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214,219 | [
"https://physics.stackexchange.com/questions/214219",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46661/"
] | I understand that the formula for kinetic energy is: $(1/2)mv^2$, which is equal to 1 Joule or 1 N-m.
If I want $m$ to be my weight (say 150lbs) and $v$ to be 40mph how do I apply it to this formula?
It would not seem like you could just plug any number (150lbs) unrelated to another number (40mph) and get back N-m.
... | Let's take a more familiar example.
If the cost of a baseball is $c$, the cost of ten baseballs is $10 c$.
This formula is not about dollars, euros, rupees, etc. It's a formula about cost, and it's true no matter what type of money you're talking about. The units you get out of the formula will depend on what you put... | I would first like to say that this equation is used in many different cases, and that this question is really broad. However, I do know one particular application of KE to motion.
First, you can't use lbs in the equation. It seems like you do not know the difference between mass and weight. Weight is the force of gra... | https://physics.stackexchange.com |
748,679 | [
"https://physics.stackexchange.com/questions/748679",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/357529/"
] | I am trying to learn what role mass of sound insulation plays in reducing amplitude of sound waves entering a room from the outside.
In a thought experiment, a person has persuaded an elephant to lean against the party wall with a noisy neighbour. Is it fair to reason that any sound wave entering the room through the p... | I don't have the maths to argue this [I'm a sound engineer not a physicist], so let me try to cover it in broad strokes.
Sound isn't all one frequency. To humans it's frequencies from approximately 20Hz to 20kHz [less as you get older]. Higher frequencies tend not to bother humans as we just can't hear them at all. Low... | In order for sound to go "through" a wall it will first have to enter the wall (i.e. the air molecules bouncing against the wall need to actually move the all) and then the moving wall has to radiate sound into air on the other side.
The wall is a lot heavier than the air, so this is a big impedance mismatch ... | https://physics.stackexchange.com |
28,461 | [
"https://stats.stackexchange.com/questions/28461",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9649/"
] | Ok so this may seem like a basic question but I'm getting confused by the mathematical notation.
I am calculating the MSE (mean squared error) between two matrices. I know how to compute this, but do not know how to denote it.
For calculating the MSE, you have to subtract <em>every</em> element of matrix 2 from <em>eve... | Assume your matrices are called $A$ and $B$, then it is usual to notate their elements with $a_{ij}$ respectively $b_{ij}$. So you could denote the sum of the squared errors as
$$
\text{SSE} = \sum_{i,j} (a_{ij}-b_{ij})^2.
$$
You would get your MSE in the usual way, by taking the average. Does this answer your ques... | Standard notation for addition/subtraction of matrices refers to elementwise addition/subtraction, so with standard notation you have:
<span class="math-container">$$\mathbf{A}-\mathbf{B} = \begin{bmatrix}
a_{11} - b_{11} & a_{12} - b_{12} & \cdots & a_{1m} - b_{1m} \\
a_{21} - b_{21} & a_{22} - b_{22}... | https://stats.stackexchange.com |
26,235 | [
"https://mechanics.stackexchange.com/questions/26235",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/13642/"
] | Engine Control Module
Powertrain Control Module
Engine Control Unit
Reading about them online, they seem to be the same thing, computers.
So what are the spcific difference between them? Is the other one any better?
| From my personal experience with this particular subject you have many variables that come into play.
My shop specializes in computer systems on some of the newer vehicles (Mostly Japanese), but we do work on anything given the chance. ECM, PCM, and ECU are generally manufacturer specific. I usually see ECU when referr... | The term ECM could (just as @cloudnyn3 says) be used for both Electronic Control Module or Engine Control Module. Different brands has different names for the same stuff, and also same name for different stuff, which can get a little confusing.
The term ECU is often used for Electronic Control Unit (which could be mo... | https://mechanics.stackexchange.com |
80,043 | [
"https://stats.stackexchange.com/questions/80043",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/600/"
] | I have large data set of $\approx 10^6$ points where each point contains the information of a
<pre><code>(year, count)
</code></pre>
of a particular event. There are many counts for a each year. Looking at the histograms of counts for a given year, I've conjectured that they follow a Poisson distribution. By generati... | The direct answer to the question - how to deal with small expected counts - is that one might either
(a) combine ranges of cells at the end (a very common approach),
(b) use a different (and perhaps better) goodness of fit test, or
(c) consider dropping the chi-square approximation, and see if one can deal with ... | This doesn't entirely answer your question regarding how to implement the goodness of fit test. But with a sample size that large, your data will almost certainly fail any test comparing it to a Poisson distribution even if your distribution closely resembles a Poisson distribution (unless, of course, you simulated Poi... | https://stats.stackexchange.com |
2,654,331 | [
"https://math.stackexchange.com/questions/2654331",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/453082/"
] | I'm talking about functions like:
$$p^2-3pq+2q^2-p+3q-2$$
It is fairly easy to factorize homogeneous ones but I don't understand how to deal with non-homogeneous ones. Help?
| You can set up the factorization as $$(p+Aq+B)(p+Cq+D)$$ and arrive fairly easily, by comparing coefficients, with equations like $$AC=2$$$$A+C=-3$$ so symmetrically $A=-1,C=-2$ and similarly obtain the values of $B$ and $D$
| $p^2-(3q+1)p+2q^2+3q-2$ is a quadratic in $\,p\,$ with discriminant:
$$
\Delta = (3q+1)^2-4(2q^2+3q-2)=q^2 - 6 q + 9=(q-3)^2
$$
Therefore the roots in $\displaystyle\,p\,$ are $\,p_{1,2}=\dfrac{3q+1\pm \sqrt{\Delta}}{2}=\dfrac{3q+1\pm (q-3)}{2}=\begin{cases}2q-1 \\q+2\end{cases}\,$, and the quadratic factors as $\,(p... | https://math.stackexchange.com |
2,721,363 | [
"https://math.stackexchange.com/questions/2721363",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/118056/"
] | I'm studying the proof of the Darboux-Weinstein theorem, but I'm very confused about a step.
Let $M$ be a smooth manifold, $Q\subseteq M$ be a compact submanifold, and $\omega_0, \omega_1 \in \Omega^2(M)$ be two symplectic forms on $M$ such that $\omega_0|_Q = \omega_1|_Q$, in the sense that for all $q \in Q$, the bil... | As Amitai says in the comments, the map
$$f:M \times [0,1] \to TM^* \otimes TM^*$$
$$(p,t) \to (p,t\omega_{0,p}+t(\omega_{1,p}-\omega_{0,p}))$$
is continuous. This is immediate from the local representation:
$$\pi^{-1}(U) \stackrel{\Phi}{\simeq} U \times L(\mathbb{R}^n,\mathbb{R}^n;\mathbb{R})$$
$$(p,\omega) \to (p,\... | Let $(q,t)\in Q\times[0,1].$ You know that $\omega_t$ is non-degenerate at $q$. Hence there is an open rectangle $U_{q,t}\times V_{q,t}\subset M\times[0,1]$, containg $(q,t)$, such that $\omega_s$ is non-degenerate at $p$ for $(p,s)\in U_{q,t}\times V_{q,t}.$ Due to compactness of $[0,1]$, a finite number of the $V_{q,... | https://math.stackexchange.com |
3,335,550 | [
"https://math.stackexchange.com/questions/3335550",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/679311/"
] | <blockquote>
How many liters of a <span class="math-container">$25\%$</span> percent saline solution must be added to <span class="math-container">$3$</span> liters of a <span class="math-container">$10\%$</span> percent saline solution to obtain a <span class="math-container">$15\%$</span> percent saline solution?
<... | Let <span class="math-container">$x$</span> represent the number of liters of <span class="math-container">$25\%$</span> saline solution that is added to the three liters of <span class="math-container">$10\%$</span> saline solution. Then the total volume of the <span class="math-container">$15\%$</span> saline soluti... | Let <span class="math-container">$l$</span> the liters that you need.
Then, <span class="math-container">$\underbrace{\frac{1}{4} \cdot l}_\text{l liters of a 25%} + \underbrace{\frac{1}{10}\cdot 3}_\text{3 liters of a 10%} = \underbrace{\frac{15}{100} \cdot (l+3)}_\text{(l+3) liters of a 15%}$</span>
Can you take it... | https://math.stackexchange.com |
110,935 | [
"https://cs.stackexchange.com/questions/110935",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/106305/"
] | Maybe I am wrong, but I read that when we categorise problems in their respective complexity classes, we use worse-case analysis.
Why don't we use the average case?
I imagine we could have a problem in NP when we look at it's worse-case, but when we look at it's average-case we could have a really efficient algorithm... | Because average case requires a definition of "average". Specifically, average over what distribution of inputs?
Worst-case does at least give you an objective guarantee: whatever input you consider, it won't be worse than this. That sort of guarantee still has some value even if the worst-case inputs aren't represent... | If you want to categorize a problem in a way that makes it comparable to other problems, then you need to categorize it the same way as everyone else does.
If you are only interested in one particular problem, then you can analyze it any way you like. You might look at the worst case, or the average case, or you can ... | https://cs.stackexchange.com |
546,447 | [
"https://physics.stackexchange.com/questions/546447",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206319/"
] | Let's say <span class="math-container">$ \begin{bmatrix} 1\\ 0\\ \end{bmatrix} $</span> and <span class="math-container">$ \begin{bmatrix} 0\\ 1\\ \end{bmatrix} $</span> are the eigenvector of <span class="math-container">$\hat S_z$</span>, is the state <span class="math-container">$ -1\begin{bmatrix} 1\\ 0\\ \end{bma... | Yes they are, and not only those two but there are infinitely many vectors representing the same physical state. Don't forget that physical states in QM are represented by rays in Hilbert space. So in general, any state <span class="math-container">$|\psi\rangle$</span> it represents the same physical situation as <spa... | They both represent the same eigenstate. There is a global phase in the last eigenstate, but in the end, the global phases are not crucial since what is important is the square module of your eigenstate, which has the same value.
| https://physics.stackexchange.com |
151,675 | [
"https://physics.stackexchange.com/questions/151675",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59952/"
] | I was thinking about this on the bus (exam this week :P).
What would happen if two people played catch in outer space?
Lets say person A and B are in space at rest, A throws a mass m at B, what would happen?
Would A move backwards at the same speed? My guess was yes, because of Newton's third law.
Now, what would ... | Conservation of momentum works here like everywhere else. When A (with mass $m_A$) throws a ball with mass $m_b$ with velocity $v$, then $v_A=-v_b\frac{m_b}{m_A}$ so that after the ball is thrown, the net momentum is zero; note that the ball will not be moving towards $B$ at velocity $v$ but instead at $v-v_A$ since $A... | Would A move backwards at the same speed?
no..
Momentum will be conserved,not speed and since A has greater mass than the ball so his speed will be less..
if A throws the ball with speed 'u1',then his speed(in the backward direction) will be m1u1/M1
where m1 is the mass of the ball and M1 is the mass of the person A
No... | https://physics.stackexchange.com |
171,413 | [
"https://stats.stackexchange.com/questions/171413",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/25805/"
] | Let say I have train set of categories $C_1,\ldots,C_s$. Each category has different size. I want to divide the data to 10 subsets, each one is 10% of the train set and then perform 10 rounds of leaving out one subset for test and train on the other 9 subsets. (I.e. I want to perform 10-fold CV).
Now, there are two me... | Making sure that the splits have (roughly) equal relative frequencies of each class is a form of <strong>stratification</strong>, so you're asking whether to do stratified resampling or not.
Practically relevant differences between the two approaches will occur only for data where at least some class has very few cas... | From purely intuitive viewpoint, imposing exactly the same distribution of classes across all the folds seems not justified: this way you take it as ground truth that the distribution will be the same in all datasets in the world that model may encounter in the future.
To put differently, if $D$ is your data, $I$ is ... | https://stats.stackexchange.com |
67,028 | [
"https://biology.stackexchange.com/questions/67028",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/37272/"
] | I don't quite get this concept. An obese individual will have a greater fat content in their body, and thus will have 45% water in their bodies (for example), versus a slim person that will have 75% of body water and a much lower fat level.
