qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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239,889 | [
"https://stats.stackexchange.com/questions/239889",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/134530/"
] | I have 10 values that come from an exponential distribution. And I'm trying to draw the likelihood function by fixing these values and changing the unknown alpha.
I calculated the function and did a rescale of the function so that it would integrate to 1.
But the result is a really flat function with only one peak. A... | The likelihood is
$$
f(y_1,\ldots,y_n;\lambda) = \prod_{i=1}^n f(y_i;\lambda) = \lambda^n \exp\left[-\lambda \sum_i y_i\right].
$$
The log-likelihood is
$$
l = n\log\lambda - \lambda \sum_i y_i.
$$
The maximum likelihood estimate is $\hat{\lambda} = 1/\bar{Y} = 3.634619e-05$, so you might want to plot the functions ... | [Much too long for comments and this contains at least a partial answer...]
<ol>
<li>There's no reason to scale a likelihood to integrate to 1. It's not a density.</li>
<li>Rather that require people to understand your code to figure out what you're trying to achieve, <em>first</em> explain what you're trying to imple... | https://stats.stackexchange.com |
89,785 | [
"https://math.stackexchange.com/questions/89785",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/287/"
] | Okay so I am studying for my PDE course and I am convering Fourier transforms. In fact I am using fourier transforms to find a solution to the heat equation on an infinite length rod.
After going through the derivation of the fourier transform and applying it to the heat equation we get the following solution:
$$u(x... | As $t \to 0$ the kernel $K(x,t)$ tends to the Dirac delta function $\delta(x)$ (which is not actually a function, but a so-called <em>distribution</em>, or <em>generalized function</em>).
You can recognize this at least informally because the area under $K(x,t)$ stays constant, equal to $1$, but as $t \to 0$ it becomes... | Heat equation describes the dispersion of heat by inspecting the way how the temperature evolves in time.
By either physical intuition or mathematical analysis on the behavior of the heat equation, we find that law of superposition holds. Then, as we think of point mass or point charge in physics, we can think of some... | https://math.stackexchange.com |
67,729 | [
"https://softwareengineering.stackexchange.com/questions/67729",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19216/"
] | I am a Biology student, who has changed my career to IT and have been working in the software field for the past 4 fours under the <strong>QA (auditing processes for ISO9001 purposes)</strong>. Now I'm a Software QA Execute and have decided to increase my knowledge on QA. What are the next steps I can look for?
Are t... | If you are auditing, you need to get ahold of your country's equivalent of the US GAAP (Generally Accepted Accounting Priniciples) and learn it in depth. Even if you are not auditing financial systems, some concepts such as internal controls are most helpful in auditing systems as I find that developers are unaware of ... | Do you like breaking things? QA is all about breaking stuff, then telling the guys who can fix it how. Don't know if a certification exists for this, but if you constantly void warranties that is a good start.
| https://softwareengineering.stackexchange.com |
65,434 | [
"https://dba.stackexchange.com/questions/65434",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/38247/"
] | I have these three tables, <code>user</code>, <code>categories</code> and <code>files</code>
In <code>users</code>, table I have a column <code>user_id</code>
<img src="https://i.stack.imgur.com/QCq0m.jpg" alt="enter image description here">
And I have this query that shows all Categories.
<pre><code>SELECT `catego... | So it was actually my application that was escaping characters. The old version of the program ran with postgres 8.0, which would expect escaped characters, but postgres 9.3 is fine with unescaped characters.
I changed my app so it would no longer escape characters, removed any reference to the standard_conforming_st... | <blockquote>
I am updating a program at work that communicates with a postgreSQL 9.3 database. I need to turn off an option in the postgresql.conf file called standard_conforming_strings, so that I can store backslashes properly in the database.
</blockquote>
These two things are completely unrelated. You may want t... | https://dba.stackexchange.com |
3,386,478 | [
"https://math.stackexchange.com/questions/3386478",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/504183/"
] | In each cell of a 20 x 20 table an integer is written , such that for every 7 rows and 7 columns that we consider the sum of these 49 cells (the cells where the rows and columns intersect) is an even number. Prove that all the numbers in the table are even.
| HINT to an alternate solution, partly inspired by @JaapScherphuis and partly inpsired by linear algebra (modulo <span class="math-container">$2$</span>, i.e. in <span class="math-container">$\mathbb{F}_2$</span>).
Let <span class="math-container">$A$</span> denote the original <span class="math-container">$20\times 20... | Here is one way to do it.
First prove that the sum of any 4 cells in a rectangle (the intersection of two rows and two column) is even. This is done by carefully selecting various sets of 7 rows by 7 columns, and subtracting them from each other.
Next you have to see that you are free to rearrange the rows or rearran... | https://math.stackexchange.com |
536,298 | [
"https://math.stackexchange.com/questions/536298",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/35540/"
] | <em>You are exploring a hidden cave when suddenly, your flashlight goes out. Luckily, you have a 10-inch wax candle with you... Whew! You light the candle, but you must get out of the cave quickly, because every two minutes, one inch of the wax candle melts. Also, once the height of the candle reaches 2 inches or less,... | Go through the word problem carefully, noting each piece of (possibly-) relevant information at a time. Then try to build up a function/equation/whatever you need from the information.
For example, in this problem you might make the following quick observations:
- The candle is $10$ inches tall.
- The length of the ... | The algebraic representation of <em>what</em> function? There's your starting point.
What are the quantities involved?
<ul>
<li>The amount of time in minutes since you lit the candle: call that $t$.</li>
<li>The height of the candle in inches: call the <em>h</em>.</li>
</ul>
Now, you need to figure out what $t$ will... | https://math.stackexchange.com |
518,252 | [
"https://math.stackexchange.com/questions/518252",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/65271/"
] | I need some critique and suggestions on how to go over this question:
Prove that $x_n$ converges, and find $\lim_{n\rightarrow \infty} x_n$:
$x_1 > 0 $, $x_{n+1} = \frac{1}{2}(x_n + \frac{5}{x_n}) \ \forall n \geq 1 $.
Here's how I solved it:
Let $x_1 =1 \Rightarrow x_2 = 3 \Rightarrow x_3 = \frac{28}{12} <... | You have the right idea. You have a recursive formula and to show it has a limit, first show it is bounded--this can be done by induction, then show it is monotone, and then yes it correct to assert that $lim$ $a_{n+1}$ = $lim$ $a_n$.
| $$
x_{n+1} - \sqrt{5} = \frac{1}{2}\cdot\frac{(x_n-\sqrt{5})^2}{x_n}
$$
so if $x_0 \ge \sqrt{5} $ then with the equation above $x_n \ge \sqrt{5}$
then
$$
x_{n+1}-\sqrt{5} \le \frac{1}{2\cdot\sqrt{5}}(x_n-\sqrt{5})^2
$$
then
$$
x_{n}-\sqrt{5} \le \left(\frac{1}{2\cdot\sqrt{5}}\right)^{2^{n}-1} (x_0-\sqrt{5})^2
$$
th... | https://math.stackexchange.com |
2,277 | [
"https://dsp.stackexchange.com/questions/2277",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/1035/"
] | I'm trying to decipher what exactly this statement means. So if I have a signal which has no pure sinusoidal components, does that mean I can't decompose my signal completely into sine-waves which may be amplitude/phase/period shifted? And so I would conclude that there is also like a saw-tooth component or a square-... | It contains no spikes in its frequency spectrum. (What is the Fourier transform of a sinusoid?)
| As Emre said, what they probably mean that there are no <em>individual</em> (as in, stand alone), sinusoidal components. (Spikes in the spectrum), in the example they are using. (Perhaps it is a sum of many sinusouds).
I think you would be hard pressed to come across a signal that is not composed of complex exponentia... | https://dsp.stackexchange.com |
13,093 | [
"https://mechanics.stackexchange.com/questions/13093",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7016/"
] | I used to have both P1166 and P1167 error codes on my 2001 Honda Accord (F23A4 engine).
I fixed the P1166 by replacing the O2 sensor.
For about a day, everything looked wonderful (i.e. no <code>check engine</code> light on).
Then, (after a day), the dreaded <code>check engine</code> light turned on again.
I used my... | The Air/Fuel Ratio (A/F) sensor 1 is installed in the exhaust system and detects oxygen content in the exhaust gas. The A/F sensor transmits output voltage to the Engine Control Module (ECM). <em>A heater for the sensor element is embedded in the A/F sensor (sensor 1). If the A/F sensor (sensor 1) voltage is low, the a... | P1166 indicates a blown or malfunctioning heater core fuse. I know that O2 sensors have resistive elements inside that are activated when the engine is cold. O2 sensors operate more efficiently when they are hot. The heater element is on until the engine is at normal operating temp then it switched off.
P1167 is the ... | https://mechanics.stackexchange.com |
126,374 | [
"https://physics.stackexchange.com/questions/126374",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46211/"
] | In studying the aerodynamics of modern aircraft equipped with high-lift devices, I have discovered that quite a number of distinct trailing vortices are present in the immediate wake of an airplane in flight (e.g. off the outboard edge of the flap, the wingtip, etc). However, they always manage to roll-up into a solita... | Intuitive start of an answer:
If you have counter rotating vortices they have zero net angular momentum (to first order). If they merged they would have to have no motion -> where did the energy go. In between the two axes of rotation the fluid moves in the same direction and has no mechanism for dissipation.
By cont... | Because where they come close together the air in between circulates in such a way as to join them in a single path.
<img src="https://i.stack.imgur.com/dnRab.png" alt="enter image description here">
Floris is right, but maybe this picture helps.
| https://physics.stackexchange.com |
116,558 | [
"https://physics.stackexchange.com/questions/116558",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46233/"
] | Newton's third law is defined as $F_{12} = -F_{21}$
Is friction a product of this law? For example, if I take my hand and slide it across the floor in the $+x$ direction... My hand exerts a force $F_1$ on the floor. According to Newton's third law, the floor should exert a force of $F_2$ on my hand, and $F_2 = -F_1$... | No, it's not a <em>product</em> (i.e. a result) of Newton's third law. The third law only says that the force of friction the floor exerts on your hand is accompanied by a frictional force of equal magnitude exerted by your hand on the floor. It doesn't actually explain why either force of friction has to exist at all.... | NO FRICTION IS NOT THE REACTION FORCE
the frictional force provided by your hand on the table is accompanied by a frictional force exerted by the table on your hand. That is the reaction force here
| https://physics.stackexchange.com |
121,531 | [
"https://dba.stackexchange.com/questions/121531",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39098/"
] | I have the following graph:
<ul>
<li>B granted select on D and D granted select on E and E granted select on G.</li>
<li>B has grant select with grant option and has granted select D with grant option.</li>
<li>D has grant select with grant option and has granted select E with grant option.</li>
<li>E has grant select... | When you grant permissions to a user using the <code>WITH GRANT OPTION</code> clause, then subsequently revoke that permission, SQL Server will prevent the revoke unless you explicitly add the <code>CASCADE</code> option to the <code>REVOKE ...</code> statement.
This prevents a security risk whereby you grant <code>WIT... | It seems to be something to be corrected by Microsoft.
The only way I see is to drop the impacted users and recreate them with the needed permissions ...
@++ ;)
| https://dba.stackexchange.com |
88,591 | [
"https://physics.stackexchange.com/questions/88591",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/34304/"
] | We know that a point on the rim of a rolling body traces out a cycloid during one turn. Why is the length of the cycloid a constant = 8r. Shouldn't length of cycloid depend on speed of rolling body. For example, a faster body should trace out a cycloid which has a longer length than a slower body. What is the flaw in m... | If the ladder is slipping on the floor as well as the wall, then the point of rotation is where the two normal forces intersect. This comes from the fact that reaction forces must pass through the instant center of motion, or they would do work.
In the diagram below forces are red and velocities blue. If the ladder ro... | The ladder falls because it experiences unequal moments from the normal reactions at both its ends. That is to say that the surface pushes on the ladder from the bottom as well as the side. In the absence of tangential contact forces such as friction, the ladder rotates and falls.
