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 |
|---|---|---|---|---|---|
41,922 | [
"https://mathoverflow.net/questions/41922",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2926/"
] | Can someone give an explicit example of a group with two generators $a$, $b$, such that $a^2 = b^3 = 1$ and $a b$ has infinite order, but which is not isomorphic to the free product of $\mathbb{Z}_2$ and $\mathbb{Z}_3$?
| It is straightforward to calculate that the commutator subgroup $G' = D$ of $G = \langle a,b \mid a^2, b^3 \rangle$ is a free group on the generators $x=bab^{-1}a$, $y=b^{-1}aba$, where $|G:D|=6$.
Now $(ab)^6$ is equal to the commutator $x^{-1}yxy^{-1}$, which lies in $D'$ but not in $D''$, so if we add any nontrivial... | The free product <span class="math-container">$\mathbb Z_2$</span> and <span class="math-container">$\mathbb Z_3$</span> (i.e. PSL(2, <span class="math-container">$\mathbb Z$</span>)) is Gromov-hyperbolic (as every virtually free group) and non-virtually cyclic. Therefore by a result of Olshanskii, "SQ-universality of ... | https://mathoverflow.net |
209,916 | [
"https://softwareengineering.stackexchange.com/questions/209916",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/78245/"
] | I have
<pre><code>if (!b && c || a && c)
//do action a
else
//...
</code></pre>
Due to some internal relationship between a, b, and c. <code>!b && c || a && c</code> <strong>is proved to be equivalent to</strong> <code>(! a && b) || c</code>.
I just wonder will <code>(! a... | a good optimizer will make any difference here moot
you can think in how the short circuit works:
with <code>if ((!b && c) || (a && c))</code> you get
<pre><code>if(b)goto OR2;
if(c)goto then_lbl;
OR2:
if(!a)goto else_lbl;
if(!c)goto else_lbl;
then_lbl://...
</code></pre>
while with <code>if((! a &... | Are you sure it's
<pre><code>(! a && b)
</code></pre>
rather than
<pre><code>!(a && b)
</code></pre>
?
If not, the brackets are unnecessary and just lead to confusion.
Either way, generally the less operations you have the better for the computer, and in both AND or OR conditions it's better to... | https://softwareengineering.stackexchange.com |
76,162 | [
"https://physics.stackexchange.com/questions/76162",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29183/"
] | Many documentaries regarding the double slit experiment state that they only send a single photon through the slit. How is that achieved and can it really be ensured that it is a single photon?
| In the double slit experiment, if you decrease the amplitude of the output light gradually, you will see a transition from continuous bright and dark fringe on the screen to a single dots at a time. If you can measure the dots very accurately, you always see there is one and only one dots there. It is the proof of the ... | Quantum dots. nanoscale semiconductor materials that can confine photons in 3 dimensions and release them a measurable time after. Based on material used the decay time is known empirically. frequency is also known. the latter is sufficient to calculate the energy of one photon. The former is then sufficient to calcula... | https://physics.stackexchange.com |
121,650 | [
"https://cs.stackexchange.com/questions/121650",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/109346/"
] | This is actually a problem that our professor gave us, and I'm clueless of how to answer this. I browsed through various sources, but none were helpful regarding this question.
The question is,
<blockquote>
In the definition of semantics of logic, P implies Q is defined as
true under the assignment of both P and ... | This question is a soft question IMO, it assumes there's common ground about what "should be true" independent of definitions but it doesn't clarify what those assumptions are. If I were to break it down, I'd say it's looking for a particular bit of reasoning (e.g. a proof or an inference rule) to hold and then asking ... | In classical propositional logic, we define <span class="math-container">$P \rightarrow Q$</span> to be <span class="math-container">$\neg P \vee Q$</span>. But if we redefined the semantics of implication as suggested above, this would no longer hold.
| https://cs.stackexchange.com |
6,915 | [
"https://electronics.stackexchange.com/questions/6915",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | I'm trying to get the Timer2 period match interrupt on my dsPIC33FJ128GP802 working. I want it to interrupt after ~480 cycles. I'm using MPLAB C30.
I have, to initialize the timer and interrupt:
<pre><code>// Initialize Timer2, which is used for output timing.
T2CONbits.TON = 1;
T2CONbits.TSIDL = 0;
T2CONbits.TCKPS =... | I just looked at the code I wrote a while ago to set up timer 2 for a periodic interrupt of 1 ms for a PIC24F (essentially same timer hardware as dsPIC33F), and it looks like so:
<pre><code>#define CPU_CLK_RATE 32000000L
#define PERIPH_CLOCK_RATE (CPU_CLK_RATE/2L)
#define TIMER_2_RATE 1000L
#define TIMER_2_PRE 64L ... | The datasheet seems to suggest you should clear TON, initialize the timer, then set TON. Many example sequences end with setting TON, they don't start with it.
Many devices latch working values out of their configuration registers when they're enabled... so you should always disable, configure, then enable. Be very... | https://electronics.stackexchange.com |
14,667 | [
"https://mathoverflow.net/questions/14667",
"https://mathoverflow.net",
"https://mathoverflow.net/users/622/"
] | In complex projective geometry, we have a specified Kähler class $\omega$ and we have a Lefschetz operator $L:H^i(X,\mathbb{C})\to H^{i+2}(X,\mathbb{C})$ given by $L(\eta)=\omega\wedge \eta$. We then define primitive cohomology $P^{n-k}(X,\mathbb{C})=\ker(L^{k+1}:H^{n-k}(X)\to H^{n+k+2}(X))$, and we even have a nice t... | The primitive classes are the highest weight vectors.
Hard Lefschetz says that the operator $L$ (which algebraic geometers know as intersecting with a hyperplane) is the "lowering operator" $\rho(F)$ in a representation $\rho
\colon \mathfrak{sl}_2(\mathbb{C})\to End (H^\ast(X;\mathbb{C}))$. The raising operator $\rh... | If you take Poincare duals, then the wedge product becomes intersection, and the Kahler form $\omega$ becomes a hyperplane $H$. Then, the primitive cohomology in dimension $n - k$ consists exactly of those classes whose duals (which are homology classes in dimension $n + k$), when we intersect with $k + 1$ generic hype... | https://mathoverflow.net |
103,889 | [
"https://physics.stackexchange.com/questions/103889",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26686/"
] | Jackson's Electrodynamics defines the Drude-Lorentz model as a set of harmonic oscillators (running over indices $j$ below), which, if you write out the equations of motion and rearrange a little, gives you the the famous DL equation for the permittivity of a material:
$$\epsilon(\omega) = \epsilon_0 + \frac{Ne^2}{m}\... | This is a classic question. The trains travel one hour till the collision. So the bird flies a distance of 60 km. Which is in contradiction with the other answer.
| Can you rephrase the question? I don't understand what you're asking.
[Would comment, but insufficient reputation]
So maybe a good way to start is to describe the distance remaining between the trains as a function of time, which seems to me like it should be
$$ d(t) = 60 - 60t, 0<t<1$$
since in the rest fra... | https://physics.stackexchange.com |
651,542 | [
"https://electronics.stackexchange.com/questions/651542",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/318043/"
] | I am planning to use ACS712 5A current sensor in my project an I was wondering if anyone knows if this sensor measures just the Active Current or also the Reactive Current.
The datasheet doesn't say anything particular, and I wonder if that may or may not affect the calculations. The controller input pins are connected... | It's not that simple.
Regardless of the type, a regulator in general is a capacitive (reactive) load. When connected directly across the mains, depending on the design, there are going to be reactive currents which basically bring extra burden on the transmission lines: The apparent power will increase while the real (... | <blockquote>
<em>I'm trying to design an AC/DC power supply with around 15V/25A output</em>
</blockquote>
That's a power requirement of 375 watts out <-- take note because any formal design produced by an IC supplier (such as reference designs by TI) must use PFC if above around 75 watts out.
If using PFC then a con... | https://electronics.stackexchange.com |
107,465 | [
"https://electronics.stackexchange.com/questions/107465",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40695/"
] | Why do we use rms values? I can't get my head around why these values are used. I am doing an intro course to elec eng and we get given some values (normally voltages) in rms and others not, and we are expected to calculate other values but I don't know when to calculate rms or when to calculate something else.
I real... | We use RMS when we are interested in the power delivered by a source (into an ohmic load). For a DC voltage that power is proportional to V^2: P = I * V, and I = V / R, hence V appears twice in the formula.
So the power at any one moment is proportional to V^2. Hence the average power is proportional to mean( V^2 ). W... | <blockquote>
we seem to use rms even when we don't square anything and we aren't
interested in calculating power...
</blockquote>
Yes, we do and, we also calculate the current through a capacitor by using the RMS quantities despite there being no net power dissipated or taken (the capacitor is purely reactive) yet... | https://electronics.stackexchange.com |
155,594 | [
"https://softwareengineering.stackexchange.com/questions/155594",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31364/"
] | I have the following setup in my project:
<pre><code>public class WebApiApplication : System.Web.HttpApplication
{
public static ISessionFactory SessionFactory { get; private set; }
public WebApiApplication()
{
this.BeginRequest += delegate
{
var session = SessionFactory.OpenSe... | Which of these represents the minimum useful addition to the work that your application does? Usually I take the view that a job on a queue should represent a useful work unit: whether it completes or cancels, you should end up with the system in a consistent state.
That situation is mostly defined by your problem dom... | First of all: why are these Fetch and Send tasks combined anyway?
If they depend on each other anyhow (use data from the other or have to be processed in a certain order), the "Job" should be atomic, be kept and processed together within the node.
On the other hand, if the "Job" is the representation of a communicat... | https://softwareengineering.stackexchange.com |
1,892,692 | [
"https://math.stackexchange.com/questions/1892692",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | we hae a cylindrical tank which is full and depth is 10 meters. The rate at which the depth of liquid drops is proportional to the square root of the depth of the liquid. After draining for 20 minutes, the tank has now depth 5 meters. How long it takes for tank to empty?
attempt:
Let <span class="math-container">$H(t)$... | $$ \frac{dH}{dt} = k\sqrt{H} \implies \int \frac{ \mathrm{d} H }{\sqrt{H}} = \int k ~\mathrm{d} t \implies 2 \sqrt{H} = kt + C$$
$H(0)=10$ and $H(20)=5$
$$ C=2\sqrt{10}~~ k=\frac{\sqrt{5}-\sqrt{10}}{10}$$
Hence $$ 2\sqrt{H} = \left(\frac{\sqrt{5}-\sqrt{10}}{10}\right)t+2\sqrt{10}$$
$$\Leftrightarrow H= \left(\left(... | I would say no.
The question says the rate of fall in liquid level is proportional to $√H$ and not equal to.
SO you should take $dh/dt=-k√h$.
Then integrate this equation with the limits for h as 10 to h and for t as 0 to t.
You will get $2(√h -√10)=-kt$. ----(1)
Now put $t=20$ and $h=5$ in this equation to get th... | https://math.stackexchange.com |
261,904 | [
"https://softwareengineering.stackexchange.com/questions/261904",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/134483/"
] | Sometimes I have clients that from start gives you huge flow of words about "how task should be done in details", like "you must use SQL Server here", "should do this in do-while-loop", "should make two functions like that, and they should run in parallel", etc..
But they never-ever give you any word about "what is th... | Fire them. Refer them to your worst enemy. You don't need the headaches. If they don't know what they want, neither will you, and the amount of trouble you will go through, finding out what is needed, IS NOT WORTH whatever they're planning on paying you.
Many years ago, a drinking buddy of mine gave me a piece of w... | <em>Even if you ask them about this questions directly, they only can say "I don't know, but this work should be done".</em>
Your job is now to explain to them <strong>why</strong> you need that information. As far as s/he is concerned, you don't need to know, you just need to do what they say.