Is this because fat is made up of about 10% water, so the more fat you have in... | Fat mass does not take up water. It brings with it less water percentage than lean mass and so a person with more fat mass will have relatively less % body water. Additional mass as fat contributed relatively less water than additional mass as lean tissue.
Consider a 50 kg individual who is extremely lean. From you... | All living cells have water content. Fat tissue is made up of living cells, but fat cells have much more triglyceride and lipid content than water content. So fat tissue still has some water content even though it is mostly made of lipids.<br>
An obese person should have more total body water because of this, and also ... | https://biology.stackexchange.com |
492,797 | [
"https://physics.stackexchange.com/questions/492797",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/237339/"
] | I think that uniform velocity implies constant speed but not constant direction. while constant velocity implies constant speed without any changes in direction.
Both tell us that there's no acceleration (since magnitude of velocity is constant).
The same goes for acceleration: both imply constant magnitude, but only... | I don't believe the distinction between "uniform" and "constant" in this context is important: I would use them interchangeably. I certainly have not encountered any serious technical usage of these terms in this context that relied on an implicit knowledge of any such difference. In general, I would take both "uniform... | Regardless of what you call it, in order for an object to not be accelerating both the magnitude of its velocity (speed) has to be constant AND its direction (path) needs to be in a straight line (aka rectilinear motion).
In order for the direction of an object to change it must experience a net force and thus an acce... | https://physics.stackexchange.com |
739,068 | [
"https://math.stackexchange.com/questions/739068",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/89174/"
] | Can I just pick a number in the set and then prove it's not constructible? Thx
| By definition a number field $K$ is a finite extension of $\mathbb{Q}$, so in particular, every element of a number field is algebraic, thus no transcendental number can be an element of a number field.
This is why number fields are also called <strong>algebraic number fields</strong>, since their elements are algebra... | Here's something worth noting: if $\{(a+bt) \mid a,b \in \mathbb{Q}\}$ with $t$ transcendental over $\Bbb Q$ <em>were</em> a field of <em>any</em> sort, then $(a + bt)^2 = a^2 + 2abt + t^2 = c + dt$ for some $c, d \in \Bbb Q$. Then $t^2 + (2ab - d)t + (a^2 - c) = 0$; but this implies the the degree of $t$ over $\Bbb Q... | https://math.stackexchange.com |
8,189 | [
"https://mathoverflow.net/questions/8189",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2394/"
] | What's the cardinality of a single equivalence class of Cauchy sequences in ℚ?
To clarify, I'm not asking for the cardinality of the real numbers, but for the cardinality of the set of Cauchy Sequences that are equivalent to any single real number.
| It's the same as the size of the real numbers. Here's a rough sketch of the proof.
For each element of (0,1) (which has the same cardinality as the reals), I'm going to construct a distinct sequence of rationals that converges to 0.
Think of an element of (0,1) in binary, so as an infinite sequence of 0s and 1s. Fo... | The answer is that the cardinality is equal to that of the continuum: i.e., that of the real numbers, which is (independent of the continuum hypothesis!) also equal to the the cardinality of the power set of the natural numbers.
Here's a sketch of a construction; you should try to fill in the details.
(i) Essential... | https://mathoverflow.net |
3,073,631 | [
"https://math.stackexchange.com/questions/3073631",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/624671/"
] | <ol>
<li><span class="math-container">$\inf_A (cf+g) \le c \inf_A f + \inf_A g$</span> for all <span class="math-container">$c\in \mathbb{R}$</span>.</li>
<li><span class="math-container">$\inf_A (cf+g) \ge c \inf_A f + \inf_A g$</span> for all <span class="math-container">$c\in \mathbb{R}$</span>.</li>
</ol>
I know t... | Let <span class="math-container">$a+b=n=c+d$</span>. Then <span class="math-container">$$ab=cd\implies a(n-a)=c(n-c)$$</span> so that <span class="math-container">$$an-a^2=cn-c^2,$$</span> or<span class="math-container">$$(a-c)n=a^2-c^2=(a-c)(a+c)$$</span>
Either <span class="math-container">$a-c,$</span> and we are ... | Only an idea: if <span class="math-container">$$a+b=c+d$$</span> we get by squaring
<span class="math-container">$$a^2+b^2=c^2+d^2$$</span> since <span class="math-container">$$ab=cd$$</span> so we get
<span class="math-container">$$a^2-c^2=d^2-b^2$$</span> or <span class="math-container">$$a^2-d^2=b^2-c^2$$</span>
| https://math.stackexchange.com |
76,781 | [
"https://mathoverflow.net/questions/76781",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15797/"
] | for the Verma module $M(\lambda)$, it has a dual $M(\lambda)^{\vee}$,
also as $n^{-}$ module, $M(\lambda)$ isomorphic to $U(n^{-})$
so it is very nature to ask for the dual Verma module $M(\lambda)^{\vee}$ whether
there is such similar property, like as $n^{+}$ module ,whether there exists an iso??
and how to understa... | As an $\mathfrak n ^+$ modules, all dual Vermas are isomorphic to $U(\mathfrak n^-)$ where we use the coadjoint action, identifying $\mathfrak n^-$ with the dual of $\mathfrak n ^+$ using the killing form.
| As I'm sometimes tempted to do when Ben offers a concise answer, I'll attempt to provide a little wider context to the narrow question being asked. The construction of a Verma module as an induced module is easy and direct, going back more or less to the enveloping algebra methods of Chevalley and Harish-Chandra for... | https://mathoverflow.net |
164,343 | [
"https://mathoverflow.net/questions/164343",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7341/"
] | For simplicity, let us consider only a functor out of a small category $\mathcal{C}$ to $Set$,
$$
f:\mathcal{C}\to Set,
$$
The Grothendieck construction produces a category (category of elements) $El(f)$ whose objects are $\sqcup_{c\in \mathcal{C}} f(c)$. Grothendieck construction provides a universal way to compute th... | For any (pseudo)functor $f:C\to \mathrm{Cat}$, its Grothendieck construction $\mathrm{El}(f)$ is, as you have said, its oplax colimit. The <em>lax limit</em> of $f$ can also be computed as the category of <em>sections</em> of the Grothendieck construction. I.e. its objects are functors $s:C\to \mathrm{El}(f)$ for whi... | Like Eric has said --- the construction trivializes on discrete (co)presheaves.
So, let me try to describe the general case. There are two difficulties: first, your question is about covariant functors, and in case of Grothendieck construction we are used to contravariant functors; second, I am going to describe the c... | https://mathoverflow.net |
2,852,000 | [
"https://math.stackexchange.com/questions/2852000",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/577234/"
] | The probability that we have 1 number twice is : 2/6
The probability that we have two numbers twice is 2/6*2/6
And the other 2 must be random: 2/6*2/6*1/6*1/6
However the answer is 0.347
How should I proceed to get such answer?
| The total number of equally probable arrangements of 6 dice rolls is $6^6$
To get exactly on double:
there are 6 ways to choose the number to be doubled,
and then $\binom 54 =5$ ways to choose the remaining 4 non repeated numbers
finally there are $\frac{6!}{2!}$ ways to arrange those numbers
So the probability o... | Taking $R$ for repeated numbers and $S$ for single numbers, there are $\binom 62 = 15$ patterns to choose from (e.g. $RRSRRS, SRRRSR$). Then within the repeated numbers $a,b$ there are $\binom 31=3$ patterns when we have an $a$ first: $aabb, abab, abba$.
So we have $15\cdot 3=45$ templates to fill from the available n... | https://math.stackexchange.com |
101,042 | [
"https://cs.stackexchange.com/questions/101042",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/-1/"
] | It seems intuitive that there's no list data structure which has <span class="math-container">$\mathcal{O}(1)$</span> worst case time complexity for random access and a worst case complexity better than <span class="math-container">$\mathcal{O}(n)$</span> for insertion: if insertion is allowed to affect only a <em>sma... | Yes, you can have both as fast as possible random access and faster-than-full-rebuild insertion time.
I assume you know how dynamically growing arrays work. Also, I assume you know how to make them work in <span class="math-container">$O(1)$</span> worst-case. These techniques allow us to focus on the problem for list... | As accessing to an element is in <span class="math-container">$O(1)$</span>, it would be something like an array. And, if this assumption is true, your discussion would be near the concept of "Dynamic Array". It's insertion to the array is <span class="math-container">$O(1)$</span> and amortized <strong>cost of <span c... | https://cs.stackexchange.com |
767,759 | [
"https://math.stackexchange.com/questions/767759",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/64774/"
] | As the tile says, is $\left | i^{n} \right | = 1$ for all real values of n?
| Since $|i^n|=|i|^n$, and $|i|=1$, then for all $n\in\mathbb R$ $|i^n|=|i|^n=1$ for the simple reason that $1$ raised to <strong>any</strong> real exponent is still $1$.
| Here's a less algebraic, more geometric explanation: $i$ denotes the vector $(0,1)$ in the complex plane, and multiplication by $i$ just rotates points in the plane 90 degrees counterclockwise. So $i^n$ is just a rotation of $(0,1)$ by 90 degrees counterclockwise $n-1$ times, i.e. a rotation of $(0,1)$ by $90(n-1)$ deg... | https://math.stackexchange.com |
495,639 | [
"https://math.stackexchange.com/questions/495639",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93671/"
] | Let A be the set of all composite numbers and let d be such a number that for every element <strong>a</strong> of A, <strong>a</strong>+d is also a composite number. I want to show that such a number d cannot exist, but especially in view of the fact that some odd number are also composite have trouble doing that.
| The result does not hold if $d=0$.
We will show that for any $d\gt 0$, there is a composite $a$ such that $a+d$ is prime.
Take a large number $N$. For definiteness let $N=d+2$. Then the numbers $N!+2$, $N!+3$, and so on up to $N!+N$ are all composite. The composites may continue for a while beyond $N!+N$. Let $p$ b... | Assume $d>0$ is such a number. The set $S=\{\,4+kd\mid k\ge0\,\}$ contains infinitely many primes. Let $p$ be the smallest such prime. Then $a=p-d$ is composite and $a+d$ is not.
| https://math.stackexchange.com |
198,974 | [
"https://stats.stackexchange.com/questions/198974",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/93932/"
] | I have been recently doing two-sample analysis and have a little trouble interpreting the resulting $p$-value. The $p$-value was 0.12, thus at the risk rate of 5% I cannot say the samples are different.
<strong>However, does $p=0.12$ still mean I can say there is a detectable difference between samples, just not as ob... | The wikipedia for p-value should give you a precise definition. Essentially, it's the probability how your null hypothesis would be inconsistent to your data.
With a p-value of 0.12, you would need a large significance level to reject your hypothesis.
<ul>
<li>You can think like there is some difference between the s... | If you want an interpretation that corresponds to the posterior probability of the alternative hypothesis being true, then you would likely want a Bayesian analysis. A frequentist analysis (as you had conducted) may or may not have the Bayesian properties one "intuitively desires" (such as allowing such an interpretati... | https://stats.stackexchange.com |
38,161 | [
"https://mechanics.stackexchange.com/questions/38161",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/16810/"
] | If you drive a naturally aspirated car hard for a good 10 minutes (red line every few minutes), is it bad to turn the car off straight away? Should you drive calm for a while, or let it idle for some time? If so, which, and for how long?
| There is no need to continue to run a naturally aspirated car after hard driving. Just shut it off an let it cool down. It is suggested you do this with turbocharged vehicles to give the turbo a chance to spin down and cool down which will help with its longevity. There's nothing in a naturally aspirated engine which n... | On track, it is typical to take a cool down lap to allow the brakes and drive components to cool down. On the road, I doubt you can get things hot enough to warrant driving a few extra minutes of calm driving however, here is what I do after going out for a spirited drive:
<ol>
<li>Turn on to my home street (or whatev... | https://mechanics.stackexchange.com |
4,219 | [
"https://quantumcomputing.stackexchange.com/questions/4219",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/3023/"
] | What does it mean by <em>''qubit can't be copied''</em> ?
