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 |
|---|---|---|---|---|---|
85,126 | [
"https://cs.stackexchange.com/questions/85126",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/58433/"
] | For any simple, connected, undirected graph $G(V,E,w)$ with each carrying distinct positive edge weights, is it true that MST will contain all the edges which do not lie in any cycle of $G$?
I think MST can take any edge of irrespective of the fact whether it is an edge of cycle (like I simply use Kruskal's), Also I a... | I think you need to be more precise in your reading of the statement, though it could be better phrased. A different version is "if $e$ is an edge of $G$ and it is not in any cycle in $G$, it must be in any MST of $G$". This <em>doesn't</em> say that edges that are in cycles can't be in the MST, it just says that any e... | It is simply not true that "<em>MST can take any edge of irrespective of the fact whether it is an edge of cycle (like I simply use Kruskal's)</em>". Think of <em>Prim's Algorithm</em>. Every iteration divides the graph into two sets - $Set A$ always forms a single tree. Each step adds to $tree A$ a light edge that con... | https://cs.stackexchange.com |
680,659 | [
"https://physics.stackexchange.com/questions/680659",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/209185/"
] | Energy flux for an Em wave is defined by the poynting vector <span class="math-container">$(1/\mu_0) E \times B$</span>
The energy is also proportional to <span class="math-container">$E^2 $</span>
If you take for example the simplest form of generating light, the hertzian dipole. E and B are both proportional to <spa... | Hertzian dipole's radiated power is proportional to <span class="math-container">$\omega^2$</span> provided you keep the current amplitude constant. You can get higher power at low frequency by increasing current. The energy of the photon at a certain frequency is irrelevant: two heaps of sand can have the same mass ev... | You are confusing the electromagnetic field energy in a volume
with the energy of single photon.
Light is made up of photons.
The energy of a single photon with frequency <span class="math-container">$f$</span> is given by <span class="math-container">$E=hf$</span>,
which is very tiny.
For example: a red photon has ene... | https://physics.stackexchange.com |
66,697 | [
"https://quant.stackexchange.com/questions/66697",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/24074/"
] | My independent variable is the monthly returns of Stock A. My dependent variable is the monthly returns of Stock B. Returns are calculated using [(price at end of month) / (price at beginning of month)] - 1.
If I run a simple linear regression, I get a regression coefficient of 2 for Stock A. Since my data are returns,... | You'll find the same issue with all of the greeks.
I would say that the standard rule for delta is the following:
If you're talking about a single option/strategy, then people will talk about delta percentage*.
If you're talking about a single option/strategy, and you don't plan to hedge the delta when it tades (i.e. y... | If you want to split hairs, as I like to do, there are 2 ways to express Delta.
"Pure Delta" is a fraction, i.e. a number between 0 and 1 (for a Call). In terms of units, it is a pure number.
"Position Delta" is equal to Delta times the size of your Call position. If you have Calls on 100 shares and... | https://quant.stackexchange.com |
235,976 | [
"https://softwareengineering.stackexchange.com/questions/235976",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/106432/"
] | When I look at things like Twitter, it seems like the idea is so simple to implement initially that the founder does not have to be very technically talented. Basically it's just a guy with a good idea. But when an app / software blows up and entails much harder engineering problems, how does the founder deal with it? ... | When you get large enough that scaling well really matters and you have to start dealing with things like caching and database tuning, hopefully you are making enough money that you can hire somebody who specializes in performance tuning (or even better, a team of people, each specialized in a different sub-area).
Whe... | The founders of the company can come from a lot of different backgrounds: they might be marketing folks, or sales folks, or just someone in a different industry altogether who want to build their own organization. They might be money guys trying to cash in on a hot industry idea. So it's pretty common in the early days... | https://softwareengineering.stackexchange.com |
110,190 | [
"https://softwareengineering.stackexchange.com/questions/110190",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7369/"
] | During TDD training based on medical software case we are implementing the following story: "When user presses Save button, system should add patient, add device and add device data records".
The final implementation will look something like this:
<pre><code>if (_importDialog.Show() == ImportDialogResult.SaveButtonIs... | <blockquote>
But in the second case if test fails, we are not sure what is exactly wrong.
</blockquote>
I think that would largely depend on how good error messages the test produces. In general, there are different ways to verify that a method has been called; e.g. if you use a mock object, it will give you a preci... | <strong>The Granularity in your example seems to be the difference between unit- and acceptance tests.</strong>
A unittest tests a single unit of functionality, with as few dependencies as possible. In your case, there could 4 unittests
<ul>
<li>does AddPatient add a patient (i.e. calls the relevant database function... | https://softwareengineering.stackexchange.com |
161,132 | [
"https://softwareengineering.stackexchange.com/questions/161132",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/61998/"
] | We are continually revamping our front end developer test that we do in-house after a candidate has passed an online test. The online test has questions such as:
<ul>
<li>How does a for loop start?</li>
<li>What is the correct way to write a JavaScript array?</li>
<li>Write the css selector for the 3rd list item withi... | <strong>Switch it up, get the interviewee talking about past experience...</strong>
What will really help separate the wheat from the chaff is questions that drill deeper and require context to answer. Past experience is the best context but even theoretical answers show at the minimum some level of understanding.
<s... | Some examples
<ul>
<li>Provide bugged code, and ask for explanation and solution.</li>
<li>General trouble shooting, for example, front end devs need to know about networking protocols, dream up a scenario.</li>
<li>Always space for a crazy question like " How many camels are in Egypt", and just see how they reason i... | https://softwareengineering.stackexchange.com |
100,805 | [
"https://physics.stackexchange.com/questions/100805",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20731/"
] | When you bite something in two pieces, e.g. a piece of hard candy, you hear the sound through two sources: vibrations in the air, entering your ears from the outside and internal vibrations in your skull.
What I have noticed is that there is a difference in (the way I perceive*) the sound intensity when my ears are p... | The functions $e^{i \bf p \cdot \bf x}$ as functions of $\bf x$ are linearly independent for different $\bf p$'s, hence every coefficient in the linear superposition (that is, in the integral) must be zero.
| The reason you can get rid of the integral and the exponential is due to the uniqueness of the Fourier transform. Explicitly we have,
\begin{align}
\int \frac{ \,d^3p }{ (2\pi)^3 } e ^{ i {\mathbf{p}} \cdot {\mathbf{x}} } \left( \partial _t ^2 + {\mathbf{p}} ^2 + m ^2 \right) \phi ( {\mathbf{p}} , t ) & = 0 \\... | https://physics.stackexchange.com |
1,295,464 | [
"https://math.stackexchange.com/questions/1295464",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/213493/"
] | I've been going through some of my notes when I found the following inequality for $a,b,c>0$ and $abc=1$:
$$
\begin{equation*}
\sqrt{2}(a+b+c) \geq \sqrt{1+a^2} + \sqrt{1+b^2} + \sqrt{1+c^2}
\end{equation*}
$$
This was what I attempted, but that yielded no result whatsoever:
$$
\begin{align}
\sqrt{2}(a+b+c) &\g... | Hint
$$\sqrt{2}x-\sqrt{x^2+1}\ge\dfrac{\sqrt{2}}{2}\ln{x},x>0$$
it is easy to prove by derivative.
so
$$\sqrt{2}a-\sqrt{a^2+1}\ge\dfrac{\sqrt{2}}{2}\ln{a}\tag{1}$$
$$\sqrt{2}b-\sqrt{b^2+1}\ge\dfrac{\sqrt{2}}{2}\ln{b}\tag{2}$$
$$\sqrt{2}c-\sqrt{c^2+1}\ge\dfrac{\sqrt{2}}{2}\ln{c}\tag{3}$$
$(1)+(2)+(3)$
$$\sqrt{2}(a+... | here is another way which is not use derivative:
first we need to know: $\sqrt{\dfrac{x+y+z}{3}} \ge \dfrac{\sqrt{x}+\sqrt{y}+\sqrt{z}}{3}$ (1)
to prove it, we have $\sqrt{\dfrac{x+y}{2}} \ge \dfrac{\sqrt{x}+\sqrt{y}}{2} \implies \sqrt{\dfrac{x+y+z+t}{4}} \ge \dfrac{\sqrt{x}+\sqrt{y}+\sqrt{z}+\sqrt{t}}{4}$
let $t= ... | https://math.stackexchange.com |
484,150 | [
"https://physics.stackexchange.com/questions/484150",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/191014/"
] | I don't understand the reason scales measure the normal force instead of the weight.
| I'll give an answer based on intuition (which illustrates the physics).
The scale only measures the portion of the weight that is <em>applied</em> to the scale.
Imagine you tie a string to a weight and place the weight on the scale. If you pull up slightly on the string the scale will read less, even though the weigh... | Scales measure the force being applied to their plate, through springs or circuits. The force on the plate of the scale is the force from the object on it. It is Newton's Third Law pair with the Normal force on the object.
The scale measures the normal force because the force on the object and the normal force are ne... | https://physics.stackexchange.com |
215,575 | [
"https://security.stackexchange.com/questions/215575",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/214893/"
] | Old IoT devices and some low-power devices are not capable of doing encryption or use weak encryption methods like TLSv1.0. What could be the risks of using such devices and unencrypted protocols like HTTP?
| The same as using plaintext (unencrypted and unauthenticated) communication elsewhere.
What exactly that means, depends on your threat model.
<h1>Smart Bulb, Dumb Protocol</h1>
Imagine you had a smart lightbulb in your home. You could use an app to control the brightness and the warmth of the bulb. It even offers an... | The big concern with unencrypted IoT devices is not just privacy issues so much as the vulnerability of the device itself. Let's say you have a smart refrigerator that sends unencrypted API calls to a server that also communicates with the app on your phone to let you know when you need to buy more milk.
IoT devices ... | https://security.stackexchange.com |
145,583 | [
"https://cs.stackexchange.com/questions/145583",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/123018/"
] | I saw this question on my college "Design of Algorithms" exam but I could not solve it:
Given an array <span class="math-container">$A[1..n]$</span> of integers. find an element which is repeated at least <span class="math-container">$\frac{n}{2}$</span> times using <strong>Divide and Conquer</strong> algorit... | Without sorting the array, you could use the following divide-and-conquer algorithm. For simplicity, I will suppose that one searches an element that appears strictly more than <span class="math-container">$\frac{n}{2}$</span> times, but it could also be done with the equality case.
<pre><code>Algorithm: Majority(A)
In... | This is probably the simplest but not the optimal way to solve your problem.
Since you can use <span class="math-container">$O(n\log{n})$</span> time and your algorithm needs to use Divide and Conquer, you can solve the problem by:
<pre><code>1. Use Merge Sort to sort the array A
2. For i = 1...n/2 ... | https://cs.stackexchange.com |
31,818 | [
"https://physics.stackexchange.com/questions/31818",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10475/"
] | I was reading around about the Radio Frequency and its effect on the GAS/Petrol forecourts, suddenly i came across something posted by someone,
"I personally went on a trip with some friends, one who received a nasty shock every time he tried to enter the car. Since he was the only one receiving these shocks I theoriz... | <blockquote>
I couldn't understand how the static electricity could cause the shock
from the car ?
</blockquote>
Although the car looks like it should be insulated by the rubber tires they are actually quite good conductors so touching the car is a lot like touching any other grounded metal object.
<blockquote>
... | Shoes which isolate something will allow the build-up of electricity.
Rubber tires are usually not conductive although special ones are being manufactured to make them conductive for sensitive situations such as delivering gas. In the USA they are marked 'UL'. Since it was a car it's a near certainty that they were no... | https://physics.stackexchange.com |
145,342 | [
"https://mathoverflow.net/questions/145342",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41592/"
] | Mostly I see a partition of a set <span class="math-container">$A$</span> defined as a collection of non-empty disjoint sets whose union is <span class="math-container">$A$</span>.