To solve a problem with such a situat... | https://physics.stackexchange.com |
3,614,873 | [
"https://math.stackexchange.com/questions/3614873",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | If I have <span class="math-container">$A \iff B,$</span> does that means <span class="math-container">$A$</span> is sufficient for <span class="math-container">$B$</span> to occurs and <span class="math-container">$B$</span> is necessary for <span class="math-container">$A$</span> to occurs?
I am confused about the d... | <span class="math-container">$A$</span> is a <strong>sufficient</strong> condition for <span class="math-container">$B$</span> is symbolised as <span class="math-container">$$A \to B$$</span>
<span class="math-container">$A$</span> is a <strong>necessary</strong> condition for <span class="math-container">$B$</span> i... | If <span class="math-container">$A \implies B$</span> then <span class="math-container">$B$</span> is necessarily true when <span class="math-container">$A$</span> is true. As well, <span class="math-container">$A$</span> is a sufficient condition for <span class="math-container">$B$</span> to be true.
If <span class=... | https://math.stackexchange.com |
394,673 | [
"https://math.stackexchange.com/questions/394673",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/20801/"
] | This is a question from an old Oxford undergrad paper on calculations in $\mathbb{Z} [\sqrt{10}]$. We equip this ring with the Eucliden function $d(a+b\sqrt{10})=|a^2-10b^2|$. I want to prove the following results:
<ol>
<li>If $d(x)=1$, then $\frac{1}{x} \in \mathbb{Z} [\sqrt{10}]$</li>
<li>Any non-zero element of $\m... | It seems to me that (1) and (3) are dealt with adequately in the comments (but I would be happy to incorporate that here if you need). For (2), the key point is that the ring is Noetherian, which is effectively a consequence of the Hilbert basis theorem, implying that a polynomial ring $\mathbb{Z}[x]$ is Noetherian, an... | The set Z[10] makes use of <em>half-primes</em>, which must occur in even numbers. This is pretty normal for many of these sorts of systems. These half-primes live in some other part that have this same ratio, ie $a\sqrt{5}+b\sqrt{2}$. In some systems, like z[3], there are even uits in there, eg $(\sqrt{6}+\sqrt{2})... | https://math.stackexchange.com |
24,382 | [
"https://quantumcomputing.stackexchange.com/questions/24382",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/19636/"
] | A density matrix <span class="math-container">$ρ$</span> is called extreme if the only way to write <span class="math-container">$ρ$</span> as <span class="math-container">$ρ = p σ + (1 − p) τ$</span> ,
with <span class="math-container">$σ ∈ S_d$</span>, <span class="math-container">$τ ∈ S_d$</span>, and <span class="m... | Here's a sketch which you can fill in the details of.
The spectral theorem says that for any density matrix <span class="math-container">$\rho$</span> there exists an orthonormal basis <span class="math-container">$\{|v_i\rangle\}_i$</span> and <span class="math-container">$\lambda_i \geq 0$</span> with <span class="ma... | Another easy method for me. If <span class="math-container">$\rho=|\psi\rangle\langle\psi|$</span>, then we have
<span class="math-container">$$
Tr\left( \rho ^2 \right) =1=Tr\left( \left( p\sigma +\left( 1-p \right) \tau \right) ^2 \right)
\\
=Tr\left( p^2\sigma ^2+\left( 1-p \right) ^2\tau ^2+p\left( 1-p \right) \le... | https://quantumcomputing.stackexchange.com |
392,881 | [
"https://mathoverflow.net/questions/392881",
"https://mathoverflow.net",
"https://mathoverflow.net/users/174195/"
] | Find a pair of functions <span class="math-container">$f,g:\mathbb{R}\to\mathbb{R}$</span> such that:
<ul>
<li><span class="math-container">$f$</span> is smooth and compactly supported (say, on <span class="math-container">$[0,1]$</span> but this isn't crucial),</li>
<li><span class="math-container">$g(x)>0$</span> ... | With your hypotheses above, <span class="math-container">$\widehat{g}:\mathbb{R}\to\mathbb{R}$</span> is a uniformly continuous function such that <span class="math-container">$\displaystyle \lim_{|\gamma|\to\infty} \widehat{g}(\gamma) = 0$</span>, and <span class="math-container">$$\widehat{f}(z) := \int f(t)e^{-2\pi ... | This is not possible, even if we only assume <span class="math-container">$f \in C_c(\mathbb{R})$</span> and <span class="math-container">$g \in L^1(\mathbb{R})$</span>.
Of course it is equivalent to ask for <span class="math-container">$\hat{f} \hat{g} \equiv 0$</span>. By the Riemann-Lebesgue lemma (or just dominate... | https://mathoverflow.net |
23,565 | [
"https://quantumcomputing.stackexchange.com/questions/23565",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/18259/"
] | I have a quantum circuit with <span class="math-container">$N$</span> qubits represented by the unitary <span class="math-container">$U$</span>. The initial state is <span class="math-container">$| 00...0\rangle$</span> and <span class="math-container">$\psi=U|00...0\rangle$</span>.
Given <span class="math-container">$... | Not in general, no.
Consider the state
<span class="math-container">$$
|\psi\rangle=\frac{1}{\sqrt{2}}\left(|0x\rangle+|1\bar x\rangle\right)|+\rangle
$$</span>
for <span class="math-container">$x\in\{0,1\}$</span>. We have <span class="math-container">$\langle Z_i\rangle=0$</span>, and <span class="math-container">$\l... | 2 assumptions for my answer (because I did not really understood your setup):
<ul>
<li>Let's assume a pure state like |0010110> (not superposition)</li>
<li>Assume you are doing the same experiment again and again (because in each time you collapse and project your state)</li>
</ul>
The N Zs operator is actually cou... | https://quantumcomputing.stackexchange.com |
2,284,027 | [
"https://math.stackexchange.com/questions/2284027",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/389937/"
] | How can the following differential equation be solved?
$\frac{d^2 r}{d \theta^2} + 4r = 5\sin(3\theta)$ for $\frac{\pi}{5} \le \theta \le \frac{3 \pi}{5}$ that satisfies $\frac{d r}{d \theta} = - 2$ when $\theta = \frac{\pi}{2}, r=1$.
| Your solution is fine. An alternative solution is to prove that the eigenvalues of $A$ are non-negative. In fact if $\lambda$ is an eigenvalue of $A$ and $X$ is an eigenvector associated then
$$X^TAX=\lambda X^TX\ge0\implies \lambda\ge0$$
hence $$\det(A+I)=\chi_A(-1)\ne0$$
because $-1$ isn't an eigenvalue of $A$. Henc... | Yet another way:
<strong>Lemma:</strong> Let $\lambda$ be any eigenvalue of the matrix $A$, with eigenvector $v$:
$Av = \lambda v; \tag{1}$
then for any scalar $\mu$, $\lambda + \mu$ is an eigenvalue of $A + \mu I$, also with eigenvector $v$:
$(A + \mu I)v = (\lambda + \mu)v. \tag{2}$
<strong>Proof of Lemma:</str... | https://math.stackexchange.com |
84,152 | [
"https://datascience.stackexchange.com/questions/84152",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/104860/"
] | I'm concerned that I'm attempting the impossible with my neural network. This is the scenario:
I have a 2D square world. In it, I create five circles of random size and position. I then classify one of them as the correct answer, based on the following rules:
<ul>
<li>If <em>any</em> circle's radius is > THRESHOLD, ... | Yes, they absolutely can 'learn' conditional rules.
It turns out I had a bug in an activation function, and I (eventually) got this network to learn this problem. It learned it incredibly well, and very quickly. Amazing things, these NNs :) Big thanks to those that answered and commented!
| Centering the data on zero and scaling to variance of one helps with a lot of classification problems but in this case it would remove information that's needed to solve your problem as I understand it.
Another possible problem is the loss function, which you don't mention at all in your question. I would suggest somet... | https://datascience.stackexchange.com |
62,434 | [
"https://stats.stackexchange.com/questions/62434",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/21599/"
] | I heard that "for ungrouped binary data, the deviance cannot be approximated by
a <span class="math-container">$\chi^2$</span>-distribution." Is it true? Why?
| The context for this question is that, it is a remark comes after one says that "This ($\chi^2$) approximation is not good when some of $n_i$s are very small, or the fitted probabilities are near zero or unity."
The phrase "ungrouped binary data" suggests that data are listed by subject number and $m_i=1$ for each $i$... | Build a standard two way contingency table where the rows are the ungrouped observations and columns are success/failure. You can prove that the chi-squared statistic is exactly equal to your number of observations. The fact that the test statistic depends only on the volume of observations suggests that it is not usef... | https://stats.stackexchange.com |
1,752 | [
"https://softwareengineering.stackexchange.com/questions/1752",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/389/"
] | In fact this question is about cautions to be taken to enhance quality user experience and reduce avoidable support calls.
| A lack of proper input validation is one of those things which tends to lead quite quickly to users doing "bad" things with your application, when it should really be handled by the programmer.
I've seen legacy apps where users have been trained to:
<ul>
<li>not enter apostrophes in names</li>
<li>not enter any symbo... | I once got a customer support call because my app just disappeared. Turned out they opened another app on top of it.
... I decided not to ensure that didn't happen again, since it was the users computer illiteracy that caused the problem, not the app. Anything I could have done to fix it would have lead to a poor us... | https://softwareengineering.stackexchange.com |
4,057 | [
"https://quantumcomputing.stackexchange.com/questions/4057",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/2391/"
] | As a part of a discussion with my 'classical' friend, he insisted that making a a state machine for calculating the outcome of quantum computer is possible; so, simply calculate the outcomes of (known) algorithms on supercomputers and store their results in a Look-up table. (Something like storing the truth table).<br>... | Suppose that you have a quantum algorithm with $2^{60}$ possible inputs. Suppose also that it would take 1 nanosecond to run this on a supercomputer (which is unrealistically optimistic!). The total time required to run through all possible inputs would be 36.5 years.
Clearly it would be much better to just run the in... | For a specific quantum algorithm that uses 40 qubits, your friend makes a good point. One can just calculate the truth table (one might find this hard, but assume that one can) and use it as reference. Of course this starts to get ridiculous as you increase the number of qubits, not just because of the number of inputs... | https://quantumcomputing.stackexchange.com |
52,670 | [
"https://stats.stackexchange.com/questions/52670",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5795/"
] | I was reading the paper <em>``A significance test for the lasso''</em> by Lockhart, Tibshirani <em>et al</em> and was considering the issue of applying regularization in the applied sciences (for example, behavioral sciences).
When do statisticians consider it acceptable to apply regularization methods like LASSO to s... | If you do any significance testing (and remove insignificant parameters from your final model), you are biasing your nonzero parameters away from zero. In fact this problem affects model selection of various kinds.
One way to avoid this bias away from zero is to regularize by shrinkage.
There are still other reason... | Regularization is just another way of estimating parameters. In ordinary least squares, we get our parameter vector via <span class="math-container">$\hat\beta_{ols}=(X^TX)^{-1}X^Ty$</span>. In ridge regression, we modify the estimate.
<span class="math-container">$$
\hat\beta_{ridge}=(X^TX+\lambda I)^{-1}X^Ty
$$</span... | https://stats.stackexchange.com |
3,802,301 | [
"https://math.stackexchange.com/questions/3802301",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/800089/"
] | <h1>How to solve <span class="math-container">$x_1+\cdots+x_p=30, \text{where }x_i+x_{i+1}=1, i \in \{1,2,...,p-1\}$</span>?</h1>
<h2>ps.</h2>
Obviously we can get a special solution when <span class="math-container">$p=60, x_1=x_2=\cdots=x_{p-1}=0.5$</span>. What I am confused about is how to find general solution in ... | We claim that given <span class="math-container">$x_1 = k$</span>, we can find the values of all <span class="math-container">$x_i, i\in[p]$</span>. In particular, <span class="math-container">$x_i = \begin{cases}
k & x \text{ is odd} \\
1-k & x \text{ is even}
\end{cases}$</span>
We will show t... | Hint: Let's solve for everything given <span class="math-container">$x_1$</span>. We have
<span class="math-container">$$x_1+x_2=1\implies x_2=1-x_1$$</span>
<span class="math-container">$$x_2+x_3=1\implies x_3=1-x_2=1-(1-x_1)=x_1,$$</span>
et cetera. Can you find a general way to express <span class="math-container">$... | https://math.stackexchange.com |
74,053 | [
"https://electronics.stackexchange.com/questions/74053",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20314/"
] | I have unfinished schematic with PCB. When I add net in schematic, the route is not visible in PCB and I cannot connect pins. Why? I am adding two screenshots for better understanding of problem, first screenshot is a schematic and a second one is pcb of same schematic!
