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 |
|---|---|---|---|---|---|
57,076 | [
"https://dba.stackexchange.com/questions/57076",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/33067/"
] | I am new to databases and trying to solve one problem in which I have to build a simple database having few entries and then querying that database and then recording that answers from the database. I have to send many queries one by one. It is kind of experiment to learn database.
Could anyone suggest which simple sof... | I would suggest using Postgres as the database for a beginner. This is the most ANSI compliant one of the open source databases. Unlike MySQL, it wont teach you any bad habits.
Pretty much all languages support querying Postgres, MySQL and SQL Server - just pick the languages you want to learn.
| The simplest - shell script running psql commands :) Otherwise, any high-level language can be used for the sake of experiment to learn database - ruby, python, java, etc.
| https://dba.stackexchange.com |
2,304 | [
"https://electronics.stackexchange.com/questions/2304",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/399/"
] | I've got a battery powered synth that uses two 9v batteries to make a split rail power supply (±9 and ground). I'm trying to use a regular AC-DC power adaptor to replace the batteries. The adaptor outputs 12v and I'm regulating it down to 9v with the LM317 voltage regulator. To get the required -9v I'm using the ICL766... | Add capacitors between each power rail and ground. They'll act like short circuits to the high-frequency noise. I see that you have one between the -9 V rail and ground-- that's a good start.
The type of capacitor you use can make a difference. Electrolytic caps, for example, are relatively cheap, but they only delive... | I would use the ICL7660S instead. A couple of benefits --
<ul>
<li>The S version switches at 35KHz which is above the audio range.</li>
<li>The S version can switch 12V. If you did a +-12V conversion you
could do a +-9V linear regulation on the output. This will reduce
the noise. </li>
</ul>
You should be able to ad... | https://electronics.stackexchange.com |
2,450,282 | [
"https://math.stackexchange.com/questions/2450282",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/485808/"
] | The probability that John goes to swimming pool on Monday is 0.8. If he goes to the pool on Monday the probability that he goes on Tuesday is 0.3. If John does not go to the swimming pool on Monday the probability he goes on Tuesday is 0.9. Find the probability that John goes exactly one of the two days.
| Let:
<ul>
<li>$A$ = {John goes to the pool on Monday},</li>
<li>$B$ = {John goes to the pool on Tuesday}.</li>
</ul>
In your post, we have the following pieces of information:
<ul>
<li>$\mathbb{P}(A) = 0.8$,</li>
<li>$\mathbb{P}(B \mid A) = 0.3$, </li>
<li>$\mathbb{P}(B \mid \overline{A}) = 0.9$ .</li>
</ul>
What y... | Let $M=1$ denote the event that he goes on monday and $T=1$ denote tuesday. $M=0$ not going on monday, same for $T=0$.
We know $P(M=1)=0.8 \Rightarrow P(M=0)=0.2$, $P(T=1|M=1)=0.3 \Rightarrow P(T=0|M=1)=0.7$, $P(T=1|M=0)=0.9$ and we have to find the probability $P(M+T=1)$.
Now utilize Kolmogorov's definition of condit... | https://math.stackexchange.com |
628,161 | [
"https://physics.stackexchange.com/questions/628161",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/295691/"
] | I don't understand why <span class="math-container">$\langle x|p \rangle$</span> is momentum eigenstate of which eigenvalue is p at position basis. (It appear at Griffiths, Quantum mechanics 3rd, example 3.9)
I'm not sure, but I try thinking about following:
At (time independent) Schrodinger equation and eigen equation... | Although it would be great if you were comfortable with Dirac notation still I will try my best.
Eigenvalue equation for momentum operator look like:
<span class="math-container">$$P|p\rangle =p|p\rangle$$</span>
You can compare it with the form:
<span class="math-container">$$\text{Operator - Vector }\rightarrow \text... | What he means is that <span class="math-container">$|p\rangle$</span> is the momentum eigenstate with eigenvalue <span class="math-container">$p$</span>, i.e. <span class="math-container">$\hat{p}|p\rangle=p|p\rangle$</span>, where <span class="math-container">$\hat{p}$</span> is the momentum operator and <span class="... | https://physics.stackexchange.com |
218,484 | [
"https://mathoverflow.net/questions/218484",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41103/"
] | This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficients of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients ar... | I assume you mean Weierstrass parametrization. Then $-x/y$ is the standard coordinate near 0, and the relevant formulas can be found in Silverman's book on elliptic curves.
| Suppose that $C$ is given by a homogeneous Weierstrass equation $f(x,y,z)=0$. Then there is a unique series $\xi(x)=\sum_{k>0}\xi_kx^k$ such that $\xi(x)=x^3+O(x^4)$ and $f(x,1,\xi(x))=0$. This can be found quite efficiently by successive approximation. Now put $$\chi(x_0,x_1,x_2)=\sum_{i,j,k\geq 0}\xi_{i+j+k+2}x... | https://mathoverflow.net |
240,176 | [
"https://electronics.stackexchange.com/questions/240176",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/113560/"
] | In Buck Converter, when switch in ON, Vi(I/P voltage)=Vl(inductor Voltage)+Vo(O/P voltage)when we switch it On, current increases linearly(according to the wikipedia) then Vl=L<em>di/dt=constant and Vo(=R</em>I) increases linearly. So Vl+Vo increases but then it must be equal to Vi which in constant in ON cycle. How is... | An inductor has inductive properties plus some DC resistance, but by itself it is a linear device, much like a resistor is a linear device by itself. <em>The current through the inductor is linear because the voltage is either fully ON or OFF at the mosfet switch. The inductor core can only magnetize or demagnetize at ... | When a buck regulator is operating correctly, the short amount of time that the transistor switch is closed does not significantly raise the output voltage. Yes, this is an approximation to reality but it holds good for very decent estimations. Consider that the output has a large value capacitor - it will not change i... | https://electronics.stackexchange.com |
137,893 | [
"https://dba.stackexchange.com/questions/137893",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/94095/"
] | I have to generate simple report from three tables named customer, product, and order. My report should have a column that shows whether the customer ordered that product or not. How could I get the Y or N value based on customer id that exists on order with the product id? Sample table with data is as below:
<pre><c... | Seems like you need all combinations of products and customers (so a <code>CROSS JOIN</code> between the two tables) and then a correlated <code>EXISTS</code> subquery. This could either be a correlated subquery in the <code>SELECT</code> list:
<pre><code>SELECT
c.customer_id,
p.product_id,
CASE WHEN EXI... | Provided customer_id and p.product_id are primary keys in customer and product
<pre><code>select c.customer_id, c.name, p.product_id,
nvl((select 'Y' from dual
where exists (select null from order o
where o.product_id=p.product_id and o.customer_id=c.customer_id)),'N') order_stat
from customer c
full oute... | https://dba.stackexchange.com |
348,174 | [
"https://softwareengineering.stackexchange.com/questions/348174",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/243640/"
] | Lately I've been interacting with a handful of SOAP APIs from different enterprise systems and I'm somewhat puzzled that oftentimes the WSDLs seem to indicate that they should be receiving XML data as a "string". For example a WSDL indicate the service expects data conforming to the following snippet of XSD for some op... | Normally this isn't good design. There is not much of a contract is all the service is: "insert giant string here".
The WSDL should define a contract which is explicit between the callee and caller. If all the contract is an undefined string format, it will be difficult and cumbersome to work with.
However, somet... | I may be slightly wrong on the historical details, but I believe that originally, SOAP was designed to operate as an RPC (Remote Procedure Call) system. You would define a service like you would a function in a procedural programming language, with argument and return types, e.g. <code>function foo(string arg1, int arg... | https://softwareengineering.stackexchange.com |
2,069 | [
"https://ai.stackexchange.com/questions/2069",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/2682/"
] | Here is one of the most serious questions, about the artificial intelligence.<br>
How will the machine know the difference between right and wrong, what is good and bad, what is respect, dignity, faith and empathy.<br>
<br> A machine can recognize what is correct and incorrect, what is right and what is wrong, depend o... | Right and wrong only exist relative to some goal or purpose.
To make a machine do more right than wrong, relative to human goals, one should minimize the surface area of the machine's purpose. Doing that minimizes the intrinsic behavior of the AI, which enables us to reason about the right and wrong behaviors of the A... | I'd like to answer this in detail, but it requires some fairly complicated theory that you don't have access to. Essentially this is related to the Abstraction Valuation Paradox. Don't bother trying to look that up. It's part of several years of research that hasn't been published yet. The research has shown that there... | https://ai.stackexchange.com |
3,875,580 | [
"https://math.stackexchange.com/questions/3875580",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/758112/"
] | I am trying to find the limit of <span class="math-container">$$\lim_{x \to 0}\frac{\cos(2x)-1}{\sin(x^2)}$$</span> Can someone give me a hint on how to proceed without applying L'Hôpital's rule. I tried using the trig identity <span class="math-container">$\cos(2x)-1 = -2\sin^2(x)$</span> but that doesn't seem to be u... | Note that
<span class="math-container">$$
\lim_{x \to 0}\frac{\cos(2x)-1}{\sin(x^2)} =
\left(\lim_{x \to 0} \frac{x^2}{\sin(x^2)}\right) \cdot \left(\lim_{x \to 0} \frac{\cos(2x) - 1}{x^2}\right)\\
= \left(\lim_{x \to 0} \frac{x^2}{\sin(x^2)}\right) \cdot \left(\lim_{x \to 0} \frac{-2\sin^2(x)}{x^2}\right)
$$</span>
F... | As you had, it is <span class="math-container">$$\lim_{x\to 0}\frac{-2\sin^2(x)}{\sin(x^2)}=\lim_{x\to 0}\left(\frac{x^2}{\sin x^2}\times \frac{-2\sin^2 x}{x^2}\right)=\lim_{x\to 0}\frac{-2\sin^2x}{x^2}=\lim_{x\to 0}\frac{-2\sin x\frac{\sin x}{x}}{x}=-2\lim_{x\to 0}\frac{\sin x}{x}=\boxed{-2}$$</span>
This is simply re... | https://math.stackexchange.com |
17,692 | [
"https://mathoverflow.net/questions/17692",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1353/"
] | Is there any way to define the orientation of an orientable smooth manifold using sheaves (when our smooth manifold is viewed as a locally ringed space) without our definition being overly contrived?
| In the study of (finite-dimensional?) paracompact and locally compact (?) spaces there is Verdier's topological duality theorem, expressed in terms of a dualizing complex (which is built up from a sheafification process using duals of compactly-supported cohomologies of open subspaces, or something like that). It is p... | A manifold supports a so-called orientation sheaf, which unfortunately I cannot recall how to define except to say it is the sheaf of sections of the orientable double cover of the manifold. I vaguely recall that this may be discussed in Dold's book on algebraic topology. An orientation is then a global section of the ... | https://mathoverflow.net |
516,810 | [
"https://physics.stackexchange.com/questions/516810",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/179637/"
] | I read that the Schrodinger equation for a non-local potential is given by
<span class="math-container">$$-\frac{\hbar^2}{2m}\nabla^2\psi(x)+\int V(x,x')\psi(x')dx'=E\psi(x).$$</span>
In case of a local potential,
<span class="math-container">$$ V(x,x')=V(x)\delta(x-x').$$</span>
In what sense, one is 'local' and the o... | In your nonlocal potential, the potential that your partical feels at each point in space depends not on the value of some single function, but the sum (Integral) of all the values of a function defined over all space. This comes up a lot in multi-particle QM. Consider trying to find the electron repulsion in the heli... | Let me make some complements. What James Johns said about Helium atom is a quite a good
example.
Basically, if we are capable of solving the many body Schrodinger equation directly, then no non-local potential appears. We have no non-local interaction in the nature. However, if we want some effective models or make s... | https://physics.stackexchange.com |
1,340,479 | [
"https://math.stackexchange.com/questions/1340479",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/245150/"
] | Suppose that the random variable X has moment generating function M(t)= $$e^{at} \over 1-bt^2$$ for -1< t <1. It is found that the mean and variance of X are 3 and 2 respectively. Find a+b.