I see one reference that allows empty sets to be included in the partition: (Potter, M. <em>Set theory and its philosophy</em>, 2004, Oxfor... | In Bourbaki's terminology the elements of a partition may be empty (cf. E.II.4.7).
| In German you see the term "disjunkte Zerlegung" for this concept, which roughly means "disjoint decomposition".
| https://mathoverflow.net |
192,171 | [
"https://electronics.stackexchange.com/questions/192171",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/72718/"
] | Experimenting with blinking LEDs, I learned about creating delays with either a software loop or a timeout from a timer.
I know that for a simple blinking LED program, where the processes aren't that complicated and timing isn't crucial, using either wouldn't matter. But in more of a time-crucial multitasking context w... | You need to go to the bank (which is just around the corner) and do your laundry. Going to laundry requires you to wait for the washer to finish, and then wait for the the dryer to finish.
How would you go about performing these tasks?
On a lazy day, you could just do the laundry and then go to the bank. It's not tha... | It largely depends on what you want to achieve.
For a software blocking delay like you have set up, you will not be able to service interrupts and maintain a constant interval. If you add more code into the loop the delay will change, potentially unpredictably or inconsistently if you have variable control flow block... | https://electronics.stackexchange.com |
109,646 | [
"https://softwareengineering.stackexchange.com/questions/109646",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35740/"
] | Recently I've finished learning about multithreaded programming on single shared objects, but was curious about how different things would be in order to successfully program on multiple shared objects?
| This is a very hot current research topic. The question of how to properly share data between multiple, concurrent, processing units, doesn't have obviously good answers yet.
Some of the issues that change and you should think about:
<ul>
<li>With multiple shared objects, you'll want to have different threads being a... | The difference is that usually when you have multiple shared objects, they live in some sort of collection (like a hash table, linked list, tree, or whatever). This requires some kind of pattern for how the locking will work.
The simplest solution is to have one lock for the collection. A thread can acquire the lock, ... | https://softwareengineering.stackexchange.com |
3,972,861 | [
"https://math.stackexchange.com/questions/3972861",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/737853/"
] | The question is contained in the title. I know that for metric spaces completeness is not invariant under homeomorphisms. What happens if we consider the same problem in the category of normed spaces with continuous linear maps as morphisms?
| Functions are morphisms in the category of sets. A morphism <span class="math-container">$$e:S\rightarrow X$$</span> from any singleton S set to another set X (object in category Set), "picks out" an element of X. The composition of a morphism <span class="math-container">$$f:X\rightarrow Y$$</span> with the... | (This should be rather a comment, but I will post it as an answer as it is too long)
Besides exponential objects as mention in the comments there is another way of 'evaluating' functions/morphisms:
In a general category we replace the elements (in the set-theoretic sense) with morphisms:
Let <span class="math-container... | https://math.stackexchange.com |
208,645 | [
"https://mathoverflow.net/questions/208645",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31045/"
] | In group theory the number of Sylow $p$-subgroups of a finite group $G$, is of the form $kp+1$.
So it is interesting to discuss about the divisors of this form. As I checked it seems that for an odd prime $p$, there is not any divisor $a$ of $p^4+1$, where $1<a<p^4+1$ and $a=kp+1$, for some $k>0$.
Could you ... | There's none indeed.
<b>Lemma</b>: if $1<m<n$ are coprime integers then $mn+1$ does not divide $n^4+1$.
First observe that for any $m,n$, of $mn+1$ divides $n^4+1$, then it divides $n^4m^4+m^4=((nm)^4-1)+1+m^4$, and since $mn+1$ clearly divides $((nm)^4-1)$, we deduce that it also divides $1+m^4$.
To prove the... | Let $p$ be prime. Assume that $q \mid p^4+1$, where $q = ap+1$ for some
$a \in \mathbb{N}$.
Then $(p^4+1)/q \equiv 1 \!\! \mod p$, hence
$p^4+1 = (ap+1)(bp+1)$ for some $b \in \mathbb{N}$.
Now we have $p^4 = abp^2+(a+b)p$, respectively, $p^3-abp-a-b = 0$. Therefore, effectively
we are looking for solutions to the diop... | https://mathoverflow.net |
165,296 | [
"https://math.stackexchange.com/questions/165296",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/34230/"
] | Let $A,B$ be a $n \times n$ matrices such that $\det(B) = 1$. Will the spectrum
(set of eigenvalues) $AB$ be same as that of $A$. Or, at least is $\mbox{Trace}(A) = \mbox{Trace}(AB)$ ? If not, what can we say about the change in spectrum and trace in $A$ and $AB$.
| If two matrices $A,B$ have the same nonzero determinant, then $\det(A^{-1}B)=1$ so $A$ and $B$ are in the same class under multiplication by matrices of determinant $1$. Hence among invertible matrices the <em>only</em> invariant quantity under such multiplication is the determinant itself (of course any function of th... | No. Consider $n=2$, $A=I$, $B$ a diagonal matrix with entries $2, 1/2$ on diagonal. $\det B=1$, but both trace and spectrum of $AB$ are different from those of $A$.
You can't really say anything about the spectrum except that it will not change the product (that is, determinant), which is easy to see by generalizing t... | https://math.stackexchange.com |
492,783 | [
"https://physics.stackexchange.com/questions/492783",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228781/"
] | <blockquote>
Faraday's Law of induction states that the work done per unit charge by the (induced) electric force along a loop of wire, or the emf, is minus the rate of change of magnetic flux through the loop/surface and is given by the equation
<span class="math-container">$$\mathcal{E}_{Ind.}=\oint \vec E_{Ind.}... | This is where it's a good time to "converse with the math". Let's look at the equation:
<span class="math-container">$$\mathcal{E} = \oint_\gamma \mathbf{E} \cdot d\mathbf{l}$$</span>
which in this case equals <span class="math-container">$\mathcal{E}_\mathrm{ind}$</span>. This is based on the work formula:
<span cl... | <blockquote>
The minus sign is necessary because the induced current must travel in a way such that the induced magnetic field produces a change in flux that is <strong>opposite to that of the original magnetic field</strong>
</blockquote>
The phrase in bold is incorrect as it could be in the same direction as tha... | https://physics.stackexchange.com |
93,972 | [
"https://softwareengineering.stackexchange.com/questions/93972",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1973/"
] | I work on a pretty old application which was converted from DOS and flat files for storing information to Paradox tables using the BDE then to MySQL relational database.
The older devs say that the reason they have no idea how to properly create a table in 3nf is because their code predates relational databases and t... | The relational model was first formulated by E.F. Codd in 1969, and was first implemented in various IBM databases in the '70s. It also looks to me like the first edition of C. J. Date's seminal "An Introduction to Database Systems" was published around 1974.
I was hearing noise about relational databases in the 80s, ... | Well... at least since the 80's. I got my training at a well-known Software company in the Netherlands and way back then we were all taught about data normalisation. Normalisation probably has been around just as long as relational databases, which originated in the early 70's.
| https://softwareengineering.stackexchange.com |
187,241 | [
"https://mathoverflow.net/questions/187241",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5259/"
] | Let $B$ be a compact manifold, and $\hat{B}\to B$ be the maximal abelian covering of $B$; i.e. $\hat{B}$ is the quotient of the universal cover with respect to the commutator subgroup of $\pi_1(B)$. Given $H\subset H_1(B)$, we can further quotient $\hat{B}$ with respect to $H$ to get a covering $X\to B$ with group of d... | This is false. It is false for first cohomology and the maximal abelian cover of the classifying space of the integral Heisenberg group. The integral Heisenberg group $H(\mathbb Z)$ of $3\times 3$ upper triangular matrices with integer entries and 1s on the diagonal. The abelianization is $\mathbb Z^2$ given by taking ... | I am not too comfortable with spectral sequences and in particular I do not see the obstruction statement in Matthias's answer. It seems there is a direct construction of an invariant cocycle for the total space of the fibration Matthias suggested. I would guess it is a translation of Matthias's answer into less techni... | https://mathoverflow.net |
29,106 | [
"https://dsp.stackexchange.com/questions/29106",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/5392/"
] | I want to take FFT of my signal and reconstruct it back via IFFT. It seems the real part of odd numbered samples and image part of even numbered samples are multiplied by -1 which can be observed below:
For example if I have
<pre><code> [995] (-0.382624, 0.000000) std::complex<double>
[996]... | I am not fully sure about your code, but swapVectorWithIn() does shift your input vector by half of its lengths (or in Fourier terms: It shifts the spectrum so that the DC component is in the middle of the spectrum and not on the left side).
The output you show comes from doing an FFT, bringing the DC component to the... | Basic Fourier theory: you appear to have multiplied your signal with <code>+1 -1 +1 -1 +1 -1</code>. This is a very high frequency wave, at precisely the Nyquist frequency in fact.
The energy at the Nyquist Frequency is stored in your last FFT bin. And you wouldn't be the first programmer to have a one-off error, espe... | https://dsp.stackexchange.com |
142,278 | [
"https://security.stackexchange.com/questions/142278",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/128428/"
] | This is a problem that I have beaten my head over for quite some time.
I want to embed malicious code into a program , and when a victim opens it it will give me access to a meterpreter session on the device, for this i use an application named Shellter, which is a program used to embed metasploit payloads into appl... | <strong>Note: This is different for internal victims(On ur own LAN)</strong>
For external victims,
LHOST of the payload should be your public IP. Reason is that LHOST is embedded within the first stage payload. It must be able to connect back to the handler which means if the victim is outside the LAN, the payload sta... | The <code>LHOST</code> is simply the ip address that is reachable from your attacker. I'm going to assume that you are using a reverse shell payload or something that needs to connect back to you, otherwise the <code>LHOST</code> is not needed.
If you are on the same network, <code>10.0.2.15</code> should work. If tar... | https://security.stackexchange.com |
267,222 | [
"https://security.stackexchange.com/questions/267222",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/230952/"
] | FDE tools like VeraCrypt will encrypt the whole system <em>drive</em> when the machine uses legacy boot mode (MBR). But they will only encrypt the system <em>partition</em> if the machine uses EFI boot mode (the EFI partition remains unencrypted).
Most sources state that EFI boot mode (with secure boot enabled) is more... | Both MBR and GPT disks (generally used for BIOS/CSM and UEFI, respectively) require one partition that is not encrypted. The system-verification/key-unwrapping/decryption code has to live somewhere that isn't itself encrypted, after all! The distinction between creating a small (~100MB for Bitlocker; not sure about Ver... | If the attacker has full physical access and BIOS/EFI access they may as well install their own MOK certificate and modify your bootloader/install their own boot loader, so if you have reasons to believe it has happened, you need to reset secure boot certificate storage. So here's another caveat, EFI/BIOS password.
Mod... | https://security.stackexchange.com |
150,114 | [
"https://electronics.stackexchange.com/questions/150114",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/50319/"
] | i'm trying to use TMR0 on a PIC18F2420 to time the opening of a device and display the percentage it is opened. the issue i'm having is that it has frozen up pretty much all other operations. i'm not quite sure where i went wrong. if anyone could help i'd greatly appreciate it. i have my internal clock set for 4MHz and... | It's hard to follow what you think your code is supposed to do since it's pretty much devoid of comments. Besides, your code isn't working, so it's irrelevant anyway. Let's step back and think about how to best attack this problem.
You apparently want to track how much accumulated time some digital signal spends in ... | You probably have too much "stuff" happening inside your interrupt handler.
There is certainly some duplication, for example you have "TMR0IF=0;" both in your if/else as well as in your "Counter1" function which you call immediately after the if/else.