You need to explain th... | https://softwareengineering.stackexchange.com |
73,148 | [
"https://stats.stackexchange.com/questions/73148",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31659/"
] | Let us say we have this regression
$$\ln(y) = a + B_1(age) + B_2\ln(savings) + B_3\ln(income+1)$$
When carrying out the regression we obtain:
$$\ln(y) = 0.3445 + 0.5(age) + 0.4556 x_1 + 0.55566 x_2$$
How would one interpret the coefficients in each case? Of particular concern is the income coefficient. An increas... | If income is typically much larger than 1, you could ignore the $+1$ for interpretation and use the usual statement for linear log-log-models: "A 1% increase in income is associated with a $100\% \cdot (1.01^{0.55566}−1)=0.5544\%$ increase in the geometric mean of $y$. Or, a bit less precise but better to understand: "... | Assuming everything else stays constant,
(change in y) / (y) = B3 * (change in income) / (1 + income)
LHS is your percentage change in y. Put the values in the RHS. So for a 1% increase in income, change in income is 0.01 and income is 100. Gives you a result straightaway as B3 * (1/101)% or 0.0055%.
| https://stats.stackexchange.com |
20,340 | [
"https://astronomy.stackexchange.com/questions/20340",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/16132/"
] | My question is about the equivalence about having an event horizon and having a singularity.
In one side the implication looks pretty obvious:
<ul>
<li>A singularity implies having an event horizon and therefore a black hole. Since the mass is compressed in a zero volume space, if you get close enough there will be ... | <blockquote>
Does having an event horizon imply the existence of a singularity?
</blockquote>
An event horizon is not an inherent component of any given object. It's not like once a star turns into a black hole, it suddenly gets an event horizon. The event horizon is merely a mathematical boundary which defines the ... | A real neutron star would start to collapse when the strength of its gravity exceeds the strength of the neutron degeneracy pressure, before it has an event horizon.
As you approach the event horizon, the force required to stop a stationary mass from falling in approaches infinity. So I don't think any finite force, f... | https://astronomy.stackexchange.com |
69,179 | [
"https://stats.stackexchange.com/questions/69179",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12329/"
] | I am having an issue with using neural networks. I started with something simple. I just used nntool with one hidden layer (with one neuron) with linear activation function. For the output also, I used the linear activation function. I just fed my Xs and Ys to the neural network tool and got the results on the testing ... | Basic questions are good.
In this application you have lots of data and the opportunity to collect many more. This makes the calculations so easy you can practically do them in your head using fundamental principles. I will share the standard progression of thinking that a statistician will automatically go through ... | To test for changes pre and post within one group you should carry out a repeated-measures ANOVA (repeated-measures T-test). If you want to know how many measurements you would likely need to obtain 1% (.01) certainty you can calculate this doing a statistical power calculator.
I hope that helps!
| https://stats.stackexchange.com |
582,294 | [
"https://physics.stackexchange.com/questions/582294",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275725/"
] | Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
| The ideal gas law <strong>only holds for <strong>gases in equilibrium</strong></strong>. Processes which involve successive equilibria steps are called reversible and those which don't are irreversible. The free expansion of a gas is an irreversible process which contains many non equilibrium steps and therefore the id... | If the vessel is open, there is no well definite volume. Leaving a part non-equilibrium processes like free expansion, in equilibrium situations, working with an open vessel implies that <strong>neither <span class="math-container">$V$</span> nor the number of moles <span class="math-container">$n$</span></strong> are ... | https://physics.stackexchange.com |
43,409 | [
"https://softwareengineering.stackexchange.com/questions/43409",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12697/"
] | My friend is a project manager for a software company. The most frustrating thing for him is that his <strong>engineers frequently leave their jobs</strong>. The company works hard to recruit new engineers, transfer projects, and keep a stable quality product. When people leave, it drives my friend crazy.
These engine... | If many people are leaving the job, then it is a clear sign that the work environment is not suitable for them. This can be because either the work environment is generally poor, e.g. poor management, a lot of overtime, poor job satisfaction.
But it can also be because the company does not provide the means for the i... | When an organization has higher-than-usual turnover, there's ALWAYS a reason and it is ALWAYS management.
<ul>
<li>If the only way an engineer can get a raise is to change jobs, he'll do it.</li>
<li>If the only way an engineer can get better working conditions is to change jobs, he'll do it.</li>
<li>If the only way ... | https://softwareengineering.stackexchange.com |
3,060,456 | [
"https://math.stackexchange.com/questions/3060456",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/622713/"
] | Can any one explain me the intuition behind this formula ? (with permutation example)
<pre><code>P(n, k) = P(n-1, k) + k* P(n-1, k-1)
</code></pre>
| Here is an example which should give you some insight into how I believe you should think about the formula.
Let's say <span class="math-container">$P(n, k)$</span> counts the number of teams of <span class="math-container">$k$</span> people you can make from a roster of <span class="math-container">$n$</span> people,... | Okay, define a word <span class="math-container">$x=x_1\ldots x_k$</span> of length <span class="math-container">$k$</span> over the alphabet <span class="math-container">$[n]=\{1,\ldots,n\}$</span> to be a <span class="math-container">$k$</span>-permutation of <span class="math-container">$n$</span> if <span class="ma... | https://math.stackexchange.com |
135,262 | [
"https://cs.stackexchange.com/questions/135262",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/23150/"
] | In the alpha-beta pruning version of the minimax algorithm, when one evaluates a state <code>p</code> with <span class="math-container">$\alpha$</span> and <span class="math-container">$\beta$</span> cutoff and gets a <code>v</code> value, i.e.,
<em>v = alphabeta(p, <span class="math-container">$\alpha$</span>, <span c... | There's two simple reasons, one fundamental and one related to our current technology. First the technical one: volatile storage is (generally) faster than non-volatile storage. It has fewer requirements - it only needs to store the data for a short while until it gets refreshed, so it's not a surprise that it often is... | @orlp is already discussed speed. There's probably more than could be added (e.g., about latency vs. bandwidth), but let's leave that aside for now.
<h3>Write Endurance</h3>
Instead, let's start by considering a completely separate point: write endurance. Most SSDs use Flash memory. Writing to Flash memory slowly wears... | https://cs.stackexchange.com |
76,760 | [
"https://softwareengineering.stackexchange.com/questions/76760",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/75803/"
] | I was curious, what other architectures exist for business or user focused development that aren't written using web applications. Are these architectures used today?
If you are or were in the business world and you need to connect to an application from a remote location, what technology would you use (that isn't we... | <ul>
<li><strong>Email</strong> — still in use. Still a distributed service.</li>
<li><strong>Instant messaging + VoIP</strong> — Even though there are some implementation, which use web interface, it's still not based on web architecture. If standard protocol is used, it's most likely to be XMPP, which is ... | There are plenty of applications out in the business world today that use fat winform type client where the data for the application is remote.
Most common method today for a business user to connect remotely is through VPN. The connections these days are actually quite fast. While there is a small delay accessing any... | https://softwareengineering.stackexchange.com |
361,884 | [
"https://softwareengineering.stackexchange.com/questions/361884",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13913/"
] | Our team has decided to move to a microservice approach for newly developed features. We've decided to keep a database/datastore per service and to split the services along the business function they perform. As we move this direction we're creating the services as necessary. This means that not only have we created a ... | <h2>Why ?</h2>
In C, C++, Python, Java, C#, Groowy, and Swift (historical order of appearance), and certainly in many other languages as well, the usual logical and-operator (mostly <code>&&</code>) works with short-circuits.
In some languages such as ADA (i.e. <code>and</code>), the short-circuit form req... | <code>&&</code> and <code>||</code> at least in java (and I guess in groovy as well) mean that the operation is short-circuited, i.e. as you said the right hand side will be evaluated if and only if it's necessary.
<code>&</code> and <code>|</code> evaluate both sides.
So if you're using <code>&&<... | https://softwareengineering.stackexchange.com |
49,728 | [
"https://chemistry.stackexchange.com/questions/49728",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/29062/"
] | My son asked this over the weekend and I didn't have a good answer: how come with polyprotic acids we assume that the release of each $\ce{H+}$ is progressively harder, but with bases like $\ce{Ca(OH)2}$ we write $\ce{Ca^2+}$ and $\ce{2OH-}$ as the products?
What I know about, say, sulfuric acid, seems to suggest that... | The $\ce{H+}$ is bonded covalently to the rest of the molecule. So, when you take off the first $\ce{H+}$, the molecule fundamentally changes. It becomes another molecule. The second $\ce{H+}$ is being taken away from a different species and so it is governed by a different equilibrium.
In $\ce{Ca(OH)2}$, $\ce{Ca^2+}$... | This is not a general rule. Much like with acids for <em>some</em> bases we write progressive capture of one proton at a time. It all depends on the nature of the acid/base.
In the case of $\ce{Ca(OH)2}$ you don’t have a molecule like $\ce{HO-Ca-OH}$ or something like you can assume for $\ce{HO-SO2-OH}$ (sulfuric acid... | https://chemistry.stackexchange.com |
95,717 | [
"https://security.stackexchange.com/questions/95717",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/43921/"
] | I'd like to explain my understanding first then ask a question.
This question is meant as a simpler overview of other question..and talks about implication and not process as much.
My understanding is this:
<ul>
<li>client connects to server</li>
<li>server sends its public key</li>
<li>client checks with third par... | Your understanding is pretty much correct, except for the fact that a client normally doesn't send a public key, but generates one on the spot (slightly simplified).
The reason this is fine is that the server is normally like a web server, and thus "everyone" can connect to it.
If you need to authenticate clients (i.... | You are close, when the client connects, the server sends over the certificate which incorporates its public key. With this certificate the browser checks if it for the right URL, if the date is valid and check if it trusts whoever signed it (the root CA).
If all this checks out, the client will generate a (symmetric... | https://security.stackexchange.com |
2,756 | [
"https://softwareengineering.stackexchange.com/questions/2756",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36/"
] | Coding standards are common in any software development organization, but how important are they to follow? I can understand the need for some consistency, but when dealing with simple things like the position of braces, line length, etc., I'm not sure excessively strict standards contribute much to software developme... | Asking everyone to 100% adhere to the same standard code formatting guideline is like asking everyone to collaborate separately on writing a 100 page paper with the same writing style.
Hopefully everyone will write the paper in English (or same language), but different styles will be apparent. Some will write it we... | For formatting standards, I follow what everybody else is doing. If they are using PascalCase for everything, then I use PascalCase. If they use _camelCase, then I use _camelCase. Why? Because it limits the amount of reformatting I do, and limits what others have to do to make it "look good". Formatting standards are u... | https://softwareengineering.stackexchange.com |
224,904 | [
"https://stats.stackexchange.com/questions/224904",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20981/"
] | When I am using k-folding to split my labelled data (labelled as signal or background) and train k classifiers on it, I believe I am not allowed to assume that the distributions of the classifier output variable on, for example, signal, is the same among the k test samples of the k folds.
I am not talking about statis... | <strong>(answer was updated to mention HEP)</strong>
Given that question author's background I'm assuming this question is about high energy physics (HEP).
In HEP we need unbiased quality estimation and we want to make use of all available data (since for many analyses amount of available data is very limited) at th... | <blockquote>
Is there a best practice that I am not aware of?
</blockquote>
There is at least a standard practice that you seem not be aware of:
$k$-fold cross validation results (if used for validation as opposed for training purposes, see below) are used as an approximation to measuring the generalization error o... | https://stats.stackexchange.com |
13,182 | [
"https://cogsci.stackexchange.com/questions/13182",
"https://cogsci.stackexchange.com",
"https://cogsci.stackexchange.com/users/908/"
] | Does dopamine spread and interact across the whole brain? If not, which areas are affected most and which least?
| Quoting my thesis:
<blockquote>
CNS Dopamine/DA projections primarily emerge from two subcortical basal ganglia nuclei in the brain stem, travelling along three major pathways (Purves et al., 2004).