In a note, it is saying that:
<blockquote>
Copying a qubit means <span class="math-container">$$U|\psi\rangle_A|0\rangle_B=|\psi\rangle_A|\psi\rangle_B$$</span>
<em>i.e</em>; applying a <em>unitary</em> transformation on the qubit state. It is explained as, if ... | All operations on quantum states are unitary operations. We don't make the rules, this is just how nature seems to work. So if you want to define an operation that copies a qbit, it has to be a unitary operation. That unitary operation would look like this:
$U|\psi\rangle_A|0\rangle_B=|\psi\rangle_A|\psi\rangle_B$
So... | As already mentioned in the other answers, the crucial point is that copying means implicitly that the state of the original qubit is <em>unknown</em>, i.e. given a qubit in an unknown state, you want to prepare a second qubit to be in exactly the same state.
To make it more intelligible, there is a less mathematical ... | https://quantumcomputing.stackexchange.com |
550,624 | [
"https://physics.stackexchange.com/questions/550624",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10725/"
] | Frisbees normally generate lift because their "wing" is moving through air,
so what would happen if I just get the frisbee spinning without pushing its
center of mass forward? Assume there is no gravity so there is no falling
"parachute effect".
Let's define a frisbee as a 2D cross section which is rotated about the ... | I agree with Rusian. It will produce lift because the skin friction drag of the spinning frisbee will cause the air to move outward from its center as a result of centrifugal force. When the air reaches the lower lip of the frisbee it will be directed downward by the lip, and thereby create lift.
| Imagine a frisbee hanging still (no rotation) in an endless sea of air (no gravity). Obviously, the frisbee will not move. When the frisbee is rotating though, there will develop a rotating motion of air inside the inner confines of the frisbee. This results in a vertex of air moving away from the frisbee (from the non... | https://physics.stackexchange.com |
549,662 | [
"https://physics.stackexchange.com/questions/549662",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/209383/"
] | Example:
When one studies the spin statistics theorem, one of the phrases that's been repeated a lot was that "the spin statistics theorem was derived from relativistic physics... there's no way to prove it in non-relativistic physics."
However, if it could not be derived from non-relativistic physics, why does one ... | Physics is not just a branch of math: it is a method for modeling phenomena in the real world. If a fact is proven experimentally, but a theory fails to account for it, it is a problem with the theory, rather than with the reality.
E.g., spin arises naturally in relativistic theory, but there is no reason why it shoul... | It boils down to two things:
<ol>
<li>You're right that in a general nonrealativistic theory, spin-statistics theorem does not necessarily hold.</li>
<li>But we assume that our actual nonrelativistic physics is really only an approximation to a more fundamental and relativistic nature. Thus, the nonrelativistic theor... | https://physics.stackexchange.com |
49,879 | [
"https://dsp.stackexchange.com/questions/49879",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/36250/"
] | $x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $
we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$
Its auto-correlation function $C[n]$ is <strong>uniquely</strong> defined as:
$$
C[n]=\sum_{i=0}^{L-1} x[i+n]x^*[i]
$$
$C[n]$ also has the periodic property: $$C[n+L]=C[n]\tag{1}$$
And ''conjugate-symmetry'' ... | Let's look at the case $x[n] \in \mathbb{R}$, where $x[n]$ is real.
Autocorrelation is basically convolution of the signal with it's time inverse. This can be easily expressed in the frequency domain.
$$ \mathscr{F}\Big\{ r_{xx}[n] \Big\} = \mathscr{F}\Big\{ x[n] \Big\} \cdot \mathscr{F}\Big\{ x[-n] \Big\} $$
$$R... | There is in general, as @Hilmar's answer points out, no unique solution to the question of a sequence that has the given perodic autocorrelation function. In the simplest case, that a <em>shifted</em> version $y$ of any sequence $x$ (e.g. $y[n] = x[n-3]$ for all $n$) has the same autocorrelation function as $x$. Sim... | https://dsp.stackexchange.com |
394,603 | [
"https://mathoverflow.net/questions/394603",
"https://mathoverflow.net",
"https://mathoverflow.net/users/61949/"
] | Let <span class="math-container">$S_n$</span> be the finite group given as <span class="math-container">$n \times n$</span> permutation matrices.
Define for a given field <span class="math-container">$K$</span> the algebra <span class="math-container">$B_n$</span> as the subalgebra of <span class="math-container">$M_n(... | Let <span class="math-container">$K$</span> be a field. The literal answer has already been given by several people but let me try and get at the algebraic structure and provide a quiver with relations (<em><strong>see the addition</strong></em>). Let <span class="math-container">$J$</span> be the <span class="math-c... | For starters one can think about an algebraically closed field of characteristic zero. I will only sketch, so there is no need to accept it as an anwer. One can think in terms of representation theory. This <span class="math-container">$K^n$</span>, viewed as a representation of <span class="math-container">$S_n$</span... | https://mathoverflow.net |
3,793 | [
"https://stats.stackexchange.com/questions/3793",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1641/"
] | Is there a term that describes what I'm trying to do below?
Also, how would you do this using something like JMP or Excel? (or do I need to code this in something like perl?)
Given this sort of data:
<pre><code>ID| opened | closed | quantity
--------------------------------------
1 | 2010-01-01 | 2010-01-03 |... | Use SUMIF() to compute the total open to date and the total closed to date. The difference at any time is the total currently open.
Let's suppose the data you show are in the range A1:D4 in Excel. Reserve four columns for your output: the two shown plus two for intermediate calculations. Let's suppose they are colu... | One simple algorithm which could be implemented easily would be:
Step 1:
Add variables to your data frame; one for each time you want to graph. In pseudo code
<code>if time_i >= opened AND time_i < closed then quantity else 0</code>
Step 2:
sum the rows for each generated time variable to get the quantity at... | https://stats.stackexchange.com |
1,471,118 | [
"https://math.stackexchange.com/questions/1471118",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/83567/"
] | <blockquote>
Let $G$ be an abelian group and $x\in G$ is an element of finite order $m$. Then for every $n$ such that $GCD(n,m) = 1$ there exist $y \in G$ such that $ny=x$.
</blockquote>
How do I prove this one? Is the fundamental theorem of finitely generated abelian groups applicable here?
| There is a <em>very</em> elementary proof, which uses only the fact that <span class="math-container">$\mathbf N$</span> is a well-ordered set:
Suppose <span class="math-container">$p$</span> divides <span class="math-container">$ab$</span> and <span class="math-container">$p$</span> does not divide <span class="math-c... | This is a very elementary proof (which is due to Dean Hickerson):
Call a triple $(p, a, b)$ of positive integers "bad" if $p$ is prime and $p\mid ab$, but $p\nmid a$ and $p\nmid b$.
Suppose that a bad triple exists. Among all bad triples, consider those in which $p$ is minimal. Among all such triples, choose one in... | https://math.stackexchange.com |
13,361 | [
"https://security.stackexchange.com/questions/13361",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/8855/"
] | I was browsing a website, and stumbled across a sample scheme for password-protecting web pages. The owner of the website specifically had a page that invited people to attempt to hack it.
I wanted to give it a try, so I wrote up a quick python script a few hours ago to try brute-forcing the password. (Which, in ret... | First off, let me say this: I respect the ethics of anyone who would ask this kind of question (rather than just closing their eyes, walking away, and forgetting the whole thing). My compliments to you.
Ultimately, this is a matter of personal ethics, so it is hard to give advice. You need to do what <em>you</em> fe... | Disclaimer: I'm not an IT guru nor a security expert.
First, I agree with @D.W. that it can't hurt to contact the site owner and explain what happened. (For all you know, the 509 responses may be totally unrelated to your haywire script.)
Second, in the future, it's a simple matter to include your email address or... | https://security.stackexchange.com |
188,364 | [
"https://electronics.stackexchange.com/questions/188364",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/80332/"
] | I would like to power a LED off a 1,2 volt rechargeable battery,850mAh,energizer without any resistors.Since the LED has a forward voltage around 2 volts,working fine when connected to a 1,5 volt alakaline AA battery,it's obvious that the voltage isn't a problem.However,I am not so sure about the current.Would the LED ... | <blockquote>
Would the LED be fried if I connected it to this battery?
</blockquote>
Depends on two factors. The Battery's Internal Equivalent Series Resistance, and the IV Curve of the LED. The 2V stated Forward Voltage of the LEDis likely at 20mA, the typical Forward Current for the stated expected life of the LED... | No, because when the supply is below the LED's forward voltage only a very small amount of current (hundreds of microamps, if that) will be able to flow; if the LED is visible at all it will be <em>very</em> dim.
The danger with too high a voltage is that the amount of current that is allowed to flow will be too high ... | https://electronics.stackexchange.com |
3,058,076 | [
"https://math.stackexchange.com/questions/3058076",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/287662/"
] | Let <span class="math-container">$f$</span> be a function <span class="math-container">$\mathbb C \to \mathbb C$</span>. I am not assuming <span class="math-container">$f$</span> is analytic on <span class="math-container">$\mathbb C$</span>, so Cauchy-Goursat does not apply.
Suppose <span class="math-container">$\ga... | It's true that, as the square size approaches zero, the contributions from the individual squares tend to zero. But as the square size approaches zero, the <em>number</em> of squares tends towards infinity! For your argument to work, you need some sort of guarantee that the rate at which the integrals on the individual... | Kenny Wong has nicely explained why your proposed argument is wrong. The conclusion of the argument is also false, and in fact is false in the strongest possible way: the result of Cauchy's theorem is true <em>only</em> for analytic functions and no others. More precisely, the following theorem (known as Morera's the... | https://math.stackexchange.com |
43,233 | [
"https://physics.stackexchange.com/questions/43233",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12958/"
] | Now in the end of my MSc in physics I've been contemplating in enrolling in a Phd in theoretical physics. Before that I think I would do best to re-study some subjects. My question is then, what books should I follow for that? I'm thinking about getting a better understanding of classical mechanics and follow Goldstein... | Goldstein's and Jackson's are the examples of widely used graduate level textbooks, however it should be used already in your MSc course. Griffith's in the other hand is widely used in physics undergraduate EM course.
I don't know the level of math and physics that you have, but probably it would be good to start stud... | A thorough overview of theoretical physics, from a uniform point of view and with lots of explanations is given in the 10 volumes on Theoretical Physics by Landau and Lifshitz.
Though not covering the newest things they start from scratch (though assuming some background that you surely have with a MSc) and are a nea... | https://physics.stackexchange.com |
486,331 | [
"https://physics.stackexchange.com/questions/486331",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/234729/"
] | Suppose I am pushing a box on table with <span class="math-container">$10$</span> N force due to friction it is not moving and if i applied <span class="math-container">$20$</span> N the box started accelerating. Then, how does the box apply <span class="math-container">$20$</span> N force on me?Well actually,I really ... | The difficulty you are having is quite common when first learning Newtons laws because you think Newton’s third law means the forces always cancel each other and nothing should accelerate. They don’t. You have to look at the net force acting on each body individually and apply Newton's second law to each individually.
... | <ol>
<li>Imagine that you have springs instead of your hands. If you push the box, the springs are compressed, shortened by the force from the box. (No box, no compress as you move.)</li>
<li>The side of box on which you push is slightly deformed - imagine that it is from very springy material, so you can see it. As yo... | https://physics.stackexchange.com |
113,875 | [
"https://physics.stackexchange.com/questions/113875",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21441/"
] | Let's consider an electron in some sort of potential well. Suppose $|i\rangle$ is an $i$th eigenstate, and we want to prepare the electron in state with state vector (up to normalization) $|\psi_1\rangle=|1\rangle+|2\rangle$.
We can prepare such a state arbitrarily precisely by e.g. making the barrier finite (but stil... | This is, to the best of my knowledge, not doable without some sort of 'forgetfulness' on your part, or on the part of the physical systems you use to prepare your state.
