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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282,607 | [
"https://physics.stackexchange.com/questions/282607",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62173/"
] | Briefly, which physical theories are expected to be time reversal invariant? That is, the mapping of $t\to -t$ will not alter the physics.
Even in Classical Mechanics (CM) it is not obvious if time reversal ought to leave things invariant:
<ul>
<li>On the one hand the three laws of Newton seem to be time-agnostic. (e... | First of all, it's worth explaining what a time-reversal actually is: given a PDE (such as the Schrödinger equation or Newton's equations for a classical system) which describes the dynamics of the physical quantity $q(t)$. Here, $q(t)$ is the trajectory associated to the initial condition $q(0) = q_0$ and may stand fo... | As for your first question, yes a bit bonkers. The best way to think of it without getting so complicated is to understand that time symmetry is a micro-symmetry, valid for all of the basics forces of nature, except the weak forces. just like CP.
For the macroscopic physics entropy and losses due to heat and friction... | https://physics.stackexchange.com |
316,183 | [
"https://softwareengineering.stackexchange.com/questions/316183",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/103381/"
] | I have a class, Customer which has some basic properties on it such as <code>firstname, surname, email, dateofbirth</code>. I have written another class called <code>CustomerValidation</code> which currently has one public method and three private methods. The public method is:
<code>public bool ValidateCustomer(Custo... | If I'm following correctly you are considering using an API that only provides a dumb interface into your data, ie you can't query through the API you can only request all the data in one go.
So if you want to look up the Product for one user you have to fetch all, lets say, 20 million products and on the client side ... | If you want to ease load on your servers where the webservices providing REST endpoints live, there is no other way than to introduce caching to these servers.
You could specify a constraint that a client would have to introduce cache in his application so he does not hit your services that often, but how are you goin... | https://softwareengineering.stackexchange.com |
63,786 | [
"https://stats.stackexchange.com/questions/63786",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1005/"
] | I heard that:
<ul>
<li>Under the null hypothesis, the distribution of p-values is flat over $[0,1]$.</li>
<li>Under the alternative hypothesis, the distribution of p-values is skewed towards $0$.</li>
</ul>
Is there a situation under which the distribution of p-values is skewed towards $1$?
| It is also possible to have the effect in practice, when the null hypothesis is true but not all the assumption for the test are given. For example, the classical (non Welch) t-Test assumes equal variance in both groups. In the case that both groups are equally sized a violation is usually not that bad, otherwise the n... | That can happen in a one-sided test when your "true" parameter is inside the region of the null hypothesis but not on the boundary. Consider the following example in Stata where the "true" parameter (in this case mean) is 1:
<pre><code>clear all
program define sim, rclass
drop _all
set obs 100
gen x = rno... | https://stats.stackexchange.com |
304,546 | [
"https://electronics.stackexchange.com/questions/304546",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/133086/"
] | In comparing the <strong>physical layer</strong> of CAN and RS485, I am trying to find the advantages of either one over the other. I found out that they are quite similar. Both are good in terms of common mode rejection and both need protection against ESD and overvoltage. I found just one significant advantage of CAN... | When comparing the <i>physical layer only</i>, CAN and RS-485 are similar in that they both use differential signaling. This gives them both good common mode noise immunity.
The main difference is that RS-485 uses symmetric signaling. One line is 5 V and the other 0 V to signal one state, then flipped to 0 V and 5 V... | RS485 uses +/- 400mV not 0-5V so the termination resistor is smaller wattage than CAN bus. There is an advantage that many (everyone) seems to miss. Because RS485 is actually bidirectional around 0V ie it must be a full H bridge, this means current flows one way or the other. It's not about the voltage levels but the a... | https://electronics.stackexchange.com |
68,919 | [
"https://mathoverflow.net/questions/68919",
"https://mathoverflow.net",
"https://mathoverflow.net/users/75935/"
] | Is there an integer $m\geq 1$ such that $2^m+3^m$ is a perfect power?
| If you really wanted to prove this (and I'm afraid that I'm not sure why you would), you could invoke a Theorem of Darmon and Merel for $n=2$ and $3$, check that there are no solutions with $p \leq 5$, say, and then write down the usual $(n,n,n)$ Frey curve, assuming $n \geq 5$ is prime (which leads to a weight $2$, le... | By the Fermat theorem: n is not divisible by p.
| https://mathoverflow.net |
2,317,694 | [
"https://math.stackexchange.com/questions/2317694",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/450438/"
] | <strong>Question</strong>: Let T: $\mathbb R^{3} → M_{2\times 2}(\mathbb R)$ be the linear transformation defined by $$T((a,b,c)) = \begin{bmatrix}
a & 5a\\
c & 3c\\
\end{bmatrix} $$
Consider the bases $\alpha = \{(0, 1, 0),(0, 1, 1),(1, 1, 0)\}$ of $\mathbb R^{3}$ and
,
$\beta = \{... | Consider the three standard unit vectors,
$$\begin{align*}
T(1,0,0) &= \pmatrix{1&5\\0&0}\\
T(0,1,0) &= \pmatrix{0&0\\0&0}\\
T(0,0,1) &= \pmatrix{0&0\\1&3}\\
T(a,b,c) &= a\pmatrix{1&5\\0&0} + c\pmatrix{0&0\\1&3}
\end{align*}$$
Kernal: Solving the equation $T(a,... | You say that the kernel $Ker(T) = \{0\}$
What happends if you calculate $T(0,b,0)$?
Remember that $ImT = \{ M \in M_{2\times 2} : M = T(a,b,c) \ (a,b,c) \in \mathbb{R^3}\}$
| https://math.stackexchange.com |
2,586,091 | [
"https://math.stackexchange.com/questions/2586091",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/376476/"
] | My thinking was that if gangster A shoots gangster B, then gangster B will also shoot gangster A since they are the closest together, forming a pair. Since 55 is odd, then one must survive since 55 is 1 mod 2.
| The pair of gangsters with lowest pairwise distance will shoot each other. If some other gangster shoots any of those two, then there will be at most $52$ bullets aimed at the remaining $53$ gangsters, and hence at least one will survive.
If no other gangster shoots any of those two, the problem is reduced to the case... | We will argue by contradiction. Assume everyone died.
Nobody can shoot the same guy twice since there are only 55 bullets and 55 people to kill.
So, WLOG$^{\ast}$,by renumbering $g_1$ shoots $g_2$, $g_2$ shoots $g_3$, ..., $g_{55}$ shoots $g_1$.
$^\ast$As N.S. noted there there can be different connected componen... | https://math.stackexchange.com |
438,941 | [
"https://softwareengineering.stackexchange.com/questions/438941",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/415522/"
] | Currently I am reading <code>UML Distilled - Third Edition</code> (Martin Fowler) to catch up some new thoughts and spot interesting things I am not yet aware of.
On of those things I came up is the differentiation between generalization and classification.
In <code>Chapter 5 - Class Diagrams: Advanced Concepts</code>,... | <strong>There is more than one way to shave a cat.</strong>
In an ideal organization which has a good testing process, and where only experienced developers work who regularly write unit tests, you can leave verification of correctness fully to the authors and dedicated testers. Here PRs can be restricted to verify if ... | If you attempt to double check code in PRs you are effectively writing the code yourself and will end up having no time for anything but PRs
Instead decide what the rules for passing a PR are and check that they have been followed. For example.
<ol>
<li>Are there automated tests</li>
<li>Do they pass</li>
<li>Does the ... | https://softwareengineering.stackexchange.com |
101,023 | [
"https://security.stackexchange.com/questions/101023",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/87555/"
] | I've moved onto a project where they are implementing a system whereby a user's email address can be used multiple times by different people - i.e. users can sign up as many times as they want with an email address as there's no unique constraint. The theory is that they won't have actual access to the email account so... | I'm assuming that in the case of duplicate accounts, different passwords are used as the means of distinguishing between these accounts?
i.e. if there are two <code>bob@example.com</code>s, one with password <code>foo</code> and one with <code>bar</code> then the password will be checked to find out which account to l... | If the user uses forgot password then the new password will be sent to the email address with which he has logged in.
This makes the user whose email address is used accessing the password and can use it to login and perform actions.
| https://security.stackexchange.com |
26,502 | [
"https://electronics.stackexchange.com/questions/26502",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8078/"
] | i try to do something like this:
<pre><code>always @ (negedge speed_dec or negedge speed_inc)
begin
do something
end
</code></pre>
This doesn't work as checking for 2 negative edges is to demanding and results in only checking for the clock.
I tried do do the check manually:
<pre><code> reg old_key0;
always ... | The <code>always@</code> is a sensitivity list and generally <em>not</em> a checking list i.e. it doesn't work as an <code>if-else</code> block.
Instead, it indicates when the register/latch specified in the block needs to change states, typically on a clock edge (register) or level change (latch).
If you're trying t... | What you wrote is perfectly valid Verilog. For example, one case where an always block depends on two edges is in describing a flip-flop with asyncronous reset:
<pre><code>wire d;
reg q;
always @ (posedge CLOCK or posedge RESET) begin
if (RESET)
q <= 0;
else
q <= d;
end
</code></pre>
An... | https://electronics.stackexchange.com |
5,253 | [
"https://stats.stackexchange.com/questions/5253",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1950/"
] | After reading a dataset:
<pre><code>dataset <- read.csv("forR.csv")
</code></pre>
<ul>
<li>How can I get R to give me the number of cases it contains?</li>
<li>Also, will the returned value include of exclude cases omitted with <code>na.omit(dataset)</code>?</li>
</ul>
| <code>dataset</code> will be a data frame. As I don't have <code>forR.csv</code>, I'll make up a small data frame for illustration:
<pre><code>set.seed(1)
dataset <- data.frame(A = sample(c(NA, 1:100), 1000, rep = TRUE),
B = rnorm(1000))
> head(dataset)
A B
1 26 0.07730312
2 ... | Briefly:
<ol>
<li>Run <code>dim(dataset)</code> to retrieve both <em>n</em> and <em>k</em>, you can also use <code>nrow(df)</code> and <code>ncol(df)</code> (and even <code>NROW(df)</code> and <code>NCOL(df)</code> -- variants are needed for other types too).</li>
<li>If you transform e.g. via <code>dataset <- na.o... | https://stats.stackexchange.com |
384,154 | [
"https://softwareengineering.stackexchange.com/questions/384154",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/323704/"
] | I have two paths:
<ul>
<li><code>/students</code></li>
<li><code>/students/{id}/addresses</code></li>
</ul>
...with the following behavior:
<code>POST</code> to <code>/students</code> - <code>201 Created</code> (if successfully created the Student)
<code>POST</code> to <code>/students/{id}/addresses</code> - <code>2... | You should never use exceptions as a flow-control device. Check for the existence of the Student first, then add the address. As you noted, this give you more control over the messaging you send, plus you keep all the logic in the same flow (as opposed to returning messages from both the main block and the exception ha... | It may certainly be a valid concern to reduce latency and demand on the backend for performance reasons. But that pales in comparison to correctness:
TOCTOU, fully written as Time-Of-Check-Time-Of-Use, is a very well known error coming from thinking in a strictly linear model (like cooperative multi-threading in Windo... | https://softwareengineering.stackexchange.com |
2,993,758 | [
"https://math.stackexchange.com/questions/2993758",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I want to show the following identity
<span class="math-container">$$\mathbb{E}X=\int_0^\infty \Pr(X>t) dt$$</span>
where <span class="math-container">$X$</span> is a continuous random variable taking positive values.
We have
<span class="math-container">\begin{align}\int_0^\infty \Pr(X>t) dt&=\int_0^\inft... | <strong>Edit</strong>: First, I'll deal with the case where <span class="math-container">$P$</span> is absolutely continuous, with a density <span class="math-container">$p_X(s)$</span>. We have shown that
<span class="math-container">$$ \int_0^\infty \Pr(X > t) dt = \iint_R p_X(s) \ dsdt,$$</span>
where <span class... | If the integrand is a nonnegative function then switching the order of integration is allowed, so:
<span class="math-container">$$\begin{aligned}\mathbb{E}X & =\int_{0}^{\infty}sP_{X}\left(ds\right)\\
& =\int_{0}^{\infty}\int_{0}^{\infty}\mathbf{1}_{\left(0,s\right)}\left(t\right)dtP_{X}\left(ds\right)\\
&am... | https://math.stackexchange.com |
179,324 | [
"https://physics.stackexchange.com/questions/179324",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/79192/"
] | How do I find the centre of mass with given coordinates?
