qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
187,845 | [
"https://mathoverflow.net/questions/187845",
"https://mathoverflow.net",
"https://mathoverflow.net/users/49822/"
] | Koebe–Andreev–Thurston theorem (known also as the circle packing theorem) says that any planar graph can be realized by a set of (interior-) disjoint disks corresponding to vertices, such that two discs are tangent iff the corresponding vertices are connected to each other.
Where can I find the/a proof of this theorem... | There are many proofs, and I'm not claiming that the following list is complete. New references are welcome.
(First proof)
<ul>
<li>Paul Koebe, Kontaktprobleme der konformen Abbildung, Ber. Verh. Sächs. Akad. Leipzig 88 (1936), 141–164 (German)</li>
</ul>
(Thurston's rediscovery and related)
<ul>
<li>Andreev, E. M... | EDIT. There are very many published proofs.
For example, Colin de Verdiere (Forum Math., 1 (1989) 395-402), or
Charles R. Collins and Kenneth Stephenson, A circle packing algorithm, Computational Geometry 25 (2003) 233–256.
Thurston's original proof is elementary: he gives an algorithm for finding the
(essentially uni... | https://mathoverflow.net |
185,933 | [
"https://physics.stackexchange.com/questions/185933",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70392/"
] | Have two experiments ever been done such that the set up is identically the same, (when I say identically I mean down to the atomic level). Of course the experiment would have to be very simple. If it has been done do we see differences in the results (as would be expected with the probabilistic nature of quantum mecha... | Sure! In fact, this is one of the great strengths of atomic physics--if you and I are doing two experiments on rubidium atoms then (assuming we use the same isotopes) then our atoms will be exactly the same. Your rubidium atom and my rubidium atom are simply identical. So plenty of atomic physics is very repeatable, an... | The simplest answer to your question is probably the single-slit experiment. If you shoot two electrons consecutively in the same direction towards a plate pierced with a slit, then two dots will appear at different positions on the screen placed behind the plate. The difference in the positions is almost entirely due ... | https://physics.stackexchange.com |
280,856 | [
"https://electronics.stackexchange.com/questions/280856",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/136204/"
] | I'm currently working on a project about I/O with FPGA. I am using TTL-232R-3v3 cable for serial communication between my laptop and DE0-nano. I want to know if it is possible to send a signal on RX wire to FPGA and light up LEDs with that signal or is UART needed?
Any advice or guidance would be greatly appreciated, ... | Serial port communications idle high (1). If this is hooked up directly to the FPGA and routed to an LED without a logical inversion you will see the LED light up (assuming proper voltages and current drive). To turn the led (mostly) off you can send a binary 0x0000_0000 constantly via the serial port and the led sho... | Your adaptor cable connects to a USB port at one end and provides a UART-style serial port with LVTTL levels at the other. The cable converts USB communications into a UART serial port.
You will need to implement a UART core within your logic design for your FPGA. This will receive serial data from, and transmit seria... | https://electronics.stackexchange.com |
79,833 | [
"https://security.stackexchange.com/questions/79833",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/66844/"
] | As part of an increase in the security measures for our company, we're moving to making sure all password logins (databases, servers, etc), are done through a password prompt and never using stored passwords. The hope here is that if a company laptop were to go missing, we wouldn't need to change all our passwords.
I... | This is a fallacy on several levels.
First, you can't expect people to remember passwords that are both strong and unique to each service. It's just not gonna happen. Implementing this is just begging to have "passwords.xlsx" pinned to half the users desktops (the other half will use "passwords.docx").
Second, trying... | This is the wrong solution for this problem. First, no, it is not safe to assume that passwords can't be recovered from on disk or in memory. On disk is the real threat...If you're up against adversary who can pull data off of RAM, you're probably up against an adversary you can't defeat in any case.
Additionally... | https://security.stackexchange.com |
390,369 | [
"https://physics.stackexchange.com/questions/390369",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/185010/"
] | I'm new here. Given the Lagrangian,
$ L=\frac{1}{2}∂_{μ}\Phi (∂^{μ}\Phi)^{*} − \frac{λ}{4}(\Phi\Phi^{*} - 1)^{2}$
and its energy-momentum tensor
$T^{\mu}_{\nu}=\frac{\partial L}{\partial(\partial^{\mu}\Phi^{*})}\partial_{\nu} \Phi -δ^{μ}_{ν}L $
For the element $T^{0}_{0}$ I get
$T^{0}_{0}=\frac{1}{2}\dot{\Phi}^{2... | The correct canonical normalized Lagrangian should be
$$
L = ( \partial^\mu \Phi)^*( \partial_\mu \Phi ) - \frac{\lambda}{4} ( \Phi^* \Phi - 1 )^4 \,.
$$
The canonical energy momentum tensor is
$$
T^\mu{}_\nu = \frac{\partial L }{ \partial( \partial_\mu \Phi ) } \partial_\nu \Phi + \frac{\partial L }{ \partial( (\par... | You aren't applying the energy-momentum tensor in the right way. You should sum over both fields. Check again your formula!
Edit: You have to consider the complex field like an other field.
Edit2: The correct formula is given by
$$T^\mu_{\nu} = \frac{\partial L}{\partial (\partial_\mu \phi_a)}\partial_\nu \phi_a - \d... | https://physics.stackexchange.com |
1,361,982 | [
"https://math.stackexchange.com/questions/1361982",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/254711/"
] | This is a question from Iran's national grad school entrance exam.
In the answers key, the answer was that the following language is regular but I doubt it is true, I proved using pumping lemma that it isn't regular, but I wanna make sure that my proof is correct.
Please check my proof, and tell me your idea.
Is this l... | Let $A = \{0, 1\}$ be the alphabet and let
$$
L = \{yxzx^Ry^R \mid x,y,z \text{ belongs to } \{0,1\}^+ \}
$$
I claim that $L$ is regular and equal to $K$, where
$$
K = 00A^+00 \cup 01A^+10 \cup 10A^+01 \cup 11A^+11
$$
<strong>Proof</strong>. If $u \in L$, then $u = yxzx^Ry^R$ for some words $x,y,z \in A^+$.
Let $v = y... | The language is regular. It’s the union of the following four languages, each of which is clearly regular:
$$\begin{align*}
L_1=\left\{00z00:z\in\{0,1\}^+\right\}\\
L_2=\left\{11z11:z\in\{0,1\}^+\right\}\\
L_3=\left\{01z10:z\in\{0,1\}^+\right\}\\
L_4=\left\{10z01:z\in\{0,1\}^+\right\}\\
\end{align*}$$
The problem wit... | https://math.stackexchange.com |
93,144 | [
"https://cs.stackexchange.com/questions/93144",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/86741/"
] | I had a question regarding LL(<span class="math-container">$k$</span>) grammars. I came across a problem that I attempted to solve, but my answer varied from the solution and I wasn't sure why.
<span class="math-container">$$L = \{a^{n + 2}b^mc^{n + m}\ :\ n \ge 1,\ m \ge 1\}$$</span>
The grammar I came up with is:
... | An LL parse produces a leftmost derivation, which means that at each point in the derivation, the leftmost non-terminal must be replaced by one of its productions. The issue is to decide which production to use.
A grammar is LL(k) if the production to be used in the leftmost derivation can always be determined by exam... | You can easily transform this grammar to LL(1) by extracting the common prefix <span class="math-container">$b$</span> in both productions of <span class="math-container">$B$</span>, a procedure called left-factoring.
You get this:
<span class="math-container">$B \to b B'$</span>
<span class="math-container">$B' \to... | https://cs.stackexchange.com |
14,624 | [
"https://mechanics.stackexchange.com/questions/14624",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7811/"
] | I have a 1980 Honda Prelude and have only driven it a few hundred miles per year for the 10 years I've owned it. Redid the clutch when I got it, with new cylinders and everything.
Last week I got in it having not driven the car for several months, and the clutch was just dead. No hydraulic pressure at all. Two days ag... | Your best (easiest/cleanest) bet is to replace the master/slave cylinder assembly. The main part of play here is <em>lack of use</em>. What happens is seals dry out and when you then subsequently use the clutch, extra wear is put on the seal, which allows it to wear much quicker. You can avoid this situation by driving... | most likely it because of wear and tear.sitting unused for long periods is also another cause. the rubber seals must have dried up. i bet its time to replace your slave and master cylinders.
| https://mechanics.stackexchange.com |
1,812 | [
"https://mathoverflow.net/questions/1812",
"https://mathoverflow.net",
"https://mathoverflow.net/users/812/"
] | While many of us have had the experience of learning mathematics informally by osmosis or more formally in classes, there are times when we have to sit down and systematically learn, without the benefit of a class, large amounts of mathematics. For instance, there might be a technique that we need from a field we are ... | Many have remarked that they first understood a subject only when they first taught it.
| I try and find a simple example to play with that until I am comfortable. Then I pretend that all examples are like the toy. Soon I realize that's not true, but by then it's easier to see where the new behavior comes from. Then it's time to repeat the process.
| https://mathoverflow.net |
428,633 | [
"https://physics.stackexchange.com/questions/428633",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84158/"
] | Stars are so far away that their apparent width is essentially zero when compared to any pixel of a camera or TV screen.
And yet we can still see them.
According to our eyes stars have a finite albeit very small width. Why is this, and what is this width?
| <blockquote>
Stars are so far away that their apparent width is essentially zero when compared to any pixel of a camera or TV screen.
And yet we can still see them.
</blockquote>
In an electronic sensor (CMOS or CCD for example), the pixel sums all the light that reaches it. Even if light only falls on a small part of ... | The light beam from a very distant star wiggles about in position by a tiny amount due to the effects of passing through the earth's uneven atmosphere on its way towards your eye. In this way it then excites more than just a single photoreceptor in your eye or pixel in an imaging device and thereby produces a "visible"... | https://physics.stackexchange.com |
114,893 | [
"https://electronics.stackexchange.com/questions/114893",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38544/"
] | In the analysis of a feedback control system is it important that a sub-network be itself stable. i.e. if I were to break apart the main complex system and just study a single feedback loop, is it significant that that sub-network be stable itself or does one just consider the whole larger network?.
<img src="https:/... | The stability of a compound system is also influenced by the cancellation of poles and zeros RHP (right-half plane). In this case, the resulting system is stable when observed externally, but can exist internal signals which can grow without limit (in practice <strong>saturation</strong>, <strong>damage</strong>, ...).... | You need to study the whole and not the parts. Just looking at a S-domain analysis you can see where certain poles and zeros come from and it should be clear that if you remove certain poles and zeros by removing an larger scale feedback loop that the circuit will ring. i.e. it's by tailoring the placement of these po... | https://electronics.stackexchange.com |
50,238 | [
"https://softwareengineering.stackexchange.com/questions/50238",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12197/"
] | So..I am going to have a phone interview with a company tomorrow. I never had a phone interview before so I don't know anything about it except that I am going to talk to someone over the phone.
This is a PHP developer position. Is she/he going to ask PHP questions only? or is she/he going to ask any other questions?
... | Imagine a regular interview, but with more broad and general questions with the aim of determining whether you are good enough to warrant spending the time for an in person interview. That's pretty mmuch all there is to it.
Except you can do phone interviews wearing only your underwear.
| It's Just like a real interview, they can ask anything. But they don't want to waste anyone time with travel and Such.
Usually 15 min, to to see if you meet base requirements, but I have had them go to 1.5 hours.
Take it very Seriously, if you do well they will bring you in for a face to face.
| https://softwareengineering.stackexchange.com |
122,371 | [
"https://physics.stackexchange.com/questions/122371",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/27808/"
] | We know that a simple application of Gauss's law tells us that the field inside of a uniformly charged spherical shell is zero. Does this hold for all uniformly charged closed surfaces? If so, how could we prove this? Or does it hold only for certain shapes?
| Let us ask the question the other way round. Given a conductor closed shape and a zero field inside, what are the possible surface charge distributions and when is one of them constant ?
