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 |
|---|---|---|---|---|---|
9,731 | [
"https://security.stackexchange.com/questions/9731",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | I want to securely connect to an API, but I'm not sure how I should obtain the CA cert for the verification step.
I've seen some people get the certs using e.g.:
<pre><code>openssl s_client -connect graph.facebook.com:443 -showcerts
</code></pre>
Is this method for obtaining certs secure? Should I use some other met... | I have seen this done with SSH key authentication by phone. The procedure was for me to generate private and public keys and send the public one to the hosting provider via email. They would then phone me, read out half of the fingerprint and require me to read out the other half. If they matched, they would put my ... | I'm just reading this and I see you got an answer that works for you... but the really nerdy answer is "it depends". If you're trying to get an SSL server cert, any hit to the SSL server will get you the cert in the same way - the server will offer it and give proof of possesion as part of the SSL protocol.
The criti... | https://security.stackexchange.com |
560,577 | [
"https://physics.stackexchange.com/questions/560577",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/267998/"
] | I was trying to obtain the brachistochrone as a function of time, and I failed several times because I wrongly assumed that the <span class="math-container">$v=\sqrt{2gy}$</span> vector points downwards (vertical vector). However, in order to get the solution, the correct assumption was that this vector was the tangent... | I am not entirely sure, but I think you made two wrong assumptions in your calculations. First of all, dv/dt is not equal to g. In general, for an object in free fall, the derivative of the velocity vector is equal to the gravitational acceleration vector, which points downwards and has the magnitude of g. But an objec... | The brachistochrone is the trajectory of the falling mass as it slides along the curve. Velocity is always tangent to the trajectory.
| https://physics.stackexchange.com |
758,467 | [
"https://math.stackexchange.com/questions/758467",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/140775/"
] | Classify the group (Z4 x Z2)/({0} x Z2).
I know the order of (Z4 x Z2)/({0} x Z2) is 4, and groups with order 4 are either the Klein-4 Group or Z4. I know Z4 is abelian and cyclic and the Klein-4 Group is abelian and noncyclic. I also have a theorem that states since 4 and 2 are not relatively prime, Z4 x Z2 is not cy... | We only care about the last three digits obviously, so the possible sums of just those three die are $100a + 10b + c$, where $a$, $b$, and $c$ are all between $1$ and $6$, inclusive.
We check the divisibility by taking this modulo $8$. If the result is equivalent to $0$, then it is divisible.
Setting up the equivalen... | Here's a generalization:
The sample space for a six-sided die is $S = \{1,2,3,4,5,6\}$.
<strong>Theorem:</strong> There are exactly $\color{blue}{3}^n$ n-tuples $(x_{n-1}, x_{n-2}, \cdots, x_1, x_0)$ that satisfy $f(n) = 10^{n-1}x_{n-1} + 10^{n-2}x_{n-2} + \cdots + 10x_1 + x_0 \equiv 0 \mod{2^n}$ for $x_i \in S$
<s... | https://math.stackexchange.com |
6,588 | [
"https://electronics.stackexchange.com/questions/6588",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/938/"
] | I was looking for an equivalent MOSFET and haven't had any success.
I'd like to know if are there any websites or software which gives a list of alternative equivalent components?
<hr>
<strong>Edit:</strong>
The purpose of this question is not only for MOSFET's, but for any type of component.
I want to learn how ... | many distributors offer a cross reference search.
For something as simple as a mosfet i would probably just go to digikey, head to the mosfet section and enter the parameters in the digikey search options from the datasheet of the part you have. Then compare datasheets for the results.
| Go to a vendor that might sell it, then check their cross reference. For example for a National analog part I would go to TI, Linear and Analog Devices. Also their FAE or the distributor's FAE.
| https://electronics.stackexchange.com |
93,855 | [
"https://electronics.stackexchange.com/questions/93855",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/34230/"
] | Been using Altium and multi sheet projects for a while.
My latest project involves a lot of signals so I'm trying to keep things tidy using lots of labels, ports, busses.
So I have a bus for <em>enable</em> signals going from the microcontroller sheet, to the stuff that needs to be enabled. And the same for fault cond... | When net labels are made part of a bus they don't need to be explicitly connected like in the right side of the first image. It is sufficient to have a bus somewhere with the same denomination as the netlabels, and these will be connected automatically.
So what happens in the first image is that the bus definition is ... | I'd say yes you do have floating signals.
In picture 2, the diagonal lines are just graphical elements, they are not wires.
also: Did you specify the sub-schematic in the second picture as "REPEAT"?
| https://electronics.stackexchange.com |
113,490 | [
"https://physics.stackexchange.com/questions/113490",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/31340/"
] | Is matter still vibrating at absolute zero temperature? If it isn't, wouldn't we then be able to know both its position and momentum?
| A system at absolute zero will still have nonzero uncertainty in position and momentum.
As an example, consider the simplest vibrating system, the one dimensional harmonic oscillator with (angular) frequency $\omega$ and mass $m$. In it's ground state (i.e. the lowest possible energy for the system) the position proba... | There will still be vibrations due to zero-point energy. So it's still impossible to know both its position and momentum.
| https://physics.stackexchange.com |
23,085 | [
"https://mathoverflow.net/questions/23085",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4821/"
] | I would like to find a reference for the following fact:
every finite dimensional complex representation of a reductive Lie algebra is semisimple.
| The statement is false. The standard definition of "reductive" for a finite dimensional Lie algebra $\mathfrak{g}$ over an arbitrary field of characteristic 0 is given in a number of equivalent ways by Bourbaki in Chapter 1 (1960) of their treatise on Lie groups and Lie algebras: section 6, no. 4-5. By definition, ... | You can find the proof in Serre's "Lie Algebras and Lie Groups", in chapter "Semisimple Lie Algebras", section "Complete Reducibility"
| https://mathoverflow.net |
91,319 | [
"https://softwareengineering.stackexchange.com/questions/91319",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30664/"
] | I found many things when searching, but nothing that seemed both updated and complete.
In last quarter of 2010 I remember reading what were very sad news for me, as WebSockets were disabled in most (if not all? can't remember) modern browsers that supported it by default due to security concerns in the proxy protocol ... | <strong>Delegates in C#:</strong> Think of a delegate as a class, but an instance of that class would be a method rather than an object. The delegate is defined by the signature of the method which will be assigned to it. The instance variable may be called as if it were the method itself.
Given this example:
<pre><c... | Delegates are quite simply functions as objects. You can create them, pass them around, and then call them when you like. You could trivially convert a delegate into a polymorphic class with a method, for example.
<pre><code>public delegate int SomeFunc(int);
public int Square(int i) {
return i * i;
}
public int D... | https://softwareengineering.stackexchange.com |
213,318 | [
"https://physics.stackexchange.com/questions/213318",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95956/"
] | A variable force $\vec{F} = 3x^2y \vec{i}$ (unit vector) is acting on an object that travels on a square loop in a clockwise direction starting from the origin to (0,5) then (5,5) then (5,0) then back to (0,0). How much work is done on the particle by the force during one complete trip around the square?
It should be... | This is like calculating a line integral only. <br>
Work done, $W= \oint_C \vec F\cdot d\vec r = \oint_C 3x^2ydx=\int_I 3x^2ydx +\int_{II} 3x^2ydx +\int_{III} 3x^2ydx +\int_{IV} 3x^2ydx$ <br>
Now for path I, (0,0) to (0,5): $dx = 0$
$$\int_I 3x^2ydx = 0$$
Now for path II, (0,5) to (5,5): $y=5$
$$\int_{II} 3x^2ydx = 1... | Your force $F=3x^2y\hat{i}$ has only x component suggest that it is acting only in x direction. So, motion along y axis does not cause any work done by the force, as it is perpendicular to the direction of force. <em>Work is said to be done only along x axis</em> . So,<br>
$$W= F.S\\ = \int_{_(0,5)}^{(5,5)}{f.dx} + \i... | https://physics.stackexchange.com |
59,355 | [
"https://stats.stackexchange.com/questions/59355",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/25805/"
] | I develop an application in which i constantly get samples of heart pulse.
I defined an interval of t seconds.
In each t seconds I have n samples.
In every interval, I want to calculate the tendency of those n samples. For example, lets say I have n = 5, and I have samples with values {70, 88, 95, 103, 115}. I want ... | Heart rates vary in a cyclic pattern that is driven by the respiratory rate. Inspiration causes decreased filling of the left atrium and the heart rate increase to maintain cardiac output. You need to detrend the respiratory influence.
Because the instantaneous heart rate is just the inverse of the RR interval, you do... | The second approach based on a correlation won't tell you anything about the direction of the trend. At its base it is the same as the first approach - fits a simple linear regression - but it is giving you one of the least useful bits of output from fitting that model. So of the two, the first approach, based on lin... | https://stats.stackexchange.com |
2,584,688 | [
"https://math.stackexchange.com/questions/2584688",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/389906/"
] | Consider normed spaces $X$ and $Y$. You can assume that they are Banach spaces if needed. Let $\mathcal{L}(X, Y)$ denote the spaces of bounded linear operators from $X$ to $Y.$ Now consider the set
$$\Omega=\{T \in L(X,Y): T \textrm{ is onto}\}.$$ Is $\Omega$ open with the norm topology?
| We've seen in another answer that this is false if $X$ is not a Banach space.
<blockquote>
<blockquote>
<strong>Lemma</strong> Suppose $X$ is a Banach space, $T:X\to Y$ is linear and bounded, $0<\epsilon<1$, $\delta>0$, and for every $y\in Y$ there exists $x\in X$ with $||x||\le\delta ||y||$ and $||Tx-y... | $\Omega$ is not open in general, at least if $X$ and $Y$ are not assumed to be Banach.
Consider $c_{00}$, the space of all finitely-supported sequences, equipped with $\|\cdot\|_2$.
Define $A : c_{00} \to c_{00}$ as
$$A(x_1, x_2, x_3, \ldots) = \left(x_1, \frac12x_2, \frac13x_3\ldots\right)$$
$A$ is bounded and on... | https://math.stackexchange.com |
2,368,084 | [
"https://math.stackexchange.com/questions/2368084",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/421436/"
] | <blockquote>
Solve the following system of mods for $x$.
$3x$ $\equiv$ $5\ (mod \ 7)$<br>
$7x$ $\equiv$ $5\ (mod \ 15)$
</blockquote>
This is my current work, but am stuck about 75% of the way through:
1) Find multiplicative inverse of $7\ mod\ 15 $
$7b$ ($mod$ 15) = 1
so $b$ = $13$.
$13$ * $7... | It is also straightforward by "definition" of the radius of convergence, since $\limsup\sqrt[n]{|c_n|}=\lim \frac{1}{\sqrt[2n]{(2n)!}}$, and $\sqrt[2n]{(2n)!} \to + \infty$, which can be seen by the inequality
\begin{align*}
\sqrt[2n]{(2n)!} &\geq \sqrt[2n]{\left(\frac{2n}{2}\right)^n} \\
&=n^{1/2}.