<img src="https://i.stack.imgur.com/o7aJ8.png" ... | Are you sure the schematic and board are in sync? Are you adding a net between pins on the schematic?
Beyond that, it is difficult to come up with a meaningful answer with such little information.
<h2>Added:</h2>
You now say you are not adding a net between pins on the schematic, and no, I really can't see much of ... | I have reconnected ZCEN signal from IC to connector and now the problem has been solved! ZCEN signal from IC is now connected to connector in PCB!
| https://electronics.stackexchange.com |
90,306 | [
"https://chemistry.stackexchange.com/questions/90306",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/57475/"
] | According to me, ammonia should be the stronger base for two reasons:
<ol>
<li>$\ce{-C_6H_5}$ group shows $-I$ effect, due to which electron density on $\ce{N}$ atom of benzylamine decreases</li>
<li>steric hindrance in benzylamine is more than that in ammonia</li>
</ol>
But their $\mathrm{pK_b}$ values are: benzylam... | Everything you said is correct, except that it is more relevant to consider the inductive effect of methyl on nitrogen: electron density is donated to nitrogen.
The inductive effect of phenyl is on the methyl, decreasing its ability to donate electron density to nitrogen, but apparently not completely.
I suppose tha... | Benzylamine is <span class="math-container">$\ce{C6H5CH2NH2}.$</span> Therefore, <span class="math-container">$\ce{NH2}$</span> group is bonded to <span class="math-container">$\ce{C6H5-CH2}$</span> unit which has greater +<em>I</em> effect. Therefore, it increases electron density on <span class="math-container">$\ce{... | https://chemistry.stackexchange.com |
530,902 | [
"https://physics.stackexchange.com/questions/530902",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/254032/"
] | <blockquote>
"One second is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the cesium 133 atom."
</blockquote>
Can we alternatively define it as, <strong>Frequency of Cs-133 atom?</strong>
| There's no such thing as "frequency of Cs-133 atom" to be defined. Atoms don't have any natural freqencies. But the light produced when atoms change their state does.
You can define the frequency of the light produced by the transition between two energy levels of Cs-133 to be 9,192,631,770 Hz, and that will lead to ... | This is <strong>already</strong> a definition based on cesium atom radiation frequency. By definition frequency is number of events per second. Cs-133 atom makes 9,192,631,770 radiation cycles per second, so it has <span class="math-container">$9\,192\,631\,770\,\textrm{Hz}$</span> radiation frequency. Or if we want to... | https://physics.stackexchange.com |
61,535 | [
"https://physics.stackexchange.com/questions/61535",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10971/"
] | I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part and a radial part. When dealing with the angular part of $\psi$, the book claims that the angular part "must" be an eige... | It has to do with the Laplacian $(\nabla^2)$.
When trying a separable solution
$$\psi(r,\theta,\phi) = R(r)\Theta(\theta)\Phi(\phi)$$
You will get two ODE's, a radial and an angular equation. They must be equal to separation constants. Turns out the angular part is the $L^2$ operator. You can rewrite
$$H \psi = E \p... | The operator $L^2$ is a symmetry of the Hamiltonian, which means that $[H,L^2] = 0$. This means that we can find simultaneous eigenfunctions to $H$ and $L^2$ since $HL^2 | \psi \rangle = L^2 H | \psi \rangle = \ell (\ell + 1) E | \psi \rangle$. The operator $L^2$ does not depend on the radial coordinate, thus the angul... | https://physics.stackexchange.com |
129,010 | [
"https://security.stackexchange.com/questions/129010",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/25333/"
] | I'm a little bit rusty with MITM attack and its preventions.
Where is the right network position where to install arpwatch? If you place it in the router you can only prevent host2gateway mitm. To prevent intra-netwrok MITM (host to host connection), you should place an instance of arpwatch on each node.
Am I right?... | The purpose of a TPM module is to ensure that there is absolutely no way to obtain the keys stored on it. Whether or not it actually fulfills that purpose is a topic for another question. For now let's assume that it works as designed. That means when the TPM module is destroyed, so is the key, and so is any hope to de... | If the TPM 'breaks' or becomes otherwise inaccessible, all cryptography dependent on keys stored by the TPM also breaks. This is the most concise and inclusive way I could think to put it.
I say 'cryptography' because the TPM does more than just encryption. Encryption is just one use of cryptography, as are signatures... | https://security.stackexchange.com |
141,252 | [
"https://cs.stackexchange.com/questions/141252",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/1342/"
] | Consider a multiset of <span class="math-container">$n$</span> integers, where each integer is between <span class="math-container">$1$</span> and <span class="math-container">$3 M$</span>. The sum of all integers is <span class="math-container">$3 S$</span>. There are three bins. The capacity of each bin is <span clas... | Yes, there is a polynomial time solution. It is not very pretty, so simplifications or alternative approaches are welcome.
TL;DR: the exact weights are rarely important, so we can round them up to a multiple of <span class="math-container">$K := \lceil \frac{3M}{n^3} \rceil$</span> or something similar (there are only ... | Tricky. You’d sort the items in descending order and put them into the bins. If all items are in the bins, there is a gap of <span class="math-container">$3 M$</span>. You can show easily that any item of size <span class="math-container">$x \leq 1.5 M$</span> will fit. In general, if the gap is <span class="math-conta... | https://cs.stackexchange.com |
306,565 | [
"https://softwareengineering.stackexchange.com/questions/306565",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54644/"
] | I've just refactored some code that managed a global state cache of values that didn't have locking to use double check locking. Other than moving the initialisation to a single source (the cache was being set in a controller method), the main reason was to make sure only one thread was performing the initialisation at... | If the web request is <em>only</em> required to initialize the cache, then you're correct. Throw a lock around the whole thing. Why bother making N requests when you're going to ignore all but the first one that returns?
If the request is required regardless of the cache, then your colleague is correct. Allow all N re... | If you want to do lazy initialization, you should consider using <code>Lazy<T></code>. Don't reinvent this wheel.
If you would prefer to do eager initialization, you should consider using <code>Task<T></code>.
| https://softwareengineering.stackexchange.com |
254,532 | [
"https://dba.stackexchange.com/questions/254532",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/77963/"
] | <ul>
<li>I want to store only 3 states in a column (if it was 2, I would use a boolean)</li>
<li>I considered using an ENUM('up', 'down', 'none') but it seems ENUMs take some significant space</li>
<li>Is there a better way to store only -1 0 and 1 in a PostgresQL column?</li>
</ul>
| If you want to save space, you can use the <code>"char"</code> data type. It stores a single byte.
you can cast <code>integer</code> or <code>text</code> to <code>"char"</code>:
<pre><code>SELECT 'u'::"char", 'd'::"char", 'n'::"char";
char | char | char
------+------... | A bit of a hack, but is you make the column nullable you can still use a bool, with a null value as the third value.
Boolean still uses 1 byte in Postgres, though.
| https://dba.stackexchange.com |
229,387 | [
"https://dba.stackexchange.com/questions/229387",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/13283/"
] | To be very flexible and move database to different servers more easily, we came up with the idea of using an alias per database. So by simply changing a DNS entry, we can route all queries to a different database server without changing the connection string or re-deployment of the respective client application.
To cl... | One minor drawback would be that you would need to add a Subject Alternative Name (SAN) to the certificate that is bound to SQL Server if you are using encrypted connections. This could be a significant pain if you have a "shared" server that hosts a number of smaller applications and you want to set up an alias for e... | Be aware that when you use DNS CNAME with a SQL database you need to be aware of the TTL setting.
This setting tells a system how long the DNS entry should be cached for before a trip back to the DNS server is required.
You will probably need to adjust the TTL in advance so that when you do make the switch, you don't h... | https://dba.stackexchange.com |
32,119 | [
"https://astronomy.stackexchange.com/questions/32119",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/28254/"
] | I know that you can calculate the distance to another star for example, by using the phenomenon redshift to determine how much it has redshifted because of the expansion of the universe. But how do you know what the original frequency/wavelength of the light was? (And if all of my above statements are wrong, how do you... | Red shift is used for measuring the distance to very distant stars (galaxies mostly, in fact). The secret is to use spectral lines. Specific elements when very hot emit light at very specific colours and you can spot the pattern of those colours when the whole pattern has been shifted towards the red and see how far it... | There are various ways of measuring distances in the universe which depend on the range in which we are measuring.
<ol>
<li>Parallax method: Up to 100 - 1000 ly</li>
<li>Exploiting period luminosity relation of Cephied variables: Up to 3 - 10 Mpc</li>
<li>Tully Fisher relationship: Intergalactic distances</li>
<li>Hub... | https://astronomy.stackexchange.com |
101,092 | [
"https://softwareengineering.stackexchange.com/questions/101092",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12349/"
] | I suppose this question is going to be immediately flagged as subjective, but which do you think is better:
<pre><code>double volume(double pressure, double n_moles, double temperature) {
return n_moles * BOLTZMANN_CONSTANT * temperature / pressure;
}
</code></pre>
or
<pre><code>double volume(double P, double n, d... | Depends on who is reading it. If you can guarantee that for all eternity, the next programmer who reads your code is also familiar with thermodynamics, then yes, go for the truncated version.
My personal style is to use such variables (whose abbreviations are commonly known in the field), but include their description... | I prefer this:
<pre><code>/* This function calculates volume using the following formula:
*
* n * R * T
* v = ---------
* P
*/
double volume(double pressure, double n_moles, double temperature) {
return n_moles * BOLTZMANN_CONSTANT * temperature / pressure;
}
</code></pre>
In other words, explain... | https://softwareengineering.stackexchange.com |
636,637 | [
"https://electronics.stackexchange.com/questions/636637",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/315327/"
] | I am looking for ideas on how to detect the bus position of a module (PCB card) when they stack up.
I am designing a PCB module that is going to be controlled and connected to a carrier board. This PCB module can be stacked up, from 1 to 16 (imagine like a building where the base is the carrier board, and each floor is... | <strong>Shift Register</strong>
Consider using any kind of shift register.
There are loads of ways to achieve this. One would be with SPI hardware, where there's a clock and the devices are daisy-chained
<pre><code> +---------+ +---------+ +---------+
CPU -> |MOSI MISO|---|MOSI MISO|---|MOSI MISO| --->... | Will each unit be intelligent enough to this? It has a bucket-brigade bus wire, so each unit inputs on a pin a data signal then outputs that to the next floor if appropriate.
If an IDENT message calling out a particular module is sent, e.g. IDENT Bluetooth, then each module seeing that message waits 5 milliseconds bef... | https://electronics.stackexchange.com |
225,902 | [
"https://softwareengineering.stackexchange.com/questions/225902",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/82558/"
] | I am starting my first project in OpenGL/GLSL and I was wondering, how do you work with code of shaders?
Because it needs to be const char and syntax higlighting shows everything in the same color (as string) and so its difficult to navigate in code.