We have E[X]=3 and Var[X]=2. I know that M'(0)=E[X]. I solved the equation and found that a=3, but I got stuck here. I kno... | Differentiating the MGF once results (using the product rule), and setting $t$ to $0$ results in:-
$$\frac{d}{dt}M(0)=\left.\frac{ae^{at}}{(1-bt^2)}+\frac{2bte^{at}}{(1-bt^2)^2}\right|_{t=0}=a=E\{X\}=3$$
Differentiating twice, using the product rule again to each of the two terms of the first derivative, leads (after s... | Or you can do it by:
Transforming $M_X(t) = \frac{e^{at}}{1+bt^2}$ to $M_{X-a}(t) = \frac{1}{a+bt^2}$.
Then, $M'_{X-a}(0)=0$ and $M''_{X-a}(0) = 2b$.
$\implies$ $E(X-a) = 0$ and $E(X-a)^2 = b$
This way you can do it a lil bit faster.
| https://math.stackexchange.com |
48,229 | [
"https://mathoverflow.net/questions/48229",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8720/"
] | Let <span class="math-container">$G$</span> be a group and let <span class="math-container">$k$</span> be a field (characteristic 0 if you want). Let <span class="math-container">$L$</span> be the graded Lie ring associated to the lower central series of <span class="math-container">$G$</span>, that is, <span class="ma... | The
<em>continuous cohomology</em> of a group $\Gamma$ is the direct limit
$$H^*_{\text{cts}}(\Gamma;\mathbb Q)=\lim_{\longrightarrow}\ H^*(\Gamma/K;\mathbb Q)$$
of the cohomology of all its finitely generated nilpotent quotients
$\Gamma/K$. The basic properties of continuous cohomology are
established in Hain, "Algebr... | Yes, there is a connection. The cohomology of the Lie algebra is connected to the cohomology of the group via a spectral sequence.
I'm going to assume $k$ is a field of characteristic $p \geq 0$. Then it is a result of Lazard (<em>Sur les groupes nilpotents et les anneaux de Lie</em>, Ann. Sci. Ecole Norm. Sup. (3), 1... | https://mathoverflow.net |
64,178 | [
"https://cs.stackexchange.com/questions/64178",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/59243/"
] | <h1>Background</h1>
I am currently taking an Algorithm and Analysis course and doing some extra studying on my own from the text book. This is not a homework question or exercise even. I am just trying to understand completely how the authors are doing the combining of terms in the time/cost equation for Insertion-Sor... | The time complexity of the insertion sort is O(n<sup>2</sup>) in the worst case(array in decreasing order) and O(n) in the best case(array in non decreasing order). These bounds result from the variance in the number of iterations of the inner while loop or in other words the while loop dominates the running time of th... | So you question is how to go from:
<pre><code>T(n)= c1(n)+c2(n−1)+c4(n−1)+c5(n−1)+c8(n−1)
</code></pre>
to
<pre><code>T(n)= (c1+c2+c4+c5+c8)n−(c2+c4+c5+c8)
</code></pre>
Step 1 (Expand the statement):
<pre><code>T(n)= c1(n)+c2(n)−c2+c4(n)−c4+c5(n)−c5+c8(n)−c8
</code></pre>
Step 2 (Group similar elements):
<pre><... | https://cs.stackexchange.com |
4,237,757 | [
"https://math.stackexchange.com/questions/4237757",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/319008/"
] | I want to show that
<span class="math-container">$$ n^{-\overline{s}} = \overline{n^{-s}}$$</span>
for complex <span class="math-container">$s$</span> and integer <span class="math-container">$n$</span>.
A simpler challenge is to show that
<span class="math-container">$$ e^{\overline{i\theta}} = \overline{e^{i\theta}}$... | Seems that you are assuming that <span class="math-container">$\theta$</span> is real:
<span class="math-container">$$e^{i\theta} = \cos \theta + i \sin \theta.$$</span>
<span class="math-container">$$\overline{e^{i\theta}} = \cos \theta - i\sin \theta
= e^{-i\theta}=e^{\overline{i \theta}}.$$</span>
| Let <span class="math-container">$-s = x + iy$</span>, and therefore <span class="math-container">$-\overline{s} = x - iy$</span>. Then <span class="math-container">$n^{-s} = n^x n^{iy} = a+ib$</span>, and <span class="math-container">$n^{-\overline{s}} = n^x n^{-iy}= c+id$</span> for some <span class="math-container">... | https://math.stackexchange.com |
82,549 | [
"https://security.stackexchange.com/questions/82549",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/69151/"
] | I have a script that can only run successfully with root permissions
But in development it's really hard to run with root permissions (in my development environment) so I add 'sudo' when ever it's required inside the code and remove it before I push changes to production.
Obviously this is not a good practice since e... | The security risks are in the sudoers file.
if the sudoers file restricts the users to only safe operations and is either passwordless or requires a password every time. there is no danger.
This means that the <strong>actions performed under sudo must be safe and free from exploits</strong> like shell injection, al... | If someone who does not understand your script runs it as a normal user, leaving these 'sudo's inside would give them the illusion that your script cannot do anything only a root user can while it actually can.
| https://security.stackexchange.com |
188,217 | [
"https://softwareengineering.stackexchange.com/questions/188217",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/82366/"
] | I want to write a server side application which allows several users to exchange files (not above 3MB) in the following way: user A connects to (server) S. User B connects to S. User C connects S. User A sends a file. Users B and C "see" that a file was/is being uploaded and start downloading it.
My main concern is re... | If this is what you want:
<pre><code>(Client A) ---> (Server) ---> (Client B)
</code></pre>
then the simplest solution is to split the problem in two parts, have the "Client A" send the file to the server, then have "Client B" grab the file once it's completely uploaded by "Client A". You can easily do that wit... | What's wrong with plain old garden variety FTP (File Transfer Protocol), or even TFTP (Trivial File Transfer Protocol)?
Granted, they're older than your father's memory of his first kiss, but they still work.
Now, both FTP and TFTP want the file to be on the server before they serve it to download clients. If what y... | https://softwareengineering.stackexchange.com |
3,003 | [
"https://mathoverflow.net/questions/3003",
"https://mathoverflow.net",
"https://mathoverflow.net/users/644/"
] | Since there is no "free field generated by a set", it would seem that
1) there is no monad on Set whose algebras are exactly the fields
and
2) there is no Lawvere theory whose models in Set are exactly the fields
(Are 1) and 2) correct?)
Fields don't form a variety of algebras in the sense of universal algebra sin... | 1 and 2 are correct, for a simple reason. If <em>C</em> is a category satisfying either 1 or 2 then <em>C</em> has a terminal object. But there is no terminal object in the category of fields (and ring homomorphisms), because there are no maps between fields of different characteristic.
For the same reason, the ca... | Fields are not algebraic. An algebraic theory, for example, has free objects: there are free rings, free groups, a free monoids. The free functor is left adjoint to the forgetful functor to sets (okay, I'm talking about models in Set). There are, though, no free fields.
One can extend one's idea of an "algebraic th... | https://mathoverflow.net |
46,804 | [
"https://mathoverflow.net/questions/46804",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7311/"
] | I was writing up some notes on harmonic analysis and I thought of a question that
I felt I should know the answer to but didn't, and I hope someone here can help me.
Suppose I have a compact Riemannian manifold $M$ on which a compact Lie group $G$
acts isometrically and transitively---so you can think of $M$ as $G/K... | The Peter-Weyl theorem tells you that $L^2(G)$ is isomorphic to $\bigoplus_{\pi}\pi\otimes\pi^*$ as $G\times G$ representation, where $\pi$ runs through all irreducible unitary representations.
It follows that
$$
L^2(G/K)\cong L^2(G)^K\cong\bigoplus_\pi \pi\otimes(\pi^*)^K.
$$
So, the first thing you absolutely need, i... | For G/K symmetric the joint eigenspaces of the G-invariant differential operators on G/K are all irreducible. Also each irreducible subspace of H has multiplicity bounded by one. For this see my "Groups and Geometric Analysis?" Ch. V Theorems 4.3 and 3.5. Concerning the Laplace Beltrami operator L, the Casimir o... | https://mathoverflow.net |
102,396 | [
"https://softwareengineering.stackexchange.com/questions/102396",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12139/"
] | Do software developers who choose not to put code optimization, standards and best practices as a top priority, create more useful code than those developers who want to worry about optimization, implementation of coding standards and practices above completing tasks on time?
How do these differing methodologies compa... | No, they'll only get respect from the project's owner of the moment.
They'll get <strong>trashed</strong> for years by:
<ul>
<li>future maintainers,</li>
<li>future testers,</li>
<li>future project owners,</li>
<li>future managers,</li>
<li>and pretty much anyone involved with the codebase in the future.</li>
</ul>
... | Do I agree with developers who don't care about code optimization and practices? <strong>No.</strong>
Do they do the job they need to do? <strong>Yes.</strong>
A business is about making money, and the only way to make money is to release products. This usually means that projects have strict schedules, which means... | https://softwareengineering.stackexchange.com |
6,431 | [
"https://chemistry.stackexchange.com/questions/6431",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/2196/"
] | <blockquote>
The energy required to remove both electrons from the helium atom in its ground state is <span class="math-container">$79.0\;\mathrm{eV}$</span>. The energy required to ionize helium (i.e. to remove one electron) is -
(A) <span class="math-container">$24.6\;\mathrm{eV}$</span>
(B) <span cl... | We can use Bohr's atomic model to calculate the ionization energy of <span class="math-container">$\ce{He+}$</span>.
The ionization energy will be the amount of energy we must give to the electron of singly ionized helium to remove it apart from the nucleus to infinity. That gives <span class="math-container">$IE_2=E_{... | Taking half the total value of both ionization energies isn't a bad initial approach. You were just one step shy of finding the answer (without calculations). Each additional ionization energy will be greater than the last because the potential will be greater; the fewer the electrons, the less electron-electron repuls... | https://chemistry.stackexchange.com |
19,216 | [
"https://stats.stackexchange.com/questions/19216",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1991/"
] | In what circumstances would you want to, or not want to scale or standardize a variable prior to model fitting? And what are the advantages / disadvantages of scaling a variable?
| Standardization is all about the weights of different variables for the model.
If you do the standardisation "only" for the sake of numerical stability, there may be transformations that yield very similar numerical properties but different physical meaning that could be much more appropriate for the interpretation. T... | One thing I always ask myself before standardizing is, "How will I interpret the output?" If there is a way to analyze data without transformation, this may well be preferable purely from an interpretation standpoint.
| https://stats.stackexchange.com |
1,948,760 | [
"https://math.stackexchange.com/questions/1948760",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/344468/"
] | Let $X$ be a metric space and let $S \subset X$. We denote the set of limit points of $S$ as $L(S)$. I want to show that $L(L(S)) \subseteq L(S)$, that is, any limit point of the set of limit points of $S$ is a limit point of $S$. I've worked on it and come to a solution, but I'd just like some confirmation on whether ... | You can always find a neighbourhood around $x$ that is contained in the neighbourhood around $p$.
Let $p\in L(L(S))$. If $p\in L(S)$, then done. If not, by the definition of accumulation points, for any neighborhood $G_1$ (open set) of $p$, there is $G_1\cap (L(S)-\{p\})\ne \varnothing$. Pick a $x\in G_1\cap L(S)$ and... | You actually don't need to choose a new neighborhood around $x$. In fact it doesn't work unless you use the same one.
The neighborhood $U$ of $p$ contains $x$. The same neighborhood $U$ is a neighborhood of $x$, so it contains an element of $S$. Since the choice of neighborhood was arbitrary we're done.
| https://math.stackexchange.com |
212,475 | [
"https://security.stackexchange.com/questions/212475",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/194908/"
] | Lets say I have the latest windows 10 version. I also have DU meter for checking my network usage
I know that in windows there is a linked list of processes that many rootkits tend to remove themselves from to hide from the task manager. I'm not sure if this is still possible in Windows 10, or even if it is possible, ... | The resource manager or third party monitoring tools are software running on the computer. They could have vulnerabilities which a knowledgeable attacker could exploit with a malware in order to manipulate their output.