\end{align*... | Use d'Alembert classical ratio test.
Let $u_n(z)=\frac {(-1)^nz^{2n}}{(2n)!} $.
$$\lim_{+\infty}\frac {|u_{n+1}(z)|}{|u_n(z)|}=$$
$$=\lim_{+\infty}\frac {|z|^2}{(2n+1)(2n+2)}=0$$
the series is absolutely convergent for all complex numbers $z $.
the radius is infinite.
$$\sum_{n=0}^{+\infty}u_n(z)=\cos (z) $$
| https://math.stackexchange.com |
251,397 | [
"https://physics.stackexchange.com/questions/251397",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/114099/"
] | So gravitational potential is given by $V(r)={\frac{GM}{r}}$
and the tangential velocity of a satellite is the square root of
$V$, i.e. $\sqrt V$. So how do these two relate, if at all?
| The relation is indeed correct. Let me show you why.
This type of problem is solved by equating forces. Other classical mechanics problems are by equating energies or, in rare cases, momentum.
The gravitational potential indeed is
$$ V(r) = G \frac Mr \,.$$
This is not directly useful for this problem. Here you rathe... | It's called the virial theorem: in a bound system, the average of the potential energy of a $\frac{1}{r}$-potential V is related to the average of the kinetic energy T like $\frac{\langle V \rangle}{2} = - \langle T\rangle$.
| https://physics.stackexchange.com |
167,688 | [
"https://electronics.stackexchange.com/questions/167688",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/72586/"
] | The firmware of my module supports UART <code>printf()</code> which I think could be good for debugging, but how could the messages be read? I'm currently using just a USB-to-Serial cable. I've tried using PuTTy, but all I see is gibberish, e.g.,
<blockquote>
β)βΙβ]
ββββ9~β!ββ!ββββββJ=ββHβ]
... | Have you checked your baud,start,stop settings? Try with different values (e.g. 9600,n,8,1)
| If you have some money to invest I recommended a logic analyser.
I suggest: www.saleae.com.
In this capture software you can set up communication (USART, SPI, I2C ..) and see the decoded data in various ways.
| https://electronics.stackexchange.com |
43,969 | [
"https://physics.stackexchange.com/questions/43969",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6764/"
] | I have been trying to derive <strong>why</strong> relativistic momentum is defined as $p=\gamma mv$.
I set up a collision between 2 same balls ($m_1 = m_2 = m$). Before the collision these two balls travel one towards another in $x$ direction with velocities ${v_1}_x = (-{v_2}_x) = v$. After the collision these two b... | Assume that the relativistic momentum is the same as the nonrelativistic momentum you used, but multiplied by some unknown function of velocity $\alpha(v)$.
$$\mathbf{p} = \alpha(v)\,\, m \mathbf{v}$$
Then in the primed frame, the total momentum before the collision is just what you had, but multiplied by $\alpha(v_... | Relativistic momentum is not defined as $p= \gamma m v$. For instance, this expression does not apply to photons, which are massless particles <strong>[*]</strong>.
In the Lagrangian formalism of mechanics the momentum is defined as
$$p\equiv \frac{\partial L}{\partial v}$$
Using the relativistic Lagrangian for a fr... | https://physics.stackexchange.com |
1,628,649 | [
"https://math.stackexchange.com/questions/1628649",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/308347/"
] | If you count (4 4 3) as one combination, you cannot count (4 3 4) as another.
My approach is $\dfrac{4^3}{3!}$, but obviously this does not work. I don't know why it doesn't work, and I don't know how I should solve the problem.
| <strong>An easy way :</strong>
Take , $\displaystyle a_n=\frac{1}{n!}$. Then , $\displaystyle \frac{a_{n+1}}{a_n}=\frac{1}{n+1}\to 0 \text{ , as } n\to \infty $.
So by <strong>Cauchy's second limit theorem</strong> , $\displaystyle a_n^{1/n}\to 0 \text{ , as } n\to \infty$.
| Think about AM-GM, you get<br>
$(\frac{1}{n!})^{\frac{1}n}\le\frac{2}{n+1}$
| https://math.stackexchange.com |
313,166 | [
"https://electronics.stackexchange.com/questions/313166",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/36229/"
] | For a particular design, I need to take an unregulated voltage from a battery and regulate 5 different DC voltages from it. What's worse is that I need step-up and step-down converters. What's <em>even worse</em> is that some voltages need more current than others.
<em>Note: To clarify the question, I've given the spe... | I have often wondered this myself, and each time what I come down to is a trade-off. The most obvious trade-off is the following:
Pro: Cascading them generally causes the lower-voltage regulators to stay cooler (you're not dropping as much voltage with them, so you're wasting less power in the form of heat).
Con: You... | You should also take care about making your system failsafe. I will go in a details by explaining what I've done in a recent project.
I've had battery pack and DC/DC to 5V/6A and in a need of 24V/2A supply. There were 2 options, use one DC/DC to to 24V/2A and the cascade that with 5V DC/DC supply or take Vpack->5V and... | https://electronics.stackexchange.com |
23,144 | [
"https://stats.stackexchange.com/questions/23144",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9315/"
] | I have a variable Net Promoter Score (NPS) which is an item on a survey, the answer format is ordinal, 0 to 10.
Then, there are sub-questions on the same survey, some are ordinal, some are categorical.
I would like to determine which sub-question or which group of sub-questions are the best predictors of NPS. The goa... | No, it is not acceptable. The repetitions are what provide the weight of the evidence.
If you remove your duplicates, a four-leaf clover is as significant as a regular, three-leaf clover, since each will occur once, whereas in real life there is a four-leaf clover for every 10,000 regular clovers.
Even if your priors... | I agree with the previous answer but here are my reservations. It is advisable to remove duplicates while segregating samples for training and testing for <strong>specific classifiers</strong> such as Decision Trees. Say, 20% of your data belonged to a particular class and $\frac{1}{4}^{th}$ of those seeped into testin... | https://stats.stackexchange.com |
143,214 | [
"https://mathoverflow.net/questions/143214",
"https://mathoverflow.net",
"https://mathoverflow.net/users/39212/"
] | Assume that $B$ and $A$ are two positive definite matrices. Take $B^*$ a block diagonal matrix with block $B_{11}$ and $B_{22}$ of $B$. This means the following:
$$
B=\left[\begin{array}{ll}
B_{11}& B_{12}\\
B_{21}&B_{22}
\end{array}\right],
B^*=\left[\begin{array}{ll}
B_{11}& 0\\
0 &B_{22}
\end{array}\... | A quick counterexample to your conjecture is
\begin{equation*}
A = \begin{pmatrix}
13 & 3 & -13 & -5\\
3 & 4 & -3 & 4\\
-13 & -3 & 13 & 5\\
-5 & 4 & 5 & 10\\
\end{pmatrix},\quad B = \begin{pmatrix}
15 & 3 & -14 &... | From the comments, a true version is $$2^n\det(I+AB^*)\geq \det(I+AB), \quad (1)$$ where $n$ is the dimension of $A, B$.
The proof is easy, as $2^n\det(I+AB^*)\geq\det(I+2AB^*)$. Can $2$ be replaced by a smaller constant in (1)?
| https://mathoverflow.net |
192,386 | [
"https://electronics.stackexchange.com/questions/192386",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/87504/"
] | I know that voltage regulation is give by
$$ V.R.= \frac{V_{nl} - V_{fl}}{V_{fl}} \cdot 100 $$
where \$V_{nl}\$ is the no load output voltage and \$V_{fl}\$ is the full load output voltage.
I can easily solve for a particular case but can I find out theoretically which one has a better voltage regulation?
| Average output voltage for a 50Hz mains and half wave rectification is approximately:
\$\sqrt{2} V_{RMS} - V_F - \frac{20ms\cdot I_{OUT}}{2 C}\$ where VF(I) is the forward voltage of the rectifier, and C is the filter capacitor value
For full wave rectification it is :
\$\sqrt{2} V_{RMS} - 2V_F - \frac{10ms\cdot I_... | half-wave, full wave, 3phase rectifier on their own don't really indicate which provides the better voltage regulation.
Half wave only facilitates pulsed powerflow every half cycle. a full wave rectifier facilitates almost continuous, but pulsed powerflow. 3phase facilitates a significant continuous flow of power
... | https://electronics.stackexchange.com |
296,832 | [
"https://softwareengineering.stackexchange.com/questions/296832",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/161917/"
] | A significant portion of the application I work on every day consists of Javascript that outputs a lot of (what might as well be) Excel spreadsheet formulas. Yes, Excel is barely a Turing-complete language, but the formulas are more than complex enough to qualify as "code". They're not meant to be human-readable or hum... | I would generally argue that there are uses. Those uses might not apply to you in this specific scenario, but they might.
<ul>
<li>What happens when your integration tests fail?</li>
</ul>
Now you get to dig into the code to narrow down what the actual root cause was. If you had unit tests for just the formula genera... | A shorter form of your question would be "does unit tests make sense for a compiler". I believe the answer to that question is a strong yes. You need to know that the smallest parts of your transformation pipeline do what they should. You need to know that they're combined correctly and so on.
I'd say that unit tests,... | https://softwareengineering.stackexchange.com |
1,423,676 | [
"https://math.stackexchange.com/questions/1423676",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/176371/"
] | Given the usual topological space $(\Bbb{R}, \tau_d)$ of $\Bbb R$ where $d$ is the Euclidean metric, a subset $X$ of $\Bbb R$ is said to be connected if the subspace topological space $(X,\tau _X)$ is connected, i.e. the clopen sets in $(X,\tau _X)$ can only be $\emptyset, X$.
My professor's lecture notes have proved ... | To elaborate on the comment of @Giovanni, you can do the following.
First, it is a nice exercise for you (which uses only the definitions), to show that
A topological space $(X,T)$ is connected if and only if each continuous function $f :X \to \{0,1\}$ is constant. Here, $\{0,1\}$ is equipped with the discrete topol... | If you already know that either $sup(G_1)=b$ or $sup(G_2)=b$ and not both, that is enough to prove the union of some of them with $\{b\}$ is open. If, for instance, $sup(G_1)=b$ and $sup(G_2) < b$, then there's some open ball from the subspace topology $\tau_{(a,b]}$ centered in $b$ entirely contained in $G_1 \cup \... | https://math.stackexchange.com |
73,357 | [
"https://electronics.stackexchange.com/questions/73357",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4682/"
] | I may be pushing physics here so please tell me if I am. I have a signal I'm trying to anti-alias at 50Hz (sampling at 100Hz). The problem is my input signal is essentially an Amplitude Modified square wave that matches the sampling frequency with a very short duty cycle (~2-5%, settable). I'm timing my samples so that... | The easiest and most effective way of doing this is <strong>not</strong> to filter your signal but start taking plenty of ADC samples as soon as you hit the area you want to sample. Carry on sampling until the pulse is about to change and stop sampling.