The nigrostriatal pathway, connecting the substantia nigra and the striatum, is mainly implicated in higher motor control... | <ol>
<li>Parts of the brain affected by dopamine
Dopamine exerts different effects in different regions and pathways throughout the brain. In the <strong>mesolimbic pathway</strong>, dopamine is believed to be involved in motivation and addiction due to the feelings of reward and pleasure associated with dopamine rele... | https://cogsci.stackexchange.com |
71,278 | [
"https://dsp.stackexchange.com/questions/71278",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/23196/"
] | Let's say I have a 1D signal of size <span class="math-container">$N$</span> and am trying to filter it with a 10-tap FIR filter mask. When <span class="math-container">$N$</span> is large, the number of multiply-accumulates would approximately equal
<span class="math-container">$$2 \times 10 \times N = 20N\quad\text{f... | There is probably a bit of a misconception here. In many application the signal is runnning all the time or is VERY long: modem, audio stream, video etc. In this case you can't really define the "length" of the signal. The relevant metric is here "number of operations per input sample" not the &quo... | I think you need to refine your definitions.
The computational complexity for an <span class="math-container">$n$</span>-element convolution on <span class="math-container">$m$</span> points of data is <span class="math-container">$\mathcal{O}(n\cdot m)$</span>. Your <span class="math-container">$\mathcal{O}(n)$</span... | https://dsp.stackexchange.com |
39,357 | [
"https://electronics.stackexchange.com/questions/39357",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11970/"
] | I have a problem which is somehow related to detecting a peak. Let me summarize the problem a little bit, so it might be clear to you. I have to signals, both are not periodic and I know when they start and when they end. I also know the signal has exactely one peak. The signal might be a bit noisy, but I think this co... | I don't especially like the idea of doing this with a differentiator, because your gaussian pulse has a relatively flat top, so there will be a time when the derivative is <em>nearly</em> zero, so that the moment when you detect the peak will be fairly noise sensitive.
If the shape and amplitude of the input pulse is... | If you are sure there is only a single peak, then you can differentiate the signal and compare to zero. I'm a bit rushed right now, but a simple way to make a differentiator is a opamp in inverting configuration with a capacitor on its input.
One problem with a differentiator is that it is susceptible to noise. Put ... | https://electronics.stackexchange.com |
64,482 | [
"https://datascience.stackexchange.com/questions/64482",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/86638/"
] | I have a time series of features <span class="math-container">$x_1,x_2,x_3,...,x_n$</span>. I want to make a prediction <span class="math-container">$y_1,y_2,y_3,...,y_n$</span> for each timestep. However, in my training data some of the <span class="math-container">$y$</span> can be nan. I'd like the fit to just ignor... | I suggest implementing it this way :
<ol>
<li>Set the nan value to 0 or any other value</li>
<li>when compiling keras model use parameter sample_weight_mode='temporal'</li>
<li>You can use masking on top of this by supplying the weight as the mask (sequence of values 1 if not nan 0 otherwise).</li>
</ol>
The steps a... | You can use mean fill or predict that missing y value. Given the <span class="math-container">$y_1,y_2,y_3,\cdots ,y_n$</span> for each training sample, you can fill in the missing by mean of that <span class="math-container">$y$</span> across training examples, or interpolate
| https://datascience.stackexchange.com |
214,296 | [
"https://stats.stackexchange.com/questions/214296",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/115406/"
] | I'm currently working with accelerometer based raw data (100 hz). Now I want to low pass filter this timeseries of accelerations for further analyses.
I tried different filters like the simple moving average (SMA) or the exponential moving average (EMA) filter. But both methods produce lag, which I want to avoid. Are t... | You actually had your answer right there.
$P(H=hit)$ is the marginal probability. It reads "The probability of getting hit.". It is the proportion of people that got hit crossing the street, irrespective of traffic light.
$P(H=hit|L=red)$ is the conditional probability. It reads "The probability that you get hit, <st... | $H$ and $L$ are random variables. $H$ takes a value in $\{ \text{hit, not hit} \}$ and $L$ takes a value in $\{ \text{red, yellow, green} \}$. In this example, the joint distribution $P(H, L)$ gives the probability of two things both happening: that $H$ takes a particular value $h$ and $L$ takes a particular value $l$.... | https://stats.stackexchange.com |
607,728 | [
"https://physics.stackexchange.com/questions/607728",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/282947/"
] | If I in my reference frame observe an object near the speed of light I can calculate the lorentzfactor which tells how slow the objects clock is going. Is it's velocity then slower? Say its reference frame is given by <span class="math-container">$S´$</span> and mine is given by <span class="math-container">$S$</span>.... | In addition two the (by now) two excellent answers, let's consider that what you assume (time dilation causes an object to move slower) were true.
Let's assume the object <span class="math-container">$A$</span> to be in an inertial frame of reference <span class="math-container">$S'$</span> which has (relative to our &... | The time dilation equation <span class="math-container">$t' = \gamma t$</span> means that when one second passes in your reference frame then you observe <span class="math-container">$\gamma < 1$</span> seconds pass in the reference frame of the moving object. But one second has still passed in your reference frame,... | https://physics.stackexchange.com |
47,090 | [
"https://stats.stackexchange.com/questions/47090",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3269/"
] | I am training a SVM classifier based on a given document collections. I started from using 500 documents for training, then I add another 500 for training, and so on. In other words, I have three training sets, 500, 1000, 1500. And the smaller training set is a subset of the sequential larger set. I validate the model ... | <strong>Increasing training size does not neccessarily help the classifier</strong> and rather, may lead to a degradation in the generalization ability.
Regarding your own experiment, the factor of such unexpected degradation in performance given the increase in the training size could be one of the following:
<stron... | One possibility is that the data is not linearly separable, or the best linear separation doesn't give the best classifier. So, a common approach is to use a soft margin. The amount of slack should be increased with the size of the training set. If you aren't doing this, then you may get worse results with more data.
| https://stats.stackexchange.com |
468,395 | [
"https://electronics.stackexchange.com/questions/468395",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/156012/"
] | I am going through Texas instrument web bench design suit and get 40% efficiency for some booster circuits
if booster can handle the load (Vout and Iout) according to design given by TI
what is the disadvantage of having 40% efficiency over 70% or 85% efficiency design?
is the booster unstable?
will bolster fail at... | <blockquote>
if booster can handle the load (Vout and Iout) according to design given by TI what is the disadvantage of having 40% efficiency over 70% or 85% efficiency design?
</blockquote>
It'll get hot, and waste heat.
<blockquote>
will booster waste energy as heat?
</blockquote>
Yes. You can figure this out... | The main disadvantage of low efficiency is energy loss. If you don't care about that, the booster can handle it, and the power supply can deliver the extra power required, then it's not important - to you.
All boosters have low efficiency at low power because they consume a fixed amount of 'quiescent' power which is n... | https://electronics.stackexchange.com |
653,494 | [
"https://physics.stackexchange.com/questions/653494",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/307895/"
] | I'm reading calculus book by Morris Kline. This book treats physics because calculus grew out of physical and geometrical problems. I have no background about physics and got a question while reading the book.
<span class="math-container">$$F = \frac{GmM}{r^2}$$</span>
When considering a tennis ball and the earth with ... | They both move towards each other. But the acceleration of, and thus distance traveled by, the earth is infinitesimal compared to the the ball because the mass of the earth is so much greater than the ball.
From Newton's 2nd law, the acceleration of the ball towards the earth is
<span class="math-container">$$a_{ball}=... | Both will move to keep the centre of the mass of the system stationary as there is no net external force. Gravitational forces are internal forces when considering as a system. Gravitational forces on each body are equal by magnitude. According to Newton's law of motion, <span class="math-container">$F=ma$</span>, thes... | https://physics.stackexchange.com |
242,898 | [
"https://electronics.stackexchange.com/questions/242898",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/115028/"
] | In DC, for example at 12V, will a longer power wire (lets say 10 meters vs 10 centimeters) cause a high current consumption?
| Power can be expressed as \$P = IV\$. We also know that Ohms law says \$V = IR\$. Putting these two together, we get the expression:
$$P = \frac{V^2}{R}$$
In your case you have a fixed voltage source - so \$V=12\mathrm{V}\$. Put that in to the equation we get:
$$P = \frac{12^2}{R} = \frac{144}{R} = \frac{144}{R_{wir... | A real example of where a longer wire will cause greater current consumption is a switching DC to DC converter - it may work across a range of input voltages such as 5V to 20V to produce a constant (say) 10V on the output.
When it is fed from 20V and the final load is (say) 10 ohms, the power demand is 10 watts (100 ... | https://electronics.stackexchange.com |
365,083 | [
"https://physics.stackexchange.com/questions/365083",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/92860/"
] | The stationary state wavefunctions for the infinite square-well of width $a$ are given by $$\psi_n(x)=\sqrt{\frac{2}{a}}\sin{(\frac{n\pi x}{a})}.$$ These correspond to energies, $$E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}.$$ Suppose we are to modify the width of the well, such that the new width is given by $2a$. Then, the new... | The standard heuristic story is based on the Heisenberg uncertainty principle $\Delta x \cdot \Delta p \geq \hbar / 2$. The lower the uncertainty in a particle's position, the greater the uncertainty in its momentum (and vice versa). If a particle is confined to a box, then the uncertainty in its position certainly can... | In the infinite well, the kinetic energy $p^2/2m$ is the only quantity that matters because $V=0$ inside the well. Since
$$
\frac{p^2}{2m}\to -\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\, ,
$$
the kinetic enery is proportional to the curvature of the wave function.
If the well is narrow, the wavefunctions will have higher... | https://physics.stackexchange.com |
622,067 | [
"https://physics.stackexchange.com/questions/622067",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/232973/"
] | As far as I can see, symmetry is something that is preferred at lower temperature. For example a crystal lattice has discrete translational symmetries at <span class="math-container">$T=0$</span>, but at <span class="math-container">$T>0$</span> this symmetry is not exact anymore. A rotational machine works fine if ... | A lattice actually is a great example of how you appear to have <em>less</em> symmetry at low temperatures, <em>not more</em>! And, funnily enough, this works in exactly the same way that that many expect it to work in particle physics!
If you have a gas, the atoms are apparently isotropic. If you move from one place t... | Where there is a symmetry there is a conservation law in quantum mechanics.
Because conservation laws ( charge, momentum, energy) have proved useful in the past
and because, even when they have been broken e.g CP symmetry they have been rescued ( in this case by CPT symmetry), it seems logical to carry on with them.T... | https://physics.stackexchange.com |
1,687,821 | [
"https://math.stackexchange.com/questions/1687821",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/313194/"
] | Given $V :\Bbb R^n \to \Bbb R^n$ is a linear transformations with a standard matrix
$A = [V]$.
Let $B = \left[\vec{b_1}, ..., \vec{b_n}\right] \in M_{n\times n}(\Bbb R)$ with a $\operatorname{rank}(B) = n$
So, how would I prove that the set of vectors $D = \{\vec{b_1}, ... ,\vec{b_n}\} $ is a basis for $\Bbb R^n$
a... | $$3(5^{k+1} - 1) + 4(3 \cdot 5^{k+1}) = \\ 3 \cdot 5^{k+1} - 3 + 12 \cdot 5^{k+1} = \\ 15 \cdot 5^{k+1} - 3 = \\ 3 \cdot 5 \cdot 5^{k+1} - 3 = \\ 3 (5 \cdot 5^{k+1} - 1) = \\ 3 (5^{k+2} - 1).$$
In going from the first line to the second line, I distribute the $3$ through on the first term in the sum: $3(5^{k+1} - 1) ... | Continuing from where you left off:
$$ \frac{3\;\cdot\;5^{k+1} - 3 + 12\;\cdot\;5^{k+1}}{4} $$
Considering the numerator:
$$3\;\cdot\;5^{k+1} + 12\;\cdot\;5^{k+1} -3$$
$$5^{k+1}(3+12)-3=$$
$$5^{k+1}(15)-3=$$
$$5^{k+1}(5.3)-3=$$
$$5^{k+2}(3)-3=$$
$$3(5^{k+2}-1)$$
So your original expressing is:
$$\frac{3(5^{k+... | https://math.stackexchange.com |
218,994 | [
"https://electronics.stackexchange.com/questions/218994",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/99780/"
] | I'm trying to build an 8bit counter in Verilog. I specifically need to create a module that I instantiate 8 times. I have followed the diagram below (and assumed that I can just build on it to make it 8 instead of 4 bits). It appears what I have built instead is a shift register, it can shift ones and zeros - instead o... | Your schematic shows a T-type flip-flop, which toggles when its input is high. Your rtl code, on the other hand, implements a regular D-type flip-flop. Your module should instead read:
<pre><code>always@(posedge clk, negedge clr)
begin
if(~clr)
q <= 1'b0;
else
q <= q ^ t;
end
</code></pre... | Is it an 8bit binary counter being built? Like 0000 0001 -> 0000 0010 -> 0000 0011 -> ?