Depending on your compiler's optimisation abilities you might ... | https://electronics.stackexchange.com |
1,135,475 | [
"https://math.stackexchange.com/questions/1135475",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/165656/"
] | Here is the full question:
Let $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ and let $r = \|\vec{r}\|$. Let $\vec{F} = r^p\vec{r}$. Find all values of $p$ for which div $\vec{F} = 0$
I'm a bit confused on this as it seems that at any point in the vector field, $r^p$ cannot equal zero for any value of $p$ unless $r = 0$, then ... | Observe that in taking one of the partial derivatives we find that
\begin{eqnarray*}
\frac{\partial}{\partial x} x \left (x^2 + y^2 + z^2 \right )^{\frac{p}{2}} & = & \frac{p}{2} x \cdot (2x) \left (x^2 + y^2 + z^2 \right )^{\frac{p}{2}-1} + \left (x^2 + y^2 + z^2
\right )^{\frac{p}{2}} \\
& = & px^2... | Let's express the divergence in spherical coordinates. $F$ being independant from $\theta$ and $\phi$, the divergence has a very simple expression $$\nabla.F=\frac{1}{r^2}\frac{\partial{(r^2F_r)}}{\partial{r}}$$ which is $0$ when $$\frac{\partial{r^{p+3}}}{\partial{r}}=0$$ and this is identically zero iff $p=-3$
| https://math.stackexchange.com |
114,873 | [
"https://softwareengineering.stackexchange.com/questions/114873",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/14341/"
] | The dry principle states:
<blockquote>
"Every piece of knowledge must have a single, unambiguous,
authoritative representation within a system."
</blockquote>
However when writing tests for code you are describing the expected behavior for the system twice (once in the code and once in the test). I know both desc... | You are operating on a faulty premise.
The code is not a description of the expected behavior, only the requirements and test cases are. And even then, the requirements and tests define two sides of the behavior. The requirements define the characteristics and functionality of the software system as a whole and test d... | No, it doesn't violate the DRY principle because unit tests don't reproduce the functionality, they only make sure the functionality (re: responsibility) operates properly. In the case of a unit test, the method you're testing still maintains <code>authoritative representation</code>. Your test code may look very simil... | https://softwareengineering.stackexchange.com |
43,266 | [
"https://cs.stackexchange.com/questions/43266",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/34306/"
] | I have a problem that is a bit complex, and I don't know what method/model I should use to express it (much less solve it).
Let's say we have a lot of employees and a few jobs to be done. Each employee ranks the jobs they want most.
Easy. Bipartite matching, with weighted edges. Or Hungarian algorithm. Right?
Now th... | The problem is that the terms <em>RISC</em> and <em>CISC</em> are marketing terms, not science or engineering terms. The terms are supposedly acronyms for "Reduced Instruction Set Computing" and "Complex Instruction Set Computing." Your assumption that 3 addresses is much more complicated than 0 addresses is <em>logi... | To understand the technical aspects which survive (as @WanderingLogic said marketting aspect dominated quite quickly), of the RISC/CISC dichotomy you need to consider four points:
<ul>
<li>it is not really a dichotomy but more a continuum</li>
<li>history is important: RISC came as a reaction to tentative to close the... | https://cs.stackexchange.com |
69,073 | [
"https://quant.stackexchange.com/questions/69073",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/60319/"
] | I'm stuck at a problem and I'm not sure on how to proceed. My question is how would one go about and integrate the following
<span class="math-container">$$\sigma\int_{t}^{T}\mathrm{e}^{a\cdot u}\cdot (W_{u}-W_{t})du.$$</span>
I've been stuck with this problem for quite some time. Thanks in advanced!
| By the stationarity of the increments of Brownian motion, we have the following equality in law and an almost sure equality coming from a simple change of variable
<span class="math-container">$$\sigma \int_t^T e^{au} \left(W_u - W_t\right)du \overset{law}{=} \sigma \int_t^T e^{au}W_{u-t}dt = \sigma \int_0^{T-t} e^{a\l... | Once we get to the point of <span class="math-container">$$\int_0^{T-t} e^{au}W_udu$$</span> (thanks Shiva), we could conclude in the following way:
it is Gaussian since limit of Gaussians (the step-wise constant approximating functions are clearly Gaussians);
its mean is <span class="math-container">$$ \mathbb E \Big[... | https://quant.stackexchange.com |
3,604,170 | [
"https://math.stackexchange.com/questions/3604170",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/384082/"
] | Let <span class="math-container">$\{(x_1, x_2, \cdots) | x_i \in \mathbb{R}\}$</span> be a vector space over <span class="math-container">$\mathbb{R}$</span>.
Let <span class="math-container">$(0, 1, 2, \cdots), (1, 2, 3, \cdots), (2, 3, 4, \cdots), \cdots$</span> be elements of <span class="math-container">$\{(x_1,... | Consider the map
<span class="math-container">$$
\begin{gathered}
f:\left( { - 1,1} \right) \to R \hfill \\
x \to \tan \left( {\frac{\pi }
{2}x} \right) \hfill \\
\end{gathered}
$$</span>
| You can also use <span class="math-container">$\arctan:\Bbb R\to(-\pi/2,\pi/2)$</span>. It's a homeomorphism. And clearly <span class="math-container">$(-1,1)$</span> and <span class="math-container">$(-\pi/2,\pi/2)$</span> are homeomorphic.
| https://math.stackexchange.com |
685,218 | [
"https://math.stackexchange.com/questions/685218",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/124055/"
] | Let $G = \langle V,E\rangle$ be a tree. Prove that if $v \in V$ and $\deg(v) \ge 2$ if you remove $v$ the tree becomes unconnected.
It seems obvious but I can't state a formal prove.
| A <strong>tree</strong> is an undirected graph in which any two vertices are connected by exactly one simple path. Let $u\in V$ be a vertex of $G$. By definition of tree, there is unique between $u$ and $v$. So, if you remove $v$ from $G$, then there does not exist path between $u$ and $v$. Thus, $v$ and $u$ are in dif... | <em>Hint:</em> Trees are characterized by the fact that there is a unique path between any two vertices.
| https://math.stackexchange.com |
4,306,152 | [
"https://math.stackexchange.com/questions/4306152",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/791969/"
] | <blockquote>
Denote by <span class="math-container">$C^n([a,b])$</span> the <span class="math-container">$n$</span> times continuously diffrentiable functions on the interval <span class="math-container">$[a,b]$</span>. Prove that the norms <span class="math-container">$\|f\|=\operatorname{max}_{0\leq k\leq n}\operator... | Hint:
By Taylor's theorem,
<span class="math-container">\begin{align}
|f(x)|&=\left|\sum_{k=0}^{n-1}f^{(k)}(a)\frac{(x-a)^k}{k!}+f^{(n)}(\xi)\frac{(x-a)^n}{n!}\right|\\
&\leq \sum_{k=0}^{n-1}|f^{(k)}(a)|\frac{(b-a)^k}{k!}+\sup_{\xi \in [a,b]}|f^{(n)}(\xi)|\frac{(b-a)^n}{n!} \\
&\leq C_0\left(\sum_{k=0}^{n-1... | Suppose <span class="math-container">$X$</span> is a vector space with two norms <span class="math-container">$\|.\|_1$</span> and <span class="math-container">$\|.\|_2$</span> defined on it. Let <span class="math-container">$I:(X,\|.\|_1)\to(X,\|.\|_2)$</span> be the identity map as you defined, which is one-to-one an... | https://math.stackexchange.com |
308,096 | [
"https://dba.stackexchange.com/questions/308096",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/162483/"
] | I am exploring couple of solutions:
<ol>
<li>Log shipping - say a large query is running and meanwhile the log shipping process is triggered. Will this stop the query or delay the log shipping restore? Clearly this will have no impact on the primary db.
</li>
<li>AG - when a large query is running and meanwhile the mir... | There are several inefficiencies, and a few "errors". That is, I think the query would "run".
<ul>
<li>Filtering should go in a <code>WHERE</code> clause; <code>ON</code> controls how the tables are related.</li>
<li>Since it looks like you want to filter on <code>creditor_name</code>, use <code>JO... | <blockquote>
Can I use the operators(AND & OR) like this in a LEFT JOIN after ON?
</blockquote>
Yes, you can use <code>AND</code> and <code>OR</code> operators within your <code>JOIN</code> clause.
<blockquote>
Is this query correct and most efficient way of achieving this?
mysql.
</blockquote>
The below conditions... | https://dba.stackexchange.com |
104,465 | [
"https://mathoverflow.net/questions/104465",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7206/"
] | Suppose that $P$ is a forcing poset in $V$. If $\pi$ is an automorphism of $P$ then $\pi$ extends to automorphisms of the names by induction: $$\pi\dot x = \lbrace(\pi p,\pi\dot y)\mid (p,\dot y)\in\dot x\rbrace$$
I've been stuck on the following proposition for quite some time now and I don't see an argument for, nor... | It depends on the forcing notion, on the generic filter, on the
group of automorphisms and on the name $\dot x$.
First, there are some trivial cases where it is normal, such as
the case of a check name $\check x$, which is fixed by every
automorphism $\pi$, and so that subgroup is the whole group and hence normal. Sim... | I think Joel's example can be easily modified to use a hereditarily symmetric name. Use Cohen's original model for the negation of choice, i.e., use Cohen forcing to add an $\omega$-sequence of generic reals, and let the filter be the finite-support filter on the group $\mathcal G$ of permutations of the positions in ... | https://mathoverflow.net |
188,969 | [
"https://dba.stackexchange.com/questions/188969",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8344/"
] | I have a table in Postgres 9.6 db that is structured like this:
<pre><code>Table "public.pricings"
Column | Type | Modifiers
---------------------------+-----------------------------+-------------------------------------------------------
id... | You can simply check if the value is the default value, e.g.:
<pre><code>select *
from pricings
where unconfirmed_matrix_prices = '"{}"';
</code></pre>
Note that an empty jsonb value should be written down as '{}', so the default value <strong>is not</strong> an empty jsonb. This may be problematic with some kind of ... | This is a very bad idea.
<pre><code>not null default '"{}"'::jsonb
</code></pre>
That's not storing an empty object. That's storing a JSONB string literal of <code>"{}"</code>. You <em>never</em> want that. You normally want to confine it to a specific subtype instead, something like this..
<pre><code>not null defau... | https://dba.stackexchange.com |
4,593,093 | [
"https://math.stackexchange.com/questions/4593093",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/356910/"
] | I'm computing integrals <span class="math-container">$u_i$</span>, where
<span class="math-container">$$u_i = \int_a^b s^i G(s) ds$$</span>
and <span class="math-container">$a$</span> and <span class="math-container">$b$</span> are constants.
Now I want to estimate the error in <span class="math-container">$u_i$</span>... | Here I will consider evaluating the integral by discretizing at prescribed intervals according to the information provided in an edit, considering the values of <span class="math-container">$G$</span> as Gaussian random variables and computing the variance of the resulting sum as a function of the number of points in t... | Here is my derivation for the propagation-of-error method. Eqn (3) is the trapezoidal rule. There is no restriction on the spacing of <span class="math-container">$s$</span>.
<span class="math-container">$$\eqalignno{
\mu_i &\approx \sum_{j=1}^{n-1} {\textstyle{1\over 2}}( s^i_j G_j + s^i_{j+1} G_{j+1}) ( s_{j+1}- ... | https://math.stackexchange.com |
219,984 | [
"https://softwareengineering.stackexchange.com/questions/219984",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/40238/"
] | I am working on a web application implemented in C#, that follows MVC conventions.
This application contains a page that allows me to create or update a Wingding. The view passes a complete Wingding Model back to the controller for me to create or update.
The problem is that the page also has a checkbox that allows m... | Sounds like you're looking for a View Model.
The View Model is an object that encapsulates only the data that is required for the View to display. Example:
<pre><code>public class UserInformationViewModel
{
public string DisplayName { get; set; }
public string Address { get; set; }
public string City { g... | There're multiple solutions:
1.) IMHO the cleanest solution is to have that checkbox as a separate field and pass it to the controller, so it knows what to do.
2.) You can use a PresentationModel pattern to encapsulate everything the controller needs to know and pass that object.