Average your ADC samples - that's all you have to do and if you c... | Some ideas:
<ol>
<li>Get rid of the anti-alias filter. Your signal is in the aliased band, so anti-aliasing with a LPF will necessarily eliminate your signal. If the high-frequency noise is not too bad, maybe you can just live without the filter.</li>
<li>What your sampling scheme does is use aliasing as an advantage ... | https://electronics.stackexchange.com |
443,463 | [
"https://softwareengineering.stackexchange.com/questions/443463",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/423558/"
] | We have 2 vehicle types in our system <code>Car</code> and <code>Bike</code>. Both can be associated with a <code>Report</code>.
There are components in our system which operate on <code>Report</code> but when dealing with the report they need to check if the report is for a <code>Bike</code> or for a <code>Car</code>.... | I think you have the wrong decision criteria in focus.
You are trying to make this decision based on a few additional queries which may be required to determine the vehicle type. This is first and foremost a performance argument. But performance should only become of interest when you have a real, measurable bottleneck... | The question as stated is a bit vague.
<blockquote>
trying to decide between these 2 options:
<ol>
<li>Create a report type for each ...</li>
<li>Create only 1 report type Report</li>
</ol>
</blockquote>
Based on what you have disclosed so far, definitely go with option 2.
There are clearly commonalities among vehicles... | https://softwareengineering.stackexchange.com |
466,098 | [
"https://electronics.stackexchange.com/questions/466098",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/87338/"
] | I am attempting to select a temperature sensor for a controlled heating application. The sensor will need to be inserted into a chamber with a cartridge heater and steel ball bearings inside of some stainless steel tubing. I would like to meet the following specifications:
<ol>
<li>Temperature control between 160.0 an... | The / provides the nominal ratings at different operating conditions.
On the high end: 75% duty cycle, when the motor drives a 0.28kW load the rated current is 0.95A, spins at 2660 rpm, geared down to 176 rpm has a pf of 0.85.
Low end: 25% duty cycle, 0.071kW load at 0.75A, spins at 650 rpm, geared down to 43 rpm has... | <blockquote>
I need to know Rated power.( This has a code. I cant understand that.)
</blockquote>
The two power ratings, 0.07 kW and 0.28 kW are the ratings at the two motor speeds, 650 RPM and 2660 RPM. That would be consistent with two-speed operation with full torque available at each of the two speeds. I believe... | https://electronics.stackexchange.com |
62,306 | [
"https://security.stackexchange.com/questions/62306",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/42356/"
] | I recently applied for a second credit card for my partner to use on my account and was surprised when her preset PIN number turned out to be the same as mine.
Coming from a development background I assumed PINS were hashed somehow.
It seems very unlikely this is a coincidence, why are credit card PINs not stored has... | What's the use of hashing a 4 digit PIN? You only need 10.000 rounds to get the PIN back, even if each PIN has its own salt. They are probably stored encrypted, for local employees etc, but for an engineer working there it won't be a big problem to get the PIN out of the database.
| I've seen this happen to a former colleague: he complained that when he asked his bank for a new card, he got one with the same PIN number.
Possible explanations:
<ul>
<li>PINs are generated randomly, but stored "in the clear" somehow; when you request a new card it gets primed with the stored pin</li>
<li>A strike o... | https://security.stackexchange.com |
2,474,895 | [
"https://math.stackexchange.com/questions/2474895",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/460436/"
] | In a ring If product of finite elements is a unit then can we say each element as unit
For ex., if $q_1 q_2 ... q_m$ is a unit, then can we say each of $q_i$ $\forall i$ is a unit
how to prove this?
| Not in general. The ring of linear transformations of an infinite dimensional vector space contains elements $a,b$ such that $ab=1$ but $ba\neq 1$, and neither $a$ or $b$ is invertible. The linear transformations $a$ and $b$ can be given as "shift" operators that move the elements in the basis, such that one shifts the... | Suppose the product $q_1 q_2....q_m$ is a unit in Ring $R$ which means that there exists some $u\in$ $R$ such that $q_1 q_2....q_m u$ =$1$,where $1$ is the identity in ring $R$.
Now clearly $q_1$ is a unit in $R$.
And $q_2....q_m u$ = $q_1^{-1}$ or $q_2....q_m u q_1$=$1$ and by similar arguements we can say that $q_... | https://math.stackexchange.com |
56,103 | [
"https://softwareengineering.stackexchange.com/questions/56103",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13249/"
] | I have a philosophical question about the MVP pattern: I have a component that checks whether a user has access to a certain privilege. This privilege turns on or off certain UI features. For instance, suppose you have a UI grid, and for each row that gets bound, I do a security check to see if certain features in th... | The security check belongs in the model, and data that should not appear in the UI should not be available to the view at all. Otherwise you have to duplicate the security logic in every view you have on the data, and a mistake in any of them will lead to a security flaw in your product.
| <blockquote>
<blockquote>
As per the MVP pattern, which component should security checks fit into, the presenter or the view? Since the view is using it to determine its accessibility, it seems more fitting in the view, but it is doing database checks and all inside this business component, and there is business ... | https://softwareengineering.stackexchange.com |
567,935 | [
"https://electronics.stackexchange.com/questions/567935",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/287011/"
] | What I mean is that when I plug my charging brick into the wall it produces 5V DC from 120V AC.
Why can't a charging brick have 5V DC input to it and have it output 120V AC?
| It just doesn't work that way. It's a different operation so different hardware is required.
Like how running an signal backwards through an adder won't make it subtract.
The circuit itself has a defined input and a defined output terminal and you can't just try and shove something into the output and hope it comes out... | The 120V AC to 5V AC transformer inside your brick works both ways. But that is possible only for AC to AC.
The "problem" is the 5V AC -> 5V DC conversion ("rectification") that happens after the transformer. This one is done by simple diodes and it's that process what's not reversible. You would... | https://electronics.stackexchange.com |
397,648 | [
"https://electronics.stackexchange.com/questions/397648",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/73597/"
] | Can you <code>define</code> a bit slice in Verilog?
For example, is this possible:
<pre><code>`define opcode 5:3 // is this possible?
reg [ 7:0 ] a, b;
...
if ( a[ `opcode ] == someValue ) // a[5:3]
doStuff
if ( b[ `opcode ] == someValue ) // b[5:3]
doStuff
</code></pre>
| You can <code>`define</code> almost any text you want. You would have to use <code>a[`opcode]</code> with the backtick.
SystemVerilog gives you some other options.
The <code>let</code> construct declares a name for an expression.
<pre><code>let opcode = a[5:3];
...
if (opcode==someValue)
</code></pre>
You can use... | Yes, you can.
But it's probably cleaner and easier to simply break the register into fields using wires:
<pre><code>wire [2:0] a_opcode = a[5:3];
if (a_opcode == someValue) ...
</code></pre>
How many different registers are you going to be extracting opcodes from?
| https://electronics.stackexchange.com |
1,791,211 | [
"https://math.stackexchange.com/questions/1791211",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/79594/"
] | I am trying to prove that if $M$ is a $k$-manifold in $\mathbb R^n$, then $TM=\{(p, v): p \in M, v \in T_pM\}$ is a manifold. Here, $T_pM$ is defined as a subset of $\mathbb R^n$.
I know that questions about this problem have already been asked in this website, but my question is very specific:
Let $(p, v) \in TM$ be... | Let's say $a$ other people will vote for party/candidate $A$ and $b$ other people will vote for party/candidate $B$. Presumably their decision is independent of yours (unless this post motivates you to go and try to persuade them to change their mind :-).
If you stay home, candidate $A$ will receive a share $\frac a{a... | The thing about this is if you are not voting and you only for the party x stands for then if you don't vote you are not helping X to reduce Y's lead.
In voting the the number of votes is always limited, so when you vote for X you are reducing Y's 1 vote and increases X's lead.In order to overcome one vote of Y,X needs... | https://math.stackexchange.com |
166,104 | [
"https://softwareengineering.stackexchange.com/questions/166104",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31662/"
] | In our Scrum teams we use a backlog, which mostly contains functional topics, but also sometimes contains technical topics. The advantage of having 1 backlog is that it becomes easy to choose the topics for the next sprint, but I have some questions:
<ul>
<li>First, to me it seems more logical to have a separate tech... | I'm no expert but I'd say you can only have one backlog per team. The team needs to decide which issues are urgent and which ones can be postponed. If you separate the issues into separate types of stacks you go against the core idea that is at the heart of scrum, which is that there is a pool of issues and each sprint... | What you're referring to is commonly called 'technical debt'. It can sometimes be difficult to see how technical debt work fits into the scrum process, in the same way that defects can.
What you are proposing is similar to suggesting that there be a separate 'defect backlog' as well, splitting the backlog into 3.
Per... | https://softwareengineering.stackexchange.com |
18,788 | [
"https://astronomy.stackexchange.com/questions/18788",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/10657/"
] | Is there a way to determine the age of a black hole. Suppose 100 Billion years from now, if two black holes have exactly the same mass(say 30 Mβ). One of them formed 10 Billion years from now and other formed 20 billion years from now. At t = t0 + 100 Billion years, looking back into the past, Can we predict how old th... | From looking at the Black Hole alone, there is no possibility of determining its age. The state of the Black Hole is fully determined by a few fundamental variables (mass, angular momentum and electric charge). This is the statement of the famous dictum <em>A black hole has no hair.</em> Hawking radiation in special is... | No you can't say anything about their ages and yes, their Hawking radiation is different... not that you could detect the difference. In more detail:
If your two black holes began with identical mass, but at different times, the younger hole would have lost less mass than the other through Hawking radiation, with an a... | https://astronomy.stackexchange.com |
76,105 | [
"https://softwareengineering.stackexchange.com/questions/76105",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1928/"
] | Many applications include 'static data': data that doesn't really change during the lifetime of the application. For example, you might have a list of Sales Areas that is likely to be a fixed list for the foreseeable future.
It isn't uncommon to find this static data in a database table (often because you want to refe... | How about load them into a cache (usually implemented as a hash table) when the application starts up? If you do that then you don't even have to query the database (well, not more than once).
I would also suggest avoiding hard-coding anything. Add default indicators (initially in the DB table and also in the cache st... | An alternative to the DB or hard coding is to use a config file read at start-up time. You could then store this data in a read only structure within your code.