Besides malware acting on the computer it is possible that an attacker modified the source code of ... | Since you are asking about rootkits, I will answer your question in the term of rootkits. There are several other methods.
First very little basics. There are 2 types of rootkits. User mode rootkits, which are designed to run in the user mode. The user mode is the the space in which a normal program (like Word or Fire... | https://security.stackexchange.com |
16,971 | [
"https://mathoverflow.net/questions/16971",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1353/"
] | Why do algebraic geometers still use the term "quasi-compact" when they almost never deal with Hausdorff spaces? They certainly use "local" rather than "quasi-local" (local = quasi-local + noetherian), so is there any reason other than historical contingency?
Do algebraic geometers who do work in other fields still ... | The condition of quasi-compactness in the Zariski topology bears little resemblance to the condition of compactness in the classical analytic topology: e.g. any variety over a field is quasi-compact in the Zariski topology, but a complex variety is compact in the analytic topology iff it is complete, or better, proper ... | I think it comes from Bourbaki. In french, "compact" is what you call "quasi-compact and Hausdorff". Calling a non-Hausdorff space compact would make no sense hence "quasi-compact".
I imagine it is the same thing for "local = quasi-local + noetherian". For me, a commutative ring is local if it has only one maximal i... | https://mathoverflow.net |
206,693 | [
"https://physics.stackexchange.com/questions/206693",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/92641/"
] | Since $F=ma$, the force should change if acceleration changes shouldn't it?
And since acceleration is the rate of change of velocity, can velocity be constant if acceleration changes?
| I think you're confusing acceleration with velocity. If a body experiences a constant force, the value of acceleration is also constant, which means the value of velocity increases/decreases in a linear fashion, depending on whether the body is accelerating (<span class="math-container">$a>0$</span>) or decelerating... | If the force on a body is constant, it will accelerate uniformly. The velocity will be a linear function of time, and the position will be a quadratic function. This is a very common scenario with falling objects. For objects near the surface of the Earth, the force of gravity is very nearly constant. Without frict... | https://physics.stackexchange.com |
223,499 | [
"https://electronics.stackexchange.com/questions/223499",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51023/"
] | For now, I'm sending bytes from FPGA (verilog) to serial at <strong>115200 bps</strong>.
I would like to send at higher speed and connect to a bluetooth module (RN42).
<ul>
<li>UART (SPP or HCI) and USB (HCI only) data connection interfaces.</li>
<li>Sustained SPP data rates - 240Kbps (slave), 300Kbps (master)</li>
<li... | HCI/SPP refer to the communication protocol. They both use a standard UART, just at different baud rates. However, the SPP mode and HCI mode are very different. HCI mode bypasses a large part of the Bluetooth software stack, so you would have to implement that yourself somewhere if you want to use HCI mode. To chan... | Each bluetooth SPP device have 3 speeds:
<ul>
<li>local speed over UART port, </li>
<li>ideal over-the-air speed, </li>
<li>real transmission speed (speed decreased by collisions, etc). </li>
</ul>
Both ends of bluetooth link can have different UART speeds. Both ends have FIFO buffers, some also flow control. Everyt... | https://electronics.stackexchange.com |
688,598 | [
"https://physics.stackexchange.com/questions/688598",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/123113/"
] | Imagine I am inside an isolated rocket of arbitrarily small size, and I have a spinning flywheel right next to me. Now suppose my rocket passes through the event horizon / Schwarzschild radius of a simple Schwarzschild black hole.
By the equivalence principle, I should not notice myself and the rocket passing through t... | <blockquote>
since classically no object can escape the black hole once it passes the event horizon, it seems as though the flywheel should break as it passes through the event horizon, because for every piece going one way, the antipodal piece of it goes the opposite direction.
</blockquote>
This analysis is incorrect... | This is not a direct answer, but an investigation of an analogous situation that helped me understand Dale's answer. I'm posting it here in case anyone else finds the discussion illustrative. (But you should still upvote Dave's response!)
This question is part of a more general class of phenomena: a spatially-extende... | https://physics.stackexchange.com |
351,548 | [
"https://softwareengineering.stackexchange.com/questions/351548",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32242/"
] | Over the years I've been switching back and forward on the idea of creating <strong>Sugar Classes</strong>.
Sooner or later I find myself repeating the same operation over an existing type. Like string manipulation, date-time calculations... in these cases I am tempted to wrap the object into a custom class and get so... | I have a whole library for lots of this stuff, especially on string operations. Often these methods are just 3-liners, but now they are just at one place.
I don't see a bad thing, because the code is reused heavily, lots of checks are in most methods I probably wouldn't bother to write, if I did write it somewhere in ... | The problem with such classes and methods is not apparent in the individual case.
You will notice the code smell however, when you have built up a large library of them and are importing it into all your code bases just to use one or two of the functions.
Basically it comes down to a responsibility question, and it'... | https://softwareengineering.stackexchange.com |
720,069 | [
"https://physics.stackexchange.com/questions/720069",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/295887/"
] | How many frames of reference are there in the twins paradox of relativity? Does each velocity get its own frame, or is it each acceleration?
It seems so natural to talk about the frame of reference attached to the rocket for the whole journey of the twin, but also to talk of the change of frames of reference being the ... | It depends on the detailed set-up of the thought experiment. However, if you assume the travelling twin's periods of acceleration are negligibly short, then there are three inertial frames to consider, namely the frame of the Earth, the frame of the outbound twin and the frame of the returning twin. In that set-up, the... | Different people use the word "frame" in a great variety of ways. The answer to this (and to your other questions about frames) depends on what <strong>you</strong> mean by the word "frame". Since you haven't told us that, there's no way to answer your question.
At every event in spacetime, there ... | https://physics.stackexchange.com |
513,339 | [
"https://math.stackexchange.com/questions/513339",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/97708/"
] | $f: \mathbb D(f) \subset \mathbb R \rightarrow \mathbb R$. I have to prove that $\mathcal C_f = \{x\in \mathbb R : \text{ f is continuous at } x\}$ is a Borel set. So I define
$A_n=\{x∈\mathbb R:\exists \delta>0 \text{ such that }∀x_1,x_2 \in (x-\delta, x+\delta)(∣f(x_1)−f(x_2)∣<1 / n)\}$
and I plan to show tha... | Define
$$
f_{\ast}(x) = \sup_{\epsilon > 0} \inf_{|y-x|<\epsilon} f(y)
$$
Then, I claim that for any $p\in \mathbb{Q}$,
$$
S_p = \{x : f_{\ast}(x) > p\}
$$
is open.
Proof : Suppose $x_0 \in S_p$, then there is $\epsilon > 0$ such that
$$
\inf_{|y-x_0|<\epsilon} f(y) > p
$$
Then, for any $x$ such that... | In general $\mathcal C_f$ is not a Borel set. For example, let $\phi$ be the Cantor-Lebesgue function that is an increasing continuous function from $[0,1]$ onto $[0,1]$. Now define the function $\psi: [0,1]\rightarrow [0,2]$ with $\psi(x)=\phi(x)+x$, where it is a strictly increasing continuous function that maps $[0,... | https://math.stackexchange.com |
296,298 | [
"https://physics.stackexchange.com/questions/296298",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/121505/"
] | What is the difference between <strong>classical correlation</strong> and <strong>quantum correlation?</strong>
| Correlation is first and foremost a term from statistics. Given a system that consists of two (or more parts), it quantifies how much I can predict about the second system if I have knowledge of the first in comparison to how much I can predict about the second system without that knowledge.
For instance, if I have a... | It feels like the answer was that "any correlation that is not classical is quantum". That is correct but it doesn't really explain where the quantum nature comes from and what it really is. In quantum mechanics, as opposed to classical mechanics, the outcome of an observable doesn't have to always be the sam... | https://physics.stackexchange.com |
173,155 | [
"https://electronics.stackexchange.com/questions/173155",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/77676/"
] | If I have a diode(ideal one) and I apply -5 V in the anode and -4 V at the cathode then the diode conducts?? I have the diode characteristic in mind but the graphs refers to v. Is this v equal to V(anode)-V(cathode)?
| "I apply -5 V in the anode and -4 V at the cathode then the diode conducts??"
No - you've made the anode <strong>more negative</strong> than the cathode so it will be reverse biased (see the number line) and no current can flow (diode acts as an ideal open circuit).
<img src="https://i.stack.imgur.com/sU8vk.png" alt=... | No current flows. With the cathode one volt more positive than the anode that diode is reverse biased.
As others have mentioned any ideal diode with a voltage across it is reverse biased. (else it would be non-ideal, or evaporate)
| https://electronics.stackexchange.com |
221,962 | [
"https://physics.stackexchange.com/questions/221962",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/100301/"
] | I'm curious to know why a tennis ball bounces forwards after it has made contact with the ground considering I throw it forwards and downwards at the ground.
I understand that is bounces up because of the force of the ground on the ball (Newton's third law).
The speed reduces to zero when it makes contact with the g... | First, $l_a$ is not the transpose of $l^a$. There would typically be a sign change on some components to account for the metric. This is referred to as the <em>adjoint</em> instead, and the transpose is equal to the adjoint <em>only for the Euclidean metric</em>. Compare with quantum mechanics, where you often deal w... | indices can be raised and lowered by the global metric <span class="math-container">$g_{ab}$</span> which can be obtained via
<span class="math-container">$$g_{ab}=-l_{a}n_{b}-n_{a}l_{b}+m_{a}\bar m_{b}+\bar m_{a}m_{b}$$</span>
with <span class="math-container">$g^{ab}=(1/g_{ab})$</span>
| https://physics.stackexchange.com |
4,168 | [
"https://mechanics.stackexchange.com/questions/4168",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/891/"
] | For a few months now my 1999 Toyota Avalon XLS (California model - this apparently affects the emissions specs - I'm in NY however) with around 105k miles has been giving me these totally random periods of revving at idle between 500-750 RPM (sounding like a cat purr) and then continuing that feeling when I'm diving an... | A couple thoughts on things to check are:
<ul>
<li>Failing idle air controller</li>
<li>Sticking EGR valve</li>
</ul>
| The scanner you have might not be able to read non-active codes. Some of the auto parts chains will do a scan for free. Have them check for codes your scanner might not recover.
| https://mechanics.stackexchange.com |
344,599 | [
"https://softwareengineering.stackexchange.com/questions/344599",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/199195/"
] | I keep hearing the term and all google searches lead me to articles on compilers. I just wanna understand what the term compile target means :|
UPDATE: To give some context: I've heard it said that web assembly is a compile target for for other languages such as C, C++, Rust etc.
| Compilers are, in essence, translators that take input in one language and produce output in another. For example, Eiffel Software's compiler takes Eiffel-language input and produces C. GCC for Intel reads C-language input and produces x86 assembly. The GAS assembler for Intel takes x86 assembly and produces x86 obj... | In translation, whether language is a natural language like English, or an artificial one like C, we use the terminology <em>source</em> and <em>target</em> to talk about the <em>input</em> and <em>output</em> of a translation system. In natural language translation, the <em>system</em> is the competent human brain cap... | https://softwareengineering.stackexchange.com |
287,622 | [
"https://physics.stackexchange.com/questions/287622",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/133633/"
] | Stars can be crushed by gravity and create black holes or neutron stars. Why doesn't the same happen with any planet if it is in the same space time?
Please explain it in simple way. Note: I am not a physicist but have some interest in physics.
| In very simple terms which I hope you will understand.
The gravitational force of attraction depends on mass and distance.<br>
For the atoms which make up the Earth there are two forces acting on them, the gravitational attraction due to all the other atoms and the Coulomb/electrostatic repulsive force between the e... | Planets <em>are</em> crushed by gravity! That's why, for example, Earth is a densely packed spherical rock rather than a loose cloud of dust.
