/53626",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/46962/"
] | As title. When we want to request following page numbers 2,4,4,2,5,2,1,1,3,1, is clock replacement better? What are the advantages and disadvantages of them?
Thanks~
| Coincidentally, for your reference string, both LRU and CLOCK replacement strategies generate the same number of page faults, five if you count all frame loads, including the first three to initially fill the buffer. In addition, both algorithms generate page faults at the same times. Of course, this won't be the gener... | Please consider that operating system texts show examples with a few frames and a few dozen references, while my PC here has 8 GiB RAM, i.e., 2 million 4 KiB frames, and does millions of memory references a second. And that isn't a large machine by any stretch.
It can be proved that OPT is optimal. For performance of ... | https://cs.stackexchange.com |
2,590 | [
"https://electronics.stackexchange.com/questions/2590",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/776/"
] | I'm relatively new to electronics, and I'm trying to make a thermometer using a LM335 temperature sensor. By reading the datasheet I thought it was simple, connect up 5V to a resister, then to the V+, connect up V- to GND, and I should get somewhere just below 3V when reading the V+ pin.
However, when I do this, I'm ... | Are you sure you have it connected properly? If you are getting 4.83V at V+ and
4.88V at your supply it sounds like you have an open circuit.
Check the pinout against the datasheet. On page two they are showing the <strong>bottom</strong> views
of the package.
| What value resistor are you using?
From the datasheet, LM335 needs about 400uA to 5mA of current. Assuming the diode will drop 3V, 2V is dropped across the resistor. To give between 400uA to 5mA, your resistor value should be between 400ohm to 5kohms.
| https://electronics.stackexchange.com |
138,478 | [
"https://mathoverflow.net/questions/138478",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $R$ be a commutative ring with identity and let $f \in R[x]$. There are well known characterizations for $f$ to be a nilpotent element of $R[x]$ or to have a multiplicative inverse in $R[x]$. Is there any characterization for idempotent elements in $R[x]$ ?
| Let $f = a_0 + a_1x + ... + a_nx^n$ be idempotent. Then $a_0^2 = a_0$. Also
$a_0a_1 + a_1a_0 = a_1$. Multiply by $a_0$ to get $a_0a_1 = 0$ which
means that $a_1 = 0$ and by induction it is easy to show that $a_2 = ... = a_n = 0$
Therefore <strong>$f$ is idempotent iff its constant term is idempotent and other coeff... | Here's a geometric argument. Idempotents in a (commutative) ring $R$ are naturally in bijection with clopen subsets $C\subseteq \operatorname{Spec} R$ (given a clopen subset, take the element of $T$ that is $1$ on $C$ and $0$ on its complement; every idempotent is of this form). Now $\mathbb{A}^1_k$ is connected for ... | https://mathoverflow.net |
195,797 | [
"https://mathoverflow.net/questions/195797",
"https://mathoverflow.net",
"https://mathoverflow.net/users/52842/"
] | If $\Gamma = C(G, S)$ is the (undirected) Cayley graph of a finite group $G$ with generating set $S$, then $G \le \operatorname{Aut}(\Gamma)$, the "full" automorphism group of $\Gamma$.
<blockquote>
When is it true that $G \cong \operatorname{Aut}(\Gamma)$? In other words, when is a group $G$ (isomorphic to) the au... | First, some terminology: if $G\cong\mathrm{Aut}(\Gamma)$ then $\Gamma$ is often called a GRR (for graphical regular representation). This may help in looking for references. Determining whether a Cayley graph is a GRR given $G$ and $S$ is very difficult in general.
One necessary criterion is the following: let $\mathr... | A group $G$ is said to admit a graphical regular representation (GRR) if there is a graph $\Gamma$ such that $Aut(\Gamma) \cong G$ and $G$ acts regularly on the vertices of $\Gamma$. Such a graph is called a GRR of the group $G$.
A graph $\Gamma$ is said to be a GRR if $Aut(\Gamma)$ acts regularly on the vertices of... | https://mathoverflow.net |
415,233 | [
"https://softwareengineering.stackexchange.com/questions/415233",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/293499/"
] | When we work with legacy code and need to do changes, we first write tests on the current behavior. That way we can implement new changes with confidence. We can even refactor the code.
Legacy code is often bad code, and after some refactoring the code may be simpler, easier to test. Since the refactor has been validat... | Automated tests ARE code, so maintaining this code makes sense, including refactoring tests when appropriate. However:
<ul>
<li>productive code and tests have different quality requirements
<ul>
<li>don't invest time into things that don't matter</li>
</ul>
</li>
<li>productive code should have a single source of truth... | <blockquote>
When we work with legacy code and need to do changes, we first write tests on the current behavior. That way we can implement new changes with confidence. We can even refactor the code.