<pre><code>const char *shader = ..."void main()\n"...;
</code></p... | One thing you can do to make including shader code in C(++) source files more convenient is defining a macro like this:
<pre><code>#define GLSL(x) "#version #150\n" #x
</code></pre>
Example:
<pre><code>const char* shader = GLSL(
out vec4 outColor;
void main() {
outColor = vec4(1.0, 0.0, 0.0, 1.0);
... | some use separate files and include them as resources, some use macros, some use external files and read them in at runtime.
both of the external file options will allow syntax highlighting
and technically you don't need <code>const char*</code>, just a <code>char*</code> will do (it is implicitly convertible)
| https://softwareengineering.stackexchange.com |
185,591 | [
"https://mathoverflow.net/questions/185591",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40117/"
] | Let $b \in (0,1)$, $m\in \mathbb{N}$ and $a>0$. I want to bound
$$\sum_{k=m+1}^\infty b^{k^a} \leq c \; b^{m^a}, $$
where $c>0$ is independent from $m$.
Is there a simple way of proving this inequality with $c$ not beeing too large?
Edit: $c$ can only be independent from $m$ if $a>1$. Otherwise it has to gro... | For $a\ge 1$, the quantity $(m+k+1)^a-m^a$ is increasing w.r.to $m\ge0$ (because $x\mapsto x^a$ is convex). So for $0<b<1$, the term $b^{(m+k+1)^a-m^a} $ is decreasing w.r.to $m\ge0$, and so is $\sum_{k\ge0}b^{(m+k+1)^a-m^a}=b^{-m^a} \sum_{k> m}b^{k^a}$. That is, we have
the required bound with $$c=c(b):= ... | The sum converges for positive $a$ by the integral test, and since the summand is decreasing, the sum is closely approximated by the integral. The integral can be evaluated easily. Since I am lazy, I used Mathematica:
<pre><code>Assuming[0 < b < 1 && a > 0 && y > 0, Integrate[b^(x^a), {x, y... | https://mathoverflow.net |
1,658 | [
"https://cstheory.stackexchange.com/questions/1658",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/1491/"
] | Assume that you are given a set of n points in the plane and you want to check whether they form a convex n polygon, i.e., if they all lie on the convex hull. I was wondering if anyone knows how to do this in o(nlogn) time, i.e., without computing the CH.
| Thats seems unlikely, at least in the comparison/algebraic tree models. Definition first:
A point set $P$ is in convex position if no point of $P$ can be written as a convex combination of the remaining points of $P$.
Now, deciding if a set of $n$ numbers are all distinct takes $\Omega(n \log n)$ time (this is known ... | If you assume all the points are in the convex hull and you can find a point that is inside the convex hull, then you can find the order of the points in $O(n log n)$ time by taking the angle from the interior point to every point in your set and sorting this.
Once you know the order of the points, the angle from each... | https://cstheory.stackexchange.com |
189,214 | [
"https://dba.stackexchange.com/questions/189214",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/137222/"
] | I'm trying to build a database to manage my school marks. Here in Germany we have different "categories". For example we have one category for all our written work and one for our tests. I want to have a defined number of "categories", each of them has its own list of marks. How do I have to design my database? I have ... | Thanks to those who contributed in the comments, I have reduced the query time from ~8000 ms to ~1650 ms by:
<ul>
<li>Adding an index on the timestamp column only (~2000 ms improvement).</li>
<li>Removing the extra timestamp-to-char-to-timestamp conversion (or adding <code>date_trunc('week', event_time)</code> to the ... | To solve a quick date between query issue. I converted dates to Unix time (UTC) (I only needed “second” accurancy but you could go finer if you need to)
Then create a method to convert your dates to a bigint/long (include your Timezone conversion here). Then run your query and just search between the 2 integers. May so... | https://dba.stackexchange.com |
55,062 | [
"https://quant.stackexchange.com/questions/55062",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/47467/"
] | I would like to compare two strategies through the alpha Carhart obtained. The idea is to find out which one is more profitable (or the least bad). For the first strategy, I obtained a significant negative alpha. For the second one, the alpha is positive but not significant.
I would like to be sure to interpret this co... | <h1>Setup</h1>
From your question, I assume you have two strategies <span class="math-container">$A$</span> and <span class="math-container">$B$</span> with excess returns <span class="math-container">$R_{A,t}, R_{B,t}$</span>. You model these excess returns using the Carhart 4-factor models (FF3 factors + the fourth m... | Sadly, your experiment doesn't prove what you want at all! ;-(
It simply says that <em>after adjusting for style biases</em>, one did better than the other. It's very possible that the other did better than the one, because it was more exposed to the winning styles and less exposed to the losing styles in the sample pe... | https://quant.stackexchange.com |
100,346 | [
"https://electronics.stackexchange.com/questions/100346",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7726/"
] | So I have a circular buffer on an embedded device that I need to persist throughout the code. Specifically, I need to have it be able to be used in the main and also in an interrupt handler (these are both in separate files). I know how to do this in assembly by manually loading registers but I'm having trouble cleanly... | PNP and NPN transistor are diametrically different: NPN transistor conducts current / switched on when saturated (specified current applied to its base) while PNP transistor inhibits current / switched off when <del>saturated</del> current applied to its base (cut-off condition).
The NPN transistors on your circuit di... | Even the NPN transistor is going to have problems driving a regular LED. The LM741 is capable of supplying up to about +8V from a +10V supply and this will create a voltage of about +7V on the anode of the LED. The cathode of the LED is connected to -10V and this will burn and fry a regular LED. You probably need a cur... | https://electronics.stackexchange.com |
39,750 | [
"https://quant.stackexchange.com/questions/39750",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/11723/"
] | Why does the Black Scholes Equation imply the returns are log-normally distributed??
How can we tell that the returns of the underlying asset wouldnt be normally distributed??
| The Black-Scholes-Merton (1973) model implies that <strong>the prices</strong> of the underlying asset at maturity $S_T$ are log-normally distributed $$ln(S_T)\sim N\big[ln(S_0)+(\mu-\frac{\sigma^2}{2})T,\;\sigma^2T\big]$$ so that the logarithmic returns to maturity $ln(\frac{S_T}{S_0})$ are normally distributed $$ln(\... | <ol>
<li>BS assumes prices NOT returns are log-normally distributed. Why making that assumption? 1.log-normal is not perfect but OK to fit potential prices distribution. 2.The nature of log-normal distribution will force the left tail to be above zero. 3. There are definitely distributions work better than log-normal i... | https://quant.stackexchange.com |
1,375,623 | [
"https://math.stackexchange.com/questions/1375623",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/257167/"
] | I was asked to calculate $$\lim_{x \to 0}x\cot x $$
I did it as following (using L'Hôpital's rule):
$$\lim_{x\to 0} x\cot x = \lim_{x\to 0} \frac{x \cos x}{\sin x} $$ We can now use L'Hospital's rule since the limit has indeterminate form $\frac{0}{0}$. Hence $$\begin{align}\lim_{x\to 0}\frac{(x \cos x)'}{(\sin x)'} ... | Welcome to MSE! As best as I can tell your reasoning is sound, although as other users pointed out you could have done this in a few less steps. Regardless, your work is clear and your answer is correct. On an aside I am happy to see that you formatted your question with $\LaTeX$. I added some additional formatting to ... | HINT: rewrite your term in the form
$$\frac{\cos(x)}{\frac{\sin(x)}{x}}$$
| https://math.stackexchange.com |
608,793 | [
"https://electronics.stackexchange.com/questions/608793",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/307534/"
] | Why does a space heater (electric fan heater for home use) have a fuse?
Isn't the house itself connected via a circuit breaker? Wouldn't that stop potential safety issues?
PS: First post on here :)
| The breaker is sized to prevent the house wire from catching fire or melting, but things connected to it don't necessarily draw the full current it can support. If these device fail short, they can get hot enough to produce enough heat to cause fires long before the breaker trips. The breaker might not even trip in som... | The breaker installed in the house protects the cable to the wall outlet. The maximum current of this breaker is selected depending on the length, the crossface and the ambient conditions of the cable. This breaker should act if there is a short circuit in the cable to the outlet or the outlet itself. It should also ac... | https://electronics.stackexchange.com |
191,124 | [
"https://stats.stackexchange.com/questions/191124",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/86275/"
] | One of the purposes of ridge regression is to curb the effects of outliers which may cause the regression coefficients to be so large and hence cause a highly biased model.
That's why the constraint $\Sigma\beta_j^2<s$ is imposed, forcing the coefficients to not exceed a certain value.
Here is my issue. An outlie... | Ridge regression is a modification of linear regression. Linear regression is the best linear unbiased estimator (BLUE). They key word is "unbiased." Linear regression should give the smallest mean square error (MSE) of any unbiased linear estimator. Ridge regression adds bias in exchange to reduce variance, thus creat... | The ridge estimator is very susceptible to outliers, much like the OLS estimator. The reason for that is that we still depend on the least squares minimization technique and this does not allow large residuals. Hence the regression line, plane or hyperplane <em>will be</em> drawn towards the outliers.
There has been c... | https://stats.stackexchange.com |
224,821 | [
"https://security.stackexchange.com/questions/224821",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/199846/"
] | I would like to protect my flash drives to being infected when I put it in another computers or devices. After some research, I found that I will not be able to reach this level of protection by using only software solutions (correct me if I'm wrong).
However, I don't have a flash drive with hardware protection and m... | You cannot protect the stick from being "infected", if by "infected" you mean that the other computer writes a malware file onto it - unless you have a USB stick with a hardware write protection.
What you want to protect is your own computer against <em>executing</em> that file from the USB stick and thus becoming inf... | <strong>Yes there is.</strong>
You want a forensic <strong>USB Write Blocker</strong>.
The write blocker plugs into the questionable computer and your USB plugs into the write blocker, allowing only reads from your thumb drive and blocking writes.
Write blockers start at around $150 and go up.
| https://security.stackexchange.com |
2,389,951 | [
"https://math.stackexchange.com/questions/2389951",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/368128/"
] | I suspect that $\mathbb{Q}[2^{1/3}]=\{x \in \mathbb{R}; ∃a,b \in \mathbb{Q}(x =a+b\cdot2^{1/3})\}$ is not a field. This is because $2^{1/3} \cdot 2^{1/3} = 2^{2/3}$ is not in $\mathbb{Q}[2^{1/3}]$. However, I am having difficulty proving the statement:
There does not exist $a,b \in \mathbb{Q}$ such that $a+b\cdot2^{1/... | If $x^2=a+b\,x,$ we have $x^3=a\,x+b\,x^2=a\,x+b\,(a+b\,x)=a\,b+(a+b^2)\,x$. If $x=2^{1/3},$ we'd have $2^{1/3}=\frac{2-a\,b}{a+b^2},$ a rational number. Let $n$ be the smallest positive integer so that both $n\,2^{1/3}$ and $n\,2^{2/3}$ are integers. Then, $m=n(2^{1/3}-1)=n\,2^{1/3}-n$ is an integer $<n$, and $m\,2... | Let $\zeta=\sqrt[3]2$, and assume $\zeta^2=a+b\zeta$ with $a,b\in\mathbb Q$.
Then
$$ 2 = \zeta(a+b\zeta) = a\zeta+b\zeta^2 = a\zeta+b(a+b\zeta) = (a+b^2)\zeta + ba $$
and because $1$ and $\zeta$ are linearly independent over $\mathbb Q$ we must have $a+b^2=0$ and $ab=2$.
But then $a=-b^2$ and $ab=-b^3$. But there is n... | https://math.stackexchange.com |
152,743 | [
"https://stats.stackexchange.com/questions/152743",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7579/"
] | I have a file with sales for one complete year. Multiple customers, month number and total sales (per customer):
<pre><code>Customer | Month | Sales
------------------------
A | 1 | 100
A | 2 | 120
A | 3 | 90
B | 1 | 50,000
B | 2 | 49,000
B | 3 | 51,50... | Yes. The simplest case is if that there is no dependence between your errors.
If your model is
$$y_t = \beta_0 + \beta_1 t + \left[ x_{t,1} \beta_2 + \cdots + x_{t,p}\beta_{p+1} \right]+ \epsilon_t$$
where $\epsilon_1, \ldots, \epsilon_T \overset{iid}{\sim} \text{Normal}(0, \sigma^2)$, $t$ is time, and the $xs$ are ... | Linear regression does not make any assumptions about evenly spaced observations, so you should be fine.
