qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
2,962,696 | [
"https://math.stackexchange.com/questions/2962696",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/596442/"
] | I want to calculate this integral without residue theorem: <span class="math-container">$$ \int_0^{2\pi} \frac{1}{\cos^2(x) +2\sin^2(x)}\,\mathrm{d}x$$</span>
I know the antiderivative: <span class="math-container">$$ \int \frac{1}{\cos^2(x) +2\sin^2(x)} \mathrm{d}x = \frac{\arctan(\sqrt{2}\tan(x))}{\sqrt2}$$</span... | The error in the original argument is that if you treat <span class="math-container">$\arctan$</span> as being a function, for example choosing the principal branch which has range <span class="math-container">$(-\frac{\pi}{2}, \frac{\pi}{2})$</span>, then <span class="math-container">$F(x) = \frac{\arctan(\sqrt{2} \ta... | Note that
<span class="math-container">$$I=\int_{0}^{2\pi}\frac{dx}{\cos^2x+2\sin^2x}=\int_{0}^{2\pi}\frac{dx}{1+\sin^2x}=\int_{0}^{2\pi}\frac{\csc^2x}{2+\cot^2x}dx=2\int_{-\infty}^{\infty}\frac{du}{u^2+2}, $$</span>
where <span class="math-container">$u=\cot x$</span>. Since integrand is an even function and the int... | https://math.stackexchange.com |
189,447 | [
"https://mathoverflow.net/questions/189447",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12395/"
] | According to Chapter 4 of Beilinson, Bernstein, and Deligne's "Faisceaux Pervers" (Asterisque 100, 1980) the inverse image $Rf^*$ with respect to a finite morphism $f$ is right t-exact with respect to the perverse t-structure. Is there an example that shows that it is not necessarily t-exact? Is there a class of finite... | By Noether normalisation any affine variety admits a finite map $f$ to affine space. Hence it is enough to find an example of an affine variety for which the constant sheaf is not perverse. (In this case $f^* \mathbb{Q}_{\mathbb{A}^n}[n]$ will provide a counter-example.)
Now it is easy to find examples where the const... | My idea was to consider $f \colon X \to Y$ of dimension $d$ such that $a_Y^\ast \mathbf Q[d] \cong IC_Y$ but $a_X^\ast \mathbf Q[d] \not\cong IC_X$, where $a$ denotes the map to a point and all functors are derived. Then $a_X^\ast \mathbf Q[d] = f^\ast IC_Y$ can not be perverse, so $f^\ast$ is not t-exact.
(Incorrect... | https://mathoverflow.net |
62,047 | [
"https://mathoverflow.net/questions/62047",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8257/"
] | Let $K$ be the field of fractions of
$\mathbb{C}[[z]]\otimes_{\mathbb{C}}\mathbb{C}[[w]]\subset \mathbb{C}[[z, w]].$ Given
a formal power series in $t, f\in \mathbb{C}[[t]],$ is there any simple criterion which
will conclude that $f(zw)$ does not belong to $K?$ I suspect that
$f(zw)\in K$ if
and only if $f(t)$ is a r... | <strong>Theorem 1.</strong> Let $f\in\mathbb{C}[[t]]$. Then $f(zw)\in \mathbb{C}[[z]]\otimes_{\mathbb{C}}\mathbb{C}[[w]]$ if and only if $f\in\mathbb{C}[t].$
<strong>Proof.</strong> The "if" part is obvious. For the "only if" part assume that $f\notin\mathbb{C}[t]$ but
$$f(zw) = \sum_{i=1}^n g_i(z)h_i(w),$$
where $g_i... | If $e^{zw}=\frac{\sum_{i=1}^{a} f_i(z)g_i(w)}{\sum_{j=1}^b u_j(z)v_j(w)}$,
$e^{zw}(\sum u_j(z)v_j(w))=\sum f_i(z)g_i(w)$
$\frac{\partial^{n}}{\partial w^n}e^{zw}(\sum u_j(z)v_j(w))=\frac{\partial^{n}}{\partial w^n}\sum f_i(z)g_i(w)$
$\sum_{k=0}^n C^k_n z^k e^{zw}(\sum u_j(z)v^{(n-k)}_j(w))=\sum f_i(z)g_i^{(n)}(w)$
... | https://mathoverflow.net |
3,644,117 | [
"https://math.stackexchange.com/questions/3644117",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/756147/"
] | I am reading Fraleigh in which Fraleigh proves that <span class="math-container">$f(x) = x^3 + 3x+ 2$</span> is irreducible over <span class="math-container">$\mathbb{Z}[5]$</span>. He explains that the if <span class="math-container">$f(x) = x^3 + 3x+ 2$</span> were reducible over <span class="math-container">$\mathbb... | <strong>The answer is <span class="math-container">$5$</span>.</strong>
Much thanks to @JohnBentin for pointing out the embarrassing flaw in my previous solution.
We may easily calculate the values of <span class="math-container">$a_2,a_3$</span> and <span class="math-container">$a_4$</span> by hand, and this gives u... | Start from recurrence relation <span class="math-container">$a_{n+1} = a_n(a_n+1)$</span>, it is clear if we start from any <span class="math-container">$a_1 > 0$</span>, <span class="math-container">$a_n$</span> will be a strictly increasing sequence.
If for some <span class="math-container">$N$</span>, we have <s... | https://math.stackexchange.com |
311,334 | [
"https://stats.stackexchange.com/questions/311334",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/171377/"
] | I'm trying to analyze results from two areas at two different time points. On area A we performed an intervention, and on area B we did not. Then we asked customers whether they liked a particular part of our service, and we did that before and after our intervention. The customers were different in the two periods, so... | The difference in differences is what is called an interaction in statistics (as Dimitriy Masterov has already pointed out). You want to test whether the time effect is different when you intervene compared with when you don't.
Your data is most naturally modelled as binomial, i.e., the number of top scores out of tota... | The easiest solution is to use the linear regression formulation of DID:
<ol>
<li>Regress the binary customer ratings on a constant, a post dummy, an area A dummy, and the interaction of last two. It may be appropriate to add other regressors measuring characteristics that are time-invariant at the individual level, b... | https://stats.stackexchange.com |
218,247 | [
"https://physics.stackexchange.com/questions/218247",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98369/"
] | Is potential energy calculated between a system? More specifically, if we say 'potential energy of a ball with respect to earth', does it mean that the Earth + the ball is a system?
| Potential energy is the energy due to configuration of the system.
If you keep three charges very, very far from each other, then the potential energy of the system is very effectively zero.
But when you bring them close together to a specified coordinate, then the <strong>potential energy of the system</strong> in... | Potential Energy is calculated of a system, ie, a system possesses potential energy and the capacity to do work with it. If you a raise a ball of weight <em>mg</em> to a height <em>h</em> above the surface of the earth, then the total potential energy of the ball will be <em>PE = mgh</em> as you have done work against ... | https://physics.stackexchange.com |
7,155 | [
"https://stats.stackexchange.com/questions/7155",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1347/"
] | People often talk about dealing with outliers in statistics. The thing that bothers me about this is that, as far as I can tell, the definition of an outlier is completely subjective. For example, if the true distribution of some random variable is very heavy-tailed or bimodal, any standard visualization or summary s... | As long as your data comes from a known distribution with known properties, you can rigorously define an outlier as an event that is too unlikely to have been generated by the observed process (if you consider "too unlikely" to be non-rigorous, then all hypothesis testing is).
However, this approach is problematic on ... | You are correct that removing outliers can look like a subjective exercise but that doesn't mean that it's wrong. The compulsive need to always have a rigorous mathematical reason for every decision regarding your data analysis is often just a thin veil of artificial rigour over what turns out to be a subjective exerc... | https://stats.stackexchange.com |
898,181 | [
"https://math.stackexchange.com/questions/898181",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/94971/"
] | I just analysed this equation for real matrices
$$
A^2=\begin{pmatrix}a&b\\c&d\end{pmatrix}^2=I
$$
From the main diagonal of $A^2$ we must have $a^2+bc=bc+d^2=1$ showing that $d=\pm a$.
<strong>CASE 1:</strong> If $b=0$ we have $a^2=d^2=1$ so then $c=0$. If $c=0$ the same argument renders $b=0$.
<strong>CASE... | Since $A^2=I$, the minimal polynomial of $A$ has simple roots, and therefore $A$ is diagonalisable. $A=P^{-1}DP$ with $P$ invertible and $D$ diagonal. The equation $A^2 = I$ implies $D^2=I$ so $D$ is a diagonal matrix with $1$ or $-1$ on the diagonal.
Conversely, if $D$ is a diagonal matrix with $\pm 1$ on the diagona... | This is an alternative method to find all possible $2\times 2$ matrix $A$ such that $A^2=I$ so the polynomial $x^2-1$ with simple roots $\pm1$ annihilates $A$ and then $A$ is diagonalisable over $\Bbb R$ and
$$\operatorname{sp} A\in\{-1,1\}$$
hence
<ul>
<li>if $\operatorname{sp} A=\{1\}$ then $A=I$</li>
<li>if $\ope... | https://math.stackexchange.com |
3,231,340 | [
"https://math.stackexchange.com/questions/3231340",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/63178/"
] | In my Calculus lecture, we were given the following exercise to solve in class:
<blockquote>
Find the value of <span class="math-container">$c$</span> that makes <span class="math-container">$|x - 3| < 1 \Rightarrow |x + 5| < c$</span> true.
</blockquote>
This is what I came up with:
<span class="math-contai... | <span class="math-container">$|x-3|<1$</span>
<span class="math-container">$-1<x-3<1$</span>
<span class="math-container">$2<x<4$</span>
<span class="math-container">$2+5<x+5<4+5$</span>
<span class="math-container">$7<|x+5|<9$</span>
So, <span class="math-container">$c \ge9$</span>
| <span class="math-container">$c$</span> should be a constant. And <span class="math-container">$|x-3|<1$</span> implies <span class="math-container">$2<x<4$</span>. Now compute the distance between <span class="math-container">$x$</span> and <span class="math-container">$-5$</span>, we have <span class="math-c... | https://math.stackexchange.com |
116,388 | [
"https://cs.stackexchange.com/questions/116388",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/111265/"
] | I was trying to approach this proof, after multiple reads and attempts I am getting nowhere. If someone could help me out that would be great. Should I use the pumping lemma, if so how show I start, what word should I choose? Or should I use closure-properties and if so what irregularity should I show? I am genuinely s... | Let <span class="math-container">$L = \{0^i1^j : i \neq j\}$</span>. You can prove that <span class="math-container">$L$</span> is not regular in many ways. Here are some examples.
<strong>Closure properties</strong>
If your language were regular then so would <span class="math-container">$0^*1^* \setminus L$</span> ... | The language <span class="math-container">$L=\{0^i 1^j : i \neq j\}$</span> can be written equivalently as <span class="math-container">$L=\{0^i 1^j : i \lt j\} \cup \{0^i 1^j : i \gt j\} = L_1 \cup L_2$</span>.
Now if we prove using the Pumping Lemma that either of the languages <span class="math-container">$L_1$</sp... | https://cs.stackexchange.com |
160,602 | [
"https://softwareengineering.stackexchange.com/questions/160602",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/28424/"
] | When debugging, I sometimes find that I make some changes and I am not 100% sure why those changes correct some bug in the program. Is it essential to understand every single detail about why some bugs were occurring and why certain changes eliminated those bugs? Or is it common among developers to sometimes get the pr... | I would say that it is essential to understand every single detail about why some bugs were occurring and why certain changes eliminated those bugs, <strong>and</strong> it is also common among developers to sometimes get the program working without really knowing the details about why the fix worked!
The art of chang... | If you think a client is mad about it taking too long to fix a bug, imagine how mad they will be about a bug recurring that you claimed was fixed, or a fix for one thing making something else worse. If your fix is only a workaround or mitigation, customers will usually still welcome it, but you must be honest about wh... | https://softwareengineering.stackexchange.com |
199,785 | [
"https://softwareengineering.stackexchange.com/questions/199785",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/91748/"
] | I am doing contract work for various clients and I was wondering how best to go about safeguarding myself against non-payment. The projects will be ASP.NET web applications, most likely intranet-based.