The most obvious way is to flip a coin and decide which of $|1⟩$ and $|2⟩$ you want to prepare, and <em>not</em> record the outcome of the coin, and ... | If you can find and measure an observable that has $\vert \psi \rangle = \vert 1 \rangle + \vert 2 \rangle$ as an eigenstate, you could measure the value of this operator on random electrons and select those that are in the desired linear combination of states. Otherwise, I think you cannot fabricate a pure state.
| https://physics.stackexchange.com |
111,532 | [
"https://stats.stackexchange.com/questions/111532",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/53332/"
] | Let's say that we have a model:
$y + x = \epsilon$, $\epsilon \sim N(0, 1)$.
After observing a value for $y$, we can write $x$ as:
$x = \epsilon - y$
Since $y$ is just a constant, and $\epsilon$ is standard normally distributed, it seems that we can claim:
$\epsilon - y \sim N(-y, 1)$
and thus:
$p(x \mid y) = N(... | There are two ways to interpret your statement $\epsilon \sim \mathcal N(0, 1)$. If $\epsilon \sim \mathcal N(0, 1)$ is taken to mean that $\epsilon$ is <em>marginally</em> $\mathcal N(0, 1)$ then your logic falls apart at concluding that $[\epsilon - y \mid Y = y] \sim \mathcal N(-y, 1)$. This is because there is no r... | "Since y is just a constant..."..it is not a constant. It is a sample from a distribution. The errors follow!!
| https://stats.stackexchange.com |
294,487 | [
"https://softwareengineering.stackexchange.com/questions/294487",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/174043/"
] | Right now we're implementing a (honestly overly complex) role-based permissions system where users will be assigned to roles and those roles will be granted permissions on some combination of resources. Fairly traditional, and I think fairly straightforward to implement database-wise by linking a table of <code>users</... | Preferable any type of user action should be controlled in the same way. Administrators as just users (don't tell them I said that :-)), just with a set different set of permissions.
Perhaps these permissions do not fit in the current permissions model because the model is only applied to basic database actions.
A pe... | In this case I would go with the hybrid solution.
Like you say, the other options are essentially hardcoding the special permissions in one way or another.
In this case I'd look at the security scheme set up in most DBMS systems:
<ul>
<li>Users can get specific permissions on tables in specific databases</li>
<li>Us... | https://softwareengineering.stackexchange.com |
182,192 | [
"https://electronics.stackexchange.com/questions/182192",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/77885/"
] | I have gone through tons of forum discussions and videos and books but they all explain in terms of mathematical equations that factor the input by a 'larger than 1' number. What happens physically inside?
| This is grossly simplified, but I think you're asking for a very simple answer, so take it in the spirit it's offered.
The key lies in the fact that for some semiconductors/junctions,
a) you can talk about majority and minority charge carriers, roughly electrons and holes, depending on whether the material is p-type... | Transistors make use of semiconductors. Nowadays it means pretty much exclusively silicon. You have N-type (more electrons) and P-type (less electrons). When you put differently treated pieces of silicon together, you create <em>junctions</em> (PN junction, etc.). You can bias (put voltage on) a junction, that makes it... | https://electronics.stackexchange.com |
100,097 | [
"https://math.stackexchange.com/questions/100097",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/15462/"
] | I am trying to solve the following limit:
$$
\lim_{x \to 1^+} \frac{x^x+\frac{x}{2}-\sqrt x-\frac{1}{2}}{\log(x)-x+1}
$$
My attempt was to substitute $x$ with $1+y$, which results in the following:
$$
\lim_{y \to 0^+}_{y<1} \frac{(y+1)^{y+1}+\frac{y}{2}-\sqrt{1+y}}{\sum_{n=1}^\infty (-1)^n\frac{y^{n+1}}{n+1}}
... | If you can't use L'Hopitals rule then your best bet is to use series expansion about x=1. This is basically what you're already doing with your transform $y=1+x$.
The tricky part is that you're going to have to use the binomial theorem on two of the bits on the top line:
$$(1+y)^{(1+y)} = 1 + (1+y)*y + \ldots = 1 + y... | You should apply de L'Hospital rule. You will get
$$
\lim_{x \to 1^+} \frac{x^x+\frac{x}{2}-\sqrt x-\frac{1}{2}}{\log(x)-x+1}=
\lim_{x \to 1^+} \frac{x^x(\log(x)+1)+\frac{1}{2}-\frac{1}{2\sqrt x}}{\frac{1}{x}-1}=-\infty
$$
The other way is using Taylor series as follows
$$
\lim_{x \to 1^+} \frac{x^x+\frac{x}{2}... | https://math.stackexchange.com |
40,047 | [
"https://astronomy.stackexchange.com/questions/40047",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/37057/"
] | Since atmospheres don't end abruptly but gradually get thinner the higher you go, I wonder how we can get the total mass of an atmosphere if we don't know where exactly it ends. E.g. the Earth's atmosphere's mass is defined as 5.1480 × 10<sup>18</sup> kg. Does this value include the exosphere (which doesn't have an abr... | There is a simple<span class="math-container">$^*$</span> way to know the total mass of the atmosphere: measuring the pressure it exerts on the surface, which necessarily integrate all of the atmosphere above ground level.
If you take an atmospheric pressure of <span class="math-container">$1\cdot10^5$</span> Pa, it is... | Suppose the atmosphere has a density that decays exponentially with height.
e.g.
<span class="math-container">$$ \rho = \rho_0 \exp[-h/h_0]\ ,$$</span>
where <span class="math-container">$\rho_0$</span> is the density at some surface and <span class="math-container">$h_0$</span> is a characteristic height scale on whic... | https://astronomy.stackexchange.com |
41,808 | [
"https://quant.stackexchange.com/questions/41808",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/29447/"
] | I was going through some paid video on options. The tutor in the video asked the following question:
Person $A$ has the following portfolio at the start of April
<ul>
<li> Portfolio of options with vega $20,000$ expiring end of April.
<li> Portfolio of options with vega $-40,000$ expiring end of May.
<li> Portfoli... | It seems like he is assuming that the shorter term volatilities change more than the longer term ones and the relatively sensitivity is proportional to $1 / \sqrt{T}$. Thus, this hedge is not against a parallel shift of the surface. This is not an uncommon assumption and the corresponding vegas are often referred to as... | Your tutor is calculating the increase in total variance. The black-scholes model has the variance term of sigma^2 * Time-to-expiry.
Hence, when the monthly volatility increases by 1%, the effective increase for the 3mth option is sqrt(3) * 1%, the 2mth option is sqrt(2) * 1% etc.
He explicitly assumes the vega is re... | https://quant.stackexchange.com |
30,555 | [
"https://physics.stackexchange.com/questions/30555",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8609/"
] | Clearly the SUSY anti-commutation relations involve momentum, and thus the generator of translations in spacetime:
<span class="math-container">$$\{ Q_\alpha, \bar{Q}_{\dot{\beta}} \} = 2 (\sigma^\mu)_{\alpha \dot{\beta}} P_\mu . $$</span>
So I would say that naively SUSY has 'something to do with spacetime' since the... | SUSY <em>has</em> something to do with spacetime since its generators $Q$ carry spin angular momentum, so they change the spin of the state they act on, hence SUSY is a spacetime symmetry. And this kind of generators is called fermionic generators. (compare with the generators of gauge symmetries, which are unphysical ... | The group of supersymmetry transformations is an extension of the Poincare group, which is the isomorphism group of Minkowski spacetime. So it contains the Poincare group. However, the supersymmetry transformations are not symmetries of Minkowski spacetime. Rather they are the symmetries of a supermanifold which con... | https://physics.stackexchange.com |
133,497 | [
"https://mathoverflow.net/questions/133497",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25511/"
] | Hello everyone,
Let $S_g$ be a compact orientable surface of genus $g \geq 2$, and let $\mathcal{A}$ be the set of $\mathcal{C}^{\infty}$ Riemanniann metric on $S_g$ endowed with the topology of uniform convergence.
Let $h$ be in $\mathcal{A}$. Since $g \geq 2$, $S_g$ is covered by $D^2 \simeq \mathbb{R}^2$, and $h$... | If you take any reasonable probability measure on $\mathcal{A}$, then with probability $1$ there should be a single point of maximum curvature ; then the isometry group of $\tilde h$ must preserve a $\Gamma$-orbit, namely the set of the maximum curvature points in the universal covering. You should also be able to sing... | It follows from Theorem 1.3 of the paper of Farb and Weinberger, "Isometries, rigidity and universal covers", MR2456886 that either $\text{Iso}((D^2,\tilde{h}))$ is discrete in which case it contains $\Gamma$ with finite index, or the metric $h$ has constant negative curvature in which case, after scaling the metric, w... | https://mathoverflow.net |
443,019 | [
"https://physics.stackexchange.com/questions/443019",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/153014/"
] | I have seen free body diagrams of submerged objects that show the buoyancy force acting on the centre of mass of the object. However, the buoyancy force arises due to pressure differences between the upper and lower surfaces of the object. Therefore I have been thinking that the buoyancy force should be sketched in the... | The universe is expanding overall, and galaxies have relatively small “peculiar velocities” relative to the expanding universe. If you ignore the latter, then if the universe were to stop expanding, the galaxies would stop moving apart.
So the “motion” of galaxies due to the expanding universe is quite different from ... | Whether you say that the universe is expanding, or that the galaxies are moving away from each other, is just a matter of what reference frame you choose to use. Both descriptions are equally legitimate.
If you imagine a rigid grid with uniform spacing in all spacial directions, then it is natural to say that the gala... | https://physics.stackexchange.com |
26,726 | [
"https://electronics.stackexchange.com/questions/26726",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8154/"
] | I'm starting developing .NET MicroFramework with Netduino. My softwares are not rebotic oriented, they are mostly related to reproducing video and related stuff. (I know that in order to reproduce video I'll need more powerful processors then Netduino but I'm using it to study now).
But one thing that keeps in my mind... | Almost every board from GHI electronics has schematics and some also have PCB layout available.
You can search for a single-chip netfm solution like the USBIZI (that is a NXP LPC2388 micro), and starts from there...
| 1 - Buy everything you can. If you can buy a module from another company, there had better be some very compelling reasons why you want the design time, risk, inventory, and warranty replacement costs.
2 - Prototype local, shop global. Buy prototypes close to home. Time zones are easier to deal with, you can visit ... | https://electronics.stackexchange.com |
429,532 | [
"https://electronics.stackexchange.com/questions/429532",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/216450/"
] | I read that PLL are used in CPU to generate the clock, but I can't understand why.
I don't really have any guess of why this is.
| There are several reasons for this. A phase locked loop, or PLL, is a circuit that is used to generate a stable frequency that has a specific mathematical relationship to some reference frequency. Specifically, it is a circuit that is used to control some sort of electrically tunable oscillator (usually a voltage con... | PLLs can be used to multiply and divide frequencies. CPUs that have PLLs to generate their clocks are highly reconfigurable. The clock speed can be varied relative to the external reference clock over a wide range, and it's the PLL that makes this possible.
| https://electronics.stackexchange.com |
129,250 | [
"https://electronics.stackexchange.com/questions/129250",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5778/"
] | I'm facing a dilemma on how to route correctly in order to minimize noise on a data signal line. In the example bellow there is a 2-layer flexible PCB (which is very thin). The copper layer is 1OZ and the routing is 5mil. Red is Top layer and blue is bottom layer.
The blue wires are connected to LEDS which turn on or ... | <ol>
<li>Route straight, without any kinks, therefore minimize inductive coupling. Expanding according to @Majenko's comment: Cross your traces at right angles.</li>
<li>Route as thin as possible to minimize capacitive coupling.</li>
<li>Route as a single trace. Multiple signal connections that only slightly differ in ... | From the original question
<blockquote>
flexible PCB (which is very thin)
</blockquote>
Are you familiar with IPC-2223 and have a copy?
Are you aware where on the flexi the bend will occur?
The layout in the 1st will more than likely rule that layout routing out.
As to #2, #3 or #4 these appear at right-angles,... | https://electronics.stackexchange.com |
1,360,462 | [
"https://math.stackexchange.com/questions/1360462",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/174970/"
] | <blockquote>
If $u$ is a harmonic function defined on the complex plane and $f$ is entire then show that $u\circ f$ is harmonic.