The potential is solution of the Laplace equation and can written as
$$V(r,\theta,\phi)=\sum_{\ell=0}^\infty \sum_{m=-\ell}^\ell \le... | It doesn't hold for arbitrary shapes.
The reason it works for spheres is that when you have a spherical charge distribution and a concentric spherical Gaussian surface, the whole system is invariant under rotations around the center of the spheres. If the electric field were different at different points on the Gaussi... | https://physics.stackexchange.com |
109,438 | [
"https://cs.stackexchange.com/questions/109438",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/21507/"
] | I am learning compiler in my Uni. I have been through all major compiler techniques like top-down parsing, bottom-up parsing, Lexical analyzer, Symbol table, etc. I have a good understanding of them, but I am still confused about the course.
What is the point of learning all these things? What are their applications?... | Let me break up several possible interpretations of your question:
<strong>What is the purpose of learning compilation?</strong>
There are several possible answers:
<ol>
<li>So that you know how to build a compiler should you have to. This is not a good answer nowadays.</li>
<li>Part of the goal of the computer scie... | Because you are a <strong>Computer Science</strong> major and you have to deal with all these.
A few months ago, I was also having the same question, while studying for the Computer Architecture finals, why am I even dealing with all these root level stuff, assembly code, optimizations while my friends from IT and Sof... | https://cs.stackexchange.com |
1,367,816 | [
"https://math.stackexchange.com/questions/1367816",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/87313/"
] | You have $N$ wires that all extend from one location to a second distant location. The wire ends at both locations are unlabeled, and the goal is to label them all (on both ends) with distinct labels $1,2,\ldots, N$ so that the two ends of the same wire have the same label for every wire. I.e., the goal is to match eve... | For <span class="math-container">$N=1$</span> You need no trips. For <span class="math-container">$N=2$</span> the operations are not enough to solve the problem in any way. For <span class="math-container">$N\geq3$</span>, at least two one-way trips are necessary, because in the first trip, you can't distinguish a wir... | I have found a provably optimal solution for odd $N$ if we assume that you can only test connectivity at the second location, and only tie/untie at the first location. First label the wires $1$ to $N$ at the first location.
Then tie together wires in pairs in consecutive order, i.e. $(1,2)$,$(3,4)$, and so on, and le... | https://math.stackexchange.com |
262,005 | [
"https://physics.stackexchange.com/questions/262005",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86340/"
] | It is shamefully charge-free. But presumably, if we can tune its velocity, a lot of interesting things can be done, right?
So, was there any proposal for obtaining high velocity neutrons?
| I was puzzled by this same thing when I took QFT classes several years back. After thinking about it, the reason is so trivial as to not merit an explanation in the literature, especially Peskin and Schroeder.
Look at th LHS of your first equation:
$\begin{align}\sum_{s,s'}\bar{v}^{s'}_a(p_2)\gamma^\mu_{ab}u^s_b(p_1)... | An $A_{ab}B_{bc}$ yields a $C_{ac}$. Contracting all indices, but the outer ones of your expression yields a $[(\not{p}_2-m)\gamma^\mu(\not{p}_1+m)\gamma^\nu]_{dd}$. Now executing the $dd$ contraction is just the trace.
| https://physics.stackexchange.com |
710,606 | [
"https://math.stackexchange.com/questions/710606",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/45767/"
] | I have a quick question regarding limits of a function
How do I show that the limit of $f(x)$ tends to 0 as $x \rightarrow \infty$ where
$$f(x) = (x+2)(k^x) $$
where $0<k<1$.
Can I say that the limit of the left product converges to $\infty$ but the second limit converges to $0$ and so the whole limit converge... | You cannot say that, for example, if I have $f(x) = (x^2) \cdot \frac1x$, then the left product converges to $\infty$ and the second converges to $0$, but the whole limit is $\infty$.
My advice here is to use L'Hospital's rules, as $$f(x) = \frac{x+2}{\left(\frac{1}{k}\right)^x}.$$ Both functions, $x+2$ and $\left(\fr... | I would suggest that you rewrite the second term:
$$k^x = e^{x\cdot\ln{k}}$$
Then: $X = x\cdot\ln{k}$.
When $x \rightarrow \infty$, $X \rightarrow -\infty$ ($\ln(k)$ is negative). You can rewrite the whole by also developing: $$f(x) = \frac{X}{\ln{k}} \cdot e^{X} + 2 \cdot e^{X}$$
The second term clearly converges ... | https://math.stackexchange.com |
27,899 | [
"https://cs.stackexchange.com/questions/27899",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/17945/"
] | I came across a proof that an AVL tree has <span class="math-container">$O(\log n)$</span> height and there's one step which I do not understand.
Let <span class="math-container">$N_h$</span> represent the minimum number of nodes that can form an AVL tree of height <span class="math-container">$h$</span>. Since we're l... | You can continue as same as line 4 the process like that:
$$ N_h > 2N_{h-2}> 2(2 N_{h-4})>2(2(2 N_{h-6}))>\cdots$$
As you can see, the indexs are decreasing by substracting $2$ in each step when you use the inequality. So, the process stops when the index $h$ takes $0$, but from the indexs behavior the hal... | Assuming $h$ even, by induction
$$N_h>2N_{h-2}>2^2N_{h-4}>2^3N_{h-6}>\cdots 2^{h/2}N_0$$
because you go up two levels $h/2$ times.
| https://cs.stackexchange.com |
197,801 | [
"https://physics.stackexchange.com/questions/197801",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23816/"
] | I know there are different types of direct reactions like inelastic scattering and such. But is the main difference between direct and compound reactions that one excites (Or at least can) the whole nucleus (Compound), while the other does not ? And if so, what is the extra energy used for in direct reactions, if not e... | I would argue that this is like saying that the main difference between roses and rosemaries is the smell, in the sense that they differ in many things while both being flowers, and you are arbitrarily selecting a difference to be the outstanding one.
The differences between direct reaction (DR) and compound nucleus r... | compound reaction:=the typical reaction time of compound reaction which is 10^-14 to 10^-15 second
direct reaction:=the typical reaction time of direct reaction which is of the order of 10^-21 to 10^-22 second
| https://physics.stackexchange.com |
954,374 | [
"https://math.stackexchange.com/questions/954374",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/115078/"
] | Integrating $\frac{x}{1+x^2}$ becomes $\ln \sqrt{x^2 + 1}$
Why is this? Is there a formula or a fact that makes this so. Integrating this a lot different than integrating something easy like $X^2$.
| Now that the formula is clear, we can use
$$\int\frac{f'(x)}{f(x)}dx=\log |f(x)|+C$$
since $\;x=\frac12(2x)=\frac12(x^2+1)'\;$ , and thus
$$\int\frac x{x^2+1}dx=\frac12\int\frac{(x^2+1)'}{x^2+1}dx=\frac12\log(x^2+1)+C=\log\sqrt{x^2+1}+C$$
| <strong>Hint:</strong> Whenever you see a fractional expression like this where the numerator is very nearly the derivative of the denominator, you should suspect that the expression may be the derivative of the log of the denominator.
There will typically be a constant multiplier that you will have to put in (and als... | https://math.stackexchange.com |
501,350 | [
"https://electronics.stackexchange.com/questions/501350",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/253234/"
] | I have two recently dead tower fans. The first, I've had for over 6 months, no problems. Recently, I moved it to a new room an plugged it into a different outlet. It died within a day: it seems to be just the main motor, the controls still work as does the separate motor for swiveling the fan. Took it apart to look for... | Finally got it looked at - turns out the outlet is 220V. There are no special markings on it (aside from the T-shape marking it as a 20A outlet) and all rest of the apartment is 110V (standard here in the US). Guess it's always worth testing unfamiliar outlets.
| Oh yes, it happens all the time. It is called a <strong>Lost Neutral</strong>.
The fix 99% of the time is to call the power company on their "report outage" number and get them to fix a problem out on the pole. They should do this for free.
Almost all residential power (except half of the Philippines) is delivered... | https://electronics.stackexchange.com |
317,359 | [
"https://physics.stackexchange.com/questions/317359",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62489/"
] | It is said that in a spaceship, you need to spend as much energy to brake as you spent for accelerating. An electric car, however, charges its batteries while braking, thus it actually recovers energy by braking.
Both facts somehow seem intuitive to me, but aren't these two observations contradicting each other?
<str... | <h2>The main point is that the space-ship is a closed system and the car is not</h2>
Consider that to conserve momentum we need to give something else the momentum our decelerating object had before.
<ul>
<li>In the case of the space-ship this requires ejecting something in the opposite direction to the direction of tr... | There is one particular omission in the existing answers that I'd like to rectify.
It is that there is a very special context in which you can do the problem, which answers the question in the affirmative with very little actual effort. In this reference frame the travelling spaceship appears to start at rest and then... | https://physics.stackexchange.com |
238,625 | [
"https://security.stackexchange.com/questions/238625",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/241454/"
] | In addition to the authentication techniques that are based on “something you
have”, “something you know” and “something you are”, authentication techniques that consider “somewhere you are” are also used. Why? Does it add further security?
| “Somewhere you are” is <strong>NOT an authentication factor</strong>, despite what you might have read elsewhere. It is an <em>authorization</em> factor.
Indeed, it does not answer the question "are you who you claim to be?", but instead it answers "should you be there? / are you authorized to be here?&q... | "Where you are" can be defined in many useful ways.
For instance, location can be determined to be within a certain building. This is useful when it is a work account where you should only be logging in from that building. So, if you are logging in from the building's network, then there is a level of trust t... | https://security.stackexchange.com |
388,843 | [
"https://physics.stackexchange.com/questions/388843",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/186201/"
] | A CNOT gate can be written as follow:<br>
$$\begin{pmatrix}1 & 0 & 0 & 0 \\\ 0 & 1 & 0 & 0 \\\ 0 & 0 & 0 & 1 \\\ 0 & 0 & 1 & 0 \end{pmatrix}$$
So using the CNOT gate on $ \psi = |0\rangle$ and $ \phi = |1\rangle $ can be written as:
$$\mathrm{CNOT}(\psi, \phi) =\begin{... | You're doing a direct sum instead of a tensor product of the two vectors; as such, your input state is wrong.
A direct sum operates by concatenating the two vectors:
<span class="math-container">$$
\psi \oplus \phi
=
\begin{pmatrix}\psi_1\\\psi_2\end{pmatrix}
\oplus
\begin{pmatrix}\phi_1\\\phi_2\end{pmatrix}
=
\begin{... | For the CNOT gate matrix as you've written it, the basis for the state space is $\{|00\rangle,|01\rangle,|10\rangle,|11\rangle\}$. As such, the input state you started with was actually $|00\rangle + |11\rangle$, and you ended, as you should, with $|00\rangle+|10\rangle$. If you wanted to start with the state $|01\rang... | https://physics.stackexchange.com |
1,334,463 | [
"https://math.stackexchange.com/questions/1334463",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/54865/"
] | I have a quick question: is there any sufficient condition (theorem, lemma, proposition,...)
<br>
to show that a graph (vertices do not have the same degree) is balanced bipartite?
| No odd cycles (which guarantees that the graph is bipartite) and regular (aka, all vertices have the same degree).
| One sufficient condition is that the graph has two vertices.
If instead you want a necessary and sufficient condition, then you will not find any efficient one, because it can be used to solve bin packing which is NP-hard.
| https://math.stackexchange.com |
27,640 | [
"https://electronics.stackexchange.com/questions/27640",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6138/"
] | Is there a way to convert a .sch file in Eagle 6 to Eagle 5?
| No. Generally speaking, conversions from later versions of software to previous versions are not feasible, especially with CAD programs, because of the additional features that are added. In theory, it would be possible, but it would be extremely difficult, and very few users would require it.