I don't have any more details than that. I imagine that the client will want to run and test the applications from th... | Unless you install your ASP.NET application on hardware that you alone have admin on, no. An unscrupulous client can take it without paying, and pay some unscrupulous programmer to work around any trap you leave.
Include clauses in your contract allowing you to collect both interest and collection expenses if they fai... | Since your source needs to be on the web server and the server needs to read it, it's pretty difficult to protect your code unless you alone control the server.
The client will want to see the product working but that doesn't necessarily have to be on their server/network. If you can mock up the client's environment (... | https://softwareengineering.stackexchange.com |
388,042 | [
"https://physics.stackexchange.com/questions/388042",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/83398/"
] | The Standard Model contains an extreme fine-tuning: the Higgs mass is very small compared to what it would naturally be, by a factor of around $10^{15}$. Lots of theories extending the Standard Model are designed to remove this problem.
Model builders sometimes speak of individual models being fine-tuned in a very di... | There is a difference between <em>large hierarchies</em> and <em>fine-tuning</em>.
We don't know how the values of the constants of the Standard Model (or its extensions) are set. Instead, we assume some prior – a sensible one is that the logarithm of the constant in question is uniformly distributed over some range. ... | This doesn't exactly answer your question, but it's worth noting that there's a qualitative difference between the way that the Higgs mass and the way that many BSM parameters are "fine-tuned".
The Higgs mass is only "very small compared to what it would naturally be" in a "natural" theory of quantum <em>gravity</em> ... | https://physics.stackexchange.com |
133,759 | [
"https://physics.stackexchange.com/questions/133759",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/48784/"
] | In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is.
Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: $\text{mass}\times\text{velocity}$.
I think that considering that mass is constant:
<ul>
<li>if Ke must be different also the velocity o... | <blockquote>
if mass is assumed to be <strong>constant,</strong> the <em>velocity</em> of the centre of mass
of the system has to be different after the collision for the kinetic
energy to be different.
However, if the momentum of the system is conserved, <em>the velocity</em> of
the centre of mass of the ... | A simple counterexample:
Imagine <em>two particles</em> with opposite direction and equal speed. The center of mass does not move, yet the kinetic energy of the system is non-zero.
Now let both particles come to rest (by friction, hitting a wall, whatever). The kinetic energy is now zero, and total momentum has been ... | https://physics.stackexchange.com |
197,940 | [
"https://security.stackexchange.com/questions/197940",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/191614/"
] | I created a lab environment which has Windows 7 and Kali Linux in VMware.
In Kali Linux, I opened Wireshark and started to listen to traffic on eth0. After that, in my Windows 7 machine, I opened an HTTP site and entered some login information to that site.
Wireshark was able to capture that login information.
How d... | The reason why Wireshark can capture all packets is because of the NAT environment. IN NAT, VM's in VMware will use the physical adapter. That's the NIC of my computer. So VMware provides the ethernet card to the VM's. Both Windows 7 and kali will use the same ethernet card because VMware points my ethernet card to thi... | This is actually not a security question at all. The question you want to be asking is how one node on a network can see the packets that are not destined for it. For this answer, you need to understand how Ethernet networking works.
Ethernet networks are broadcast networks, meaning that every node on the same segment... | https://security.stackexchange.com |
170,792 | [
"https://physics.stackexchange.com/questions/170792",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75561/"
] | I have one question regarding total heat losses from water surface. Water is heated with immersion heater in open condition in a room. Heat losses from the top of the pan to air is to be calculated. And basically three mechanisms of heat transfer viz. by convection, evaporation and radiation is associated with it. (Con... | Since it is being heated by an immersion heater,so convection process is must along with radiation which increases with the increase of temp.but since surface area is not so large,evaporation process can be neglected, i think.
Let me know what you think.
| Under atmospheric conditions , the most important heat loss mechanism is convection as this involves the physical medium , which is air. That is the most abundant element in a room atmosphere. Conduction needs to be considered if the physical solid material area is significant. Radiation in most cases is not very relev... | https://physics.stackexchange.com |
3,755,490 | [
"https://math.stackexchange.com/questions/3755490",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | The minimum value of the function <span class="math-container">$f(x, y)=4 x^{2}+9 y^{2}-12 x-12 y+14$</span> is
<em>My work</em>
<span class="math-container">$$
\begin{aligned}
\text f(x, y) &=4 x^{2}+9 y^{2}-12 x-12 y+14 \\
&=\left(4 x^{2}-12 x+9\right)+\left(9 y^{2}-12 y+4\right)+1 \\
&=(2 x-3)^{2}+(3 y-2... | Work out the partial derivatives of the function, namely
<span class="math-container">$$ \frac{\partial f}{\partial x} = 8x - 12, \qquad
\frac{\partial f}{\partial y} = 18y - 12 $$</span>
Now you set both derivatives equal to zero to find the stationary points: <span class="math-container">$8x - 12 = 0$</span> and ... | If a function attains a minimum at point <span class="math-container">$(x_0, y_0)$</span> then both partial derivatives at this point are zero.
In this case, derivative with respect to <span class="math-container">$x$</span> is
<span class="math-container">$$
f(x, y)=8 x -12
$$</span>
and the derivative with respect to... | https://math.stackexchange.com |
8,401 | [
"https://biology.stackexchange.com/questions/8401",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/3575/"
] | We can cure many diseases nowadays, and thus the natural selection is very limited.
Plus, mankind spent the whole beginning of its existence in almost the same hostile environment, and that's where he evolved the most, whereas our environment is changing very quickly. So, can we say that mankind froze, if not stopped, ... | Not at all.
<ul>
<li>Mutations accumulate independent of medical progress. In fact harmful mutations which would otherwise cause an individual to die can now be "cured" thus if anything increasing the gene pool. </li>
<li>Typically medical progress extends our lives when we are much older, thus we have already passed... | Keep in mind that most people live in environments where antibiotics are of limited availability and hygiene is not as rigorous as in the "western" world. Combine this with high population densities and you get, if anything, more natural selection due to the spread/proliferation of pathogens and the subsequent mortalit... | https://biology.stackexchange.com |
616,232 | [
"https://physics.stackexchange.com/questions/616232",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/248319/"
] | I have a question regarding the (discrete) Fourier Transform of the retarded Green function (I neglect hats on operators):
<span class="math-container">$$G(i,j;t)=-i\theta(t)\langle \{c_i(t),c^\dagger_j \} \rangle $$</span>
specifically the conversion from position, <span class="math-container">$i$</span>, to momentum,... | Although this is often discussed as a Fourier transform, in the context of a descrete lattice with periodic boundary conditions we can treat it simply as a canonical/unitary transformation <span class="math-container">$S$</span>, <span class="math-container">$S^{-1}=S^\dagger$</span>, to a new basis:
<span class="math-... | I answered my own question at the last step. Basically the FT needs to look at the definition of <span class="math-container">$\hat{c}_k$</span> in terms of combinations of <span class="math-container">$e^{ix_ik}\hat{c}_i$</span> (a FT). Taking the adjoint of this will flip the sign of the exponential. This means that:... | https://physics.stackexchange.com |
30,999 | [
"https://scicomp.stackexchange.com/questions/30999",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/22717/"
] | I am developing a code to simulate fluid flow with biological substances present in the flow. This involves the standard Navier-Stokes equations coupled to some additional biological models. There are many parameters/constants.
I have written functions to handle the major computations, but a problem I am having is the... | If you have constants that will not change before runs, declare them in a header file:
<pre><code>//constants.hpp
#ifndef PROJECT_NAME_constants_hpp
#define PROJECT_NAME_constants_hpp
namespace constants {
constexpr double G = 6.67408e-11;
constexpr double M_EARTH = 5.972e24;
constexpr double GM_EARTH = ... | Another alternative that may be in line with your train of thought is to use a namespace (or nested namespaces) to properly group constants. An example might be:
<pre><code>namespace constants {
namespace earth {
constexpr double G = 6.67408e-11;
constexpr double Mass_Earth = 5.972e24;
constexpr d... | https://scicomp.stackexchange.com |
71,112 | [
"https://electronics.stackexchange.com/questions/71112",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22937/"
] | I am designing my very first PCB for a robotics project I am working on. The project will be using through hole components. I was not able to get all the traces to work on 1 layer, so I added a second layer, the board layout is shown below:
<img src="https://i.stack.imgur.com/rbhkY.png" alt="PCB Board">
Given this b... | No, the holes through the board should be plated, which means that they are lined with metal that makes a good connection from front to back. In my experience, capillary action will suck the solder all the way through the holes anyway. However, it looks like you are planning to control some significant currents so you ... | A few things:
<ol>
<li>Does this board pass design rule check?</li>
<li>All of your traces are the same width. I don't know what your current requirements from your power supply are, but I will almost guarantee you want to make your power traces thicker.</li>
<li>I would strongly recommend putting your uC in an IC soc... | https://electronics.stackexchange.com |
513,634 | [
"https://physics.stackexchange.com/questions/513634",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247164/"
] | I was removing bearings from a motorcycle wheel. The bearings are fitted with a compression fit. I was trying to remove them with a regular hammer (~500g head)but the bearings wouldn't move. Using a lump hammer (3 kg head) was much more effective. In theory this should be Force = mass * acceleration. I was hitting the ... | Assuming you apply the same work to both (Force * distance) then they will both gain equal kinetic energy. <span class="math-container">$$m_bV_b^2=m_sV_s^2$$</span>
taking <span class="math-container">$ m_b = 6 m_s$</span> so <span class="math-container">$\sqrt{6}V_b = V_s$</span> now let's calculate the ratio of momen... | The larger hammer has more inertia (resistance to acceleration) so transfers its momentum to whatever you hit. The lighter (less massive) hammer decelerates quickly when it meets the object you’re hitting.
| https://physics.stackexchange.com |
488,248 | [
"https://stats.stackexchange.com/questions/488248",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/294655/"
] | I am looking for an explanation as to how the ANCOVA results, below, show that the means of the groups defined by IndVar1 and IndVar2 are not equal, after accounting for the covariate, Covar.
I think the answer is that the intercept is adjusted (due to the covariate), and the p-values of IndVar1 and IndVar2 are still s... | The answer is as I suspected. The intercepts are adjusted due to the covariate, and if one of the p-values of the two grouping variables is significant, then the <strong>adjusted</strong> means of all of the groups are not equal.
| I may be misunderstanding what you're asking here, so please clarify if I have misread something. As currently written, my understanding is that you have a factor, <code>IndVar1</code>, with some number of levels and another factor, <code>IndVar2</code>, with also some number of levels. Your question is then how the re... | https://stats.stackexchange.com |
67,735 | [
"https://security.stackexchange.com/questions/67735",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/55343/"
] | I know the use of keyloggers. What I wish to know is how a hacker can install the keylogger onto the victim's system? If it can be done by XSS then to where this keylogger is actually installed (I mean to the client system or browser or somewhere else)? And also how the response of keyboard press reaches the attacker?
| Keyloggers are usually programs which run in background on the users operating system. There are lots of ways to install these on the users machine. Some examples are:
<ol>
<li>The attacker learns about a vulnerability in the victims web browser which allows to download and install arbitrary programs from the web, and... | In addition to the informative answer of Philipp.
Key Loggers are highly appreciated by attackers, this is the gold to watch for. Many advances have been made, up to replacing a keyboard with a 'tapped' keyboard or even have a 'tapped' mouse put in place.
More advanced are almost 'invisible' devices which proxy the... | https://security.stackexchange.com |
57,891 | [
"https://chemistry.stackexchange.com/questions/57891",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/32493/"
] | My lecturer today said that when an applied magnetic field, $B_0$, is applied, the electron with spin parallel to $B_0$ is higher in energy than the electron with spin antiparallel to $B_0$. Similarly, in protons, it is the opposite; parallel spin is lower in energy and antiparallel spin is higher in energy. Why is tha... | In addition to the other answer, the energy of a magnetic moment in a magnetic field is $E=-\bar{\bf{\mu}}.\bar{\bf{B}}$ where the dot indicates the dot product between the two vectors $\bar{\bf{\mu}}$ and $\bar{\bf{B}}$, thus the energy is lowest when the magnetic dipole is parallel to the field $B_0$; $E=-\mu B_0$. ... | In short: electrons and protons have magnetic moments. Electrons are negatively charged, and the direction of their magnetic moments is reversed from that of protons.