</blockquote>
Actually I don't understand the question properly. As, $f$ is entire so, $f=u_1(x,y)+iv_1(x,y)$ , where $u_1$ and $v_1$ are harmonic and satisfies Cauchy-Riemann equations. B... | Harmonic functions are normally defined as maps from the $\mathbb{C}$ to $\mathbb{R}$, so $u \circ f: \mathbb{C} \rightarrow \mathbb{R}$.
Now to answer your question: Note that on simply connected sets every harmonic function is the real part of a holomorphic function. So $u=Re(g)$ for some holomorphic $g$.
Now we ha... | $u$ is harmonic if and only if
$$
\frac{\partial}{\partial z}\frac{\partial}{\partial\bar{z}}u=0\qquad\text{or equivalently}\qquad u_{xx}+u_{yy}=0\tag{1}
$$
$f$ is analytic if and only if
$$
\frac{\partial}{\partial\bar{z}}f=0\qquad\text{or equivalently}\qquad \frac{\partial}{\partial z}\bar{f}=0\tag{2}
$$
If $f=g+ih$,... | https://math.stackexchange.com |
330,770 | [
"https://softwareengineering.stackexchange.com/questions/330770",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/206473/"
] | I often find myself puzzled with such a questioning. I need to version my projects for two reasons:
<ul>
<li>publish source code with its whole history so that <em>people</em> will be able to get into it, explore it and make use of it.</li>
<li>archive my project with its whole history so that <em>I</em> will be able t... | You could consider a "root" repo containing your private tools/hooks/scripts, and a submodule for your public sources. The submodule would know nothing of the parent project and would have a "clean" history.
I should mention that I'm not really a fan of submodules, they are quite convoluted to work with IMO, but they ... | <code>.gitignore</code> only helps you to be selective on commit.
If you want different files pushed to different repositories, you need different commits, so probably separate branches.
You could keep only your sources on the <code>master</code> branch, and fork another branch <code>master.personal</code> from it, ad... | https://softwareengineering.stackexchange.com |
51,986 | [
"https://mechanics.stackexchange.com/questions/51986",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/34886/"
] | This is a 1979 Leyland Sherpa 230 1.7 L Petrol "O-series" engine.
I'm suspecting a blown head gasket and if this is confirmed I'll be removing the aluminium head and getting it resurfaced at the engineers.
I've read and it makes sense that the aluminium head is more vulnerable to warping than cast iron due to its ma... | Used to work on these and 99% you will be fine just doing the head.
Do check the block - decent straight edge and feeler gauges...
Make sure it is clean when you put it back together and follow the instructions precisely to torque it back down. Can’t temember if it tells you to use new bolts, but if it does - then do... | I watched a YouTube video once about a guy who had a recurring head gasket problem. The solution was to re-torque the bolts after first use. I'm no expert, so don't criticize me too much if I'm wrong here -- it's just a suggestion.
| https://mechanics.stackexchange.com |
661,142 | [
"https://physics.stackexchange.com/questions/661142",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/307354/"
] | <h3>Question</h3>
Are moving charges and time-varying electric fields really <strong>distinct</strong> causes of magnetic fields??
<hr />
<h3>Various EM Phenomena</h3>
Two larger purposes are providing some Background to make sure I follow Maxwells equations, and gaining any intuition about these four or five seemingly... | A not-so-well-known fact is that it is possible to obtain a complete solution for the Maxwell equations provided you assume the charge and current distributions fall sufficiently fast as you go to spatial infinity. These solutions are generalizations of the Coulomb and Biot--Savart laws for time-dependent cases and are... | Pulling some highlights from Alves’ detailed answer:
<strong>Q3: Maxwell Equations</strong>
The four Maxwell Equations (five relationships) are best understood as:
<hr />
1.Electric charges <em>cause</em> electric fields that converge/diverge to/from the charge: <span class="math-container">$$\nabla \cdot \vec{E} = \fr... | https://physics.stackexchange.com |
60,218 | [
"https://physics.stackexchange.com/questions/60218",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20330/"
] | This is a conceptual question in a solution I am trying to understand.
<strong>Problem statement:</strong>
I have a balloon with a volume of V $m^3$. The outside air temp is $K$ kelvin
and mass to lift is $m$ kg.
I am to find the temperature inside the balloon to barely lift the given mass.
The formula used is $F_{... | Kinetic energy need not be carried by any special carrier particle. Kinetic energy is inherent in any moving body or particle.
If you look closely at the conservation of energy/work energy theorem, all you get is that $$\Delta\left(\frac12mv^2\right)=\int \vec F\cdot d\vec x$$
The left hand side is (change in) "kinet... | All particles gravitate, so they carry gravitational potential energy. (Strictly speaking energy isn't always well-defined in general relativity, but you were asking for an answer low in technical details. Strictly speaking, one should better speak about the stress-energy densitites). They also carry energy associated ... | https://physics.stackexchange.com |
498 | [
"https://chemistry.stackexchange.com/questions/498",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/271/"
] | It seems from a brief search of the literature that 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF4) is a prototypical room temperature ionic liquid (RTIL) that has been studied extensively. However, numerous -- almost limitless -- combinations of cations and anions that give rise to ionic liquids are possible.... | This is a very good question. These compounds have been studied for long enough that most people working with them "know" the answers to these questions, but the answers are buried in physical chemistry articles from 20 or more years ago. The imidazolium tetrafluoroborate salts are popular RTILs because 1) they have th... | Another answer could be that they're so popular bebcause of their potentional as fuel for ion thrusters to increase the engine's specific impulse.
| https://chemistry.stackexchange.com |
2,843 | [
"https://mechanics.stackexchange.com/questions/2843",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1517/"
] | <strong>Car:</strong> Polo TDI 2004 1.4 with 190,000 km (118,060 miles) on the clock. While
<strong>Issue:</strong> driving it intermittently (distance/time are not factors it seems) it starts to spew black/dark grey smoke and all power is lost (feels like the turbo has turned off). If I turn the car off and immediat... | A common fault on variable-vane turbos (which I'm not sure whether the 1.4 has) is hitting limp mode due to overboosting. This can happen if a turbo has had an easy life around town and is coked up, then you suddenly ask it for some performance down the motorway or similar. However, this doesn't normally come with any ... | I have a Polo classic 1.4 TDI
Had the same problem of loosing power.
The vacuum unit on the Turbo have a steel pipe, and a rubber vacuum pipe fit over it.
The point of the rubber pipe get hot, or is hard on the tip, so I loos boost pressure.
I cut a inch of it and replace it back with a proper clamp, and it look if the... | https://mechanics.stackexchange.com |
260,420 | [
"https://stats.stackexchange.com/questions/260420",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/146347/"
] | I have conducted a logistic regression analysis using dummy variables in R. I would like to convert the outputted oddsratio standard error to probability (interpreted as risk) standard error. I am able to convert the outputted odds ratio to risk through:
<ol>
<li>ln(odds) = intercept + ln(odds ratio)</li>
<li>odds = ... | Work on the log scale for as long as you can and then convert to the scale of odds at the last moment. So compute the confidence interval on the log scale and then convert the limits and the estimate to the odds scale as in your step 2. I suppose you could compute a standard error for the odds using the delta method bu... | You can do the following to calculate odds ratios with custom CI.
<pre><code>library(oddsratio)
fit.glm <- glm(admit ~ gre + gpa + rank, data = data.glm, family = "binomial")
calc.oddsratio.glm(data = data.glm, model = fit.glm,
incr = list(gre = 380, gpa = 5), CI = .70)
predictor oddsratio ... | https://stats.stackexchange.com |
28,080 | [
"https://mechanics.stackexchange.com/questions/28080",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/16041/"
] | I have a 2008 Hyundai Santa Fe GLS, 2.7 L V6, 2WD, 5-speed manual, 113,000 miles.
I recently replaced the Canister Purge Valve, because the solenoid was burned up and check engine light was on for that code. I noticed when I was replacing it that it must have been replaced once before because it was not the OEM part (... | The Purge is controlled by the PCM with a pulse width modulated switch signal. It is normal for it to cycle rapidly. This allows small amounts of the fuel vapor to be metered into the cylinders. This method allows the system maintain fuel control.
One of the main jobs of the evaporative control system purge valve is ... | Something i just learned is that if you have an electric gas peddle than if you ever reset the computer system you need to recalibrate the peddle. Super simple u just turn key to On but dont start the car wait for all the dash lights to go out. Ur electric warning light and or ur check engine light may still be on th... | https://mechanics.stackexchange.com |
152,887 | [
"https://electronics.stackexchange.com/questions/152887",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16948/"
] | I'm developing a project that requires ICs that are in a QFN package, some have a slug on the bottom of the IC. Since these are QFNs, I'm not interested in hand soldering these; so I'm leaning toward using the toaster oven method to solder the components in place.
However this is my first time doing this and I want to... | There are a couple of things going on here.
First of all, many isolation transformers do NOT isolate the ground terminal on the load side; they simply connect it through to the ground on the supply side. I've never understood this reasoning, but there it is. This means that the input ground of your scope <em>is still ... | I have a couple of power supplies intended for electrophoresis use and they have a ground fault indicator. In the case of my power supplies, this fault indicator trips when there is <em>either</em> a missing AC ground OR if the power supply negative terminal is connected to earth ground.
So check your supply for both... | https://electronics.stackexchange.com |
123,464 | [
"https://physics.stackexchange.com/questions/123464",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52960/"
] | I have a bar of length $L$, mass $m$, and negligible width. The bar can rotate along an axis through its center of mass (the rotation is in the $x$-$y$ plane), and also can move up and down (in the vertical axis).
<blockquote>
My question is: What is the (gravitational) potential energy of this bar?
</blockquote>
... | Integrating each mass slice and just taking the center of mass yield the same result. That is because:
$$PE = g \int y \, {\rm d}m = m g y_{cm}$$
from the definition of the center of mass
$$y_{cm} = \tfrac{\int y \,{\rm d}m}{m} $$
| Okay, first of all, your question is unclear.<br>
'Potential energy of a bar' has no meaning whatsoever. PE is of a system of interacting objects or particles. We sometimes just say that the PE of a mass $m$ at a height $h$ from the ground is $mgh$. But strictly speaking, this is actually the PE of the system: Mass-$m$... | https://physics.stackexchange.com |
452,237 | [
"https://physics.stackexchange.com/questions/452237",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214136/"
] | Since the tension force is a central acting force, the torque on an orbiting ball about that center is zero. But if the rope is cut down during motion the torque would still remain zero. This would mean that angular momentum of the orbiting ball should be conserved, but I find everywhere that ball will move in a straig... | The flaw in your reasoning is thinking that straight line motion at constant velocity does not constitute constant angular momentum about some point, but it actually does.
Angular momentum is given by<span class="math-container">$^*$</span>
<span class="math-container">$$\mathbf L=\mathbf r\times\mathbf p$$</span>
Wit... | The planets will continue moving with the momentum they have at the moment the Sun disappears, apart from mutual attraction. These orbitals conserve planetary angular momentum is conserved. This is clear from the formula <span class="math-container">$L = \vec r \times \vec p$</span>. <span class="math-container">$r \si... | https://physics.stackexchange.com |
14,273 | [
"https://datascience.stackexchange.com/questions/14273",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/21560/"
] | I have a factor variable in my data frame with values where in the original CSV "NA" was intended to mean simply "None", not missing data. Hence I want replace every value in the given column with "None" factor value. I tried this:
<pre><code>DF$col[is.na(DF$col)] <- "None"
</code></pre>
but this throws the foll... | You need to add "None" to the factor level and refactor the column DF$col. I added an example script using the iris dataset.
<pre><code>df <- iris
# set 20 Species to NA
set.seed(1234)
s <- sample(nrow(df), 20)
df$Species[s] <- NA
# Get levels and add "None"
levels <- levels(df$Species)
levels[length(le... | You can use this function :
<h3>forcats::fct_explicit_na</h3>
<pre><code>library(forcats)
fct_explicit_na(DF$col, na_level = "None")
</code></pre>
<h3>Usage</h3>
It can be used within the mutate function and piped to edit DF directly:
<pre><code>library(tidyverse) # for tidy data packages, automatically loads d... | https://datascience.stackexchange.com |
11,208 | [
"https://cs.stackexchange.com/questions/11208",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7675/"
] | If I am given a graph which forms a tree, I am interested in finding a vertex which maximizes the minimum distance to any leaf.