IN the rare (but not impossible) case where you edit this data you will have to restart the app. If this is not possible you can write a more complex config m... | https://softwareengineering.stackexchange.com |
1,891,676 | [
"https://math.stackexchange.com/questions/1891676",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/219836/"
] | By definition the PDEs are used to model equilibrium phenomena, involving only spatial variables. Say for example I was given the two-dimensional Laplace equation,$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0$ whose solution is defined on the bounded, open domain $\Omega$ with either of the thr... | You might start by recognizing that $ABD$ and $ADC$ are similar triangles, because they share the angles $\angle DAC$ and $90$ degrees. Therefore,
$$\frac{y}{4} = \frac{z}{x} = \frac{9}{y}$$
We can rearrange $y/4 = 9/y$ to obtain $y^2 = 36$, so $y = 6$, which allows us to answer (b). Then by the Pythagorean theorem,
$$... | You can use just the Pythagorean theorem. There are three right triangles in your picture given by the three right angles (notice that $\angle ABD$ is right). With those three triangles we get the following equations.
\begin{cases}
z^2 = 25 + x^2 \\
y^2 = 16 + x^2 \\
81 = z^2 + y^2
\end{cases}
Substituting the... | https://math.stackexchange.com |
375,242 | [
"https://mathoverflow.net/questions/375242",
"https://mathoverflow.net",
"https://mathoverflow.net/users/64444/"
] | Consider the Cuntz algebra <span class="math-container">$\mathcal{O}_n$</span> with <span class="math-container">$n \geq 2$</span> and let <span class="math-container">$\text{End}(\mathcal{O}_n)$</span> be the set of all (unital) <span class="math-container">$\ast$</span>-endomorphisms of <span class="math-container">$... | This is true: <span class="math-container">$\mathcal O_n$</span> is singly generated, i.e. there exists <span class="math-container">$x\in \mathcal O_n$</span> such that <span class="math-container">$C^\ast(x) = \mathcal O_n$</span>. In particular, if <span class="math-container">$\phi, \psi \colon \mathcal O_n \to B$<... | Although not exactly what the OP has in mind,
there is another interesting characterization of endomorphisms of <span class="math-container">$\mathcal O_n$</span> in terms of single elements. Namely
there is a one-to-one correspondence between endomorphisms of <span class="math-container">$\mathcal O_n$</span> and un... | https://mathoverflow.net |
291,067 | [
"https://electronics.stackexchange.com/questions/291067",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/132067/"
] | I am trying to understand why there is variations in resistance values, in other words, why there is difference in the value of the resistance between color code and the measured resistance. Also, how to manufacture more precise resistors?
| The energy per cycle delivered to the transformer that has the biggest load is determined by the on-time of the switching transistor. During the on-time, the current ramps up (fairly linearly) thus storing energy in that transformer's primary winding. When the transistor turns off, that stored energy is released to the... | If this is about two flyback cores and windings, then the load on the (#1 core) secondary winding may mismatch the load on the (#2 core) secondary winding, leading to different voltage/time during the 'flyback' phase. So, there's no
way to prevent DC currents in one core from changing its inductance, and
ruining the m... | https://electronics.stackexchange.com |
668,638 | [
"https://physics.stackexchange.com/questions/668638",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300178/"
] | We know that the rules of relativistic addition are more complicated than those for simple classical cases. For example, we can have two frames of reference, and if we know the motion of the frames themselves, and the velocity of an object in one frame, we can use the formula to get the velocity of the object in the ot... | The easiest way is to use four-vectors. If an object has three-velocity <span class="math-container">$\mathbf{u} =\begin{bmatrix} u_x \\ u_y \\ u_z \end{bmatrix}$</span> in one frame, its four-velocity is
<span class="math-container">$$\gamma_u\begin{bmatrix} c \\ u_x \\ u_y \\ u_z\end{bmatrix}$$</span>
The general for... | You can use the rest frame of the "object" as one of your reference frames. In your example, you could say that <span class="math-container">$\mathbf{v}_s$</span> is the velocity of the object's frame with respect to the unprimed frame, and <span class="math-container">$-\mathbf{v}_s'$</span> is the velocity... | https://physics.stackexchange.com |
47,485 | [
"https://mechanics.stackexchange.com/questions/47485",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/31974/"
] | My <strong>1999 Honda Accord LX 2.3 4DR</strong> is making a sound like the old days bearings did.
I have a great mechanic who even took it to another mechanic. Neither could say which was bad: the $4,000 transmission or the $700 wheel bearings.
How can I test it myself?
| Normally a wheel bearing hum or rumble will change in intensity depending on whether the bearing is loaded or unloaded...this can be tested at slower speeds (on a clear road) by weaving from side to side to load the bearing races.
If its a manual transmission then the hum/whine of worn mainshaft bearings will increase... | You can test by driving on the road around 30-40 mph and making some swerves left and right. Listen to the sound. If the sound increases swerving to the right, then the left bearing is bad. If it gets louder going to the left, then the right bearing is bad. This is because the weight is being transferred to those wheel... | https://mechanics.stackexchange.com |
155,248 | [
"https://cs.stackexchange.com/questions/155248",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/154263/"
] | I'm trying to find a regular expression to describe the following language:
<span class="math-container">$\{a^n xa^n | nβ₯1,x β Ξ£^* \}$</span>
where <span class="math-container">$Ξ£$</span> = {a,b}
So far I've come up with
<span class="math-container">$aa^* (aUb)^* aa^*$</span>
but I don't think that accounts for <span c... | Your language consists of all words that start with <span class="math-container">$a$</span> and end with a different <span class="math-container">$a$</span>, which yields the regular expression <span class="math-container">$a(a+b)^\ast a$</span>. Note that every word that at first seems <em>unbalanced</em>, e.g. <span ... | Your problem is that your language is not a regular language, so you are not going to find a regular expression, whatever you try. Neither is anyone else.
To see very easily that it is not regular: A regular language has a finite state machine. Now take the strings a^n b for every possible integer n. What is the shorte... | https://cs.stackexchange.com |
257,789 | [
"https://softwareengineering.stackexchange.com/questions/257789",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/124757/"
] | The function foo, has a nested function; bar. Calling foo with a second set of arguments feeds them into bar if bar is returned at the end of foo. How does this work and what is it called?
Are there any uses for it over simply having a single set of arguments that calls the function normally?
<pre><code>def foo(arg1)... | This is called higher-order programming, or, using functions as first-class values. In this case, a function returning a function.
The use of it compared to simply having a single set of arguments only becomes apparent when the "second set of arguments" is not provided, i.e. when <code>foo("hello")</code> is used by i... | I can't speak to the Python-ness of this, but in schemes that frequently use function handlers/callbacks, I'll use your construct for creating these:
<pre><code>def getErrorHandler(message):
def onError(error):
print message + ":" + error
return onError
panicHandler = getErrorHandler("Panic");
warning... | https://softwareengineering.stackexchange.com |
352,985 | [
"https://electronics.stackexchange.com/questions/352985",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/113967/"
] | I have a Hitachi Li-ion charger (without the case) that suppose to charge 10 18650 cells in series (hitachi powertool battery made of 10 high drain cells). That's an official 36V rating of the charger that suppose to deliver at least 42V to fully charge a 10-cell li-ion battery.
The charger was used initially exactly ... | \$R_{\theta JA}\$ is one small part of the story. The main part of the story is \$R_{\theta JC}\$ (at 1.5 Β°C/W), because this is the junction-to-case thermal resistance and it adds to the heatsink thermal resistance to give the lowest (normally) path for heat.
So, if the thermal resistance of the heatsink is (say) 6 Β°... | There is no connection between "circuit is linear" and \$P=(V_{in}-V_{out})*I\$. Your circuit is non-linear because it has non-linear components: a MOSFET, some LEDs and a comparator.
Also, ignoring small losses in the resistors, your circuit has a single contour so \$I_{in}\$ will be the same as \$I_{out}\$ no matter... | https://electronics.stackexchange.com |
12,906 | [
"https://cs.stackexchange.com/questions/12906",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/8880/"
] | Given $m,n\in\mathbb{N}$, finite alphabet $A=\{a,b,c\}$, and $L=\{(a^m,a^n)\}^*=\{(a^{mk},a^{nk})|kβN\}\subseteq A^*\times A^*$.
Is this binary language $L$ regular over $A(2,\$)$ (i.e. $\{Aβͺ\{\$\}\}\times \{Aβͺ\{\$\}\}\setminus \{\$,\$\}$)?
For example, is this binary language $L=\{(a^3,a^7)\}^*=\{(a^{3k},a^{7k})|kβ... | There is no specific formula for calculating it as jmite already mentioned. You have to realize that $\mathcal{O}$ notation serves to merely estimate the number of cycles a certain process takes to execute. It's not an exact representation or quantity.
For instance, lets say you had the following function:
<pre><code... | There is no such formula. If there were, it would solve the halting problem, because we could take an algorithm (Turing machine), find its big-$\Theta$ complexity, then return true or false depending on if it was $\Theta (\infty)$.
For Big-O (upper bounds), there's technically a formula, since all functions are in $O(... | https://cs.stackexchange.com |
52,831 | [
"https://cs.stackexchange.com/questions/52831",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/15072/"
] | So the knapsack problem has an integer programming formulation as follows,
$$ \max_x v\cdot x\\s.t \\x_i \in \{0,1\}\\w\cdot x \leq C$$
Now consider the second integer program which might be a variation of the knapsack integer program.
$$ \max_x v\cdot x\\s.t \\x_i \in \{0,L_i\}\\ x_i \leq R \cdot \delta_i\\ \delta... | A simple greedy approach works here: choose the $k$ elements having maximal $v_i L_i$.
| Yes, the problem can be solved with dynamic programming, in pseudo polynomial time. Let $f(j,k)$ be the largest value attainable for a particular value of $k$ when we constrain to use only the first $j$ elements of $x$ (i.e., when we are constrained to $x_{j+1} = x_{j+2} = \dots = x_d = 0$). Then you can express $f(j... | https://cs.stackexchange.com |
279,223 | [
"https://stats.stackexchange.com/questions/279223",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/48979/"
] | I am a newbie to ML. I was reading about neural networks and was confused about the learning part of the network.
Say there are some classes of images $c_1$ to $c_{k}$ and a neural network is trying to learn to classify a given image into these classes. Further assume that it achieved a very good accuracy(99.999%, wha... | Neural network learns a set of weights, so that when your data is multiplied by them and passed through some non-linear functions, they are able to predict the target variable as actually as possible.
You can argue that this is a low-level answer to your question, but at least it does not give you the false sense of w... | An artificial neural network (ANN) learns in your (supervised) classification problem, just like any other ML model, a function <span class="math-container">$h_{model}$</span> which approximates the 'true' unknown function <span class="math-container">$h_{data}$</span>. These functions map an input image to the set con... | https://stats.stackexchange.com |
73,297 | [
"https://physics.stackexchange.com/questions/73297",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26143/"
] | I have a question about the generalization of gauge transformation with two antisymmetric indices.