Intuitively, the potential energy is lowest when the magnetic moment is aligned with the magnetic field, as is the case with the proton. Because electr... | https://chemistry.stackexchange.com |
700,213 | [
"https://physics.stackexchange.com/questions/700213",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/129729/"
] | I'm a computer engineering student working on my senior project that involves some optics. Illadvised though it may be, I'm contemplating building a telescope based on a simple achromatic refractor design for use in an automated astrophotography rig. I'm trying to work out how to build a compact telescope such as comme... | The question lacks some information. Specifically, the angular size of the Orion nebula, and the linear diameter of the camera sensor.
The Orion nebula is about <span class="math-container">$1$</span> arc degree in size (Google). This means that the angular size of the image will also be about <span class="math-conta... | The focal length in this context determines the size of image. Therefore, when you photograph an object at a large distance you would select a larger focal length so that the object appears larger in the image.
There is always a range of distances in which objects would appear in focus. This range becomes larger for la... | https://physics.stackexchange.com |
349,109 | [
"https://physics.stackexchange.com/questions/349109",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/126734/"
] | We know that we can write the energy of a particle as a function of position $\mathbf{x}$ like this:
$$E(\mathbf{x}) = \frac{\mathbf{p}^2(\mathbf{x})}{2m} + V(\mathbf{x})$$
Where $\mathbf{p}$ is the momentum and $V(\mathbf{x})$ is the potential energy. ($m$ stands form mass and $E$ for energy).
And we know that $E(\mat... | Simple: $\vec{p}^{\prime}(\vec{x})$ is <em>not</em> $m\vec{a}$. In particular, $\vec{p}^{\prime}$ is the space derivative of $\vec{p}$, but $m\vec{a}=m\partial_t\vec{v}=\partial_t(m\vec{v})=\partial_t\vec{p}$.
You can correct your argument by noting that $\partial_t\vec{x}=\vec{v}$ and applying chain rule.
| <strong>Hint:</strong>
$$
\frac{d}{dx}\left(\frac {p^2}{2m}\right) \\
=\frac{p}{m}\frac{d}{dx}p \\
=\frac{p}{m}\frac{dp}{dt} \frac{dt}{dx}
$$
| https://physics.stackexchange.com |
122,299 | [
"https://chemistry.stackexchange.com/questions/122299",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/50406/"
] | I have been told that when <span class="math-container">$\Delta V=0$</span>, work done will be zero <span class="math-container">$(W=0)$</span>. I know that, in cyclic process <span class="math-container">$\Delta V$</span> will be zero, since it's a path function and <span class="math-container">$\mid W \mid$</span> i.... | The reversible work is <span class="math-container">$W=\int{PdV}$</span> over the path of the process. This integral is not zero for the cyclic process (involving V changing) even through <span class="math-container">$\Delta V$</span> from beginning to end of the process is zero. So, whoever told you that <span class... | I'm not sure about my answer but I think this is how it goes.
<span class="math-container">$\Delta G=-W$</span> (useful work);
<span class="math-container">$= \Delta H-T \Delta S$</span>
<span class="math-container">$= P + \Delta V -T \Delta S$</span>
Therefore even though <span class="math-container">$\Delta V$</sp... | https://chemistry.stackexchange.com |
1,931,687 | [
"https://math.stackexchange.com/questions/1931687",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/368510/"
] | I have an issue (sorry for bad usage of signs) proving
\begin{equation}
\int\limits_{1}^{i} \mathrm{e}^{z^{2}} \mathrm{d}z \le \mathrm{e}\sqrt{2}
\end{equation}
I'm also supposed to tell why its independent of way. I thought that I might be able to change the contour to a quarter of the unit circle, $|z|=1$, but then... | <blockquote>
\begin{equation}
\int\limits_{1}^{i} \mathrm{e}^{z^{2}} \mathrm{d}z \le \mathrm{e}\sqrt{2}
\end{equation}
</blockquote>
This inequality does not make sense since the integral is a complex number. It should be
$$\left\lvert \int_1^i e^{z^2}\, dz\right\rvert \le e\sqrt{2}$$
To obtain this estimation, no... | On the line segment from $1$ to $i$, we have the estimate
\begin{align}
|e^{z^2}|\leq e^{|z|^2} \leq e.
\end{align}
| https://math.stackexchange.com |
24,205 | [
"https://mathoverflow.net/questions/24205",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7/"
] | The set up is $C$ is a curve and $J$ is its Jacobian. On the $C \times J$ there is the Poincare bundle $P$ which is the universal family of degree zero line bundles on $C$. For every integer $d$ there is also a line bundle $P(d)$ on $C \times J$ which is a family of line bundles of degree $d$ on $C$.
I've seen a con... | For your first question, if you want a proper universal property it is defined
by a variety $J^{(d)}$ and a line bundle $L^{(d)}$ on $C\times J^{(d)}$ which is
of degree in the $C$-direction, i.e., of degree $d$ on each fibre $C\times
x$. The universality then says that for every $X$ and every line bundle $M$ on
$C\tim... | The point is that $q_{2*}P(g-1)$ is a torsion-free sheaf, because it is the image of a torsion-free sheaf. Its support is concentrated on the Theta divisor; but this means that it is torsion, so it must be 0.
| https://mathoverflow.net |
143,238 | [
"https://stats.stackexchange.com/questions/143238",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/67583/"
] | I'm conducting a meta-analysis using the Hedge's g effect size statistic. Many of the studies are only reporting:
<ol>
<li>pre-treatment mean score</li>
<li>pre-treatment standard deviation</li>
<li>post-treatment mean score</li>
<li>post-treatment standard deviation</li>
<li>sample size</li>
</ol>
With this informat... | Unfortunately, if that really is all the information you have, then there is no way to get either #1 or #2 -- one way or another you need to know (or be able to deduce) the correlation between pre-test and post-test scores.
| Yes, as others have mentioned, you will need to know the correlation between pre- and post-test scores to calculate an effect size.
However, this correlation value can be imputed to obtain reasonable results, especially if you can draw upon previous research and/or have a strong theoretical rationale for the particul... | https://stats.stackexchange.com |
29,876 | [
"https://scicomp.stackexchange.com/questions/29876",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/27791/"
] | Say, I have this code
<pre><code>double start = MPI_Wtime();
ParallelMatrixVectorProductRotuine(...);
double end = MPI_Wtime();
</code></pre>
How do I interpret the numbers I am getting. For instance, with 1 process I get something like
<pre><code>1.7342
</code></pre>
For two processes I get
<pre><code>1.0023
1.... | That depends on your goal.
For one process it's obvious that $t$ is the wall-time of the entire program launch.
For two processes, you got $t_1$ and $t_2$ which correspond for the walltime on processors 1 and 2.
Usually, one is interested in the total time it took to solve the problem - aka overall walltime, which wi... | There can be any number of reasons for different times on different processes.
<ol>
<li>If one process has lots of local work after the last MPI communication, it will report a longer running time.</li>
<li>If one process concludes with an eager send, it will report a shorter running time than the other process, which... | https://scicomp.stackexchange.com |
184,109 | [
"https://softwareengineering.stackexchange.com/questions/184109",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/78863/"
] | So I'm fairly new to programming in the real world (outside of academic projects) and have come across lots of posts saying that using <code>instanceof</code> is a bad thing to use to determine what class a specific object is.
My situation is that I have three classes, a base product class, one that extends off that a... | The reason <code>instanceof</code> is discouraged is that it's not OOP.
There should be no reason for the caller/user of an object to know which concrete class it is an instance of beyond which type the variable it is declared as.
If you need different behavior in subclasses add a method and implement them differentl... | <code>instanceof</code> isn't necessarily a bad thing, however it is something that one should look at.
An example of where it works correctly is in a place where one gets a collection of the base type and you only want the ones of a subtype. Getting the network addresses from <code>NetworkInterface.getNetworkInterfa... | https://softwareengineering.stackexchange.com |
264,912 | [
"https://security.stackexchange.com/questions/264912",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/271649/"
] | As the title says, in the rules of engagement I have my scope, used method, etc. but I've been wondering if I should also include a list of tools (such as NMAP, Dirb/Ffuf, etc.) that might be used.
And if not, how should I be transparent with the client about the way I'm going to perform the pentest?
My concern is that... | You should explain your methodology, but a full list of tools usually isn't included for several reasons:
<ul>
<li>You don't actually know all the tools that you're going to use before you've finished testing.</li>
<li>Most clients don't really care and won't read it anyway.</li>
<li>Some tools have names that are not... | There is no rule, but in addition to the executive summary you will normally submit a more technical report with your findings.
The executives usually don't have a clue about tech, but there is usually an IT team, who will look at your report too, and assess the results. Quite probably they will take part in remediatio... | https://security.stackexchange.com |
114,553 | [
"https://math.stackexchange.com/questions/114553",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/23187/"
] | Let $G=(V,E)$ a graph. Prove that $G$ has no cycles if and only if $G$ has $n-m$ connected components where $n$ is the number of vertices of $G$ and $m$ is the number of edges of $G$.
The thing I did is that since $G$ has no cycles then $ \frac{m}{n} <1$.
Can someone give me some hints-ideas?
Thank's in advance!
| A tree is a connected graph with $n - 1$ edges. If you take any edge away from a tree, the number of components increases. If you add any edge to a tree, a cycle is created. So, your situation is a forest of $n - m$ trees, i.e., $n - m$ connected components, each of which is a tree. If you take away any edge, it cr... | Add to the statement the claim that the graph has at least $n-m$ connected compenents (regardless of whether it has cycles); then for any $n$ one can apply induction on $m$. For $m=0$ the graph never has cycles and always has exactly $n$ connected components, so the base case is OK. Now let the graph have $m>1$ edge... | https://math.stackexchange.com |
2,341,369 | [
"https://math.stackexchange.com/questions/2341369",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/392865/"
] | $\lim_{n\rightarrow \infty }\left ( n-1-2\left (\frac{\Gamma(n/2)}{\Gamma((n-1)/2)} \right )^2 \right )$
| It is best to proceed using the following approximation for $\Gamma $ function $$\log \Gamma(x) =x\log x-x+\frac{1}{2}\log\frac{2\pi}{x}+\frac{1}{12(x+1)}+o(1/x)$$ and therefore we have $$2\log\frac{\Gamma(x/2)}{\Gamma ((x-1)/2)}=\log\frac{x-1}{2}+(x-1)\log\frac{x}{x-1}-1-\frac{1}{3(x+1)(x+2)}+o(1/x)$$ or $$2\log\frac{... | Note that
$$
{{\Gamma (n/2)} \over {\Gamma (n/2 - 1/2)}} = \left( {n/2 - 1/2} \right)^{\,\overline {\,1/2\,} }
$$
where $x^{\,\overline {\,a\,}} $ denotes the <em>Rising Factorial</em> (rising Pochammer).
It is an increasing function for $1<n$.<br>
Because of that and considering the rules for summing the exponent... | https://math.stackexchange.com |
45,087 | [
"https://mathoverflow.net/questions/45087",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8430/"
] | While playing around with certain non-negative matrices, I got stuck at the following question.