I am sure this problem has been studied before.
Does anybody know the name of this problem or an algorithm for solving it?
| To find a vertex of maximum distance from any leaf, you can perform a breadth-first search starting from many starting points, i.e. the leaves. Because a BFS visits each node by the shortest possible path from the source(s) of the search, we can easily attribute to each node the distance to the nearest leaf.
<ul>
<li>... | Perform breadth-first seach from all leaves in parallel, i.e. visit all neigbours of all leaves, then their respective neighbours, and so on.
The node visited last is your winner.
If you let all searches share the <code>visited</code> flag, no vertex is visited twice. Since we have a tree, also every edge is visited o... | https://cs.stackexchange.com |
354,575 | [
"https://physics.stackexchange.com/questions/354575",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75734/"
] | Suppose you have two blocks, stacked, and the top block, of mass $m_1$, is subject to a force $$\textbf{F} = F_1 \; \textbf{e}_x$$ and there exists friction $u_k$ between the blocks but the lower block is placed upon a frictionless surface. The force on the lower block is given by
$$\textbf{F}_f = m_1g\mu_k\; \textbf... | The reason you get the same result as if $F_f$ were simply applied to the bottom block is because $F_f$ <em>is</em> a force applied to the bottom block. Whether it's applied to the top or the side is not relevant.
The mass of the top block will have an effect on the acceleration of the top block which you are assumin... | <ul>
<li>The <strong>origin</strong> of the force acting on the bottom block doesn't matter. It could be either a spring or what so ever. In your example it is the friction force
$F_f = m_1 g \mu_k$.</li>
<li>If a force $F$ acts on a body of mass $m_2$, the mass accelerates by $a_2 = F/m_2$.</li>
<li>The force is actin... | https://physics.stackexchange.com |
237,389 | [
"https://softwareengineering.stackexchange.com/questions/237389",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/100991/"
] | <h1>Scenario</h1>
I haven't faced this requirement before, so I'm not confident with my solution. Our team drew up a plan to design a web application using a basic HAT stack for a project with a 4 month development time. We presented it to the client, who added two big new requirements. The requirements were:
<ul>
<l... | The biggest problem you have is going to be with the databases. Within relational databases, you've got some dialectical differences between them (things that postgres does differently than mysql or oracle) - different functions, different column types. This will make writing the proper query and creating the proper ... | There are two problems here:
<ul>
<li>Getting the client to understand what's possible, and what's not. Especially, development can't be accelerated arbitrarily by throwing money or manpower at it. It would be better to identify priority features that have to be present in the first release, and optional features that... | https://softwareengineering.stackexchange.com |
179,154 | [
"https://security.stackexchange.com/questions/179154",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/97047/"
] | I just went through a penetration test, and what was wierd was we had a comment back about a potential data leak via DNS snooping (I realise this is boiler plate, and also this is an internal only DNS, which adds complexity):
<blockquote>
For instance, if an attacker was interested in whether your company
utilizes... | You are in the same boat as many, many other technology companies. If the pentest company did not factor in all of your points above into some <em>context</em> for the risks they identified, you might want to consider changing companies.
Information disclosure presents a <em>risk</em>. You need to assess that risk and... | Shoudln't the pentesters gauge whether your security is up to snuff while taking into consideration the level of information leakage? An attacker can gather all the information about your company, but information on a company itself doesn't get you past firewalls. You still need to execute all the technical bits to car... | https://security.stackexchange.com |
170,619 | [
"https://softwareengineering.stackexchange.com/questions/170619",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/28140/"
] | I believe that if you have your repositories use an ORM that it's already enough abstracted from the database.
However, where I am working now, someone believe that we should have a layer that abstract the ORM in case that we would like to change the ORM later.
Is it really necessary or it's simply a lot of over head t... | That way lies madness. It is highly unlikely that you would ever need to change ORMs. And if you ever decide to change the ORM, the cost of rewriting the mappings will be a tiny fraction of the cost to develop and maintain your own meta-ORM. I would expect that you could write a few scripts to do 95% of the work nee... | The ORM provides an abstraction for your data layer to be independent of its RDBMS, but it may not be enough to "untie" your business layer from your data layer. Specifically, you should not let objects that map to RDBMS tables to "leak" directly into the business layer.
At the very least, your business layer needs to... | https://softwareengineering.stackexchange.com |
14,122 | [
"https://chemistry.stackexchange.com/questions/14122",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7002/"
] | What are the chemical reactions and/or chemical processes that take place during SFE(supercritical fluid extraction)? Namely supercritical $\ce{CO2}$.
| Supercritical fluid technology is used primarily to enhance the chemical extraction process. The solubility of a compound in a supercritical solvent increases as the system pressure increases at constant temperature. This is due to the highly pressurized supercritical solvent disrupting the intermolecular attractive f... | Ideally no reactions should occur during an SF extraction. In all the extractions a solvent is used to extract different substances from a matrix. In SFE the solvent is a supercritical fluid, in most of the cases is used $CO_{2}$ but not always. The chemicals process related to the extraction is mainly the solubilizati... | https://chemistry.stackexchange.com |
500,565 | [
"https://physics.stackexchange.com/questions/500565",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/227641/"
] | If a ball was thrown to a wall, How could we calculate the impulse on the wall ?
For example, if I throw a <span class="math-container">$2kg$</span> ball with <span class="math-container">$ 4m/s$</span>, and it returned with the same speed but in the opposite direction, so the impulse on the ball would be <span class... | Let the mass of the ball be <span class="math-container">$m$</span> and that of the wall (and the Earth) be <span class="math-container">$M$</span>.<br>
The initial velocity of the wall is <span class="math-container">$\vec v_{\rm i}$</span> and that of the wall is zero.<br>
The final velocity of the wall is <span clas... | As the other answers have pointed out, its because <span class="math-container">$I=m\Delta v$</span> applies to the <em>net</em> impulse. The wall transfers nearly all of the impulse down into the ground, and into the earth, so the net impulse on the wall is nearly 0, even though the impulse on the wall from the ball ... | https://physics.stackexchange.com |
665,816 | [
"https://math.stackexchange.com/questions/665816",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/114291/"
] | prove this identity :
$$\sin(x+y)\sin(x-y)=\sin^2 x - \sin^2 y$$
I tried solving it with additional formulas but I can't get the right answer. I get
$$\sin^2 x \cos^2 y-\cos^2 x \sin^2 y$$
| $\sin^2 x \cos^2 y-\cos^2 x \sin^2 y=\sin^2 x(1-\sin^2 y) -(1-\sin^2 x) \sin ^2 y$
$=\sin^2 x -\sin^2 x\sin^2y -\sin ^2 y + \sin^2x\sin^2y$
$=\sin^2 x - \sin ^2 y$
| Use the identity $$\sin(x\pm y)=\sin x\cos y\pm \sin y\cos x$$
and we can get
\begin{align*}
LHS&=\sin(x+y)\sin(x-y)\\
&=(\sin x\cos y+\cos x\sin y)(\sin x\cos y-\cos x\sin y)\\
&=\sin^2x\cos^2y-\cos^2x\sin^2y \\
\end{align*}
See if you can take it from here using the identity $$\sin^2x+\cos^2x=1.$$
| https://math.stackexchange.com |
41,660 | [
"https://mathoverflow.net/questions/41660",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9924/"
] | Given an operator $f\colon R^m\to R^n$, can one always find a non-zero vector
$x\in \{ 0,1 \}^m$ such that $\|f(x)\|/\|x\|\ge0.01\|f\|$? (Here I denote by
$\|\cdot\|$ both the Euclidean norms in $R^m$ and $R^n$ and the induced
operator norm.) The answer may well be negative -- any examples?
<hr>
In case the answer to... | The answer is no. First, to understand the question, WLOG $f$ is symmetric and positive definite; a general $f$ has a polar decomposition $f = os$ and the orthogonal factor $o$ has no effect on any of the norms in question. Then, WLOG $f$ is a rank 1 projection. The second and subsequent eigenvalues of $f$ do not in... | Of course no. Remember that the operator norm of $A$ wrto the Eucliedan norms is the attained at an eigenvector of $S:=A^TA. $ Try a suitable simple binary $2\times 2$ matrix and compare the values of $\|Ax\|$ on the eigenvectors of $S$ and in the three nonzero binary vectors $(01), (10), (11).$
However, if instead ... | https://mathoverflow.net |
302,177 | [
"https://physics.stackexchange.com/questions/302177",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140781/"
] | A ball sitting in a person's hand is at rest. The ball is thrown into the air. There must be some upward acceleration which is greater than the acceleration due to gravity, since in order for the ball to move, the upward force must be greater than the force of gravity. Since the mass of the ball doesn't change, the acc... | First we need to clear up the concept of acceleration. There is only one linear acceleration of the object. There is not an acceleration due to gravity and a separate acceleration due to the push of the hand. There are two <em>forces</em> (push of the hand and weight) which combine to give the actual, single accelerati... | Actually, when a body is projected upwards, the only force acting on it once it is released is gravitational force, and the only acceleration is caused by gravity, and is downwards. When you project a body, it must have some initial velocity. Using the equation of motion, $$v= v_0+at$$ we can say that if a body is pro... | https://physics.stackexchange.com |
175,966 | [
"https://mathoverflow.net/questions/175966",
"https://mathoverflow.net",
"https://mathoverflow.net/users/55956/"
] | Let $\pi _1:SS\to Grpd$ denote the fundamental groupoid functor, from simplicial sets to groupoids, and let $N:Grpd\to SS$ denote the nerve functor. Then $\pi _1$ is left adjoint to $N.$
On simplicial sets we consider the usual model category and on groupoids the model category structure inherited by the one given by ... | Just for fun, here's a purely abstract way of seeing neither of these can happen:
The functors you wrote down both preserve weak equivalences, so are morphisms of relative categories, and induce adjunctions of the associated $\left(\infty,1\right)$-categories, which are $\infty$-groupoids and $1$-groupoids (which is a... | The fundamental groupoid does not preserve homotopy limits. The simplest examples can be obtained from the path-space sequence $\Omega X\to \operatorname{pt}\to X$ which shows that $\Omega X$ is the homotopy limit of $\operatorname{pt}\to X\leftarrow \operatorname{pt}$. If $\pi_1$ preserves homotopy limits, then the fu... | https://mathoverflow.net |
127,464 | [
"https://dba.stackexchange.com/questions/127464",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/77575/"
] | On Windows Server 2008 R2, when I am trying to startup Oracle 11g database it shows an error:
<pre class="lang-none prettyprint-override"><code>SQL> startup
ORACLE instance started.
Total System Global Area 3206836224 bytes
Fixed Size 2180024 bytes
Variable Size 1996491848 bytes
Databas... | if you do not have problems with your disks and the controlfile is corrupted you can do the following:
start the database in nomount (startup nomount), then check the output of the command
<pre><code>show parameter control
</code></pre>
(run the command in sqlplus). If the command shows more than one control file, y... | While investigating the cause of the problem we must be able to find the problem area. The top most error(ORA-00204) says that the Oracle process is unable to read the block from control file. <BR>
Second error(ORA-00202) specifies the name of the control file which the Oracle process is unable to access and read. <BR>... | https://dba.stackexchange.com |
1,411,161 | [
"https://math.stackexchange.com/questions/1411161",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/258068/"
] | $F(k)$ = $$ \lim_{n\to \infty}{\frac{1^k + 2^k +...+n^k}{(1^2 + 2^2 +...+n^2)*(1^3 + 2^3 +...+n^3)}} $$
I need help in finding $F(5)$ and $F(6)$.