On the other hand you might consider weighting your samples, depending on what you are looking for.
| https://stats.stackexchange.com |
80,259 | [
"https://stats.stackexchange.com/questions/80259",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28380/"
] | Assume that I have a dataset that contains the dates that measurements were made on a group of people. Thus, unique people identifiers, measurement results, and dates of measurements are available. Now assume that I have a another version of the same dataset from a different source, and that there are differences betw... | If you have two datasets that are supposed to be the same data then testing for significance is silly - if there is the slightest possibility that the differences could be significant, then at least one of the data sets is junk, unless the data sets are so huge that even negligible differences are significant.
You hav... | You have the entirety of both datasets, so it would not make sense to do a statistical test. For example if you tried to test
Ho: the datasets are not different
Ha: the datasets are different
and you find even one difference between the datasets, they are different and Ho would be rejected with certainty (p-value =... | https://stats.stackexchange.com |
27,406 | [
"https://mathoverflow.net/questions/27406",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5292/"
] | Is there a notion of a dimension associated to free resolutions like projective and injective dimensions associated to projective and injective resolutions? My guess is that it coincides with projective dimension but couldn't find any reference talking about this. Any help or tips will be appreciated!
| I'm sort of stealing the idea from t3suji, but here goes:
If the module is projective, i.e. $PD = 0$, then $FD \leq 1$.
If the module is not projective, i.e. $PD > 0$, then $PD = FD$.
The first statement is t3suji's comment. The second statement follows by first observing that if $F$ is the free module on infinit... | It does not coincide with projective dimension because a projective module is not necessarily isomorphic to a free module (while a projective $P$ has a trivial projective resolution $0 \to P \to P \to 0$).
In fact, projective modules that admit a free resolution are precisely the ones that are stably free (i.e. become ... | https://mathoverflow.net |
127,046 | [
"https://cs.stackexchange.com/questions/127046",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/109635/"
] | Does an NDTM have the power to combine computational branches ie. can a result from branch A be used in the next step in the computation along branch B? Can branches use each others' results, diagrammatically 'merging'?
Example:
Branch i arrives at the number b after n steps, branch j arrives at the number c after 2n... | One view, explained by Tom here, is that nondeterministic branches work in parallel.
A more standard view, I think, is to view nondeterminism the way it is treated in physics, in logic, and in Dijkstra/Hoare style algorithm specification: at certain points, multiple continuations are possible, one of which will be tak... | No, that's not how non-determinism work.
You can think about non-determinism as parallel universes. All the branches runs concurrently, in a different plane, and to itself it seems like it's the only run in the world.
The language accepted by a non-deterministic turing machine is every word that there exists a univer... | https://cs.stackexchange.com |
22,192 | [
"https://dba.stackexchange.com/questions/22192",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10725/"
] | I need to do a <code>SELECT</code> query where I get the value of the field "money". The field doesn't actually exist in the database. I just need the query to return this field with a fixed value; in this case a value in USD.
How do I return a constant value in a <code>SELECT</code> statement?
| If the value is always going to be the same you can do something like this:
<pre><code>SELECT 'USD' AS `MONEY`, a.*
FROM INFORMATION_SCHEMA.SCHEMATA AS a
</code></pre>
Just replace a.* with the columns you want to return and INFORMATION_SCHEMA.SCHEMATA with the schema and table(s) you want to query.
I hope this i... | @fedejp you don't have to insert the 'AS'. You can simply write 'INFORMATION_SCHEMA.SCHEMATA a' because the 'AS' is understood.
And if there's only one table in the query (no joins) then you don't need to use an alias and none of the fields specified need 'a.' in front of the field name, as there's no confusion as to ... | https://dba.stackexchange.com |
173,598 | [
"https://security.stackexchange.com/questions/173598",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/110133/"
] | I'm doing an internship in a very little company and I need to configure the network. They have a Cisco router. I couldn't find the logs to login so I called their internet provider. Apparently they configured the Cisco router and doesn't allow customers to configure it. Only them can configure the router when asked.
... | Forwarding port 80 is no more insecure than any other port. In fact, port forwarding itself is not inherently insecure. The security concern is that it allows services that are normally protected behind some kind of firewall to be accessible publicly. If the exposed service has any vulnerabilities or misconfigurations,... | Port 80 is not more insecure by itself than any other port. Simply it is the common HTTP port so it has very high risks of being scanned, and applications behind it are expected to be web applications.
That is were security admins begin to see red flashing lights. It is possible to make secure web apps, but that is a ... | https://security.stackexchange.com |
194,275 | [
"https://softwareengineering.stackexchange.com/questions/194275",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/71589/"
] | When developing on a long-running branch (here defined as living longer than one release), what's the most accepted practice(s) to keeping the branch current with its origin while keeping the history relatively clean prior to merging back?
As an example, consider the origin branch (<code>m</code>) and a (topic) branch... | The best practice is to keep an accurate history and just do a straight merge. That way, if you introduce a bug at <code>C</code>, someone investigating it can say, "Oh, that makes sense because it was done before we put feature <code>F</code> into <code>origin</code>, but not merged until today." It also has the ben... | You have a couple of options depending on branch t.
If branch t is also a remote branch with multiple developers working on it. I think that best way is doing the merges that you are suggesting. Rebasing and doing a forced push seems like a risky way to do things. I try to avoid changing a pushed history.
If the b... | https://softwareengineering.stackexchange.com |
190,667 | [
"https://mathoverflow.net/questions/190667",
"https://mathoverflow.net",
"https://mathoverflow.net/users/53197/"
] | Let $f\colon X \rightarrow Y$ be a proper morphism with $Y$ Noetherian (and even affine, if you wish), and let $\mathscr{A} = \bigoplus_{n \ge 0} \mathscr{A}_n$ be a quasi-coherent graded $\mathscr{O}_X$-algebra of finite type. Is the quasi-coherent graded $\mathscr{O}_Y$-algebra $f_* \mathscr{A}$ of finite type?
A... | No, that is not true, and there are several similar (and standard) examples. For one, let $Y$ be $\text{Spec}(k)$, let $X$ be an elliptic curve over $k$ (there are many other varieties one could use), let $f$ be the unique $k$-morphism, let $\mathcal{L}$ be an invertible sheaf on $X$ that is algebraically equivalent t... | What you're overlooking for the motivating situation (which should have been mentioned in the question as posed so that readers would have more context) is the final part of EGA III$_1$ 3.3.1. (Note that $Y'$ and $g$ there play no role whatsoever, by the way.)
In the setup of that result, set $\mathscr{S}$ to be the s... | https://mathoverflow.net |
243,154 | [
"https://softwareengineering.stackexchange.com/questions/243154",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/134748/"
] | I've been trying to think of a way of declaring strongly typed typedefs, to catch a certain class of bugs in the compilation stage. It's often the case that I'll typedef an int into several types of ids, or a vector to position or velocity:
<pre><code>typedef int EntityID;
typedef int ModelID;
typedef Vector3 Position... | These are <em>phantom type parameters</em>, that is, parameters of a parameterised type that are used not for their representation, but to separate different “spaces” of types with the same representation.
And speaking of spaces, that’s a useful application of phantom types:
<pre><code>template<typename Space>
... | I had a similar case where I wanted to distinguish different meanings of some integer values, and forbid implicit conversions between them. I wrote a generic class like this:
<pre><code>template <typename T, typename Meaning>
struct Explicit
{
//! Default constructor does not initialize the value.
Explicit(... | https://softwareengineering.stackexchange.com |
51,014 | [
"https://cstheory.stackexchange.com/questions/51014",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/65626/"
] | For a non-empty <span class="math-container">$3-SAT$</span> with <span class="math-container">$n\geq3$</span> variables and <span class="math-container">$T\geq1$</span> non-identical non-degenerate clauses <span class="math-container">$C_i$</span>:
<span class="math-container">$$S=C_1 \wedge \ldots \wedge C_T$$</span>
... | 2-SAT is NL-complete so separating 2-SAT from Clique would separate NP from NL, also a major open problem.
| I think there is at least one model of computation where 2-SAT is easy and Clique is provably hard: resolution refutation complexity (i.e. how hard is to deduce contradiction from the initial clauses using resolution inference rule). If you think about decision problem instead of refutation, you may ask "how hard ... | https://cstheory.stackexchange.com |
140,147 | [
"https://security.stackexchange.com/questions/140147",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/127705/"
] | If I used an exploit to gain root access, but my ultimate goal is cracking the passwords for each user, what is the fastest way to do this?
I know I can use john on the shadow file, but if I'm in a timed environment with limited CPU power, is there a faster way that takes advantage of already being root?
| If your ultimate goal is to actually get the password in plain text, then unless there's severe misconfiguration or undiscovered flaw in the password hashing method used, then no, there isn't a faster way to crack password than brute force.
Few points you could exploit: if you can get the shadow file out of the system... | If you are root on the system you can subvert the binaries used for login and directly capture the passwords the users enter. Depending on the strength of the passwords used and the frequency users log in this might be faster than trying to crack the passwords with brute force.
| https://security.stackexchange.com |
208,383 | [
"https://physics.stackexchange.com/questions/208383",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/71328/"
] | How do we know that we are really living in 3 dimensional world?
We can draw 3D in a paper that is one dimension. So, maybe the world around us just looks 3D! how can we prove that we're living in 3 dimensional world not one dimensional?
| The simple proof is that you can tie your shoelaces.
This is a proof because you can only tie a knot in an (approximately) 1D object in three dimensions. In lower than three dimensions it's impossible because that would require the shoelace to self intersect. In higher than three dimensions it's impossible because the... | Think what one dimension means: everything going forward or backwards in a line from -infinity to infinity.
1) A car would flatten you in one dimension, and there are billions of cars people etc in motion. As we exist there is an extra dimension. So we need two dimensions at least.
2) Walking in two dimensions you... | https://physics.stackexchange.com |
61,294 | [
"https://security.stackexchange.com/questions/61294",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/46853/"
] | I am trying to learn about Cyber Bullying and I was thinking that if in future I get bullied, then what I can do?
I have learned how to use Maltego, but if someone damages your reputation, then is there any option by which I can erase all that data from the Internet and build my reputation? I have read some solutions... | As for wiping the slate clean if someone tarnishes your reputation, you can request that websites disable the account but depending on the site they don't have to.
As for seeking revenge, don't. Be thankful that the individual exposed a character flaw. Harden yourself to the internet. When you do this, you cannot be c... | There is no real answer to this question. Unless there is a crime and investigators can track the user, there is little you can do to track down real users from their online accounts.
As for deleting data from the Internet, at best you might find different services that might respond to such requests, but that is up ... | https://security.stackexchange.com |
78,750 | [
"https://electronics.stackexchange.com/questions/78750",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11339/"
] | I have a simple question: would I be able to send a video signal (composite) to each relay per camera? The reason is that I only have one video input but need to be able to use two cameras (not at the same time, though).
I have my drawing that I sketched out of what I <em>think</em> the hookup may need to look like.
... | Composite video is very forgiving and you can definitely use relays to basically perform the same function as unplugging camera 1, and plugging in camera 2, and vice versa.