Why do you need it?
| No, although it would be pointless anyway. Nobody with more than a couple neurons rattling around their skull is running Eagle 6. That was a major change from version 5, with a completely new file format. It will be a year or two at least before version 6 is ready for real work. Let the clueless continue to find th... | https://electronics.stackexchange.com |
153,953 | [
"https://security.stackexchange.com/questions/153953",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | I understand that Perfect Forward secrecy is meant to prevent the data sent between the client and server being decrypted in case the private key is leaked some time after the data being sent.
But why do we need something complicated like Diffie-Hellman key exchange to do this? Couldn't we simply use XOR instead, like... | Anyone observing the exchange can just trivially calculate K!
<pre><code>K = (K xor R1) xor (K xor R1 xor R2) xor (K xor R2)
</code></pre>
This are exactly the three messages which are sent in your protocol...
| Perfect Forward Secrecy is not possible using only pure symmetric cryptographic primitives. However, if we relax the conditions (like compromise of the long term secret of just one principal not both) then PFS can be achieved using pure symmetric primitives.
| https://security.stackexchange.com |
620,835 | [
"https://physics.stackexchange.com/questions/620835",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/255220/"
] | As an layman and outsider who has read some of Dirac, I want an understanding of how important absolute size is to quantum mechanics - like wondering if it is a necessary or sufficient condition (along these lines).
As far as I understand things, like all good theories, quantum mechanics is a mix of empirical data (man... | There is a fundamental constant of nature that establishes the scale over which quantum effects become dominant and readily measured with special tools. It is called <em>Planck's constant</em> and it is a very, very tiny number, which means that quantum effects like uncertainty only kick in at very, very tiny length sc... | When you go bowling do you invariably score a strike every time? I would guess not.
All the inaccuracies in your aiming and throwing of the ball are quantum effects becoming visible in the chaotic system that your body is. By practicing you can improve the signal to noise ratio of your performance, but you can never re... | https://physics.stackexchange.com |
14,270 | [
"https://quant.stackexchange.com/questions/14270",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/5233/"
] | <strong>**Question is at the bottom**</strong>
Suppose you have a portfolio of bonds A, B, and C with the following characteristics:
(the "Frequency" column is the # of coupon pmts per year and also the # of compounding periods)
<pre><code>Bond | Coupon Rate | Frequency | Years to Maturity | YTM (%) | FV ($)
A ... | If I understand correctly the question, you wish to completely hedge the interest rate risk (defined as a parallel shift in the yield curve). If that is the case, you should use modified duration, which is the price sensitivity, rather than the MacAulay duration. They are usually close in value, but not quite the same.... | "I think we need to find the proportion of bond D that will make the overall duration 0" ... by doing so, you will be matching the duration of bond D, because it has the shortest one.
In order to immunize portfolio, you should have some benchmark duration you want to match. If it is the one of bond D, than your sugge... | https://quant.stackexchange.com |
617,340 | [
"https://electronics.stackexchange.com/questions/617340",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/269074/"
] | Sorry for my noob question. I am very new to debugging hardware circuit boards.
A circuit board was not working. After measuring a voltage rail it was jumping from 12V to 0V, and back to 12, etc. what kind of behavior does this typically indicate?
The board randomly worked by not doing anything besides probing a few ar... | It could be an intermittent connection of some kind, something like a bad solder joint or a hairline crack in the board or a lifted pad on a single-side PCB. You can troubleshoot many of that kind of fault with copious quantities of light and close visual inspection at various angles.
Of course if it got wet, then ther... | Others had excellent suggestions. When we see odd behavior in circuit boards the first thing we try is to clean the board in isopropyl alcohol using an ultrasonic cleaner. Flux between high impedance pins will often cause stray currents that can pull pins low that should be high. It doesn't cost much (other than time) ... | https://electronics.stackexchange.com |
159,939 | [
"https://electronics.stackexchange.com/questions/159939",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25270/"
] | what does it signify ? At pole/zero frequencies the response of a system goes to infinity/zero, so I think same is the case with poles/zeros at infinity, but how do these poles/zeros affect the design of system ?
| Poles at infinity are obtained when the order of the numerator is higher than the order of the denominator. Consider a transfer function G(s) with a numerator of order n, and denominator of order m, and with n>m. There will be n finite zeros and m finite poles and, as s->infinity, the m poles will cancel m of the numer... | Suppose we have a system with system response of \$H(s)\$ (i.e. the Laplace transform of the impulse response).
Then \$H(s)\$ has a zero/pole at infinity if the function
$$H(1/s)$$ has a zero/pole at \$s = 0\$. This is a definition, so there is no derivation.
If there is a pole at infinity, this means that the fre... | https://electronics.stackexchange.com |
521,638 | [
"https://physics.stackexchange.com/questions/521638",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | We define specific heat of a substance as,
<span class="math-container">$$s=\frac{S}{m}=\frac{1}{m} \frac{dQ}{dT}$$</span>
where <span class="math-container">$s$</span> is the specific heat, <span class="math-container">$S$</span> is the heat capacity and <span class="math-container">$m$</span> is the mass of the sub... | Even if it is often written as <span class="math-container">$dQ/dT$</span>, heat capacitance is not a derivative, in general, and heat is not a function of <span class="math-container">$T$</span>. It would be more correct to write
<span class="math-container">$$
C_X = \frac{Q_X}{\Delta T},
$$</span>
where the subscript... | The proper equations for defining specific heats, or specific heat capacities, are the following:
<span class="math-container">$$c_{p}=\Bigl(\frac {\delta h}{\delta T}\Bigr)_P$$</span>
<span class="math-container">$$c_{v}=\Bigl(\frac {\delta u}{\delta T}\Bigr)_P$$</span>
Where <span class="math-container">$c_p$</span... | https://physics.stackexchange.com |
2,083,962 | [
"https://math.stackexchange.com/questions/2083962",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/380874/"
] | <blockquote>
I know how to solve this using the squeeze theorem, but I am supposed to solve only using L'Hôpital's rule
$$\lim\limits_{x \to \infty} \frac{\sin(x)}{x-\pi}$$
</blockquote>
<strong>I tried</strong>:
$$\lim\limits_{x \to \infty} \frac{\sin(x)}{x-\pi} = \lim\limits_{x \to \infty} \frac{d/dx[\sin(x)]... | Unfortunately L'Hopital would not help since this does not satisfy the <em>assumptions</em>.
Note that
$$
\left|\frac{\sin x}{x-\pi}\right|\leq\frac{1}{|x-\pi|}\to 0
$$
as $x\to\infty$.
What is the point <em>not</em> to use the squeeze theorem?
| I bet that your problem is, in fact, to compute
$$\lim _{x \to \color{red} \pi} \frac {\sin x} {x - \pi} ,$$
so either you have mistyped $\infty$ instead of $\pi$, or there is a typo in the text where you took this from.
In this case, L'Hospital's theorem could be used, but it's not necessary, because
$$\lim _{x \t... | https://math.stackexchange.com |
78,112 | [
"https://physics.stackexchange.com/questions/78112",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20884/"
] | The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them.
However, the total energy can also be calculated through the volume integral of magnitude squared of the electric over all space: $$W = \frac{\e... | Let us call the two electric charges $Q$ and $q$ with electric fields $|{\bf E}_Q|=\frac{k_e |Q|}{r^2_Q}$ and $|{\bf E}_q|=\frac{k_e |q|}{r^2_q}$, respectively. Here $k_e=\frac{1}{4\pi\varepsilon_0}$. The energy
$$\tag{0} U~=~\frac{\varepsilon_0}{2}\iiint_{\mathbb{R}^3}\! d^3r ~|{\bf E}_Q+{\bf E}_q|^2~=~U_Q+U_q+U_{Qq... | Point charges pose a problem because their self energy $\rightarrow \infty$ as their size$\rightarrow 0$
It represents the work done in assembling a point charge, whereas you're only interested in the work done in moving charges in the fields of other charges. You therefore need to subtract the energy stored in the el... | https://physics.stackexchange.com |
122,725 | [
"https://mathoverflow.net/questions/122725",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13441/"
] | I believe that the following questions are very basic, but I don't know how to get a reference.
Consider a curve in the plane $C\in \mathbb C^2$ with a singularity at $0$ and suppose it is
unibranch at zero (i.e. analytically irreducible). Then I guess one should be able to define "arithmetic genus defect" of the cu... | The difference between the geometric genus of the singularity and the geometric genus of a
smoothing (this one being called the arithmetic genus of the singularity) is often called
the <em>delta invariant</em>. If $A$ is the local ring of the singularity, $B$ its normalization, then the delta invariant is the dimension... | Another way to compute the delta invariant in pratice: let $m_1$ be the multiplicity of the curve at the point $p_1$ you are looking for. You blow-up $p_1$, and look for singular points of the strict transform of the curve which lie on the exceptional curve obtained. Denote by $m_2,\dots,m_k$ the multiplicities obtaine... | https://mathoverflow.net |
576,028 | [
"https://physics.stackexchange.com/questions/576028",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/230132/"
] | I came to this conclusion for the following reasons (thanks to the people who answered my recent questions):
<ul>
<li>A photon pushing a mirror(*) loses energy in the form of a red shift (*through radiation pressure and total reflection);</li>
<li>Pushing a mirror against a photon makes it gain energy in the form of a ... | First of all, there is always a reference frame in which the photon does not lose energy.
That being said, the only constraint is that the momentum transfer from the photon to the mirror has to be orthogonal to the 4-velocity of the mirror.
So if we work along the <span class="math-container">$z$</span>-axis, with:
<sp... | A typical explanation of radiation pressure does not have a photon losing any energy. It is simply a consequence of a particle bouncing normally off a mirror transferring twice its momentum to the mirror.
I don't see the distinction between that and the calculation of ideal gas pressure, which assumes elastic collision... | https://physics.stackexchange.com |
169,436 | [
"https://physics.stackexchange.com/questions/169436",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75020/"
] | Could a nuclear reactor run (controllably) in Prompt-Critical mode? It would have a much higher power output than a normal nuclear reactor. Could it be controlled by some high-tech material that absorbs neutrons when an electric current is applied to it (so the reaction time would be fast enough)?
| This question doesn't make much sense in terms of pure terminology.
A prompt neutron is a neutron which is emitted right when the fission event happens. For a recap, a fissile nucleus absorbs a neutron and then splits into two large fragments and makes several smaller particles in the process, which usually includes 2... | The point of prompt criticality is there are enough prompt neutrons to keep the reaction going. Prompt neutrons are produced something like 0.001 nanoseconds (1E-12 seconds) after the neutron is absorbed.
If you want to control something that is prompt critical, you need a control system that can react in that type of... | https://physics.stackexchange.com |
379,424 | [
"https://softwareengineering.stackexchange.com/questions/379424",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/247488/"
] | File Top.h
<pre><code>#include <string>
...some code...
</code></pre>
File Bottom.h:
<pre><code>#include "Top.h"
void someFunction() {
string s = new String();
...
}
</code></pre>
The Bottom.h does not contain an include for the string header, but the code will work because it's implicitly been included ... | This is a common but unsolvable problem with C++. A header provides some declarations. How the header provides these declarations is an implementation detail, and it is completely valid if the header provides a declaration by including another header. This is quite common in header-only libraries, or large libraries su... | A rule that you <em>should</em> follow in languages like C, C++, Objective-C is that every single header file compiles on its own. This is achieved here (so someone including bottom.h doesn’t need to remember to include top.h an string).
In practice, the case of removing a header like string from top.h is rare, the c... | https://softwareengineering.stackexchange.com |
131,881 | [
"https://mathoverflow.net/questions/131881",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33520/"
] | Let $p$ be a prime other than 5 or 7. Are $A_p$ and $S_p$ the only subgroups of $S_p$ that contains a $p$-cycle and a double transposition?