I tried converting it into summation form and using the progression formulas of $n^2$ and $n^3$ but it was of no use.
| <strong>Theorem:</strong> Define $S_r(n)=1^r+2^2+...+n^r$, $$\frac{n^{r+1}}{r+1}\leq S_r(n)\leq\frac{(n+1)^{r+1}}{r+1}$$ for any positive $r\geq0$
Then $$\frac{12n^{k+1}}{(k+1)(n+1)^3(n+1)^4}\leq{\frac{1^k + 2^k +...+n^k}{(1^2 + 2^2 +...+n^2)\cdot(1^3 + 2^3 +...+n^3)}}\leq \frac{12(n+1)^{k+1}}{(k+1)n^3n^4}$$
So, $$F(... | You only need the largest terms in the fraction, the rest converge to 0. What are the leading constants in $\sum_{j=1}^{n} k^5, \sum_{j=1}^{n} k^2, \sum_{j=1}^{n} k^3$?
| https://math.stackexchange.com |
8,068 | [
"https://mechanics.stackexchange.com/questions/8068",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2002/"
] | I had quite a morning with my 1986 BMW K75 this weekend. The plan was to ride the bike to a friends house to store it for the winter. The weather was pretty cold on this particular morning, perhaps 15*F (-9*C), and the bike refused to start, the first time I've ever had any starting issues with this bike.
This bike ha... | Warmer weather this weekend provided an opportunity to try to get the bike running again. I wanted to give myself the best shot possible, so I installed new spark plugs and picked up some starting fluid.
I also found the source of the change in exhaust note that occurred after the backfires. In fact, the difference w... | I have seem auto mufflers split wide open by an exhaust backfire. Back in the mid 70's and early 80's it used to be one of the top reasons for muffler warranty rejection. You may have damaged a single or several of the internal baffles in the mufflers. This may or may not be a problem. If it is now loud enough it to be... | https://mechanics.stackexchange.com |
141,706 | [
"https://electronics.stackexchange.com/questions/141706",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/59833/"
] | <img src="https://i.stack.imgur.com/Ympac.png" alt="enter image description here">
You can see that Is was labeled as going towards the voltage source when doing KCL at node a. Can someone tell me why? Is it not supposed to go into the node?
| It is just by convention.
If you draw all the currents as either going out of a node (or into a node) a node you can say:
<blockquote>
The sum of all currents going out of a node are equal to 0
</blockquote>
Obviously then some of the current will have negative values if they are infact flowing into the node, but ... | It's arbitrary. The three currents is, i, and Ic were chosen to go in the same direction so that they will sum to zero without worrying about signs.
You could as easily draw the arrows the other direction.
If the current is actually going in the opposite direction, then the sign of the solution will be negative.
| https://electronics.stackexchange.com |
2,905,005 | [
"https://math.stackexchange.com/questions/2905005",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/220674/"
] | I understand
$'ln(x) = \frac{1}{'e^{ln(x)}} =\frac{1}{x} $
But if I use the chain rule in the denominator to calculate the derivative
$'e^{ln(x)} => ('e^{ln(x)})('ln(x))=(x)(\frac{1}{x})=1$
But then
$\frac{1}{x}\neq\frac{1}{1}$
What am I doing wrong?
| The devil is in the detail. In your first equation it must be 1/e^Ln(x)=1/x. For the following reason: suppose f,g are differentiable. The chain rule then says:
f(g(x))’=f’(g(x))*g’(x)
So if g is the inverse function of f, f(g(x))=x then differentiation gives:
1= f’(g(x))*g’(x) I.e.
g’(x)=1/f’(g(x)) when the denomi... | $f(x)=e^x$ and $f^{-1}(x)=\ln(x)$. By direct computation we see that
$(f^{-1})'(x)=d/dx(\ln(x))=1/x$
By the inverse function rule, this should be equal to $\frac{1}{f'(f^{-1}(x))}$. Well, $f'(x)=e^x$ and hence $\frac{1}{f'(f^{-1}(x))}=\frac{1}{e^{\ln(x)}}=\frac{1}{x}$ as desired.
| https://math.stackexchange.com |
94,517 | [
"https://mathoverflow.net/questions/94517",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20729/"
] | This question has been bugging me for some time.
Take the hamiltonian for the hydrogen atom: $$\hat{H}=-\frac{1}{2}\nabla^2-\frac{1}{r},$$ acting on (a domain contained in) $L^2(\mathbb{R}^3)$. It is standard fact that this is an unbounded operator which has a countable infinity of eigenvalues, all of which are negati... | First of all, the Hamiltonian in question is defined on <span class="math-container">$L^2(\mathbb R^3)$</span>, not on <span class="math-container">$L^2(\mathbb R)$</span>. This is important because in the one-dimensional case the potential would have a non-integrable singularity which complicates things seriously. On ... | I looked in Anatoly's references, and <em>Quantum mechanics for mathematicians</em> by Leon A. Takhtajan does have the calculation of the continuum wavefunctions, though it does not do the <span class="math-container">$k=0$</span> case.
The eigenfunction <span class="math-container">$f_l$</span> at energy <span class="... | https://mathoverflow.net |
63,083 | [
"https://cs.stackexchange.com/questions/63083",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/41751/"
] | Say you have a string <code>S</code> and wish to store indices of it, e.g. letter at index 3 of "toast" is 'a'. Seems that people generally consider an index as taking <code>O(1)</code> space to store*. But doesn't it take <code>O(log(|S|))</code> space?
If we use binary bits...
<ul>
<li>length 4 string => index must... | These are correct (unless you explicitly specify a non-standard model of computing):
<ul>
<li>$O(1)$ space,</li>
<li>$O(1)$ words of space,</li>
<li>$O(\log|S|)$ bits of space.</li>
</ul>
| Depends on which model you are interested in.
On RAMs with the <em>uniform</em> or <em>unit</em> cost model, (not too large) numbers take constant space to store, and constant time to work with.
On RAMs with the <em>logarithmic</em> cost model and TMs, they take logarithmic space.
| https://cs.stackexchange.com |
311,124 | [
"https://dba.stackexchange.com/questions/311124",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/223196/"
] | I have 2 database clusters that operate independently. In the future, I may need to move the records for a customer from cluster 1 to 2. I have a bash script where I do server-side copying of the table records into CSV files from cluster 1 and then restore them into cluster 2.
The associations between data use sequenti... | Rick James' answer made me aware that (whyever) the conf file was not read. So I copied <code>/etc/mysql/mysql.conf.d/mysqld.cnf</code> to <code>/etc/mysql/my.cnf</code>. That one <em>is</em> read fine.
I then had to define (in <code>my.cnf</code>):
<pre><code>[mysqld]
innodb_tmpdir=$yourNewTmpPath
innodb_temp_data_fil... | <pre><code>mysqld --help --verbose
</code></pre>
At about line 13, it will say where the config file is. It is probably not spelled the way you spelled it. Mine says
<pre><code>...
Default options are read from the following files in the given order:
/etc/my.cnf /etc/mysql/my.cnf ~/.my.cnf
...
</code></pre>
| https://dba.stackexchange.com |
12,462 | [
"https://physics.stackexchange.com/questions/12462",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4551/"
] | In astrophysics, I often come across the speed of sound. I understand that, broadly, it represents the speed at which perturbations travel through a medium. But there's more than one speed of sound. The most common seem to be <em>isothermal</em> and <em>adiabatic</em>, which are defined as $c_s^2=(dp/d\rho)_T$ and $c_s... | Fluids are complicated systems described by non-linear differential equations that can't be reasonably treated in a full generality (certainly not analytically). Just consider the kinds of waves that propagate in the sea -- deep or shallow water, solitons, tsunami and many others (this is not to say that these are soun... | The isothermal sound speed applies when the cooling timescale is very fast compared to the propagation speed of the wave. Often in astrophysics the temperature of the gas is set by thermal balance between heating sources and radiative cooling and the timescale to get into balance is short compared to the sound wave t... | https://physics.stackexchange.com |
425,119 | [
"https://physics.stackexchange.com/questions/425119",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/200265/"
] | Was it simply that the density and/or kinetic energy got too low, because of expansion? Or was it something about the weak force itself (which I thought gelled around $10^{-10}$s?
For the CMB, photons decoupled because charged particles disappeared (recombined). But for neutrinos, their reactions involved electrons, p... | The general criterion for thermal equilibrium is that the neutrinos must couple to the radiation field (via charged particles) on timescales that are small compared with the timescale on which the temperature of the universe is changing.
Whether this condition is met depends on <em>both</em> the energy of the neutrino... | before one second, the density of the universe was high enough that interactions between them and the other constituents of the universe were common enough to put them all into thermal equilibrium, even though the interaction cross-sections themselves were tiny. After one second, the neutrino energies and the density o... | https://physics.stackexchange.com |
205,384 | [
"https://security.stackexchange.com/questions/205384",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/201560/"
] | I'm wondering what the best tactic is to transfer dangerous files from an internet connected machine to an offline, separated from the web, virtual machine.
Why should I do that? Because I want to examine how small viruses, malware, spyware, etc. works, but without the risk that the beast gets released and infect my ... | You have a bit of an XY problem. The problem is not how to safely transfer files to your sandbox. The problem is how to not accidentally transfer the files to a non-sandbox. This is minorly complicated by the fact that your sandbox is virtual, so you will have to transfer the files into a non-sandboxed piece of hard... | Use a virtual machine that can control a USB device, and that <em>takes away control by the host machine</em>, i.e. the host machine no longer sees the USB when it is inserted.
Then transfer the files by cheap USB stick and physically destroy it afterwards<br />
(Or store it safely for future investigation)
Sorry, I ... | https://security.stackexchange.com |
101,024 | [
"https://chemistry.stackexchange.com/questions/101024",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/41411/"
] | fluorinated ethylene propylene (FEP) is close relative of poly(tetra-fluoroethylene) (PTFE), both only contain fluorine and carbon atoms,both have very similiar properties yet FEP is relatively transparent while PTFE is opaque, why?
| Otherwise clear plastics lose their transparency from crystallization of the polymer. The crystalline phases have different refractive indices and when a sufficient number form the light becomes so scattered that the material is no longer transparent. Note this is an extensive property and if a material is thick enoug... | The transparency of a plastic does not depend on its nature but on how it is made.
To get a transparent plastic it must be cooled very fast when it is in molten state.
If the cooling is too slow, the polymer begins to order it self in more or less crystalline domains.
When it is not isotropic anymore, it is also n... | https://chemistry.stackexchange.com |
3,894,927 | [
"https://math.stackexchange.com/questions/3894927",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/812806/"
] | How does the following matrix algebra reduce dimensionally
<span class="math-container">$$\left( \frac{\boldsymbol{\Sigma}^{-1} \boldsymbol{1} }{\boldsymbol{1}^\top \boldsymbol{\Sigma}^{-1} \boldsymbol{1}}\right)^\top$$</span>
given that <span class="math-container">$\boldsymbol{\Sigma}$</span> is the covariance matrix... | There are essentially two ways:
<ul>
<li>Through the properties of matrix multiplication and <span class="math-container">$(AB)^\top=B^\top A^\top$</span> and <span class="math-container">$(A^{-1})^\top=(A^\top)^{-1}$</span>: <span class="math-container">$$\left(\frac{\Sigma^{-1}1}{1^\top\Sigma^{-1} 1}\right)^\top=(\Si... | Assuming your column of ones is a column vector, then the top is a column vector so the transpose is a row vector. So it's not a scalar. Write it as <span class="math-container">$$\left( \boldsymbol{\Sigma}^{-1} \boldsymbol{1} (\boldsymbol{1}^\top \boldsymbol{\Sigma}^{-1} \boldsymbol{1})^{-1}\right)^\top$$</span>and it... | https://math.stackexchange.com |
372,425 | [
"https://physics.stackexchange.com/questions/372425",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56605/"
] | Using the plane wave ansatz
$$\phi(x) = e^{ik_\mu x^\mu}$$
the solution to the Klein-Gordon equation $(\Box + m^2) \phi(x) =0$ can be written as a sum of solutions, since the equation is linear and the superposition principle holds, as
$$\phi(x) = \sum_{{k}} \left( Ae^{ik_\mu x^\mu} + Be^{-ik_\mu x^\mu} \right).$$
How... | Let us start with the ansatz (I'll assume mostly plus metric signature)
\begin{equation}
\hat\phi(x) = \int \frac{\mathrm{d}^3 \mathbf{k}}{(2\pi)^{3/2}}\left(\hat A_\mathbf{k} e^{i k\cdot x} + \hat B_\mathbf{k}e^{-ik\cdot x}\right)
\end{equation}
where $\hat A_\mathbf{k}$ and $\hat B_\mathbf{k}$ are some arbitrary o... | You might feel more comfortable if we run the reasoning 'in reverse' a bit. I'm basically just recounting what all the standard texts do, but without jumping ahead in the interpretation.