There's just not <em>enough</em> crushing 'force' to do more than that.
| https://physics.stackexchange.com |
174,436 | [
"https://electronics.stackexchange.com/questions/174436",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/56428/"
] | Or is there any other trick to do it?
I need to change a baud rate of my Bluetooth module, I have tried it via Windows Bluetooth settings of the particular Bluetooth device, but that doesn't work.
I am using <code>Bluetooth serial terminal</code> Windows 8 program to send and receive data from the Bluetooth device.... | To read the device configuration, you have to connect to X5 instead of X4 (as pointed out by @Simon Richter). Change your settings to match what is shown below:
<img src="https://i.stack.imgur.com/9BaDH.png" alt="ready to examine configuration">
Click "Start" to read the configuration. When it finishes, you can set a... | There is no way to read back the current configuration.
If your development board is wired for JTAG mode, as it looks like from your screenshot, then simply writing a new configuration will update the FPGA only and leave the configuration flash alone, so a power cycle will reload the flash and everything is back to as... | https://electronics.stackexchange.com |
4,205 | [
"https://chemistry.stackexchange.com/questions/4205",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1274/"
] | I'm going to have an online machine shop build a part for me using a CAD drawing that I specify.
Typically, these parts are made of aluminium, but this manufacturer also mills parts out of these plastic materials:
<ul>
<li>Polypropylene (PP)</li>
<li>Polystyrene (PS)</li>
<li>High impact polystyrene (HIPS)</li>
<li>A... | Most plastics consist of linear molecules with little inter-molecular interactions, so most plastics melts too easy. The only ones you mentioned having a chance are polyuretanes and polyamides. They have (CO)(NH) fragments, that forms strong intermolecular hydrogen bonds. So, they are ones of the strongest polymeric ma... | Glass filled nylon molds well, wears well and is most resistant to heat with regards to the plastics you mentioned
| https://chemistry.stackexchange.com |
202,474 | [
"https://mathoverflow.net/questions/202474",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30726/"
] | Let $G = GL_n$ over a field $F$, and let $\gamma \in G(F)$ be a semisimple element. The characteristic polynomial $c_\gamma(t)$ of $\gamma$ encodes a fair bit of information about $\gamma$. Importantly (for me at least), $c_\gamma(t)$ decomposes into linear factors (over $F$) if and only if $\gamma$ lives in a maxima... | There is a problem you will face in generality. I don't think such a minimal field extension exists, and there isn't a nice invariant.
Let $V$ be any vector space with a quadratic form, and let $-V$ be the same vector space with minus that quadratic form. Then $V \oplus -V$ is a vector space with a split quadratic fo... | There is a natural analogue of the characteristic polynomial morphism for any semisimple (or reductive) algebraic group. I will assume below that we work over an algebraically closed field $k$ (because I have only used it in that case and it is assumed in the references I know), but I think it does just what you want f... | https://mathoverflow.net |
1,256,635 | [
"https://math.stackexchange.com/questions/1256635",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/233966/"
] | Let $\sigma(x)=\frac{1}{1+e^{-x}}$ be the sigmoid function.
How to solve such kind of equations?
\begin{align*}
\sigma(x+y)+\sigma(x-y)=a\\
\sigma(2x+y)+3\sigma(3x-y)=b\\
\end{align*}
I guess this kind of equations are related to neural networks. I don't know how to solve it.
Thank you very much.
| If $e^{-x} = s$ and $e^{-y} = t$, the system becomes
$$ \eqalign{ {\frac {s{t}^{2}+s+2\,t}{ \left( st+1 \right) \left( t+s
\right) }}&=a\cr {\frac {3\,{s}^{2}{t}^{2}+{s}^{3}+4\,t}{ \left( {s}^{2}t
+1 \right) \left( {s}^{3}+t \right) }}&=b }
$$
Multiply by the denominators and you have a system of polynomial ... | If $z$ is small, you can write $$\sigma(z)=\frac{1}{1+e^{-z}}=\frac{1}{2}+\frac{z}{4}+O\left(z^2\right)$$ and then the solutions of the equations write $$x=2 (a-1)$$ $$y=11 a-2 b-7$$ If this is not the case, Robert Israel gave the rigorous answer.
| https://math.stackexchange.com |
57,697 | [
"https://datascience.stackexchange.com/questions/57697",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/76779/"
] | I just started to work with feature selection. Let's say I have a decision tree model. I get its feature importances by <code>tree.feature_importances_</code>.
In my model out of around 30 features, 20 of them has importance value of zero. Does that mean that I should discard those low importance value features from m... | As for many questions, the answer is "it depends":
<ul>
<li>features which have a low individual importance may still add predictive power to your model, because the model benefits from combining their information together with information of other features.</li>
<li>However they may introduce noise in the model and c... | Introduction to Data Science with Python book says
<blockquote>
However, if a feature has a low feature_importance , it doesn’t mean that this feature
is uninformative. It only means that the feature was not picked by the tree, likely
because another feature encodes the same information.
</blockquote>
So in th... | https://datascience.stackexchange.com |
193,264 | [
"https://stats.stackexchange.com/questions/193264",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/102432/"
] | (Disclaimer: This is not a homework question). I am trying to teach my self some elementary probability, and I thought of this following example: Imagine you are playing a game involving two coins. In order to win the game you must flip heads before your opponent. That is, if they flip heads first they win and you l... | [I've put some material on how to sum geometric progressions and expectation of geometric random variables at the end; this answer relies on such results but they're fairly well known so I figured I wouldn't start with them. If any readers are not, then skip to the end to see one way to get them out. It's worth doing s... | Let us define a <em>round</em> of tosses as two tosses; the first toss
by A who tosses a coin with $P(\text{Heads}) = p_1$ and the
second toss by B who tosses a coin with $P(\text{Heads}) = p_2$.
The outcomes of a round and the corresponding probabilities are
$$\begin{matrix} HH & &p_1p_2\\
HT & &p_1... | https://stats.stackexchange.com |
16,833 | [
"https://physics.stackexchange.com/questions/16833",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4004/"
] | In my math course we're taught to solve PDE (partial derivative equations) like transport equation:
$$
c\frac{\partial u}{\partial x} +\frac{\partial u}{\partial t}~=~0.
$$
If $u(x,t)$ is the quantity transported and $c$ has speed dimension (according to my book), $\frac{\partial u}{\partial t}$ must be speed too. Wha... | $\frac{\delta u}{\delta t}$ does not always have the dimension of speed. It is the change rate of physical quantities respect to time, $u$ can be mass or concentration of electric charge (density) or probability density $\rho$ in quantum physics.
So if we only consider the classical physics (i.e. heat conduction can ... | The best example for this equation is a dragged clump. Imagine a gas on a one-dimensional lattice being dragged to the right by an external force. At each time, each particle is moved to the right by one unit. There are additional random motions of the particles, but they have this drift superposed on top.
If you have... | https://physics.stackexchange.com |
132,251 | [
"https://mathoverflow.net/questions/132251",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27398/"
] | Let $A$ an abelian variety over a field $k$ and $A^{*}$ the dual abelian variety.
How can we relate the étale cohomology of $A$ with etale cohomology of $A^{*}$?
| The Weil pairing induces a perfect pairing $T_\ell A \times T_\ell A^\vee \to \mathbf{Z}_\ell(1)$, and $T_\ell A = H^1_{et}(\bar{A},\mathbf{Z}_\ell)^\vee$ (here, $\bar{A}$ denotes $A \times_k \bar{k}$). Further, $H^i_{et}(\bar{A},\mathbf{Z}_\ell) = \wedge^iH^1_{et}(\bar{A},\mathbf{Z}_\ell)$. One also has $A^\vee = \mat... | Let me add something to what Timo Keller says rightly. What he said can be reformulated
as $H^i_{et}(A,{\bf Z_\ell})$ and $H^i_{et}(A^*,{\bf Z_\ell})(1)$ are canonically dual
of each other. This should be understand that there are dual not only as $\bf Z_\ell$-modules,
but also as $Gal(\bar k / k)$-representation, and ... | https://mathoverflow.net |
154,406 | [
"https://softwareengineering.stackexchange.com/questions/154406",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35848/"
] | I have the following :
<pre><code>public class doCheck(){
public void performCheck(){
try {
perform all checks......
}
catch(Exception e){
logger.error("Exception occured in class doCheck in method performCheck");
thrown new MyNewException(e.getMessage(... | That depends on whether your code base is hidden or not. If you ship the product to the client then he can inspect the Java byte code trivially anyway, so logging class names doesn’t reveal any information the user cannot get anyway.
For a server-side application, this is still true. However, it <em>may</em> be a secu... | @Konrad answered the direct question, however your exception handling has one minor and two serious problems. Since you originally posted to codereview.SE, here they are:
<ol>
<li>Logging an exception before throwing is pointless. Log it where you handle it, and don't bother catching it if you don't plan to handle ti.... | https://softwareengineering.stackexchange.com |
137,977 | [
"https://mathoverflow.net/questions/137977",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $F$ be an infinite field and $R$ a subring of $F$. suppose that $[F:R] < \infty$ (Index of $R$ in $F$ as a subgroup is finite). Does this force $R$ to be equal to $F$?
| Suppose $[F : R] = n$ is finite. I first claim that the integral domain $R$ is a subfield of $F$. For if $0 \neq \theta \in R$, then we have inclusions of $R$-modules
$$R \subset R \cdot \theta^{-1} \subset R \cdot \theta^{-2} \subset \ldots$$
where in each case $R \cdot \theta^{-j-1}/R \cdot \theta^{-j} \cong R\cd... | Related result (W. R. Scott, “On the multiplicative group of a division ring” <i>Proc. Amer. Math.Soc.</i> <b>8</b> (1957) no. 2, 303–305): given a division ring $F$ (commutative or otherwise) and a division ring $R \subsetneqq F$, we have $$[F^{\ast} : R^{\ast}] = |F|$$ where $R^{\ast}$ and $F^{\ast}... | https://mathoverflow.net |
117,321 | [
"https://chemistry.stackexchange.com/questions/117321",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/58796/"
] | During water electrolysis, the electrochemical reaction on the cathode side can be expressed as protons combined with electrons to form hydrogen. I believe this electrochemical reaction is a heat release process, but I don't know the reason.
Why protons combined with electrons will release heat?
It will be better if ... | If the process of uniting protons and electrons is assumed to occur isothermically in a vessel of constant volume, then the heat released will be equal to the change in internal energy of the system:
<span class="math-container">$$q_v=(\Delta U)_v$$</span>
Now if the mixture were to behave as an ideal gas, the chan... | One way to think of it is the electrical potential energy of the separated charges is released (as heat energy, eventually) when the charges unite. First the energy will be released as photons, and these photons will be absorbed by nearby molecules, causing them to increase in kinetic energy, which on the macro scale, ... | https://chemistry.stackexchange.com |
42,832 | [
"https://mathoverflow.net/questions/42832",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3509/"
] | Let $c$ be a $W^{1,2}$-curve into a (compact Riemannian) manifold $Q,$ defined on some open interval $I$. Let $t_0\in I$ and $\xi_0\in T_{c(t_0)}Q$ be arbitrary. I am looking for a citeable reference for the following statement: There is a unique $W^{1,2}$-vector field $\xi$ along $c$ satisfying
(i) $\nabla_{\dot{c}}\... | Since $W^{1,2} \subset C^0$ and the zero-th order term of (i) depends linearly on $\dot{c} \in L^2$, the usual rewrite-as-integral-equation proof seems to work and is rather straightforward. I don't recall seeing this written down anywhere, but it's easy to verify and summarize.
| You will find a proof in Appendix D (Theorem D.1)
of my book `A Tour of SubRiemannian Geometry'.