As for $p = 5$, the dihedral group $D_{10}$ contains a 5-cycle and a double transposition. For $p = 7$, the group $PSL_3(\mathbb{F}_2)$ (acting on the projective plane of order ... | I believe that it was already known to Jordan that if $n \geq 8$ and $G$ is a primitive subgroup of $S_n$ containing a double transposition, then $G$ contains $A_n$. As a subgroup of $S_p$ containing a $p$-cycle is primitive, the answer to your question is ``yes".
| There is a way to prove this via analogy with a proof approach which works for transpositions and 3-cycles.
For transpositions and 3-cycles on 4 or more points, the same proof (more or less) works easily to show that a primitive permutation group on $n$ points containing a transposition (resp., a 3-cycle) must be $S... | https://mathoverflow.net |
324,212 | [
"https://physics.stackexchange.com/questions/324212",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21146/"
] | The Wightman axioms are a set of postulates for quantum field theory that make it a little bit more rigorous than usual, being usually presented as:
<blockquote>
<ol>
<li>The states of the system are unit rays in a Hilbert space that carries a unitary representation of the Poincaré group.</li>
<li>The $4$-moment... | This is just a complement to Slereah's answer.
I think you are confused by the word "axioms" in Wightman axioms.
These are not axioms like ZFC that mathematicians see as basic accepted truths and then go on to build on them proofs of various theorems. Here you are dealing with analogues of "axioms" of a vector space l... | The point of the Wightman axioms isn't to make a quantum field theory, it's to make a bare minimum of what a quantum field theory should obey, on some rather broad notion of what is probably reasonable. You might have noticed that the Wightman axioms don't include a fair bit of rules that are fairly common in most QFTs... | https://physics.stackexchange.com |
63,284 | [
"https://cs.stackexchange.com/questions/63284",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/58073/"
] | In the book <em>Computability, Complexity, and Languages</em> (2<sup>nd</sup> edition), Martin Davis writes in chapter 1 (Preliminaries), section 2 (Functions):
<blockquote>
A <em>partial function on a set</em> $S$ is simply a function whose domain is a subset of $S$. An example of a <strong>partial function on $\ma... | There's no contradiction, here. The first case defines the partial function $g\colon \mathbb{N}\to\mathbb{N}$ given by
$$g(n) = \begin{cases}
x &\text{if $x\in\mathbb{N}$ and }x^2=n\\
\text{undefined} &\text{if no such $x$ exists.}
\end{cases}$$
As the text says, "the domain of $g$ is the set of perfect squ... | In the second example, $h(n)$ is defined for all natural numbers $n$; when $n$ is not a square, $h(n)$ is some irrational quantity, and in particular not a natural number.
In other words, the set of natural numbers is not closed under taking square roots: for example, $\sqrt{2}$ is not a natural number.
| https://cs.stackexchange.com |
177,447 | [
"https://physics.stackexchange.com/questions/177447",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/78379/"
] | I know that this might be a duplicate question, but I have not found any satisfactory answers that clear up my lack of understanding. Here is my question. Say a sloth hangs on a tree in the middle of nowhere. Therefore, he has some gravitational potential energy $mgh$. Next, say he falls to the ground. From the work-en... | Conservation of energy, as you note, holds for "the system." For instance, if you push on a ball, that ball gains energy, but the energy of the ball is not conserved--only the energy of you and the ball. In this case, the system needs to include more than just "the sloth" because the sloth is not an isolated system--th... | There is an external agent that removes mechanical energy from the sloth, namely the normal force exerted by the ground. You are right that no net work is done, but remember it is the work-<em>kinetic-energy</em> theorem: The net work equals the change in kinetic energy of the sloth.
| https://physics.stackexchange.com |
116,266 | [
"https://security.stackexchange.com/questions/116266",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/103038/"
] | I recently setup my own CA, and imported the CA cert into devices across the company. I then deployed certificates to our various servers, etc.. All using SHA-1 signatures (the default in the tool I was using: XCA).
Today I discovered the SHA-1 warning in chrome when browsing any of our servers. Oops. Can I just i... | With regards to Chrome browser:
<ol>
<li>Self-signed certificate that is inside your trust store is OK with SHA-1.</li>
<li>Root cert is OK with SHA-1. (This is just repeating point 1 in other words.)</li>
<li>All the other certificates in the chain need to be SHA-2. SHA-1 generates a warning.</li>
</ol>
The cause fo... | <ol>
<li>There's no difference in scope of security about a self-signed or brand-signed certificate : you <strong>must</strong> use a solid bricks to build a durable walls. I'm using SHA-512, and it seems to be fine</li>
<li>There's a good practice to use same security/encryption schemas everywhere, it makes things sec... | https://security.stackexchange.com |
159,955 | [
"https://mathoverflow.net/questions/159955",
"https://mathoverflow.net",
"https://mathoverflow.net/users/48056/"
] | If $n$ is a positive integer, let $r(n)$ denote the number of representations of $n$ as a sum of products of pairs of positive integers. (Here, the order of the terms in the sum does not matter, but products with the same answer are regarded as different, even if they contain the same two numbers in a different order.)... | Put $F(z)= \prod_{n=1}^{\infty} (1-z^n)^{-d(n)}$, where $d(n)$ is the number of divisors of $n$. The problem asks
for the asymptotics for
$$
R(N) = \frac{1}{2\pi i} \int_{|z|=r} F(z) z^{-N} \frac{dz}{z},
$$
where the integral is taken over any circle with radius $r<1$. A standard way of obtaining asymptotics... | Put
$$
H(z) = \sum_{n\geq 1}r(n)z^n = \prod_{n=1}^\infty\left(1-\tau(n)z^n\right)^{-1} = \exp\left(\sum_{n=1}^\infty\sum_{\nu=1}^\infty\frac{\tau(n)z^{n\nu}}{\nu}\right),
$$
and $f(t)=H(e^{-t})$. Then by the Mellin transform
$$
e^{-t} = \int_{2-i\infty}^{2+\infty}t^{-s}\Gamma(s)\;ds
$$
we get
$$
\log f(t) = \frac{1}{2\... | https://mathoverflow.net |
62,018 | [
"https://dba.stackexchange.com/questions/62018",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36347/"
] | I'm working with a legacy application that started out with little data years ago (developed by a third party custom for this client), and now we're seeing MySQL load skyrocket on this query alone.
The fact that they have actual data now years later is why we're noticing the performance hit at this time. Just not sure... | I will add to the recommendations made by @RolandoMySQLDBA.
It looks like notes.cid should be a foreign key related to customers.id.
You might try replacing the SELECT DISTINCT sub query with an EXISTS sub query. The select distinct will look for all related notes. An exists may perform better since it only check ... | <h1>SUGGESTION #1</h1>
You have no meaningful indexes. That can have a detrimental effect on execution since the MySQL Query Optimizer has no help in searching.
You should all the following indexes
<pre><code>ALTER TABLE customers ADD INDEX bigindex (status,deadlead,purchased,last_updated);
ALTER TABLE notes ADD IND... | https://dba.stackexchange.com |
48,345 | [
"https://mechanics.stackexchange.com/questions/48345",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/32105/"
] | We have a 2017 Outback without a sunroof and with the built-in roof-rack. Assuming I lay towels on the roof and have good straps, what would the arguments be against just laying the bicycles flat on the roof and strapping them down?
| Bike racks are about safety and convenience.
These two go hand in hand because you can easily and securely mount the bike without thinking about how to strap it or where to strap it, etc. Having it securely mounted means the bike will not get damaged from straps pulling on the wrong places (warping a rim for example)... | Plenty of room in an Outback to remove the front wheel and put the bikes in the back. For me, the minimal expense of a bike rack would be good value compared to a roof repair if part of the bicycle hits it or scratches it.
In my experience, I'd recommend a towbar mounted rack (if you have a towbar). It's too easy to f... | https://mechanics.stackexchange.com |
27,972 | [
"https://mathoverflow.net/questions/27972",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6772/"
] | Is it true that a line bundle is relatively ample iff its restsriction to fibers is? If so, what would be the reference?
| If you admit the map to be proper and the schemes to be reasonably good it is true.
A reference I know is Lazarsfeld's book "Positivity in algebraic geometry", paragraph 1.7.
| EDIT : my previous answer was wrong. Thanks to BConrad for pointing it out.
Here is a counterexample if the map is not proper. Let $X$ be the plane, let $Y$ be the blow-up of the plane in one point, and $U$ be $Y$ with one point of the exceptionnal divisor removed. Let $f|_U:U\to X$ be the projection and consider the ... | https://mathoverflow.net |
108,668 | [
"https://stats.stackexchange.com/questions/108668",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/52432/"
] | I'd like to raise a controversial point: if you need instrumental variables, your model is wrong.
<h3>Basic endogeneity problem and the IV solution</h3>
Let us suppose the basic framework of endogeneity and instrumental variables (IV): we want to estimate the regression function $E(y|x,z)$, and choose a linear model ... | Here are Cameron and Trivedi (Microeconometrics, 2005) explaining the tight connection between IV consistency and correct model specification:
<ul>
<li>"The essential condition for consistency of IV is condition 1 in Section 4.8.6, that the instrument should be uncorrelated with the error term. No test is possible in ... | You raise too many issues, and for most of them any answer will probably be seen as being primarily opinion-based, so this post may be quickly closed.
To provide some comments on some of them:
<blockquote>
Quote: If a model has poor prediction power, it is a poor representation of
reality.
</blockquote>
This w... | https://stats.stackexchange.com |
338,503 | [
"https://softwareengineering.stackexchange.com/questions/338503",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/218159/"
] | I have a SQL query that is around 50 lines long.
I'm wondering what would be the be the most maintainable and readable method for executing this, as it looks quite large. So far, I have thought of the following options:
<ul>
<li>Create a stored procedure in the database</li>
<li>SQL query is inline, in the method</li... | This depends heavily on how you manage your sources and your DB schema, the query itself and what it is used for, and the kind of evolvability and reusability you expect for the query.
Storing queries as views or stored procedures in the database is an option if the application which uses the query is versioned togeth... | Longer queries are better to be stored on database server. That will save your data being transmitted and save you from SQL injection too.
Also such procedures are pre-compiled on the database server, so you save on that, too.
| https://softwareengineering.stackexchange.com |
2,255,699 | [
"https://math.stackexchange.com/questions/2255699",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/428730/"
] | $f(x) = \dfrac{x^{2}}{1+2x}$
To turn this into a power series I recall the similar looking geometric series,
$f(x) = \sum\limits_{n=1}^{\infty} x^{n} = \frac{1}{1-x} = 1 + x + x^2 + x^3 + x^5 +\cdots$
And not I can mutate my original function to fit the form the geometric series:
$f(x) = \dfrac{x^{2}}{1-(-2x)}$
$f... | $A=\begin{pmatrix}3&2\\ 2&3\end{pmatrix}\implies A^2= \begin{pmatrix}3&2\\ 2&3\end{pmatrix}\begin{pmatrix}3&2\\ 2&3\end{pmatrix} =\begin{pmatrix}13&12\\ 12&13\end{pmatrix}$
Then $$A^2+bA+cI_2=0\implies \begin{pmatrix}13&12\\ 12&13\end{pmatrix}+b\begin{pmatrix}3&2\\ 2&3\e... | This is an application of the <strong>Cayley-Hamilton Theorem.</strong>
<blockquote>
Every square matrix satisfies its own characteristic function.
</blockquote>
Compute the <strong>characteristic polynomial</strong> of
$$\mathbf{A}=
\left(
\begin{array}{cc}
3 & 2 \\
2 & 3 \\
\end{array}
\right)
$$
$$ \... | https://math.stackexchange.com |
12,589 | [
"https://datascience.stackexchange.com/questions/12589",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/21145/"
] | I am on a binary classification problem with the AUC metrics. I did a random split 70%, 30% for training and test sets.
My first attempts using random forest with default hyper-parameters gave me auc 0.85 on test set and 0.96 on training set.