<ul>
<li>We begin with the canonically quantized Klein-Gordon field $\phi(\mathbf{x})$ and its conjugate momentum $\pi(\mathbf{x})$... | https://physics.stackexchange.com |
249,524 | [
"https://softwareengineering.stackexchange.com/questions/249524",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/48312/"
] | The C11 standard says the arrays, both sized and variable length "shall have a value greater than zero." What is the justification for not allowing a length of 0?
Especially for variable length arrays it makes perfect sense to have a size of zero every once and a while. It is also useful for static arrays when their... | The issue I would wager is that C arrays are just pointers to the beginning of an allocated chunk of memory. Having a 0 size would mean that you have a pointer to... nothing? You can't have nothing, so there would have had to be some arbitrary thing chosen. You can't use <code>null</code>, because then your 0 length a... | Let's look at how an array is typically laid out in memory:
<pre><code> +----+
arr[0] : | |
+----+
arr[1] : | |
+----+
arr[2] : | |
+----+
...
+----+
arr[n] : | |
+----+
</code></pre>
Note that there isn't a separate object named <code>arr</co... | https://softwareengineering.stackexchange.com |
180,509 | [
"https://security.stackexchange.com/questions/180509",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/19973/"
] | When trying to send an email over smtp with SSL in Java code I get the following exception:
<blockquote>
PKIX path building failed:
sun.security.provider.certpath.SunCertPathBuilderException: unable to
find valid certification path to requested target. Failed messages:
javax.mail.MessagingException: Could not ... | The certificate authority was Comodo which was fine, after running <code>keytool -printcert -sslserver host</code> as per Dave's comment, I found out the problem was on my end with my virus scanner (Avast) inserting its own certificate. Even after disabling SSL scanning and SMTP scanning the certificate still showed as... | If the SMTP server is using a self-signed certificate and you did not import the certificate as trusted this exception would be the expected one and something would be wrong (insecure) with your code if you would not get such an error. If instead the certificate should be signed by a public CA it might be a problem tha... | https://security.stackexchange.com |
859,285 | [
"https://math.stackexchange.com/questions/859285",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/159628/"
] | I'm confused on if I should count a subset as one element or if I should count all the elements of that subset when computing cardinality.
Example:
Given the set $A = \{1,2,3,\{4,5,6\}\}$ does $A$ have a cardinality of $4$ (using the convention where I count the subset as just one element) or does it have a cardinali... | Assuming we take matrices under the usual norm, i.e. for $A \in \mathbb{R}^{n \times n}$:
$$
\|A\| = \sqrt{\sum_{i,j = 1}^n |A_{ij}|^2}
$$
we can show that the Euclidean matrix group is homeomorphic to $\Bbb R \times \Bbb R \times S^1$. This form should be easier to work with.
In other words, show that
$$
\left( \beg... | The upper left $2 \times 2$-block parameterizes a familiar space, call it $X$. The $(x,y)$-entries give a copy of $\mathbb{R}^2$. The group is homeomorphic to $X \times \mathbb{R}^2$ and therefore the fundamental group of the Euclidean group is isomorphic to $\pi_1(X)$.
| https://math.stackexchange.com |
94,892 | [
"https://mathoverflow.net/questions/94892",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21269/"
] | Let us denote by the symbol $\mathcal{G}$, a group of functions $f: \mathbb{R} \rightarrow \mathbb{R}$ (with the composition operation) that is additionally closed under all affine change of variables of the form (homothety):
$$ h(x) = mx, m>0$$
In other words, I would like the following property to hold for any a... | If $G$ contains the linear group consisting of all functions of the form $h_m(x) = mx$ then obviously it satisfies your conditions.
Conversely, by the definition of the derivative,
(*) $lim_{m \to \infty} (h_m^{-1} f h_m(x)) = f'(0) x$
So the closure $\bar G$ of your group (in some appropriate topology) contains all... | Let $G$ be any group of functions. Let $H$ be the group of all compositions of functions of the form $f(mx)/m$ where $m>0$ and $f\in G$. Then $H$ is a group of the sort you're looking for, and all such groups arise in this way.
| https://mathoverflow.net |
201,697 | [
"https://physics.stackexchange.com/questions/201697",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52363/"
] | I'm having a little trouble understanding what makes a planetary orbit explicitly elliptical. Is it simply that the initial velocity was different from the circular orbit case for a given starting position (radius from the sun) and this becomes an elliptical orbit (or more generally, an arbitrary conic section)?
Is t... | There is in fact more information contained in the eccentricity. The Kepler problem (in fact, every two body problem with an inverse-square force) has a subtle symmetry: It is symmetric under certain rotations of the four dimensional space. By Noether's theorem, every symmetry of a system corresponds to a conserved qua... | The orbit (in polar coordinates) of a body under a inverse-square force, $-K/r^2$, is given by
$$r(\phi)=\frac{L^2/mK}{1+\sqrt{1+\frac{2L^2E}{mK^2}}\cos\phi},$$
where $E$ and $L$ are the energy and the angular momentum of the particle. The equation above is just the polar representation of a conic section of conic para... | https://physics.stackexchange.com |
662,432 | [
"https://physics.stackexchange.com/questions/662432",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266050/"
] | Consider a physical quantity <span class="math-container">$\phi$</span> that is globally conserved.
From Feynman's argument (in his volume 2 I think), which states that local conservation follows from global conservation due to special relativity, we can say that <span class="math-container">$\phi$</span> is locally co... | Paul T. provides a good answer regarding the case where the height of the bottoms of the poles are the same (which is what was asked for in the question). The main difference in that case is due to the different heights of the centers of mass of the two rods.
However, you might ask, what if the centers of mass of the ... | Yes. As described in the questions, there is very small difference between the acceleration of the two poles with the shorter one accelerating faster.
<h1>The difference</h1>
The gravitational force acting on a pole is
<span class="math-container">$$F = \frac{GMm}{r^2},$$</span>
where <span class="math-container">$M$<... | https://physics.stackexchange.com |
108,640 | [
"https://softwareengineering.stackexchange.com/questions/108640",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36811/"
] | Is the execution time of a unit test useful for anything? Is a unit test an appropriate place for any sort of code profiling? Why or why not?
<strong>Sample Use Case</strong>:
<ul>
<li>Every unit test lists name, pass/fail, and execution time.</li>
<li>Time is also calculated per unit test class and total test suite ... | One of the most important rules about unit tests is they should run <strong><em>fast</em></strong>.
Developers should be able to run the whole suite of unit tests in seconds, and definitely not in minutes and minutes. Developers should be able to quickly run them after changing the code in anyway. If it takes too lon... | <blockquote>
Is the execution time of a unit test useful for anything?
</blockquote>
Yes.
<blockquote>
Is a unit test an appropriate place for any sort of code profiling?
</blockquote>
Yes.
<blockquote>
Why?
</blockquote>
Because you need facts and measurements. If a test suite is slow, it's important to ... | https://softwareengineering.stackexchange.com |
358,460 | [
"https://electronics.stackexchange.com/questions/358460",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51754/"
] | I have a piece of memory which I need to access cell by cell:
<pre><code>parameter RAM_LENGTH = 1024;
reg [7:0] mem [RAM_LENGTH - 1:0];
</code></pre>
I need to iterate cells sequentially. It looks like there are at least two ways to do this. The first approach is to index memory as if it were C array of bytes:
<pre>... | Both approaches are viable, depending on what you want the synthesized implementation to be.
The indexed version would typically be used if you want the memory to be implemented using the internal block ram in the target device. In this case, the clock speed is limited by the memory access time.
The shift register v... | Use block RAM to construct a FIFO buffer. All of the FPGA vendors have a "wizard" of some sort to help configure FIFOs, since it's such a commonly-used subcircuit.
| https://electronics.stackexchange.com |
14,285 | [
"https://chemistry.stackexchange.com/questions/14285",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/6889/"
] | here is a problem :
<img src="https://i.stack.imgur.com/TjNSJ.jpg" alt="enter image description here">
What I did " as shown in the picture below "
I rewrote the information given in terms of reactants and products ( equations )// in Part 1
Then I used the Hess law to obtain the desired result //in part 2
in part ... | You forgot that you only need 1/2 mole of $\ce{O2}$. Since the product is $\ce{MgO}$, the third equation in step one should be:
$$
\ce{1/2O2(g) -> O(g)} \space \space \rm{249.35 ~kJ/~mol}
$$
Note that I divided the bond dissociation energy of $\ce{O2}$ by two as well.
This is a very common mistake in Born-Haber t... | Thanks for showing your work. We're given that
$$\ce{\Delta H_{f} (MgO (s))~ =~ -601$.$8 ~kJ/mol}$$
So any balanced equation we write that has MgO as the product will have this same heat of formation. An equation that produces MgO and allows us to solve the problem is
$$\ce{Mg^{+2}(g) + O^{-2}(g) -> MgO (g)}$$
Th... | https://chemistry.stackexchange.com |
127,951 | [
"https://physics.stackexchange.com/questions/127951",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56031/"
] | The coupling constants (in the gauge theory) fix an inner product on the lie algebra of the gauge group and we use it to define strength of the fields. we are using ad-invariant inner products which are determined by some numbers. In other words, the set of all ad-invariant inner products form a space of more than one ... | You may always promote "couplings constants" (charge, mass, etc...) to fields. Now, as a physicist, you need to make some contact with reality. So you have to tell why and which field you are using (for instance the Higgs field (up to a constant), which has a $SU(2)$ charge, is used to replace a constant mass coupling... | The Einstein equivalence principle states :
<blockquote>
The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and <strong>its location in spacetime</strong>.
</blockquote>
Emphasis added. Note that this principle has done well in expla... | https://physics.stackexchange.com |
570,602 | [
"https://physics.stackexchange.com/questions/570602",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/265942/"
] | In the EM Lagrangian, the QCD Lagrangian, and the charged and neutral weak current Lagrangian, there is always a <span class="math-container">$\psi$</span> term and its adjoint <span class="math-container">$\bar{\psi}$</span>.
The <span class="math-container">$\psi$</span> term can represent a Dirac spinor for EM, or a... | A field operator annihilates a particle, or creates an antiparticle. The adjoint does the opposite, it creates a particle or annihilates an antiparticle.
| It has largelly the same meaning as the adjoint wave function in the usual QM. <span class="math-container">$\psi$</span> is a complex function, and one can write two equations for both real and imaginary parts of <span class="math-container">$\psi$</span>, or equivalently two equations for <span class="math-container"... | https://physics.stackexchange.com |
98,221 | [
"https://electronics.stackexchange.com/questions/98221",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1623/"
] | Is it possible to set a <code>STD_LOGIC_VECTOR(6 DOWNTO 0)</code> with a constant like so:
<pre><code>signal s1: std_logic_vector(6 downto 0);
s1 <= 12;
</code></pre>
Or do I have to define it as a set of bits?
| You can do it, but not directly.
Something like this should work:
<pre><code>s1 <= std_logic_vector(to_unsigned(12,7));
</code></pre>
or
<pre><code>s1 <= std_logic_vector(to_unsigned(12,s1'length));
</code></pre>
Of course at the begining of your file you should declare:
<pre><code>library ieee;
use ieee.s... | wzab's answer is precisely what you asked. So I'll just remind that you can go the other way round. You could declare <em>s1</em> as an integer, say:
<code>signal s1: integer range 0 to 127;</code>
and that will keep your code free from type conversions, at least until you have to push the signals out of the chip. De... | https://electronics.stackexchange.com |
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