Starting from Eq. (3.7.6) in Polchinski's string theory book p. 108.
$$S_{\sigma} = \frac{1}{4 \pi \alpha'} \int_M d^2 \sigma g^{1/2} \left[ \left( g^{ab} G_{\mu \nu}(X) + i \epsilon^{ab} B_{\mu \nu} (X) \right) \parti... | The answer to this question is best understood in terms of differential forms.
Thanks to the antisymmetry of $B_{\mu\nu}$ and $\epsilon^{ab}$, the component $S_B = k \int_M \epsilon^{ab} B_{\mu\nu} \partial_a X^u \partial_b X^\nu$ of the action which contains $B$ can be written $S_B = k\int_M X^*B$, where $X: \mbox{M}... | The variation of the Lagrangian density is :
$$\delta \mathbb L= i\epsilon^{ab} \partial_a X^\mu \partial_b X^\nu(\partial_{\mu} \zeta_{\nu} - \partial_{\nu} \zeta_{\mu}) \tag{1}$$
The chain rule for partial derivatives gives :
$$\partial_a \zeta_{\nu} = \partial_a X^\mu ~~\partial_{\mu} \zeta_{\nu}\tag{2}$$
and... | https://physics.stackexchange.com |
652,507 | [
"https://physics.stackexchange.com/questions/652507",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/290802/"
] | I have been reading about effort to push lasers into the hard X-Ray and soft Gamma Ray range, been quoted as one of the most important problems in physics according to Vitaly Ginzburg.
However, would a coherent light wave in the opposite side of the spectrum be feasible or more challenging than one with such high frequ... | Using polarising beam splitters will produce polarisation fluctuations at the output ports. The polarisation of a single output will vary from linear to circular with a phase shift between the two arms of the interferometer. Normally we measure intensity fluctuations between the two output ports, this requires non-pola... | Use non-polarizing beam splitters if you need to ask.
But if you understand polarization and interference, then by combining polarizing beam splitters and waveplates you can also achieve most effects, and for some applications this is a good way to proceed.
| https://physics.stackexchange.com |
572,626 | [
"https://physics.stackexchange.com/questions/572626",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/239502/"
] | Since clouds exist in lumps and are non-uniformly distributed, one would expect rainfall to be non-uniform as well. But as far as I can tell, rainfall is more or less uniform over a large region.
I suspect that turbulence might be at play here and cause the dispersal of raindrops, but I'm not really sure.
<strong>EDIT<... | Your intuition is correct.
If the sled is not to tip over or otherwise lose contact with the ground, the sum of the vertical forces on the sled must equal zero and the sum of the moments about any point on the sled must be zero.
Neglecting the weight of the rocket, summing the vertical forces give us
<span class="math-... | You are concerned about rotational stability. You have the vertical force equation: <span class="math-container">$N_f$</span> + <span class="math-container">$N_r$</span> - mg = 0 with two unknown N's at the front and rear. Combine that with a torque equation taken about the front support: Hh + <span class="math-contai... | https://physics.stackexchange.com |
52,395 | [
"https://softwareengineering.stackexchange.com/questions/52395",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4942/"
] | Thinking that there might be others, but not sure -- but before getting into that, let me explain what I mean by static and dynamic data sources.
<ul>
<li><strong>Static</strong> (or datastore) - Meaning that the data's state is non-changing, and if was changed, that would be a new state, and the old data would be con... | To me there are as many types of data as what you want to do with them. All data whether you call it static or dynamic is meant to change. The thing you need to know is how it changes and what you need to do when it changes.
You can think of the most static data as constants. If you can guarantee that some data will n... | The terms <em>static</em> and <em>dynamic</em> can refer to many different things in computing (memory allocations, typing systems, etc), so you'll probably want to use different terminology. In finance, we have <strong>historical</strong> data and <strong>streaming</strong> data, though the distinction isn't based on ... | https://softwareengineering.stackexchange.com |
1,929,124 | [
"https://math.stackexchange.com/questions/1929124",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/58675/"
] | Can someone please help me find the limit of this equation?
$$\lim_{n\to\infty}\log_{4n^2-2}\left(1-\frac{5n^2-7n+3}{8n^2-8n+2}\right)+2$$
| It is not a counterexample, since you can take
$$
S = \{(x,x+z,z) \mid y\in\mathbb{R}\}.
$$
Let us show that this subspace satisfies $U\oplus S=\mathbb{R}^{3}$ (the other is similar).
A basis for $U$ consists of the vector $(1,0,0)$. A basis for $S$ consists of $(1,1,0)$ and $(0,1,1)$.
You can easily chech that $A=(1... | The assertion in title is true in the more general context of finite dimensional spaces.
$\Rightarrow$ is true because $\dim V= \dim U+\dim S=\dim W+\dim S$.
$\Leftarrow$: if $\dim U=\dim W<\dim V$, we have to find a subspace $S$ such that $\;U\oplus S=W\oplus S=V$.
By the <em>avoidance lemma</em> for vector spac... | https://math.stackexchange.com |
340,620 | [
"https://physics.stackexchange.com/questions/340620",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/159692/"
] | I got a task, I don't quite know how to solve.
<blockquote>
I've got the following Hamiltonian:
$$
\hat H = \frac{B}{\hbar^2}\hat{\mathbf S}_1\cdot \hat{\mathbf S}_2+\frac{C}{\hbar}\left(\hat S_{1z}+\hat S_{2z}\right), \qquad \hat{\mathbf S}_{j=1,2}=(\hat S_{jx},\hat S_{jy},\hat S_{jz}).
$$
($B,c$ constants)
... | It's mostly about frequency. The feel sensors in your skin have low frequency capability. At high frequencies, they feel only the average.
The average of a sustained sound is 0. You said yourself "<b>±</b>200 Pa". The ± part means that there are both positive and negative pressure peaks. Averaged to... | Whenever you're dealing with human experience, you must avoid mistaking a stimulus with the sensation it causes. In a room at 60 degrees Fahrenheit, a metallic table feels colder than a wooden table, even though their temperatures are the same; that's because you don't experience the temperature of an object, but rath... | https://physics.stackexchange.com |
1,599,120 | [
"https://math.stackexchange.com/questions/1599120",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/189192/"
] | I have to test the convergence of the following series:-
$$\sum_{n=1}^\infty\sqrt[3]{n^3+1}-n$$
My approach is as follows :-
$$n^3+1>1=\sqrt[3]{n^3+1}>1=\sqrt[3]{n^3+1}-n>1-n$$
Now since$\sum 1-n$ diverges, the series under consideration diverges.
Is this right or wrong?
| <strong>Hint</strong>
Let $a=\sqrt[3]{n^3+1}$ and $b=n$. Then,
$$a-b=\frac{a^3-b^3}{a^2+ab+b^2}=\frac{1}{a^2+ab+b^2}.$$
Observe that $a \geq b$, therefore
$$\sqrt[3]{n^3+1}-n=a-b \leq \frac{1}{3b^2}=\frac{1}{3n^2}.$$
Now use comparison to claim convergence.
| Itβs actually convergent. Treat your general term $\sqrt[3]{n^3+1}-n$ as a fraction with $1$ underneath, and then multiply top and bottom by
$\bigl(\sqrt[3]{n^3+1}\,\bigr)^2+n\sqrt[3]{n^3+1}+n^2$. Use the fact that $\sqrt[3]{n^3+1}>n$ as well.
| https://math.stackexchange.com |
3,899,341 | [
"https://math.stackexchange.com/questions/3899341",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/820898/"
] | I need to prove <span class="math-container">$((0,1)\cap\mathbb{Q})\cup((2,3)\cap\mathbb{Q}) $</span> is isomorphic to <span class="math-container">$(0,10)\cap\mathbb{Q}$</span>. I have tried by looking for a bijective relation between sets and Yi think my best try has been a piecewise function:
<span class="math-conta... | Let <span class="math-container">$a_n=1-\frac1n$</span> and partition <span class="math-container">$(0,1)$</span> as
<span class="math-container">$$(0,1)=\bigcup_{n=1}^\infty (a_n,a_{n+1}].$$</span>
Likewise, let <span class="math-container">$b_n=2+\frac1n$</span> and partition
<span class="math-container">$$(2,3)=\big... | First, find an irrational "hole" in <span class="math-container">$(0,10)$</span>, let's say <span class="math-container">$Z=\pi$</span>.
Can you now construct an order-preserving bijection of <span class="math-container">$(0,1)\cap\mathbb Q$</span> to <span class="math-container">$(0,Z)\cap\mathbb Q$</span>? ... | https://math.stackexchange.com |
3,530,515 | [
"https://math.stackexchange.com/questions/3530515",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/746608/"
] | Vector space <span class="math-container">$V = \Bbb{R}^4$</span> with the Sub-spaces
<span class="math-container">$W_1=$</span>{<span class="math-container">$(x,x+y,x+z,z)|x,y,z \in \Bbb{R}$</span>}
<span class="math-container">$W_2=$</span>{<span class="math-container">$(a,b,a,b)|a,b \in \Bbb{R}$</span>}
choose on... | <span class="math-container">$$I=\int_{0}^{e^{\pi}}|\cos (\ln x)| dx= -\int_{-\infty} ^{\pi} e^t~ |\cos t| dt$$</span>
<span class="math-container">$$\implies I=-\int_{-\infty}^{0} e^{t} |\cos t|~ dt-\int_{0}^{\pi/2} e^{t} \cos t ~dt+\int_{\pi/2}^{\pi} e^{t} \cos t~ dt$$</span>
<span class="math-container">$$\implies I... | Here's a solution based on GEdgar's hint.
<span class="math-container">$$\begin{aligned}
\int_0^{e^{\pi}} |\cos (\ln x) |\; dx &= \int_{-\infty}^{\pi} |\cos u |\; e^u \; du\\
&= \int_{\pi/2}^{\pi} |\cos u |\; e^u \; du +\sum_{k = 0}^{\infty} \int_{-k\pi -\pi/2}^{-k\pi +\pi/2} |\cos u |\; e^u \; du \\
&= \l... | https://math.stackexchange.com |
78,419 | [
"https://physics.stackexchange.com/questions/78419",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23635/"
] | I'm reading and working my way through "Plasmonics Fundamentals" by Stefan Maier and I've come across a step in the workings that I'm struggling to understand when working out the electromagnetic field equations at a dielectric-conductor interface. At the stage I'm stuck there are six coupled equations for the field co... | Bare with me, I don't remember every little step, but I hope this derivation helps you.
First remember how a wave travels through a waveguide (dielectric).
$$ E(x,y,z) = E^{0}(x,y)e^{-\gamma z}$$
$$ H(x,y,z) = H^{0}(x,y)e^{-\gamma z}$$
Then consider Ampere's and Faraday's Laws for a source-free region. $$ \triangled... | Hints:
<ol>
<li>We are evidently only supposed to solve for $z$-dependence (as opposed to $x$- and $y$-dependence).</li>
<li>Note that the two variables $E_z$ and $H_z$ can be eliminated.</li>
<li>In the reduced coupled ODE system of four first-order ODEs and four variables $(E_x,E_y,H_x,H_y)$, note that the variables... | https://physics.stackexchange.com |
216,312 | [
"https://softwareengineering.stackexchange.com/questions/216312",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15950/"
] | I have a web application that I expect to go viral pretty quickly.