For example if we have four objects with mass $m$ at coordinates of a square $(0,0,0),(0,0,a),(0,a,0),(0,a,a)$ or another example with eight objects with mass $m$ at coordinates of a cube $(2a,a,a),(2a,-a,a), (2a,a,-a),(2a,-a,-a)$ and $(4a,a,a), (4a,-a, a), (4a,... | $$\vec{X}_{cm} = \frac{1}{M} \sum_i m_i \vec{x}_i$$
where $m_i$ is your mass of particle $i$, $\vec{x}_i$ is the position of particle i, and $M$ is your total mass.
| This is really just a comment on Dargscisyhp's post - please don't upvote this.
The equation Dargscisyhp has given you is a vector equation i.e. the $\vec{x}_i$s are vectors. You do the calculation by adding vectors. If you're uncomfortable with this then you can find the $(x_c, y_c, z_c)$ coordinates for the centre o... | https://physics.stackexchange.com |
140,220 | [
"https://mathoverflow.net/questions/140220",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16702/"
] | Let $M$ be a Riemannian manifold, and let $x, y \in M$ be non-conjugate points.
Let $r, R>0$ be two numbers. I am looking for a bound on the number of geodesics between $x$ and $y$ of Length between $r$ and $R$, like "there are at most $N(r, R)$ geodesics between $x$ and $y$", depending on the curvature of $M$.
I... | I think that no such bounds exist. For example, you can take $M$ to be a (complete) surface of revolution in Euclidean $3$-space that has negative curvature bounded from below by $-1$ and that is asymptotic to the classic pseudospherical surface (i.e., a 'spike' going off to infinity). On such a surface, you can find... | I think that for any manifold with negative curvature having positive injectivity radius $\delta>0$ you get an upper bound of the form $C\delta^{-n} e^{c(R+d(x,y))}$ where $n$ is the dimension $c,C$ depend on the curvature and the dimension. The argument I have in mind actually yields a bound depending only on the i... | https://mathoverflow.net |
265,073 | [
"https://mathoverflow.net/questions/265073",
"https://mathoverflow.net",
"https://mathoverflow.net/users/100719/"
] | I encountered the following identity in a paper on number theory,
$$\int_{-\infty}^{\infty}\frac{dW}{(W+i)^{\frac{3}{2}}(W^2+1)^s}=\frac{e^\frac{-3\pi i}{4}\sqrt{2}\pi \Gamma(2s+\frac{1}{2})}{2^{2s}\Gamma(s+\frac{3}{2})\Gamma(s)},$$
with $Re(s) > 0$ and $i=\sqrt{-1}$.
Since the author did not give the proof for... | To evaluate $\int_{-\infty}^\infty {dx\over (1+ix)^a\,(1-ix)^b}$, view this as $\int_{-\infty}^\infty \widehat{f_a}(x)\,\overline{\widehat{f_{\overline{b}}}(x)}\,dx$ where $f_c$ are functions whose Fourier transforms are $(1+ix)^{-c}$. Use the Gamma-function identity
$$
\int_0^\infty e^{-ty}\,t^c\;{dt\over t}\;=\; y^{-... | <em>Mathematica</em> gives an alternative expression for the same integral valid for ${\rm Re}\,s>-1/4$:
$$ \int_{-\infty}^{\infty}\frac{dW}{(W+i)^{\frac{3}{2}}(W^2+1)^s}=-\frac{1+i}{\sqrt{\pi } (2 s+1)} \sin (2 \pi s) \Gamma (1-2 s) \Gamma \left(2 s+\tfrac{1}{2}\right).$$
Not sure if <em>Mathematica</em> output ... | https://mathoverflow.net |
596,968 | [
"https://physics.stackexchange.com/questions/596968",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140512/"
] | Consider that we are working with a joint system composed of system A with basis <span class="math-container">$|\alpha_j\rangle$</span> and system B with basis <span class="math-container">$|\beta_j\rangle$</span>, we may write a general density matrix for the joint system with respect to tensor product basis <span c... | If <span class="math-container">$\big\{|\alpha_j\rangle\big\}$</span> is a basis for the Hilbert space <span class="math-container">$\mathcal H_A$</span> and <span class="math-container">$\big\{|\beta_k\rangle\big\}$</span> is a basis for <span class="math-container">$\mathcal H_B$</span>, then <span class="math-contai... | Short answer: apply both sides of the equation to an arbitrary ket basis vector, and things will simplify a lot.
The truth of that equation doesn't have anything to do with the fact that it's a joint system, or that it is a density operator. It would be true for any operator, and any orthonormal basis.
After you apply ... | https://physics.stackexchange.com |
359,873 | [
"https://softwareengineering.stackexchange.com/questions/359873",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/144461/"
] | Is it bad practice to use an incrementing primary key to refer to a real world field, such as an id number for an employee?
Suppose that 1 is a valid id number for an employee. I am really tempted to use the incrementing primary key as the id number. But I might have ignored some potential problems it might cause. I've... | The primary key's one and only job is to be the primary key. Ask it to do something else and suddenly it has reasons to change that have nothing to do with being the primary key.
A famous example of this was when Steve Jobs found out he was going to be listed as employee #2 after Wozniak at #1. He couldn't take this s... | Primary key is meant to uniquely identify a record. If the record is something that can be identified in the real world by some attribute (an employee definitely fits that description), then choose something that is immutable through time and space. GUID might be a good choice, but it can be a bit too big in some cases... | https://softwareengineering.stackexchange.com |
390,730 | [
"https://physics.stackexchange.com/questions/390730",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/143541/"
] | I have a few doubts about the canonical ensemble. Let's consider a system A in contact with a heat reservoir.
1) To derive the probability of the system being in a state $E_r$, we consider the probability of the reservoir being in the state $E_t$ - $E_r$ where $E_t$ is the total energy of the system.Then we try to fi... | The force acts on every element of a 3d object.
Take for example a 3d charged object. The charges can be distributed any way at all. They could be uniform, or not. One side could be positively charged, the other negative. And so on.
That 3d object has an element of charge existing at every point. (More precisel... | A vector field defines a situation where the magnitude and direction of vectors are a function of location only. We can best understand this on a rotating rigid body where the linear velocity of each particle $\boldsymbol{v}$ depends on its location $\boldsymbol{r}$.
$$ \boldsymbol{v} = \boldsymbol{\omega} \times \bol... | https://physics.stackexchange.com |
144,514 | [
"https://physics.stackexchange.com/questions/144514",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/63394/"
] | Would the mass of burnt firewood be equal to the mass of firewood before burning?
Then where does that heat come from?
According to Einstein's equation, $E=mc^2$ Shouldn't there be some mass going out of the Earth which contradicts the law of mass conservaton?
| <blockquote>
Would the mass of burnt firewood be equal to the mass of firewood before burning?
</blockquote>
You won't get a good answer by simply looking at the "burnt firewood". The combustion is using oxygen from the air, and it is creating carbon dioxide and many volatilized materials that will disperse in the ... | The law of the conservation of mass was superceded by the more general law of conservation of energy when it was realized that mass and energy were equivalent. Anyway, you are correct. The mass of the combustion products will always be less than the mass of the original materials. The difference being equivalent to the... | https://physics.stackexchange.com |
565,310 | [
"https://physics.stackexchange.com/questions/565310",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/258774/"
] | In Peskin & Schroeder - Chapter 6 - the authors make the following approximation when <span class="math-container">$-q^2\rightarrow\infty$</span>
<span class="math-container">$$\int_0^1 \!\!d\xi\, \frac{-q^2/2}{-q^2\xi(1-\xi)+m^2} \simeq \frac{1}{2}\int_0d\xi\, \frac{-q^2}{-q^2\xi+m^2} + \begin{pmatrix}\!\text{equa... | Here's what I could conjure up. I don't like it cause of sweeping infinities under the rug so feel free to downvote/not accept.
Let
<span class="math-container">\begin{align}
f\left(\frac{m^2}{-q^2} \right) = \frac{1}{2} \int_0^1 d\xi\; \frac{1}{\xi(1-\xi)+\frac{m^2}{-q^2}}.
\end{align}</span>
Then
<span class="math-co... | I would like to share my workings which starts from (6.62) and higher orders might be easier to be extracted.
<span class="math-container">$\int^1_0(\frac{m^2-q^2/2}{m^2-q^2\xi(1-\xi)})d\xi$</span>
<span class="math-container">$=\large{\int^{1/2}_{-1/2}(\frac{m^2-q^2/2}{m^2-q^2(\xi'+\frac{1}{2})(\frac{1}{2}-\xi')})d\xi... | https://physics.stackexchange.com |
216,139 | [
"https://security.stackexchange.com/questions/216139",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/18266/"
] | Some doctors' offices give a personal email address, like Yahoo! or Gmail for patients to email medical records. What questions should I be asking them to make sure the email account is secure? Even if they supply an email address associated with their website, doesn't mean it's secure.
| I would advise against sending your medical records directly in an e-mail, although, this doesn't mean it isn't secure, but there is simply no way for you to know what sort of stuff is going on with that doctors email for sure.
You can use 2 channels for communication. On e-mail channel you provide your medical record... | There are no questions you can ask to make sure it's secure, because it simply isn't. Email is often encrypted, but that's only part of the story. Due to the way email works, it may be encrypted between servers, but each server between you and the destination will have a plaintext copy (ie the encryption isn't end-to-e... | https://security.stackexchange.com |
165,328 | [
"https://softwareengineering.stackexchange.com/questions/165328",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/65559/"
] | I have been offered an <code>"opportunity"</code> to take over maintenance of a small internal website run by my group that provides information about schedules and photos of events the groups done.
My manager sent me the link to the site and I checked it out. The site looked clean and neat but loaded in ~5 seconds. I... | Beware of the Iceberg Syndrome!
With an iceberg, the vast majority of it is located under the water, with just a small percentage being visible. Likewise with a website, the vast majority of it is hidden out of view from the user.
Changing the site from nested tables to CSS/DIV's will take a considerable amount of t... | <h1>Nested Tables Aren't Necessarily Bad</h1>
There are things you can do with nested tables that you can't with CSS and <div>s, especially with regard to re-sizable width layouts. Tables may be old fashioned, but they are more versatile and work equally well on every browser. I personally prefer CSS <em>where ... | https://softwareengineering.stackexchange.com |
237,588 | [
"https://physics.stackexchange.com/questions/237588",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/108473/"
] | Imagine that you are falling into object with huge gravity (i.e. black hole) that does not have any atmosphere.
The question is - before you hit the ground, can the gravity itself (which would be extremely huge) kill you? And if so, how exactly that could be done? All parts of your body are affected same and in the sa... | Yes gravity can kill you because as you approach something super dense like a black hole, the gravity will change with the square of the distance which means that eventually the gravity at your feet would become significantly larger than at your head. This gravitational gradient is referred to as tidal forces and is th... | It's fair to say that the "spaghettification" problem occurs where there's a strong enough gravitational <em>gradient</em> across a typical body-distance - but your question seems to ask about cases where the gravity is great - extreme, but uniform (at least in terms of human proportions/distances).
Einstein’s princip... | https://physics.stackexchange.com |
380,080 | [
"https://physics.stackexchange.com/questions/380080",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/137842/"
] | We know that as we get closer and closer to a point charge, the electric potential approaches infinity.
Since electric potential at the surface of a spherical shell is finite (Gauss law) , so on moving away from the surface it would fall. In other words, it would be finite as well.
But if I think this way: Take an in... | You may be somewhat confusing electrical field and electrical potential. But in both cases, the flaw in your reasoning is the same: the distance from the infinitesimal charge may be infinitisimal small but <strong>so is the charge</strong> (infinitesimal small). You cannot avoid a proper integral or using Gauss law.
| The problem here is symmetry. Use Gauss's law on an infinite sheet of charge. You get a finite (and constant field):
$$ E = \frac{\sigma}{2\epsilon_0} $$.