Let $A$ be a <em>strictly</em> positive-definite $n \times n$ matrix ($n \ge 3$), with ones on the diagonal, and all other entries in the range $[0,1]$. How should I go about proving a tight bound on the sum of the entries ... | When $n\ge3$, there does not exist such a bound. To see this, take $n=3$ and the following matrix
$$A=\begin{pmatrix}
1 & a & 0 \\\\ a & 1 & a \\\\ 0 & a & 1 \end{pmatrix}.$$
If $a< 1/\sqrt2$, it is positive definite with non-negative entries. However
$$1^TA^{-1}1=\frac{3-4a}{1-2a^2}$$
is not... | Let $M$ be a zero/one random symmetric matrix with zero diagonal. Presumably the eigenvector $v$ corresponding to the smallest eigenvalue of $M$ is not perpendicular to the all-ones vector 1 with high probability. Choose $v$ to be normalized so that $d = 1^T v > 0$ and $v^T v = 1$. Then choose $\alpha>0$ so that ... | https://mathoverflow.net |
3,629,572 | [
"https://math.stackexchange.com/questions/3629572",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/668300/"
] | Let <span class="math-container">$N$</span> be a normal subgroup of <span class="math-container">$G$</span> and let <span class="math-container">$\pi∶G \rightarrow G/N$</span> be the homomorphism <span class="math-container">$\pi(a) = aN.$</span>
Suppose <span class="math-container">$K$</span> is a subgroup of <span cl... | If <span class="math-container">$T$</span> is a theory, the reduct of <span class="math-container">$T$</span> to the language <span class="math-container">$L'$</span> is <span class="math-container">$T\cap \mathrm{Sent}(L')$</span>, where <span class="math-container">$\mathrm{Sent}(L')$</span> is the set of <span class... | <s>Yes, since the reducts of <span class="math-container">$T$</span> and <span class="math-container">$T'$</span> are still the same sets, with some of the logical structure removed. Any embedding <span class="math-container">$\pi: T \to T'$</span> will still be an embedding between the reducts.</s>
Misread the questi... | https://math.stackexchange.com |
130,969 | [
"https://security.stackexchange.com/questions/130969",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/118456/"
] | <strong>Given:</strong>
A WebService which stores user Data and a server with a database.
A Administrator which can acces the sever wit hthe webservice and the server with the database.
Foreach user is a dedicated database.
<strong>Aim:</strong>
Store the data in a way so that even not the administrator can acce... | The rule is that if the data is in clear text at any moment on a machine it is accessible to the admin of the machine. Because by definition, an admin can use administrative tools and can read memory of any process or install spys on any network route.
Doing so without good reason is of course a professional fault and... | <blockquote>
For me it would feel a little awkward to ask him for a "MasterKey".
</blockquote>
It does not if the core of the service is to ensure that only that person can access the data by first decoding them.
The authentication via an third party is in that case is not useful, you will be better off handing it... | https://security.stackexchange.com |
147,088 | [
"https://mathoverflow.net/questions/147088",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29625/"
] | Here is a power series, which looks a bit like a Hypergeometric function series, but I don't think that it is. Has anyone any idea what it is? Here $n,p,r$ are integers with $n\ge 0$ and $p\ge r\ge 0$:
$$
f_{n,p,r}(x)\,=\,\sum_{s=0}^p \frac{x^s}{s!}\ \frac{p!\,(2n+p+s+2)!\,(n+r+s+2)!}{(p-s)!\,(2n+r+s+3)!\,(n+s+2)!}
$$... | Henry is almost right; the sum can be written as
$$\frac { \left( 2n+p+2 \right) !\, \left( n+r+2 \right)!}
{ \left( 2n+r+3 \right) !\, \left( n+2 \right) !}
{}_{3}F_{2}\left({{2n+p+3,n+r+3,-p\,\,\,}\atop {2n+r+4,n+3}}\Bigm |-x\right)$$
For $x=-1$ (no need to assume $r\le p$) the sum can be evaluated by Saalschütz's ... | According to Mathematica, for $r=p$, the sum for $x=-1$ gives
$$
\frac{(n+1) \left(-\frac{1}{4}\right)^p \left(\frac{1}{2} (2 n+3)\right)! p! (2
n+p+2)!}{(2 n+3)! (n+p+1) \left(\frac{1}{2} (2 n+2 p+3)\right)!}
$$
This formula can can be proven using Zeilberger’s algorithm [D. Zeilberger, The method of creative teles... | https://mathoverflow.net |
550,665 | [
"https://physics.stackexchange.com/questions/550665",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/256911/"
] | I'm having trouble finding the potential inside an insulated sphere by setting the potential at the center of the sphere to 0 and then integrating from there.
I know that if I set the reference voltage to infinity, then the potential outside the sphere is <span class="math-container">$kQ/r$</span> and the potential i... | The integrand is the same as for the case <span class="math-container">$V(\infty) =0$</span>, you only have to change the first endpoint of the integral to <span class="math-container">$0$</span> instead of <span class="math-container">$\infty$</span>:
<span class="math-container">$$V(x) = -\int_0^x \vec{E}\cdot d\vec{... | Potential at center of the sphere is the potential of bringing the charges to surface of sphere added to the potential caused by the layers of the bulk of sphere. Hint : the key word here is layer of the bulk
| https://physics.stackexchange.com |
82,768 | [
"https://physics.stackexchange.com/questions/82768",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/31920/"
] | Assume we look at an interaction between 2 fermions
$V \sum_{k_i,k_j,k_m,k_n} c_{k_i}^\dagger c_{k_j}^\dagger c_{k_m} c_{k_n} \delta_k $
where $\delta_k$ conserves momentum. We can directly write down a few terms from the sum
$ ... + \underbrace{c_{k_1}^\dagger c_{k_2}^\dagger c_{k_3} c_{k_4}}_{i=1,j=2,m=3,n=4} + \u... | The mistake is that interaction terms do not correspond to what you wrote, which is indeed $0=0$. You forgot that in general, $V$ depends on the $k_i$'s, with the ad hoc sign changes when its arguments are exchanged. When $V$ is assumed to be a constant, one does not sum over all possible $k_i$'s, but only a subset (se... | As an addition an example to Adam's answer, consider the action for the superfluid normal transition in liquid helium-4:
$$
F = \int dx \left( \frac{\hbar^2}{2m}|\nabla \phi(x)|^2 - \mu |\phi(x)|^2 + \frac{V_0}{2}|\phi(x)|^4 \right)
$$
Fourier transforming the latter interaction term (which by the way comes from assumi... | https://physics.stackexchange.com |
412,510 | [
"https://physics.stackexchange.com/questions/412510",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/198677/"
] | This is probably a very simple question, but I wonder how the amount of radioactive substance is related to the radiation it emits and therefore the harm it does to the body.
If I held 0.1g of barium-137 in my left hand and 10g of it in my right hand, for the same amount of time, would my right hand have been damaged ... | The search term to use in order to learn about this is "linear no-threshold," or LNT. This is the hypothesis that the biological harm is proportional to the radiation dose. It's hard to get reliable data, but LNT appears to be a poor approximation at low doses.
At low doses, there may even be an effect called radiatio... | There are different aspects to this, as you may have gathered from the other answers.
One aspect is the amount of ionization that is produced in your tissue. This is a simple linear relationship. Each unit of a particular kind of radiation produces the same amount of ionization. It produces the same amount of energy d... | https://physics.stackexchange.com |
13,086 | [
"https://engineering.stackexchange.com/questions/13086",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/9468/"
] | During the heat treatment process, people use clay to harden the steel in certain areas like the spine. Then they have to go through another process to make the steel tough. I need very hard steel and want to know will the hard steel be brittle and able to withstand large amounts of pressure? I ask because the steel is... | It depends what you want to achieve and what you mean by 'strength'. .
Heat treating can be used to increase the yield stress of a hardenable steel (to a greater or lesser extent depending on the alloy and process used). But what it won't do is to increase the stiffness of the part as hardening and tempering have no ... | In steel hardness is closely related to tensile strength so a hardened steel will have both high hardness and high tensile strength.
Toughness is a bit more difficult to quantify than strength but in general is the ability to resist impact and resistance to brittle fractures. Ductility plays a part in toughness as it... | https://engineering.stackexchange.com |
29,707 | [
"https://mathoverflow.net/questions/29707",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2310/"
] | Take a time interval $[0,T]$, and a filtered probability space $(\Omega,P,\mathcal{F},\mathcal{F}_t)$. If $X \in L^1(\mathcal{F}_T)$, then $M_t = E [X \ | \ \mathcal{F}_t]$ is a martingale. If I want the martingale $M$ to have continuous or right continuous paths, is there a condition I can impose on the filtration t... | Generally speaking, you cannot do this at the level of conditions on filtration since conditional expectation is defined up to modifications on zero measure sets. For example, take $T=1$, and the probability space be $[0,1]$ with Borel sigma-algebra and Lebesgue measure. Let $X(\omega)=\omega$ and all sigma-algebras f... | Hi,
The thing is that both your original process and the càldlàg modification of it, are equivalent with respect to your probability measure (if the usual hypothsesis hold).
Probabilisticly speaking, there is nothing that can be said about your original process that cannot be said from your modification (if the usua... | https://mathoverflow.net |
285,990 | [
"https://physics.stackexchange.com/questions/285990",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59964/"
] | I'm struggling to understand the concept of spontaneous symmetry breaking. I understand that the sign of the coefficient $\mu^2 > 0$ in the Higgs potential:
$$ V(\phi) = \mu^2 \phi^{\dagger} \phi - \frac{\lambda}{4} (\phi^{\dagger}\phi)^2 $$
Leads to the minimum of the classical potential being nonzero and the Higg... | If I understand it correct, then in a nutshell, you are asking why is the VEV independent of spacetime. If the Higgs field had different values at different points in space i.e., if it had a spacetime variation, then the gradient term would give a positive contribution to the Hamiltonian, and hence, the total energy wi... | The OP asks:
<blockquote>
I understand that the circle of degenerate minima form a spherical
shell $\phi^{\dagger}\phi=\frac{\nu^2}{2}$, so why does the Higgs
field choose the same point on this shell across all space?
</blockquote>
The shape of the potential that gives rise to the degenerate minima, forms this... | https://physics.stackexchange.com |
38,723 | [
"https://electronics.stackexchange.com/questions/38723",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10906/"
] | When selecting a multimeter, what should one look for in terms of safety features and measurement capabilities?
What can you look for in the specifications to tell a good meter from a crappy one (besides price)?
I'm looking at cheaper multimeters for hobby use - so I don't need super high accuracy, and am not plannin... | <strong>Accuracy</strong>. Which is something else completely than resolution. Your meter may have 4 digits, that's a 0.1 % resolution, but if its accuracy is only 1 % that last digit is useless.
Accuracy is given by two numbers, an absolute error and a relative error. The relative error is the one expressed in %, l... | <strong>Good things to look for if you may be tempted to poke at light switches, wall outlets power supplies etc or anything over 50V or that might be near something > 50V once in a blue moon.</strong>
<ol>
<li>Safety - HRC fuses, MOVs, creepage/clearance distances, overlapping case halves.</li>
<li>Separate sockets f... | https://electronics.stackexchange.com |
549,085 | [
"https://physics.stackexchange.com/questions/549085",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/234017/"
] | The onset of turbulent flow ranges greatly, for pipe flow I came across the information that the onset of turbulent flow occurs at approximately <span class="math-container">$Re=10^4$</span>, while for boundary layers on the airplane's wing the onset can be as high as <span class="math-container">$Re=10^6$</span> to <s... | Sure, it's possible. These guidelines are just that -- guidelines -- and it's possible that different flow configurations would be outside of those guides.
For example, the flow over a wing guideline is based on a wing at normal conditions, flying freely in the atmosphere in straight and level flight. But if that win... | I want to add to the accepted answer:
There are two things necessary for a flow to become turbulent. First of all, the laminar flow has to be unstable, i.e. a small perturbation increases in size and strength and leads to turbulent flow. This is indicated by the Reynolds number. As already mentioned, the Reynolds numbe... | https://physics.stackexchange.com |
168,784 | [
"https://physics.stackexchange.com/questions/168784",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74645/"
] | It's my understanding that surface tension is caused by hydrogen bonding. My question is whether or not we can break that bond, without physical contact. Could we use electricity, light, heat, or magnetic forces to remove that surface tension? A specific example would be a test tube of distilled water. Could one of tho... | You can't remove the entire surface tension and still have a surface (without tension the water will just atomise under thermal fluctuations and vaporise).