How can I control traffic to it so that it doesn't crash under too much load?
This application doesn't require user login.
It will be properly load tested, but I am not really sure what kind of traffic to expect until I make it live.
| It is harder to control without a login.
Another option is to protect the site with an "access key" that you can then give out to your beta users. I personally don't like these and they will inhibit initial expansion of your site since all users will need this key and the site won't be indexed by Google etc.
Your be... | What is your bottleneck?
Assuming that bandwith is your problem, e.g. by serving high-res images, then using a CDN will be beneficial.
If your site is computationally expensive, then load-balancing between multiple servers sounds like the way to go. Hosting your webapp in a cloud will make this scaling easier, and yo... | https://softwareengineering.stackexchange.com |
395,012 | [
"https://mathoverflow.net/questions/395012",
"https://mathoverflow.net",
"https://mathoverflow.net/users/138274/"
] | In <span class="math-container">$\mathbf{ZF}$</span>, it is possible for a set <span class="math-container">$A$</span> to be infinite but not to admit a countable set. In other words, for any <span class="math-container">$\alpha\in\omega$</span>, there is an injection from <span class="math-container">$\alpha$</span> i... | Start with your favourite model of <span class="math-container">$\sf ZFC$</span>, your favourite regular cardinal <span class="math-container">$\mu$</span>, and your favourite limit cardinal <span class="math-container">$\lambda>2^\mu$</span>.
Now consider the <span class="math-container">${<}\mu$</span>-support ... | Yes, it is possible; one can see this by a variant of a standard proof of the consistency of ZF + <span class="math-container">$\neg$</span>AC, as witnessed in symmetric submodels of forcing extensions. Start with universe <span class="math-container">$V=L$</span>. Let <span class="math-container">$\lambda$</span> be a... | https://mathoverflow.net |
54,915 | [
"https://dsp.stackexchange.com/questions/54915",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/39075/"
] | (From Schaum's Outlines, DSP, second edition, problem 5.25, second part of problem)
What's the procedure to find the Phase and Group Delay of:
<span class="math-container">$$
H(e^{j\omega}) = e^{-j\theta}\left( \frac{e^{-j(\omega-\theta)}- |\alpha|
}{1-|\alpha|\ e^{-j(\omega - \theta)}} \right)
$$</span>
Book says t... | Define a frequency response
<span class="math-container">$$\tilde{H}(e^{j\omega})=\frac{e^{-j\omega}-|\alpha|}{1-|\alpha|e^{-j\omega}}\tag{1}$$</span>
and note that the group delay <span class="math-container">$\tilde{\tau}(\omega)$</span> corresponding to <span class="math-container">$(1)$</span> is related to the g... | Just apply the definitions.
<span class="math-container">$$\begin{align}
H(e^{j\omega}) &= \Re\Big\{H(e^{j\omega})\Big\} + j \Im\Big\{H(e^{j\omega})\Big\} \\
\\
&= \Big| H(e^{j\omega}) \Big| e^{j \arg\{H(e^{j\omega})\}} \\
\\
&= \Big| H(e^{j\omega}) \Big| e^{j \phi(\omega)} \\
\end{align}$$</span>
Wher... | https://dsp.stackexchange.com |
43,577 | [
"https://datascience.stackexchange.com/questions/43577",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/65425/"
] | I'm starting my machine learning study and I'm trying to figure out a simple question:
Let's say that I have two models, one that recognizes cats, and another one that recognize dogs.
Now I have a camera and I want to recognize both cats and dogs using my models.
Obviously, I don't want to create a third model to ... | There could a skewed power envelope or non-stationary data. As a result, off-the-shelf feature scaling could attenuate the signal.
There are feature scaling techniques that tend to work better for audio signals, examples include: RMS level (Root Mean Square Level), Cepstral Mean Subtraction (CMS), RelAtive SpecTrAl (R... | Your results sound like your classifier is not working at all assuming your classes are evenly distributed.
Are you applying the regularization to the entire data set or the fields that have the larger magnitude? If to the whole data set, I would only apply to the fields with the greater magnitude.
While some NNs are... | https://datascience.stackexchange.com |
369,850 | [
"https://softwareengineering.stackexchange.com/questions/369850",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29526/"
] | I'm looking for some advice about which line of code is more appropriate, readable, and maintainable.
<h1>1:</h1>
<pre><code>var result = mediator.Send(query).Result;
</code></pre>
<h1>2:</h1>
<pre><code>var accountDetails = mediator.Send(accountFilter).Result;
</code></pre>
The above code was taken from a Web API... | Short answer: <strong>No</strong>
Long answer:
No, vague names are far less maintainable than precise names. You won't rename things on a weekly basis (and if you do, you should ask yourself "What is the reason for this"). Changing the result type is a rather big change, so if I were to get a <code>detailProxyBroker</... | IMHO most of your "pro" arguments are flawed, but let us discuss them one-by-one:
<blockquote>
If the query needs to change and return a different type, we don't have to remember to rename the result variable.
</blockquote>
If the query returns a different type in such a way that a name like <code>accountDetails</c... | https://softwareengineering.stackexchange.com |
242,250 | [
"https://mathoverflow.net/questions/242250",
"https://mathoverflow.net",
"https://mathoverflow.net/users/801/"
] | I am interested in a particular group $G$, where
$$ (A_4\times C_\ell) \lhd G \lhd S_4 \times D_\ell$$
Here, $C_\ell$ is cyclic, $D_\ell$ is dihedral of order $2\ell$, and the two inclusions both have index $2$. Since
$$ (S_4\times D_\ell)/(A_4\times C_\ell) \cong C_2\times C_2,$$
my description of $G$ could be one of ... | This is all about Clifford's theorem in the complex case, which I treat in detail. The Klein $4$ subgroup that is acting on $A_{4}\times C_{\ell}$ contains three involutions: one inverts the $C_{\ell}$ but centralizes the $A_{4}$, one induces the outer automorphism of $A_{4}$, but centralizes the $C_{\ell}$, and the th... | Your group is a semidirect product of $S_4$ with the abelian group $C_\ell$. The action is $\pi x \pi^{-1}=\text{sign}(\pi) x$ (where $C_\ell$ is written additively). So over an algebraically closed field the Mackey machine gives you all irreducible representations: they are classified by pairs $(\chi,\zeta_\ell^i)$ wh... | https://mathoverflow.net |
17,881 | [
"https://stats.stackexchange.com/questions/17881",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2526/"
] | A usual test of significance when looking a two populations is the t-test, paired t-test if possible. This assumes that the distribution is normal.
Are there similar simplifying assumptions that produce a significance test for a time series? Specifically we have two fairly small populations of mice that are being trea... | p*, the threshold below which we would reject the null hypothesis, is normally written as $\alpha$, and is known as the false-positive rate. A "false-positive" error is the error of rejecting the null hypothesis when it is actually true, and is also called a "Type-I" error. However, the interpretation of $\alpha$ mus... | "By accident" is not well defined here. The p-value is the chance of getting results as extreme or more extreme than those you got in a sample if the null hypothesis is true in the population.
| https://stats.stackexchange.com |
123,121 | [
"https://chemistry.stackexchange.com/questions/123121",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/72973/"
] | What is the relationship between the three concepts in the title?
I know all centrosymmetric molecules are achiral, but not all achiral molecules are centrosymmetric. Thus, there are no molecules that are centrosymmetric and chiral, but all other combinations exist.
What about having a dipole moment vs. centrosymmetr... | A molecule can't be chiral if it has an <span class="math-container">$S_n$</span> improper rotation (note that <span class="math-container">$S_1$</span> is equivalent to a mirror plane and <span class="math-container">$S_2$</span> is equivalent to inversion). Chirality is only possible in the <span class="math-containe... | Concerning chirality, the best link is to remember that any molecule that has an improper rotation symmetry (an <span class="math-container">$S_n$</span> axis in the Schoenflies notation or <span class="math-container">$\overline n$</span> in Hermann-Mauguin notation) is achiral. <span class="math-container">$S_1$</spa... | https://chemistry.stackexchange.com |
373,804 | [
"https://electronics.stackexchange.com/questions/373804",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/131848/"
] | I recently joined a small startup as the only HW designer (working in Altium 18) and am looking for ways to optimize my design time without having access to a full-fledged CAD team. In my previous jobs there was always a dedicated team of people who would manage libraries and design parts upon request. In my current si... | I use Eagle instead of Altium, but I don't think that makes a difference to this answer.
I would never use someone else's parts, no matter how "official" they are. Maybe it's different in Altium, but in Eagle it's not really all that hard to make parts. Vetting someone else's would probably take about the same time,... | 1) I always design my own parts libraries. I like the ability to keep styles consistent between designs. You don't get this with third party libraries. It's a bit of a pain at the beginning, but once you get the basic parts done you only find yourself making new ones every now and again, and it's really not an issue fo... | https://electronics.stackexchange.com |
144,830 | [
"https://physics.stackexchange.com/questions/144830",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | So today I was asked a question which I found very simple yet I honestly couldn't explain (embarrassingly).
One of my mum's friends who knows I'm a scientist asked me "If I turn the light off in a room why does the light instantly disappear"
To phrase it up in a more scientific way :
If we took a box of light and s... | The solution boils down to examining what is meant by the term <em>instantly</em> in:
<blockquote>
<em>"If I turn the light off in a room why does the light instantly disappear"</em>
</blockquote>
All of the visible photons in the box cannot instantly disappear since the information about the source going out only ... | As time passes there is a fast aborption of photons by the cavity walls (or the walls of the room) followed by the emission of photons of longer wave lengths (infra-red radiation) which we do not see. That's why it becomes dark.
Of course, if the cavity isn't completely sealed up there will be radiation loss to the un... | https://physics.stackexchange.com |
4,111,803 | [
"https://math.stackexchange.com/questions/4111803",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/455717/"
] | Assume that <span class="math-container">$U$</span> is a random variable on <span class="math-container">$(β¦,\mathcal{F},P)$</span> with <span class="math-container">$UβΌU[0,1]$</span>. Let <span class="math-container">$Y= \min(U,1βU)$</span>. I am asked to find <span class="math-container">$E(U\mid Y)$</span>.
I have f... | Here is a short proof which makes use of symmetry.
Let <span class="math-container">$A\in \sigma(Y)$</span> and write <span class="math-container">$A=Y^{-1}(B)$</span> for some Borel set <span class="math-container">$B$</span>, so that <span class="math-container">$1_A=1_{Y\in B}$</span>.