Should it be specifically done only with T Flip Flops only?
May be a JK FF chain. Pull all the J&K high. Clock to the first FF. Connect the Q outputs directly to the clocks of consecutive FFs (If it's ~Clock input) Otherwise u... | https://electronics.stackexchange.com |
67,960 | [
"https://softwareengineering.stackexchange.com/questions/67960",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/980/"
] | Do you think that its a good idea when a junior programmer needs help to always jump in and try to educate them? Or will they ignore all the "teaching to fish" advice you give them and just focus on the "fish" you just brought them? Do you let them always figure things out on their own, knowing that mistakes are the be... | At one of my jobs, I was both learning and teaching(because I of course don't know everything, but I know more than some)
Do not <strong>at all costs</strong> lay your hands on the keyboard. This is frustrating both for you, and the person you are teaching. Even if you give them step by step instructions, when you put... | I have learned to help them architect and stop there. Pick the right tools, draw up a general design to a complex problem or two, and let them go at it. If they come back and ask for advice, give it to them in small chunks. If they don't, let them be.
You are totally right about the "burnt and frustrated". They w... | https://softwareengineering.stackexchange.com |
180,434 | [
"https://mathoverflow.net/questions/180434",
"https://mathoverflow.net",
"https://mathoverflow.net/users/49056/"
] | $Φ_n(1)$ and $Φ_n(−1)$ for the cyclotomic polynomials are well-known.
I am now looking for
$$Φ_n(i)$$
and/or
$$Φ_n(−i)$$
with i the complex unit.
At this moments my endeavours result in intricate categorizing of values
for $n$ e.g. as $4$, $2^k$, $4p$, $p^k$ with $p$ prime and considerations about
the prime facto... | The question has already been answered by Vladimir Dotsenko, but as Wolfgang Tintemann is still interested in a solution using Möbius inversion, let me expand the comments I made above.
Since $\Phi_n(-i)=\overline{\Phi_n(i)}$, it is enough to deal with $i$. We are going to prove
$$\Phi_n(i)=\begin{cases}
i-1&n=1,\... | Let me try to summarize what I said in the comment to your question and what I implicitly used in what did not fit in the comment. As you will instantly see, the answer is lengthy because of high-school level exercises you have to do along the way, not because some important ideas were missing.
I suggest to use the fo... | https://mathoverflow.net |
506,285 | [
"https://physics.stackexchange.com/questions/506285",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/81812/"
] | The speed of light is absolute, but time is relative. So would a light-year for us on earth be a different distance from a light-year on a different uniformly moving object? Why or why not?
| The distance light travels in a given period is the same for every observer. That's the whole point of relativity.
You can figure out for yourself almost all the effects predicted by relativity if you start with that assumption and think through its consequences.
Indeed, the reason why times have to be relative is t... | A light-year is exactly 9,460,730,472,580,800 meters, the distance light travels in one Julian <em>Earth</em> year. Time dilation is irrelevant to its definition.
| https://physics.stackexchange.com |
362,928 | [
"https://mathoverflow.net/questions/362928",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41619/"
] | Let <span class="math-container">$X$</span> be an infinite dimensional Banach space. Let <span class="math-container">$\Lambda_{0}$</span> be the set of all finite dimensional subspaces of <span class="math-container">$X$</span> directed by the inclusion <span class="math-container">$\subseteq$</span>. For each <span c... | The answer to question 1 is yes.
Suppose that <span class="math-container">$T^*B_{X^*}$</span> is not compact. Since it is norm closed, there is
<span class="math-container">$\epsilon >0$</span>
and an infinite subset <span class="math-container">$S$</span> of <span class="math-container">$B_{X^*}$</span> so tha... | The answer to question 2 is yes.
The proof you already know since you proved that <span class="math-container">$T$</span> compact implies <span class="math-container">$\hat{T}$</span> is zero. (For someone who has not thought about this, it is immediate from the elementary fact that a bounded net in <span class="mat... | https://mathoverflow.net |
3,075,272 | [
"https://math.stackexchange.com/questions/3075272",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/494522/"
] | Let <span class="math-container">$A,B$</span> be two <span class="math-container">$n \times n$</span> matrices. How to show <span class="math-container">$\text{Tr}(AB) \leq \|A\|_F\|B\|_F$</span>.
My try:
Using Von Neumann trace inequality we have
<span class="math-container">$$
\text{Tr}(AB) \leq \sum_{i=1}^n \sigm... | Apply Cauchy-Schwarz: <span class="math-container">$$\sum_i \sigma_{A,i} \sigma_{B,i} \le \sqrt{\sum_i \sigma_{A,i}^2} \sqrt{\sum_i \sigma_{A,i}^2} = \|A\|_F \|B\|_F$$</span>
| By Cauchy-Schwarz, we have
<span class="math-container">\begin{align}
\operatorname{Tr}(AB) = \sum^n_{i=1} \sum^n_{j=1} a_{ij}b_{ji} \leq&\ \sum^n_{i=1}\left( \sum^n_{j=1}|a_{ij}|^2\right)^{1/2}\left( \sum^n_{j=1}|b_{ij}|^2\right)^{1/2}\\
\leq&\ \left(\sum^n_{i=1} \sum^n_{j=1}|a_{ij}|^2\right)^{1/2} \left(\sum... | https://math.stackexchange.com |
3,664,739 | [
"https://math.stackexchange.com/questions/3664739",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/780359/"
] | Given that <span class="math-container">$0 < a , b , c < 1$</span>.
Prove that <span class="math-container">$\frac{1}{1 - \sqrt{ab}} + \frac{1}{1 - \sqrt{bc}} + \frac{1}{1 - \sqrt{ca}} \leq \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$</span>.
I tried using modified C.S. and brute-force. But , it deman... | We have <span class="math-container">$\sqrt{ab}\leq \frac{a+b}{2}$</span> so <span class="math-container">$1-\sqrt{ab}\geq 1-\frac{a+b}{2}>0$</span>, which implies
<span class="math-container">$$\dfrac{1}{1-\sqrt{ab}}\leq \dfrac{2}{2-a-b}$$</span>
And using the simple inequality <span class="math-container">$\frac{... | The RHS is
<span class="math-container">$$\sum_{n=0}^\infty(a^n+b^n+c^n).$$</span>
The LHS is
<span class="math-container">$$\sum_{n=0}^\infty(\sqrt{a^nb^n}+\sqrt{a^nc^n}+\sqrt{b^nc^n}).$$</span>
For each <span class="math-container">$n$</span>,
<span class="math-container">$$a^n+b^n+c^n=\frac{a^n+b^n}2+\frac{a^n+c^n}2... | https://math.stackexchange.com |
25,688 | [
"https://dba.stackexchange.com/questions/25688",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11212/"
] | In SQL Server 2008 I created a Sql Server Agent Alert last week to monitor deadlock events. The Alert calls a job with no schedule sending the xml deadlock graph token obtained through WMI SELECT * FROM DEADLOCK_GRAPH. The job calls a SP that stores the graph and an email is sent.
I have been monitoring the Sql Server... | <blockquote>
Should I remove the id field?
</blockquote>
I would recommend keeping it.
You may not need the field <em>now</em>, but in the future, it can really help you out -- what if you need to store details of the files for each log entry?
I don't know how large this table will get and how quickly, but adding ... | <ul>
<li>If you don't have joins on this table, no updates and no deletions, then you don't need keys at all. </li>
<li>If this is not the case, and <code>messageId</code> is unique, then you can make it a primary key. </li>
<li>If it's not unique, but <code>(messageId, exportedDateTime)</code> is, then make this a c... | https://dba.stackexchange.com |
90,908 | [
"https://stats.stackexchange.com/questions/90908",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/42350/"
] | I'm trying to understand the exact meaning of the $F$-values and what are we testing in the ANOVA table for a simple linear model in <code>R</code>:
<pre><code>> asdf=lm(carb~weight+protein+age)
> anova(asdf)
Analysis of Variance Table
Response: carb
Df Sum Sq Mean Sq F value Pr(>F)
weight ... | For <code>age</code>, $F=1.0812=\frac{MS_\text{age}}{MS_\text{Residuals}}$. The same is true of the other $F$ values replacing <code>age</code> with <code>weight</code> or <code>protein</code>. This partials out the variance in <code>carb</code> that is related to the other two factors not being tested directly by the ... | The <code>anova</code> function in R, when given only 1 model, produces the "Sequential" sums of squares. This means that each term is adjusted for those above it (to the left in the model formula) and don't include those below (to the right). So in your example you are testing weight vs. intercept only, protein + we... | https://stats.stackexchange.com |
9,537 | [
"https://computergraphics.stackexchange.com/questions/9537",
"https://computergraphics.stackexchange.com",
"https://computergraphics.stackexchange.com/users/10461/"
] | When I was writing a software rasterizer for my university class, we did culling in eye coordinates. Essentially, we use cross product to get a normal from the 3 vertices (in eye coordinates), then we dot product that normal with one of the 3 vertices (since we are in eye coordinate, that vertex is essentially a vecto... | Here is how I found this can be solved.
(The below also happens at the start, just fyi)
<pre><code> float tmin = std::numeric_limits<float>::lowest();
float tmax = std::numeric_limits<float>::max();
</code></pre>
Add an additional check:
<pre><code>if(rayDir.x == 0.0f)
{
if (rayOrigin.x() < box.... | This is a C++ implementation. Slab is the space between a pair of parallel planes.Test if ray R(t) = p + t * d intersect against bounding box bb.
<pre><code>bool IntersectRayBB( const double* p, const double* d, const BoundingBox& bb, double& tmin, double* q )
{
double tolerance = 1e-9;
tmin = 0.0;
... | https://computergraphics.stackexchange.com |
51,599 | [
"https://quant.stackexchange.com/questions/51599",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/40793/"
] | These are simple questions, i know what is a structured product and how you price it but i'm a bit confused regarding the process.
Let's say client buys a simple product for 1Y, guaranteed capital and 100% of the upside.
So as a structurer you receive 100 from the client, you put 95 in the ZC, you will have 100 in 1 y... | If a structured product trader can directly hedge in the market, he will usually do it. Here your example is a little too simplified, many structured products have features that cannot be easily hedged in the market because they are path dependant (barriers), or illiquid (typically a 5 years 60% put on a single stock).... | In the simplest case, he books the structured product as a sale of the call at 5, he then enters the market and buys a call at 3, so he pockets 2 on the trade.
| https://quant.stackexchange.com |
158,739 | [
"https://electronics.stackexchange.com/questions/158739",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15734/"
] | I would like to know the difference between different types of Grounds like Power-GND vs Pre-GND. Are all the grounds not same? Cant we connect the device to any one of these grounds?