($\sigma$ is the charge density). It does not matter how close you get, or how far you get: the problem is scale independent, because at any point, you <em>always<... | https://physics.stackexchange.com |
278,801 | [
"https://physics.stackexchange.com/questions/278801",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75628/"
] | Is there any relation between quantum spin and gravity?<br>
Are there experiments that show or motivate that there is or isn't a relation between the two?
| All things are related to each other in one way or another. So I will instead answer the following question:
<blockquote>
How is spin related to gravity?
</blockquote>
First, there are two different things people usually mean by spin. It can be the physical spin of elementary particles ($1/2$ for standard model fer... | The involvement of spin in gravitation is an inescapable corollary of the marriage between gravity and quantum field theory (QFT). QFT (and for that matter the Standard Model) hinges on the existence of Dirac fermion and the rational way of incorporate gravity into Dirac spinor Lagrangian is the Einstein–Cartan–Sciama–... | https://physics.stackexchange.com |
1,160,296 | [
"https://math.stackexchange.com/questions/1160296",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/211457/"
] | I need to evaluate $$\int \sin^{-1}(x)\cos^{-1}(x) \, dx.$$ Can anyone please give me an idea or a hint ? Thanks.
| we will use the fact that $\sin^{-1} x + \cos ^{-1} x = \pi/2$ and a change of variable $\sin^{-1} x = t, x = \sin t, dx = \cos t \, dt$ with these we get $\begin{align}\int \sin^{-1}(x)\cos^{-1}(x) \, dx &=
\int t(\pi/2 - t)\cos t \, dt \\
&=\int (\pi/2 t - t^2) \, d \cos t \\
&= (\pi/2 t - t^2)\cos t ... | If you prefer an answer that doesn't use trig identities, you can use integration by parts twice. You know the derivative of arcsin/arccos, and you can find the integral of the other through a table or another integration by parts. This will leave you with some function multiplied by another arccos or arcsin, depending... | https://math.stackexchange.com |
85,164 | [
"https://datascience.stackexchange.com/questions/85164",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/107215/"
] | I have a query regarding Pandas data manipulation.
Let's say I have a dataframe, df with following structure.
<pre><code>A B C
1 1 7
5 3 3
3 3 2
7 5 2
5 NaN 2
</code></pre>
We have 3 columns in the dataframe A, B & C.
B column consists of mean values wrt A.
For example,
Value of B in 3rd row (which is 3) is mean of... | Assuming you don't have NaNs in the first two entries of column B, the following code works
<pre><code>index_nan = df.index[df['B'].isna()] #get all indices where B has NaNs
new_df = pd.DataFrame({'B': [np.mean(df['A'][i-2:i+1]) for i in index_nan]}, index=index_nan)
df.update(new_df) #update those values of column ... | Thank you for the above answer!
That definitely works. However, I found a more efficient way in terms of computation using <code>np.rolling</code>
<code>df['D'] = df['A'].rolling(min_periods=1, window=3).mean()</code>
<code>df['B'] = np.where(df['B'].isnull,df['D'],df['B'])</code>
<ul>
<li><code>np.rolling</code> helps... | https://datascience.stackexchange.com |
380,847 | [
"https://mathoverflow.net/questions/380847",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6101/"
] | Let <span class="math-container">$K$</span> be a compact subset of <span class="math-container">$\mathbb R^n$</span> with <span class="math-container">$n\ge 2$</span> (say if you like <span class="math-container">$n=2$</span>, which is possibly sufficiently representative).
<strong>Q:</strong> <em>Does there exist a cl... | Not always.
Let <span class="math-container">$K$</span> be a subset of an ambient space <span class="math-container">$V$</span> (<span class="math-container">$V=\mathbf{R}^2$</span> is fine, but doesn't matter) that is the closure of a discrete subset <span class="math-container">$D$</span>, such that <span class="math... | Here is a proof that the answer is positive for a totally disconnected <span class="math-container">$K$</span>. I will prove it in the case <span class="math-container">$n\ge 3$</span> since for <span class="math-container">$n=2$</span> there exists a homeomorphism <span class="math-container">$h: R^2\to R^2$</span> se... | https://mathoverflow.net |
10,927 | [
"https://electronics.stackexchange.com/questions/10927",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3208/"
] | I've acquired some Sanyo Denki 103H5208-1241 stepper motors and I can't find the data sheet for it for the life of me. I've spelunked their catalogs and such looking for them.
Where can I find them or can I safely use another stepper data sheet interchangeably?
| If you have a specific part number and don't get a good result with the full thing, start stripping off parts and see if that helps. For instance, ATMEGA169PA-AU defines an exact part you can order, but searching for "ATMEGA169PA" or "ATMEGA169" probably would give more helpful results.
For your case, "103H5208-1241"... | Sanyo Denki
Type 103H5208-0842 or -1241
STEPPER MOTOR, 1.8 deg 200 steps/rev when full-stepping
PIN1 / RED = A
PIN2 / BLUE= B
PIN3 / YL = A-
PIN4 / ORG = B-
PIN5 / WHT = COMMON
PIN6 / BLK = COMMON
Description
1.6 or 2.0 ohm motors
Current per Phase: 1.2A unipolar 1A bipolar
External Depth: 39mm
External... | https://electronics.stackexchange.com |
275,633 | [
"https://mathoverflow.net/questions/275633",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Let $\kappa\geq\aleph_0$ be an infinite cardinal, and suppose that ${\cal A}$ is a collection of subsets of $\kappa$ such that for all $A\in {\cal A}$ we have $|A| = \kappa$ and for $A,B\in {\cal A}$ with $A\neq B$ we have $|A\cap B|<\kappa$. Is there $D\subseteq \kappa$ such that for all $A\in {\cal A}$ we have
<o... | This is false in general when $\kappa=\omega$. Let $\mathcal{A}=\langle A_\alpha:\alpha<\mathfrak{c}\rangle$ be an almost disjoint family of size continuum, and let $\langle D_\alpha:\alpha<\mathfrak{c}\rangle$ list all subsets of $\omega$.
For each $\alpha<\mathfrak{c}$, one of $A_\alpha\cap D_\alpha$ and $... | At least, this is true if $|\mathcal A|=\aleph_0$, and also if $|\mathcal A|<\kappa$.
In the former case ($|\mathcal A|=\aleph_0$) we can write $\mathcal A=\{A_1,A_2,\ldots\}$. Choose now elements $a_1\in A_1$, $a_2\in A_2$, $a_3\in A_3,\ldots$ so that $a_2\notin A_1$ (this is possible as $|A_2|>|A_1\cap A_2|$),... | https://mathoverflow.net |
554,088 | [
"https://physics.stackexchange.com/questions/554088",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262369/"
] | Is there any special reason why Pauli matrices are:<br>
<span class="math-container">$\sigma _1=\left(
\begin{array}{cc}
0 & 1 \\
1 & 0 \\
\end{array}
\right)$</span>, <span class="math-container">$\sigma _2=\left(
\begin{array}{cc}
0 & -i \\
i & 0 \\
\end{array}
\right)$</span>, <span class="math-c... | This apparent paradox is resolved by relativity of simultaneity.
Consider observer O at rest relative to points A and C, and observer O' moving towards point A. Both observers are at point B, equidistant between A and C.
Photons are emitted simultaneously from points A and C. This statement, in a question about relat... | Point B' is not the same distance away from A and C. Therefore, the photons will not reach point B' at the same time. The observer at B' will not see the photons cross; that observer will see one photon moving in one direction, and then, after some time delay, the other photon moving in the other direction.
| https://physics.stackexchange.com |
47,286 | [
"https://math.stackexchange.com/questions/47286",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/6418/"
] | If I have a poisson distribution for some variable x such that $\lambda = 100$, is it possible to linearly adjust that variable to generate probabilities for smaller increments?
For example, if I have on average 100 customers arriving an hour ($\lambda = 100$) can I generate probabilities for a half-hour period by sim... | Let us look at your example. You have a random variable $X$, which has Poisson distribution, with parameter $\lambda=100$. The probability that there will be $k$ "events" in time $t$, where $t$ is measured in hours, is<br>
$$e^{-100t}\frac{(100t)^k}{k!}.$$
Let $Y$ be a new random variable, the number of events in ti... | (Original answer deleted.)
EDIT: If $X = \{X_t: t \geq 0\}$ is a Poisson process with rate $\lambda$, then
$$
{\rm P}(X_t=k)=\frac{{e^{ - \lambda t} (\lambda t) ^k }}{{k!}}.
$$
Suppose that $\lambda=100$. If $t=1$, then
$$
{\rm P}(X_t=k)=\frac{{e^{ - 100} (100) ^k }}{{k!}},
$$
while if $t=1/2$, then
$$
{\rm P}(X... | https://math.stackexchange.com |
62,698 | [
"https://datascience.stackexchange.com/questions/62698",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/84845/"
] | I know how to feed data to a <strong>multi-output Keras model</strong> using numpy arrays for the training data. However, I have all my data in a single <strong>TFRecords file</strong> comprising several feature columns: an image, which is used as input to the Keras model, plus a sequence of outputs corresponding to di... | After playing around with <code>tf.data.map</code> operations I found the answer was easier than expected, I simply had to preprocess the data and put all the labels for each output of the model as a different key of a dictionary.
First I create a dataset from the tfrecords file
<pre><code>dataset = tf.data.TFRecord... | Considering your model recevie an <code>image</code> as input and has two outputs <code>age</code> and <code>gender</code>, and that you have generated a TFRecord with them. You can decode and use your TFRecord through <code>tf.data</code> this way:
<pre class="lang-py prettyprint-override"><code>decode_features = {
... | https://datascience.stackexchange.com |
849,324 | [
"https://math.stackexchange.com/questions/849324",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/119483/"
] | I am reading a paper which claims that the following series diverges:
$\sum\limits_{n=2}^{\infty}\frac{1}{nH_{n-1}}$ where $H_{n}$ is the $n$'th harmonic number $\sum\limits_{m=1}^{n}\frac{1}{m}$.
I tried a comparison test: Since $H_{n} < n$ each denominator $nH_{n-1} < n^{2}$ but that only lets me bound this f... | Use the estimate $H_{n-1}\le C\log(n)$ for a suitable constant $C$.
Then it suffices to show that $\sum^\infty_{n=2} \frac{1}{n\log(n)}$ is divergent, which follows by the integral comparison test:
$$\int_2^R \frac{dt}{t\log(t)}=\log(\log(R))+\text{const.}\rightarrow \infty$$
as $R\rightarrow\infty$, albeit the conv... | Integral test argument combined with the comparison $H_{n} \sim \log n$ is quite famous, so here I demonstrate another possible approach:
<blockquote>
<strong>Proposition.</strong> Suppose $a_{n} > 0$ and $\sum a_{n} = \infty$. If we denote $s_{n} = a_{1} + \cdots + a_{n}$, then
$$ \sum_{n=1}^{\infty} \frac{a_{... | https://math.stackexchange.com |
106,206 | [
"https://electronics.stackexchange.com/questions/106206",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/32739/"
] | I have some device with ac/dc adapter [9v, 500mA], and I want to replace the adapter with batteries.
If I used [6 * 1.5v] battries, is that acceptable? do I have to worry about the max current of the batteries? could the current of the batteries exceeds 500mA?
whenever I try to measure the current of the device conn... | You don't have to worry about providing too much current. The current is determined by the voltage and the load. To need to make sure that you can provide <em>enough</em> current.
In your case, it should work out fine. An AA battery (alkaline) can provide at least one amp, so your 500mA is within spec.
However, AA'... | If you wire your batteries up in series to get the voltage you require, the current will be the same as from a single battery, if you do need to change this you need to wire another set of 6 in parallel.
That having been said, a very quick search showed that most AA batteries are rated to give a max of about 2400mA, w... | https://electronics.stackexchange.com |
121,714 | [
"https://physics.stackexchange.com/questions/121714",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/971/"
] | I was on a commercial flight in a 737 stationary at idle on a taxiway. It had recently stopped raining so the relative humidity was likely near 100% and the air temperature was about "light jacket" level. I was in a window seat forward of the engine intake so I could see the whole intake.