It may not look like what you want at first glance, since
that theorem is stated in a more general context, applicable to parallel transport
in principal bundles. Take the vector fields $X_a$ there
to be the sta... | https://mathoverflow.net |
77,121 | [
"https://dba.stackexchange.com/questions/77121",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/21747/"
] | I have asked my question on Stackoverflow but have not really gotten any answers so I am trying over here now.
I have the MySQL query that is ran in a PHP script below.
What it does is Inserts a new Project Task record if one does not exist with that ID number.
If a record exist with the ID number, then it UPDATE th... | Below is my final working solution. It turns out that moving this...
<pre><code>date_modified = (CASE
WHEN name <> values(name)
OR description <> values(description)
OR status <> values(status)
OR type <> values(type)
... | I would suggest pulling out the in-line sql. Then, create a procedure / trigger that you can apply the proper <code>IF</code> blocks to catch the absolute values you are looking to UPDATE. For instance:
<pre><code>IF (date_modified = _this_ ) THEN
SET _new_var_for_date_ := _this_desired_timestamp_;
ELSEIF (date_modi... | https://dba.stackexchange.com |
76,434 | [
"https://security.stackexchange.com/questions/76434",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/60935/"
] | It is common knowledge that any servers exposed to the internet needs to be placed in a DMZ. However, a web application sometimes need to get user input and updates to backend database tables etc. How and where would you place the database server. In the DMZ, or allow database connections through the DMZ firewall back ... | For a reasonable level of security, the answer is really neither. The database should be housed in it's own zone, not the DMZ with the web server, or in the internal network zone. This allows additional levels of protection both against intrusion from the public Internet should the web server or web application be c... | Ideally the application would be written to conform to a 3 tier architecture.
<img src="https://i.stack.imgur.com/lJbX5.png" alt="enter image description here">
In this scenario it is common for the Presentation Layer to reside in a WebDMZ, the Application Layer to reside in an AppDMZ and the Data Layer to reside on ... | https://security.stackexchange.com |
311,183 | [
"https://electronics.stackexchange.com/questions/311183",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7236/"
] | What's the risk of using PSU that is underpowered?
Is there risk to the device drawing the power?
I have a TPLINK AC1900 Onhub Router. It is missing the PSU (12VDC, 3A)
I have a 12VDC <strong>2</strong>A. I <em>think</em> the only risk is that I'll blow the PSU ( I guess it might heat up as well. Perhaps dangerously?... | All concern scenarios are possible, including that the combination will work. All depends on details of PSU design and TPLINK and PSU design margins. Consider the following:
<ol>
<li>PSU might have no problem if it is designed to switch to constant current mode when the load reaches the threshold, with proportional dr... | Yes, you might overwork the PSU, worst case I can imagine is setting it on fire and burning down your house.
Also keep in mind that your router might "brown out"; reset randomly because it does not get the power it needs. So it might not be quite functional, but you can always try. If you are lucky, there is enough de... | https://electronics.stackexchange.com |
8,440 | [
"https://electronics.stackexchange.com/questions/8440",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/619/"
] | I heard in a recent presentation that the XBox 360 uses an <strong>eFuse</strong> to prevent users from reverting back to prior boot/firmware image. What is an eFuse and how do they work?
| It's an irreversible part of the chip which is "burnt" out (without causing damage to the rest of the chip) and is usually a single configuration bit. The bit (and subsequent bits) might control something like software version, or whether the Xbox supports 1080p, or whether you can play certain region discs... Pretty m... | According to Wikipedia
<blockquote>
In computing, eFUSE is a technology invented by IBM which allows for the dynamic real-time reprogramming of computer chips. Speaking abstractly, computer logic is generally 'etched' or 'hard-coded' onto a chip and cannot be changed after the chip has finished being manufactured.... | https://electronics.stackexchange.com |
171,224 | [
"https://physics.stackexchange.com/questions/171224",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/68493/"
] | Quite a quick and hopefully simple question. The TDSE takes the form $$i\hbar\frac{\partial\lvert\psi\rangle}{\partial t}=H\lvert\psi\rangle$$ and so if we take the dual of this to find the time evolution of a bra, we find $$-i\hbar\frac{\partial\langle\psi\lvert}{\partial t}=\langle\psi\lvert H$$ which is all pretty o... | <blockquote>
Why doesn't that apply here, so we get $<\psi|\frac{\partial}{\partial t}$ instead?
</blockquote>
For one thing, the expression:
$$
<\psi|\frac{\partial}{\partial t}
$$
makes no sense because the derivative is not operating on anything...
To explain further: The quantity
$$
\frac{\partial|\psi\r... | Just to add to what has been said above.
Your notation is a little bit confusing as in the final line you have the Hamiltonian not acting on anything (convention that operators act from the left). I wouldn't swap the order of operators in Dirac notation but would represent the Hermitian conjugate Hamiltonian by $H^\da... | https://physics.stackexchange.com |
51,908 | [
"https://astronomy.stackexchange.com/questions/51908",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/49081/"
] | If the universe was at so much heat at the singularity point at big bang , Then the light of CMB must be gamma rays (high energy photons) but how did they transfer into microwaves?
| The very early universe was unimaginably hot. But we don't get any signal from this period of time because it was also opaque.
The early universe was full of plasma - the form of matter which is so hot that electrons are free from their nuclei. Plasma is normally opaque. When the universe cooled to a temperature about... | The cosmic microwave background radiation was emitted 300 to 400 thousand years after the big bang. At the time, the radiation was primarily in the near infrared range, what a blackbody at about 3000 kelvins would radiate. (That's about where a red giant or red dwarf radiates.) The expansion of space has made the frequ... | https://astronomy.stackexchange.com |
342,233 | [
"https://math.stackexchange.com/questions/342233",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/63554/"
] | a) (a,b,1)<br>
b) (a,0,c)<br>
c) (a,b,c) where $a-b=c$<br>
d) (a,b,c) where $a\cdot b = 0$
My professor said to check three properties:<br>
1) $0$ is there<br>
2) Closed by addition of vectors<br>
3) Closed by multiplication of real-valued scalar
The answers I have are:<br>
a) No<br>
b) Yes<br>
c) Yes<br>
d) No<br>... | Let’s see which of the four subsets contain $\langle 0,0,0\rangle$, the zero vector.
<ol>
<li>Is it possible to choose real numbers $a$ and $b$ so that $\langle a,b,1\rangle=\langle 0,0,0\rangle$? Clearly not, so the zero vector is not in this set, and this set is therefore not a subspace of $\Bbb R^3$.</li>
<li>Is it... | Yes, in each case you need to determine if all three properties hold. If any one or more of the properties does not necessarily hold, then the option is not a subspace of $\mathbb R^3$.
Hints:
For $(a)$, is there any way $(0, 0, 0) \in (a, b, 1)$? Property 1 fails. There can be no zero vector in the set.
<hr>
For ... | https://math.stackexchange.com |
2,097,985 | [
"https://math.stackexchange.com/questions/2097985",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/404841/"
] | Given the sequence
$$a_1=a_2=1;\ a_ {n+2} = 3a_n + 2\sqrt{2a_n^2 + 2a_{n+1}^2}$$
prove that $a_n$ is an integer for all $n\in\mathbb N$.
<strong>Attempt</strong>
It is enough to show that $2a_n^2 + 2a_{n+1}^2$ is a perfect square. That means it's an even perfect square and so divisible by 4; thus $a_n^2+a_{n+1}^2=2k^... | $a_{n+2}\ =\ 3a_n+2\sqrt{2a_n^2+2a_{n+1}^2}$
$\implies\ \left(a_{n+2}-3a_n\right)^2\ =\ 8a_n^2+8a_{n+1}^2$
$\implies\ a_n^2-6a_{n+2}a_n-8a_{n+1}^2+a_{n+2}^2=0$
Treat this as a quadratic equation in $a_n$. The discriminant is
$\Delta_n\ =\ 36a_{n+2}^2+32a_{n+1}^2-4a_{n+2}^2 = 4\left(8a_{n+1}^2+8a_{n+2}^2\right)$
Th... | Let $b_n=\sqrt{2a_n^2+2a_{n+1}^2}$. Show that $$b_{n+1}=3b_n+4a_{n}.$$
| https://math.stackexchange.com |
7,277 | [
"https://mechanics.stackexchange.com/questions/7277",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3779/"
] | Its gone 150000 KM (93,205 miles). Would its engine be reliable to last another couple of years? Should I be on the lookout for any noises the engine makes that signal trouble?
Thanks
| It depends, mainly, on how well the car has been maintained. If it has been looked after, serviced regularly, and had the belts changed at the appropriate intervals, then yes, it should last a lot longer than that - I'd expect to get a good 150,000 miles / 250,000km out of most modern engines without too much trouble.
... | Which engine does it have, the 2.5 4.2 or 4.0 straight 6
The 4.0L is one of the most reliable engines out there, however being a jeep it has other problems, the engine is generally the last thing to fail.
| https://mechanics.stackexchange.com |
163,038 | [
"https://electronics.stackexchange.com/questions/163038",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70914/"
] | So in my electronics textbooks I see brief mentioning of PNP transistors but very little description of current flow and there are no actual equations or formulae for calculating collector current, collector voltage, and V[CE](collector-emitter potential difference). So how does one compute these properties and how do ... | NPN and PNP transistors work essentially the exact same way. PNP's just reverse the voltage and current flow. So for an NPN, to bias it on you have the base at 0.7V ABOVE the emitter, for a PNP you would have the base 0.7V BELOW the emitter. For an NPN, current flows INTO the base. For PNP, current flows OUT of the bas... | Actually they are same. Just reverse some sign and change some parameter. A book from streetman illustrates this part with the example of PNP rather than other book with NPN.
| https://electronics.stackexchange.com |
14,766 | [
"https://mechanics.stackexchange.com/questions/14766",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7902/"
] | Recently, i had a discussion with someone about tire width. I claimed, that with bigger (wider) tires, a car would have more traction/grip. The person i was discussing this with, agreed with me, up to a certain point. He said, that if the tires were too wide for the car, the opposite would happen, less traction/grip. H... | Well, both of you are correct. In general terms, a wider tire has a greater contact patch with the ground, so can provide traction. As your friend stated, though, the tread pattern/depth will have a lot to do with how the tire performs during inclement whether.
Take for instance a race tire which is rated at a width ... | Wider tires will give better grip on dry pavement up to a point. Once the tire gets too wide it won't heat up enough to get good grip. Also wider tires will be more susceptible to hydroplaning.
This is why motorcycle tires are just about impervious to hydroplaning. I've ridden my bike in pouring rain at 75 mph wi... | https://mechanics.stackexchange.com |
1,799,396 | [
"https://math.stackexchange.com/questions/1799396",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/306538/"
] | Assume we have two $n \times n$ real nondegenerate matrices $ A^2 $ and $B^2$, such that
$$
A^2 \geq B^2 > 0,
$$
where "$\geq$" means positive semidefinite (Loewner) ordering. Does the following inequality holds for any real matrix $C$
$$
ACA \geq BCB \ ?
$$
If not, under which conditions on $C$ (or additional cond... | I don't know if there are any nice (i.e. not-too-strong) conditions for the inequality to hold, but I'm sure that it doesn't always hold, even when $C$ is positive definite. Counterexample:
\begin{align}
A&=A^2=I,\\
B&=B^2=\frac12\pmatrix{1&1\\ 1&1},\\
C&=\operatorname{diag}(1,4).
\end{align}
In thi... | In [Theorem 2.6a, 1] it is proven using Fuglede-Putnam that
<blockquote>
<strong>Proposition.</strong> For $I \geq A, B \geq 0$ we have $\sqrt{A} B \sqrt{A} \leq B$ if and only if $AB = BA$.