In my application I have a low frequency audio amplifier called "TA8229K" which has 15 pins.<br>
On this picture, on this diagram there... | Most likely the power amp ground has significantly more current on it than the preamp so they provide separate pins so that you can run separate ground wires back to a single point at the power supply next to the power supply filter capacitor(s). Otherwise, if you just connect the two grounds together at the IC, the in... | Power ground and preamplifier ground. Join the two at one point. Any ground not associated with the power amp ground should not carry any power amp ground current so feed power ground directly to the chip and tee off preamp ground from it.
| https://electronics.stackexchange.com |
335,803 | [
"https://mathoverflow.net/questions/335803",
"https://mathoverflow.net",
"https://mathoverflow.net/users/82067/"
] | Let <span class="math-container">$S$</span> be a non-empty, possibly infinite, set of integers, all of which are greater than <span class="math-container">$1$</span>. For a given group <span class="math-container">$G$</span>, let <span class="math-container">$S[G]$</span> denote the collection of statements
<span clas... | Here is an answer to the second question. Call <span class="math-container">$S$</span> an <em>abelian forcing set</em> if <span class="math-container">$S[G]$</span> implies that <span class="math-container">$G$</span> is abelian.
<strong>Proposition.</strong> If <span class="math-container">$S$</span> is an abelian f... | See the Monthly article: Joseph A. Gallian and Michael Reid, <em>Abelian Forcing Sets</em>, Amer. Math. Monthly, Vol. 100, No. 6 (Jun. - Jul., 1993), pp. 580-582.
Gallian and Reid show that a set <span class="math-container">$S$</span> of integers is abelian forcing if, and only if, the greatest common divisor of the ... | https://mathoverflow.net |
856,475 | [
"https://math.stackexchange.com/questions/856475",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/13439/"
] | In a precalc text, in the chapter on geometric progressions and series, we're told of the formula
$S=\frac{a(1-r^{n+1})}{1-r}$
and that:
$S=\frac{a}{1-r}$ is valid for $|r|<1$
We're then asked to find the sum of $3+\sqrt{3}+1+...$
Literally that's all the information given, including the "...".
The text gives... | First thing is you should have cancelled $3$ in the numerator and denominator, so $\frac{3\sqrt3}3$ becomes $\sqrt3$. So
$$\dfrac{3+\frac{3\sqrt3}3}{\frac23}=\frac32(3+\sqrt3)=\frac32(\sqrt3)(\sqrt3+1)$$
| Hint:
$$\begin{align}
\frac{3}{1-\frac{1}{\sqrt{3}}}&=\frac{3}{1-\frac{1}{\sqrt{3}}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\\
&=\frac{3\sqrt{3}}{\sqrt{3}-1}\\
&=\frac{3\sqrt{3}}{\sqrt{3}-1}\cdot\frac{\sqrt{3}+1}{\sqrt{3}+1}
\end{align}$$
| https://math.stackexchange.com |
349,849 | [
"https://softwareengineering.stackexchange.com/questions/349849",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/180329/"
] | According to <strong>David West</strong>, <strong><em>Object Thinking</em></strong> involves identifying Objects in the problem/business domain that mirror real-world objects; the interface would then reflect the behaviors of that object.
What would happen if we had an object class with <em>alot</em> of different beha... | There is a difference between a thing and things <em>related to</em> that thing. To illustrate, consider your example:
<pre><code>public class OrderBatch{
public Customer getCustomer(){...};
public void addOrder(){...}
public void removeOrder(Order order){...}
public List<Order> getOrders(){...}
... | An order batch is a real thing. Its responsibility is keeping a bunch of order items together. That makes it a fairly complex entity that requires a lot of management tasks. So be it. As long as they make sense in the order batch context, that is just fine.
What is typically named a God class is a class that has hetro... | https://softwareengineering.stackexchange.com |
96,733 | [
"https://cs.stackexchange.com/questions/96733",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/75336/"
] | I know its very hard to show a human what the 4th dimension would look like and the mind can't even comprehend more dimensions, but what about a computer?
How many "dimensions" can a computer handle?
Or maybe a better way to ask, does computing power exponentially increase when extra dimensions are added?
| You are confused by physical manifestation of (space-time) dimension versus mathematical definition of dimension.
Mathematics (the language of computing) is all about modeling and generalizing reality. Therefore, much more can be represented and calculated that cannot be seen or even does not exist in the real world. ... | Computers can handle arbitrarily many dimensions. Indeed, machine learning often involves problems with many dimensions (in some cases, infinitely many!).
As a simple example, if $(x,y,z),(x',y',z')$ are two 3D vectors (the vectors point from the origin to the given coordinate), then the angle $\theta$ between them is... | https://cs.stackexchange.com |
1,591,852 | [
"https://math.stackexchange.com/questions/1591852",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/224871/"
] | Suppose that P(a) = True, P(b) = False and P(x) ⟹ P(y) for all x,y∈S satisfying x≤y, where ⟹ stands for logical implication. Which of the following statements CANNOT be true?
(A) P(x) = True for all x ∈ S such that x ≠ b
(B) P(x) = False for all x ∈ S such that x ≠ a and x ≠ c
(C) P(x) = False for all x ∈ S such tha... | <blockquote>
In this question I am unable to get why we have a terminology of implication here.
</blockquote>
Because that is the problem you've been given. The idea is clearly to test your understanding of implications and of partial orders. Having separate concepts mixed together in problems is quite common. In fa... | Firstly, as a point of correct use of MSE, your question should be self-contained. In particular we shouldn't have to read the title to find hypotheses for the question. Anyway the mathematics
Note that a lattice can't have two minimal elements, your tagging is incorrect.
So we have the following facts:
<ol>
<li>$a$... | https://math.stackexchange.com |
90,689 | [
"https://softwareengineering.stackexchange.com/questions/90689",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18523/"
] | After being hacked companies often give numbers and details on how much of their data was compromised e.g "13K user and passwords".
After a possible intrusion how do you know what the hacker did in your server?
| Security Stack Exchange has a range of Questions and Answers in this area - you should have a look.
While post-incident forensics is quite a mature field, and I have managed a number of these, it is high cost, and most organisations take the sensible view of assuming worst case - the attacker could have accessed every... | Assume a worst case scenario. Examine your logs, figure out everything they <em>might</em> have gotten access to, and assume they took a copy of all of it.
| https://softwareengineering.stackexchange.com |
125,200 | [
"https://mathoverflow.net/questions/125200",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22337/"
] | I'm trying to develop an intuition for Cech cohomology geometrically, but am currently failing. A lot of people seem to say that the groups $H^n$ measure obstructions to gluing local sections to get global ones. However I don't see how this works, and I think it's because I don't understand coboundaries.
I see that $H... | Let $U$ denote the space we're working on and $\{U_i\}$ an open cover of $U$ (obviously $U$ may be an open set of an ambient space, but that plays no importance here). Let's assume that there is a sheaf $\mathscr F$ on $U$ and for each $i$ a section $s_i\in\mathscr F(U_i)$.
Gluing the $s_i$ means to find a section $s\... | Regarding higher cohomology, I was about to write another comment, but the comments are getting a bit long, so let say <em>a few</em> words here. Cech theory is really a generalization of simplicial cohomology, as Liviu explained, and this is really the best way to understand where the formulas come from. But if you fi... | https://mathoverflow.net |
35,039 | [
"https://mathoverflow.net/questions/35039",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8153/"
] | Let $n$ be a positive integer.
<blockquote>
Let $S \subseteq \mathbb{R}^n$. Is the Hausdorff dimension of the boundary of $S$ always smaller than the Hausdorff dimension of $S$?
</blockquote>
I have not found anything concerning those questions in some looked up books, I was not able to prove one of the statements,... | "Smaller" in the sense of $\le$ ... If $S$ is closed and has Hausdorff dimension $< n$, then $S$ has empty interior, so (as noted by Joel) $S$ is its own boundary, and thus we have equality for the two dimensions. And of course if (perhaps not closed) set $S$ has dimension $n$, then the boundary could have any dime... | The set of rational numbers has Hausdorff dimension 0, while its boundary is the set of real numbers, with Hausdorff dimension 1.
| https://mathoverflow.net |
333,052 | [
"https://stats.stackexchange.com/questions/333052",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/198519/"
] | I'm seeking direction for the fit of a 5-point Likert scale attitudinal survey response to a 4-point scale that omits the center or Neutral response.
I am challenged by a very large corporate customer to assign and justify the assignment of the mid-range respondent answers to a 4-point model ranging from very satisfie... | The answer is two-fold:
(1) The encoder network needs to be expressive enough (wide enough and deep enough) to be able to map the nonlinear input space to something close to $\mathcal{N}(0,I)$.
(2) In addition to (1) (I added a 3rd hidden layer to the MNIST example I described in the question), when I increase the nu... | It's ok for $Q(z|X)$ to be different from $\mathcal{N}(0, I)$, because when we sample from the VAE, we're not trying to reconstruct $X$ anymore. Instead, we're trying to sample some $X \sim \mathcal{X}$ where $\mathcal{X}$ is the distribution of all images in the dataset.
Imagine of the latent space were actually a un... | https://stats.stackexchange.com |
4,304,624 | [
"https://math.stackexchange.com/questions/4304624",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/986778/"
] | Prove there are at least <span class="math-container">$100!$</span> ways to write <span class="math-container">$100!$</span> as a summation of numbers in <span class="math-container">$\{1!,2!,...,99!\}$</span>. (each number can be used multiple times.)
I have no idea how to solve this question. First, I thought of usin... | If <span class="math-container">$n$</span> is even, then there are <span class="math-container">$1+\frac{n}{2}$</span> ways to write it as a sum of <span class="math-container">$1$</span> and <span class="math-container">$2$</span>.
<hr />
If <span class="math-container">$n$</span> is divisible by <span class="math-con... | Assumed that question intends <em>at least</em> <span class="math-container">$100!$</span> ways. Also assumed that order of terms deemed irrelevant. That is for <span class="math-container">$N = 4$</span> it is presumed that if there were <span class="math-container">$6$</span> terms, that consisted of <span class="m... | https://math.stackexchange.com |
240,403 | [
"https://physics.stackexchange.com/questions/240403",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/94439/"
] | Consider the hypothetical scenario where 2 particles are headed for each other in a collision course but neither interact with a common force. Do these particles simply pass through each other?
| If you apply a greater force than $mg$ you will do more work and the book will accelerate, so as well as gaining gravitational potential energy it will also gain kinetic energy.<br>
The work that you do will equal the sum of the gain in gravitational potential energy and the gain in kinetic energy.
| Applying a force greater than the book's weight will cause it to accelerate upwards. The books potential energy near the surface of the planet depends, as you said, on the mass of the book, the acceleration due to gravity and the height above the surface.
The formula for gravitational potential energy is actually $U =... | https://physics.stackexchange.com |
100,418 | [
"https://datascience.stackexchange.com/questions/100418",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/61445/"
] | As per demos, we are expected to install AllenNLP using following command:
<pre><code>pip install allennlp==2.1.0 allennlp-models==2.1.0
</code></pre>
But it always throws error:
<pre><code> ERROR: Could not find a version that satisfies the requirement torchvision<0.9.0,>=0.8.1 (from allennlp==2.1.0) (from vers... | It seems I have immediately found an answer, so I shall post it here for the sake of others in the same situation.
I found on a website that the following code achieves the same result:
<pre><code>df.at[index, 'id'] = path # 26300 nanoseconds
</code></pre>
Calculations:
<pre><code># FORMULA
(time, ns * no. of rows)/... | I think you are trying to change all the values in certain column to abspath you can simply use apply function
<pre><code>def full_path(x):
return "my path" + "specific values" + ".jpg"
df[list(df.keys())[0]]=df[list(df.keys())[0]].apply(full_path)
</code></pre>
If not I have one more ... | https://datascience.stackexchange.com |
1,308,659 | [
"https://math.stackexchange.com/questions/1308659",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/245130/"
] | I know that the converse of this is true. I was looking for some counterexamples proving this statement false.
| Consider:
$$f(x)=\begin{cases} 1 \text{ if } x\in \mathbb{Q}\\
-1 \text{ if } x\not\in \mathbb{Q}\end{cases}$$
Then $\lim\limits_{x\to 1} |f(x)|=1$ but $\lim\limits_{x\to 1}f(x)$ doesn't exist.
| Take $f(x) = -x$ and consider say $x \to 3$ then
$$
\lim_{x \to 3} |f(x)| =3
$$
but this does not mean that
$$
\lim_{x \to 3 }f(x) = 3
$$
Other nice examples are given above.
| https://math.stackexchange.com |
334,984 | [
"https://softwareengineering.stackexchange.com/questions/334984",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/230641/"
] | If all data types are made non-recursive using tricks like a table of node IDs linking to data and data uses only other node IDs to form a graph, then can all memory be managed using just Reference Counting?