Apart from that, I believe, the way ... | https://softwareengineering.stackexchange.com |
76,074 | [
"https://dsp.stackexchange.com/questions/76074",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/58138/"
] | I know this is probably a very trivial question, but I am completely stuck. Let <span class="math-container">$C$</span> be a linear <span class="math-container">$[n,k,d]$</span> Code. Then the interleaving of depth <span class="math-container">$t$</span> is the Code <span class="math-container">$C(t)=\{(c_{11}, \dots, ... | Consider the distance between the two interleaved codewords formed from codewords <span class="math-container">$\mathbf c_1, \mathbf c_2, \ldots, \mathbf c_t \in C$</span> and <span class="math-container">$\,\mathbf 0, \mathbf c_2, \ldots, \mathbf c_t \in C$</span> where <span class="math-container">$\mathbf c_1$</span... | You may have misunderstood "minimum distance". It's the smallest Hamming distance of all the <em>pairs</em> of codewords in the code. The Hamming distance is the same for any pair of codewords regardless of how you order the bits/symbols so the minimum distance of the code is unchanged.
| https://dsp.stackexchange.com |
278,982 | [
"https://softwareengineering.stackexchange.com/questions/278982",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/174457/"
] | I am starting to design a typical product based MySQL database but I keep running in circles on how to design the tables.
I have many types of products
<ul>
<li>Jeans</li>
<li>Tshirts</li>
<li>Dresses</li>
</ul>
Which have many of the same attributes
<ul>
<li>Size</li>
<li>Price</li>
<li>Colour</li>
</ul>
But som... | Do not make a table for every product.
This problem has been solved many ways. Try this:
Make a product (or products) table, put your common product attributes in the product table, then make an attribute table and a productattribute table, something like:
<pre><code>attribute
---------
attributeId
attributeName
at... | One approach would be to design your database similar to how you would define a class hierarchy, where you define base table(s) (classes) that provide the common attributes, and then you add additional tables that provide specific attributes to extend the table to the specific products.
Define a base product table
<p... | https://softwareengineering.stackexchange.com |
3,280,033 | [
"https://math.stackexchange.com/questions/3280033",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/506847/"
] | Let <span class="math-container">$G$</span> and <span class="math-container">$H$</span> be groups so that <span class="math-container">$|G|=21$</span>, <span class="math-container">$|H|=49$</span>. If <span class="math-container">$G$</span> has no normal subgroups of order 3, find all homomorphisms <span class="math-co... | The kernel of <span class="math-container">$f\colon G\to H$</span> must be normal and hence cannot be of order <span class="math-container">$3$</span>.
Nor can it be of order <span class="math-container">$7$</span> or <span class="math-container">$1$</span> because then the image would have an element of order <span cl... | Whenever you define a homomorphism <span class="math-container">$f \colon G \rightarrow H$</span>, you will get the normal subgroup <span class="math-container">$\text{ker}(f) \subset G$</span>. By Lagrange's theorem the order of a subgroup divides the order of group, such that the order of the kernel is either <span c... | https://math.stackexchange.com |
95,007 | [
"https://physics.stackexchange.com/questions/95007",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28118/"
] | Say you have a hollow sphere with a uniformly distributed charge on the surface. Why is the electric field everywhere inside the sphere zero?
For the centre, its easy to add the vectors from the surface charges and show they sum to zero because of symmetry.
But can you show me how the field cancels out to zero for p... | It is very simple, but strictly applies to a conducting sphere.
From ANY point inside a sphere, draw a double cone that is zero dimension at that point.
The cross-section of the cone, can be any shape.
The two ends of the cone intersect the sphere in two similar shaped curved surfaces. Any line from a point inside... | Because any Gauss surface made inside the hollow sphere encloses no charge so the net flux is zero. And if the Gaussian surface is shrunk to zero dimension, the electric field is zero at that point.
| https://physics.stackexchange.com |
216,253 | [
"https://math.stackexchange.com/questions/216253",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/34100/"
] | Let $S = \{ (a_1, a_2, a_3)\in \mathbb{R}^3 | \ a_1 + a_3^2\cdot\sin( a_1 +a_2) \geq a_3 \}$
then, how can I, show that S is closed under Euclidean Metric.
| A function $f\colon \mathbb{R}^3 \to \mathbb{R}$ is continuous
iff
the inverse image of every open set $U\subset \mathbb{R}$ is open in $\mathbb{R}^3$
iff
the inverse image of every closed set $A\subset \mathbb{R}$ is closed in $\mathbb{R}^3$.
Now relabeling $a_1,a_2$ and $a_3$ as $x,y,z$, moving $a_3$ to the L... | <strong>Hint:</strong>
I would suggest to rename the coordinates to say $a,b,c$, and then consider <em>convergent</em> <strong>sequences</strong> $(a_n,b_n,c_n)\in S$, and prove that the limit still satisfies the condition of $S$, by arguing with <em>continuity</em> ($\implies$ <em>sequential continuity</em>) of multip... | https://math.stackexchange.com |
581,898 | [
"https://physics.stackexchange.com/questions/581898",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/272059/"
] | When discussing systems which we want to be cold, but which <em>lose</em> cold by taking in heat from the ambient environment, what's the "I'm a smart physicist" way of saying "cold loss"?
If I were discussing loss of heat from a kiln or an oven to the ambient environment, I would say "thermal ... | Engineers would call it <em>heat leakage</em>. For refrigeration systems, the direction of the leak is into the system; for heating systems, the direction is out of the system.
| Joking aside, I think this is a reasonable question. You might be fridge designer who wants to describe the continuous power your fridge has to draw in order to maintain a low temperature. A perfectly sealed fridge, once cooled down, would require no power to remain cold. A real-world fridge has to keep switching on an... | https://physics.stackexchange.com |
591,444 | [
"https://stats.stackexchange.com/questions/591444",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/369589/"
] | I have the following model written. I have chosen for field as a random factor. I understood that an interaction between a fixed and random will be written as a fixed effect. As a result, I have the following model:
<pre><code>myGLMM4R <- glmmTMB(spp.richness ~ treatment + moment_datacollection + treatment * moment_... | I found the problem myself and is actually quite simple. Due to the fact that I have written the model the following
<pre><code>spp.richness ~ treatment + moment_datacollection + treatment*moment_datacollection +(1|field) + field*treatment + field*moment_datacollection
</code></pre>
Here I have written the interaction ... | With <code>field</code> being a factor, you consider a formula right-hand side of the form:
<pre><code>... + field + (1 | field) + ...
</code></pre>
That means you model the interaction of intercept and <code>field</code> as both a fixed and a random effect, which leads to redundancy. You could e.g. set the fixed effec... | https://stats.stackexchange.com |
371,381 | [
"https://physics.stackexchange.com/questions/371381",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99943/"
] | Does an object necessarily needs physical contact in order to move, because as far as I can guess.. energy doesn't have to be contained in matter in order to work, just like heat works in distance.
The kinetic energy is not the only force that can make the object move.
| Gravity and the electromagnetic field are good examples.
Earth orbits around the Sun without any physical contact, a bit of physical contact with the Sun could make a disaster ... .
Or in a magnetic field, any charged particle depending on its charge is pushed or pulled by the magnetic field.
Take two magnets and draw ... | Physical contact is mainly a <em>human illusion</em> anyway.
Suppose your hand pushes a pint of beer across a table. Both hand and glass are made up of atoms/ions/molecules, all of which are nuclei surrounded by electron clouds. These electrons in the glass and the hand repel each other. In reality hand and glass neve... | https://physics.stackexchange.com |
18,677 | [
"https://mathoverflow.net/questions/18677",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2260/"
] | Can anyone provide me with the reference for the following fact
(idea of the proof will be appreciated too):
Cohomology ring with $\mathbb Q$-coefficients of a group $G$ (I don't know precisely what the assumptions are: reductive complex algebraic group or maybe complex Lie group G with some restrictions. The cases I'... | If $G$ is a connected Lie group (or just a connected loop space with finite homology) then $H^*(G,\mathbf{Q})$ is a Hopf algebra. Graded connected Hopf algebras over $\mathbf{Q}$ are always tensor products of exterior algebras in odd degrees with polynomial algebras in even degrees. Since polynomial algebras are infini... | For $GL_n(\mathbf{C})$ and $SL_n(\mathbf{C})$ we can use the Leray spectral sequences of the mappings to $\mathbf{C}^n\setminus \{ 0\}$ that take a matrix to its last column. For other compact Lie groups (and $\mathbf{Q}$-coefficients) see e.g. A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces h... | https://mathoverflow.net |
129,891 | [
"https://security.stackexchange.com/questions/129891",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/117351/"
] | I'm looking at NAS (network attached storage) to use as one of several backup storage devices to store my data, since I cannot find a DAS (direct attached storage) with RAID functionality (all of the devices I've looked at seemed to be NAS). I'm worried mainly about the security of the NAS because it will contain sensi... | A NAS is not necessarily connected to the Internet, e.g. my NAS has a local 192.168 address which is not routed. In addition I have blocked that IP address from getting Internet access through the DSL router. The NAS itself is protected via username and password.
There are a few attack vectors, of course:
<ol>
<li>th... | It is generally assumed that your NAS is set for local access and not exposed to the external network via port forwarding or DMZ ... if this is not the case please update your question accordingly.
Given this assumption, the NAS can be considered as vulnerable as the rest of your internal network. If you download a v... | https://security.stackexchange.com |
59,248 | [
"https://physics.stackexchange.com/questions/59248",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15959/"
] | Cu has an unpaired electron in 4s, but it is diamagnetic. I thought that it has to be paramagnetic. What am I missing?
| You can't derive the existence or magnitude of diamagnetic properties just from unpaired electrons. On the contrary, diamagnetism mostly comes from the complete shells. They behave as electric current loops that orient themselves in a certain way in the external magnetic field.
Copper has lots of these complete shells... | What is missing here ist the relation to physical/chemical
status of that "copper".
What are You talking about? Copper metal? Copper
atoms as vapour? Copper ions I or II in aqueous
solution?
As a matter of fact, copper atoms are paramagnetic
(one unpaired electron is enough despite the number of
the paired ones!... | https://physics.stackexchange.com |
94,476 | [
"https://electronics.stackexchange.com/questions/94476",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9243/"
] | Is there a way to make a fan/cooler generate electricity by rotating its blades using the forces of nature?
I just tried rotating different coolers and fans I have at home with a 2 volt pocket flashlight lamp attached to the wires, but it wouldn't light up. Then I remembered that there are controllers installed to mak... | DC-powered fans often use a brushless permanent-magnet motor along with some control electronics. The motor itself could act as a generator, but the electronics generally won't allow any power the motor could generate to escape. Taking apart such a motor would likely allow one to make a generator, though I doubt it c... | I have had several turbines. The scientific problem is that wind energy rises on the CUBE of velocity. here is twice as much energy at 14 mph as at 12 mph. So any machinery has an immensely wide range of possible utilization. Also small turbines approach the speed of sound at the tip and get into trouble that way. L... | https://electronics.stackexchange.com |
76,166 | [
"https://electronics.stackexchange.com/questions/76166",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/26470/"
] | I'm new to software sound synthesis, but I have a question that I can't seem to find the answer to.
I understand that, for example, a square wave at 100 Hz has its third harmonic at 300 Hz with 1/3 the amplitude; its fifth harmonic at 500 Hz with 1/5 the amplitude; ad infinitum...
My question is, how many multiples d... | As usual, there are several issues:
<strong>What is the highest frequency required?</strong>
The hearing ability of a normal young human is 20 Hz to 20 KHz, although most people are in the 20 Hz to 15 KHz. If you add harmonics that are higher in frequency than 20 KHz, almost nobody will notice and almost no sound sy... | The mathematical answer would be infinite harmonics required.
The practical answer is: This depends on how much variation from the ideal waveform, the application can afford. The terminology used for instance in operational amplifier datasheets, Total Harmonic Distortion, illustrates this.
Real-world circuits do not ... | https://electronics.stackexchange.com |
157,296 | [
"https://stats.stackexchange.com/questions/157296",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/74780/"
] | Suppose I know that the true population proportion of a mutation is p = 0.3493119. I want to know that given power = 0.8, what's the proportion of of mutation in my sample of n = 30? Here's what I have so far:
1 - cdf((x-p)/sqrt(p*(1-p)/30) = 0.8
Since p = 0.3493119, I can solve for x and I get x = 0.276055. So does ... | I would say "Yes"power is alway associated with hypothesis testing it relates to sample size, type I error and both H1 and H0.