But you can certainly <em>reduce</em> the influence of hydrogen bonds and thus surface tension. Heating up the water is the simplest method - it will drown out the... | All water in liquid form has some surface tension. This inter-molecular attraction can be weakened by the kinetic energy of the water molecules i.e. heat. Thus, you can be heating the water.
| https://physics.stackexchange.com |
103,501 | [
"https://softwareengineering.stackexchange.com/questions/103501",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35213/"
] | I'll be working as a development lead for a startup and I've suggested that we use VMs for development. I'm not talking about each developer having a desktop with VMs for testing/development, I mean having a server rack where all VMs are managed and have the developers work from a microPC (ChromeOS anyone?) locally, o... | What are you hoping to save, as a fraction of the development budget? It seems to me that you are worrying about an epsilon. The cost of machines for developers is less than 5% of the total cost to keep a developer on staff. Therefore the only important question is "will it save developers time?" It could, if they ... | I think you're being penny-wise and pound-foolish.
First of all, machine costs are <em>trivial</em> compared to the cost of a developer. You should work at maximizing productivity, not minimizing machine cost.
Second, latency (not bandwidth) is the key to many programming tasks -- especially text editing. For every ... | https://softwareengineering.stackexchange.com |
81,460 | [
"https://electronics.stackexchange.com/questions/81460",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2426/"
] | I've built a clock out of a PIC16F877, some LEDs and other stuff...
To set the time in 5 minute intervals, I'm using a 22K ohm potentiometer connected between GND and +5V with the contact connected to analog input RA0 on my MCU.
It works, but it badly fluctuates between values. It's a 10bit ADC, and I'm looking at th... | You have noise in your system, plain and simple. How you handle it is the same ways that you handle any other noise: remove the source of the noise, or filter out the noise. Some things to consider are:
<ul>
<li>Long cables can cause noise. Shorten them, or use shielded cables</li>
<li>Use differential measurements... | From memory, the ADC input on this PIC requires the "signal" to be a "low" output impedance (22kohm pot would be too high) and this means having a capacitor across the input pin. The ADC type on these devices are "successive approximation" and they will cause noise on the input pin - this will be seen as a measurement ... | https://electronics.stackexchange.com |
271,312 | [
"https://stats.stackexchange.com/questions/271312",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/137444/"
] | Let $X_i$ be an iid random variable having pdf $f(\mathbf{x}|\theta)$, where $E(X_i) = 6\theta^2$, and $\theta > 0$.
I have calculated an estimator for the parameter ($\theta$) of $f(\mathbf{x}|\theta)$ to be $\hat{\theta} = \sqrt{\bar{x}/6}$. To prove that this is an unbiased estimator, I should prove that $E(\ha... | Say $Q$ is unbiased for $\theta^2$, i.e. $E(Q) = \theta^2$, then because of Jensen's inequality,
$$\sqrt{ E(Q) } = \theta < E \left( \sqrt{Q} \right)$$
So $\sqrt{Q}$ is biased high, i.e. it will overestimate $\theta$ on average.
<em>Note</em>: This is a strict inequality (i.e. $<$ not $\leq$) because $Q$ is ... | Note that for any estimator (with finite second moment) that $E(\widehat{\theta^2}) - E(\hat\theta)^2$ $=$ $\text{Var}(\hat\theta)\geq 0$ with equality only when $\text{Var}(\hat\theta)=0$ (which is easy to check doesn't hold).
Replace the first term on the LHS of that inequality by using your result for unbiasedness... | https://stats.stackexchange.com |
97,591 | [
"https://chemistry.stackexchange.com/questions/97591",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/64631/"
] | I have a question regarding this formula for Gibbs free energy of a system: <span class="math-container">$$\Delta G=\Delta H-T\,\Delta S$$</span>
According to the second law of thermodynamics: <span class="math-container">$T\,\Delta S\ge\Delta Q$</span> and to my understanding, <span class="math-container">$\Delta H$</... | You didn't do anything wrong here. This was a very good observation. This is one of the criteria of spontaneity, which I believe you haven't learnt yet.
As you correctly wrote, <span class="math-container">$\Delta G$</span> can only be negative or 0 for any reaction. This is actually a consequence of the second law of ... | <blockquote>
What am I doing wrong here?
</blockquote>
You are missing the possibility of non-PV work.
<blockquote>
According to the second law of thermodynamics: <span class="math-container">$T\,\Delta S\ge\Delta Q$</span> and to my understanding, <span class="math-container">$\Delta H$</span> is just the same as <spa... | https://chemistry.stackexchange.com |
195,722 | [
"https://softwareengineering.stackexchange.com/questions/195722",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/85305/"
] | I am trying to measure the running time of different crypto algorithm. e.g. how long it takes to encrypt/decrypt a block of plaintext. May I ask if <code>C</code> with <code>OpenSSL</code> is the best PL to do this?
| By far, the language question is a matter of fashion. The best language for getting stuff done is the one you know. The best language for personal development is one you don't.
<code>C</code> would work just fine.
| The same (both PL and library) that you'd use for production because libraries differ in implementation details, and benchmark from one PL/library is not representative of performance with another PL.
| https://softwareengineering.stackexchange.com |
1,384,508 | [
"https://math.stackexchange.com/questions/1384508",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/258387/"
] | <blockquote>
Let $f: R\to R$, and ($f\circ f\circ f)(x) = (f\circ f)(x) + x$, $x$ $\in \mathbb R.$<br>
Prove that $f$ is injective.
</blockquote>
My Solution:
Let $x_1, x_2\in \mathbb R.$ and $f(f(x_1)) = f(f(x_2)) = y$
($f\circ f\circ f)(x) = (f\circ f)(x) + x$
$f((f\circ f)(x)) = f(f(x)) + x$
$f(f(f(x))) = f... | You should prove that $f(x_1) = f(x_2)$ implies $x_1 = x_2$. So your solution is not acceptable. You should start with $f(x_1) = f(x_2)$ then say this implies $f(f(x_1)) = f(f(x_2))$ and then complete as you did
| It looks on the right path if not a bit long: Suppose that $f(x) = f(y)$. Then $$f(f(x)) = f(f(y))\quad \text{and} \quad f(f(f(x))) = f(f(f(y))).$$ Subtract the second equation from the third to get $x=y$.
| https://math.stackexchange.com |
1,794,613 | [
"https://math.stackexchange.com/questions/1794613",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/324603/"
] | I'm new to stats and I facing problems in finding the median of a PDF.
I have to find the median of this PDF
$$ f(x) =
\begin{cases}
cx^2, & \text{if 0 $\le$ $x$ $\le$ 3} \\
0, & \text{otherwise}
\end{cases}$$
<strong>How I'm trying to solve it</strong>
<em>First I found the value o $c$</em>
$$\int_0^3 c... | <ol>
<li>You made an error. The setup is correct, but $c = 1/9$.</li>
<li>Why did you stop? Follow through next time.
$$\frac12 = \int_0^m \frac{1}{9}x^2\,dx = \frac{1}{27}m^3-\frac{1}{27}(0)^3 = \frac{1}{27}m^3.$$
This gives $m = \sqrt[3]{27/2}.$</li>
</ol>
| Your approach is correct, however $c=\frac{1}{9}$ and not $c=\frac{1}{26}$.
As for your second point, what you can do is find your antiderivative (with respect to $x$) and evaluate it from $0$ to $m$ like you would a definite integral, but set that equal to $\frac{1}{2}$. Then you can solve for $m$.
| https://math.stackexchange.com |
31,476 | [
"https://chemistry.stackexchange.com/questions/31476",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1888/"
] | Flame tests are a common way of identifying trace amounts of alkali metals (and to a lesser extent alkaline earth metals) in mixtures. Certain salts of $\ce{Ba, Sr}$ are also used in fireworks for their ability to impart a colour to the flame.
Although predominant among s block elements this behaviour is also seen in... | All elements colour the flame <em>somehow</em>. The salt that is held into the flame dissociates <em>homogenously</em> (i.e. you’re not creating unpaired ions but rather single metal atoms and their counter-radicals), the heat energy excites the electrons and when they fall back down they emit photons at certain wavele... | When you impart heat, atom receive it as extra energy. Due to which electron in outer shell jumps to higher shell position. This electron when falls back to it original position it emits photons of specific wavelengths.
Also, different atoms have different number of valence electrons, thus different element emits pho... | https://chemistry.stackexchange.com |
153,671 | [
"https://softwareengineering.stackexchange.com/questions/153671",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3139/"
] | I have made a product which I have used the GPL licence, and am now getting pull requests from other authors.
The product also has a less restrictive commercial license available for purchase.
Can I include the submitted code with the commercial licensed product?
| The short answer is "no."
The code that your submitters are writing is covered by copyright, and that copyright is assigned to the submitters. Since the project is GPL, they have agreed that the code may be released under the GPL. You will need to get permission from the submitters (all of them!) to release the code u... | This is why many "serious" Open Source projects insist that contributors assign the copyright of their work to the project. That means that the project itself owns <strong>all</strong> the code, and can do whatever it wants with it. Some projects do this to ensure that they can sue people who violate the license (<em... | https://softwareengineering.stackexchange.com |
125,410 | [
"https://stats.stackexchange.com/questions/125410",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/25626/"
] | In testing for equivalence via the two one-sided test approach with confidence intervals, a (1–2α) × 100% confidence interval is calculated to check for equivalence. I assume this is because you calculate a CI for mean of group a and mean of group b.
But why is not it possible to calculate a 95%-CI of the difference b... | The answer to this question is that 90% is possible because of a logical fact that makes this "bonus" in confidence possible. In the TOST procedure, two one-tailed tests are conducted at a 5% level. The type 1 error rate stills remains at 5% because if one test decision is a type 1 error, the other one cannot be a type... | The $1-2\alpha$ is not because you calculate the CI for each group separately. It is because you calculate the "inequivalence" to the upper and to the lower end separately. The parameter $\theta$ lies in the equivalence interval $[\epsilon_L, \epsilon_U]$ iff $$\theta \geq \epsilon_L \wedge \theta \leq \epsilon_U.$$
E... | https://stats.stackexchange.com |
16,127 | [
"https://scicomp.stackexchange.com/questions/16127",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/9756/"
] | I want to pass additional parameters to the ode45 function in MATLAB. There are many questions already on this, but I also have a 'flag' argument in my function.
<pre><code>function [xdot,isterminal,dircn]=spp(t,x,flag,f)
</code></pre>
Usually, while calling ode45, something like this would work if spp did not have a... | I do not exactly know how to treat 'flags' but usually when I need to pass extra variables to the ode I define them as 'global' in the main .m file and also in the file where I define the function I give to the ode.
Or you might use the varargin function .
| Why don't you simply pass flag the way you are passing f?
<pre><code>[t,x,te,xe,ie]=ode45(@(t,x)spp(t,x,flag,f),[0 2*pi/OMEG],[xin;xdin],options);
</code></pre>
(Global variables in MATLAB often cause problems and it is best to avoid them, if possible.)
Maybe I'm missing something here?
| https://scicomp.stackexchange.com |
276,237 | [
"https://physics.stackexchange.com/questions/276237",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5050/"
] | In the annihilation of pairs $e^{+}$ and $e^{-}$, two gamma photons are formed. Is the reverse process, ie, if we collide two photons, will they form an electron and positron?
| The reverse process to electron-positron annihilation is called pair production. It is the time reversal of pair annihilation and is a perfectly viable process with exactly the same amplitude as for annihilation. Note that this is so because quantum electrodynamics is symmetric under time reversal.
Why two photons and... | The production of electron/positron pair is not the reversal of annihilation. To do this, you need a photon of greater than 1.02 MeV. When that passes a massive object, there is a possibility that it will split into a positron and electron.
The problem with the reverse process is that the resultant photons are 0.51 ... | https://physics.stackexchange.com |
668,066 | [
"https://physics.stackexchange.com/questions/668066",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300178/"
] | I've been reading statistical mechanics, and I read the following on Wikipedia, on the article on Fermi-Dirac Statistics derivation in the micro-canonical ensemble :
<blockquote>
Suppose we have a number of energy levels, labeled by index <span class="math-container">$i$</span>, each
level having energy <span class="ma... | Consider a system of <span class="math-container">$N = \sum_i n_i$</span> identical fermions, with the discrete hydrogen spectrum. In this case the energy levels are, in Coulomb units, well known to be <span class="math-container">$E_n = - 1/2n^2$</span> or, since I used "i" to refer to the <span class="math-... | There's three concepts: quantum state, energy level, and the number of fermions in a particular energy level. In general, there can be many states which occupy the same energy level, as the first quote above explains.