</blockquote>
That may be reflecting sometimes your working process, but in my experience, a way more efficient process i... | https://softwareengineering.stackexchange.com |
107,259 | [
"https://physics.stackexchange.com/questions/107259",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/37125/"
] | I have a simple static mechanical system, but I reach a conclusion that seems to me counter-intuitive:
<img src="https://i.stack.imgur.com/ueJV4.png" alt="enter image description here">
There is a pulley fixed to the ceiling and there is a weight fixed to a rope which goes through the pulley and is fixed to a point o... | The rope on the left pulls the weight and the pulley towards each other. The rope on the right pulls the floor and the pulley towards each other. Each of these pull downwards on the pulley with force $T$. The total downward force on the pulley is $2T$.
The pulley doesn't move because the ceiling pulls upward on it har... | If there is no air drag, the pulley and the rope are frictionless and massless, the rope is not slacking anywhere, the rope is unstretchable and the rope is attached at exactly the centre of mass of the object so that no torque is produced, <strong>yes</strong>.
How is it counter-intuitive? It may seem like that it wo... | https://physics.stackexchange.com |
904,577 | [
"https://math.stackexchange.com/questions/904577",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/170642/"
] | I'm not sure how to express this function in piecewise form without using absolute values:
$$
f(x) = 3|x-2| - |x+1|$$
I know how to do it when there is just one absolute value, such as:
$$g(x) = 3+|2x-5|$$
$$
g(x)=
\begin{cases} 2x-2& \text{; }x\ge\frac52\\
8-2x&\text{; }x<\frac52 \end{cases}
$$
To... | The only places where we need to break the function into "pieces" are those points where the expression inside each absolute value becomes zero. This occurs at $x = -1$ and $x = 2$.
Accordingly, we consider what the function looks like on each of the intervals $(-\infty,-1)$, $(-1,2)$, and $(2,\infty)$.
For $x < ... | Try expressing each of the parts - $3|x-2|$ and $|x+1|$ in piecewise form first. This tells you where the behaviour of the function is going to change: at $x=-1$ and $x=2$. So you have three intervals to look at: $\{x < -1\}$, $\{-1 \le x \lt 2\}$ and $\{x \ge 2\}$. Then all you have to do is see how the two functio... | https://math.stackexchange.com |
72,816 | [
"https://dba.stackexchange.com/questions/72816",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/44715/"
] | I am creating Clustered Column Store Index in SQL Server 2014. <img src="https://i.stack.imgur.com/nRSVq.png" alt="enter image description here">
I am getting error as
<blockquote>
"Timeout expired. The timeout period elapsed prior to completion of the operation or the server is not responding. (Microsoft SQL Serv... | If you use Query Analyzer(QA) go to Tools -> Option -> Connection.Reset all the values using 'Reset to Default' Button.By default there is no time out on QA.
Or, write your <code>CREATE INDEX</code> or <code>ALTER TABLE</code> statement in the query window and run it.
Setting the time out in SQL Server to -1 will pr... | In Management Studio for SQL 2014, the timeout for the designers is held in Tools > Options > Designers > Table and Database Designers with a default of 30 seconds.
<img src="https://i.stack.imgur.com/TTmis.png" alt="enter image description here">
However, as the syntax is so simple for creating a clustered columnsto... | https://dba.stackexchange.com |
562,415 | [
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"https://physics.stackexchange.com/users/160162/"
] | [Ref. Core Principles of Special and General Relativity by Luscombe, page 246]
Let's say we have any two covariant derivative operators <span class="math-container">$\nabla$</span> and <span class="math-container">$\nabla'$</span>. Then there exists a tensor <span class="math-container">$C^{\alpha}_{\mu\nu}$</span> suc... | If your confusion is with the apparently missing factor of <span class="math-container">$1/2$</span>, note that
<span class="math-container">$$\nabla_{[a}\nabla_{b]} \equiv \frac{1}{2}(\nabla_a\nabla_b-\nabla_b\nabla_a)$$</span>
Symmetrization and antisymmetrization brackets come defined with a factor of <span class="m... | The if <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> are (contravariant) vector fields, the torsion tensor <span class="math-container">$T(X,Y)$</span> is defined as
<span class="math-container">$$
\nabla_X Y-\nabla_Y X-[X,Y]=T(X,Y)
$$</span>
where <span class="math-container">$T... | https://physics.stackexchange.com |
121,283 | [
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] | There are two cyclist. They start off with equal velocity $v_0$.
The first one bikes a straight path, while the other bikes through a valley, something like this:
<img src="https://i.stack.imgur.com/pQ8pp.jpg" alt="Like this ______/">
We assume friction doesn't affect either cyclist, so only gravitational potential e... | First, you should add some measures to your trajectories:
<img src="https://i.stack.imgur.com/IKQRe.png" alt="enter image description here">
Then you start working out the potential and kinetic energies:
<img src="https://i.stack.imgur.com/qOKuj.png" alt="enter image description here">
From that, you can get the ve... | If there is no friction (and no pedaling), you can easily determine that the velocity of the cyclist on Path 2 is always higher than the velocity of the cyclist on Path 1. This is because any potential energy is converted in kinetic energy.
You also know that this will at least for a part be reflected in the horizonta... | https://physics.stackexchange.com |
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