Every 30 seconds or so a clou... | Your reasoning seems to be that because $\frac{t}{\sqrt{1-v^2}}\to \infty$ when $v\to 1$, it must be the case that $\frac{t}{\sqrt{1-v^2}}\to 0$ as $v\to 0$. But in fact when $v=0$ we have
$$
\frac{t}{\sqrt{1-v^2}} = \frac{t}{\sqrt{1-0^2}} = \frac{t}{\sqrt{1}} = \frac{t}{{1}} = t.
$$
So time does not pass infinitely ra... | There seems to be some confusion. First of all, there is no such thing as a concept of absolute or "complete" rest. Everything is moving in a different inertial frame. Second, time dilation works the other way around from what you described. You would be more likely to witness the end of the universe if you were travel... | https://physics.stackexchange.com |
24,934 | [
"https://quant.stackexchange.com/questions/24934",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/16991/"
] | <strong>Delta of an option is defined as ratio of change in price of call option to change in price of underlying securities</strong>. If, $c_t$ is call option price at time $t$ and $S_t$ is the price of underlying securities, then the delta of call option is:
$$\Delta(t)=\frac{\partial c_t}{\partial S_t}$$
If <stro... | Here, we assume that the bottom is zero and the top is $K_2-K_1$. Then, in mathematical form, the ${\color{blue} {blue}}$ option payoff is given by
\begin{align*}
& \ (K_2-K_1)\pmb{1}_{S_T \le K_1} + (K_2-S_T)\pmb{1}_{K_1 < S_T \le K_2} \\
=& \ (K_2-K_1)\pmb{1}_{S_T \le K_1} + (K_2-S_T)\left(\pmb{1}_{S_T \le... | Think like this:
<ol>
<li>Start with a long call option for K1. This would give you a payoff reflected at K1.</li>
<li>Short some cash to move the payoff vertically down.</li>
<li>Short a call option for K2. The payoff of this short option will offset the payoff of your long call option for <code>>K2</code>.</li>
<... | https://quant.stackexchange.com |
370,847 | [
"https://electronics.stackexchange.com/questions/370847",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/185290/"
] | I am designing a power supply for a flight controller, and I am finished with the regulating and almost everything else. I want to have a polyfuse on both of my inputs, but I don't know how to pick the right one. I don't really know much about the power consumption of the application, as it can vary. But, the maximum o... | <blockquote>
Can anyone explain I_trip and I_hold to me?
</blockquote>
The fuse is guaranteed not to trip if the current is less than I_hold.
The fuse is guaranteed to trip if the current is more than I_trip.
You need to choose a polyfuse with I_hold larger than your maximum load current consumption, or it may nu... | The I<sub>trip</sub> of a a polyfuse is the current at which the fuse 'trips'; when it goes high-impedance. Then, when it is in the high-impedance state, if the current through it goes below I<sub>hold</sub>, it will return to its low-impedance state (though not perfectly; it will still be higher resistance than it was... | https://electronics.stackexchange.com |
3,229,643 | [
"https://math.stackexchange.com/questions/3229643",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/673221/"
] | <blockquote>
Area defined by <span class="math-container">$x^2+y^2 \leq 1$</span> and <span class="math-container">$y\geq x(x^2-16)$</span>
</blockquote>
One very obvious way would be to find the points of intersection which would be messy and subject to many conditions. I was trying to solve this using polar coor... | Say <span class="math-container">$A$</span> is the set where <span class="math-container">$x^2+y^2\le 1$</span> and <span class="math-container">$y>x(x^2-16)$</span> and <span class="math-container">$B$</span> is the set where <span class="math-container">$x^2+y^2\le 1$</span> and <span class="math-container">$y<... | I would solve the System
<span class="math-container">$$x^2+y^2=1$$</span> and <span class="math-container">$$y=x(x^2-16)$$</span>
The solutions are looking terrible!
Taking a calculator we obtain
<span class="math-container">$${x\approx -0.0623934, y \approx 0.998052}, {x \approx 0.0623934, y \approx -0.998052}$$</spa... | https://math.stackexchange.com |
271,105 | [
"https://electronics.stackexchange.com/questions/271105",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/130931/"
] | When I was about 10 years old playing with lamps, I accidentally picked up a wire completing a circuit for a lamp plugged into the wall (120 V AC U.S. standard). I'm not sure if it was the hot or neutral wire, but I had completed the wire from hand to hand. I had a shock and dropped the wire in slightly less than a sec... | <strong>You got lucky.</strong>
Electrocution isn't an exact science. There are multiple things which make a difference:
<ul>
<li>The current which flows through a person depends on the resistance. That in turn depends on whether the skin is wet or dry, the area of skin in contact with the wire, and a lot of other bi... | Milliamps <em>can</em> kill you, but that doesn't mean it <em>will</em> kill you.
There are countless variables involved, one of the most important of which is your <em>skin resistance</em> (which limits current significantly if your skin is dry). Also, it sounds like the current flowed through your arm, down your sid... | https://electronics.stackexchange.com |
571,587 | [
"https://electronics.stackexchange.com/questions/571587",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/220456/"
] | I am trying to understand the working and function of the integrator and differentiator circuits using op-amps.
Can someone tell me why we need to use op-amps for that function? Selecting just the right value of RC components (appropriate time constant values) according to our input signal would also perform the same f... | You don't need the opamp, in theory. A simple, passive, RC circuit gives you am integrator or differentiator (otherwise known as first order low pass/high pass filter).
One problem is output impedance and loading. The opamp allows you to create a similar circuit which has very low output impedance, and whose characteri... | Yes - a simple RC circuit can be used (theoretically !) as an integrator - under the assumption that the time constant T=RC is very large. For example:, with R=100k and C=10µF the pole frequency is wp=1 rad/s and the range of intergation will approximately start for w>100 rad/s.
What does the opamp? It not only allo... | https://electronics.stackexchange.com |
4,525,187 | [
"https://math.stackexchange.com/questions/4525187",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1089967/"
] | Let <span class="math-container">$f:\mathbb{R}\rightarrow\mathbb{R}$</span> be a differentiable function with <span class="math-container">$f(0)=0$</span>. If <span class="math-container">$y=f(x)$</span> satisfies the differential equation <span class="math-container">$\frac{dy}{dx}=(2+5y)(5y-1)$</span>, then the value... | <span class="math-container">$F(y)=(2+5y)(5y−1)$</span> is positive for <span class="math-container">$y>\frac15$</span> and <span class="math-container">$y<-\frac25$</span> and negative on the interval in-between. Starting with <span class="math-container">$y_0=0$</span> the solution will thus fall between the co... | The solution of your DE is rather
<span class="math-container">$$x=\frac1{15}\ln\left|\frac{5y-1}{5y+2}\right|+C$$</span>
with <span class="math-container">$C$</span> given by
<span class="math-container">$$0=\frac1{15}\ln\frac12+C,$$</span>
hence
<span class="math-container">$$x=\frac1{15}\ln\left|\frac{2(5y-1)}{5y+2}... | https://math.stackexchange.com |
73,769 | [
"https://physics.stackexchange.com/questions/73769",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26264/"
] | We know
$$E = q V$$
where $E$ is the energy (in Joules), $V$ is the potential difference (in Volts), and $q$ is the charge. Why is this equation true and how we prove it?
| There are various ways to decide which of the assumptions are primary and which of them are their consequences but $E=VQ$ may be most naturally interpreted as the definition of the potential.
The potential energy is a form of energy and the potential (and therefore voltage, when differences are taken) is <em>defined</... | There are several (equivalent) ways to look at this. One is to say that for any conservative force <span class="math-container">$\mathbf{F}$</span>, one can <em>define</em> the potential energy <span class="math-container">$E_p$</span> as an associated potential field such as <span class="math-container">$\mathbf{F}=-\... | https://physics.stackexchange.com |
58,493 | [
"https://mathoverflow.net/questions/58493",
"https://mathoverflow.net",
"https://mathoverflow.net/users/39843/"
] | Is there an efficient algorithm for finding the solution $x$ of
$b = Ax$
that minimizes the Hamming weight of $x$, where
<ul>
<li>$A$ is a nxm-matrix over the field $\mathbb{F}_2$ ("integer matrix modulo 2") of rank $n$,</li>
<li>$n<m$, say $m=500$, $n=200$,</li>
<li>$b$ is a $n$-length fixed vector over $\mathbb... | No (unless P=NP). This is the decoding problem for error-correcting codes and it is known to be NP-complete.
| A reasonably good solution can perhaps sometimes be found with the LLL-algorithm:
Consider the lattice of $\mathbb Z^{m+1}$ spanned by $(\xi,1),(k_i,0)$ and the vectors $(2,0,\dots,0,0),(0,2,0,\dots,0,0),\dots,(0,\dots,0,2,0)$, where $\xi$ is an arbitrary solution (lifted to the integers) modulo $2$ and where $k_1,k_2,... | https://mathoverflow.net |
138,669 | [
"https://stats.stackexchange.com/questions/138669",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/36540/"
] | Many books and many posts on this site define the likelihood as a function of model parameters. However, does the output associated with every possible model parameter have to be unique? For example, it seems that for some two configurations of the model parameter, the observed data can be equally likely.
So, my ques... | <blockquote>
Many books and many posts on this site define the likelihood as a function of model parameters.
</blockquote>
If you specify a value for each of the parameters*, you will have at most one value for the likelihood.
<ul>
<li>(along with everything else you need to have specified, of course)</li>
</ul>
... | A real-valued function $f$ associates to a vector or real entry $θ\in\Theta$ a real number $f(θ)$, that is,
\begin{align*}f:\ \Theta &\longrightarrow \mathbb{R}\\ \theta &\longrightarrow f(\theta)\end{align*}Once the data $(x_1,\ldots,x_n)$ is observed and thus fixed, the <em>likelihood</em> associates with a g... | https://stats.stackexchange.com |
161,441 | [
"https://softwareengineering.stackexchange.com/questions/161441",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/37408/"
] | I've created an application framework using the unit of work and repository patterns for it's data layer. Data consumer layers such as presentation depend on the data layer design. For example a CRUD abstract form has a dependency to a repository (IRepository).
This architecture works like a charm in client/server env... | You can add idea 1 on top of idea 2. So I would start with idea 2.
I would avoid having lengthy conversation stored locally at the client end. It will result in synchronization complexity and the client may end up being very chatty (and thus slow).
Try looking at your web service as a facade. Try sticking to a single... | If you stop worrying about your data and start thinking about your domain model it will become much more clear. I now see you are stuck with unit of work, repositories, data operations, layers and adapters but you forget about your business.
What I would suggest to do is to have proper rich domain model designed and h... | https://softwareengineering.stackexchange.com |
724,778 | [
"https://math.stackexchange.com/questions/724778",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/117991/"
] | This is part of a larger problem where I am trying to find the derivative of a vector valued function. I feel like I'm missing something simple. NOTE: $c$ can be a function of $x$ and $y$.
| We compute
$$(x^2 - y^2)^2 + (2xy)^2 = x^{4} - 2x^{2}y^{2}+ y^{4} + 4x^{2}y^{2} = x^{4} + 2x^2 y^2 + y^4 = (x^2 + y^2)^2$$
Hence
$$\sqrt{(x^2 - y^2)^2 + (2xy)^2} = \sqrt{(x^2 + y^2)^2} = x^2 + y^2$$
We are trying to find $c$ for which
$$ (x^2 + y^2) \leq c \sqrt{x^2 + y^2}$$
If we let $z = x^2 + y^2$ we obtain
$... | If you think about where your quadratic function comes from, it is the representation of $z=(x+iy)^2 = (x^2-y^2)+i(2xy)$ where $z=x+iy$. So you want to be considering
$$|z^2| = |z|^2.$$
That is, your "constant" needs to be $|z|$.
| https://math.stackexchange.com |
632,003 | [
"https://electronics.stackexchange.com/questions/632003",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/320318/"
] | Apologies for poor phrasing and structure, this is my first post.
I am trying to learn how to implement 555 to create a PWM with variable duty cycle (for control of LED brightness)
Rather than the usual potentiometer route, I would like to use length of button press to control the duty cycle.
Eg. While Button presse... | Your design requires state-based control of an oscillator and PWM generator.
Two 555s can give you the oscillator and PWM generator. However, they're the much smaller part of your total circuit. The state-based control is the IC-hungry part if done with conventional circuitry.
Using an MCU makes for a far simpler circu... | What gave you the idea that you can build this using 555s only? I mean: yes, a 555 is good enough to implement a NAND gate, so theoretically you could build MCU using those, and run whatever code you'd want to - but that's not what you had in mind, right?