</blockquote>
(The matrix $\sqrt{A} B \sqrt{A}$ models the sequential measurement of first $A$ andthen $B$ in quantum mechani... | https://math.stackexchange.com |
155,998 | [
"https://electronics.stackexchange.com/questions/155998",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | I built a circuit with a 5V power supply and a 300-ohm resistor. With a multimeter I did the measurements of resistance, voltage, and current across the resistor. The values were:
\$R = 298 \mathrm{\Omega} \$
\$E = 4.94 \mathrm{V}\$
\$I = 16 \mathrm{mA}\$
So I made the calcs to obtain the power dissipated by the r... | It's partly the precision of your measurements, and partly the effects of the meter you were using.
When you measured the voltage, you put the meter in parallel with the resistor and measured 4.94 volts, which is the value that your power supply is producing.
When you measured the current, you put the meter in series... | What difference? I don't see a difference.
79 = 81.9 (±3.5%). Note that there are three separate measurements involved, and one of them is squared. 76.3 is a bit lower, but also note that it is a function of three measurements (resistance, and current twice). You'd expect the current measurement to be a lit... | https://electronics.stackexchange.com |
71,161 | [
"https://softwareengineering.stackexchange.com/questions/71161",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12791/"
] | One of my friends has worked for nearly 10 years, asked me why he needs to learn new things such as unit-testing, MVC, Multi-tier architecture (he creates 3-tier application but designs like 2-tier), Object-oriented programming or etc?
He has worked for a decade without unit-testing, uses code-behind and structure pro... | The most practical answer would be <strong>to secure his position</strong>.
Even if gets projects for now and all seems fine, there is always a danger of one day falling behind the younger and smarter who know modern tools and technologies.
Another argument is to look out for ideas <strong>to make the work more effic... | It sounds as if your friend was in a very common trap for programmers: His employer needs an expert for the kind of code he has right now. As the code he has now becomes more and more outdated, finding experts for that kind of code is getting harder and harder. So he's paying your friend a high salary to keep him from ... | https://softwareengineering.stackexchange.com |
49,844 | [
"https://dba.stackexchange.com/questions/49844",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/28228/"
] | Let's say I have two tables that are related in that one table contains a column that is a key to the other table. In other words, it would be a 1:1 or 1:* depending on constraints.
Let's call it an Customer/Orders relationship to give it some context.
However, let's say the requirement is that there be no referen... | It is still a foreign key, because it's a feature of your data. However, it is not enforced by a referential integrity constraint.
In my view this would mean that the foreign key would be present in the logical model ERD, but absent in the physical model.
| FK is not the only (even though preferable) way to enforce referential integrity. Triggers can be used as well - in your case you can validate integrity during inserts(updates are not allowed if I understood you well), and let deletes go through. It's not ideal, but it enforces integrity to some extent...
In any cas... | https://dba.stackexchange.com |
18,994 | [
"https://security.stackexchange.com/questions/18994",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/12369/"
] | I'm trying to figure out the best practices for accessing my devbox from a public terminal.
Most sources I've found recommend protecting the box with some kind of two factor authentication, such as adding a "command=" prefix to the authorized_key that forces entering some sort of one-time-password.
My question is, wh... | A passphrase-encrypted key provides two-factor authentication, but only if used correctly. It is easy for the user to misuse the key, providing only a single factor, and the server cannot detect incorrect usage. Hence a passphrase-encrypted key cannot be considered two-factor without additional assumptions. From the po... | The <strong>General Assumption of Security</strong>(*) is:
<blockquote>
The attacker is smarter than you, he has a bigger computer, he knows your own software better than you, and he is after you, specifically.
</blockquote>
So one has to assume that the keylogger will also monitor SSH session and slurp keys from t... | https://security.stackexchange.com |
313,911 | [
"https://electronics.stackexchange.com/questions/313911",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/153600/"
] | The textbook I'm reading implements 1-bit adders using built-in primitive modules:
<pre><code>module yAdder1(z, cout, a, b, cin);
output[0:0] z, cout;
input[0:0] a, b, cin;
wire[0:0] tmp, outL, outR;
xor left_xor(tmp, a, b);
xor right_xor(z, cin, tmp);
and left_and(outL, a, b);
and ... | Why not use Boolean operators?
<pre><code>assign Z = (a != b) != c;
assign cout = (a && b) || ((a != b) && cin);
</code></pre>
All three options are functionally equivalent ways of implementing a standard full adder.
The simple answer to your question (and to my rhetorical one) is probably simply th... | No one in industry uses bit-wise models. Less typing, equivalent functionality. Perhaps more optimized in the simulator.
| https://electronics.stackexchange.com |
172,312 | [
"https://mathoverflow.net/questions/172312",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50438/"
] | I would appreciate any help with the following problem:
Let $(M,g)$ be a 3 dimensional Riemann manifold with boundary. Let $ \Gamma $ be a surface of sufficient regularity dividing M into two connected components $M_{+}$ and $M_{-}$. Is it possible to construct a harmonic function such that it is zero on $\Gamma$ and ... | Depends on what you mean by "sufficient regularity". No simple interpretation will work. Think of the disk $|z|<10$ on the plane split by the parabola $y=x^2$. Put $v(z)=u(z+iz^2)$. Then $v$ is still harmonic in the disk $|z|<2$ and vanishes on its real diameter $(-2,2)$. Thus we have the identity $v(\bar z)=-v(z... | Despite @fedja's trenchant observations/example, there are configurations that are not hostile to a construction as suggested. In 2D, for example, on an annulus (with concentric circles), it is easy to make harmonic functions that are 0 on one of the bounding circles but not on the other.
In 3D (and generally), a simi... | https://mathoverflow.net |
179,589 | [
"https://electronics.stackexchange.com/questions/179589",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/80778/"
] | I'm making a power supply using some decade switches and resistors. The idea is to dial a voltage, much like a resistor substitution box, but get a voltage out instead of a resistance. I'm using the LM350 (high current version of LM317), but the LM317 voltage drop makes it nearly impossible to get a circuit that will... | The answer is simple - just connect the 'ground' end of your switched resistors to -1.25V, then the regulator's output will go down to 0V.
A stable -1.25V can be produced with an adjustable 3 terminal negative voltage regulator (eg. LM337) or two silicon diodes in series with a resistor, fed from a higher (negative) s... | I'm sorry to say I'm completely flummoxed.
Can we start at the beginning, please?
Here's how an LM350/LT1084 works:
The way the regulator is designed is that you first decide what output voltage you want, (V1) then you arrange the voltage divider R1R2 so that with the desired voltage on U1's OUT pin the voltage on t... | https://electronics.stackexchange.com |
35,581 | [
"https://cs.stackexchange.com/questions/35581",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/6687/"
] | Given the Grammar has no unit or ɛ-productions,<br>
What is minimum & maximum number of shifts and reduce needed by bottom-up parser?
| No, sometimes you can recognize their union. As an example, take a language where it and its complement are undecidable. Then their union is decided by a TM that always says yes.
| Let $U\subseteq \mathbb{N}$ be any unrecognizable set. Let $L_1 = \{0, 2, 4, \dots\} \cup \{2n+1\mid n\in U\}$ and $L_2 = \{1,3,5, \dots\} \cup \{2n\mid n\in U\}$. $L_1$ and $L_2$ are both unrecognizable but their union is $\mathbb{N}$.
| https://cs.stackexchange.com |
491,829 | [
"https://stats.stackexchange.com/questions/491829",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/228897/"
] | So this is sort of a general/basic, likely dumb question. I'm hoping to get a general idea, to better guide what I search/read. How do these terms relate to each other. I know with Bayesian theory, you use priors to inform the model, where in frequentism you're just using the variables you have measured to build the mo... | Because this generalizes nicely to other types of regression models. That way we can express them all in a similar way (possibly with a link function - in your linear regression case the link function is just the identity function). This makes it easier to think of them in a similar way (and also to have similar progra... | Well, if <span class="math-container">$E(XB + e) = XB$</span> we are showing that <span class="math-container">$E(e) = 0$</span>.
| https://stats.stackexchange.com |
30,599 | [
"https://mathoverflow.net/questions/30599",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7332/"
] | Let A be an artin ring which is also a finitely generated algebra over Z.
Show that $|A|<\infty$.
If A would have been a field then I know how to prove it. I know that A is a product of local rings, so I could restrict the question to Local artin rings that are finitely generated algebra over Z. But how does this ... | Take $A$ local (you already reduced to it), with $m$ the max. ideal. I claim that $A/m$ is a finite field. Suppose first that it has char. 0. Then we get injections $\mathbb Z \to \mathbb Q \to A/m$. By Zariski's lemma, $\mathbb Q \to A/m$ is finite, since it is of finite type.
Now (unfortunately I don't have it on me... | As you already mentioned, it is enough to show that every local artinian ring $A$, which is of finite type over $Z$, is finite. Let $m$ be the maximal ideal of $A$. By a standard filtration argument, we may assume $m^2=0$. Now $A/m$ is a finite field (since it is of finite type over some $Z/p$, apply Noether Normalizat... | https://mathoverflow.net |
81,794 | [
"https://softwareengineering.stackexchange.com/questions/81794",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/21598/"
] | <br>
I'm about to begin a big PHP project with a friend. It's my first time using PHP and I've been wondering wether I should try developing on Linux since it's so popular.<br>
I've had some past experience with Linux and the choice of an editor won't be hard since I know vim (though I've looked at VS.PHP and it's putt... | It depends what you call web development and how you do want to work.
For instance running Photoshop natively is impossible (sure with some VM or "emulation" there are ways to do that or you can simply use GIMP.)
If you're planning to do pure coding - it depends on what you love during development.
<ul>
<li>You w... | One advantage it might give you is that it is more likely to match the deployment environment, although with Windows improved support of PHP that's not necessarily the case. I've found it more of an advantage to use Linux when developing in Ruby on Rails more than with PHP as you can run into a lot of little annoyance... | https://softwareengineering.stackexchange.com |
1,062 | [
"https://security.stackexchange.com/questions/1062",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/396/"
] | I'm under the impression that if all the ISPs were required to filter on the source IP address of all outbound packets, that spoofing would be reduced considerably.
<ul>
<li>Are any ISPs implementing this practice?</li>
<li>Should they?</li>
</ul>
| One of the main issues is with fast switching at the core routing level. A long time ago when I was a Cisco Engineer, the cisco core routers could fast switch very effectively and provide minimal latency, but if you wanted to source filter then this would turn off fast switching and add hugely to the latency - No ISP i... | Some ISP's are starting to come to the conclusion that preventing spoofing will save them money in the long term. We find them now starting to lump anti spoofing along with anti DDoS in terms of things which will cost them money in the short term, but will lighten their network load and be able to be sold as value add ... | https://security.stackexchange.com |
121,263 | [
"https://electronics.stackexchange.com/questions/121263",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/49391/"
] | First and foremost I’d like to warn you that I’m not a native English speaker. Sorry in advance for my mistakes. And also I’m kinda a newbie in terms of electronics; so go easy on me please, I will try to be as understandable as I can.
I have a project to carry out dealing with piezo technology. I have to flash an LED... | <ol>
<li>At first sight, I would say the \$1k\Omega\$ resistor is used in combination with the \$560k\Omega\$ resistor as a voltage divider. This might sound like it decreases the sensitivity but the voltage output level of a piezo depends highly on the frequency spectrum of a push and the load impedance. The internal ... | First it would be nice if you had a part number for the piezo.
The next thing I'd would try and do is make a model of the piezo.
(So do a search.. maybe a pressure sensitive voltage source with a capacitor in series?)
Now your questions. (my answers are my best guess and should be checked against your circuit.)
1.)... | https://electronics.stackexchange.com |
399,090 | [
"https://softwareengineering.stackexchange.com/questions/399090",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/347734/"
] | I have two users in my program, one's a Programmer and the other's an Administrator. The Administrator is capable of doing everything the Programmer can do, but also has some additional roles (such as adding new users).
When writing my table diagram, with a use case such as "Edit Program", I need to have it initiated ... | A lot of this does depend on the format of the tables for your use cases. There are many different formats out there, all slightly different.
<blockquote>
When two users can initiate a use case, how would I write that? Would I put something like "Initiated by Programmer or Administrator", would I need to have it wri... | Here's an idea: stop making every use case worry about who started it.