All the Pauli Exclusion principle says is that each fermion must occupy a different <em>sublevel</em>.... | https://physics.stackexchange.com |
223,424 | [
"https://physics.stackexchange.com/questions/223424",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/37677/"
] | In the same way as there are <em>electromagnetic</em> and <em>gravitational</em> waves that update the information on their respective field, is there an analogue for the weak and strong forces?
| No, there are no weak or strong waves in the sense as there are for electromagnetic or gravitational waves.
The electromagnetic and gravitational waves are <em>classical</em> objects, they are possible vacuum solutions to the classical equation of motion for the field strength of the respective force, and can be radia... | In QM most stuff boils down to particles.
For example, electromagnetism is mediated by photons and EM radiation is literally just beams of photons.
We should then have a couple of obvious candidates for strange and new kinds of radiation.
The strong force is mediated by gluons and there are 8 types of gluons. At a l... | https://physics.stackexchange.com |
51,499 | [
"https://mathoverflow.net/questions/51499",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5309/"
] | Is there a finite set of primes, $S \subset Spec(\mathbb{Z})$ such that if $K$ over $\mathbb{Q}$ is a number field such that every $p \in S$ is completely split in $K$ then $K=\mathbb{Q}$? If so, what do we know about such $S$'s?
| This is not even true for quadratic extensions. Given primes $p_1, p_2, ... p_n$ find a prime $q \equiv 1 \bmod 4p_1 ... p_n$, which exists by Dirichlet's theorem, and consider $K = \mathbb{Q}(\sqrt{q})$.
| No. If d is a square modulo p for all p in S, then all p in S split in $\mathbb{Q}(\sqrt d)$.
| https://mathoverflow.net |
270,638 | [
"https://mathoverflow.net/questions/270638",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41650/"
] | Let $X$ be a smooth projective surface such that $\chi(O_X)=1$ and $K_X^2\geq 3$(or just $K_X^2>0$). Let $D$ be $(-1)$-class, i.e: $D^2=-1,D^2+D.K_X=-2$(equivalently, $D^2=-1, \chi(-D)=0$). I wonder whether we can show that $D$ is effective.
If $X$ is rational surface and $K_X^2>0$, then such $D$ is effective. ... | It is easy to find counterexamples with $X$ of general type. Take $S$ of general type with $\chi(S)=1$, $K^2_S>1$ and nonzero torsion in $Pic(X)$ (there are plenty of such surfaces, even with $h^1(\mathcal O)=h^1(\mathcal O)=0$). Now blow up $S$ to get $X$ and an effective $-1$ curve $E$ and set $D=E+L$, where $... | Assume $X$ is minimal. Since $S$ is of general type (see my comment), $K_{X}$ is nef ($K_{X}.C \geq 0$ for all curves C). By definition we have $K_{X}.D = -1$, therefore $D$ cannot be effective.
| https://mathoverflow.net |
238,254 | [
"https://security.stackexchange.com/questions/238254",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/11027/"
] | I work as a solutions architect for web-based systems on AWS. As part of this role, I often respond to Information Security questionnaires. Nearly all questionnaires request information about data encryption at-rest and in-transit. However only a much smaller percentage ask about other security aspects, such as passwor... | Your threat model is focused on external parties breaking in. But the threats are broader than that.
Low-level hardware backups, VM snapshots, and disposed hardware can all contain data. And because these things tend to be seen to have lower risks, they are often mishandled. So, it's not a "Mission Impossible"... | <blockquote>
This is not to challenge the value of encryption at rest, it is very cheap to access, so there is no reason not to enable it, but where does it sit in terms of priorities?
</blockquote>
It is cheap when you use the lower layers to do the encryption (disk for instance). It gets expensive (in terms of archit... | https://security.stackexchange.com |
565,449 | [
"https://physics.stackexchange.com/questions/565449",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/261461/"
] | As we all know, the probability current density in quantum mechanics is defined as: <span class="math-container">$$\textbf{J}=\dfrac{\hbar}{2mi}(\Psi^* \nabla \Psi-\Psi \nabla \Psi^*)$$</span> For simplicity let us work in one dimension and let us suppose a wave function <span class="math-container">$\Psi= A\ \text{cos... | A solution of the free one-dimensional Schroedinger equation:
<span class="math-container">$$ i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \psi}{\partial x^2}\,\,\,\quad \text{(1)} $$</span>
is:
<span class="math-container">$$\psi = A e^{i(kx -\omega t)} \quad\quad\quad \text{(2)} ... | The continuity relation holds for solutions of the Schrodinger equation. <span class="math-container">$A\cos (\omega t - k x)$</span> is not a solution.
| https://physics.stackexchange.com |
15,360 | [
"https://quant.stackexchange.com/questions/15360",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/12084/"
] | I've fitted my data to a generalized pareto distribution as to model the returns in the tails more accurately. The interior is fitted with kernel distributions.
I would like to now test whether the original returns conform to the hypothesized distribution (i.e. generalized pareto distribution). Can I do this with the... | In another solution, the answer is based on replication approach. Here, we provide some other approaches for the valuation of the LIBOR rate,
\begin{align}
L(T_{i-1}; T_{i-1}, T_i) = \frac{1}{\Delta T_i}\left(\frac{1}{P(T_{i-1}, T_i)}-1\right),
\end{align}
set a $T_{i-1}$ and paid at $T_i$, where $\Delta T_i =T_i-T_{i... | <strong>Edit for Gordon.</strong>
First, fix point in time $T_0,...,T_n$ whereas $T_1,...,T_n$ are the coupon dates and $T_0$ is interpreted as the emission date of the bond. At time $T_i$, $i = 1,...,n$ the owner of the bond receives $c_i$.At time $T_n$ the owner receives the face value K.We now go on to compute the p... | https://quant.stackexchange.com |
190,764 | [
"https://security.stackexchange.com/questions/190764",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/183341/"
] | I have Spring Boot API app on the server side and VueJS app on the client side. Upon successful login, the server side sends JSON response that includes accountType with value either VIEW_GOLD or VIEW_SILVER, if accountType is VIEW_GOLD, the user is directed to view list of GoldBar object and so on like in this code in... | Every browser comes with powerful development tools. The usual hotkey to access them is <kbd>F12</kbd>.
Any user could use the JavaScript debugger of their browser to set a break-point in the line <code>if (response.data)</code>, wait until the break-point is reached, edit the value <code>response.data.accountType</c... | This is a very basic authentication problem. You have your server-side code which is supposed to provide information as response to a request.
You want your server to provide the data of a "GoldView" (whatever this is) to authorized users only. This requires the server to receive some proof that the requesting entity ... | https://security.stackexchange.com |
145,458 | [
"https://math.stackexchange.com/questions/145458",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11860/"
] | How do you solve equations that involve the $\max$ function? For example:
$$\max(8-x, 0) + \max(272-x, 0) + \max(-100-x, 0) = 180$$
In this case, I can work out in my head that $x = 92.$ But what is the general procedure to use when the number of $\max$ terms are arbitrary? Thanks for the help, here is a Python soluti... | Check each of the possible cases. In your equations the "critical" points (i. e. the points where one of the max's switches) are $8$, $272$ and $-100$. For $x \le -100$ your equation reads
\[ 8-x + 272 - x + (-100-x) = 180 \iff 180 - 3x = 180 \]
which doesn't have a solution in $(-\infty, -100]$.
For $-100 \le x \le... | Hint: You can think of $max(8-x,0)$ as a piecewise defined function.
$$
max(8-x,0) = \begin{cases} 0 \text{ if $ x\geq 8$} &\\ 8-x \text{ if $x \lt 8$} \end{cases}
$$ Apply this idea to other $max$ functions as well.
| https://math.stackexchange.com |
348,233 | [
"https://softwareengineering.stackexchange.com/questions/348233",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/181516/"
] | <strong>Note:</strong> Still learning Haskell, not reached Monoids, studying Applicative Functors.
I saw this implementation and I am not entirely clear on it:
<pre><code>instance Applicative ((->) r) where
pure x = (\_ -> x)
f <*> g = \x -> f x (g x)
</code></pre>
This is what I think:
N... | The type <code>(->) r a</code> is just an alias for <code>r -> a</code>, nothing more. Its kind is <code>*</code> (“type”).
The type constructor <code>(->) r</code> can be thought of as <code>r -> ___</code> where <code>r</code> is already known but <code>___</code> is to be filled in later. Its kind is ... | Let's use some equational reasoning.
Our functor <code>f</code> is <code>(->) r</code>, so <code>f a</code> is <code>(->) r a</code> which is just <code>r -> a</code>.
<code>pure :: a -> f a</code>, so in this case <code>pure :: a -> (r -> a)</code>.
<code><*> :: f (a -> b) -> f a... | https://softwareengineering.stackexchange.com |
652,156 | [
"https://physics.stackexchange.com/questions/652156",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8441/"
] | Suppose two rigid bodies collide head-on in a vacuum. Will the collision be elastic or inelastic?
In most rigid body computer systems you have to specificy a coefficient of restitution for the collision, so the answer would depend on that. But this is a post-hoc mechanism used so we can better model real world system... | <blockquote>
Suppose two rigid bodies collide head-on in a vacuum. Will the
collision be elastic or inelastic?
</blockquote>
A collision between two rigid bodies is elastic. A rigid body is an idealization of a body that does not deform or change shape. A inelastic collision always involves some degree of deformation. ... | The rigid body model is quite useful to model many interesting physical systems, and, for example, robotics heavily hinges on such a model.
The rigidity constraint simply means that all distances of the body parts keep constant during the motion. The physical consequence is that many dissipation processes, like the tra... | https://physics.stackexchange.com |
135,746 | [
"https://mathoverflow.net/questions/135746",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36506/"
] | It is known that given a set of Areas $A_f$ and normals $\vec{n}_f$ if $\sum_f A_f \vec{n}_f=0$ exist a unique convex polyhedron with given face areas and normals. (Minkowski theorem - See Alexandrov book on Convex Polyhedra).
Obviously here I'm identifying all the isometric polyhedra.
In principle with the same set ... | The convex polytope has the largest volume. This was proved in
K. Boroczky, I. Bárány, E. Makai Jr. & J. Pach: Maximal volume enclosed by plates and proof of the chessboard conjecture, Discrete Math. 69 (1986) 101–120.
For measures and convex bodies, a proof is provided by
Zhang, Gaoyong: The affine Sobolev ineq... | I believe this was how Minkowski proved his theorem (he used a variational principle to show that the sought-after polyhedron maximizes volume). For the proof, see Aleksandrov's "Convex polyhedra", section 7.2
| https://mathoverflow.net |
23,866 | [
"https://physics.stackexchange.com/questions/23866",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8236/"
] | Why the pressure of atmosphere doesn't crush you when you e.g. walk outside? I mean the density of air is $1.26 kg/m^3$, so with $100 km$ above us, it exerts much pressure on you when you walk outside.
| If you were a completely empty shell you'd likely be crushed immediately on finding yourself in the earth's atmosphere. But you are filled with stuff (blood, flesh, bones) which is also at approximately atmospheric pressure. If you consider a point on your skin, the pressure of the air on the outside pushing it in is e... | To add to Dan's answer - the same thing also applies indoors.
Even with a roof over your head the outside air presses on the windows, doors and walls with the same air pressure, and so compresses the air inside the room to the same pressure.
| https://physics.stackexchange.com |
576,004 | [
"https://electronics.stackexchange.com/questions/576004",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/277996/"
] | I am using a level translator in my design to interface between two systems. I also want an option to bypass the level translator by shorting a jumper resistor placed across terminals A and B.
What happens when I place the jumper when the level translator is assembled? Is it advisable to use it that way or do I have to... | An ordinary general-purpose switch such as an NPN transistor or n-FET can work. 2N3904 or similar for the NPN; 2N7001 or similar for the FET.