A 555, used as an analog building block, has rather ephemeral me... | https://electronics.stackexchange.com |
32,188 | [
"https://stats.stackexchange.com/questions/32188",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/144/"
] | I am doing a one way ANOVA (per species) with custom contrasts.
<pre><code> [,1] [,2] [,3] [,4]
0.5 -1 0 0 0
5 1 -1 0 0
12.5 0 1 -1 0
25 0 0 1 -1
50 0 0 0 1
</code></pre>
where I compare intensity 0.5 against 5, 5 against 12.5 and so on. These is the... | The matrix you specified for the contrasts is correct in principle. To convert it into an appropriate <em>contrast matrix</em>, you need to calculate the generalized inverse of your original matrix.
If <code>M</code> is your matrix:
<pre><code>M
# [,1] [,2] [,3] [,4]
#0.5 -1 0 0 0
#5 1 -1 ... | If the matrix at the top is how you are encoding the dummy variables (what you are passing to the <code>C</code> or <code>contrast</code> function in R) then they the first one is comparing the 1st level to the others (actually 0.8 times the 1st subtracted from 0.2 times the sum of the others).
The second term compare... | https://stats.stackexchange.com |
298,239 | [
"https://mathoverflow.net/questions/298239",
"https://mathoverflow.net",
"https://mathoverflow.net/users/123459/"
] | Let $\mathbb{R}$ act on itself by translation. Then there is no finite decomposition of a unit interval into pieces which, when translated, yields two distinct unit intervals.
More formally does there exist a partition of the unit interval $[0,1]$ into finitely many sets $S_1,...,S_n$ and a collection of finitely many... | No. Let $A$ be the free abelian group generated by the $r_a$s. We can view this as a lattice in the real vector space $A \otimes \mathbb R$. Let $n$ be the rank of this group / the dimension of this vector space.
There is a natural evaluation map $f: A \otimes \mathbb R \to \mathbb R$ from this vector space to $\mathb... | No choice is needed.
First, assuming such a paradoxical decomposition, we get another one in a large circle $C=\mathbf{R}/k\mathbf{Z}$. Now we have, on the subgroup $\Gamma$ generated by the $r_i$ (and by $x\mapsto x+1$), an explicit sequence of Følner subsets, and corresponding normalized $\ell^1$-functions $f_m$.
... | https://mathoverflow.net |
24,028 | [
"https://mathoverflow.net/questions/24028",
"https://mathoverflow.net",
"https://mathoverflow.net/users/39723/"
] | Hello,
I've been used to writing logical transformations using equality, but the other day it struck me that perhaps I should be using the biconditional $\iff$?
So my question is:
What is the difference between the biconditional iff. $\iff$ and equality = ? Can they be used interchangeably? And when should one b... | Usually the biconditional is denoted by $\leftrightarrow$ and logical equivalence is represented by $\Leftrightarrow$.
Given two compound propositions $P$ and $Q$, the proposition $P \Leftrightarrow Q$ means that $P$ and $Q$ have the same truth value for each possible combination of truth values of the variables of wh... | The worst problem with using equality in this way is that equality on propositions doesn't have a single meaning. Originally, in Boole's logic, it meant that one formula was obtained from another by a series of algebraic manipulations. Now, it might mean that the formulae belong to the same equivalence class in the L... | https://mathoverflow.net |
1,988,391 | [
"https://math.stackexchange.com/questions/1988391",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/383446/"
] | <blockquote>
The equation is given by the function $s: [0,4]\to \Bbb R$, $s(t)=t^4-4t^3+8t$. Where is the acceleration positive?
</blockquote>
<hr>
<ol>
<li>I know the velocity is $v(t)=4t^3-12t^2+8$</li>
<li>I know the acceleration is $a(t)=12t^2-24t$</li>
</ol>
I just can not get the where the acceleration is po... | <strong><em>Hint:</em></strong> Just solve the inequality $$a(t)=12t^2-24t \geq 0$$ for $t\in [0,4]$.
| Factor the acceleration,
\begin{align}
a(t) &= 12t^2-24t\\ &=12t \left(t-2 \right)
\end{align}
Note that the acceleration changes sign at the zeros and $t\geq0$.
| https://math.stackexchange.com |
245,557 | [
"https://electronics.stackexchange.com/questions/245557",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20711/"
] | While I understand that have 2 distinct shapes helps in determining which is pin 1, why does eagle have so many shapes: square, round, octagon, long, offset. Which is recommended under what circumstances?
| As well as being useful for marking particular pins, a square, octagonal or oblong pad has more copper area than a round hole of the same width. Through hole components such as connectors and large capacitors often have significant mechanical stress placed on them while the device is being operated or repaired. A large... | Because there are circumstances that you need to mark a pin in between of a series of pins. Each pin shape acts like a symbol. The pin shape recommendation depends on the allowed clearance between the pads (set by fabrication process), and your design. If it is High speed PCB then you have to account for signal interfe... | https://electronics.stackexchange.com |
188,926 | [
"https://physics.stackexchange.com/questions/188926",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/83396/"
] | Is the energy -momentum relation
$$E^2 = p^2c^2 + m_0^2c^4$$
satisfied only by free particles or even bound particles?
Does the Energy refer to total Energy(including potential) or only (kinetic +rest mass).
| The equation is just the kinetic and rest energy, it does not include potential energy. But potential energy in relativity is not the proper concept.
The linked question has some useful answers, but I think your true question is about how to learn to do things relativistically that you used to do non relativistically.... | In classical mechanics there is no distinction between free and bound as far as this relation is concerned.
In relativistic quantum mechanics (i.e. QFT), a particle that satisfies this relations is said to be "on-shell" or a physical observable asymptotically free particle. It is certainly not satisfied for virtual pa... | https://physics.stackexchange.com |
104,740 | [
"https://electronics.stackexchange.com/questions/104740",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/26231/"
] | I have a chip on one of my boards, and I cannot identify it. I tried differnet variations of search patterns but I cannot find it anywhere. The marking on the chip are in three rows as following:
0270000
DCP1227
0601
It seems to be 12 pins total, in groups of three pins in each corner.
<img src="https://i.stack.imgu... | It's a subtle point, but your thinking is going astray when you think of a 330-Hz tone as somehow conveying 660 bits/second of information. It doesn't — and in fact, a pure tone conveys no information at all other than its presence or absence.
In order transmit <em>information</em> through a channel, you need to... | This is only a partial answer, but hopefully it gets at the main points you're misunderstanding.
<blockquote>
My problem is that I'm having a hard time understanding why bandwidth relates to bit rate at all.
...
If a zero is expressed as a 30 Hz carrier frequency, a one is expressed as a 330 Hz carrier freque... | https://electronics.stackexchange.com |
248,815 | [
"https://dba.stackexchange.com/questions/248815",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/188976/"
] | I have came across several articles that mentioned that advise on not to store monetary value as decimal, but use integer instead.
The reasoning that it does not store actual value and will cause some rounding difference/errors.
But i have yet ever participate in any project that use an integer datatype for monetary va... | <blockquote>
The reasoning that it does not store actual value and will cause some rounding difference/errors
</blockquote>
This is only an issue if you are storing decimals as <em>floating point</em> decimals. A <code>float</code> should always be considered to be an <em>estimate</em> which is subject to rounding e... | If you go back as far as 1960, Fortran had three types of numbers: integers, floating point, and fixed point. Fixed point numbers were stored as integers, but with an implict power of ten multiplier. So, if you store 3.65 as a fixed point number with a scale factor of 2, the memory location would store the same bit ... | https://dba.stackexchange.com |
574,846 | [
"https://math.stackexchange.com/questions/574846",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93701/"
] | When I am going through some aptitude questions I have got this problem
<em>How many times the hours minutes and seconds hand will make equilateral triangle in 12 hours of clock</em>
I can't understand how they form the equilateral triangle as they can't be the sides of triangle, may be they should be median. If so I... | This kind of problem can be easier to handle if you rotate the clock backwards just fast enough to stop the hour hand. Then the minute hand will be seen to rotate at <span class="math-container">$330^{\circ}$</span> per hour, and the second hand at <span class="math-container">$60 \times 360 - 30 = 21570^{\circ}$</span... | A reasonable reading of the question is whether there are any times where the hands are spaced at angles of $120^\circ$. All angles will be in degrees. The hour hand moves $\frac 1{120}$ per second, the minute hand moves $\frac 1{10}$ per second and the second hand moves 6 per second. Starting at noon, the minute h... | https://math.stackexchange.com |
201,726 | [
"https://softwareengineering.stackexchange.com/questions/201726",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/52871/"
] | We've all had this experience. You go to someone who you know has the answer to a question, ask that person the question and they answer with the typical response: "why?" You explain why you need to know, and they attempt to solve your problem.
It takes time, arm twisting and patience to steer the conversation back to... | <blockquote>
<h3>Why do developers ask "why" when someone asks them how to implement a solution?</h3>
</blockquote>
Because it requires more knowledge to evaluate whether a solution is appropriate than it does to actually implement the solution.
It's very difficult to believe someone when they say, "I do... | "The question is specifically how does one engage with another programmer to ask a question, where the other has the answer and skip the debate about why the question is being asked."
You can't, at least not deterministically. The other programmer is a person, not a computer, and not your servant. If you ask them a q... | https://softwareengineering.stackexchange.com |
652,105 | [
"https://physics.stackexchange.com/questions/652105",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/305528/"
] | I understand that in terms of work done, 1 Joule is 1 newton exerted through a distance of one meter, following that logic, 2 Joules would equal 2 newtons exerted over a distance of two meters, right (<em>this to me makes sense, but mathematically doesn't work out</em>)? Also, I know that there are multiple ways to get... | No no, you are getting confused. As you already said One Joule is 1 Joule is 1 newton exerted through a distance of one meter.
Joules measure how much energy you need to give to the system to move it from point A to point B. And, as you rightly said it is measured by W=F*d. So <span class="math-container">$490 J$</span... | You seem confused in what a <strong>newton.metre</strong> actually is.
See, 10 N.m does not mean 10 newtons of force over 10 meters, that would be equal to a 100 Nm or 100 joules. The dot thing you see in between is a symbol for multiplication, as I'm sure you know.
So, 10 Nm = (x N)*(y m), where x and y can be any num... | https://physics.stackexchange.com |
599,864 | [
"https://physics.stackexchange.com/questions/599864",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/272285/"
] | Griffith's <em>Introduction to Electrodynamics, 4th Ed.</em> introduces the concept of Faraday's law by providing us with three experiments: one in which a coil is pulled out of a region of a constant magnetic field (the field is perpendicular to the area of the loop, not perpendicular to the area vector), the second w... | <blockquote>
Ultimately, and produce all electromagnetic fields, and changing the magnetic field merely delivers electromagnetic news from currents elsewhere.
</blockquote>
Here Griffith is referring to Jefimenko’s equations. Griffith correctly points out the fact that Maxwell’s equations do not have the form of a ca... | Any data communication relies on propagating electromagnetic waves. They are generated by a current in one place and converted into data, images, sound and the news elsewhere. This includes light, radio waves, internet etc. This is what is meant by the bold statement.