So, the model overfits. But the score of 0.85 is good enough for my business... | Yes, if your 0.85 AUC is good enough for your use case this is a good enough model. The performance on the training set indicates how well your model knows the training set. This we don't really care about, it's just what the model tries to optimize. The performance on the test set is an indication on how well your mod... | <blockquote>
My first attempts [...] gave me auc 0.85 on test set and 0.96 on training set. So, the model overfits.
</blockquote>
This is not quite true.
See, (<em>almost</em>) each estimator will have a better prediction score on the training data than on the testing data. It doesn't mean each estimator overfit. ... | https://datascience.stackexchange.com |
303,024 | [
"https://physics.stackexchange.com/questions/303024",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/90744/"
] | Consider the number operator:
$$ \hat{n}=c^{\dagger}c$$
Where $c^{\dagger}$ and $c$ are fermionic creation and annihilation operators. Now if we calculate $\hat{n}^2$ we get:
$$ \hat{n}^2=c^{\dagger}cc^{\dagger}c=c^{\dagger}(1-c^{\dagger}c)c=c^{\dagger}c=\hat{n}.$$
So working with operators we see that $\hat{n}^2=\hat{... | When writing a path integral starting from a Hamiltonian, one must write down all operators in normal order, as the Grassmann variables correspond to coherent states of the fermionic creation/annihilation operators
$$
\hat c|\psi\rangle = \psi|\psi\rangle.
$$
Thus, an on-site interaction term for spinless fermions doe... | Now that I know there's nothing hidden going on with matrices or components, I can say that what you're missing is that you're doing the anti-commutator of the fermionic field incorrectly. The anti-commutator is:
$$\left\{\psi(\mathbf{x}), \psi^\dagger(\mathbf{y})\right\} = \delta(\mathbf{x}-\mathbf{y}).$$ So, if we do... | https://physics.stackexchange.com |
544,546 | [
"https://stats.stackexchange.com/questions/544546",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/334714/"
] | I have been trying to solve this issue for quite a while. So, lets say that we have a Poisson process, <span class="math-container">$N = (N_t, t \geq 0)$</span> and the <span class="math-container">$\lambda = 3$</span>. Lets say that <span class="math-container">$Y = (N_2 | N_6 = 3)$</span>. Find <span class="math-cont... | Let us assume we have a Poisson process with an arrival rate of <span class="math-container">$\lambda$</span>. After some time <span class="math-container">$t$</span>, <span class="math-container">$N_t$</span> unobserved arrivals have occurred. After some more time, say <span class="math-container">$\tau$</span>, we ... | The notation '<span class="math-container">$Y = (N_2 \mid N_6 = 3)$</span>' implies that the distribution of the random variable <span class="math-container">$Y$</span> is the conditional distribution of <span class="math-container">$N_2$</span> given <span class="math-container">$N_6=3$</span>.
Now if <span class="mat... | https://stats.stackexchange.com |
489,979 | [
"https://physics.stackexchange.com/questions/489979",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29985/"
] | I thought a scenario like; lets say I am looking an object and there is nothing except this object. Is there a way to understand that if this object is stay on its position or if object moving with a constant speed and also I am moving as same constant speed with this object ? (consider there is not any friction etc.)
| You cannot tell the difference. In fact many would say there <em>is</em> no difference. If you're really in a universe where there's nothing except the object like you say, there would be no difference between just sitting still and moving at a constant speed. There are no stars to see whizzing by, no atmosphere to mak... | Constant velocity and speed have no meaning unless you specify the frame of reference with respect to which it is measured or observed. (The only exception is the speed of light).
If you see an object “moving”, then it is moving with respect to your frame of reference. If you see it as “still” it is still with respec... | https://physics.stackexchange.com |
301,483 | [
"https://mathoverflow.net/questions/301483",
"https://mathoverflow.net",
"https://mathoverflow.net/users/88894/"
] | Given a convex function $f : \mathbb{R}^n \to [0,\infty)$, the objective is to find the farthest point in the level set $\left\lbrace x \in \mathbb{R}^n \mid f(x) \leq 1\right\rbrace$ (Assuming that such set is non empty, and closed and compact), i.e.
$$
\begin{aligned}
& \underset{x \in \mathbb{R}^n}{\text{maximi... | Under your assumptions, this is a concave programming problem (i.e., minimization of a concave function subject to convex constraints) with compact constraint set, and therefore has a global minimum at an extreme of the feasible set, i.e., satisfying $f(x) = 1$. (Although there may be other globally optimal points not ... | First, for any <em>closed</em> set $\newcommand{\bR}{\mathbb{R}}$ $C\subset \bR^n$, not necessarily compact, there is a closest point to the origin. To see this pick a minimizing sequence $x_\nu$. It is bounded, admits a convergent subsequence whose limit is a point that minimizes the distance to the origin ... | https://mathoverflow.net |
18,293 | [
"https://mechanics.stackexchange.com/questions/18293",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/675/"
] | What are the dangers associated with using a spare tyre that is several years past expiry?
I have seen people do this and live to tell the tale (a spare wheel manufactured in 2003 used to hobble an Escalade for a few miles to the nearest tyre shop in 2014) but I wonder if it is risky enough to warrant changing out the... | As pointed out by @JuannStrauss, a spare tyre that is stored inboard of the vehicle will degrade more slowly over time than one of the regular wheels since it is not exposed to:
<ul>
<li>normal wear & tear from vehicle motion</li>
<li>other physical aggression (hitting a curb)</li>
<li>winter salt</li>
<li>heating... | It will degrade over time, but at a much slower rate because it's not exposed to the elements like the other four are.
| https://mechanics.stackexchange.com |
138,716 | [
"https://dba.stackexchange.com/questions/138716",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/94751/"
] | Simply I have Two Input box <br>
<ol>
<li> Start_date </li>
<li> End_date </li>
</ol>
This is my database table
<pre><code>| id | category | start_date | end_date |
| 1 | gold | 2016-05-24 | 2016-05-31 |
| 2 | silver | 2016-05-16 | 2016-05-23 |
</code></pre>
Now When I insert date like below:
<pre><code... | Simple answer:
If you want both date columns to be between the input dates:
<pre><code>SELECT category
FROM tablename
WHERE 'start_date' BETWEEN start_date AND end_date
AND 'end_date' BETWEEN start_date AND end_date ;
</code></pre>
Or if you want any of the date columns to be between the input dates:
<pre><code... | You have to use below query for your output.
<pre><code>SELECT category
FROM table_1
WHERE start_date BETWEEN '2016-05-16' AND '2016-05-31'
OR end_date BETWEEN '2016-05-16' AND '2016-05-31'
</code></pre>
| https://dba.stackexchange.com |
59,417 | [
"https://physics.stackexchange.com/questions/59417",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16620/"
] | I do not understand how any state in Hilbert Space $\mathcal{H}=\mathcal{H}_A\otimes\mathcal{H}_B$ of dimension $\text{dim}(\mathcal{H}_A)\times\text{dim}(\mathcal{H}_B)$ can be decomposed in the Schmidt basis when the Schmidt basis has size $\text{min}\{\text{dim}(\mathcal{H}_A),\text{dim}(\mathcal{H}_A)$}.
Thank you... | This is because the Schmidt bases depend on the vector you want to decompose: <em>given</em> a vector $v\in\mathcal{H}$ you can find bases $\{u_i\}$ for $\mathcal{H}_A$ and $\{v_j\}$ for $\mathcal{H}_B$ such that
$$v=\sum_k \lambda_k u_k\otimes v_k.\tag{1}$$
The bases $\{u_i\}$ and $\{v_j\}$ depend on $v$ in a nonlinea... | This follows from Singular Value Decomposition (go wikipedia it).
Given any state $\psi \in H = H_A \otimes H_B$, one can write it as
\begin{align}
\psi = \sum_{nm} W_{nm} \psi_n^A \psi_m^B,
\end{align}
where $\{ \psi_n^\xi \}$ form a basis for the subspace $H_\xi$. Let's assume that the dimensions of $H_A, H_B$ are f... | https://physics.stackexchange.com |
2,007,750 | [
"https://math.stackexchange.com/questions/2007750",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/387914/"
] | Let $A$ be an $m\times n$ matrix of rank $n$ with real entries. Choose the correct statements.
1. $Ax=b$ has a solution for any $b$.
2. $Ax=0$ does not have a solution.
3. If $Ax=b$ has a solution, then it is unique.
4. $y'A=0$ for some non zero $y$, where $y'$ denotes the transpose vector of $y$.
Option 1 and 2 are f... | <blockquote>
<strong>(a)</strong> Least root of $(1)$ lies in $(a_1,a_1+1).$
</blockquote>
Let $A=\;\{a_j \mid j = 1, 2, \cdots k\}\;$ and $\;f(x)=\sum_{j=1}^k \frac{1}{x-a_j} - 1$. Observe that:
<ul>
<li>$f'(x) = \sum_{j=1}^k \frac{-1}{(x-a_j)^2} \;\;\lt\;\; 0\;$ so $f$ is strictly decreasing on $\mathbb{R} \set... | Here is part of (a):
If $x < a_1 \le a_i$, then $x-a_i <0$ and so $\displaystyle\frac{1}{x-a_1}+\frac{1}{x-a_2}+\cdots \frac{1}{x-a_k} < 0 < 1$.
Therefore, there is no root smaller than $a_1$.
| https://math.stackexchange.com |
177,485 | [
"https://electronics.stackexchange.com/questions/177485",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/41087/"
] | I just ordered a barrel connector but it's bigger then the one i need, What is the small barrel type connector called. My original one has a yellow ring around it, Is that an indicator of what type it is?
<img src="https://i.stack.imgur.com/iOP1j.jpg" alt="enter image description here">
| <blockquote>
What is the small barrel type connector called.
</blockquote>
It's called a barrel connector with a different diameter.
Typically I see these connectors specified in 0.1 mm increments.
<blockquote>
My original one has a yellow ring around it, Is that an indicator of what type it is?
</blockquote>
W... | It's still a barrel plug. Whip out your calipers to verify, but I'd say that's a 4.0mm/0.7mm barrel plug.
| https://electronics.stackexchange.com |
26,224 | [
"https://electronics.stackexchange.com/questions/26224",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7661/"
] | I was looking to build a system for high currents (say ~30 amps) and a friend suggested vacuum tubes. In theory, vacuum tubes seemed more robust for high current applications, but after looking around, and I found a bunch with relatively low current ratings (~10mA.)
I wanted to avoid mechanical relays if possible beca... | A very short answer with not too much detail goes like this:
<ul>
<li>Tubes are good at medium to high voltage and low current.</li>
<li>Transistors (especially MOSFETs) are good at low to medium voltage and high current.</li>
</ul>
Exceptions exist, but for the common and most used examples of said parts, the above.... | Tubes exist which can be used to switch very high currents and voltages. You can do a search on <em>hydrogen thyratron</em> as one example. Thyratrons tend to be used in laser, radar and other relatively exotic applications, but have also been (ab)used by Tesla coil fans.
They work more like SCRs than conventional t... | https://electronics.stackexchange.com |
24,279 | [
"https://electronics.stackexchange.com/questions/24279",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/740/"
] | This unusual plug interfaces an electric hair dryer to the 120V 60Hz mains. The thing that makes it peculiar is that when it is tipped back and forth, a small 'clunk' can be felt, as something inside shifts in response to being tilted.
It is a small boxy thing, about a 1.75" x 1.25" x 1", has no ground lug, but is po... | I was inclined to say it was a ground fault current interrupter. However, those that I am familiar with have manual test and reset buttons.
I did a search to see if an auto-reset version exists, and apparently it does.
| No buttons on it? Frequently there is a little breaker in those boxes, and they have an exposed reset button on them. I'm going to guess self resetting thermal breaker inside, with some springy or loose fitting mechanical elements that are moving around.
| https://electronics.stackexchange.com |
7,541 | [
"https://mathoverflow.net/questions/7541",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2043/"
] | The following question was posed to me a while ago. No one I know has a given a satisfactory (or even a complete) proof:
Suppose that $M$ is an $n$ x $n$ matrix of non-negative integers. Additionally, suppose that if a coordinate of $M$ is zero, then the sum of the entries in its row and its column is at least $n$.