The followings are R code to show the power curve for OP's cases (one tailed at 0.05 level, by approximate a normal distribution.
<pre><code>mu<-30*0.35
sd<-sqrt(30*0.35*(1-0.35))
c&... | This is for binomail distribution not by approximation.
<pre><code>#under binomail distribution, one tail,
qbinom(0.05,30,0.35) #critical rigion
n<-seq(6,30,1) #numbers bigger than critical region
pow<-pbinom(n,30,0.35)#one tailed test
plot(n, pow, type="l")
</code></pre>
<img src="https://i.stack.imgur.com/ZZx... | https://stats.stackexchange.com |
6,287 | [
"https://math.stackexchange.com/questions/6287",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I'm trying to simplify the following booleans:
<pre><code>Y = ¬A¬B¬C¬D + ¬A¬B¬CD + ¬A¬BC¬D + ¬A¬BCD + A¬B¬C¬D + A¬BC¬D + ABC¬D
</code></pre>
The solution is:
<pre><code>Y = ¬A¬B + ¬B¬D + AC¬D
</code></pre>
My solution is:
<pre><code>Y = ¬A¬B (¬C¬D + ¬CD + C¬D + CD) + A¬B¬C¬D + A¬BC¬D + ABC¬D
= ¬A¬B (¬C (¬D + D) ... | All your work is right. The first two terms of your answer simplify to:
<pre>
Y = ¬A¬B + A¬B¬D
= ¬B(¬A + A¬D)
= ¬B(¬AD + ¬A¬D + A¬D) // split the first term
= ¬B(¬AD + ¬A¬D + ¬A¬D + A¬D) // idempotence
= ¬B(¬A + ¬D) // combine the first two and last two terms
= ¬A¬B + ¬B¬D.
</pre>
I wouldn't have believed ... | I agree with you. The last three terms all have A required, so anything that comes out of them (your last two terms) need an A. Are you sure the given solution is right?
| https://math.stackexchange.com |
451,007 | [
"https://physics.stackexchange.com/questions/451007",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/204351/"
] | In quantum mechanics the raising operator of a system with quantum number <span class="math-container">$s$</span> and <span class="math-container">$m$</span> is such that <span class="math-container">$$\hat{S}^+|s,m\rangle = \hbar \sqrt{s(s+1)-m(m+1)}|s,m+1\rangle$$</span>
Since there must exists a <span class="math-c... | It does. All you need to do is to transform
<span class="math-container">$$
\sqrt{1+4s(s+1)}
=
\sqrt{4s^2+4s+1}
=
\sqrt{(2s+1)^2}
=
2s+1
$$</span>
(since <span class="math-container">$s\geq0$</span>) and work out the rest of the algebra.
| <span class="math-container">$1 + 4 s (s + 1) = 4 s^2 + 4s + 1 = (2s + 1)^2$</span>, so as @knzhou pointed out this indeed gives the same solutions.
| https://physics.stackexchange.com |
128,679 | [
"https://security.stackexchange.com/questions/128679",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/116113/"
] | Modern fraudsters commit identity theft by impersonation in social media, since a lot of personal information such as our names, location, contact info and other personal details are available for skilled fraudsters to commit identity theft. What can be done at a corporate level to limit corporate identity theft?
| This is a vary difficult problem from the corporate perspective. I'm assuming
from your question, you are more interested in what the business can do rather
than on what the individual can do.
I think there are two main areas that business should focus on in order to
reduce the risk of their data being compromised an... | Like you said:
<blockquote>
since a lot of personal information such as our names, location, contact info and other personal details are available for skilled fraudsters to commit identity theft.
</blockquote>
This is a problem that is hard to avoid which is why the following steps can you help you try and stay sa... | https://security.stackexchange.com |
10,647 | [
"https://physics.stackexchange.com/questions/10647",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3714/"
] | What is the dominant cause for ocean waves at a beach? Are they the result of wind/pressure difference? If so, the waves do seem to exist in similar intensity even during relative quiet times of the day.
Is there a simple mathematical model that we can quickly explain the intensity/frequency of waves with? Does the s... | Yes, primarily wind. It's called the Kelvin-Helmholtz instability. Strong winds in an area will excite a range of wavelengths, the longer wavelengths will go faster according to the deep water dispersion relation ( speed proportional to square root of wavelength). So if you see a train of waves with decreasing wavel... | The normal dominant cause of most waves you see (i.e., not a Tsunami) is frictional force between the wind and water over very large distances.
Even though the wind may not be blowing at your particular beach, it is ALWAYS blowing somewhere out in the ocean. The waves produced by this effect can (and do) travel thous... | https://physics.stackexchange.com |
549,748 | [
"https://physics.stackexchange.com/questions/549748",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/195556/"
] | In short: Does anybody know if there exists a compendium, a document, a book or a stone tablet listing the independent elements of the elastic stiffness and compliance tensors ( that is, naming the elements, e.g., <span class="math-container">$C_{1111},C_{2222},\ldots$</span> that are independent and giving the values ... | I believe the author is saying that if two objects exhibit different accelerations when subjected to the same force, there must be some property that is determining how much that object should accelerate.
As it turns out, as the force is increased, ("no matter how we produce acceleration"), the same accelerations incr... | If you have a standard for measuring force (such as a spring scale), then the force from any source (gravity, electrostatics, magnetism,etc.) can be calibrated in terms of that standard. (Hence the constants in force equations.) So a given force, from any source, acting on a given mass, will produce the same accelera... | https://physics.stackexchange.com |
49,510 | [
"https://electronics.stackexchange.com/questions/49510",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8769/"
] | the input voltage is from mp3 player.
Now, why is that when the input voltage is around 5 mv pk, there are no clipping issues but if we change the input voltage to around 400 mv pk(which is common in every mp3 player including mobile phones), there is severe clipping as described below in the picture.
<img src="http... | The R1-R2 voltage divider biases the base of Q1 at about 1.17 V.
A 0.4 V excursion below that puts it at 0.77V, which would normally keep it in forward active mode. But the 100 uF capacitor is preventing the emitter voltage from changing, keeping that node at about 0.4 V. That means you only have 0.3 V across Q1's b-... | The amplifier is going into cutoff <s>saturation</s> with the higher input signal. Also, the input biasing is off by a bit so the clipping is asymmetrical.
Actions:
<ul>
<li>Reduce the gain of the amplifier to keep the output within the linear part of its curve.</li>
<li>Change the DC biasing of the input signal to ... | https://electronics.stackexchange.com |
722,218 | [
"https://physics.stackexchange.com/questions/722218",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/333740/"
] | I was recently reading an example which showed that the average rate of energy dissipation due to resistance of the wires that are used in the transmission of electricity from a generator is not equal to the average rate at which the energy is supplied. But this would imply that current doesn't depend on the resistance... | The energy that is supplied by the generator goes to energy dissipated by the transmission wires but also (usually mostly) by the load at the other end of the transmission lines. Does that explain why it's not all consumed by the transmission lines?
| The current in the wires is partially dependent on the resistance. Typically a transmission line has a transformer at the generator and one at the consumer end. The consume applies a load <span class="math-container">$R_{L}$</span> to the secondary of the transformer. On the transmission line side of the transformer, <... | https://physics.stackexchange.com |
159,267 | [
"https://softwareengineering.stackexchange.com/questions/159267",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19033/"
] | I'm asked to perform or sit in during many technical interviews. We ask logic questions and simple programming problems that the interviewee is expected to be able to solve on paper. (I would rather they have access to a keyboard, but that is a problem for another time.) Sometimes I sense that people do know how to app... | When I was in a similar position, I would say to the interviewee: "Pretend I'm Google. If you need to search for something just say so."
In one question interviewees needed to be able to figure out the volume of a cylinder, so I didn't mind if someone said, "I'd have to Google for the formula for the volume of a cylin... | You have two approaches which work both for problem solving and short technical questions:
<ol>
<li>The first one is used by your boss: don't provide any help in order to test how the person behave in a stressful context. It is a perfectly valid approach, and may give some hints about the person. After all, once you h... | https://softwareengineering.stackexchange.com |
182,499 | [
"https://physics.stackexchange.com/questions/182499",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/77635/"
] | A balloon is rising. A stone is dropped and the stone takes $\frac{2u}{g}$ to reach ground (Nothing is known about $u$ and $g$ is the acceleration due to gravity), irrespective if the point of dropping. Find the acceleration of the balloon as a function of time. How to do this question? I came across it somewhere on th... | Starting out with the general $$z := h + v~t - \frac {g}{2}~t^2,$$
where
<ul>
<li>$t \ge 0$ is the duration since the stone had been released,</li>
<li>$z[~t~]$ is the remaining "height above ground" of the stone,</li>
<li>$h$ is the "heigt above ground" of ballon and stone at the release, and</li>
<li>$v$ is the v... | The key is this formula is not some universal truth, but information about u(t).
In the formula for the position of the stone, three constants appear: h0, v0 and g. As 2u/g should result in a time, u should be a speed: v0.
Eventually this should lead to a formula containing h(t) and u(t) of the ballon.
| https://physics.stackexchange.com |
1,962,930 | [
"https://math.stackexchange.com/questions/1962930",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Suppose G is a group and n is a natural number. Show the union of subgroups
of G of order n is not necessarily a normal subgroup of G.
I'm guessing I use proof by contradiction, but I have no idea where to begin. Do I use the trivial subgroup?
| It may we be that union is not even a subgroup. For example, the union of all the subgroups of order two in $\;S_3\;$ :
$$\left\{\;(1),\,(12),\,(13),\,(23)\;\right\}\rlap{\;\,/}< S_3$$
| <strong>Hint:</strong> Consider $G=S_3$ and $n=2$. - Or even more trival: Consider any finite $G$ and $n$ not a divisor of $|G|$
| https://math.stackexchange.com |
5,331 | [
"https://scicomp.stackexchange.com/questions/5331",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/447/"
] | I writing some robust geometric algorithms using quantization + integer arithmetic for evaluating exact predicates. However, since BlueGene's integer support is so terrible, it occurred to me that the use of integer math may (weirdly) kill the portability of the library in terms of performance.
How worried should I b... | Different vendors have different paths forward on this, and most of it is under NDA. If you really want to know, ask Intel, AMD, IBM, ARM, and maybe NVIDIA for briefings under NDA. Some of these vendors will have full support for vectorized integer instructions in the future so that integer will keep up with floating-p... | To answer your first question: I wouldn't worry about floating-point being faster than integers. If floating point operations <em>are</em> faster than regular integer operations, I don't see why you shouldn't use them. If you stay within 23 bits, all single-precision floating-point operations on integer values should b... | https://scicomp.stackexchange.com |
262,354 | [
"https://physics.stackexchange.com/questions/262354",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/115213/"
] | I'm currently trying to understand why superluminal information transport is not possible.
Therefore, I would like to get some help concerning the definition of information or the general setting.
Imagine a system in the state $|\psi +>=1/\sqrt{2}(|01>-|10>)$ (with particles A & B). Now the two particles... | Your question 1 has absolutely nothing to do with entanglement, and for that matter absolutely nothing to do with quantum mechanics. You can formulate exactly the same question this way:
You and I each have in our pockets a tennis ball that is either red or green. We somehow each know for certain that they are of th... | What kind of information are we talking about in superluminal information transport? It might be more intuitive to call it superluminal <em>communication</em>.
For the prohibited kind of superluminal information transport, you need to be able to achieve the following.
At the start of the protocol, A holds a classical... | https://physics.stackexchange.com |
60,335 | [
"https://electronics.stackexchange.com/questions/60335",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2005/"
] | It has been claimed on another board that some SMT components cannot be used in an automated production line (i.e. reflow or wave soldering) because they cannot withstand the heat/temperature. Hand soldering is used to avoid these problems.