Using this kind of open-collector/open-drain device avoids two issues:
<ul>
<li>GPIO I/O voltage vs. the SIM800H VBAT pull-up voltage</li>
<li>Host power state vs. the SIM800H po... | The intention of the circuit is to simply pull down the input to a digital pin that has a pullup. Use whatever small NPN/nMOS transistor you already have on hand/in inventory which is compatible with the external 3v3 turn-off. A BJT with a base resistor, or a small logic-level FET which can be turned on at 3v3 can be u... | https://electronics.stackexchange.com |
284,763 | [
"https://physics.stackexchange.com/questions/284763",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/132249/"
] | How can gravitational potential be negative?
Gravitation energy increases as we go higher. How is this possible when it is negative?
Please give an intuitive explanation.
Actually I'm confused by this statement: "Gravitational potential energy increases as we go higher but still remains negative."
My doubt is almos... | OK Drop a 10 kg object from a height of 10 meters. It will gain speed as it falls, and so kinetic energy. At the bottom, catch it in such a way that you charge a battery by using the kinetic energy and bring it to stop.
Just by making the object fall for 10 meters, you were able to collect some energy. This energy com... | You almost answered your own question. If you increase potential energy by going up, then you decrease by going down. Decreasing means becoming more negative. So, being in a gravity well causes an object to have less total energy than an object not in a gravity well, all else equal. If you say 0 potential energy due to... | https://physics.stackexchange.com |
77,992 | [
"https://stats.stackexchange.com/questions/77992",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/35053/"
] | I have two sets, $A$ and $B$, containing <strong>string</strong> values.
I am trying to model the relationship between sets $A$ and $B$ by computing the following distance:
$d = \frac{ \mid A \mid + \mid B \mid- \mid A \cap B \mid}{ \mid A \mid + \mid B \mid}$
$ d = \ [0,...,1 \ ] $
The more $A$ and $B$ are similar ... | It's easy enough to see that $\max\{X,Y\}=\frac{X + Y + |X - Y|} 2$ which gets you an expression for the expectation of the max in terms of the two means and the L1 distance between $X$ and $Y$.
| In general, if $X$ and $Y$ are i.i.d. with (<strong>CDF</strong>) $F(t) = P(X \leq t)$ and (<strong>PMF</strong>) $m(t) = P(X = t)$,
$$
E[\max(X,Y)] = 2 E[X\cdot F(X)] - E[X\cdot m(X)]
$$
You can derive this expression by breaking the expectation into three parts – the third part comes from the possibility that $X=Y$.
... | https://stats.stackexchange.com |
105,778 | [
"https://electronics.stackexchange.com/questions/105778",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40012/"
] | I have a transformer based AC fan controller (rated for 230V input) with five output steps ( 230V(5) - 200V(4) - 160V(3) - 140V(2) - 125V(1) ). I would like to have more fine grained steps, and am thus thinking to connect two equal transformers in series, giving me a total of 25 different steps.
The second transformer... | I'd have thought a variac might be a better solution, but yes, you can feed the output of one transformer into the input of another, and driving below its rated voltage is not going to be a problem.
You're not really connecting them 'in series', but I know what you mean.
| In principle it will operate, but transformers have losses, so it will suffer two of those losses. Additionally, you should calculate exactly what ratios this actually produces, because a number of the combinations will be the same as or similar to other combinations... so it won't necessarily be particularly fine-grai... | https://electronics.stackexchange.com |
11,335 | [
"https://quantumcomputing.stackexchange.com/questions/11335",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/4943/"
] | The book "Introduction to Spintronics" 2nd edition says on page 542 that an arbitrary single qubit rotation and a CNOT comprises a universal gate set. Is this true?
If so, why isn't this the gate set implemented in commercial quantum computing implementations? The book makes them sound straight-forward to implement i... | <blockquote>
an arbitrary single qubit rotation and a CNOT comprises a universal gate set. Is this true?
</blockquote>
Yes. If you want to understand <em>why</em>, don't go with any answers about finite gate sets such as CNOT, H, T because the proof of those usually relies on the proof of the set you've stated (so t... | <strong>Partial answer (universality):</strong>
Set of gates consisiting of CNOT, <span class="math-container">$S$</span>, <span class="math-container">$T$</span> and <span class="math-container">$H$</span> allows you to approximate any gate arbitrary accuracy.
CNOT is part of your set. Sice <span class="math-contai... | https://quantumcomputing.stackexchange.com |
3,446,574 | [
"https://math.stackexchange.com/questions/3446574",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/720004/"
] | I have been given the following problem: Let <span class="math-container">$Z=(Z_1,Z_2,Z_3)$</span> be a triple coin toss with <span class="math-container">$p=1/4$</span>. Let <span class="math-container">$Y:=\frac{1}{2}Z_1 + \left(\frac{1}{2}\right)^2Z_2+\left(\frac{1}{2}\right)^3Z_3$</span> be a random variable <span ... | You may be over thinking this: there are eight possible values for the triplet <span class="math-container">$Z$</span> and each corresponds to a different <span class="math-container">$Y$</span>. These are:
<pre><code> Z Y probability
(0,0,0) 0 27/64
(0,0,1) 1/8 9/64
(0,1,0)... | <ol>
<li>It's not continuous; the support is contained in <span class="math-container">$[0,1]$</span> but actually the support is the binary-represented numbers <span class="math-container">$0.000,0.001,0.010,0.011,0.100,0.101,0.110,0.111$</span>. Each value of <span class="math-container">$Z$</span> corresponds to exa... | https://math.stackexchange.com |
25,604 | [
"https://security.stackexchange.com/questions/25604",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/4799/"
] | How do I interpret the 2.2.1 point for PCI-DSS? Is "application server" 'one primary function' or does it need to be "program x server", "program y server" etc?
I have a collection of applications that run server side within my environment. Some of these interact indirectly with the appli... | So basically what the requirement is saying is that you need to assign one primary function per server.
The server you've described sounds like it runs a few applications for production users to utilize. This would be classified as an "application" server. However, you've also mentioned that there are multiple applica... | The one truism of PCI-DSS compliance is this:
<blockquote>
You are PCI-DSS compliant if your QSA says you are PSI-DSS compliant.
</blockquote>
I'm of the opinion that the PCI council did a pretty stinking good job of giving us a very clear and to the point standard to follow, at least as far as standards go. That b... | https://security.stackexchange.com |
54,683 | [
"https://stats.stackexchange.com/questions/54683",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17107/"
] | I am struggling with a linear regression model of the shape $y = a + b_1\text{month} + b_2\text{year}$. I have 12 months for each year and 10 years. My dependent variable is a log transformed ratio. I have understood that much that when setting such a model up in R, R automatically picks a level for each variable to go... | Peter's answer is correct. One note worth mentioning is that all other coefficients should be interpreted as marginal effects relative to baseline, which is March 2005.
So, for example, if we were to impute a fitted value for May 2008:
$$ \widehat{y} = \widehat{\alpha} + \widehat{\beta_1}*month + \widehat{\beta_2}*ye... | The intercept is the predicted value of y when the month is March and the year is 2005.
But this looks like a poor model. You should look into time series methods. This is so because time series data are not independent; e.g. the value for April 2005 is related to that for March 2005. Treating both month and year as ... | https://stats.stackexchange.com |
386,492 | [
"https://softwareengineering.stackexchange.com/questions/386492",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/302389/"
] | Suppose the client wants to build an online shopping system. If we think of use case scenario, a database or a bank would be a secondary actors to this system.
Is it valid to have a user story like
<pre><code> As a customer I want to be able to access the database so that I can view catalog items
</code></pre>
Or ... | User stories generally don't include implementation details. They aim to capture the <em>functionality</em> the user is looking for:
<blockquote>
As a customer, I want to be able to view the catalog of items for sale
As a customer, I want to be able to pay with a credit card
</blockquote>
Note that these make no mentio... | Assuming these stories are for developer/engineer. Can we frame it this way -
"As a engineer, I want to provide an interface to the customer to access catalog items from the database."
| https://softwareengineering.stackexchange.com |
1,549,546 | [
"https://math.stackexchange.com/questions/1549546",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/289862/"
] | To begin i tried to prove that the first statement implies second, but took a while to type that (now let's prove the other 5 implications, which would fullfill the circle....), I think there must be a short way to do this. Any ideas?
| <blockquote>
Statement <span class="math-container">$1$</span> is <span class="math-container">$x\in A\implies x\in B$</span>
Statement <span class="math-container">$2$</span> is <span class="math-container">$x\in A= x\in A\land x\in B$</span>
Statement <span class="math-container">$3$</span> is <span class="math-conta... | 1) Suppose $A \subset B$. $A \cap B \subset of A$ as intersections are by definition subsets of the intersecting sets. If $a \in A$ then $a \in B$ as $A \subset B$ $a \in A \cap B$ (because b is in both A and B). So $ A \subset A \cap B$. (Because every element of A is in $A \cap B$). So $A \cap B \subset of A$ an... | https://math.stackexchange.com |
141,068 | [
"https://security.stackexchange.com/questions/141068",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/128766/"
] | Does Kali Linux contain audited software which is designed to aid security and basically does not contain any backdoors?
Is this some sort of professional software or compilation of various tools from non-professional background?
Should I be using Kali Linux or should I use something else like Metasploit?
Does Kali ... | Kali is a community-built distro full of security tools from both organisations and individuals. It is not designed to be used as a day-to-day operating system. It's a quick-start, throw-away distro for security testing.
Metasploit and Kali Linux are entirely different things. In fact, Metasploit is installed on Kali ... | In short: Yes, you should be using Kali.
However, Kali contains lots of software from a non-professional background. Probably for any definition of non-professional, but definitely when it comes to earning money with it.
This is not really an issue because even for professional software you don't get any kind of secu... | https://security.stackexchange.com |
1,006,733 | [
"https://math.stackexchange.com/questions/1006733",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/118359/"
] | I was trying to count how many cards with 4 of a kind I could get from a standard deck of 52 cards in a hand of length 5.
i.e. 4 of the same value (rank) and a card with a different value.
I was told the answer was $13 \times 12 \times 4 = 624$ but I was a little confused why.
The explanation given to me was because... | Note first that in a standard 52-card deck, there is only one copy of each specific rank-suit card in the deck (i.e., only one Ace of spades, only one Ace of clubs, only one Ace of hearts, etc...)
When determining how many four-of-a-kind hands there are, you may choose to consider what suits the 4-tuple consists of as... | The four cards include all suits, and there is only one way to include all four suits. It might be 8 hearts, 8 spades, 8 clubs, 8 diamonds, Q clubs.
| https://math.stackexchange.com |
134,070 | [
"https://security.stackexchange.com/questions/134070",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/121607/"
] | Yesterday I got a new hosting space and when setting up SSH access I noticed they expect me to generate a key pair through a web interface, and then to download the private key and install it on my local system.
My question is, is it safe to transfer private keys over the internet? (of course over an SSL-encrypted con... | While the likelihood of it being compromised is small, you're better off generating it locally so that the RSA private key never leaves your system. This way you only have to upload your public key to the server.