W... | The following looks too simple, so perhaps there's a mistake, but here goes.
Let $m$ be the smallest among all row sums <em>and</em> column sums. If $m\geq n/2$, we are done.
Otherwise, $m=cn$ with $c\lt 1/2$. Suppose it is a column which has sum $m$. This column has at least $n-m$ zeroes, and each of the correspondi... | Again, very nice question!
Edit: I can get a lower bound of $\frac{3 - \sqrt{5}}{2} n^2$ as follows: Set $c = \frac{3 - \sqrt{5}}{2}$ for conciseness. Assign a (not necessarily simple) bipartite graph to $M$ in the obvious way. Now if the sum of some row is less than $cn$, there must be at least $(1-c)n$ vertices in t... | https://mathoverflow.net |
8,391 | [
"https://softwareengineering.stackexchange.com/questions/8391",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1632/"
] | In a book I'm reading there is a chapter on documentation for your code. The book is about PHP and described some easy methods but also going for some complicated and time consuming methods (xml, xsl) like DocBook.
At my current small company (5 people) we even rarely write comments, but I'm wondering if in a big comp... | Working on PHP and NetBeans, the documentation style is pretty much PHPDoc way. Thus I write a little more than what the IDE generates.
e.g. IDE generates:
<pre><code>/**
* Description for ClassA
*
*
* @author Sam-Mauris Yong
*/
class ClassA{
function __construct(){
echo "5";
}
}
<... | I follow this convention:
<pre><code>//-----------------------------------------------------------------------------
// MPlayer_PlayAlbum
//
// PURPOSE:
// Creates a playback selection of the given album and starts playing it
//
// PARAMETERS:
// int AlbumId [in] Zero based index of the album to playback,
// ... | https://softwareengineering.stackexchange.com |
342,577 | [
"https://mathoverflow.net/questions/342577",
"https://mathoverflow.net",
"https://mathoverflow.net/users/128758/"
] | Let <span class="math-container">$A(i,j), i,j=0,1,2$</span> be the covariance matrix of three random variables. If we know all the entries except <span class="math-container">$A(2,0)$</span> and <span class="math-container">$A(0,2)$</span>, how to determine the range of possible values of <span class="math-container">$... | Let us write
<span class="math-container">$$A=\left(
\begin{array}{ccc}
a & b & c \\
b & d & e \\
c & e & f \\
\end{array}
\right).
$$</span>
Then <span class="math-container">$A$</span> will be a covariance matrix iff it is positive semidefinite (<span class="math-container">$A\ge0$</span>)... | I am guessing, but I think in this case when det(A) > 0. Therefore look at det(A) = 0 as a quadratic equation in x = A(0,2), and find it's zeros, and it ought ot be the area between the zeros. Here is the circumstantial evidence: det(A) = 0 will give a semidefinite matrix, which should be the boundary between po... | https://mathoverflow.net |
499,612 | [
"https://electronics.stackexchange.com/questions/499612",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/252394/"
] | While all your great answers to my previous question are simmering in my brain (I printed out all your answers and placed a copy on my work bench to have another go at it), I have one more:
As I mentioned in a previous post, I have a new model UNI-T UT89XD meter. A unique feature is that it generates up to over 11 vo... | From first principles:
I get Vr = 123mV for approximate ripple. (Edit: 101mV is closer to the approx value)
So peak current is approximated by the load current ((Vp-Vd)/0.436 = 8.49A) plus the current due to dv/dt when the source is at 4.5 - Vr.
v(t) = Vp sin(<span class="math-container">\$\omega t\$</span>) so wh... | <blockquote>
Given values are : C = 1.4F
</blockquote>
That's 1.4 farads!
For a capacitor <span class="math-container">\$i = C\dfrac{dv}{dt}\$</span>.
So, if <span class="math-container">\$V_{peak}\$</span> is 4.5 volts, the maximum <span class="math-container">\$\dfrac{dv}{dt} = 4.5\cdot 2\cdot\pi\cdot 60\$</spa... | https://electronics.stackexchange.com |
182,083 | [
"https://softwareengineering.stackexchange.com/questions/182083",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/41217/"
] | Is the concept of OOP intimately tied to allocating objects on the heap? Is it possible to write normal OOP without creating excessive objects on the heap?
| No, OOP has nothing to do with where objects reside in memory. For example, instances of the same class can be allocated statically, on the heap, or on the stack in C++. In other languages, like Python, memory management is almost transparent, so the question of location doesn't really apply.
| Technically no, but "normal OOP" assumes dynamic allocation, for which a heap is a good general-purpose mechanism. You could certainly try using some other method, but you'd probably wind up re-inventing the heap.
| https://softwareengineering.stackexchange.com |
112,471 | [
"https://stats.stackexchange.com/questions/112471",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/32175/"
] | I have two stationary time series. I would like to check for cointegration between them. Does this make sense, and can I just use Engle-Granger Test (two step) for Cointegration for this?
| Say you have some data. Say you're willing to assume that the data comes from some distribution -- perhaps Gaussian. There are an infinite number of different Gaussians that the data could have come from (which correspond to the combination of the infinite number of means and variances that a Gaussian distribution ca... | Maximum Likelihood Estimation (MLE) is a technique to find the <em>most likely</em>
function that explains observed data. I think math is necessary, but don't let it
scare you!
Let's say that we have a set of points in the $x,y$ plane, and we want to know
the function parameters $\beta$ and $\sigma$ that most likely... | https://stats.stackexchange.com |
332,463 | [
"https://physics.stackexchange.com/questions/332463",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/155730/"
] | Is it possible that a disc is <strong>rolling up</strong> a rough inclined plane if only gravitational and frictional forces are acting on it ?<br>
What I am confused about is,<strong>which force is moving the disc up the plane</strong> as gravitational force acts in downward direction and frictional force can't be m... | Yes, it is possible. It will slow down it's rolling, but nevertheless roll uphill for a while.
The answer to your comment on the other answer is, that the friction direction <strong>doesn't depend on rolling direction</strong>! It <em>only</em> depends on other forces present. This is the case for static friction, wh... | Net force indicates acceleration, not velocity. If a disc is on an inclined plane with only gravitational, frictional, and the inherent normal force, the net force on it will be directed down the inclined plane. As Abhijeet Melkani commented, it can be moving up the inclined plane if it had an initial velocity in that ... | https://physics.stackexchange.com |
127,288 | [
"https://security.stackexchange.com/questions/127288",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/17156/"
] | One of the major up-and-coming MFA methods is U2F, which relies on an initial key exchange and challenge-response mechanism.
It's a relatively new protocol, and is only starting to see more widespread adoption, notably among big web entities like Google, but it's not the first easy-to-use, key-exhchanging, challenge-r... | Let's check out what PGP and SSH actually offer for this purpose:
<ul>
<li>PGP:<br>
Client must install PGP software which is not installed by default in the majority of the systems. Client must create a PGP key pair. Then he must send the public key to the server so that the server can use it later for validation. Wh... | <strong>Lack of portability</strong>
SSH and PGP are widely used, but they are not web technologies. There has been an equivalent web technology for many years - SSL client certificates. However, this is not much used.
The reason is the lack of portability. If you have an SSL client certificate on your home desktop, ... | https://security.stackexchange.com |
46,324 | [
"https://dba.stackexchange.com/questions/46324",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25951/"
] | I am learning about database design and I'm writing a Java GUI program with a back-end database. The main table in my database stores a different product in each row. I have some columns such as: product_id (PK), price, stock_quantity, etc. I also have eight columns that store the names of the file names for that pr... | If each image has a specific purpose then this would be OK but your column names should be more specific, such as img_thumbnail, though I would still use a separate table with columns that carry information about each images use.
The better design, especially if the images do not have specific well differentiated uses... | I think it's better to let the images have their own table. The way I've solved it is by having 3 tables.
One for the products, another one for the images
and the third for the connections.
<ul>
<li>The product table just stores information about the product and nothing about the images.</li>
<li>The image table just... | https://dba.stackexchange.com |
49,994 | [
"https://mechanics.stackexchange.com/questions/49994",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/14105/"
] | Sometimes when waiting for a traffic light, I see the reversing lights on the vehicle in front of me briefly flicker on and then off again. Most often, this is on Mercedes people vans (short buses).
This startles me, since if the vehicle were to be put in reverse by accident, it would hit me when trying to drive away ... | It's simply because some cars will illuminate the reverse lights when the drive moves the gear selector from D, through R on their way to P when stopping for extended periods.
My Porsche, and my Range Rovers before only showed the reversing light when the gear was actually engaged. Other cars seem to have the light w... | As a (former) automotive software engineer, I've spent some time working on car engine controllers.
As @Snow says, the gear lever on an automatic selects whether you're in Park, Reverse, Neutral, Drive or Low gear. The gear selection is arranged in that order, so in the industry you will frequently find this called t... | https://mechanics.stackexchange.com |
15,647 | [
"https://electronics.stackexchange.com/questions/15647",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2062/"
] | IS there any PCB design software where I can design & route common part of design (like DCDC with support circuitry), and make it some kind of 'component' - so that I can always drop it to my new project, and it will appear already routed.
There might be needed several occurrences, and if I update component - it m... | You can fake this pretty effectively in Altium Designer.
Altium has what they term "Recyclable Schematics" - Schematic layouts that you can paste into larger schematics and treat as components.
Duplicating the PCB end is a bit more work, but definitely doable (I've done it). Basically, you route the DC-DC on one boa... | You can do this with gEDA's gschem. I haven't tried with gEDA pcb, but I don't see why it wouldn't be any different from another symbol footprint.
The idea is to create a symbol of the subcircuit, design a pcb footprint for it, then stick it in your symbol library. Connections are made with nets, not pins. I've just s... | https://electronics.stackexchange.com |
645,293 | [
"https://math.stackexchange.com/questions/645293",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/73620/"
] | I have $100$ balls and on each ball is labelled a number between $1$ and $100$. No two balls can have the same number, so the interval $1\ldots 100$ is represented by the balls.
I now pick 20 balls at random, one by one without putting them back at any point. I am trying to find the probably of getting 4 certain numbe... | You have computed the probability that you get your target numbers, in the <strong>first</strong> $4$ choices, in a certain <strong>specified</strong> order. That is much smaller than the required probability.
There are $\binom{100}{20}$ equally likely ways to choose $20$ balls.
We find the number of ways to choose $... | Your solution is not correct. But, here's a hint on a different way to proceed:
<strong>Hint:</strong> You want to count all permutations (of length $20$) of distinct elements in $\{1,2,\ldots,100\}$, such that four fixed numbers (say $1,2,3,4$) are all contained in the permutation.
To do this: pick the $16$ numbers... | https://math.stackexchange.com |
2,170 | [
"https://dba.stackexchange.com/questions/2170",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136/"
] | When I create a table like this
<pre><code>create table char_test(
item varchar(10) collate SQL_Latin1_General_CP1_CI_AS
)
go
</code></pre>
I can store varchars containing <strong>≥</strong>
<pre><code>insert into char_test values ('≥');
</code></pre>
When I do a
<pre><code>select item from char_test;
</code... | varchar doesn't support <code>≥</code>: unicode only
This includes the literal <code>'≥'</code> which is varchar too
<strike>Collation here doesn't matter: this is sorting and comparison only</strike> never seen this before!
Some more SQL to use your table
<pre><code>SELECT ASCII('≥'), CHAR(61), '≥'
GO
insert into ... | If I run this:
<pre><code>select UNICODE ( '≥' )
select UNICODE ( '=' )
select UNICODE ( item ) from char_test;
</code></pre>
They all return the same number, 61. I don't think the REPLACE proves that the character is being recognized. I even changed the char_test table to have the item column defined as nvarchar(10... | https://dba.stackexchange.com |
152,103 | [
"https://dba.stackexchange.com/questions/152103",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/107833/"
] | I found a function that will properly capitalize text strings. I have a table where my fields need this function run on. Is it possible to run the function on my table?