By the way, the statement 'a changing magnetic fiel... | https://physics.stackexchange.com |
723,604 | [
"https://physics.stackexchange.com/questions/723604",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/259747/"
] | A reference frame where Newton’s second law is valid is called an inertial frame of reference. Force is absolute, so is mass(for sufficiently small speeds), so if a frame is to measure an acceleration <span class="math-container">$a_1=\frac{F}{m}$</span>, given a frame <span class="math-container">$F_1$</span> measure... | The problem with accelerating frames is that the mathematics you need to use to keep track what is really accelerating becomes very messy and counter intuitive. Imagine you accelerate down the street in your car. In your accelerating frame, you are at rest, but everyone else in the world around you is suddenly accelera... | Newton's 2nd law is valid for this frame as well because in reality, Earth is also an accelerating frame. However, non inertial frames with respect to Earth are treated a bit differently: since
the observer themself is accelerating, they will observe that other objects are accelerating in opposite direction with respec... | https://physics.stackexchange.com |
37,058 | [
"https://dba.stackexchange.com/questions/37058",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7586/"
] | There are a bunch of databases on one of our SQL servers that have no owner. Generally speaking, is it harmful to give them one? For example:
<pre><code>USE dbName;
GO
EXEC sp_changedbowner 'sa';
GO
</code></pre>
I know sa may not be the best choice, but it is just an example. My primary concern is whether or not... | You should be using DDL instead of backward compatibility stored procedures:
<pre><code>ALTER AUTHORIZATION ON DATABASE::dbName TO sa;
</code></pre>
And the owner of the database (never mind <code>sa</code>) should probably not be the account that your applications use, so this should not really have any effect on yo... | By declaring a database owner, you give that user total control over a database. Database owners have full access to all data within all tables, be able to <code>CREATE/ALTER/DROP</code> objects within the database, etc. This can be good or bad, depending on your requirements. Typically, I set all database owners t... | https://dba.stackexchange.com |
23,199 | [
"https://security.stackexchange.com/questions/23199",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15419/"
] | I am looking at setting up a pre-pay system for the food retail industry. Retailers will be able to generate random 10 digit codes and supply these to customers to enter into an app to gain the value assigned to the code. My database is similar to the following
<pre><code> +----+-----------+-------------+-----------... | The basic principle looks pretty good.
A few thoughts:
<ul>
<li>When a token is used, don't delete it. Mark it as used, store a "used" date, and delete old tokens after 6 months. Otherwise the same token serial number might be re-created by accident, because the system has no record of it ever existing.</li>
<li>Can... | Looks like a good approach to me.
You might consider whether you foresee the need for dispute resolution. Depending upon your application, maybe it's not necessary, but I think dispute resolution and billing account for a substantial portion of the complexity and challenge of many payment systems.
I think you may wa... | https://security.stackexchange.com |
45,878 | [
"https://stats.stackexchange.com/questions/45878",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8180/"
] | I was doing ANOVA in SPSS and then in R and to my huge surprise, the results from the latest version of R were incorrect.
When I use the function <code>model.tables(x,"means")</code> to get descriptive statistics, the independent variable means by the second dependent are slightly incorrect (e.g. 129 instead of 130.27... | As you point out, the individual cell means match, but where you see the problem is in the marginal means. There are multiple ways to calculate the marginal means. Suppose that the data has information on sex (male/female) and age (old/young) and we want to calculate the margin for sex. One approach is to ignore the... | @mnel is correct in that because of the unbalanced design, the order of the terms matter in the output of <code>model.tables</code>.
ADDED: In the help file for <code>aov</code>, we read that it "is designed for balanced designs, and the results can be hard to interpret without balance." So if you want simple descr... | https://stats.stackexchange.com |
579,111 | [
"https://physics.stackexchange.com/questions/579111",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/120920/"
] | I'm working on a problem from YK Lim's "Problems and Solutions on Mechanics". It is Problem 1016. Here is the statement of the problem:
<blockquote>
A mass <span class="math-container">$m$</span> moves in a circle on a smooth horizontal plane with velocity <span class="math-container">$v_0$</span> at a radius... | Your calculation is correct. The question can be answered in two ways, depending on what you're trying to do.
<ol>
<li>It could be a tautology. "Fermionic" and "bosonic" often refer to a <span class="math-container">$Z_2$</span>-grading in which the product of two odd-graded operators is even-graded... | Remember <span class="math-container">$[b,b^{\dagger}]$</span> is a c-number, so it equals its own spectation value. And as <span class="math-container">$<0|c_{i}^{\dagger}c_{i}|0>=0$</span>, then you obtain the known result.
| https://physics.stackexchange.com |
88,745 | [
"https://dba.stackexchange.com/questions/88745",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/56177/"
] | I've got two database tables:
<pre><code>Persons
id user product
1 1 3
2 1 5
3 1 7
products
id kilo
3 8
5 15
7 3
</code></pre>
I'm wondering how to count values from a database, in this case I want to get the total kilo's of products for user 1. The result should be '2... | Put kilo inside the sum() function, like so:
<pre><code>SELECT sum(kilo)
FROM `products`
WHERE `id` IN (
SELECT `product`
FROM `person`
WHERE `user` = '1'
);
</code></pre>
| This will solve your problem, use <code>SUM</code> and join in 1 query.
<pre><code>SELECT SUM(`kilo`) total_kilo
FROM `person`
INNER JOIN `products`
on `person`.`product` = `products`.`id`;
</code></pre>
Or selecting/counting for user 1 alone
<pre><code>SELECT SUM(`kilo`) total_kilo
FROM `person`
INN... | https://dba.stackexchange.com |
372,758 | [
"https://electronics.stackexchange.com/questions/372758",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/187984/"
] | let me say if I have a pack of lithium batteries connected in series and parallels, and i want to connect it to an Inverter, BUT...BEFORE I connect it to inverter, lets say it gives out 12 volts "hypothetically" some informations like 3.7 volt batteries, and 2500 mAh,<br>
lets say then the pack gives 12 volts in DC an... | I think this question needs some serious sorting out. It has several parts:
<ol>
<li>Battery cell. A "primary battery cell" stores ENERGY, which is a certain amount of Watts over certain time. A cell with 3.7V nominal and C=2500 mAh holds about 9.25 W-hours of energy. You can dump all 9 Watts in one hour, or you can s... | @Ali Chen already answered this as full as it needs to be, but based on the comments there still seems to be some confusion. I'll try to rephrase and expand a few things to see if it clicks.
First, you are calculating Watt-hours (Wh), not Watts (W). If your battery bank has 55.5Wh capacity, it can deliver 1W for 55.5... | https://electronics.stackexchange.com |
94,928 | [
"https://softwareengineering.stackexchange.com/questions/94928",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31139/"
] | What approach could You suggest, If I don't have mysql or other database support on webhost, but I need to store data ( textual information ) for website somewhere. It's informative site for school - approx 20 to 50 visitors per day, 6 to 7 categories with 3 to 5 subcategories.
Would xml files be normal ?
| XML would be perfectly fine, especially with the amount of data I'm supposing you are going to be getting/generating, a csv type list with a parser of some sort (jscript, ajax, php) that could handle it would also be acceptable.
I would also contact your webhost to find out what they have for PHP support, because if t... | Unless your webhost did something to cripple PHP, you <em>do</em> have SQLite support. Thats built into PHP5. That only requires the ability to read/write to local files.
| https://softwareengineering.stackexchange.com |
646,529 | [
"https://physics.stackexchange.com/questions/646529",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/273010/"
] | Let's say we build a train track around the earth running from the Arctic to the Antarctic and back again. A train is going to run on this track at a speed of almost the speed of light lets say <span class="math-container">$299,792,457 \;\text{m/s}$</span> (<span class="math-container">$1 \;\text{m/s}$</span> less than... | SITTING PASSENGERS:
What they see outside:
<ul>
<li>looking back, the light they observe is so much redshifted (lowered in frequency) that their eyes see nothing. Not even expensive radio equipment could detect those such long waves.</li>
<li>looking forward, the light they observe is so much blue shifted, that it's in... | What physics says is that what you have proposed is strictly impossible. The energy required to accelerate the train could not be delivered to it. Gravity would not be sufficiently strong to constrain the train to the track. The train would burn-up with friction long before it reached a tiny fraction of light speed. Th... | https://physics.stackexchange.com |
91,583 | [
"https://mathoverflow.net/questions/91583",
"https://mathoverflow.net",
"https://mathoverflow.net/users/43162/"
] | I would like to work a theorem on a article who deals with the rank one symmetric spaces.
i looked up the definition of symmetric spaces of rank one, but I did not find a satisfactory definition then what is the meaning of rank, intuitively and mathematically? please if anybody already worked with rank one symmetric s... | First the algebraic definition. A (non-compact) symmetric space is of the form $G/K$, where $G$ is a (non-compact) semisimple Lie Group defined over $\mathbb{R}$, and $K$ is a maximal compact subgroup of $G$.
Then the rank of a symmetric space is the dimension of the "maximal $\mathbb{R}$-split torus", i.e. the maxim... | This question reminds me of when I was a graduate student. At some point Gelfand asked me "What is the rank of a symmetric space" and I just spat back the usual definition, something like what Matrix found in Wikipedia. Gelfand shook his head as if I had said something really stupid and proceeded to explain:
Euclidean... | https://mathoverflow.net |
4,603,501 | [
"https://math.stackexchange.com/questions/4603501",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
If <span class="math-container">$20 x^2+13 x-15$</span> can be written as <span class="math-container">$(a x+b)(c x+d)$</span>, where <span class="math-container">$a, b, c$</span> and <span class="math-container">$d$</span> are integers, what is <span class="math-container">$a+b+c+d$</span> ?
</blockquote>... | It may go without saying (I'm not sure about your needs) that <span class="math-container">$f^{-1}$</span> exists because <span class="math-container">$f$</span> is injective.
Questions:
<ol>
<li>Since <span class="math-container">$f^{-1}$</span> is continuous, sending <span class="math-container">$h\to 0$</span> also ... | The theorem is false. What if <span class="math-container">$f(x)=x^3$</span> on <span class="math-container">$[-1,1]$</span> ? Certainly <span class="math-container">$f$</span> is differentiable and injective (in fact bijective), but its inverse is not differentiable at <span class="math-container">$0.$</span>
The theo... | https://math.stackexchange.com |
245,061 | [
"https://softwareengineering.stackexchange.com/questions/245061",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32123/"
] | Wasn't sure how to phrase that title, sorry!
I've just come across this in our code base, and was wondering what the consensus was about how to unit test it:
<strong>C#</strong> (-ish, sorry, this is paraphrased from memory)
<pre><code>class DateCalculator
{
public static DateTime CalculateLeadTime(DateTime deliv... | You're making a big mistake when you put assumptions into your unit tests about how the unit is implemented.
Consider what would happen were the implementation of OrderService to change so that it no longer used DateCalculator (or, more generally, if you wanted to test a different implementation with the same unit tes... | Ideally you should change your design a little bit and decouple <code>OrderService</code> from <code>DateCalculator.CalculateLeadTime</code> by using dependency injection:
<pre><code>class OrderService
{
Func<DateTime,WidgetOrder> _calculateLeadTime;
public OrderService(Func<DateTime,WidgetOrder> ca... | https://softwareengineering.stackexchange.com |
46,601 | [
"https://physics.stackexchange.com/questions/46601",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/955/"
] | Is there some material state that can propagate light indefinitely without dissipation or absorption, like superconductors are able to transmit current indefinitely?
If not, then the question is, why not? would some fundamental principle being violated in such a material?
| As Claudius suggests, vacuum does not absorb. But that is not a material.
You can have light that travels through a material without absorption; that happens in nonlinear optics with self-induced transparency. The full theory behind that is rather involved and you need really high intensities for that. The basic pictu... | In a normal conductor the electrons sit in energy bands, so you can change the energy of an electron by an arbitrarily small amount. By contrast, in a superconductor there is an energy gap between the ground state energy and the first excited state energy of the electron pairs. This means you cannot raise the energy of... | https://physics.stackexchange.com |
96,933 | [
"https://security.stackexchange.com/questions/96933",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/121180/"
] | I understand most of the concepts behind hashing password but this one still escapes me.
I understand that you want the hash to take some time ( a couple milliseconds) so the attacker can't brutteforce. But at the same time you don't want the hashing to take too much computer resources.
Why don't you just hash and t... | Passwords are hashed for the case that an attacker can read the hashes from the database (e.g. SQL-injection). Afterwards he can brute-force with the full speed of his own environment, often with a GPU, this is called an offline attack.
A sleep on the other hand could only protect from online attacks, even then an att... | Hashes protect passwords in case the attacker gets hold of the password database. If adding <code>sleep</code> to authentication would be enough to prevent brute forcing it would automatically mean that your threat model allows for storing the passwords in the clear because you're only worried about online attacks. Sin... | https://security.stackexchange.com |
2,910,177 | [
"https://math.stackexchange.com/questions/2910177",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/495558/"
] | <blockquote>
Show that if $A,B \in \mathcal M_n(\mathbb{R})$ are positive semidefinite and $\lambda$ is an eigenvalue of $AB$ then $\lambda \geq 0$.