Unless the use case is about permissions or roles or who's using it stop letting that be the focus.
When your use case is about editing the program I expect the user to be labeled user. If editing the program is a protected activity I expect the... | https://softwareengineering.stackexchange.com |
4,144,605 | [
"https://math.stackexchange.com/questions/4144605",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/929546/"
] | I have a differential equation of the form
<span class="math-container">$$
\frac{dV}{dt}+\frac{V}\tau=I
$$</span>
where <span class="math-container">$I$</span> is given as
<span class="math-container">$$
I=\begin{cases}I_P\sin(\omega t),&\frac{2n\pi}{\omega}\le t\le \frac{(2n+1)\pi}{\omega} \\
-I_P\sin(\omega t),&a... | Intervals of the form <span class="math-container">$[a,b)$</span> are the basis elements of <span class="math-container">$\Bbb R_l$</span>. The topology generated by this basis provides us with the complete list of open sets. Note that an arbitrary union of basis elements is also open, so<span class="math-container">$$... | <span class="math-container">$[a,b)$</span> are basis elements of <span class="math-container">$\mathbb{R}_\ell$</span>. You can take <span class="math-container">$\cup_{n=1}^\infty [a+\frac{1}{n},b) = (a,b)$</span> the union of basis elements which are also open. Therefore, <span class="math-container">$(a,b)$</span> ... | https://math.stackexchange.com |
93,871 | [
"https://mathoverflow.net/questions/93871",
"https://mathoverflow.net",
"https://mathoverflow.net/users/477/"
] | Let $(M, \xi)$ be a closed contact manifold with co-oriented contact structure $\xi = \ker \alpha$. Let $\mathrm{Cont}(M, \alpha)$ be the group of diffeomorphisms that preserve the contact form $\alpha$, and let $\mathrm{Cont}^+(M, \xi)$ be the diffeomorphisms that preserve $\xi$ with its co-orientation (i.e. that pul... | One of the problems with this question is that $\text{Cont}(M,\alpha)$ depends heavily on the choice of contact form $\alpha$, so while the previous answer shows that there is a choice of contact form for which $\text{Cont}(M,\alpha)$ and $\text{Cont}^+(M,\xi)$ can't be homotopy equivalent, it's not immediately clear i... | The map isn't surjective on $\pi_{0}$. Take $M$ to be a disjoint union of two 3-spheres, put any contact form $\beta$ on the first sphere, and put $\beta/2$ on the second sphere. There is an element of $\mathrm{Cont}^{+}(M)$ that simply interchanges the two pieces. But this map is not isotopic to a map that preserves t... | https://mathoverflow.net |
125,394 | [
"https://electronics.stackexchange.com/questions/125394",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40921/"
] | I have to derive the Fourier transform of a half triangle which is shown here:
<img src="https://i.imgur.com/XAqQD9K.png" alt="this image">
So far I got the equation of the line as 1-t/T, and now I think that I have to substitute into the Fourier transform definition with the limits set as 0 to T, but I'm not entirel... | You are absolutely right. As your function has a value of zero everywhere except from the [0, T[ interval, you don't need to set the limits any wider. Those 'outer' intervals will add nothing to the result. The integral below will give you the answer.
$$X_3(j\omega)=\int_0^Tx_3(t) \cdot e^{-j\omega t} dt=\int_0^T(1-{{... | Applying the definition of Fourier transform always work, but it's not always the best idea. There are some functions that have already been transformed and are listed in tables.
Sometimes it's better to think: how can I write my function as a sum of this known functions, so that then using linearity I can easily get ... | https://electronics.stackexchange.com |
432,248 | [
"https://electronics.stackexchange.com/questions/432248",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/214898/"
] | I have a simple question about reflection and impedance matching.
Consider a voltage generator Vg with its output impedance Zg, and suppose it drives a load Zl. In order not to have reflection, we should have Zg = Zl. Since this is not automatically true, it is important to put an input matching network which transfor... | Your question is a bit confusing because you are talking about reflection, but you also seem to be talking about discrete matching elements, and you make no mention of any transmission line.
Typically, the way this topic is taught is that two cases are presented.
<ol>
<li>Case 1 is when the distance between source an... | In mathematical terms, you can "cut" your network, let us suppose cutting your complete network into two parts, at any arbitrary point and measure the impedance looking into each part. If these two impedances are complex conjugates of each other, then this is a "matched" network which will transfer all signal power wit... | https://electronics.stackexchange.com |
165,520 | [
"https://softwareengineering.stackexchange.com/questions/165520",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/62412/"
] | In a few weeks, my project is going to be finished and I want to start getting my code ready for other people to use it.
I am going to be posting everything to GitHub so people can tweak it and hopefully make it better.
I guess what I'm asking is, what would be the best way to make sure my code is sufficiently docume... | <ul>
<li>Make sure there is a README.txt file in the root of the repository that points people to instructions on how to build it. The instructions could be in that file, or they could be in a separate file or wiki page. </li>
<li>Ideally, make it so that you can completely build and test the code with a single command... | Documentation in source file is always good, but you should publish additional documentation on a website. Explain its goal, how it works, your future plans, try to make contribution easy (otherwise... nobody will help you) and put some tutorials.
Trying to work on a project with source code documentation only is alw... | https://softwareengineering.stackexchange.com |
49,366 | [
"https://datascience.stackexchange.com/questions/49366",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/68023/"
] | I am working on a skin disease classification problem where I have successfully created a classifier ( TensorFlow + Keras ) which can classify images of two skin diseases.
The sample image needs to be classified in this manner :
<ol>
<li>Whether the sample is an image of the skin.</li>
<li>Does the skin have any two ... | The other answers are correct, I just want to expand since you seem to wonder where step 1. fits in.
I think you should add yet another class called <code>Unknown</code>. This class will be able to tell that it is not human skin, but preferably it should be even more precise. It also should be able to tell if a pictu... | You have to have sample tissues from skins with Melanoma, Psoriasis and Healthy Skins.
As is understood in the question, you developed a solution which can distinguish with 96% accuracy between melanoma and psoriasis. You are missing from the possibility of distinguish between sick and healthy skins.
The model you ar... | https://datascience.stackexchange.com |
295,001 | [
"https://mathoverflow.net/questions/295001",
"https://mathoverflow.net",
"https://mathoverflow.net/users/95347/"
] | Informally the axiom <em>schema</em> of accessibility states that for each unary function $F$ that is definable over the whole universe of discourse "in the language of set theory", like the powerset function $P$, or the singleton function $\iota$, or the set Union function $\bigcup$, etc.. for each such a function $F$... | A limited form of Replacement is provable in this theory! That of Replacing elements of a set of ordinals by ordinals, where an ordinal is defined in the usual manner after von Neumann.
Lemma: $\forall ordinals \ \alpha, \beta \ (\alpha \ ..\leq \ \beta \lor \beta \ ..< \ \alpha)$
The proof of this lemma is obviou... | <h2>Huh...</h2>
Let $\varphi$ be the formula
$$\varphi(x) \iff [1 \subset \mathsf{trcl}(x)=x \wedge (\forall a, b\in x)(a \in b\text{, }a=b\text{, or }b\in a)]$$
(read "$x$ is an ordinal larger than $1$.")
and define the function $F$ by recursion, as follows
<ul>
<li>$F(a) = \mathcal{P}(a \cup \bigcup \{ F(x) : x\in... | https://mathoverflow.net |
264,732 | [
"https://electronics.stackexchange.com/questions/264732",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/126974/"
] | I need a device for take notes
Is there any device such as a typewriter or keyboard that is portable and can save data to a USB (other than a cell phone or smathphone )
please give me a suggestion
| This is EE.SE. So in that vein I'll toss out another idea. You might look for something called a Mailstation. There are a number of closely related incarnations of it, but all of them basically amount to a keyboard with a small, built in monochrome LCD display. It runs off of AA batteries for quite some time, is easy t... | A Microcontroller with two USB OTG host ports and a usb keyboard.
| https://electronics.stackexchange.com |
139,737 | [
"https://mathoverflow.net/questions/139737",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16107/"
] | In any partial order $(P,\leq)$ it is easy to see that every chain generates (i.e., by taking the upwards closure) a filter, and any filter built as a result of the Rasiowa-Sikorski lemma in forcing is of this form. When can we reverse this?
More specifically, I am interested in the partial order of all closed subsets... | $\mathbf{Theorem}$ Let $X$ be a $T_{1}$-space. Let $\mathcal{Z}$ denote the lattice of all closed subsets of $X$. Let $M\subseteq\mathcal{Z}$ be a maximal filter. Then
$M=\{C\in\mathcal{Z}|x\in C\}$ for some $x\in X$ or $M$ is not countably generated.
$\mathbf{Proof}$ Assume that $M$ is countably generated, and $M\ne... | One interesting case, since you mention forcing, although it isn't your main case, is that ultrafilters on an atomless complete Boolean algebra are never generated by a chain (of any cardinality).
To see this, suppose that $U$ is an ultrafilter in a complete atomless Boolean algebra $\mathbb{B}$ generated by a chain.... | https://mathoverflow.net |
479,660 | [
"https://electronics.stackexchange.com/questions/479660",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/241836/"
] | I wrote a custom bootloader for the STM32F4 microcontroller and I'm able to write an application to the flash memory at the address of 0x08008000. The issue I have is when I use the jump function the application doesn't seem to execute. I have attached the jump function below. I have disabled all the peripherals, timer... | I managed to get the bootloader to work. I just needed to rename the reset_handler in the linker script and startup_stm32F40xx.s file to bootloader_reset_handler for the bootloader program.
| Renaming reset_handler in the linker script and startup_stm32F40xx.s file
<ol>
<li>Open STM32XXXXX_FLASH.ld file in your project search text Reset_Handler. replace this text with Boot_Reset_Handler.</li>
<li>Open startup_stm32F40xx.s file in startup folder search text Reset_Handler. replace this text with Boot_Reset_Ha... | https://electronics.stackexchange.com |
45,636 | [
"https://physics.stackexchange.com/questions/45636",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15631/"
] | The problem I am working on is:
<blockquote>
<em>Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You m... | The angular speed of the minute hand is actually $1.75\times 10^{-3} rad/s$. Always do a quick consistency check on your calculations. The hour hand is moving at roughly 1/10 angular speed so the orders of magnitude should differ by ~1.
| When you multiplied you minute hand I, it should have come out to be 588kg<em>m^2 not 243 kg</em>m^2
| https://physics.stackexchange.com |
1,556 | [
"https://biology.stackexchange.com/questions/1556",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/69/"
] | I'm sure that everyone is familiar with the sensation commonly known as "butterflies in the stomach". It is commonly experienced during periods of anxiety or stress (e.g. before high stakes job interviews or roller coaster rides) and apparently (after my web research) often felt in new romances without an obvious caus... | If you want to find out about the the relationship of this response to romance in particular, there's a pretty comprehensive research paper called <em>Love is more than just a kiss: a neurobiological perspective on love and affection</em>[1] which reviews a lot of the work done in this area. This is pretty good as it d... | Nervousness or excitement should cause an increase in activity in the sympathetic nervous system (the so-called "fight or flight" side of the autonomic system). Increased sympathetic activity will be associated with decreased parasympathetic activity (primarily digestion, but also crying and other "emittive" glandular ... | https://biology.stackexchange.com |
152,886 | [
"https://mathoverflow.net/questions/152886",
"https://mathoverflow.net",
"https://mathoverflow.net/users/37477/"
] | Consider smooth closed space curve (parametrised by its arc length) in 3 dimensional space.Does there exist atleast one point at which both the curvature & torsion attain extremum values?
| Imagine a 2D curve defined as follows: $x(t) := \kappa(s), y(t) := \tau(s)$;<br>
if it were true that a space curve always contains a point where curvature and torsion are simultaneously extremal, then the associated 2D curve (as defined above), would always contain a corner of its bounding box.