An example given where this was the case was film capacitors. Capacitors are o... | I have never encountered a SMD part that needed to be hand soldered.
Probably what someone ran into is a part that needed a special profile such that the board would have had to be run thru the oven twice. If this is due to a single part, it could well have been more cost effective to run the board thru the normal pr... | I can think of a few realistic situations that could have been distorted just slightly to get someone thinking there's SMT parts that can't take automated soldering:
<ul>
<li>An old part (SMT or through-hole) designed for tin-lead solder process might not be able to take the heat of a lead-free solder process.</li>
<l... | https://electronics.stackexchange.com |
11,352 | [
"https://robotics.stackexchange.com/questions/11352",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/15496/"
] | I'm designing a joint which will have to move with a velocity of ~60RPM and I have to come up with resolution requirement for the encoders within this joint. I notice however that this is easier said than done.
A 1m beam will be connected to the joint, I figured I would need to know the position of the tip of the beam... | First I would question your math that got you to the 12b sensor.
If you have a $dy$ of 1 mm over an arm that is $r = 1$ m long, then $\sin(\theta) = dy/r \rightarrow \theta = \mbox{asin}(dy/r)$. If you make the small angle approximation $\sin{\theta} \approx \theta$, then $\theta \approx dy/r$.
This is $\theta$ in r... | For rotary encoders, position is calculated by dividing the number of edges counted by the product of the number of pulses per revolution and the encoding type described above (1, 2, or 4), and then multiplying the result by 360 in order to get degrees of motion.
| https://robotics.stackexchange.com |
507,839 | [
"https://physics.stackexchange.com/questions/507839",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/227820/"
] | If we keep a heavy metallic ball on a thin sheet of paper the paper is torn and the ball drops. But according to Newton's third law of motion every action has an EQUAL and opposite reaction. So when the ball applies force on the paper the paper should apply equal amount of force on the ball and the ball should be stabl... | You have to look at the <strong>net forces</strong> on the ball and the paper individually, and not just the action-reaction pair.
Gravity exerts a downward force of <span class="math-container">$mg$</span> on the ball and the paper momentarily exerts an equal and opposite force of <span class="math-container">$mg$</s... | Downward gravitational force applied on the sheet.Reaction force on the Ball in upward direction.But thin sheet can not sustain such heavy force and breakdown and losses its continuity and comedown by gravity .At that instant Metallic ball only experiences downward gravitational force so it's fall down.
| https://physics.stackexchange.com |
112,564 | [
"https://dba.stackexchange.com/questions/112564",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/73852/"
] | I have a problem when I want to initialize a folder as a data folder:
<pre><code>postgres@ccruzado-test01:~$ /usr/lib/postgresql/9.3/bin/initdb -D /datadrive/postgresql/
The files belonging to this database system will be owned by user "postgres".
This user must also own the server process.
The database cluster will ... | Creating the data directory on Linux includes creating hard links, which is not supported on CIFS shares. This is why the creation is failing.
It's usually not a good idea to create data stores / clusters on remote shares, it might lead to issues if the share disappears in the middle of using it.
| You can follow these steps:
<ol>
<li>Check the <em>uid</em> and <em>gid</em> of the <em>postgres</em> user
<pre class="lang-none prettyprint-override"><code>bash-4.2$ id postgres
uid=1001(postgres) gid=1001(postgres) groups=1001(postgres)
</code></pre></li>
<li><em>dir_mode</em> and <em>file_mode</em> should be 0... | https://dba.stackexchange.com |
166,169 | [
"https://mathoverflow.net/questions/166169",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41654/"
] | Can there exist a right invariant killing field of a right invariant (but not bi-invariant) Riemannian metric on a Lie group?
I am especially interested in the case of $SU(N)$ with a metric of the form (at the identity):
$g(x,y) = \frac{1}{\lambda} B(x,y) + \frac{1}{\lambda^2} B(x,w)B(y,w)$ where $w$ is an arbitrary... | A right invariant Riemannian metric is invariant und all right translations. A left invariant vector field has a flow consisting of right translations (by $\exp(tX)$).
Thus each left invariant field is a Killing field. A right invariant field $R_X$ is Killing if and only if $S^2(\text{ad}_X)^*g_{e}=0$.
| There is an obvious right-invariant vector field which leaves that metric invariant: the one which extends $w$. As Peter Michor mentions in his answer, the condition for a right-invariant vector field to be Killing is that it should preserve the inner product at the identity. In your example, and letting $b = \lambda... | https://mathoverflow.net |
1,632,906 | [
"https://math.stackexchange.com/questions/1632906",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/309256/"
] | Combinatorics. Find the number of three digit numbers from 100 to 999 inclusive which have any digit that is the average of other two?
i tried to do it by making different cases but the answer did not match.
the answer is 121
| First of all, if the digits are the same, there are $9$ (those are $111,222,\cdots,999$). If the digits are different, then we can do the following.
Pick any number $a$ between $1$ and $9$ (exactly $9$ possibilities for this). The other number $b$, that is, the one you want to take the average with, must be the same $... | Let the three digits by $a, b, c$ (not necessarily in order) and let $a \le b \le c$. As one is the average of the other two, $b = c - k = a + k$ (which also means $c = a + 2k$).
$k$ can go from $0$ to $4$.
If $k = 0$, $a = b = c$ and there are 9 such options.
Otherwise there are $a$ can span from $0$ to $9 - 2k$ s... | https://math.stackexchange.com |
80,331 | [
"https://chemistry.stackexchange.com/questions/80331",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/49984/"
] | <blockquote>
Methanoic acid (<span class="math-container">$\ce{HCOOH}$</span>) is found in stinging nettles. In an analysis of the concentration of methanoic acid in a solution extracted from nettles, the solution was titrated with a standard solution of potassium hydroxide. Aliquots of the methanoic acid were transfer... | Option A implies that the rinse residual would dilute the methanoic acid that would be added to the flask after rinsing and thus your titration would indicate that the acid is a LOWER concentration than the calculated value.
You are correct in your assessment of Option B.
| <strong>A</strong> Excess water in the conical flask will have no influence whatsoever* (in first order approximation). Since you are determining the the amount of substance of methanoic acid with the titration, the volume is irrelevant. The volume you use to determine the concentration is from when you take the aliquo... | https://chemistry.stackexchange.com |
207,682 | [
"https://softwareengineering.stackexchange.com/questions/207682",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/99090/"
] | I'm developing desktop application in java/swing.
I have a component that is registered as a subscriber to many panels and gets messages (my custom event) from them. That component is something like message tray. When there is a validation error or some kind of info message it's delivered from panel to that tray by my... | There are two possibilities:
<ol>
<li>Pass the "message tray" to whatever component needs it</li>
<li>Make each component that can have controls implement the "tray" interface. That way, the holder of the internal panels is also a tray and it can dispatch the messages to it's parent tray (if any).</li>
</ol>
I like m... | Your design doesn't really violate the Observer pattern, because the pattern does not specify how subscribers get registered with the publisher. But you are violating the Single Responsibility Principle for those middle panels, because they are given the added responsibility of helping in getting the message tray subsc... | https://softwareengineering.stackexchange.com |
38,415 | [
"https://softwareengineering.stackexchange.com/questions/38415",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8622/"
] | I'm not talking about fixed price jobs, they're <em>fairly</em> straightforward. But I'm on about an hourly rate project, my question specifically relates to what to charge for.
If I have an IE/CSS issue that takes me an hour of scouring CSS to fix, is that chargeable? If I decide to use a really cool jQuery animation... | As a web developer myself who has done pricing mechanisms like this, I usually charge a little less as a general rule to keep customers happy and coming back as well as spreading the word about me. You really shouldn't think about charging for as much as you can until you have more customers than you can handle.
Havin... | Strangely enough I think it depends on how much you are charging per hour. If you ask for $120/hr I would expect that everything you do creates an immediate and beneficial result; if you are charging $50/hr that means there is a chance they will have to pay for trial/error and learning. In the end it is up to your own ... | https://softwareengineering.stackexchange.com |
11,755 | [
"https://electronics.stackexchange.com/questions/11755",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/771/"
] | Are there common sources of 434MHz noise or interference in a residential/household environment? I've been playing with some radios, and they seem to be behaving flakily at my friend's house even at close range, and working flawlessly at my house... I'm a bit stumped.
I suppose another possibility is some kind of cra... | There can be a lot of devices operating in the 433 MHz band. Many cheap radio devices (like wireless thermometers and stuff) operate on 433 MHz.
The house construction could have something to do with this as well. Did you try testing it outside (with a line-of-sight) near his house?
| PC video cards can generate a lot of hash in the 70cm band. I've found that to be a problem in my home if the wife is playing video games.
| https://electronics.stackexchange.com |
302,565 | [
"https://softwareengineering.stackexchange.com/questions/302565",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/204056/"
] | The book I am reading on Java states something confusing and unacceptable.
<blockquote>
<h1>Learning About Ambiguity</h1>
When you overload methods, you risk creating an <strong>ambiguous</strong> situation - one which the compiler cannot determine which method to use. For example, consider the following overlo... | I agree with your assessment that this is poor, wrong and/or misleading text.
As you have pointed out, the compiler will complain based on these declarations alone: no call to <code>computeBalance</code> is required. These declarations taken together are in error, there is no (legal) overloading going on here.
The i... | Obviously two methods in example are ambiguous and that code cannot be compiled because both methods have same name and same parameters.
<pre><code>public static void computeBalance(double deposit)
public static void computeBalance(double withdrawal)
</code></pre>
Author does not claim that you can compile and use ab... | https://softwareengineering.stackexchange.com |
101,400 | [
"https://mathoverflow.net/questions/101400",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22051/"
] | Suppose $A$ is a $n \times m$ matrix and $B$ is a $m \times n$ matrix. Then it is known that $det(I_{n}+AB)=det(I_{m}+BA)$.
Is there an analogous identity of the form $det(P_{1}+AB)=det(P_{2}+BA)$, where $P_{1},P_{2}$ are positive definite? Or something like it?
| Given $P$, $\det(P+AB)$ does not depend only on $BA$. For example, take $n=m=2$,
$P = \pmatrix{2 & 0\cr 0 & 1\cr}$, $A = \pmatrix{1 & t\cr 0 & 1\cr}$, $B = \pmatrix{0 & 1\cr
1 & -t\cr}$. Then $\det(P + AB) = 1 - t$ depends on $t$, but $BA = \pmatrix{0 & 1\cr 1 & 0\cr}$ doesn't depend o... | Is this what you are looking for?
$$ \det(P+AB)=\det(P)\det(I+P^{-1}AB)=\det P \det(I+BP^{-1}A)$$
Edit: the chain of equalities once ended with $=\det(P+PBP^{-1}A)$, but this only works when all matrices are square.
| https://mathoverflow.net |
403,870 | [
"https://physics.stackexchange.com/questions/403870",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/194517/"
] | I know that to have a current in a circuit we need a potential difference that creates a gradient that makes electrons move from low potential to high potential. My question is that how, in a circuit, potential difference makes the charges move so perfect ( along the wire because that would need a constantly changing f... | <strong>Acceleration</strong> is the general term for a changing velocity. <strong>Deceleration</strong> is a kind of acceleration in which the magnitude of the velocity is decreasing. The reason this might be confusing is because the word 'acceleration' is sometimes used to mean that the magnitude of the velocity is <... | Acceleration is the correct technical term for the physical quantity you mentioned in the equations you posted (i.e. <strong>a</strong>).
The term <em>deceleration</em> doesn't describe a <em>rigorously-defined standard physical quantity</em>, it's just a term used differently in different situations that means "handw... | https://physics.stackexchange.com |
157,565 | [
"https://electronics.stackexchange.com/questions/157565",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43662/"
] | <strong>My Task</strong>
I'm working on an extra work question our teacher assigned us from the book. Design a combinatorial circuit that compares two 4-bit unsigned numbers A and B to see whether B is greater than A. The circuit has one output X, so that X = 1 if A < B and X = 0 if A = B or A > B.