Note that <span class="math-co... | "Single-line" way of computing this conditional expectation. Let <span class="math-container">$Y=U\wedge(1-U)$</span>. For <span class="math-container">$y\in(0,1/2)$</span>,
<span class="math-container">$$
\mathsf{E}[U\mid Y=y]=\lim_{\epsilon\downarrow 0}\frac{\mathsf{E}[U1\{Y\in [y-\epsilon,y+\epsilon]\}]}{\... | https://math.stackexchange.com |
416,443 | [
"https://physics.stackexchange.com/questions/416443",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Quantities like position and time allow us to place our <em>origin</em> anywhere, but can the same be said for energy? I was thinking about the way we have defined the quantity gravitational potential, and for any finite distance from a 'planet' or a body, an abject would be said to have negative gravitational potentia... | To be honest, signs don't exist. Energies don't exist. They are merely methods or models or descriptions invented for us to describe forces, tendencies, absorption of radiation, impacts, vibrational motions, directions etc. So, does <em>negative</em> energy exist? We can just invent it, like you just described for the ... | The question about "existence" is philosophical one, not a physics one. Some people would argue that you can't be sure about the existence of anything, including yourself.
Physics is concerned with creating mathematical models that can make predictions about the outcome of a experiment or situation. All physical mode... | https://physics.stackexchange.com |
168,720 | [
"https://dba.stackexchange.com/questions/168720",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/120889/"
] | <h3>Table Animal</h3>
has following columns:
<ol>
<li><code>SR_ID</code></li>
<li><code>First_Name</code></li>
<li><code>Last_Name</code></li>
<li><code>PET</code></li>
</ol>
The <code>PET</code> column has a check constraint; hence it only accepts three values DOG, CAT, FISH.
<h3>Sample Data</h3>
<pre><code>+-------+-... | You can check the condition of the check constraint from <code>all_constraints</code> or <code>user_constraints</code> view.
<pre><code>SQL> create table animal(
SR_ID number,
First_Name varchar2(20),
Last_Name varchar2(20),
PET varchar2(20) constraint ckpet check (PET in ('DOG', 'CAT', 'FISH'))
);
Table creat... | There are three things that can go on in the background:
<ol>
<li>The column has a check constraint, which lists the allowed values</li>
<li>There's a referential integrity constraint linking that column to another table, which gives the allowed values</li>
<li>A trigger at insert or commit checks the supplied values ... | https://dba.stackexchange.com |
65,165 | [
"https://physics.stackexchange.com/questions/65165",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20327/"
] | Consider the following statement:
<blockquote>
If we know that the system is in the ground state, then the temperature is zero.
</blockquote>
How does this follow from the statistical definition of temperature?
| Mad props for a cool question. I'm going to justify essentially the converse of the statement because it doesn't make much sense to talk about the temperature of a system that is in a pure state.
Let's assume that we're talking about a quantum system with discrete energy spectrum (with no accumulation points) in ther... | Here I will provide an answer from the point of view of equilibrium density matrix:
<ul>
<li>The eigenequation of Hamiltonian <span class="math-container">$\hat H$</span>:
<span class="math-container">$$\hat{H}|\phi_n\rangle = E_n|\phi_n\rangle \qquad (n=0,1,2,\cdots) \tag{1}$$</span></li>
<li>The spectrum decompositio... | https://physics.stackexchange.com |
191,072 | [
"https://dba.stackexchange.com/questions/191072",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/138716/"
] | I have a query that is being made 18x slower by the presence of a single <code>WHERE</code> clause. The query plan is an index-only scan and the clause in question looks at one of the fields in the index.
This is the query and the offending clause is <code>update_id < 40581</code>:
<pre><code>EXPLAIN (VERBOSE, AN... | This kind of makes sense if your data are distributed in certain way. Without the <code>update_id < 40581</code> condition the very first entry in the index that matches <code>account_id = '1' AND attr1 = '' AND attr2 = 3 AND attr3 = 'ABC'</code> satisfies the <code>LIMIT</code> clause, because the entries are order... | There is something really weird going on here. Let's look at two lines
Slow:
<pre><code> -> Index Only Scan using updates_covering_idx3 on public.updates (cost=0.69..777.72 rows=1825 width=39) (actual time=0.782..0.782 rows=1 loops=18102)
Output: updates.time, updates.update_id, update... | https://dba.stackexchange.com |
347,585 | [
"https://electronics.stackexchange.com/questions/347585",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/173383/"
] | I have found several projects on piezo preamps but I cant find anything that can run 2 piezo inputs to make it stereo and uses potentiometer to control volume gain etc.<br><br>
What I found is "Collinβs Lab: DIY Contact Mic" from make magazine website that uses an MPF102. <br><br>
<img src="https://i2.wp.com/cdn.makezi... | <ol>
<li>Common GND , +9V and 10uF decoupling capacitor do well in stereo version</li>
<li>It would be useful not to add the output impedance of the preamp, so replace the 1.5kOhm resistor with the volume pot. Use logarithmic pot. 2200Ohm should be ok. Connect 4.7uF cap to the slider and the low volume end connector of... | Sure, you can make two circuits with a shared power source.
To change your volume, I wouldn't recommend modifying the existing circuit, I suggest connecting an op-amp amplifier with volume control after the preamp.
To control the balance, you can then modify the volume of individual channels.
To power the circuit wi... | https://electronics.stackexchange.com |
21,449 | [
"https://mechanics.stackexchange.com/questions/21449",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/12422/"
] | First post and I'm flummoxed. I have an 2009 Lexus RX350 AWD. At speeds of 70-75 one can feel the steering wheel vibrate fast. At 80mph(for testing purposes) it largely disappears. Back down to 65 the vibration in the steering dissapates greatly but one can still feel the front wheels shake.
I've done the following:
... | Have you tried swapping the front and rear wheels, you could have one slightly bent wheel.
| Paul & Handy I Did as you suggested and I was hoping for the best. Front tires to back and back to front. Made no difference. I had them install the Michelin premiere a/s and the vibration ceased. Gone. VERY happy camper. It's odd as I have the Continental control contacts on my wife's IS350C sports/ touring, car ... | https://mechanics.stackexchange.com |
735,871 | [
"https://physics.stackexchange.com/questions/735871",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/350367/"
] | If an object is of constant angular velocity, then we can derived the closed form formula of rotation matrix thanks to the theory of linear ODEs (and the closed form of <span class="math-container">$e^{[\omega]}$</span>):
<span class="math-container">$$R' = [\omega] R \Rightarrow R = e^{[\omega]t}R_0$$</span>
However, ... | You're basically asking how to find the equation to the equation
<span class="math-container">$$
\frac{d\mathbf{R}}{dt} = M(t) \mathbf{R}.
$$</span>
It can be shown that the answer can always be written as
<span class="math-container">$$
\mathbf{R}(t) = U(t) \mathbf{R}(0),
$$</span>
for a linear operator <span class="m... | Sure. The shape of the matrix that produces the rotation is the same. It's the standard [cos - sin sin cos] thing. The angle simply changes. For constant angular velocity the angle is just <span class="math-container">$wt$</span>. For constant acceleration it's just <span class="math-container">$\frac{1}{2} a t^2 + wt... | https://physics.stackexchange.com |
72,874 | [
"https://physics.stackexchange.com/questions/72874",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5248/"
] | I understand the lagrangian formulation of classical mechanics, to a degree. I can derive the Euler-Lagrange equations from the "least" action principle, and equivalently can determine the equations of motion from a given lagrangian. I can handle lagrangian exercises in textbooks with ease.
I don't quite grok it, thou... | First I want to remind you what is going on behind the scenes. You know where the particle is at some initial time $t_1$, and you know where the particle is at some final time $t_2$, and the question you are asking is, which path will get me from the initial position at the initial time to the final position at the fin... | When you get a nonsensical equation of motion like this, it means that the action has no local extrema over the space of all possible paths. (Like how the curve $y = x$ has no local minimum or maximum.) There's no path $x(t)$ such that varying the path produces only a second-order (or higher) variation in the action.
... | https://physics.stackexchange.com |
62,213 | [
"https://security.stackexchange.com/questions/62213",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/41746/"
] | Let's say that our first firewall has some vulnerability and a malicious person is able to exploit it. If there's a second firewall after it, he/she should be able to stop the attack, right?
Also, what will be the side-effects? I mean, would this slow the traffic or not? What are other possible effects like this one?
... | <img src="https://i.stack.imgur.com/JjaRg.png" alt="DMZ">
There are both advantages and disadvantages having two firewalls. While firewalls are not commonly exploited, they are prone to denial of service attacks.
In a topology with a single firewall serving both internal and external users (LAN and WAN), it acts as a... | As a rule, No.
Firewalls aren't like barricades that an attacker has to "defeat" to proceed. You bypass a firewall by finding some path through that isn't blocked. It's not so much a matter of how many obstacles you put up but rather how many pathways through you allow. As a rule, anything you can do with two... | https://security.stackexchange.com |
134,219 | [
"https://electronics.stackexchange.com/questions/134219",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5778/"
] | Is there any way to combine 2 (or more) similar LDOs with fixed output voltage so the total output current would be increased?
Buying another LDO is possible but I have a large stock of 1A LDOs and I need 3A.
| Tying multiple LDO's together is a bad idea. No two are going to have exactly the same output voltage regulation point. One will take more of the load than the other, possibly stressing it more than it should be.
No, you can't assume you know the temperature response of a regulator only because you think you know so... | There are multiple solutions you might want to consider:
<ul>
<li>using a pass transistor that can handle your required current with a single LDO</li>
<li>using ballast resistors to absorb some of the voltage variance between multiple LDOs</li>
<li>adding a current monitoring circuit to control each LDO and adjust its ... | https://electronics.stackexchange.com |
163,775 | [
"https://mathoverflow.net/questions/163775",
"https://mathoverflow.net",
"https://mathoverflow.net/users/49750/"
] | Assume that $G$ is a finite $p$-group, $p$ odd, with a non-trivial elementary abelian Frattini subgroup. Then both $\Phi(G)$ and $G/ \Phi(G)$ are vector spaces over $\mathbb{F}_p$. Is it possible to get a bound for $\dim \Phi(G)$ as a (polynomial) function of $\dim G / \Phi(G)$?
Edit: I should probably write a little ... | There can be no polynomial bound which is independent of $p$. Consider the group $G = C_{p} \wr C_{p},$ where $C_{p}$ denotes the cyclic group of order $p.$ Then $\Phi(G) = G^{\prime}$ has order $p^{p-1},$ (and is elementary Abelian) yet $[G: \Phi(G)] = p^{2}.$
| For your second question the answer is yes. The bound follows from Schreier's inequality: if $\Phi(G)$ has index $p^d$, then it follows that $\Phi(G)$ can be generated by $p^d(d-1)+1$ elements. Note that this is true without assuming that the Frattini subgroup is elementary abelian.