Furthermore is it possible to express a immutable list with the standard set of Haskell-like functions for the ... | Reference counting requires you to be more aware of object lifetimes. When creating a graph in a reference counting environment, you would create a parent object that owns all nodes in the graph. If the nodes in the graph have some concept of direction, then references from the top to the bottom can also be strong refe... | You will still have to keep track of which nodes of your graph are reachable. This could be done with a sequence of "live node" collections ordered by "generation", where as part of construction of new nodes you store what is reachable from that node, and then when you drop a generation the reference counting will coll... | https://softwareengineering.stackexchange.com |
2,457,457 | [
"https://math.stackexchange.com/questions/2457457",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Is it possible to find three complex numbers $\alpha$, $\beta$, $\gamma$ such that all the ratios $\frac{\beta-\alpha}{\gamma-\alpha}$,$\frac{\gamma-\beta}{\alpha-\beta}$,$\frac{\alpha-\gamma}{\beta-\gamma}$ have negative real part?
Of course one can start writing $\alpha=\alpha_1+\alpha_2 i$, $\beta=\beta_1+\beta_2 i... | Note that a fraction of the form $\frac{a+bi}{c+di}$ has a negative real part iff $ac+bd<0$. So yes, I think the only way to do this is by writing it in full. However, you can do this efficiently. Assuming we can find such a triplet, we derive the following set of inequalities
$$(\beta_1-\alpha_1)(\gamma_1-\alpha_1)... | For distinct $a,b,c \in \mathbb{C}$, let
\begin{align*}
x &= \frac{b-a}{c-a}\\[4pt]
y &= \frac{c-b}{a-b}\\[4pt]
z &= \frac{a-c}{b-c}\\[4pt]
\end{align*}
The question is whether it is possible for $x,y,z$ to all have negative real part.
In fact, at least two of $x,y,z$ must have positive real part.
For exa... | https://math.stackexchange.com |
422,718 | [
"https://mathoverflow.net/questions/422718",
"https://mathoverflow.net",
"https://mathoverflow.net/users/114476/"
] | We say that a topological space <span class="math-container">$A$</span> is homotopy dominated by a topological space <span class="math-container">$X$</span> if there exist continuous maps <span class="math-container">$f:A\to X$</span> and <span class="math-container">$g:X\to A$</span> such that <span class="math-contai... | Put
<span class="math-container">$$ R(n)=H^*((S^2)^{\times n}) = \mathbb{Z}[x_1,\dotsc,x_n]/(x_1^2,\dotsc,x_n^2) $$</span>
A key point is that if <span class="math-container">$u\in R(n)$</span> with <span class="math-container">$|u|=2$</span> then <span class="math-container">$u^2=0$</span> iff <span class="math-conta... | You're actually right. The cohomology algebra of <span class="math-container">$X=S^2\times S^2\times S^2$</span> with coefficients in <span class="math-container">$\mathbb{Z}$</span> is <span class="math-container">$H^*(X)=\mathbb{Z}[x,y,z]/(x^2,y^2,z^2)$</span> with <span class="math-container">$|x|=|y|=|z|=2$</span>.... | https://mathoverflow.net |
507,434 | [
"https://physics.stackexchange.com/questions/507434",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/243488/"
] | <span class="math-container">\begin{eqnarray}
\nabla \cdot \boldsymbol \tau &=& 2 \mu \nabla \cdot \boldsymbol \varepsilon\\
&=& \mu \nabla \cdot \left( \nabla\mathbf{u} + (\nabla\mathbf{u}) ^\mathrm{T} \right)\\
&=& \mu \, \nabla^2 \mathbf{u}
\end{eqnarray}</span>
Given <span class="math-conta... | The divergence of the transpose of a vector gradient is equal to the gradient of the divergence of the vector. You can prove it quickly using some index notation:
<span class="math-container">$$\nabla \cdot (\nabla \vec{u})^T = \frac{\partial^2 u_j}{\partial x_i \partial x_j} = \frac{\partial}{\partial x_i}\frac{\part... | I'm going to guess that the RHS really means
<span class="math-container">$$
\nabla^j ( \nabla_i u_j + \nabla_j u_i ) = \nabla_j \nabla_i u^j + \nabla^2 u_i .
$$</span>
Now,
<span class="math-container">$$
\nabla_j \nabla_i u^j = [ \nabla_j , \nabla_i ] u^j + \nabla_i (\nabla_j u^j) = R_{ij} u^j + \nabla_i (\nabla_j ... | https://physics.stackexchange.com |
2,860,536 | [
"https://math.stackexchange.com/questions/2860536",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/479214/"
] | <blockquote>
Task is the following: find the $\sum_{x=1}^{+∞} \frac{2^{-x}}x$
</blockquote>
I don't even know how to proceed. I know that $\sum_{x=1}^{+∞} 2^{-x} = 1$. However, is it useful here?
| Here's a neat trick. Note that
$$ \frac{\mathrm{d}}{\mathrm{d}\alpha} \sum_{x=1}^\infty \frac{2^{-\alpha x}}{x} = -\ln(2)\sum_{x=1}^\infty 2^{-\alpha x} = -\ln(2)\frac{2^{-\alpha}}{1-2^{-\alpha}}$$
Now integrate this from $\alpha=1$ to $\alpha=\infty$:
$$ - \sum_{x=1}^\infty \frac{2^{-x}}{x}= \left. -\ln\left(1 - 2^... | <strong>Hint 1:</strong> It suffices to recognize this sum as a Taylor series
<strong>Hint 2:</strong> It is in fact sufficient to know that for all $x \in (-1,1)$, we have
$$
\sum_{x=1}^\infty z^{x-1} = \frac{1}{1-z}
$$
Note that for $z = 1/2$, this is your statement. It follows that
$$
\int_{0}^t \frac{1}{1-z}\,dz ... | https://math.stackexchange.com |
3,463,658 | [
"https://math.stackexchange.com/questions/3463658",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/462971/"
] | I know from the ratio test that the series converges and I used wolfram alpha to determine that the answer is 1, but what are the steps involved to reach this answer?
| This is a (somewhat long-winded) reaction to <strong>part of</strong> the OP's revised post. My analysis only covers the query <strong>up to AND INCLUDING</strong> the following excerpt. I ask the OP to consider my reaction, and consider making another edit to his post. Then, I can (<em>iteratively</em>) examine the... | This is slightly unnecessarily complicated.
There are two partly identified sections on the board, and in the right-hand one (with the <span class="math-container">$8$</span> red squares) the total of mines is known to be <span class="math-container">$1$</span>. Thus, each red square has probability <span class="math-... | https://math.stackexchange.com |
10,678 | [
"https://dba.stackexchange.com/questions/10678",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4472/"
] | I have a simple application.This application update data of a table (B) from another table(A) which is changed every 60 sec. User may read data at any time so creating deadlock. How is this sort of problem solved in real world. Considering maximum 100 users how could I avoid deadlock. How would web application handling... | The simplest way to reduce deadlocks - proper indexing. Make sure, that client's read requests not involving table/clustered index scans - if any - this is the open gates to deadlocks
And make sure, that your index has its <code>allow_page_lock</code> and <code>allow_row_lock</code> options ON
| A deadlock involves two resources accessed in different order by different processes. For example:
<ul>
<li>Process 1 reads from table A and then updates table B</li>
<li>Process 2 reads from table B and then updates table A</li>
</ul>
This generates a deadlock when both processes are halfway done. Process 1 has a ... | https://dba.stackexchange.com |
67,930 | [
"https://security.stackexchange.com/questions/67930",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/55954/"
] | I've been told that when integrating with a 3rd party payment gateway, the other website's window should not be opened in an iFrame or a separate window - that the current application window itself should redirect to the payment gateway.
<ol>
<li>Where will I find documentation supporting this claim?</li>
<li>A new p... | Yes, VPN traffic is easily distinguishable on the network, and yes, it can also be easily blocked if the admins care for some reason. So, "a friend of yours" shouldn't really do it to circumvent IT policies. :)
| Look into setting up Stunnel, or a similar tool to wrap your traffic (VPN via TCP) in an SSL connection. The admin would have no way of knowing that this was VPN traffic, although it may be dropped by a web proxy or look suspicious if too much bandwidth was going through this connection. I've done it personally and i... | https://security.stackexchange.com |
1,325,309 | [
"https://math.stackexchange.com/questions/1325309",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/246303/"
] | Why does the carrier of an algebraic structure has to be closed under the operations of the algebraic structure?
One could also consider $(\mathbb{N}^*, \div)$. But why isn't that an algebraic structure?
| It is perfectly valid to call (informally) <em>algebraic structure</em> a set endowed with a family of partial operations. In the example you give, division is a partial operation on $\mathbb {N}$ (defined for pairs $s, t $ such that $t $ divides $s $). In this sense, for instance, a category might be called an algebr... | As your initial question may be answered by saying that this is part of the definition, let me instead give you a reason for this. Say, we start with the structure $(\mathbb R^*; \cdot, \ ^{-1}, 1)$. Then $(\mathbb Q^* , \cdot, \ ^{-1}, 1)$ is a substructure, but what exactly do we mean by this?
We mean that
<ol>
<li... | https://math.stackexchange.com |
34,970 | [
"https://softwareengineering.stackexchange.com/questions/34970",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/45599/"
] | Title is the question.
And why I am asking is because from what I read about most PHP frameworks (e.g. Code Igniter, Kohana, Cake, Zend) is that they're ether too complex, or are designed mostly for small applications (like blogs).
| I'd <em>always</em> use an off-the-shelf framework. There is almost never a <em>good</em> reason to build your own from the ground up. You'll spend a lot more time with the plumbing work and bug fixing writing your own than relying on tested and optimized methods already existing in the OS packages. Most of the framewo... | I've written virtually all of my sites from scratch. In my case, the reason is primarily because I enjoy creating things and that's also a great way to learn. It's much less fun for me to spend time trying to learn someone else's code than creating my own.
But that's just a personal reason. If you find a nice off-the-... | https://softwareengineering.stackexchange.com |
165,844 | [
"https://physics.stackexchange.com/questions/165844",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62224/"
] | How can I find the thrust, $t$, needed to keep an object with $m$ mass, in the influence of an object with $g$ gravity, from gaining or losing any altitude?
| Forces cause acceleration, or changes in speed. If your speed is constant, the total force on you must be 0.
Gravity is one force acting on you. The force of gravity is equal to your weight. It pulls you down.
To make the total force add up to 0, you need another force equal to your weight in the upward direction. ... | Take a simple example of an everyday situation where an object is kept from gaining or losing amplitude: Put the object on a shelf and let it sit there.
Now think about this situation. What is the force applied by the shelf to the object to keep it from gaining or losing amplitude?
| https://physics.stackexchange.com |
51,176 | [
"https://electronics.stackexchange.com/questions/51176",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16894/"
] | I'm studying the four kinds of amplifiers implemented through feedback in op amp circuits. When trying to relate all my previous knowledge with this, I'm getting a bit confused.
Can any BJT, MosFET, or JFET transistor be an amplifier of any kind? Are there advantages of BJT being a specific kind of amplifier?
Now, c... | It's worth noting that the mouse-snap actually <em>uses the autorouter</em> to some extent.
Depending on the routing mode you have enabled, it will behave differently. <kbd>Shift</kbd>+ <kbd>R</kbd> while in the interactive routing mode (e.g. placing traces) changes the routing mode.