In your diagram, however, you show using two relays and a "Y" splitter, which could lead to the possibility of both video signals being active at ... | I would recommend going the bus-switch direction - it is assured to work. While composite video is very forgiving - I had a solution using a SPDT for camera's in a vehicle and the specific relay i had allowed cross-talk (within the relay) between the two active signals. Now if you powered them up independently (which... | https://electronics.stackexchange.com |
2,536,550 | [
"https://math.stackexchange.com/questions/2536550",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/372201/"
] | <blockquote>
Find all function $f:\mathbb{R}-\{0,1\}$ in $$f(x)+2f\left(\frac{1}{x}\right)+3f\left(\frac{x}{x-1}\right)=x$$
</blockquote>
Attempt: put $\displaystyle x = \frac{1}{x}$, then $$f\left(\frac{1}{x}\right)+2f(x)+3f\left(\frac{1}{1-x}\right) = \frac{1}{x}$$
could some help me how to solve it , thanks
| Subtract twice from what you get from the given equation to get:
$$-f(x) + f\left(\frac{x}{x-1}\right) - 2f\left(\frac{1}{1-x} \right) = \frac{x^2 - 2}{3x}$$
Then in this equation plug $x= \frac {x}{x-1}$ to get:
$$-f\left(\frac {x}{x-1}\right) + f\left(x \right) - 2f\left(1-x\right) = \frac{-x^2+4x-2}{3x(x-1)}$$
... | Just as you replaced $x$ by $\frac{1}{x}$, you can replace $x$ by $1-x$. Then you can replace $x$ by $\frac{1}{x}$ in this new equation.
Repeating this process, I believe you will obtain 6 independent equations in the variables $f(z)$ where $z$ takes the values $$x,\frac{1}{x},\frac{1}{1-x},\frac{x}{x-1},\frac{x-1}{x}... | https://math.stackexchange.com |
440,954 | [
"https://electronics.stackexchange.com/questions/440954",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/201339/"
] | So i know this question is being asked almost everyday on thousands of forums, but i am still going to ask that same question but with a different intent.
Question #1:
As an example lets use linux bootable stick. you stick it in and you can use the whole operating system without even installing it. What i would like ... | <blockquote>
Question #1: As an example lets use linux bootable stick. you stick it in and you can use the whole operating system without even installing it. What i would like to do is have my code on SD card and plug it in a device of my own (arduino board) and have this arduino execute code (without copying it in t... | when I plug a linux stick into my computer my computer is unable to execute from that stick in the same way that an avr is unable to execute from external storage. (there are exceptions but not in the arduio case)
How it works in your computer is code that is on rom (can execute from there) runs and loads code into r... | https://electronics.stackexchange.com |
1,222,175 | [
"https://math.stackexchange.com/questions/1222175",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/203736/"
] | The number of points, having both coordinates as integers, that lie in the interior of the triangle with
vertices $(0,0) ,(0, 41$) and $(41,0)$ , is:
(1) 901 (2) 861 (3) 820 (4) 780.
I tried to find out the number of points manually, but it didn't look like the optimal method.
Thanks in advance.
| Supposing you define an inversion of $a$ as a pair of indices $i<j$ such that $a_i>a_j$, you can easily show that $(i,j)$ with $i<j$ is an inversion of $a$ if and only if $(n+1-j,n+1-i)$ is <em>not</em> an inversion of the reverse of $a$. The pair of <em>values</em> at those indices are the same in both cases,... | <em>Hints.</em>
<ul>
<li>Think of some permutation $ι$ on $[n]$ so that for any permutation $σ$ on $[n]$, “$σ$-reverse” is $σι$.</li>
<li>An inversion of any permutation $σ$ on $[n]$ is a pair $(i,j)$ with $i < j$ such that $\frac{σ(i) - σ(j)}{i-j} < 0$.</li>
<li>For permutations $σ$, $τ$ on $[n]$ you have $\fra... | https://math.stackexchange.com |
49,345 | [
"https://quant.stackexchange.com/questions/49345",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/42513/"
] | Q1. How is the <strong>implied volatility</strong> of GBPUSD and USDGBP related to each other
mathematically? Please explain this intuitively as well.
Q2. How is the <strong>historical volatility</strong> of GBPUSD and USDGBP related to each
other mathematically?
<pre><code>My take ( Please correct if i am ... | Using usual FX modelling techniques, let us assume <span class="math-container">$\text{USDGBP}_t$</span> follows Geometric Brownian Motion under the domestic risk-neutral measure, when the domestic currency is USD:
<span class="math-container">$$d\text{USDGBP}_t=(r_{USD}-r_{GBP})\text{USDGBP}_tdt+\color{blue}{\sigma}\t... | The correlation of USDGBP and GBPUSD is -1! If your sample and measurement thereof, realised or implied, but suggests <>-1, jour jargonistic problem is “Siegel’s Paradox” :-)
In log terms, ie transforming returns such that they are additive, there is no difference. They sum to zero.
The assumption with implieds i... | https://quant.stackexchange.com |
2,032 | [
"https://physics.stackexchange.com/questions/2032",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/202/"
] | If the earth's gravity exerts a net downward gravitational force on all air molecules, how come the molecules don't eventually lose their momentum and all settle down? How is the atmosphere is still miles thick after billions of years?
| First of all, gravity does continually accelerate the air molecules. I don't see how this could make them lose their momentum.
What is the net effect of gravity on the atmosphere? Simple, gravity prevents the atmosphere from flying off in space, and instead it keeps it comfortably wrapped around our planet!
The reaso... | The key ingredient is temperature.
If it were zero then all the air would indeed just fall down to the ground (actually, this is a simplification I'll address later). As you increase the temperature the atoms of the ground will start to wiggle more and they'll start to kick the air molecules giving them non-zero avera... | https://physics.stackexchange.com |
105,381 | [
"https://cs.stackexchange.com/questions/105381",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/76692/"
] | I have been looking at the Until operator and the release operator and when introduced to the release operator it was suggested that it is equivalent to:
<span class="math-container">$\phi R \psi \equiv \neg(\neg\phi U \neg \psi)$</span>
But when trying to get from the semantic definition of the Until operator to the... | First, note that you did not really get the "first part the the expression correct". The first formula is, roughly, of the form
<span class="math-container">$$
\forall i, (p(i) \lor q(i))
$$</span>
while the second one is of the form
<span class="math-container">$$
r \lor (\forall k, p(k))
$$</span>
Note the different... | Not sure whether its correct but I think that the until operator for LTL requires at least one instance of the pre condition to hold so
⊨⟺∃≥0,[]⊨∧∀≤−1,[]⊨
should really be
⊨⟺∃≥1,[]⊨∧∀≤−1,[]⊨
since you can't have without first having so the reason you get the undefined behaviour at i = 0 is because your original defin... | https://cs.stackexchange.com |
250,172 | [
"https://mathoverflow.net/questions/250172",
"https://mathoverflow.net",
"https://mathoverflow.net/users/66131/"
] | While on some work on symmetric functions, we encountered
<span class="math-container">$$f(a,b)=\frac{a^2+b^2}{1+ab}$$</span>
is an integer iff it is a perfect square, where <span class="math-container">$(a,b)\in\mathbb{N}^2$</span>. Well, it turns out that this is a well-known (well-documented) problem.
So, I propose ... | <strong>Edit:</strong> in the original formulation, it wasn't clear that $a,b$ were supposed to be positive integers. This answer solves the question for $a,b$ <em>rational</em> instead.
<hr>
The function $f$ takes every square value, once rational $a,b$ are allowed. Let $t$ be any rational number, and take the equatio... | For such equations:
$$\frac{x^2+y^2}{xy+1}=t^2$$
Using the solutions of the Pell equation. $p^2-(t^4-4)s^2=1$
You can write the solution.
$$x=4tps$$
$$y=t(p^2+2t^2ps+(t^4-4)s^2)$$
It all comes down to the Pell equation - as I said.<br>
Considering specifically the equation:
$$\frac{x... | https://mathoverflow.net |
6,018 | [
"https://mechanics.stackexchange.com/questions/6018",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3115/"
] | I'm having some concerns with my car's engine temperature. Last weekend after being stopped at an intersection, the engine temperature went up higher than usual, about 75% of the way to the red line. I believe the AC was on. Once we started moving though, it came back down to normal (just under 50%, maybe 45% or so)... | You said that the service station didn't mention having to top up the coolant, but I'd start by checking the coolant level yourself. The coolant overflow bottle should be prominent in the engine compartment, and the min/max levels should be well marked.
If the coolant level is good, perhaps you have a failing thermost... | A fan problem or radiator problem seem likely. Clean out any debris near the radiator, and check the fins for build up of leaves/bugs etc. It could be a clogged radiator - test for cold spots or drain it.
| https://mechanics.stackexchange.com |
16,516 | [
"https://dba.stackexchange.com/questions/16516",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8139/"
] | I have an SQL query whose aliases are the same as some of its subquery's aliases.
For example:
<pre><code>select *
from ROOM r
where ...
(
select *
from ROAD r
where ...
)
</code></pre>
This works fine, as the subquery's alias seems to hide the main one's.
... | It's OK for nested subqueries to use the same aliases as used in the parent query, although it might be a bit confusing for someone reading the code. The name space for aliases on a nested subquery is separate from the name space on the parent. For example the query below has a nested subquery <code>b</code> that als... | ConcernedOfTunbridgeWells, you write (emphasis mine): "On a correlated subquery you have access to the parent's aliases, so the aliases <b>must</b> be unique across the parent query and correlated subquery."
I don't believe uniqueness is required. I believe that, if an alias is used in a correlated subquery as a corre... | https://dba.stackexchange.com |
89,074 | [
"https://stats.stackexchange.com/questions/89074",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/41431/"
] | I am currently studying an M.Sc. in pure mathematics (my dissertation focuses on category/set theory)). However recently I have decided that I wish to transition to a much more applied field. During my undergrad I studied almost all pure courses, with only one statistics module.
I have enrolled in an M.Sc. in operatio... | Well, I will answer because this is almost exactly what I have done.
My undergraduate degree was in pure mathematics with a thesis on the Lowenheim-Skolem theorem, and now I am in a funded PhD program in environmental science, where most of my work is in statistics (bio&geo). So clearly, it is possible, and you p... | I don't know what the requirements are in the UK, but many good American statistics and biostatistics graduate programs even accept and fund PhD students who only have an undergraduate degree in mathematics.
| https://stats.stackexchange.com |
8,441 | [
"https://security.stackexchange.com/questions/8441",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/4885/"
] | I connect to the VPN of another company with a company-specific username and password (they aren't giving everyone the same password to every company to access it or anything ridiculous like that.) After one of our employees left, I contacted this company about updating our password. I was told they are unable to chang... | I agree this must be bad design. You may want to have password stability over certain periods for synchronization across systems or when a new system is integrated into a larger system. Except for those circumstances, you want to be able to change a password whenever a password may have been exposed, which could be an... | I think the root of it is poor design as you said. Everytime I've seen a system that can't change a password, it has been developed in such a way for various reasons, none of which are for the sake of security, and none of which are where it's the best solution to a problem.
The only design that I can think of that co... | https://security.stackexchange.com |
672,858 | [
"https://physics.stackexchange.com/questions/672858",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/305770/"
] | In volume 4, section 7 of the Landau and Lifshitz collection (second edition) the authors discuss spherical wavefunctions of photons. I'm having trouble understanding how the equality in (7.7) is obtained.
It is said that the wavefunction (in the momentum representation) of a photon having an angular momentum <span cla... | <blockquote>
Does the strain induces stress or does the stress induces strain? Or
is it both ways?
</blockquote>
When we are dealing with mechanical stress and strain, which is what we deal with most frequently, it is normally the stress resulting from loading that induces strain.
On the other hand, if we are dealing w... | In terms of cause and effect, an external force (stress) causes deformation in an object (strain) which in turn induces internal forces (stress) which oppose the external force. If the internal forces are strong enough then deformation stops at the point where the internal forces balance the external force and the obje... | https://physics.stackexchange.com |
12,952 | [
"https://astronomy.stackexchange.com/questions/12952",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/5306/"
] | If we suppose we and everything in the universe is perfectly flat. That is, we have width and depth, but no height. And we are situated on the surface of a balloon blowing up with air and expanding "outwards". Us flat people can move around on the surface of our balloon but not through it, in much the same way we na... | The answer to this question lies in cosmology.
It's because of relativity in positions. Every galaxy appears to be moving away from us and the universe we see is only the observable universe. Further points are more in the distant past, when you observe the deep field you observe the past. This may seem irrelevant ... | The centre of something ( anything ) has to be defined in some way by the properties of the something and a coordinate system.
So you can in principle define a centre to the universe, but it only has a meaning in the context of the chosen definition.