</blockquote>
I don't really know what to do here. If $AB$ was semidefinite positive we would be done but the product of positive semidefinite matrices doesn't have to ... | Let the unknowns be $\,a,b,c,d\,$ and divide the linear equations by $\,m_e\,$, then the system is of the form:
$$
\begin{align}
a^2 + b^2 &= r \tag 1 \\
c^2 + d^2 &= s\tag 2 \\
c + m a &= p \tag 3 \\
d + m b &= q \tag 4
\end{align}
$$
Substituting $\,c=p-ma\,$ and $\,d=q-mb\,$ from $\,(3)$-$(4)\,$ in... | What you have is two unknown vectors $v,w\in\Bbb R^2$ with
$$
\|v\|^2=c_1^2,\quad \|w\|^2 = c_2^2,\quad m_1v+m_2w = z,
$$
where $z\in\Bbb R^2$ is constant and also $c_1,c_2,m_1,m_2\in\Bbb R$ are constant. Hence,
$$
m_2^2c_2^2 = \|m_2w\|^2 = \|z-m_1v\|^2 = \|z\|^2-2m_1\langle z,v\rangle + m_1^2\|v\|^2,
$$
i.e.,
$$
2m_1\... | https://math.stackexchange.com |
313,015 | [
"https://math.stackexchange.com/questions/313015",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/62781/"
] | Assume $P$ is a partial order. Does it holds that $\inf (\inf(a,b), \inf(c,d)) = \inf(a,b,c,d) $? My guess is that it holds. But I don't know how to check it. Also what if instead of $\inf$ I use $\min$? It seems to be the same. Thank you for help!!
| The key words there are "for a suitable ordering of the elements of $A$ and $B$." (Another thing you may often see is "without loss of generality", or "WLOG".) It means that we may as well assume that it is precisely the first $k$ elements of $A$ are also in $B$--and if not, we'll simply reindex (relabel/rearrange) the... | Here's an alternative approach:
Let $n=|A|$, $m=|B|$. Let $A=\{a_1,\ldots,a_n\}$, $B=\{b_1,\ldots,b_m\}$.Then create the new set of pairs $P=\{(a_1,1),\ldots,(a_n,n),(b_1,n+1),\ldots,(b_m,n+m)\}$. Since all elements of $P$ are disjoint, we have $|P|=n+m$.
Now consider the function $i:P\to A\cup B$ given by $i((x,k)... | https://math.stackexchange.com |
321,549 | [
"https://stats.stackexchange.com/questions/321549",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17192/"
] | I have a dataset where every sample is taken at a certain time and belongs to a certain person. Every sample contains several features. I want to write (in mathematical notation) that a subset from this dataset is taken. This subset of the dataset are all samples up until some moment in time and can belong to all users... | Let $\mathbf{x}_{i, t}$ denote a sample (feature vector) taken at time $t$, belonging to person $i$.
Let $\mathcal{D}$ denote the full dataset.
Let $\mathcal{D_{t < \tau}} \subset \mathcal{D} = \{ \mathbf{x}_{i, t} \mid t < \tau \}$ denote the subset of all samples taken before time $\tau$.
A single sample for... | It looks like you are looking for something like "$x_{ut}\in\mathbb{R}^n$" to denote a sample taken from user $u$ at time $t$ and containing $n$ features.
To indicate the set of samples taken before a time $t_0$ and coming from a set $U$ of users (possibly a subset of the full set of users, you would write
$$ \{x_{ut... | https://stats.stackexchange.com |
116,467 | [
"https://mathoverflow.net/questions/116467",
"https://mathoverflow.net",
"https://mathoverflow.net/users/39742/"
] | Is there any counter example for the following statement?
STATEMENT:
Let $0 \to F \to A \to Q \to 0$ be a short exact sequence of abelian groups.
Assume that $F$ is a finite group, and $Q$ is a uniquely divisible abelian group.
Then, this exact sequence splits.
Please give me any advice.
| By "uniquely divisible", I guess you mean torsion-free and divisible, i.e., $Q$ is a $\mathbb{Q}$-vector space. If so, the answer to your question is that every such exact sequence splits.
It is enough to show $\mathrm{Ext}(Q, \mathbb{Z}/n) = 0$. We have an exact sequence
$$\hom(Q, \mathbb{Z}/n) \to \mathrm{Ext}(Q,... | I couldn't help thinking that there must be a lower-power proof of this. Here's what I came up with; I'd be interested if there are shorter proofs that are as elementary.
First, as both of the previous answers pointed out, unique divisibility makes $Q$ torsion-free; if there were non-zero $x\in Q$ and $n\in\mathbb ... | https://mathoverflow.net |
17,746 | [
"https://physics.stackexchange.com/questions/17746",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2653/"
] | In classical physics, I know the forces due to gravity and electrostatics. I know a lot of work has been done, but don't know the status. Is there a generally accepted theory of how the force is exchanged? If I understand correctly, electromagnetism works by exchange of photons. But electrical conductors interfere ... | The gluon description is fine, but gluons are quanta of a quantum field theory, and you can view a field theory as a theory of fields or as a theory of particles. The particles description is noncausal, the particles go back in time, so that the field description is more intuitive for me, although for some reason many ... | Forces are transmitted by the exchange of particles; photons in the case of electromagnetism, gluons for the strong force and the W/Z bosons for the weak force. The range of the force is determined by the mass of the particle. Photons are massless so the electromagnetic force has infinite range. The force is transmitte... | https://physics.stackexchange.com |
134,643 | [
"https://softwareengineering.stackexchange.com/questions/134643",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/14788/"
] | What factors do I need to consider when choosing names for identifiers such as variables? I am concerned about space issues, i.e. extra memory consumption when choosing longer names.
As an example, take these two variables:
<pre><code>bool noExp = true;
bool willNotExpireEver = true;
</code></pre>
Each one will take... | <blockquote>
Is there appropriate way to declare variables name to avoid memory or space issues.
</blockquote>
Variable names are mostly for humans. The C# compiler does not care about your name as long as it obeys language rules. So, to answer your question, there are no memory or space issues that could result jus... | First, to answer the obvious sub-question:
<blockquote>
"so is it better to name variables short..."
</blockquote>
Short answer: No.
Long answer: Variable-names are for the programmer's amusement only. The linker replaces references to variables with memory-addresses and there is no run-time overhead at all. Also... | https://softwareengineering.stackexchange.com |
539,440 | [
"https://stats.stackexchange.com/questions/539440",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/163146/"
] | One method to implement randomness in random forests is to use a random subset of the features for a split node.
What will be done at the next split node of the same branch beneath (that current / former split node)? Is it a random subset of the former subset, so, a subsubset? Because I think choosing a subset from the... | At each split, you draw a <em>new</em> random sample of <span class="math-container">$m$</span> features.
From Hastie et al. <em>Elements of Statistical Learning</em>:
<blockquote>
<strong>Algorithm 15.1 Random Forest for Regression or Classification.</strong>
<ol>
<li>For <span class="math-container">$b = 1$</span> to... | Looking at Chapter 15, second edition of Hastie, Tibshirani, Friedman "Elements of Statistical Learning", there is no subsubsetting. All features are available at all steps (by this mean that all features can be in the random feature subset that is used at each step - this is not constrained to those that wer... | https://stats.stackexchange.com |
1,153,458 | [
"https://math.stackexchange.com/questions/1153458",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/211307/"
] | If we have three events $A_i$ with $i=1,2,3$ with probability $\frac{1}{5}, \frac{1}{4}, \frac{1}{3}$ respectively. Let $X$ be the number of these events that occur.
Trying to write down a formula for $X$ in terms of indicators in order to find the expectation of $X$. Afterwards trying to find $\operatorname{Var}(X)$... | $$X=1_{A_1}+1_{A_2}+1_{A_3}$$
For expectiation you can use the linearity of the expectation function.
For variance in case of independent events you can use that $$\operatorname{Var}(U+V)=\operatorname{Var}U+\operatorname{Var}V$$ if $U$ and $V$ are independent.
For variance in case of disjoint events you can use that... | If $I(A)$ denotes the indicator of event $A$, then you've got $X = I(A_1) + I(A_2) + I(A_3)$, because you count 1 every time the corresponding event occurs. Apply the linearity of expectation to get $$E(X) = E(I(A_1)) + E(I(A_2)) + E(I(A_3)) = P(A_1) + P(A_2) + P(A_3).$$
For the variance, use the formula ${\rm Var}(X)... | https://math.stackexchange.com |
187,177 | [
"https://softwareengineering.stackexchange.com/questions/187177",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/80059/"
] | In environments where software is built internally by one team and then that software is used by other internal teams, how does one decide what the required quality should be for the produced artefacts? For example:
<ol>
<li>documentation completeness and accuracy</li>
<li>extensibility/re-usability of artefact (with... | I worked for a programming team which developed on top of a framework built by yet another internal programming team, so maybe I can share some insights I've learned.
While it's true that both teams are internal, in my experience, that grants you little extra freedom that you'd otherwise have if the objective is to pr... | <blockquote>
how does one decide what the required quality should be for the produced artefacts?
</blockquote>
I always strive for the best*, but be aware that there is a multitude of non-coding "things" that are potentially going to get in your way.
These can include scope creep, dependencies on other teams/depart... | https://softwareengineering.stackexchange.com |
476,929 | [
"https://electronics.stackexchange.com/questions/476929",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/185519/"
] | I have a transformer with 220 V primary and three secondaries;
<pre><code>1. 24 V | 1.2 A
2. 24 V | 600 mA
3. 12 V | 200 mA
</code></pre>
Each secondary have 4400uF capacitor and 100mH inductor after the bridge rectifier.
How can I estimate the inrush current and pick the proper thermistor value for limiting the inr... | There are two inrush currents, capacitor charging, and transformer saturation.
Unfortunately, they both depend on the resistance of the transformer, and the saturation inrush depends on the detail of the transformer magnetising curve, so it's somewhat easier to measure them than to gather enough good data to calculate... | You have two reasons for the inrush:
1) the iron core has been left to saturated state since the last usage.
2) the initial charging of the capacitors.
Reason 1 causes an inrush pulse which must be measured. Your linked story that you said to be too advanced is the way to find a way around it. Do not have any loa... | https://electronics.stackexchange.com |
35,601 | [
"https://electronics.stackexchange.com/questions/35601",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9458/"
] | I'm building an amplifier in a conductive metal chassis. The general grounding plan is to have an audio ground, a power ground, and a digital ground that converge at a single point on the chassis. However, my audio connectors are all panel-mount, so the shield of the connectors get grounded by contact when mounted. Tec... | Yes you should insulate the chassis ground also, from the ground star connection at the Poewr Supply.
The chassis should be connected to Earth terminal, right on the Power Input, thus all signals after the transformer should be isolated from the chassis.
Yes it matters if you insulate, because insulation from Earth a... | Often connectors have a dedicated chassis pin so you can add a selection jumper on the PCB to set as desired (e.g. chassis, floating, or circuit grounds) We used a similar connector the one below in one of our products, you can see the 4th chassis pin at the side of the "standard" pins:
<img src="https://i.stack.im... | https://electronics.stackexchange.com |
296,076 | [
"https://mathoverflow.net/questions/296076",
"https://mathoverflow.net",
"https://mathoverflow.net/users/85336/"
] | Let $L$ be a two-dimensional subspace in the space of all linear operators from $\mathbb{E}$ to $\mathbb{F}$ ($\mathbb{E}$ and $\mathbb{F}$ are linear spaces, possibly finite-dimensional). Let $A,B,C$ be three non-proportional (i. e. every two of them form a basis for $L$) linear operators from $L$. It is easy to prove... | A generalization should be like this.
<strong>Proposition.</strong> Let $L$ be a two-dimensional subspace in the space of all linear operators from $\mathbb{E}$ to $\mathbb{F}$ ($\mathbb{E}$ and $\mathbb{F}$ are finite-dimensional linear spaces). Suppose there are $k+2$ pairwise non-proportional operators $A_{1},\ldot... | Nope. Take $A = {\rm diag}(1, 1,0)$, $B = {\rm diag}(-1,0,1)$, and $C = {\rm diag}(0,1,1)$. Then $A + B = C$ so they are non-proportional, and each of them has rank $2$, but $2A + B = {\rm diag}(1, 2, 1)$ has rank $3$.
| https://mathoverflow.net |
161,979 | [
"https://dba.stackexchange.com/questions/161979",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/69166/"
] | We have a MySQL master server here which was not set up with any kind of management for the binary logs. Over time, the disk space (1 TB) was slowly filling up and it was noticed that the performance of the MySQL server was becoming worse. At the time, I didn't make any connection between disk space issues and performa... | <blockquote>
Can a lack of free disk space impact MySQL performance?