Anyways, if you want to change t... | Autorouters typically employ a scoring system for figuring out "optimal" routes. Vias cost a certain amount, distance costs, angles have a cost... The lowest cost overall "wins."
But this by no means imbues the autorouter with any sense of artistic quality or knowledge of what is aesthetically "better." There are cert... | https://electronics.stackexchange.com |
36,105 | [
"https://softwareengineering.stackexchange.com/questions/36105",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12753/"
] | Folks, I have two separate classes. One of them makes http requests/receives response to/from a server and the second one converts received JSON objects into my models (separate classes). I'm thinking it would be an idea to include this class for data converting as an inner class of my first class. Wouldn't my first cl... | Inner classes are most commonly used for objects that act directly on the enclosing class. An excellent example of this is iterators. You create a custom implementation of Iterator within your container class, and return an instance of it in your <code>getIterator()</code> or whatever method. This iterator has access t... | If it is going to over complicate things without giving you a significant improvement somewhere(execution time, etc) then I don't think it's worth it and would leave it as-is.
| https://softwareengineering.stackexchange.com |
18,333 | [
"https://stats.stackexchange.com/questions/18333",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6627/"
] | As I understand, we can get correlation by normalizing covariance using the equation
$$\rho_{i,j}=\frac{cov(X_i, X_j)}{\sigma_i \sigma_j}$$
where $\sigma_i=\sqrt{E[(X_i-\mu_i)^2]}$ is the standard deviation of $X_i$.
My concern is what if the standard deviation equals zero? Is there any condition that guarantees it ... | It's true that, if one of your SD's is 0, that equation is undefined. However, a better way to think about this is that if one of your SD's is 0, there is no correlation. In loose conceptual terms, a correlation is telling you about how one variable moves around as the other variable moves around. An SD of 0 implies... | The other thing to think about are the underlying assumptions when we talk about means and standard deviations, and correlations.
If we are talking about a data sample, one common assumption is that the data is (at least approximately) normally distributed, or can be transformed such that it is (e.g. via a log transf... | https://stats.stackexchange.com |
313,837 | [
"https://mathoverflow.net/questions/313837",
"https://mathoverflow.net",
"https://mathoverflow.net/users/99132/"
] | Let <span class="math-container">$(X,d)$</span> be a metric space, <span class="math-container">$x_1,\ldots,x_N\in X$</span> and <span class="math-container">$x_1',\ldots,x_N'\in X$</span> be atoms, and <span class="math-container">$G=\sum_{i=1}^Np_i\delta_{x_i}$</span>, <span class="math-container">$G'=\sum_{i=1}^Np_i... | There is a nontrivial counterexample for <span class="math-container">$N=2$</span>, <span class="math-container">$p=1$</span>, and <span class="math-container">$X=\mathbb{R}$</span>. Pick <span class="math-container">$x_1=-2$</span>, <span class="math-container">$x_2=2$</span>, <span class="math-container">$x'_1=-1$</s... | Without further constraints this is not true and easy to see if <span class="math-container">$X$</span> is Euclidean: Let <span class="math-container">$\Gamma$</span> be the support of an optimal coupling between <span class="math-container">$G$</span> and <span class="math-container">$G'$</span>. If for fixed <span cl... | https://mathoverflow.net |
23,196 | [
"https://quant.stackexchange.com/questions/23196",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/19002/"
] | My professor has many grammatical mistakes and errors in his questions, so apologies ahead of time. I am just trying to understand what he wants for this question,
In trinomial model, let $S_0 = 1$, $R = 0$, $u = 2$, $m = 1$, and $l = 1/2$
a.) Find all risk-neutral probabilities and the range of prices generated by ... | For question a). From the assumptions, in particular, that $R=0$,
\begin{align*}
\pi_l + \pi_m + \pi_u &=1\\
\frac{1}{2}\pi_l + \pi_m + 2\pi_u&=1.
\end{align*}
Set $\pi_m=x$, and solve for $\pi_l$ and $\pi_u$,
\begin{align*}
\pi_l &= \frac{2}{3}(1-x)\\
\pi_m &= x\\
\pi_u &= \frac{1}{3}(1-x),
\end{a... | Trinomial trees give incomplete markets so there is a range of possible risk neutral prices. So you have to find the possible probabilities that make the tree risk-neutral and see what prices you get.
You have the correct expressions. Now just have to parametrize the set of solutions. It is one-dimensional and all th... | https://quant.stackexchange.com |
77,987 | [
"https://electronics.stackexchange.com/questions/77987",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/23435/"
] | I always see a very high resistance between the gate and the ground in n-channel MOSFET common-source amplifier. What is it's role? I think it is to prevent the signal input from bypassing the MOSFET and going to ground directly, but I am not sure. Am I right or wrong?
| If I understand you correctly, you're asking why \$R_1\$ (and \$R_2\$) in the following schematic is usually taken to be very large, right?
<img src="https://i.stack.imgur.com/lKxyl.png" alt="enter image description here">
<strong>In summary:</strong>
if you take big resistors for Gate's biasing you get low power w... | The resistance you see when you look into the gate of a MOSFET is extremely high, usually several orders of magnitude larger than the gate resistor you refer to. Withouth the gate resistor it will pick up static easily and the charge build up on the gate may easily drive drain-source to conduct or even worse it may bui... | https://electronics.stackexchange.com |
35,401 | [
"https://mathoverflow.net/questions/35401",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8434/"
] | I have read a couple of proofs for the undecidability of the post correspondence problem, but neither reference gave a concrete example of two lists of words over a fixed alphabet such that the problem was undecidable for that set of two lists. In other words, the proofs showed the existence of such an example without... | As Tsuyoshi said, it doesn’t make sense to search for an undecidable <em>instance</em> of a problem. It’s only the <em>problem</em> itself that can be undecidable.
In particular, for <em>every</em> instance of PCP (or any other problem for that matter) there trivially exists an algorithm that gives the correct answer ... | I guess I don't understand why it doesn't make sense to look for an exact instance in which the problem is undecidable. In group theory the word problem is undecidable, and there are examples of particular group presentations in which the word problem is undecidable for that exact group. So there is no algorithm that... | https://mathoverflow.net |
68,355 | [
"https://electronics.stackexchange.com/questions/68355",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16910/"
] | Because inductors share similar equations in their charging/discharging cycles, I am wondering if inductors have something like charge.
Capacitors have capacitance and charge while an inductor has inductance and <strong>_</strong>?
Is there a V = Q/C function for inductors?
| <em>Magnetic flux</em> is the complement of charge.
Just as a capacitor is defined by the relationship \$Q = CV\$, an inductor is defined by the relationship \$\varphi=LI\$, where \$\varphi\$ is the magnetic flux.
Just as the capacitor formula becomes \$I = \dfrac{dQ}{dt} = C\dfrac{dV}{dt}\$ when we look at time va... | The Photon answered this question excellently, but I feel there is some relevant information that should be shared and will be of interest to some readers or the asker himself.
Firstly, I will add that inductors can also store capacitive charge. This is a know phenomenon that can be made to manifest strongly by windi... | https://electronics.stackexchange.com |
43,355 | [
"https://biology.stackexchange.com/questions/43355",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/5729/"
] | As we know that coils and loops are evolutionary variable regions where mutations,deletions, and insertions frequently occur. So does it mean that they don't have much role in the structure of protein? If it so then what are the factors for the protein core structure formation?
| Firstly, is important to remember that protein structures are dynamic due to the torsion angles between the N-terminal and C-terminal bonds. There are different conformations to expose different sequences to the outside of the protein to react/catalyze. So there is no one perfect conformation for a protein in a biologi... | Solving the 3D structure of a protein is complex problem. There are multiple layer of informations that come into play.
The first level of organization comes from secondary structure, which is in turn dictated by the AminoAcid sequence. There are common secondary structure motifs such as alpha-elices and beta-sheets. ... | https://biology.stackexchange.com |
8,860 | [
"https://bioinformatics.stackexchange.com/questions/8860",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/4783/"
] | File1:
<pre><code>ENST00000000233 ARF5
ENST00000000412 M6PR
ENST00000001008 FKBP4
ENST00000001146 CYP26B1
ENST00000002501 DBNDD1
ENST00000002596 HS3ST1
</code></pre>
File 2:
<pre><code>ENST00000000412 0.779142
ENST00000001008 0.738143
ENST00000002501 0.715315
ENST00000002596 0.713664
</code></pre>
Desired Output
<... | I like to use the <code>join</code> command for this. For your example above, you can simply use the following:
<pre><code>$ join file2 file1
ENST00000000412 0.779142 M6PR
ENST00000001008 0.738143 FKBP4
ENST00000002501 0.715315 DBNDD1
ENST00000002596 0.713664 HS3ST1
</code></pre>
This assumes your files are sorted. I... | Using awk, this can be done in the following way:
<pre><code>awk 'NR==FNR{a[<span class="math-container">$1]=$</span>2; next}<span class="math-container">$1 in a{print $1, $2, a[$</span>1]}' file1.txt file2.txt > same.txt
</code></pre>
Explanation:
<pre><code>NR==FNR (along with the next command)
</code></pre>
... | https://bioinformatics.stackexchange.com |
109,706 | [
"https://softwareengineering.stackexchange.com/questions/109706",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/37117/"
] | I have been asked by my local Association for Computing Machinery chapter to give a lecture on Android development, and while I already have some topics to cover, I was curious if the community of SO had any suggestions of things that would be interesting to hear about.
Thus selected:
<ul>
<li>OpenGL</li>
<li>Using h... | If your audience doesn't know Android but are interested in Android development and want to take the first steps I'd go with:
<ol>
<li>A bit on Android history</li>
<li>Briefly introduction to: Activities, Services, Broadcast receivers, Content providers</li>
<li>Good UI practices</li>
<li>Social media integration</li... | Cover android application components like
1.Activities<br>
2.Services<br>
3.Broadcast receivers<br>
4.Content providers
| https://softwareengineering.stackexchange.com |
82,779 | [
"https://softwareengineering.stackexchange.com/questions/82779",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19700/"
] | I'm just getting started in Android development and am working on a few small "practice" apps. As an example, one is a live wallpaper. The others are similar in terms of development effort. When these apps are done I would like to list them in the market. I may list them for free (or maybe not), and they're simple app... | <ol>
<li>Selling as a company gives your protection for your private assets from your disgruntled customers, competitors and anyone else who wants to try you out</li>
<li>Selling under a company name helps develop a brand. Real name is boring. Come up with something creative and make the name known.</li>
<li>Depending ... | Using an organization name to sell Android apps is a good idea for the same reasons it's a good idea to use public interfaces when programming instead of directly exposing private data:
<ul>
<li>It looks more stable. (A one-man organization has no ties other than to its task of providing apps; a person's name is tied ... | https://softwareengineering.stackexchange.com |
2,795 | [
"https://mathoverflow.net/questions/2795",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1202/"
] | Last year I attended a first course in the representation theory of finite groups, where everything was over C. I was struck, and somewhat puzzled, by the inexplicable perfection of characters as a tool for studying representations of a group; they classify modules up to isomorphism, the characters of irreducible modul... | Orthogonality makes sense without character theory. There's an inner product on the space of representations given by $\dim \operatorname {Hom}(V, W)$. By Schur's lemma the irreps are an orthonormal basis. This is "character orthogonality" but without the characters.
How to recover the usual version from this conce... | The trace is about the strongest general way we have to linearly project a non-abelian situation (matrices) to an abelian situation (scalars): tr(AB)=tr(BA). By using the trace, the representation theory of non-abelian groups begins to resemble the representation theory of abelian groups, i.e. Fourier analysis. (Note... | https://mathoverflow.net |
57,726 | [
"https://electronics.stackexchange.com/questions/57726",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18760/"
] | I am using a stepper drive board to control a stepper motor. It has settings for for <strong>fixed-on time</strong> when using the open-loop PWM control method.