You could easily define a different measure that produces a differe... | https://astronomy.stackexchange.com |
24,332 | [
"https://mechanics.stackexchange.com/questions/24332",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/675/"
] | Take the following tire codes, for instance:
<blockquote>
<strong>195/65R15 91 V</strong>
<strong>245/40R18 97 Y</strong>
</blockquote>
What does the "V" signify? What other letter codes are there?
| The "V" you're asking about is the Speed Rating of the tire. There's a speed rating for almost every letter of the alphabet: (note that H decided to cut in line for some reason...)
<pre><code>A1-A8 - Steps from 3 mph to 25 mph
B - Up to 31 mph
C - Up to 37 mph
D - Up to 40 mph
E - Up to 43 mph
F - Up to 50 mph
G - Up ... | That letter is the speed rating of the tyre - i.e. the maximum speed the tyre is rated for - for example, V is rated for 149mph/240kph.
Some people say you can use a lower rated tyre if you're not going to drive as fast, however many insurance companies will insist that you use a suitable rating for your car - you can... | https://mechanics.stackexchange.com |
97,129 | [
"https://electronics.stackexchange.com/questions/97129",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/34639/"
] | I have prepared a setup for 2 Xbees one connected to the PC via XCTU and the other interfaced with Atmega 168. The terminal software will send 1 and the xbee with Atmega 168 will return 1.
The code is as follows.
<pre><code>#include<avr/io.h>
#include<avr/interrupt.h>
#include<util/delay.h>
uns... | This problem is not regarding your software, because you ran the same program in both cases right? So it must be hardware. The irregularity in the 2nd case suggests that there is some baudrate mismatch. So I conclude that the problem is definitely because of the internal RC oscillators which are not accurate as you men... | I'm not 100% sure this will fix your problem but normally before sending data you'd want to check that the transmitter holding register is empty before sending a character. You could try this:
<pre><code>ISR(USART_RX_vect) // ISR for receive complete interrupt
{
data = UDR0; //making copy of data from UDR0 i... | https://electronics.stackexchange.com |
599,842 | [
"https://physics.stackexchange.com/questions/599842",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208833/"
] | In a particular reference frame with coordinates <span class="math-container">$x^\mu$</span>, we can define a current density 4-vector <span class="math-container">$J^\mu=(c\rho,\vec{J})$</span> where <span class="math-container">$\rho$</span> is the charge density and <span class="math-container">$\vec{J}$</span> is t... | From <span class="math-container">$J'^\mu=\Lambda^\mu_\nu J^\nu$</span> take derivative on both sides
<span class="math-container">$$\frac{\partial J'^\mu}{\partial x'^\mu}=\Lambda^\mu_\nu \frac{\partial J^\nu}{\partial x'^\mu}$$</span>
Note that <span class="math-container">$\frac{\partial}{\partial x'^\mu}=\Lambda^\s... | Generally
<span class="math-container">\begin{align}
&\texttt{The 4-gradient contravariant vector operator}
\nonumber\\
& \qquad \qquad \qquad \partial^{\mu}\boldsymbol{\equiv}\dfrac{\partial }{\partial x_{\mu}}\boldsymbol{=}\left(\dfrac{\partial }{\partial x^{0}}\,,\boldsymbol{-\nabla}\right)
\tag{01a}\label{... | https://physics.stackexchange.com |
412,145 | [
"https://stats.stackexchange.com/questions/412145",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/217876/"
] | Say I have a light bulb that can be on (A) or off (B). It alternates between being state A or B. It will be in state A for a duration a ~ exp(α), and in state B for duration b ~ exp(β), (parameterized by mean), back and forth
I have a hunch that P(state at time t = A) approaches α / (α + &beta... | If you're looking for an explicit solution, we can use Kolmogorov forward equations for continuous time Markov chains. In particular, we have the following rate matrix,
<span class="math-container">$$ Q = \begin{pmatrix}-\alpha & \alpha \\ \beta & -\beta \end{pmatrix} $$</span>
Let <span class="math-container... | As @LuisCiadella Comments, this is a Markov Chain. The Markovian structure is inherited from the 'memoryless' property of exponential distributions. Because of its simple structure, it is easy to give
an intuitive solution to the proportion of time spent
in State A.
Beginning in State A we will wait for average time <... | https://stats.stackexchange.com |
58,100 | [
"https://mathoverflow.net/questions/58100",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13559/"
] | What is the minimal resolution of singularities of the surface
$S^2(X^3+Y^3+Z^3)-3(S^2+T^2)XYZ=0$ which is a subset of $\mathbb{P}^1\times\mathbb{P}^2$
Please note that in this equation $[S:T]\in{\mathbb{P^1}}$ and $[X:Y:Z]\in{\mathbb {P^2}}$ and by $\mathbb{P^n}$ we mean n-dimensional complex projective space.
| Let us start by writing down the computation of the singular points in the chart $S=1$.
Writing $\lambda:=T/S$, in the chart $S=1$ we can rewrite the equation of the surface as
$$X^3+Y^3+Z^3-3(1+\lambda^2)XYZ=0.$$
This is an elliptic fibration over $\mathbb{C}$ (with coordinate $\lambda$), whose fibres are the curves... | The deleted comment was mine - I just stated that the singular locus consisted of six isolated singular points. Here is a Macaulay2 session to back up this claim:
<pre><code>Resolution of the surface S^2(X^3+Y^3+Z^3)-3(S^2+T^2)XYZ=0 in P2xP1:
Macaulay2, version 1.4
with packages: ConwayPolynomials, Elimination, Integ... | https://mathoverflow.net |
1,038,297 | [
"https://math.stackexchange.com/questions/1038297",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/80708/"
] | I have to show that each element of $\mathbb{F}_{2^n}$ is a square of some element.
Could you give me some hints how I could do that??
| Consider the map $\phi : \mathbb{F}_{2^n} \to \mathbb{F}_{2^n}$ given by $\phi(x) = x^2$. You can show that this is a homomorphism between rings (use the fact that $\operatorname{char}(\mathbb{F}_{2^n}) = 2$), so its kernel is an ideal in $\mathbb{F}_{2^n}$. As $\mathbb{F}_{2^n}$ is a field, $\ker\phi = \{0\}$ or $\ker... | In $\mathbb{F}_{q^n}$ every element $x$ satisfies $x^{q^n}=x$. In fact, for $x=0$ this is clear, and for $x \neq 0$ it follows from Lagrange's theorem applied to the multiplicative group $\mathbb{F}_{q^n}^\times$. In particular, every element of $\mathbb{F}_{2^n}$ is a square.
| https://math.stackexchange.com |
46,770 | [
"https://mathoverflow.net/questions/46770",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7521/"
] | Regarding reals as functions from $\omega$ to $\omega$, let's say a real $f$ <i>eventually dominates</i> $g$ iff $(\exists n)(\forall m > n)[ f(m) > g(m)]$. Let's say that a (non-trivial separative) forcing poset $P$ <i>doesn't always add a dominating real</i> iff there is a generic extension by $P$ which doesn'... | Stefan's answer pointed me in the right direction, and then talking it over with prof. Leo Harrington we've got an answer:
A complete Boolean algebra $\mathbb{B}$ never adds a dominating real iff for any collection $\{ u _{m,k} : m, k \in \omega \} \subset \mathbb{B}^+$ the following weaker form of weak $(\omega ,\ome... | Let me first say something about not always adding a dominating real (or anything else that can be formalized in the forcing language).
Given a forcing notion $P$, the Forcing Theorem (everthing true in the extension is forced by an element of the filter) implies that there is a dense set $D$ of conditions
that either... | https://mathoverflow.net |
149,320 | [
"https://electronics.stackexchange.com/questions/149320",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/64098/"
] | Imagine you've got two coils with exactly the same cores, but one winding is made of material with its density different from the density of winding material of the other coil.
Would that configuration make differences in these two coils properties?
Or maybe only the amperage matters?
What other things describe coil... | The magnetic flux B of a solenoid with one layer of windings is expressed as:
<img src="https://i.stack.imgur.com/ZP0In.png" alt="Flux">
<ul>
<li>μ: Magnetic properties of the core</li>
<li>N: Number of turns</li>
<li>l: Length of the coil</li>
<li>I: Current through coil </li>
</ul>
μ is constant (at least in theo... | Officially, material density it is expressed in kg/m<sup>3</sup>.
The higher the density of the conductor, the lower the resistivity, the higher the current flow per unit area.
Since a coil magnetic field strength it is proportional of N·I (ampere-turns), the higher the current passing through the same number ... | https://electronics.stackexchange.com |
64,489 | [
"https://electronics.stackexchange.com/questions/64489",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20257/"
] | [EDIT] I'm going to give mesh analysis another go, and see where that gets me.
[DOUBLE EDIT] Mesh analysis didn't get me anywhere :(
Im tearing my hair out over this problem, so any help would be greatly appreciated.
<img src="https://i.stack.imgur.com/b8HBw.jpg" alt="My working and a copy of the circuit">
Im solv... | First off, mesh analysis would be simpler because you would only have one unknown (the current in the right mesh).
As you know, in nodal analysis you are summing currents at the nodes. Current into the nodes positive and current out of the nodes negative. The way you have defined the problem you should have 3 equati... | V(A) must be 15v higher than V(B) because of the 5mA current flowing thru the 3k resistor.
So.... V(A) = V(B) + 15
I don't know if this helps in the way you want it to?
| https://electronics.stackexchange.com |
557,982 | [
"https://math.stackexchange.com/questions/557982",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/106585/"
] | I need to prove following combinatorial identities:
$$
\sum\limits_s(-1)^s\binom{p+s-1}{s}\binom{2m+2p+s}{2m+1-s}2^s=0
$$
$$
\sum\limits_s(-1)^s\binom{p+s-1}{s}\binom{2m+2p+s-1}{2m-s}2^s=(-1)^m\binom{p+m-1}{m}
$$
given the fact that
$$
(1-x)^{2k}\left(1+\frac{2x}{(1-x)^2}\right)^k = (1+x^2)^k
$$
for either $k=p$ o... | Ok, first of all there was an error in my attempt to solve, because of my misinterpreting of series $1+2x+4x^4+\dots$ as $\sum(2x)^n$ when actually (if one to find more series members) it is $1 + 2x + 4x^2 + 6x^3 + 8x^4+\dots$. Secondly, this attempt was incorrect way of solving this problem. The correct way involves a... | Suppose we seek to verify that
<span class="math-container">$$\sum_{q=0}^{2m} (-1)^q {p-1+q\choose q}
{2m+2p+q-1\choose 2m-q} 2^q =
(-1)^m {p-1+m\choose m}.$$</span>
Introduce
<span class="math-container">$${2m+2p+q-1\choose 2m-q} =
\frac{1}{2\pi i}
\int_{|z|=\epsilon}
\frac{1}{z^{2m-q+1}} (1+z)^{2m+2p+q-1} \; dz.$$</... | https://math.stackexchange.com |
301,238 | [
"https://electronics.stackexchange.com/questions/301238",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/110004/"
] | I want to make a light source that runs by main power and only uses batteries when there is a power outage.
Note: Please explain in simple terms, since I'm just a middle school student.
| What you want is called a <i>relay</i>. That's a mechanical switch that is activated by a electro-magnet. When power is applied to the magnet, the switch is one way. When power is removed, the switch goes the other way.
Relays come in a variety of switch configurations. A very common one is <i>single pole, double ... | Use a relay. There exists plenty of types which accept mains AC for control and have both opening and closing contacts. Searc for "relay" to learn the principle. That component really was a basic building block for automation 100 years ago and it still is due its robustness.
| https://electronics.stackexchange.com |
123,860 | [
"https://mathoverflow.net/questions/123860",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14024/"
] | Any other definition for algebraic number than the root of algebraic equation?
| In model theory, an object is <em>algebraic</em> in a structure $M$ if it satisfies a property that only finitely many other objects in $M$ exhibit, where by "property" here we mean one that is expressible in the first-order language of the structure. This is a weakening of definability, since $a$ is <em>definable</em>... | Assuming ZFC, one can characterize the algebraic numbers in $\mathbb{C}$ as those numbers which lie in finite orbits under the action of ${\rm Aut}(\mathbb{C})$ on $\mathbb{C}$.
| https://mathoverflow.net |
68,678 | [
"https://security.stackexchange.com/questions/68678",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/51931/"
] | Assume that I have created a CSR and I am going to buy an SSL certificate with it. Would I be able to use the SSL certificate on another machine than where the CSR was created?