<pre><code>Create Table @Garbage
(
fullname varchar(500)
,saddy varchar(500)
)
Insert Into @Garbage (fullname, saddy) VALUES
('BlAmE iT oN tHe ... | Verify your intended change using SELECT
<pre><code>SELECT
fullname = dbo.fnConvert_TitleCase(fullname),
saddy = dbo.fnConvert_TitleCase(saddy)
from
@Garbage
</code></pre>
and then, if you're satisfied, run the update below
<pre><code>update @Garbage set
fullname = dbo.fnConvert_TitleCase(fullname),
... | absolutely you can run this function on your table although you will have to apply this function to each column. However,scaler functions are bad for performance when executing on a large dataset so it may not be useful for you.
<pre><code>SELECT [dbo].[fnConvert_TitleCase]([fullname]),
[dbo].[fnConvert_TitleCas... | https://dba.stackexchange.com |
304,156 | [
"https://softwareengineering.stackexchange.com/questions/304156",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/206305/"
] | My R&D team has been working on a major product for over a year and we're using JIRA for issue management.
Now got more minor, distinct products (not related to the previous one), and would like to separate the issues, versions, etc.. related to these products.
We thought of the following options:
<ul>
<li>Diffe... | Jira tends to be project centric, not product centric. So as you have realized, products do not have a very rich model (in Jira). The is a standard field "component" which might express something similar to what you are looking for. The approach of mapping a Jira "project" to each of your product also works, but makes ... | I'd personally go this way (we are currently using this in my digital agency):
Have <strong>a distinct JIRA project for each project</strong> you are managing. This makes it easier to track issues and what's being done on each single worke you are doing.
Then have <strong>another JIRA project</strong> set up as a <em... | https://softwareengineering.stackexchange.com |
16,651 | [
"https://mathoverflow.net/questions/16651",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4291/"
] | I was reading a series of article from the Corvallis volume. There are couple of questions which came to my mind:
<ol>
<li>Why do we need to consider representation of Weil-Deligne group? That is what is an example of irreducible admissible representation of $ Gl(n,F)$ which does not correspond to a representation of ... | Regarding (1), from the point of view of Galois representations, the point is that continuous Weil group representations on a complex vector space, by their nature,
have finite image on inertia.
On the other hand, while a continuous $\ell$-adic Galois representation of $G_{\mathbb Q_p}$ (with $\ell \neq p$ of course) ... | The answer to your first question would be a Steinberg representation (i.e. under suitable normalizations, the infinite-dimensional subquotient of the induction of $(\chi|\cdot|^{-1/2},\chi|\cdot|^{1/2})$). Kudla's article in Motives II is a nice place to see this. I don't have an answer for number two.
| https://mathoverflow.net |
37,677 | [
"https://dsp.stackexchange.com/questions/37677",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/25757/"
] | <ul>
<li>Is the system $y[n] = x[n] - x[n-1]$ stable or unstable ? </li>
<li>If unstable, can you please give some examples of input signals for which the system becomes unstable? </li>
</ul>
| For BIBO stability in the case of discrete time, there is a necessary and sufficient condition given by $\sum |h[n]| < \infty$ that is if the impulse response is absolute summable then the system is BIBO stable. Clearly
$$h[n] = \delta[n] - \delta[n-1]$$ and it has a finite support, the impulse response is absolutel... | Stability has different meanings depending on the system you are observing. Here, you have a discrete system, which is linear, and time-invariant. The most common stability criterion in this case is the so-called bounded-input, bounded-output (BIBO) stability.
The question of stability is thus: <strong>if an input is ... | https://dsp.stackexchange.com |
388,543 | [
"https://physics.stackexchange.com/questions/388543",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/186037/"
] | So I recently searched up "em wave transverse proof", and I understood it pretty well enough I think.
After that, I just started to wonder if all waves are either transverse/longitudinal. If there are waves that are neither one of them, how do we put that in mathematical notation?
| Short answer: <strong>no</strong>.
For example, gravity waves (i.e. ripples) on the surface of a liquid have both transverse and longitudinal motion, so they are not purely either.
| I was wondering if there is a difference between a transverse and longitudinal wave...
Imagine a rubber rod, it flexible to the sides so you can bend it and oscillate it like a string if you do it fast enough. That would be its transverse wave behavior.
Now the same rubber rod can be compressed or decompressed and th... | https://physics.stackexchange.com |
258,934 | [
"https://math.stackexchange.com/questions/258934",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/32885/"
] | I am trying to prove this statement.
for any $a,b \in \mathbb{R}$, $$\max\{a,b\}=\frac{1}{2}\big(a+b+|a-b|\big)$$ and $$\min\{a,b\}=\frac{1}{2}\big(a+b-|a-b|\big)$$
I am eating myself not knowing where and how to start. For any guidance Iwill be thankful in tons
| Without loss of generality, we can assume that $a = \max(a, b)$ and $b=\min(a, b)$, as both of the expressions are symmetric.
So since $a \geq b$ we have $a-b \geq 0$, thus $a-b=|a-b|$, and so $\dfrac{a+b+|a-b|}{2} = \dfrac{a+b+a-b}{2}=a=\max(a, b)$.
Similarly, we have $\dfrac{a+b-|a-b|}{2}=\dfrac{a+b-(a-b)}{2} = b=\... | What is the definition of $\max\{a,b\}$? Hint: it involves two possible cases.
For each of these cases, check that the right hand side gives the same answer. Job done.
Repeat for $\min\{a,b\}$.
| https://math.stackexchange.com |
333,247 | [
"https://softwareengineering.stackexchange.com/questions/333247",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/217820/"
] | I cant for the life of me figure out why this returns 0 rather than 5. <code>i</code> keeps getting incremented before it hits the last <code>return</code> statement, however it always returns 0, from the first call in the stack. I would think that since the most recent call on the stack hits the <code>return</code> in... | The key here is <em>stack frames</em>. Lets take a look at your first example:
<pre><code>public static int incrementI(int i) {
if (i == 5){
return i;
} else {
incrementI(i + 1);
}
return i;
}
</code></pre>
On the <em>first</em> call, you have a variable named <code>i</c... | Let's look at the first snippet of code and do a case analysis.
<h2>When <code>i == 5</code></h2>
The first snippet of code is equivalent to:
<pre><code>public static int incrementI(int i) {
return i;
}
</code></pre>
<h2>Otherwise</h2>
If, however, <code>i</code> is different from 5, then the code is equ... | https://softwareengineering.stackexchange.com |
494,318 | [
"https://stats.stackexchange.com/questions/494318",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/276760/"
] | I have a regression equation whose residuals are homoscedastic but have a slight negative skew due to several outlier values. The Q-Q plot is pretty close as to what would be expected from a normal distribution, but has a slight deviation in the upper quantile that seems to be related to these values. I am trying to te... | We roll <span class="math-container">$n$</span> dice, each with <span class="math-container">$m$</span> sides
The probability of getting all ones is: <span class="math-container">$(\frac{1}{m})^n$</span>
The probability of at least a single one result is: <span class="math-container">$1-(\frac{m-1}{m})^n$</span>
and th... | Let <span class="math-container">$m$</span> be the size of the die, and let <span class="math-container">$n$</span> be the number of rolls.
Let <span class="math-container">$A$</span> be the event of rolling only 'ones' and let <span class="math-container">$B$</span> be the event of at least one 'one'.
You can use the ... | https://stats.stackexchange.com |
3,374 | [
"https://biology.stackexchange.com/questions/3374",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/158/"
] | With many foods today containing chemicals, agents and preservatives etc... What biological criteria must a new food and its constituent components satisfy biologically, to be defined as edible?
For example do they look at the chronic/acute affects of chemicals in the body?
This question is just limited to chemic... | As far as I know, edibility (wow, I'm surprised that passes the spell checker!) is not a strictly defined term, biologically or otherwise. Humans have been around eating and drinking stuff long before the scientific method was around to study this question rigorously, and before there were regulatory agencies charged w... | Much like Daniel Standage suggests, I think "edible" is more inferried than defined, sort of like looking at a black hole - its absence is defined by the activity around it. Human bodies are capable of metabolizing lots of compounds that become poisonous pass some threshold.
In medical terms there are LDmin and MLD an... | https://biology.stackexchange.com |
466,980 | [
"https://physics.stackexchange.com/questions/466980",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/225544/"
] | I've been struggling with this for a while now. I feel that proving this is actually way easier than what I think it is.
I'm just going to copy paste the question here:
<blockquote>
A light bulb (the object) is placed a distance of 753 mm from a
screen. A convex lens with a focal length of 53 mm is placed between
... | The resistance of a light bulb changes with the temperature of the filament in the bulb, and therefore changes with the voltage applied to the bulb. The resistance when it is operating at its maximum voltage may be 10 times as much as when the bulb is "off".
You didn't describe <em>exactly</em> what you did in your ex... | The resistance of the bulbs do not change at all. It is instead the <em>effective resistance</em> of the circuit that changes.
Call the resistance of a bulb <span class="math-container">$R$</span> and let your battery supply a voltage <span class="math-container">$V$</span>. That voltage must be dropped over all three... | https://physics.stackexchange.com |
156,068 | [
"https://dba.stackexchange.com/questions/156068",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/97841/"
] | Consider a table that records visits
<pre><code>create table visits (
person varchar(10),
ts timestamp,
somevalue varchar(10)
)
</code></pre>
Consider this example data (timestamp simplified as counter)
<pre><code>ts| person | somevalue
-------------------------
1 | bob |null
2 | bob |null
3 ... | The following query achieves the desired result:
<pre><code>select *, first_value(somevalue) over w as carryforward_somevalue
from (
select *, sum(case when somevalue is null then 0 else 1 end) over (partition by person order by id ) as value_partition
from test1
) as q
window w as (partition by person, value_par... | The problem is in the gaps-and-islands category of problems. It's a pity that Postgres has not yet implemented <code>IGNORE NULL</code> in window functions like <code>FIRST_VALUE()</code>, otherwise it would be trivial, with a simple change in your query.
There are probably many ways for this to be solved using window... | https://dba.stackexchange.com |
50,090 | [
"https://electronics.stackexchange.com/questions/50090",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15827/"
] | For example, in the RS232 here:
<img src="https://i.stack.imgur.com/4yS1E.png" alt="enter image description here">
or here:
<img src="https://i.stack.imgur.com/Lb2Jy.png" alt="enter image description here">
| No. Different people draw schematics differently. Sometimes it is obvious, but usually not. In the examples you gave, it is not obvious.
When it is marked, it is usually a text note next to the connector. Or sometimes it is in the part number, like "DB-9F" for a female connector.
| Here's one general guideline. It applies to connectors on the outside of the instruments. If the connector supplies power or signal, it's usually a female (F). This is done prevent shorting the signal (to something in the outside environment). A female pin is harder to accidentally short than a male pin. One can f... | https://electronics.stackexchange.com |
61,389 | [
"https://physics.stackexchange.com/questions/61389",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9398/"
] | Assumption: The only lights I have are candle, table lamp, and sunlight.
What would I need to create <em>visible</em> reflection of an object in the shallow water contained in a 5 liter bucket? Is it even possible anyhow?
What kind of light out of the three will maximize the visibility of the reflection in this case?... | If the problem with shallow water is that you see the walls and the bottom instead of only the reflection, I would just use a black bucket. Or somehow make bucket's inners black.
Moreover a bucket is a bit unpractical in this case, just a really black tray with water should suffice.
Another option is to make water bl... | For a "visible" (clean/clear) reflection we need to optimize the contrast of our image, and minimize the amount of visual "noise".