</blockquote>
Certainly a lack of disk space at all can prevent writes from happening. Especially when storage is beginning to become full (>90%, as a minimal ballpark) and the disks are fragmented, it can take some time to search where writes can ... | Is the space used by database table files? if so, yes it could affect performance if the query must read data from disk. That is why it is always a good idea to defrag tables to free up unused space. Again the performance will be depended on what kind of disk your sever is using.
| https://dba.stackexchange.com |
43,722 | [
"https://mechanics.stackexchange.com/questions/43722",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/15857/"
] | I filled up my lawnmower from a gas can earlier today and spent about 15 minutes trying to pull start it. I've checked the oil level and color and both seem fine to my inexpert eye. On two separate occasions, it seemingly randomly started and ran for about 10 seconds or so, but I haven't been able to get a third. I had... | Yes, replace the spark plug - just make sure it has the correct gap before you fit it. And, at worst you end up with a used spare...
| I would ground the outside of existing spark plug on the engine first, and verify that you can see a spark jump the exposed gap. Not the same as in a combustion chamber under pressure, but at least this way you establish that the magneto/ignition system is doing something.
| https://mechanics.stackexchange.com |
652,209 | [
"https://physics.stackexchange.com/questions/652209",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/271429/"
] | How do you explain photon as quanta of light?
I thought of photons as quanta of light which are the smallest unit of light.
But then I learned a photon can be split into two or even three photons (red-shifted, energy is conserved), and also photon can lose energy and still be a photon (Raman effect, inelastic scatterin... | Photons are quanta of light at any given frequency and corresponding wave length. If there is a laser beam at wave length <span class="math-container">$\lambda$</span>, it consists of photons which each carry an energy of
<span class="math-container">$$
E_\gamma = h \nu = h \frac c \lambda~,
$$</span>
where <span class... | nu’s answer is correct. Conceptually, the answer is that the photon is the minimum amount of light at a certain frequency. If it loses energy, it goes to a lower frequency. The energy is proportional to the frequency. If a photon splits into photons (without energy added or subtracted), the frequencies of the new photo... | https://physics.stackexchange.com |
166,162 | [
"https://physics.stackexchange.com/questions/166162",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/73619/"
] | <img src="https://i.stack.imgur.com/DyTVl.png" alt="picture of bead on hoop">
This is problem 10.13 from Fowles and Cassiday, 7e. A bead of constant mass m is constrained to slide along a thin, circular hoop of radius $l$ that rotates with constant angular velocity $\omega$ in a horizontal plane about a point on its r... | The problem is that you are thinking of defining two coordinate systems, and then trying to combine them. This is incredibly dicey and requires extremely precise thinking to make sure all terms are accounted for. I would go so far as to call it a nightmare.
Instead, just think of the position of the particle as the su... | Yeah, it looks like your generalized coordinate is simply $\theta$. If the expressions that you're getting don't seem right, then probably you're just trying to skip too many steps at once. The kinetic energy is going to be $T \propto v_x^2 + v_y^2$; we'll compute it that way alone. Let $\phi = \omega t$. The position ... | https://physics.stackexchange.com |
649,164 | [
"https://electronics.stackexchange.com/questions/649164",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/330010/"
] | What does it mean when a lightbulb is rated at 60W with 220V?
My understanding is that the input power to the lightbulb will be 60W. But what about 220V? Is it the amount of voltage the lightbulb should use?
What if you place multiple lightbulbs in series and use a 220V power supply? 220V is no longer dropped across it... | Device ratings in general can be confusing. Usually if a device that consumes power is rated at X Volts, that means that all the other ratings hold when you hold its input to X Volts. Also usually, if a device is rated at Y Watts at X Volts, then that <em>either</em> means it will consume Y Watts, or in the case of t... | <blockquote>
What does it mean when a lightbulb is rated at 60W with 220V? My understanding is that the input power to the lightbulb will be 60W. But what about 220V? Is it the amount of voltage the lightbulb should use?
</blockquote>
Yes.
<blockquote>
What if you place multiple lightbulbs in series and use a 220V powe... | https://electronics.stackexchange.com |
4,053 | [
"https://engineering.stackexchange.com/questions/4053",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/2688/"
] | I live and work in the UK, a country known for relentless roadworks.
Last week I drove through roadworks on the M1 that lasted for 18 miles, necessitating road users driving at 50 mph. Of course, almost all of this impressive stretch was simply coned off, with active work only present on one or two small sites. Signs... | I'll give you some considerations that you may not be aware of. Also, take the disclaimer that I'm in the US (but construction is construction, right?)
<ol>
<li>Frequently moving construction cones/barrels along the road is less efficient than setting them out once and only making minor adjustments to their location.<... | There is some merit in the argument that one mile on one mile off construction would be dangerous. Works vehicles would have to enter and exit every mile from live traffic. They'd go from 50mph to some stupid speed like 2mph and back every mile go get along the works.
I would seriously question though whether it's c... | https://engineering.stackexchange.com |
33,432 | [
"https://stats.stackexchange.com/questions/33432",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12492/"
] | I have ran a glm in R, and near the bottom of the <code>summary()</code> output, it states
<pre><code>(Dispersion parameter for gaussian family taken to be 28.35031)
</code></pre>
I've done some rummaging on Google and learnt that the dispersion parameter is used to fit the standard errors. I'm hoping somebody could ... | One way to explore this is to try fitting the same model using different tools, here is one example:
<pre><code>> fit1 <- lm( Sepal.Length ~ ., data=iris )
> fit2 <- glm( Sepal.Length ~ ., data=iris )
> summary(fit1)
Call:
lm(formula = Sepal.Length ~ ., data = iris)
Residuals:
Min 1Q Medi... | Let us speculate the simple situation where there is no covariate information in your data. Say, you just have observations $Y_1, Y_2, \ldots, Y_n \in \mathbb{R}$.
If you are using normal distribution to model your data, you would probably write that
$Y_i \sim \mathcal{N}(\mu, \sigma^2)$,
and then try to estimate $... | https://stats.stackexchange.com |
286,367 | [
"https://electronics.stackexchange.com/questions/286367",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/138650/"
] | I need some help designing a high current test. I know just the basic concepts of circuits so any help would be appreciated. I currently have a programmable DC power supply that can supply up to 220 Amps. I need to increment the current up to 200 Amps max through all 5 parts and measure the temperature rise. The curren... | If I measure \$R_s\$ will the measurement depend on the frequency of the RLC bridge?<br>
Generally, your bridge measurement will be larger than an ohmmeter measurement. <em>How much larger</em> depends on the quality of the inductor.
<ul>
<li>Skin resistance of the inductor's wire will increase at higher frequencies.... | A common Ohmmeter measures with a constant voltage or current. So after a short time - at usual values less than a second - you get Rs.
| https://electronics.stackexchange.com |
710,953 | [
"https://physics.stackexchange.com/questions/710953",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/318923/"
] | If you have a coil with self inductance:
<span class="math-container">$$ \varepsilon= - L \frac{dI}{dt} $$</span>
Then the current is lagging behind the voltage.
If you attach a AC source on the coil/inductor and have an AC power source, then at the highest current there is no internal resisting voltage produced bij th... | The standard Kirchoffs law does not hold. This is because there are changing magnetic fields.
Imagine I have a battery and an inductor, such that the inductance L is the inductance of the entire circuit.
<strong>Using faradays law:</strong>
<span class="math-container">$$\int \vec{E} \cdot \vec{dl} = -\frac{d \phi_{B}... | In AC circuits "voltage on inductor" means difference of electric potential between the inductor's two terminals. In your example where ideal voltage source is driving the circuit with ideal inductor, drop of potential on inductor is determined by the voltage source. For the simplest AC source, it is sinusoi... | https://physics.stackexchange.com |
160,699 | [
"https://electronics.stackexchange.com/questions/160699",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70405/"
] | I am trying to control speed of a DC motor using PWM. To reduce coupling of motor noise onto my electronics, I am using a separate power supply for both(LED and Phototransistor) and am planning to interface PWM pin from µC to motor using 6N137 optoisolator. Speed of PWM is about 20KHz as recommended by motor manufactur... | In the case of the second circuit have you made sure that the GND2 connects to the return of the 5V output supply?
I ask this because if this connection is open it could explain why the coupler is unable to pull the output low. This particular case would be where the GND connection of your scope or meter is properly c... | For the second circuit have you made sure that the GND1 connection from pin 3 of the coupler is connected to the GND of the driving circuit?
I ask this because one explanation for the non functioning of the circuit is due to your not getting any current flowing through the input diode. (You could verify input diode ... | https://electronics.stackexchange.com |
363,390 | [
"https://mathoverflow.net/questions/363390",
"https://mathoverflow.net",
"https://mathoverflow.net/users/153407/"
] | Let <span class="math-container">$S_n$</span> denote a simple random walk with i.i.d. increments <span class="math-container">$X_i$</span> such that <span class="math-container">$P(X_1 = 0) = P(X_1=1) = 1/2$</span>, i.e. <span class="math-container">$$S_0 = 0, \ S_n = X_1 + \dots + X_n.$$</span>
The behavior of <span c... | <span class="math-container">$\newcommand\D{\overset D=}$</span>
If <span class="math-container">$|q|<1$</span>, then, by the strong law of large numbers, there is a positive integer-valued random variable (r.v.) <span class="math-container">$N$</span> such that <span class="math-container">$S_k>k/4$</span> a.s. ... | The function <span class="math-container">$\lim \limits_{n \to \infty} f(x)=\sum_{k=0}^{n-1} q^{s_k}x^k$</span> becomes,
<span class="math-container">$f(x)=\sum_{k=0}^{\infty} q^{s_k}x^k$</span>.
From root test we get that radius of convergence of the series is
<span class="math-container">$\lim \limits_{n \to \infty} ... | https://mathoverflow.net |
187,297 | [
"https://mathoverflow.net/questions/187297",
"https://mathoverflow.net",
"https://mathoverflow.net/users/61387/"
] | I am interested in the type of program, which is given as input to a Universal Turing Machine (UTM) with language $L$, and for which it holds that every possible finite string $s$ of symbols in $L$ appears in the output. I am writing a paper in which I call such a program a Universal Turing Program (UTP). There are inf... | The answer seems to be no, this is not decidable.
You seem to have a concept in mind of what it means for a program
$p$ to be UTP, and it involves the idea that pieces of any given
computation history of any other program (on some fixed input)
appear on the tape during the computation of $p$ on the trivial
input.
Alt... | This might be more comment than answer, but --
This a standard trick -- running all TMs in parallel -- but I don't know if it has a name. You can probably find it used in introductory complexity textbooks like Sipser, somewhere. One keyword is "Godel numbering", which refers to the ordering of programs that you mentio... | https://mathoverflow.net |
381,030 | [
"https://physics.stackexchange.com/questions/381030",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/174725/"
] | In a dielectric medium with relative dielectric constant $\epsilon_r$, what is the Coulomb force between two free point charges $q_1$ and $q_2$ at distance $r$? Is it equal to the Coulomb force in vacuum divided by $\epsilon_r$ or $\epsilon_r^2$, i.e., whether the formula is
$$F=\frac{q_1q_2}{4\pi\epsilon_0\epsilon_rr... | The Coulomb force in a medium with relative dielectric constant $\epsilon_r$ is given by your first equation. Only from this follows the electric field strength of a spherical symmetric free charge $Q$ in the dielectric with $$E=\frac{Q}{4\pi\epsilon_0\epsilon_r r^2} \tag{1}$$ which, with the electric displacement $D=\... | The force analysis of the problem is done thanks to @freecharly. I now work it out using two other methods: virtual work and field energy. Suppose charge $q_1$ is fixed and charge $q_2$ moves along the rope by a small virtual displacement $\delta r$ away from $q_1$. The Coulomb field due to the net charge $q_1/\epsilon... | https://physics.stackexchange.com |
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