I wouldn't be too concerned about the TLS layer and data in transit, but I would be more concerned about p... | It depends on your definition of safe. If have a TLS-secured connection to the administration interface of the hosting service to keep your password (to the same service) safe from third parties, then why not trust it to transmit an SSH key, too. The hosting provider can likely access your server by other means, so the... | https://security.stackexchange.com |
3,034,103 | [
"https://math.stackexchange.com/questions/3034103",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/589930/"
] | Suppose we have <span class="math-container">$ p, q$</span> where <span class="math-container">$ p$</span> and <span class="math-container">$q$</span> are twin primes between 6,10000. Now the following sequence <span class="math-container">$pq + 2$</span> generates 22 primes . These primes are all in the congruence cla... | Look at the possible remainders <span class="math-container">$\bmod 10$</span>. The only case where <span class="math-container">$p, p+2, p(p+2)+2$</span> may be all primes is <span class="math-container">$p\equiv 9\pmod {10} $</span> (otherwise there are factors <span class="math-container">$2$</span> or <span class="... | Hint: Consider in which cases the product of two twin primes (above <span class="math-container">$5$</span>) doesn't end in <span class="math-container">$3$</span> (which would make their product plus <span class="math-container">$2$</span> end in <span class="math-container">$5$</span>).
| https://math.stackexchange.com |
36,006 | [
"https://stats.stackexchange.com/questions/36006",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11032/"
] | Often I have heard the data miners here use this term. As a statistician who has worked on classification problems I am familiar with the term "train a classifier" and I assume "learn a model" means the same thing. I don't mind the term "train a classifier". That seems to portray the idea of fitting a model as the t... | I suspect its origins are in the artificial neural network research community, where the neural network can be thought of as learning a model of the data via modification of synaptic weights in a similar manner to that which occurs in the human brain as we ourselves learn from experience. My research career started ou... | The term is quite old in artifical intelligence. Turing devoted a long section on "Learning Machines" in his 1950 <em>Computing Machinery and Intelligence</em> paper in <em>Mind</em>, and qualitatively sketches out supervised learning. Rosenblatt's original paper: <em>The Perceptron: A Probabilistic Model for Informat... | https://stats.stackexchange.com |
122,517 | [
"https://electronics.stackexchange.com/questions/122517",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43098/"
] | I am rereading an electronics book (Fundamentals of Electric Circuits; Alexander) that says that the circuits
<img src="https://i.stack.imgur.com/RXVal.png" alt="Lagging-Output RC Phase Shifter"> or <img src="https://i.stack.imgur.com/RCarf.png" alt="Leading-Output RC Phase Shifter">
have the total impedance
<block... | Let's start by pointing out that circuit 1 is the same as circuit 2 and that measuring an output across the resistor will look like a high pass filter whereas measuring it across the capacitor will look like a low pass filter. The filter will have a transitional point (or 3 dB point or half power point) at: -
f = \$\d... | Your first circuit is a low pass filter. DC up to the corner frequency (fc =1/(2*pi*R*C)) are passed through. The second is a high pass filter, all frequencies above the corner (same fc) are passed. OK, the details are more involved. I think the best thing is to get a 'scope and function generator and see what happ... | https://electronics.stackexchange.com |
451,725 | [
"https://physics.stackexchange.com/questions/451725",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20884/"
] | I am working on a simple and popular GR textbook exercise. In Dodelson's <em>Modern Cosmology</em> (p. 54), it is stated thus:
<blockquote>
The metric for a particle traveling in the presence of a
gravitational field is <span class="math-container">$g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$</span>
where <span cl... | Starting from the geodesic equation
<span class="math-container">$$
\frac{d^2x^0}{d\tau^2} = \Gamma^0_{\mu \nu} \frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\tau} = \Gamma^0_{0 0} \frac{dx^0}{d\tau} \frac{dx^0}{d\tau} \tag{1}
$$</span>
Where the last equality follows from the fact that we are in the low speed limit that you c... | If you're looking for conserved quantities, don't start with the geodesic equation. Write down the arc length as:
<span class="math-container">$$I = \int d\tau\left({\dot x}^{a}{\dot x}^{b}g_{ab}\right)$$</span>, and take set the variation with respect to each of the <span class="math-container">$x^{a}$</span> equal ... | https://physics.stackexchange.com |
144,517 | [
"https://cs.stackexchange.com/questions/144517",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/141575/"
] | In 2005 ID software open source the game Quake 3 Arena. When they did it was discovered was an algorithm that was so ingenious and all it did was calculate the inverse of a square root.
The easy way to calculate the inverse of a square root being
<pre><code>float y = 1 / sqrt(x);
</code></pre>
But then again this funct... | Inverse square root is used a lot for vector normalisation :
<span class="math-container">$$xn = \frac{x }{ \sqrt{x^2 + y^2 + z^2}}$$</span>
Which has many uses in computer graphics, such as calculating illumination.
With a traditional FPU, even a good one, this is a very time consuming operation : the multiplications ... | What you can take away from this: When you are given a problem, it is often possible to solve the problem, without solving obvious sub-problems. Like here, where you can calculate 1/sqrt(x) significantly faster than calculating the square root, and dividing 1 by the square root. ( On many implementations it is actually... | https://cs.stackexchange.com |
446,888 | [
"https://electronics.stackexchange.com/questions/446888",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/222922/"
] | I have an old project which is built on using "StdPeriph drivers" for STM32F103 MCU and Keil environment. It uses various drivers for gpio, adc, can, dac, dma, i2c, spi, tim, uart etc.
As these drivers are obsolete now so I want to move to new available ones. But I don't know how much work will be involved in migratin... | <h1>If it ain't broke, don't fix it.</h1>
The StdPeriph drivers work very well on existing STM32 MCUs, and these are going stay around for a while, as long as ST renews its 10 years longevity promise every year.
The register interface of an STM32F1 that'd be manufactured in 2029 will be exactly the same as that of o... | CubeMX can generate hardware and software initialization according to your setup, which then can be exported to any IDE (Kiel, Atollic ect.), but in that case you would be dealing with HAL drivers. HAL drivers include a complete set of ready-to-use APIs which simplify the user application implementation, which is great... | https://electronics.stackexchange.com |
18,099 | [
"https://dsp.stackexchange.com/questions/18099",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/10384/"
] | I am a self-learner of DSP by reading various books. I have accomplished basic understanding of Signals - CT and DT and a few transforms. I recently started to learn FIR / IIR Filters.
The part that I cannot understand is that they are termed as 'Filters' which for me logically means blocking / allowing from a thresho... | Filters block or allow to pass, but in the frequency domain. So you first you have to transform your vector into the frequency domain, a sum of sinusoids (Fourier, et.al., said this was possible), then apply the filter to attenuate or block some of them and pass others, then transform back to your original domain to ... | A filter applies a frequency-dependent gain to be applied to a signal.
The process you describe - removing values below a certain threshold - is not filtering in a DSP sense.
A typical FIR filter is shown below. It consists of delays, z^-1, and gains, the $b$ terms.
<img src="https://i.stack.imgur.com/3rnpm.png" ... | https://dsp.stackexchange.com |
3,646,498 | [
"https://math.stackexchange.com/questions/3646498",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/637978/"
] | Given a Banach space <span class="math-container">$X$</span> we say a sequence in <span class="math-container">$X$</span>, <span class="math-container">$\{x_n\}$</span>, converges weakly to <span class="math-container">$x\in X$</span> if
<span class="math-container">$$\lim_n \varphi(x_n)=\varphi(x) \quad \forall \varp... | <span class="math-container">$$
1111^{2019} = (11111-10000)^{2019}\equiv -(10000)^{2019} \\= - 10^{4*2019} =
-10^{5*1615}*10 = -100000^{1615}*10 \\= -(1 + 9*11111)^{1615}*10 \equiv -10 \equiv 11101 \pmod{11111}
$$</span>
| Ok, let me add my little fiddle ...
Considering <span class="math-container">$1111^2=1111*1000+1111*100+1111*10+1111$</span>
<span class="math-container">$$
\begin{matrix}
1 & 1 & 1 & 1 & \\
& 1 & 1 & 1 & 1 \\
& & 1 & 1 & 1 & 1 \\
& & & 1 & 1 ... | https://math.stackexchange.com |
105,454 | [
"https://physics.stackexchange.com/questions/105454",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45776/"
] | The free particle solution in stationary state (with definite energy) to the Schrödinger equation is
$$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$
Since the energy is definite, and hence the momentum is definite, the uncertainty in position must be infinite. How is this reflected by the probability distr... | For any function of $x$ and $t$ that depends on the combination $x\pm vt$ (for constant $v$ represents a wave with a <em>fixed</em> shape that travels in the $\mp x$ direction with speed $v$. That is to say,
$$
x\pm vt={\rm constant}
$$
In your wave function,
$$
\psi(x)=Ae^{i(kx-\omega t)}+Be^{-i(kx+\omega t)}\tag{0},
... | The terms in $A$ and $B$ represent waves traveling in opposite directions. Their values are set by the initial conditions of the problem. Some problems will involve waves traveling to the right, others to the left, others a combination of the two. Evidently your book chose to focus on a wave traveling to the right f... | https://physics.stackexchange.com |
291,122 | [
"https://stats.stackexchange.com/questions/291122",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/168590/"
] | I'm reading Baxter's "Introduction to Financial Calculus" and he defines a stochastic process as a continuous process $X_t $ that can be written as
$X_t = X_0 + \int_0^t \sigma_s dW_s + \int_0^t \mu_s ds $,
where $\sigma, \mu $ are are visible processes that satisfy $\int_0^t (\sigma_s^2 +|\mu_s|) ds $ is finite for ... | The so-called "stochastic processes" are actually Ito processes---an Ito integral plus an $\omega$-by-$\omega$ Lebesgue integral. By "visible", you probably mean <em>previsible</em>. This is not general.
The integrability condition is just there to ensure that the two summand integrals exist, in the appropriate sense.... | A stochastic process is an infinite collection of random variables, where each random variable is indexed by t (usually time but not necessarily). A random variable is a (deterministic) function of the experiment outcome ω (ω can be one-dimensional, finite-dimensional, or infinite-dimensional which it usually is if a s... | https://stats.stackexchange.com |
285,186 | [
"https://physics.stackexchange.com/questions/285186",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45627/"
] | Suppose that a cube of silicone elastomer 1cm^3, of hardness similar to a soft gum rubber (durometer equivalent of 30) was compressed by a 100 grams weight to a height of 0.5cm, and that the weight disappeared or was lifted faster than the speed of sound.
Are there some physical theories that allow me to estimate how... | If a wave is $f(x,t)=Re[e^{ikx-i\omega t}]$ with $\omega>0$, then it goes right if $k>0$ or left if $k<0$. Do you see why? Try picking two or three values of $t$ and making plots...
<em>But</em>,you can alternately write a wave as $f(x,t)=Re[e^{ikx+i\omega t}]$, and now it's reverse! $k>0$ is left-travelin... | Using the usual separation of variables method, the solution of the time-dependent Schrödinger equation is $$\Psi(x,t)=e^{-iEt}\psi(x)=e^{i(\pm kx-Et)},$$ where $\psi(x)$ is the solution to the time-independent equation and we've set $\hbar=1$.
Wave equations are characterized by having solutions of the form $f(x,t)=f... | https://physics.stackexchange.com |
48,871 | [
"https://dba.stackexchange.com/questions/48871",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6607/"
] | Pretty simple question: is it standard/best practice to backup dev and QA instances of the database?
Assume that the schema information is kept in some form of source control.
| QA and dev databases (I will refer to these as <strong>non-prod[uction]</strong> to encompass all life cycles) <strong><em>are still databases</em></strong>. So the business (in this case, might be the app dev team) needs to determine what type of disaster recovery they require.
In my opinion, SLAs don't just apply t... | Say that you have 8 developers working daily with a dev database.
They work for 8 hours/day.
Each hour costs say 100$ per developer.
That is 6400$ for one day of work on a DEV database.
In this situation, if it was up to you, would you do transaction log backups at least every hour just in case?
Or would you go with ... | https://dba.stackexchange.com |
96,108 | [
"https://cs.stackexchange.com/questions/96108",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/90025/"
] | If there is an algorithm running in time $O(f(n))$ for some problem A, and somebody comes up with an algorithm running in time, $O(f(n)/g(n))$, where $g(n) = o(f(n))$, is it considered an improvement over the previous algorithm?
<blockquote>
Does it make sense, in the context of theoretical computer science, to come... | No, an algorithm running in time $O(f(n)/g(n))$, where $g(n) = o(f(n))$, is not necessarily considered an improvement. For example, suppose that $f(n) = n$ and $g(n) = 1/n$. Then $O(f(n)/g(n)) = O(n^2)$ is a worse time bound than $O(f(n)) = O(n)$.
In order to improve upon an algorithm running in time $f(n)$, you need ... | Remember that $O(...)$ notation is meant for analyzing how the task grows for different sizes of input, and specifically leaves out multiplicative factors, lower-order term, and constants.
Suppose you have an $O(n^2)$ algorithm whose actual runtime is $1n^2+2n+1$ (assuming you can actually count the instructions and k... | https://cs.stackexchange.com |
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