Given a specific image, a surface with higher <strong>specular reflectivity</strong> will reflect more of the light without adding noise.
A surface can also have <strong... | https://physics.stackexchange.com |
76,391 | [
"https://security.stackexchange.com/questions/76391",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/63824/"
] | I'm on a laptop running Window 8.1 connected to the internet running Kaspersky. I am the sole user and administrator of this laptop.
While going about my usual work, I paused for a moment (hands off both keyboard and mouse) during which time a powershell windowed opened all by itself and started flashing. With each fla... | While I'd recommend following ekaj's suggestion and trawling your logs to be sure, it sounds very suspicious to me.
If you have allowed automated updates, it is possible that this was part of an update script...but usually updates present quite formalised user information.
Safest bet is to assume the worst - and wipe... | I know I'm super late to this party, but this question came up for me while I was searching Sec.SE in relation to another situation that I'm dealing with at work. I also think I could provide something useful that hadn't been touched upon yet. Although I'd agree with Rory Alsop, I'd also like to add something that bo... | https://security.stackexchange.com |
1,776,518 | [
"https://math.stackexchange.com/questions/1776518",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/311539/"
] | I have a hard time to understand how to do it.
I think what blocks me, is that the Rolle's theorem is usually applied to functions, yet here there aren't any. What should I do?
| Here is an explicit proof.
$$f(x) = \sqrt{x}$$ with $a=10^4$ and $b=10^4+1$
Roll's theorem is: there exist $c \in (a,b) $ such that $f'(c)=\frac {f(b)-f(a)}
{b-a}$
$$\sqrt{10^4+1}-100=\frac{\sqrt{10^4+1}-\sqrt{10^4}}{10^4+1-10^4}=f'(c)$$ where $c \in (10^4, 10^4+1)$
$$f'(c)=0.5c^{-0.5}\le0.5\times0.01 $$
and of c... | The easy way to do this is to use a consequence of Rolle's theorem: the mean value theorem, which states that for $ f $ continuous in $ [a, b] $ and differentiable in $ (a, b) $, we have
$$ f'(c) = \frac{f(b) - f(a)}{b - a} $$
for some $ c \in (a, b) $. To prove the mean value theorem, define a function $ g(x) = f(x)... | https://math.stackexchange.com |
223,273 | [
"https://mathoverflow.net/questions/223273",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78554/"
] | I have heard that an open, orientable 3-manifold $X$ (non-compact, without-boundary) that is homotopy equivalent to an orientable surface $S_g$ must itself already be homemorphic to $S_g \times \mathbb R$. There seems to be a very deep theorem behind it, however, I couldn't find any reference which would bring this up.... | I think the answer is (consistently) no.
Following Asaf's comment, let $\kappa$ be Mahlo in $L$ and let $G \subset \text{Col}(\omega,\mathord{<}\kappa)$ be an $L$-generic filter. Let $\eta$ be the least ordinal such that $\kappa < \eta$ and $L_\eta \models \mathsf{ZFC}$, and consider the model $N = L_\eta[G]$.... | i added an answer and then realized it was a complete nonsense, i was getting at the following question.
Suppose kappa is an inaccessible cardinal. Is there a transitive model M of ZFC such that
<ol>
<li>M has height kappa
</li>
<li>for some stationary in kappa set S, for every alpha in S, M computes alpha^+ correctly,... | https://mathoverflow.net |
427,762 | [
"https://physics.stackexchange.com/questions/427762",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206192/"
] | I'm having my first lectures on Quantum Physiscs. We just discussed the black body and thermal radiation. However, why does a heated body emit light? How it is that a rise in temperature produce a change in the electromagnetic field?
Feel free to use equations to answer.
| IchVerloren, welcome to Physics SE!
The thing isn't temperature changing the electromagnetic field. In its most fundamental form, temperature $T$ is the relationship between lack of information (entropy $S$) and total energy $U$:
\begin{equation}
\frac{1}{T}=\frac{\partial S}{\partial U}.
\end{equation}
It is a stat... | You are here- und deshalb bist du nicht verloren! Here is why:
The surface of a hot body can be thought of as consisting of a huge number of tiny electromagnetic oscillators which can be excited by incoming photons. They can absorb the energy in those photons, and then by oscillating they can radiate that energy away ... | https://physics.stackexchange.com |
63,452 | [
"https://stats.stackexchange.com/questions/63452",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/27666/"
] | This is a general question on logistic regression result reporting for a publication.
We have an example where two well correlated ($r=0.4, p=0.001$) blood parameters (<code>blood parameter1</code> and <code>blood parameter2</code>) are associated with blood pressure in mixed sample of men and women, however, the effe... | <strong>A simple way is to rasterize the domain of integration and compute a discrete approximation to the integral.</strong>
There are some things to watch out for:
<ol>
<li><strong>Make sure to cover more than the extent of the points:</strong> you need to include all locations where the kernel density estimate wil... | If you have a decent number of observations, you may not need to do any integration at all. Say your new point is ${\bf{x}}_0$. Assume you have a density estimator $\hat f$; sum up the number of observations ${\bf{x}}$ for which $\hat f({\bf{x}}) < \hat f({\bf{x}}_0)$ and divide by the sample size. This gives you an... | https://stats.stackexchange.com |
13,078 | [
"https://stats.stackexchange.com/questions/13078",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5404/"
] | Say you have N observations that are iid.
$$ \forall i, \quad p(X_i=x_i|\mu,\sigma,I) = \frac{1}{\sqrt{2\pi}\sigma}
\exp\left(-\frac{1}{2\sigma^2}(x_i-\mu)^2\right)$$
then
$$ p(x_1,\dots,x_N|\mu,\sigma,I) = \frac{1}{(\sqrt{2\pi}\sigma)^N}
\exp\left(-\frac{N}{2\sigma^2}[(\bar{x}-\mu)^2 + \bar{\sigma}^2]\right)$$
w... | When N is known, you can use the fact that the sample mean and variance are independent (conditionally on $\mu, \sigma$) and have known distributions. You can justify this approach because you already known that the sample mean and variance are sufficient statistics and the likelihood has to factor this way (your comme... | If you don't know the value of $N$, then we simply integrate it out, the same as any other nuisance parameter. We know that $N$ is discrete, and as long as your standard deviation is not zero, then you know that you have at least $2$ observations, so $N\geq 2$. So we write out the posterior as:
$$p(\mu,\sigma|\overl... | https://stats.stackexchange.com |
97,211 | [
"https://dba.stackexchange.com/questions/97211",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8227/"
] | I'm trying to get the rows from a table where <code>lastLoginTimestamp</code> is in last 7 days and I'm doing as follow:
<pre><code>SELECT * FROM representative WHERE DATE_SUB(lastLoginTimestamp, INTERVAL 7 DAY)
</code></pre>
<code>lastLoginTimestamp</code> is stored as a <code>VARCHAR</code> so this is where the pro... | The values seem to be Unix timestamps, stored as strings. You can use the special datetime functions that MySQL has for conversions:
<pre><code>SELECT *
FROM representative
WHERE DATE_ADD(FROM_UNIXTIME(lastLoginTimestamp), INTERVAL 7 DAY) >= NOW() ;
</code></pre>
but it won't be very good for efficiency. Much mo... | <pre><code>select from_unixtime("1427162434");
</code></pre>
the rest you will figure out
but consider formatting the historical data and just change the type and test. Can't believe that the dates are pushed to the DB as chars.
| https://dba.stackexchange.com |
14,328 | [
"https://security.stackexchange.com/questions/14328",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/9446/"
] | If an attacker were to dig up the 'outgoing feed' from my local exchange or the street cabinet, could they sniff my entire neighborhood's network traffic? Or is this infrastructure secured against this sort of attack?
| Absolutely.
In practice, though, this is a complex and very risky attack - probably going to be easier to do something else.
| Yes, they could.
It wouldn't be terribly hard: those street cabinets aren't very physically secure. At least, the ones in my neighborhood aren't. On the other hand, there's some chance of detection (a neighbor might call the police if they see some suspicious character messing around with the cabinet late at night)... | https://security.stackexchange.com |
189,044 | [
"https://softwareengineering.stackexchange.com/questions/189044",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/37924/"
] | <h2>The problem</h2>
We need to store data in a table-like way, but we have very strict space constraints (~1Mb per table of 10k+ rows). We store data like this:
<pre><code>ID | reviews | factor | score | interval | etc.
---+---------+--------+-------+----------+-----
1 | 244 | 2.4 | 10 | 4268 | ...
</... | If I'm understanding your indexes correctly they aren't the most efficient way to store them.
You can't sort your table on two keys at once anyway, thus I don't think you should try to sort it at all. Rather, sort your indexes.
10k rows--a two-byte value can refer to any entry in your table. Thus build two arrays t... | If data validity is critical, then any transformation to the data <strong>must</strong> take the data transformed from a valid state to a valid state. The transformation mechanisms should ensure validity of output given valid input. An unsuccessful transformation should fail safely, leaving the data in a valid state.... | https://softwareengineering.stackexchange.com |
647,986 | [
"https://physics.stackexchange.com/questions/647986",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/304134/"
] | When the Earth revolves around the sun, the external torque on Earth about the sun is zero, so we can say angular acceleration is zero, then why is angular velocity not constant?
| It's the angular momentum <span class="math-container">$I\omega$</span> that's constant.
As the earth moves closer or further away from the sun its moment of inertia <span class="math-container">$I$</span> changes, and so to compensate so can the angular velocity <span class="math-container">$\omega$</span>, even thoug... | The angular momentum/angular velocity of the earth is <em>not</em> constant. The oblateness of the earth means that the sun and the planets exert a torque on the earth that tries to turn the axis of rotation to be perpendicular to the plane (the ecliptic) in which the sun and the planets all lie. This torque causes ... | https://physics.stackexchange.com |
280,515 | [
"https://physics.stackexchange.com/questions/280515",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84158/"
] | The gauge groups in Yang-Mills theory can be things like $O(10)$ or $SU(5)$ but continuing the pattern from real to complex, the next obvious thing would be quaternion matrices. A group like $U(4,H)$ where $H$ is the quaternions. This is another name for $Sp(4)$ (according to Wikipedia!).
A group like $U(4,H)$ I alwa... | The structure of standard model $SU(3)\times SU(2)\times U(1)$ is chiral which basically tells you the necessity of chiral fermions. If left-handed fermions transform under a representation $R$ of the symmetry group then due to charge-conjugation relating left-handed and right-handed fermions as $$\psi_{Right}=C(\bar{\... | Well the answer of your question is not so trivial, I guess. Here is my try. I want to give a glimpse why a symplectic group is not a good choice for model building from a phenomenological point of view.
Now look at the symplectic group closely.
<ul>
<li>$Sp(1)$ is isomorphic to $SU(2)$ </li>
<li>$Sp(4)$ is isomorph... | https://physics.stackexchange.com |
10,672 | [
"https://mathoverflow.net/questions/10672",
"https://mathoverflow.net",
"https://mathoverflow.net/users/492/"
] | Suppose we have a space M with a real-valued, differentiable function F on M. Under what conditions on F will the Euler characteristic of M be expressed as a (signed) sum of Euler characteristics of components of the critical set for F? Can we relax the Morse-Bott requirement? What if the critical set isn't smooth... c... | You could have a smooth function $f : \Bbb R \to \Bbb R$ whose critical point set is a Cantor set (minima) and the centres of the complementary intervals (local maxima) -- let $f$ be some suitable smoothing of the distance function from the Cantor set (or you could use the smooth Urysohn lemma to construct the function... | (1) look up "Stratified Morse Theory" by Goresky-MacPherson; they show that in the restricted case of a stratified space (e.g., algebraic variety), there is a well-defined Morse-Euler formula for functions that are more general than Bott-Morse.
(2) if you fix an o-minimal structure (see "Tame Topology and O-Minimal St... | https://mathoverflow.net |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.