<strong>My Idea... | In your hypothetical example of trying to detect a 3VDC signal against a background of 250kVDC noise (say between the phase 1 and phase 2 power lines), imagine the signal is being measured by a well-insulated lineman who can put his DMM's positive lead on the "phase 1" 250.003kVDC wire, and the negative lead on the "ph... | EEG is low freq compared to EMG. You can isolate EEG with a high CMRR amp with a small enough gain to not saturate given EMG and other noise, then low pass filter and then amplify more.
This is not perfect, and I suspect a good deal of EEG studies may show EMG contamination, particularly early brain-machine interfac... | https://electronics.stackexchange.com |
63,403 | [
"https://cs.stackexchange.com/questions/63403",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7814/"
] | It's fairly simple to understand why the halting problem is undecidable for impure programs (i.e., ones that have I/O and/or states dependent on the machine-global state); but intuitively, it seems that a pure program's halting on an ideal computer would be decidable through e.g. static analysis.
Is this in fact the c... | Here is a proof of undecidability by reduction from the Halting problem.
<strong>Reduction:</strong> Given a machine $M$ and an input $x$, build a new Turing Machine $H$ which does not read any input, but writes $M$ and $x$ on the tape and simulates $M$ on $x$ until $M$ halts.
The behaviour of this new machine $H$ is... | No it is not, and moreover it does not depend on I/O.
Simple counterexample: write a program to find a perfect odd number (this is an open problem: we do not know yet whether one exists) - it does not take any input and does not perform any <em>impure</em> tasks; it may halt when it finds one, or may work infinitely (... | https://cs.stackexchange.com |
190,850 | [
"https://softwareengineering.stackexchange.com/questions/190850",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31875/"
] | Let's say I have an object like this:
<pre><code>function Foo() {
this.parser = new DataParser();
};
</code></pre>
Within Foo I have a method that does something like this:
<pre><code>Foo.prototype.getResponse = function(message, callback) {
var payload = {data: message, type: 'normal'};
var response = this.pa... | I would recommend to pass the type argument 'optionally' so you'd get a function like:
<pre><code>Foo.prototype.getSimilarResponse = function(message, type, callback) {
if (typeof(type) === 'function') {
callback = type;
type = 'normal';
}
var payload = {data: message, type: type};
var response = this... | See also:
<strong>The Options Argument</strong>
This is very popular in the jQuery community. It's handy when you have a lot of potential for variation that might result in a ton of args which happens all the time in UI functionality.
I'm also fond of it for regular higher-level app architecture constructors. The ea... | https://softwareengineering.stackexchange.com |
440,277 | [
"https://physics.stackexchange.com/questions/440277",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/190690/"
] | Molar heat capcity for any solid is 3R which is approximately 24J/kg-K.<br>
But specific heat of aluminium is 900J/kg-K.<br>
If the molar heat capacity is M times more than specific heat capacity (M=molar weight) the values become incorrect.<br>
Where am I going wrong?
| You are going wrong in the <strong>Units</strong>.
The Molar Heat Capacity of any solid is approximately 24<strong>J/K-mol</strong>.
Molar mass of Aluminium is around 27 grams. i.e 0.027 Kg.
Specific heat capacity of Aluminium hence is (Approximately), 24J/K-(0.027)Kg.
Which comes out to be 889J/K-Kg. Which is good ... | It depends on how you measure it. Either type of heat capacity is just how much energy it takes to raise some given amount of a substance by a given unit of temperature. The exact amount is directly proportional to amount of substance that your units consider. Specific heat capacity is measured per unit mass, while mol... | https://physics.stackexchange.com |
377,813 | [
"https://physics.stackexchange.com/questions/377813",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/175114/"
] | This is a homework problem I had that I couldn't quite figure out the reasoning behind.
A force is applied to the rim of a disk that can rotate like
a merry-go-round, so as to change its angular velocity. Its initial
and final angular velocities, respectively, for four situations are:
(a) -2 rad/s, 5 rad/s ($\Delta\... | The work done is the same in all 4 cases. The easy way of seeing this is to use the Work-Energy Theorem : work done equals change in energy. Here there is only kinetic energy, and since this depends on $\omega^2$ the minus signs make no difference, hence the change in KE is the same in each case.
However, in some cas... | There is an accelerations since the velocity changes...
But, remember that energy goes like the <em>square</em> of the velocity!
So $\Delta \omega$ in this case is not pretty useful, rather it is the square of the velocities. The energy is $\propto I\omega^2$. Since the work is the difference of energy you get it equ... | https://physics.stackexchange.com |
3,980,281 | [
"https://math.stackexchange.com/questions/3980281",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/813532/"
] | suppose I have a symmetric matrix <span class="math-container">$S$</span> with diagonal entries <span class="math-container">$s_{jj}$</span>. I'm trying to prove that none of these diagonal entries <span class="math-container">$s_{jj}$</span> can be be smaller than all the eigenvalues of <span class="math-container">$S... | Let <span class="math-container">$ a,x\in\left(1,+\infty\right) $</span>, we have the following : <span class="math-container">$$ x^{a}\int_{0}^{1}{y^{a-1}\left(1-y\right)^{x-1}\,\mathrm{d}y}=\int_{0}^{x}{y^{a-1}\left(1-\frac{y}{x}\right)^{x-1}\,\mathrm{d}y}=\int_{0}^{+\infty}{y^{a-1}f_{x}\left(y\right)\mathrm{d}y} $$<... | I just solved it and for anyone interested the answer <br />
<span class="math-container">$ \frac{\Gamma(x+a)}{x^a\Gamma(x)}=\frac{\sqrt{2\pi(x+a)}(\frac{x+a}{e})^{x+a}}{\sqrt{2\pi(x)}(\frac{x}{e})^{x}}=
\frac{\sqrt{2\pi }\sqrt{x+ a}(x+a)^{x+a}e^x}{\sqrt{2\pi }\sqrt{x }(x)^{x}e^{x+a}}=
(\frac{x+a}{x})^{\frac{1}{2}ax}\... | https://math.stackexchange.com |
3,913,741 | [
"https://math.stackexchange.com/questions/3913741",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/851159/"
] | This equation derives from physics force equations, and I have verified to make sure that the equation works. No actual physics pertains to this question. The part I need help on only requires math skills. Here is the equation:
<span class="math-container">$$\sin(\theta) - k\cos(\theta) = \frac{m_1}{m_2}$$</span>
where... | You might want to post the physics question which led you to this equation. It is likely there was a mistake in the derivation. Nonetheless,
<span class="math-container">$$\sin \theta - k \cos \theta = m_1/m_2 = \gamma$$</span>
<span class="math-container">$$\sin \theta - k\sqrt{1-\sin^2 \theta} = \gamma$$</span>
<span... | Let <span class="math-container">$sin{\theta} = x$</span>.
Then your equation becomes
<span class="math-container">$$x-k\sqrt{1-x^{2}} = \frac{m1}{m2}$$</span>
Separate the linear terms and square both sides.
<span class="math-container">$$(x-\frac{m1}{m2})^{2} = k^{2}(1-x^{2})$$</span>
It is now a simple quadratic equ... | https://math.stackexchange.com |
277,929 | [
"https://physics.stackexchange.com/questions/277929",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/129085/"
] | I have this simple yet intriguing question that struck me through an introductory Electromagnetism. Being familiar with Gauss' Law and Coulomb's Law, the "Charged Spherical Shell" excercise is something very common to me. A particular thing for this exercise is that if you use any method (at least as far as I know), be... | You are correct that the electric field is only zero at the exact center of the ring. Gauss's law and Coulomb's law always both give the same results in every situation, so if you're getting that they disagree, then you made a mistake. You almost certainly messed up in the Gauss's law calculation, because I can't thi... | For any point inside a uniformly charged sphere, the sum over all the
sphere's surface results in a zero electric field. This is because
one can make a symmetry argument, that each force from one tiny bit of the
charged area of the sphere is balanced by a projection of that area through
the point of interest, onto an... | https://physics.stackexchange.com |
3,443,181 | [
"https://math.stackexchange.com/questions/3443181",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/709919/"
] | Path: <span class="math-container">$y=x^2$</span>, from (<span class="math-container">$-\pi$</span>, <span class="math-container">$\pi^2$</span>) to (<span class="math-container">$\pi$</span>,<span class="math-container">$\pi^2$</span>)
Field: <span class="math-container">$F(x,y) = e^y\sin(x)$</span> <strong>i</strong... | I got
<span class="math-container">$$\int_{-\pi}^\pi(e^{t^2}\sin t-2te^{t^2}\cos t+2t\sqrt{1+t^2})\,dt.$$</span>
I then thought about the derivative of <span class="math-container">$e^{t^2}\cos t$</span>.
| This can actually be solved rather nicely using Green's Theorem in the plane by connecting your parameterized arc to the arc <span class="math-container">$r(t) = (-t,\pi^2)$</span> as <span class="math-container">$t$</span> ranges from <span class="math-container">$-\pi$</span> to <span class="math-container">$\pi$</sp... | https://math.stackexchange.com |
387,838 | [
"https://stats.stackexchange.com/questions/387838",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/214572/"
] | Can anyone show the mathematical steps proving
<span class="math-container">$K_{box}*K_{box} = K_{triangle}$</span>
| Consider the simple case where <span class="math-container">$K_\text{box}(x) = \mathbb{I}(0 \leqslant x \leqslant 1)$</span>. Then you have:
<span class="math-container">$$\begin{equation} \begin{aligned}
(K_\text{box}*K_\text{box})(r)
&= \int \limits_\mathbb{R} K_\text{box}(x) K_\text{box}(r-x) dx \\[6pt]
&... | I think a 1D solution would suffice to give you an idea. Let <span class="math-container">$x(t)=1$</span> when <span class="math-container">$0<x<1$</span>. Convolution with itself can be formulated as
<span class="math-container">$$y(t)=x(t)*x(t)=\int_{-\infty}^{\infty}x(\tau )x(t-\tau )d\tau =\int_{0}^{1}x(t-\... | https://stats.stackexchange.com |
3,424,618 | [
"https://math.stackexchange.com/questions/3424618",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/722602/"
] | So this is the exercise:
<blockquote>
Let A be a set of numbers consisting of 8 digits: five digits 1 and
three digits 2. For instance 11221211 is in A.
How many number in A are odd?
How many number in A are odd or start with the digit 1 (or both)?
</blockquote>
Now here's what I thought for the first ... | For the first one, it is just <span class="math-container">$7 \choose 3$</span>.
But <strong>more importantly</strong>: where does your calculation go wrong?
I think you are multiplying by <span class="math-container">$8$</span>, because there are <span class="math-container">$8$</span> possible digits for the last... | <blockquote>
How many number in <strong>A</strong> are odd?
</blockquote>
In order to produce an odd number, the last digit must be <span class="math-container">$1$</span>. In this case, we have seven available slots to place the remaining digits, four <span class="math-container">$1$</span>s and three <span class=... | https://math.stackexchange.com |
187,874 | [
"https://mathoverflow.net/questions/187874",
"https://mathoverflow.net",
"https://mathoverflow.net/users/62153/"
] | Let $k$ be a number field and $X$ be a $k$-scheme. Let $G$ be a linear algebraic group over $k$ and let $f: Z \to X$ be a $G_X$-torsor ($G_X = G \times_k X)$. We can twist the torsor $f$ by 1-cocycles in $Z^1(k,G)$ (see Skorobogatov's "Torsors and rational points" for more details), and we denote the twist of $f$ by $[... | The answer is <b>No.</b> Here is a counterexample.