Someone I know recently told me it wasn't, but I'm not entirely sure.
| <strong>No, it is not true.</strong>
The CSR defines various parameters for the certificate that you are requesting, such as the Common Name, any Alternative Names, etc. However the CSR is, ultimately, just a file, and you can do all the usual file things with it -- such as copying or moving it to another server, if y... | You don’t need the CSR in order to use the certificate. In order to have a machine authenticate with this certificate, though, the machine also needs the private key that goes with the certificate.
The private key is typically generated along with the CSR. In the simplest scenario, the private key is just a file which... | https://security.stackexchange.com |
9,829 | [
"https://mathoverflow.net/questions/9829",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2349/"
] | This is a question a friend of mine asked me some time ago. I suspect the answer is "no" but can't prove it.
Every free complex of abelian groups is isomorphic to the reduced cellular complex of some finite CW-complex; in fact, one can take a wedge of balls and Moore spaces. The question is whether there is a similar ... | Here is a sketch of an argument to show that all based chain complexes are realizable. (This might end up being pretty similar to Tyler's argument.)
First one gives an algebraic argument that by a change of basis the chain complex can be put in a standard "diagonal" form. Moreover, the change of basis can be achieved ... | It is always possible to alter an existing solution to one that has a correct basis.
Given your chain complex, use your original method to construct a CW complex X with the correct CW-chain complex, but the wrong basis. Write X<sup>(n)</sup> for its n-skeleton. To make life easy assume that it only has one 0-simplex... | https://mathoverflow.net |
3,102,196 | [
"https://math.stackexchange.com/questions/3102196",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/581242/"
] | Suppose we have vector-valued function <span class="math-container">$f : \mathbb{R} \to \mathbb{R}^n$</span> and <span class="math-container">$|f(t)|=1$</span> for all <span class="math-container">$t \in \mathbb{R}$</span>.
<blockquote>
What can we say about the inner product <span class="math-container">$\langle f(... | <span class="math-container">$|f|=1$</span> implies <span class="math-container">$\langle f,f\rangle=|f|^2=1$</span> and, as a consequence,
<span class="math-container">$$
\langle f,f\rangle'=2\langle f,f'\rangle=0.
$$</span>
| Let <span class="math-container">$f=(f_1,...,f_n)$</span>. Then
<span class="math-container">$$\langle f,f'\rangle=\sum_{k=1}^nf_kf_k'=\frac{1}{2}\sum_{k=1}^n(f_k^2)'=\frac{1}{2}(\sum_{k=1}^nf_k^2)'=\frac{1}{2}1'=0.$$</span>
| https://math.stackexchange.com |
108,799 | [
"https://security.stackexchange.com/questions/108799",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/56229/"
] | I recently noticed that the assets sent to clients aren't gzipped or minified on either my companies intranet or its public facing website.
I brought this to the attention of the networking department (who maintain the server) and asked if they could add the appropriate code to the server config.
My co-worker initi... | I've been pondering this and I don't think your networking department is justified in this opinion. It does all depend on your threat model, but given the threat model of "hacked content to slip through the clients antivirus scanner", this opinion makes no sense.
First, let's drop minification, because it's in plain ... | This should not be a security concern on which you spend energy.
Maybe your client doesn't have any anti-virus. Maybe they have bad anti-virus. If their system is vulnerable to attack by a website they visit, then that's their problem, not yours. Slowing down clients by not compressing content on the off-chance that... | https://security.stackexchange.com |
98,591 | [
"https://electronics.stackexchange.com/questions/98591",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/36036/"
] | I am learning the Verilog language. Can someone explain the questions I ask in square brackets [] :
<pre><code>module d_ff(q,d,clk,reset);
output q;
input d,clk,reset;
reg q;
always @(posedge reset or negedge clk) [what is this always @()]
if (reset)
q<= 1'b0; [what is 1'b0]
... | 1'b0 is Verilog syntax for a constant value that is a one bit number expressed in binary format with a value of zero.
A bit value of one would be expressed as 1'b1.
Similarly a four bit value in binary that is equivalent magnitude to a decimal value of 11 could be written as 4'b1011.
You could also express this sam... | <pre><code> //Module definition
module d_ff(q,d,clk,reset);
//Argument Classification: You have to tell the compiler which signals are inputs
//and which ones are outputs.
output q;
input d,clk,reset;
reg q;
//Sensitivity ... | https://electronics.stackexchange.com |
721,367 | [
"https://physics.stackexchange.com/questions/721367",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/342352/"
] | I've been learning about Bernoulli's equation:
<span class="math-container">$$P_i + pgh_i + p\frac{v_i^2}{2} = P_0 + pgh_0 + p\frac{v_0^2}{2}$$</span>
but am confused about what <span class="math-container">$P_i$</span> and <span class="math-container">$P_0$</span> truly represent. Sal from Khan Academy said that they ... | It is a <strong>definition</strong>, there is nothing deep going on.
We do this very often. If you have some object <span class="math-container">$a$</span>, you can choose to expand it in some basis <span class="math-container">$u$</span> such that <span class="math-container">$a=\sum_\alpha a_\alpha u_\alpha$</span>. ... | I can't comment with certainty on <span class="math-container">$\epsilon_{ij}(\mathbf{k},\lambda)\epsilon^{ij}(\mathbf{k},\lambda') = 2 \delta_{\lambda\lambda'}$</span>, but I suspect that it's because gravitons actually have only two independent polarizations, so this is a way to go from polarization labels (<span cla... | https://physics.stackexchange.com |
1,703,488 | [
"https://math.stackexchange.com/questions/1703488",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/260886/"
] | I have the differential equation $$ \frac{dy}{dx} = \frac{x}{2y} $$
How do I take $$ \int \! \frac{x}{2y} \, \mathrm{d}x.$$
| $\frac {dy}{dx} = \frac{x}{2y}$ this is a "Separable" diff eq.
$ 2y dy = x dx$ and integrate both sides. I know, it feels like you are playing fast and loose with the differential operators.
$\int 2y \,dy = \int x \,dx$
$y^2 = \frac{1}{2} x^2 + c$
$y = \sqrt{\frac{1}{2} x^2 + c}$
| Then $2y\ dy=x\ dx$
$$\int 2y\ dy=\int x\ dx$$
$$y^2=\frac{1}{2}x^2+c$$
$$y=\pm\sqrt{\frac{1}{2}x^2+c}$$
| https://math.stackexchange.com |
310,044 | [
"https://mathoverflow.net/questions/310044",
"https://mathoverflow.net",
"https://mathoverflow.net/users/94774/"
] | Say I have a set of $(n-1)$ linearly independent vectors $\mathbf{v}_i$ of dimension $n$ with entries $\pm1$. I am interested in finding the $n-$dimensional vector $\mathbf{u} $which is normal to the hyperplane spanned by the $\mathbf{v}_i$. In other words, $\mathbf{u}$ is orthogonal to each of the $\mathbf{v}_i$, wher... | To recap: we are given $n-1$ linearly independent vectors in ${\bf R}^n$ with $\pm 1$ entries. The original Q1 asked, in effect, if there is always a vector with $\pm 1$ entries that is orthogonal to all of the given ones. A counter examples is provided for $n=3$ by taking
$$
v_1 = e_1+e_2+e_3\quad,\quad v_2=e_1+e_2-e_... | There is a six-dimensional counterexample:
<ul>
<li>$(+1,+1,+1,+1,+1,+1)$</li>
<li>$(-1,-1,+1,+1,+1,+1)$</li>
<li>$(+1,+1,-1,-1,+1,+1)$</li>
<li>$(+1,+1,+1,-1,-1,+1)$</li>
<li>$(+1,-1,+1,-1,+1,-1)$</li>
</ul>
The normal to the linear span of these five vectors is $(2,-2,-1,1,-1,1)$.
| https://mathoverflow.net |
104,536 | [
"https://mathoverflow.net/questions/104536",
"https://mathoverflow.net",
"https://mathoverflow.net/users/290/"
] | Equivalently, is the free Lie algebra on finitely many generators over a fixed field $k$ (say of characteristic not equal to $2$) residually finite-dimensional in the sense that any nonzero element remains nonzero in some finite-dimensional quotient? Some quick Googling on my part was not successful here.
<strong>Mot... | Maybe I am missing something but let me try. The free Lie algebra is a subalgebra of the free associative algebra made Lie via the bracket. The free associative algebra is residually finite dimensional by truncating polynomials. Hence its Lie algebra is residually finite dimensional. Here I assume finitely generated bu... | I believe this is entirely equivalent to Benjamin Steinberg's answer, but one way to see this is that the quotient of a free Lie algebra on finitely many generators by the $n$th term $\mathfrak{F}_n$ of the lower central series (i.e., the ideal generated by $n$-fold bracketings of generators) is a finite dimensional Li... | https://mathoverflow.net |
634,785 | [
"https://electronics.stackexchange.com/questions/634785",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/321083/"
] | I understand that transistors have a gain, which in proportion to the base's current.
My question is quite simple:
I was wondering if, when the base had a high current (because of gain), it would affect the emitter current, even while the collector was completely off?
| There's only one relationship between currents in the transistor which is <em>always</em> true; it's an application of Kirchhoff's Current Law (KCL):
<span class="math-container">$$I_E = I_C + I_B$$</span>
Everything else is <em>conditional</em>, including the formula for current gain:
<span class="math-container">$$I_... | When there is no collector current all the emitter current is from the base and all base current flows "out of" the emitter.
If you define current gain as Ic/Ib then there is by definition zero gain, but the potential gain if collector current were to flow can be calculated.
| https://electronics.stackexchange.com |
37,710 | [
"https://electronics.stackexchange.com/questions/37710",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | Here are two routings:
<img src="https://i.stack.imgur.com/pQfiu.jpg" alt="first routing">
<img src="https://i.stack.imgur.com/e0Ddi.jpg" alt="second routing">
Which is better? On one hand, the first is bad because ground ring is one-turn coil, hence induction current will be appear. On other hand, the second is bad... | The split ring is preferable. A ring that goes all the way round acts like a loop antenna or may act as one closed winding of a transformer. The loop antenna may radiate or pick up electro-magnetic interference and if it acts as a primary transformer winding, the circuitry around the microcontroller in the middle may a... | This may be a solution:
<img src="https://i.stack.imgur.com/cbY5a.png" alt="enter image description here">
It improves on your second option in that it keeps the connections to the power connector as short as possible, given the placement of the signal connectors.
Your first option may not be too bad, however. You'l... | https://electronics.stackexchange.com |
162,170 | [
"https://physics.stackexchange.com/questions/162170",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/71886/"
] | I've been trying to get to grips with SpaceTime.
As I understand it, we move at a set rate through spacetime. Any increase in our rate of travel through space results in a decrease in our rate of travel through time (via standard vector maths, pythagoras)
Where I get confused is the implication for our perception of ... | You've hit on one of the fundamental "weirdnesses" of the Minkowski "metric". Its name "metric" is a bit misleading if you're a mathematician: it does <em>not</em> fulfil two out of the of the three axioms of the distance function defining a metric (in the topologist's words) space. There are null vectors, <em>i.e.</e... | <blockquote>
Any increase in our rate of travel through space results in a decrease
in our rate of travel through time (via standard vector maths,
pythagoras)
</blockquote>
Movement through space is not absolute; there are an infinity of relatively moving reference frames from which your 'mixture' of (rate of) s... | https://physics.stackexchange.com |
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