Even if infinite cur... | No. Consider a curve on the unit $2$-sphere, parametrized by arc length $ds$ with geodesic curvature $\rho(s)$. One easily computes that, as a curve in $3$-space, one has
$$
\kappa(s)^2 = 1 + \rho(s)^2
\qquad\text{and}\qquad
\tau(s) = \frac{\rho'(s)}{1+\rho(s)^2}.
$$
Thus, if what you were asking were true, then ev... | https://mathoverflow.net |
376,901 | [
"https://physics.stackexchange.com/questions/376901",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/36793/"
] | In three-dimensions, the rotation generators are represented by $J_1$, $J_2$ and $J_3$ where $1,2,3$ respectively stands for the generator of rotation about $x,y,z$ axes respectively. In general, in the rotation about the direction $\hat{\textbf{n}}$ is generated by $\textbf{J}\cdot\hat{\textbf{n}}$.
However, for even... | <blockquote>
Does it mean that a given rotation in 4-dimensional Euclidean space cannot be associated with a unique axis ($\hat{\textbf{n}}$) of rotation? If yes, why is that the case?
</blockquote>
Yes, this is absolutely true. The notion of a one dimensional axis is an "accident" of three dimensions. Rotations tra... | It's simply because 3-2 = 1 but 4 - 2 = 2. A rotation consists of the exchange of two axes. Since it involves two dimensions, it occurs in a plane, and there are n-2 dimensions left over. In one dimensional space, there aren't enough dimensional to do a rotation (unless you consider flipping the space a rotation). In t... | https://physics.stackexchange.com |
432,823 | [
"https://physics.stackexchange.com/questions/432823",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/193963/"
] | In the book I am studying (Zettili) the author introduces annihilation and creation operators by defining them in terms of <span class="math-container">$q$</span> and <span class="math-container">$p$</span> and showing how to write the hamiltonian of the harmonic oscilator in terms of them. I want to know if there is a... | The way you "derive" them in real life is that you know about them from <em>classical</em> mechanics.
It is absolutely astonishing that history seems to have forgotten this.
<h2>Classical harmonic oscillator in Hamiltonian form</h2>
Consider a classical undriven and undamped harmonic oscillator.
Generally speaking, i... | <blockquote>
I want to know if there is a way to derive them
</blockquote>
One can solve for the energy eigenstates <span class="math-container">$|E_n\rangle$</span> of the quantum harmonic oscillator (QHO) without the use of ladder operators and find that
<span class="math-container">$$H|E_n\rangle = (n + 1/2)\,\h... | https://physics.stackexchange.com |
3,476,356 | [
"https://math.stackexchange.com/questions/3476356",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/519456/"
] | I'd like to prove that <span class="math-container">$\forall k \exists y \forall x (x < y \Leftrightarrow \forall n (n < x \Rightarrow n < k))$</span> holds for first order arithmetic but I'm not sure where to start. I should probably do that inductively but it contains universal quantifier inside. What to do ... | It's helpful to simplify things a bit by figuring out what the analogue of "<span class="math-container">$\subseteq$</span>" is in this context.
<ul>
<li>This is a useful principle in general. Suppose I have a sentence <span class="math-container">$\varphi$</span> which is well-understood and true in some structure <s... | Set y = k + 1.<br>
Assume x < y.<br>
If n < x, then n + 1 < x + 1 <= y = k × 1.<br>
As n + 1 < k ÷ 1, n < k.
Assume for all n, (n < x implies n < k).<br>
If x = 0, then x < k + 1 = y.<br>
If x /= 0, then x has a precessor p.<br>
As p < x, p < k and x = p + 1 < k + 1 = y.
| https://math.stackexchange.com |
160,970 | [
"https://mathoverflow.net/questions/160970",
"https://mathoverflow.net",
"https://mathoverflow.net/users/48531/"
] | I am trying to understand the jet bundles but currently I am stuck on the following questions:
Let $\pi: E\rightarrow X$ be a smooth (holomorphic) vector bundle of rank $k$ over a smooth (complex) manifold $X$. I know that the bundle $J_k(E)$ of k-jets of $E$ has the structure of a vector bundle over $X$.
I would li... | (1) Locally, jets of sections are just collections of $r=\operatorname{rank}E$ jets of functions, hence, the rank of $J_k(E)$ equals $r$ times the number of multiindices $I=(i_1,\ldots,i_n)$ with $|I|\le k$.
(2) It is certainly holomorphic.
(3) It seems to me that $J_1(E)=T^*X\otimes E$.
| Let me just complete Alex' answer to 3). First of all, the jet bundles have nothing to do with any structure group; they are associated to vector bundles, period. Then $J_1(E)$ fits into an exact sequence:
$$0\rightarrow \Omega ^1_X\otimes E\rightarrow J_1(E)\,\buildrel {e}\over {\longrightarrow} \,E\rightarrow 0\ .$$
... | https://mathoverflow.net |
325,652 | [
"https://softwareengineering.stackexchange.com/questions/325652",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/238485/"
] | I'm currently re-factoring a part of our application at work. I'm normalising a data structure from a flat list of fields to a parent/child relationship. This has an impact on all layers in the application:
<ul>
<li>The database</li>
<li>Models</li>
<li>Business logic; and</li>
<li>The UI</li>
</ul>
Instead of creati... | If you're using git, you should be doing your work in a branch. Create as many commits as you like on this branch, but don't check them into your CI server. The CI build should be kept clean. You don't want other developers accidentally getting your broken code. Once you are finished your work (or at least have a c... | Don't ever leave code on just one box. Hard drives fail. People get sick. Accounts get locked out. Buildings catch on fire. And sometimes other people just need to see what you've been up to.
Use a separate branch. Commit often. Keep it in sync.
Don't commit broken code without SAYING that it's broken and HOW it'... | https://softwareengineering.stackexchange.com |
206,872 | [
"https://mathoverflow.net/questions/206872",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14105/"
] | For a topological space M, It is known from homotopy theory that the elements of the first cohomology $H^1(M;\mathbb{Z})$ are in 1-1 correspondence with homotopy classes of maps $[M,S^1]$
In my case of interest M is a smooth manifold. Take $\alpha$ and take smooth $f\colon M \to S^1$ representing $\alpha$ under the ab... | Let me assume throughout this answer that $M$ is closed, oriented, and connected. Here are some necessary conditions.
If you ask for a smooth fiber bundle, then a necessary condition is that the tangent bundle of $M$ has a trivial quotient of rank $1$, or equivalently a trivial subbundle of rank $1$. This is possible... | If $M$ is a compact and irreducible 3-manifold, one answer is provided by a theorem of Stallings, in his 1962 paper "On fibering certain 3-manifolds": $\alpha$ is represented by a fibration $f : M \to S^1$ if and only if the kernel of the associated homomorphism $\pi_1(M) \to \mathbb{Z}$ is finitely generated and that ... | https://mathoverflow.net |
642,397 | [
"https://electronics.stackexchange.com/questions/642397",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/306713/"
] | Hello I am using an MSP432 with CCS IDE, I am trying to use an array that points to the next integer in int x[i] ={} for a systick timer to increment the 16x2 lcd position while checking for if statements to execute. I keep getting (Identifier "i" undefined) error on the line mentioned in the code sample when... | First, in C and C++, you <strong>CAN'T</strong> define the array size with a variable:
<pre><code>int i;
i = 31;
int x[i] = { /* fill with elements*/ } //invalid definition because size identifier is a variable
</code></pre>
<em><strong>NOTE:</strong> From C99 it's possible. Thanks Lundin for clarification.</em>
Anothe... | The compiler error is self-explanatory. Get rid of <code>i</code>, there is no such variable. Should be<br />
<code>int x[] = { ... };</code>
| https://electronics.stackexchange.com |
74,872 | [
"https://cs.stackexchange.com/questions/74872",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/12769/"
] | I've been given the following problem in an interview (that I've already failed to solve, not trying to cheat my way past): The game starts with a positive integer number $A_0$. (E.g. $A_0 = 1234$.) This number is converted to binary representation, and $N$ is the number of bits set to $1$. (E.g. $A_0 = b100\ 1101\ 001... | Take a moment for yourself to realize that if we can only substract a power of two, and the popcount can't change we have to subtract $01$ in a position where the other number is $10$. The result of that is always $01$ in that position, and the number doesn't change anywhere else.
In other words, the game is a series ... | One way to solve such a problem is as follows:
<ul>
<li>Find the solution for a few simple values using the "memoized brute-force" approach you are suggesting.</li>
<li>Guess the answer (which positions are winning and which are losing).</li>
<li>Try to prove your answer. If you succeed, great. Otherwise, try to find ... | https://cs.stackexchange.com |
390 | [
"https://dsp.stackexchange.com/questions/390",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/416/"
] | Is there any way to take advantage of the frequency domain to make a clean/nice sampling rate reduction effect ? and how ?
Basically, deducted from my tests:
<ul>
<li>if I set to 0 the magnitude uppon a certain threshold I only get a filter(quite obvious...)</li>
<li>if I set to 0 one sample over 2 before the buffer ... | If you multiply a frequency spectrum by a low-pass filter frequency response, this could leave an area in the resulting spectrum around Fs/2 zero, or nearly so, depending on the filter response. Don't use a low-pass filter with a rectangular frequency response by just zeroing FFT bins, as this frequency response has s... | Yes, you can do what you're looking for. Think about what happens in the frequency domain when you downsample a signal in the time domain: the spectrum "folds over" on top of itself and sums, the well-known aliasing effect. If your signal is already sufficiently bandlimited, then you can obtain the downsampled time-dom... | https://dsp.stackexchange.com |
1,717,178 | [
"https://math.stackexchange.com/questions/1717178",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/250425/"
] | If $L/K$ is a finite Galois extension with group $G$, we can define the norm of an element $a\in L$ as
\begin{equation}
N_{L/K}(a)=\prod_{\sigma\in G}\sigma(a).
\end{equation}
And obviously, this product lies in $K$.
It is a natural question to ask whether the image of $L$ under this map is the whole $K$ or not.
I co... | Here is a purely Galois theoretic solution of the surjectivity of the norm for finite fields. Consider the extension <strong>F</strong>$_{q^n}$/<strong>F</strong>$_q$ and let N be the norm map between the multiplicative groups. It is well known that Gal(<strong>F</strong>$_{q^n}$/<strong>F</strong>$_q$) is cyclic, gene... | If $K = \Bbb F_q \subset \Bbb F_{q^n} = L$, then $N(x) = x(x^q)(x^{q^2})\ldots(x^{q^{n-1}}) = x^{1+q+\ldots+q^{n-1}} = x^{(q^n-1)/(q-1)}$.
So for a given $a \in K$ there can be at most $(q^n-1)/(q-1)$ solutions to $N(x)=a$. Moreover, $N$ is a group morphism $L^* \to K^*$, so its kernel is at most $(q^n-1)/(q-1)$, and ... | https://math.stackexchange.com |
50,720 | [
"https://electronics.stackexchange.com/questions/50720",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5872/"
] | In Verilog, one can conveniently use <code>_</code> anywhere in binary and hexadecimal literals. For example, <code>8'b0101_0011</code> and <code>32'hAEBB_23AF</code> are valid literals.
Is it possible to have <code>$display</code> do a similar thing? I'm trying to display a 64-bit signal in hex, which is 16 characters... | There is no automatic way to have <code>$display</code> do that. But you can format it yourself to do that.
For example, this will print a 64-bit value like you wanted, with a <code>0x</code> prefixed to the string.
<pre><code>$display("0x%04h_%04h_%04h_%04h", d[63:48], d[47:32], d[31:16], d[15:0]);
</code></pre>
In... | If your simulator supports SystemVerilog syntax, here is a function which can be used to display integers up to 64 bits. Wider values require multiple calls to the function. The function can display values as binary, decimal or hex.
<pre><code>module tb;
function string fmt (longint num, string radix, int width = 1)... | https://electronics.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.