According to the API description:
<pre><code>The fixed-on time is the amount of time that the winding will be left
turned on at the beginning of the step, i... | The fixed-on time is the time during which no current regulation is done (other than absolute current limiting). This allows for faster acceleration at the beginning of each pulse, if the motor is not in inertial motion already.
Fixed-on time ends early if current reaches desired value before time-out, and this is th... | This answer is in large part to have enough space to discuss the points made in the currently-checked answer. (I've seen many good answers from Anindo, but this one is wide of the mark, I think!)
Background: To make a stepper motor advance from one position to the next, the controller changes the voltages across the s... | https://electronics.stackexchange.com |
36,233 | [
"https://electronics.stackexchange.com/questions/36233",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6956/"
] | I'm sitting here with my Raspberry PI and some other equipment that requires digital signal (high/low, enabled/disabled).
But the Pi only has a GPIO so to get it to work I would need a microchip of some sort (guessing)?
I'm fairly new to all this, but like to play around on my breadboard.
Could anyone point me in th... | GPIO means General Purpose I/O, and that's a digital input or output (though you often can assign an alternative function to it, like I2C signals, or ADC input). Digital outputs can control other devices by using high (logical "1") and low (logical "0") levels.
"enabled/disabled", both with the "d" at the end are term... | Turn on your GPIO pin will give your around 3.3V at the pin indicating 'High',
Turn off your GPIO pin will give your around 0V at the pin indicating 'Low'.
| https://electronics.stackexchange.com |
357,245 | [
"https://mathoverflow.net/questions/357245",
"https://mathoverflow.net",
"https://mathoverflow.net/users/51189/"
] | In <span class="math-container">$1969$</span>, Margulis proved, for suitable constant <span class="math-container">$h>0$</span>and <span class="math-container">$r$</span> is a positive constant that :
<span class="math-container">$a(p)=\lim_{r\to \infty} \frac{VolS(p,r)}{e^{h r}}$</span> with (<span class="math-co... | When <span class="math-container">$M$</span> has positive curvature, the limit should always be 0. Indeed if <span class="math-container">$M$</span> has non-negative Ricci curvature, Bishop-Gromov tells you that <span class="math-container">$\frac{Vol S(p, r)}{n\omega_nr^{n-1}}\leq 1$</span>, so the volumes grow at mos... | Bishop's inequality: in any complete Riemannian manifold of Ricci nonnegative curvature, if balls around a point have radii <span class="math-container">$r$</span> and <span class="math-container">$r'=\lambda r$</span>, then their volumes have <span class="math-container">$\lambda^n V \ge V'$</span>. This is for balls,... | https://mathoverflow.net |
4,139 | [
"https://electronics.stackexchange.com/questions/4139",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1085/"
] | Why are tristates favored over multiplexers to select the output from RAM? The explanation that I've heard of is that the RAM is too large for using a multiplexer but I need more details.
A theory we've come up with is that using a multiplexer would necessitate a tree of OR-gates to select the output which would drama... | It's an issue of "fan-out" or "fan-in". So your theory is more or less accurate. However there is the additional benefit of using tristate outputs that you can attach them to a bus! If you use a CMOS Multiplexer you cannot share the wires that the output is on, if you use Tri-State devices then you can share the bus wi... | If one builds a rectangular memory array which is read using a tri-state driver in each memory cell, then one decoder circuit can control all of the cells in a row. One will need circuitry around the perimeter of the array to control it, but the amount of control circuitry will be proportional to sqrt(N)*lg(N). By co... | https://electronics.stackexchange.com |
572,013 | [
"https://math.stackexchange.com/questions/572013",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/99325/"
] | Check, if the following function, from set $A$ to $B$ are injective, surjective or bijective
$ A=\mathcal {P}(\omega),\ B=\omega\cup\{\omega\}\ and\ \forall x\in A:\ F_1(x)=\bigcup\{n\in\omega:n\subseteq x\}$
This function can't be injective i think because domain has a greater cardinality but what does $\ B=\omega\c... | You've got the right idea, but your execution is a bit off. Take $w\in\Bbb R^2$ with $\lVert w\rVert=1,$ take any $\delta>0,$ put $\epsilon=1,$ and take $0<c<\min\{1,\delta\}.$ Then, put $v=(1-c)w,$ instead. You'll see that $\lVert v\rVert=|1-c|=1-c<1,$ so that $f(v)=0,$ and so $$d\bigl(f(v),f(w)\bigr)=1\ge... | Alternatively; We have $\lim_n f(1-\frac{1}{n},0) = 0 \neq 1 = f(1,0)$. Since $(1-\frac{1}{n},0) \to f(1,0)$, $f$ cannot be continuous.
| https://math.stackexchange.com |
104,066 | [
"https://mathoverflow.net/questions/104066",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1050/"
] | In Chapter III, Theorem 7.4 of <i>The Arithmetic of Elliptic Curves</i> (first edition), Silverman gives the following lemma and proof:
<blockquote>
<b>Lemma</b>: Let <span class="math-container">$M \subset Hom(E_1, E_2)$</span> be a finitely generated subgroup, and let <span class="math-container">$M^{div} = \{ \phi \... | How do you prove that the ring of integers in a number field is finitely generated? One usually embeds them in $\mathbb{R}^{r_1}\times\mathbb{C}^{r_2}$. How do you prove that the units in a number field are finitely generated? One generally embeds them in a hyperplane in $\mathbb{R}^{r_1+r_2-1}$. Then one shows that th... | Here is an alternate proof that should be less problematic. The degree is a positive-definite quadratic form with image in $\mathbb Z$ (that's how he's extending it to $\mathbb R$, right?), so we can construct a bilinear form with image in $\mathbb Z$: $x\cdot y= deg(x,y)-deg(x)-deg(y)$. This gives a map $M^{div} \to M... | https://mathoverflow.net |
572,031 | [
"https://stats.stackexchange.com/questions/572031",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/349806/"
] | When explaining the reason for rejecting a null hypothesis, I sometimes see "p-value is small", and sometimes it's "for a test of size <span class="math-container">$\alpha$</span>, we reject it when (some condition)". I was wondering if "p-value is small" is a special case of a commonly us... | We set some value, called <span class="math-container">$\alpha$</span>, as our maximum tolerance for type I error rate. That is, we accept that our work could reject true null hypotheses <span class="math-container">$100\alpha\%$</span> of the time the null hypothesis is true. In the common situation of <span class="ma... | The outcome of a hypothesis test is reported in two ways:
<ul>
<li>The p-value is <em>p</em> where <em>p</em> is a given small number.</li>
<li>The null hypothesis is rejected at the <em>α</em> significance level; usually <em>α = 0.05</em>.</li>
</ul>
If the p-value <em>p</em> is smaller than <em>α</em>, then the null ... | https://stats.stackexchange.com |
126,050 | [
"https://electronics.stackexchange.com/questions/126050",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51761/"
] | I am trying to make a circuit for my newly installed DRL (Day running lights), what I am trying to do is have the DRL run all the time, turn off when using high beam, dimmed when headlights are on.
I bought two 5 pins relays and attempted to make a circuit for that purpose, here is an image of what I have done so far ... | Just to add to my comment with the circuit diagram.
<img src="https://i.stack.imgur.com/Hta8x.png" alt="enter image description here">
The first circuit shows the DRL(day) connected to the common pole of relay 2. (The way I think you have wired your circuit) With relay 1 unenergized the ACC(+) has a path through rela... | To dim the running lights, they could be switched from being parallel across the 12V supply to being in series by using a relay with two sets of change-over contacts.
<img src="https://i.stack.imgur.com/ngNKf.gif" alt="enter image description here">
When high beam is not selected, the relay contacts are as shown an... | https://electronics.stackexchange.com |
131,484 | [
"https://physics.stackexchange.com/questions/131484",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42462/"
] | Suppose for example that a person like me likes his water in-between. A bit colder than the room temperature but not very cold. If you have a water dispenser that pours rtp water and cold water, which one to pour in the cup first to ensure the temperature I'm looking for?
I was just thinking of it as I was pouring wa... | This is assuming no stirring, since that is a hassle.
There is a third possibility of pouring both in at the same time. That would ensure the fastest convection.
Cold then warm will be slowest since warm water rises.
Warm then cold will be slightly faster since it promotes convection.
This all depends on your perso... | I think that it makes little difference... but anyway...
You should pour the room-temperature water first, and then the cold water until you get the target temperature.
Why? Because if you pour the cold water first, it will immediately start to warm. If you leave it enough time it will actually reach equilibrium at r... | https://physics.stackexchange.com |
65,294 | [
"https://softwareengineering.stackexchange.com/questions/65294",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19799/"
] | As an employee of a company, when you write code do you feel like you have an attachment to it? Do you feel that you have some ownership of the code? Or do you write it completely detached from it without any concern about what happens to it after you've moved onto something else?
EDIT: I'm not talking about writing b... | After 30 years as a contractor, it's mixed.
<ol>
<li>It's all disposable. I've worked with hundreds of clients. I'll never see the code again. Why become attached? There's no sense of ownership.</li>
<li>It's very visible. It's more expensive than in-house code, so it gets a lot of scrutiny. Since I won't be arou... | As a more or less solo developer, the fear of having to maintain what I write is the primary driver behind me trying to not write horrible code.
| https://softwareengineering.stackexchange.com |
570,873 | [
"https://electronics.stackexchange.com/questions/570873",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/288848/"
] | I’m planning to install solar panels on the roof of one building (the charge controller and batteries are in this building), to power a DC circuit in another building. No AC equipment needs to be powered. The buildings are around 5m apart.
Is it better to link the buildings together with AC or DC? DC would be easier as... | The voltage drop is going to outrule any 12V circuit.
Rearrange the solar panel, batteries and charger as an 48V circuit. That makes a voltage drop of 1-2 volts less critical. It also brings the current down to 7.5A, which is far easier to handle.
On the receiver end, use a 48V/12V DC-DC converter.
| Voltage drop and cable gauge are both bad, but what is worse is the safety profile of such a system.
Bad fire safety is an indirect consequence of the long wires and the significant voltage drop. Your buildings are 5m apart, but buildings themselves are not sizeless. I bet on 20m of wires between the batteries and the ... | https://electronics.stackexchange.com |
530,036 | [
"https://physics.stackexchange.com/questions/530036",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/253625/"
] | Alpha Centauri is 4.3 light years away. If it exploded suddenly, would we be able to know this in advance? As the light from the supernova will not reach us before 4.3 years.
| Yes, you would get a few hours warning from the intense pulse of gravitational waves and neutrinos caused by the core collapse. Incidentally, I should say that this does not actually apply to Alpha Cen, since this is a solar-type star that will never produce a supernova.
The gravitational waves and neutrinos also trav... | No information can travel faster than the speed of light in a vacuum. Gravity also travels at this speed. So if Alpha Centaury had any change 4 years ago we would have no way of knowing it for about another 0.37 years. We see it and feel any gravitational effects from it as it was about 4.37 years ago. About 4.37 years... | https://physics.stackexchange.com |
201,916 | [
"https://mathoverflow.net/questions/201916",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41654/"
] | Is there a procedure for finding all matrices which commute with two given square and complex matrices?
For example, given two elements $A,B \in$ $\mathfrak{su}(4)$ is it possible to find all elements which commute with both $A$ and $B$ individually.
| Generically (e.g., if one of the matrices has distinct eigenvalues, or more generally, is non-derogatory; for two commuting matrices, the conditions are even weaker), the centralizer of a single matrix just consists of the polynomials in that matrix. So if you pick a pair of commuting matrices at random, the polynomial... | I am answering the two questions (A) and (B) in the OP's comment. The answer is really already contained in @RyanBudney's comment: this is a linear system ($AH = HA, BH = HB,$) so you are asking if a linear system has a solution, and if yes, describe all the solutions. The short answer to both questions is "row reducti... | https://mathoverflow.net |
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