Take $k = \mathbb Q$, $X = {\mathbb G}_{\text{m}}$, $G = \mu_2$ and $f \colon Z \to X$ the squaring map ${\mathbb G}_{\text{m}} \to {\mathbb G}_{\text{m}}$. Then $H^1(k, G) = {\mathbb Q}^\times/\text{squares}$, and its elements can be represented by squarefree integer... | This question for <em>connected</em> $G$ is exactly asking for a "strong approximation" property for the construction of torsors, and that generally fails for both tori and connected semisimple groups beyond the simply connected case (due to various phenomena explained by class field theory), and much deeper is the aff... | https://mathoverflow.net |
1,838,631 | [
"https://math.stackexchange.com/questions/1838631",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/294706/"
] | An $A$-module $M$ may be thought of as a (surjective) ring homomorphism $f: A \to E(M)$, where $E(M)$ is a ring of group endomorphisms of $M$. Then $am = f(a)(m)$.
Is there any more to this correspondence? Is there a way to frame module homomorphisms, bilinear products,... in this view?
| Yes, of course, but it's not that useful. Suppose you have two ring homomorphisms $f\colon A\to E(M)$ and $g\colon A\to E(N)$. Suppose you also have a group homomorphism $h\colon M\to N$ is a module.
For each $a\in A$, you have $f(a)\colon M\to M$ and $g(a)\colon N\to N$; so you can form the square
$$\require{AMScd}
\... | This is a very general question and can not be answered in a few words. So, may be let me describe one aspect. If $R$ is a commutative ring and $M$ an $R$-module, giving an $R$-algebra homomorphism $A\to \operatorname{End}_R M$, where $A$ is an $R$-algebra makes $M$ into an $A$-module. In the example you write above, $... | https://math.stackexchange.com |
91,556 | [
"https://dba.stackexchange.com/questions/91556",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/58403/"
] | I have to run an <code>UPDATE</code> statement on live online database with 500k records. I want to know which statement will run faster:
<pre><code>Update Table set REC_ID = isnull(REC_ID,'')
Update Table set REC_ID = '' where REC_ID is null
</code></pre>
i am using Microsoft SQL Server 2012
| Those queries won't do the same thing.
<pre><code>Update Table set REC_ID = isnull(REC_ID,'')
</code></pre>
This one will update each record and if <code>REC_ID</code> is <code>NULL</code> it will set it to <code>''</code>.
<pre><code>Update Table set REC_ID = '' where REC_ID is NULL
</code></pre>
This one will... | The only difference in above two cases is the first statement don't have a <code>where</code> clause so all the rows in the table will be updated irrespective of the fact that REC_ID is <code>NULL</code> or not. While in second case only those rows will be updated where <code>REC_ID is null</code>.
Performance would h... | https://dba.stackexchange.com |
130,262 | [
"https://cs.stackexchange.com/questions/130262",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/122943/"
] | I have a dense matrix and a set of rows. I would like to check if adding any single row from the set to the original matrix would make the new matrix rank deficient. Right now I am doing a full LU decomposition each time. This feels wasteful, and I have a hunch that I should be able to keep some information between ite... | I will assume the original matrix has <span class="math-container">$n-1$</span> rows, <span class="math-container">$n$</span> columns, and the rows are linearly independent (this is easy to check; and if it is not the case, then the problem is trivial).
Adding a new row <span class="math-container">$r$</span> will leav... | It's unnecessary to perform an LU factorization each time. Instead, you can compute a projection matrix <span class="math-container">$P$</span> from your dense matrix. Then, for any vector <span class="math-container">$x$</span> in your set, just check if <span class="math-container">$Px = x$</span>.
In particular, sup... | https://cs.stackexchange.com |
27,519 | [
"https://mathoverflow.net/questions/27519",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1150/"
] | Hello <b>MathOverflow</b>, my first question,
<i>I apologize for the LaTeX, it works in preview but not in Safari once posted.</i>
There are many methods out there that generate a list of unique unit fractions that sum to some rational number. One of the simplest is called the "Splitting Algorithm" which uses the id... | Computing a continued fraction representation for a real number x can be seen as a repeated application of two functions. Starting with some real number x in [0,1[, apply 1/x, then x+1 the correct amount of time to come back in [0,1[, then 1/x again and so on.
The theory of fuchsian groups makes use of these codings t... | Another example: there are 3x3 matrices which, when applied to a vector representing a pythagorean triple, produce other pythagorean triples. I think it is even a way to
produce all primitive pythagorean triples from (3,4,5).
In general, you are looking for a finite number of operations which produce through
composit... | https://mathoverflow.net |
587,740 | [
"https://physics.stackexchange.com/questions/587740",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/254180/"
] | I know how to write the matrix for the operator <span class="math-container">$S_y$</span> in the <span class="math-container">$\{|{↑}_z\rangle , |{↓}_z\rangle\}$</span> basis, but I don't understand how to write it in the <span class="math-container">$\{|{↑}_x\rangle , |{↓}_x\rangle\}$</span> basis.
Wouldn't the calcul... | You know what <span class="math-container">$S_y$</span> looks like in the <span class="math-container">$z$</span> basis, and you should know what <span class="math-container">$\alpha$</span> and <span class="math-container">$\beta$</span> are in
<span class="math-container">$$
|{\uparrow}_x\rangle =\alpha |{\uparrow}_z... | The four matrix elements you are looking for are
<span class="math-container">$$
\langle {\uparrow}_{x} |\hat{S}_{y}| {\uparrow}_{x} \rangle, \
\langle {\uparrow}_{x} |\hat{S}_{y}| {\downarrow}_{x} \rangle, \
\langle {\downarrow}_{x} |\hat{S}_{y}| {\uparrow}_{x} \rangle, \
\langle {\downarrow}_{x} |\hat{S}_{y}| {\do... | https://physics.stackexchange.com |
275,950 | [
"https://softwareengineering.stackexchange.com/questions/275950",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/146055/"
] | i am currently evaluating whether SCRUM would be right for our team.
One thing that i do not understand so far and have not found a satisfactory response to is how something like "complete refactoring" epics would be handled.
My specific example:
We need to migrate a very large piece of software that has been kept as ... | "shippable" doesn't necessarily mean "usable by the end user", and it doesn't necessarily mean you actually ship it. All it means is that you're done writing and testing the code, and that it has an appropriate level of quality.
With that in mind, you need to break down your epics into stories that can be completed in... | Agile focuses on value (a.k.a. "solving problems for someone")
Does this refactoring bring value? If not, or if you can't point your finger on it, then you have two alternatives: go back to the drawing board and try to understand exactly <em>what problem you are trying to solve with this</em>, or simply do not use agi... | https://softwareengineering.stackexchange.com |
202,832 | [
"https://softwareengineering.stackexchange.com/questions/202832",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18622/"
] | I created a library that is a invoker for a web service somewhere else. The library exposes asynchronous methods, since web service calls are a good candidate for that matter.
At the beginning everything was just fine, I had methods with easy to understand operations in a CRUD fashion, since the library is a kind of r... | I would design a state machine for each set of related, linked processes, and keep track of the state somewhere in a high level object, so it is easier to debug. State transitions can be traced, and invalid state transitions can be detected.
| As Frank says, write a state machine for each chunk of business logic that requires multiple async calls. Then, it's easy to interrogate the state when debugging, because you enumerated it.
In fact, start by just drawing out the state diagram. If the diagram is too complex (especially if you have multiple async calls ... | https://softwareengineering.stackexchange.com |
482,735 | [
"https://physics.stackexchange.com/questions/482735",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | The contravariant partial derivative is defined as following:
<span class="math-container">$$\partial ^\mu = \frac{\partial}{\partial x_\mu}$$</span>
where the index <span class="math-container">$\mu$</span> runs from 0 to 3. A contravariant vector under Lorentz transformation (at leas in Physics textbooks) is defined ... | Under a Lorentz transformation <span class="math-container">$y_\mu=\Lambda^{\nu}_\mu x_\nu$</span>, so <span class="math-container">$\frac{\partial}{\partial y_\mu}=\frac{\partial x_\nu}{\partial y_\mu} \frac{\partial}{\partial x_\nu}=(\Lambda^{-1})^{\mu}_{\nu}\frac{\partial}{\partial x_\nu}$</span> which is a contrava... | A more abstract and general way to look at it is the following: take <span class="math-container">$m \in \mathcal{M}$</span> a generic point on a manifold. The tangent space at the point <span class="math-container">$m$</span> is defined as the vector space spanned by all directional derivatives of the type
<span class... | https://physics.stackexchange.com |
205,438 | [
"https://electronics.stackexchange.com/questions/205438",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88003/"
] | I am confused by the concept of byte offset.
In my textbook the examples always show the word aligned byte offset as being two bits but doesn't really explain how they arrive at that value. It says they are word aligned so the offset is 2 bits. This doesn't really make sense to me because I thought words were 32 bits ... | To understand the difference between byte- and word-addressable, understand that a byte is always 8 bits, while a word may differ from system to system. Take, for example, an 8-bit system with 2 byte words. The instruction size is one word, but the bandwidth of the system is only 1/2 word. The system must be byte addre... | A four-byte word's bytes can be numbered 0, 1, 2, and 3. In binary, these values fit into two bits: 00, 01, 10, 11.
If a four byte word is aligned, then its byte address in memory is an integer divisible by four. This address has a binary representation ending in <code>00</code>: <code>XXXX....XXXX00</code>. The ad... | https://electronics.stackexchange.com |
91,308 | [
"https://mathoverflow.net/questions/91308",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10400/"
] | Let $G$ be $SL(n, F)$ for a non-archimedean local field $F$ with Iwahori subgroup $I$. Let $\mu$ be the Haar measure of $G$.
What are the properties of the function $w\mapsto \mu(IwI)/\mu(I)$ for $w$ being an element of the normalizer $N$ of the maximal Levi subgroup of $G$?
Let $d i$ denote the Haar measure on $I$.... | Two ways of thinking about $L_X$ on differential forms:
(1) Define it by using the infinitesimal flow determined by $X$. This implies that (a) $L_X$ is a degree $0$ derivation of the algebra of differential forms (because pulling back by a diffeomorphism is an automorphism of the algebra), and (b) it commutes with $d$... | The Lie derivative $L_X$ with respect to a smooth vector field $X$
is of course well-defined on the whole tensor algebra and it is a
derivation of this algebra. If $f$ is a smooth function it satisfies
$L_X (f) = X(f)$ and $L_X(df) = d(L_X(f))$. And if $Y$ is a smooth vector
field it satisfies $L_X(Y) = [X,Y]$. Since... | https://mathoverflow.net |
24,630 | [
"https://electronics.stackexchange.com/questions/24630",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7088/"
] | I want to create a generator. The current design I am looking at has several magnets along a wheel, with coils around the outside of the wheel. The wheel then spins generating current.
I know that if I alternate the poles of the magnets, I will be generating AC Current.
So my question is, If instead of alternating th... | First, there is no such thing as a DC "pulse". DC means a steady level, which a pulse by definition is not.
No, you always get AC out of a coil. The coil is driven by <em>changing</em> magnetic field. You can shove a bar magnet down a coil, but it won't produce any steady power. There will be a blip as the magnet ... | that's a very good question.
It is actually what I m experimenting these days with.If the poles of the magnets are NOT alternating that is N S N S...and so on then what you get from the coils is a pulsing DC. You do not need rectifier diodes to convert the generated voltage to DC, with their inherent voltage drop of c... | https://electronics.stackexchange.com |
8,155 | [
"https://chemistry.stackexchange.com/questions/8155",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/4343/"
] | Correct me If I am wrong, given a reaction at equilibrium, if we say add more concentration of products to the reaction, the rate going backwards would increase to try to get back to equilibrium.
I was wondering if the rate forward stays the same or slows down?
| In simple cases, the rate is equal to the rate constant "k" times the concentration. The forward rate constant and the backward rate constant don't change, but the rate of change (rate constant times concentration) will change as the concentration of a reactant or product changes.
| Yes, if we add products, then the reverse reaction will try to make more reactants. If we take away products, then the forward reaction will try to make more products. Not on topic: If you increase pressure, the side with less moles will be favoured. And more things. This is all Le Chatelier's Principle.
| https://chemistry.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.