Your first claim is true for the ... | https://mathoverflow.net |
653,909 | [
"https://physics.stackexchange.com/questions/653909",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/294608/"
] | A closed laboratory is in perfect free fall and hence is an inertial frame. This lab is falling toward the event horizon of a Black Hole. The lab is sufficiently small and the event horizon is sufficiently large such that tidal effects can be ignored. The physicist is initially unaware of the lab's proximity to the eve... | According to the phase diagrams in the link, if you start with liquid water at, say, 20Β°C and 1 atm and cool it, maintaining phase equilibrium, the liquid will shrink and evaporate (at the top, in a gravity field) to maintain a pressure of 3.2 kPa, dropping to 0.6 kPa at 0Β°C. (The liquid will start to expand at 4Β°C but... | You can use the phase diagrams from the previous Q/A you linked.
Generally, if the pressure drops outside of what a phase can sustain at a certain temperature, another phase appears in order to "fix" the pressure to a value acceptable for both phases.
If you start with like e.g. 100C water at 1 bar pressure, ... | https://physics.stackexchange.com |
75,566 | [
"https://softwareengineering.stackexchange.com/questions/75566",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/20636/"
] | Some advice here,
I've run into a system where the DAL contents of hundreds of sql command calls are split up on a class per table. There are also a Business layer which get it's data from this DAL, recieving it further to other methods and layers in other places.
Nearly 100% of those Business Methods are pure forw... | No, Static Methods are very difficult to mock or handle via dependency injection, which you probably want to testing purposes at least.
| <blockquote>
I mean static methods need to be in
heap
</blockquote>
Huh?
Static methods may indicate a less than desirable design, but they could not in and of themselves the source of any significant performance issues. There is more overhead to an instance method.
Design usually suffers from use of static met... | https://softwareengineering.stackexchange.com |
1,000,188 | [
"https://math.stackexchange.com/questions/1000188",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/188852/"
] | <blockquote>
Of two kinds of alloy, silver and copper are contained in the ratio of $5:1$ and the other in $7:2$. What weights of the two alloys should be melted and mixed together so as to makeup a $5$ lb mass with $80\%$ silver.
</blockquote>
I am stuck with the <em>$5$ lb mass with $80\%$ silver</em> as to what I... | Let $a_1$ be the amount of alloy 1 used and $a_2$ be the amount of allow two used.
Clearly $a_1 + a_2 = 5$. This is one equation.
The first alloy is $\frac{5}{6}$ silver and the other is $\frac{7}{9}$ silver. We want the final allow to be $80\%$ silver.
This gives us a second equation (the weight of silver from $a_... | Call the two weights $x$ and $y$. Then
\begin{align}
x+y & = 5, \tag{total weight} \\[8pt]
\frac 5 6 x + \frac 7 9 y & = \frac 4 5 (x+y). \tag{silver weight}
\end{align}
The common denominator in the second equation is $90$. Multiplying both sides of that equation by $90$ yields
$$
75 x + 70 y = 72 (x+y).
$$
... | https://math.stackexchange.com |
4,750 | [
"https://dba.stackexchange.com/questions/4750",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2928/"
] | My question consists of three parts:
When can I be sure that my database design is perfect?
<hr>
Is returning to the database design to change some issues (i.e, adding new column, deleting a column, changing data type, add new table, etc.) considered a bad practice or is it normal?
<hr>
Are there any websites or b... | 1) When to be sure that your database design is perfect?<br>
Your design is never perfect because the business logic and amount of data is always changing. Perfect is difficult to define
I've seen systems that were great on deployment but had poor performance after a few years of data were added. The regrettable tre... | <ol>
<li>It isn't. But because the database is usually foundational to the business (eg applications are built on top of it), it is worth working hard to get it in the best shape you can. "best" is a practical consideration and depends on your needs, not a measure of theoretical or ideological perfection.</li>
<li>Requ... | https://dba.stackexchange.com |
310,422 | [
"https://softwareengineering.stackexchange.com/questions/310422",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/207585/"
] | I have written a struct that represents latitude/longitude coordinates. Their values range from -180 to 180 for longtitudes and 90 to -90 for lattitudes.
If a user of that struct gives me a value outside of that range, I have 2 options:
<ol>
<li>Throw an exception (arg out of range)</li>
<li>Convert the value to the ... | If the core of your question is this...
<blockquote>
If some client code passes an argument whose value is invalid for the thing that my data structure is modeling, should I reject the value or convert it to something sensible?
</blockquote>
...then my general answer would be "reject", because this will help draw a... | It depends a lot. But you should <strong>decide</strong> to do something and <strong>document it</strong>.
The only <em>definitively wrong</em> thing for your code to do is to forget to consider that user input might be outside the expected range, and write code that accidentally has some behaviour. Because then some ... | https://softwareengineering.stackexchange.com |
96,016 | [
"https://physics.stackexchange.com/questions/96016",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/87745/"
] | I read in HC Verma that if we are observing the motion of a body from a rotating frame and the body under the observation is NOT in motion with respect to our frame then the centrifugal force is the sufficient pseudo force for the analysis of the motion. But if the body under observation is in motion with respect to ou... | I show you a typical situation where the centrifugal force is not enough to explain the dynamics.
Suppose the reference frame $K$ is rotating around the $z$ axis of an inertial reference frame $K_0$ with $\omega = \Omega {\bf e}_z$ and $\Omega>0$ constant.
Consider a point of matter $P$ at rest in $K_0$ far from ... | Another psuedo-force is the <strong>Azimuthal Force</strong> (Sometimes called <strong>Euler's force</strong>) it arises when there is angular accleration. It's vector equation is <span class="math-container">$$F_{Azimuthal}=\mathbf{r} \times \mathbf{\alpha}$$</span>, where <span class="math-container">$\mathbf{\alpha}... | https://physics.stackexchange.com |
97,424 | [
"https://stats.stackexchange.com/questions/97424",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/43750/"
] | Iβd like to illustrate my problem with a little (heavily abbreviated) excercise. I think it will help a lot to stress my point.
Meet Mary, Tom
and Jane. They all are programmers. Mary is a decent programmer. In
writing five programs she usually makes about 3 mistakes. Tom on the other
hand is quite bad. He makes abou... | The unnormalized posterior (prior times likelihood, i.e., the numerator) in your example is
\begin{equation}
f(X=2\mid \mu)\cdot P(\mu) = \left\{
\begin{array}{c}
\frac{\mu_j^2}{2}e^{-\mu_j} \cdot P(\mu_j), & \quad ~\mu=\mu_j,j\in\{1,2,3\} \\
0, & \quad \mu \notin \{\mu_1,\mu_2,\mu_3\}
\end{array}
\right.... | There's no point in taking the derivative to find the mode! To find the MAP, you only have to evaluate the posterior at the three possible values of $\mu$. Similarly to find the MLE, you only have to evaluate the likelihood at three possible values of $\mu$. The MAP and the MLE will not in general be the same. To s... | https://stats.stackexchange.com |
152,340 | [
"https://chemistry.stackexchange.com/questions/152340",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/100790/"
] | Yes, atomic masses are non-integral due to isotopes and binding energy. These are the two reasons I found on google and other answers on stackexchange.
But there is something else - isn't the most obvious reason for it the way atomic masses are calculated? We defined 1 amu as one twelfth the mass of a C-12 atom. Now C-... | Yes this is a valid reason, albeit a small one, almost negligible. After all, 1amu and the masses of 1 proton and 1 neutron are pretty close to each other.
Then again, the binding energy would also be negligible, if not for oxygen's <span class="math-container">$15.999$</span> which catches the student's eye right away... | The mass difference between a bare proton and a bare neutron is 1293 keV, while the mass of an electron is 511 keV. That means that the effect you're talking about is often going to be on the same order of magnitude as the difference in mass between an atom and one of its ions. In something like liquid-phase chemistry,... | https://chemistry.stackexchange.com |
16,461 | [
"https://cs.stackexchange.com/questions/16461",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/8849/"
] | I am unclear about finding the memory complexity of an algorithm.
Some places refer memory complexity as what container would be carrying for instance:
<pre><code>for i = 1 to n-1
if d[i] == d[i + 1]
d[i] = (d[i] + 5) mod 13
</code></pre>
Is considered as having $\theta(N)$ memory complexity.
At som... | Memory complexity is the size of <em>work memory</em> used by an algorithm. In the relevant Turing machine model, there is an read-only input tape, a write-only output tape, and a read-write work tape; you're interested only in the work tape. This makes sense since work memory is the additional memory that the specific... | The memory complexity of an algorithm is the amount of memory it uses.
(Just like the fact that the time complexity of an algorithm is the amount of computing time it uses.)
If the inputs to the algorithm take more than $\Theta(1)$ space, sometimes we might use the phrase "memory complexity" to refer to the amount of... | https://cs.stackexchange.com |
60,426 | [
"https://electronics.stackexchange.com/questions/60426",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/13667/"
] | I'm multiplexing 32 LEDs in a 4:8 configuration on an ATMega328 and am trying to dim them with what is probably a completely naive understanding of PWM. Note: I'm multiplexing them directly with 12 pins from the ATMega, no other chips are used at all. Basically, out of every 10 cycles of refreshing the whole display (w... | To start with, I do not, nor have I have I ever used Arduino, but I am very familiar with AVR chips and the ATmega328p in particular. If I am understanding you correctly, you are trying to dim a 4x8 matrix of LEDs. The entire matrix should be dimmed all at once, but not every LED will always be on, meaning individual o... | I'd start by removing the floating point operations from within an interrupt on an AVR because they can be very CPU intensive and depending on clock speed maybe the interrupt isn't completed when the timer is ready to next be fired. For example change:
<pre><code>uint8_t pwmMax = 10;
float pwmLevel = 0.8f;
....
if(pwm... | https://electronics.stackexchange.com |
2,726,098 | [
"https://math.stackexchange.com/questions/2726098",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/354073/"
] | In any triangle, if $\dfrac {\cos A+2\cos C}{\cos A+2\cos B}=\dfrac {\sin B}{\sin C}$, prove that the triangle is either isosceles or right angled.
My Attempt:
Given:
$$\dfrac {\cos A+2\cos C}{\cos A+2\cos B}=\dfrac {\sin B}{\sin C}$$
$$\dfrac {\dfrac {b^2+c^2-a^2}{2bc}+2\dfrac {a^2+b^2-c^2}{2ab}}{\dfrac {b^2+c^2-a^2... | Alternate approach:<br>
Cross multiply<br>
$\cos A \sin C + \sin 2C = \sin B \cos A + \sin 2B$<br>
$\cos A (\sin C - \sin B) - (\sin 2B - \sin 2C)=0$<br>
$\cos A * 2* \sin \frac{C-B}{2} \cos \frac{B+C}{2} - 2* \sin (B-C) \cos(B+C)=0$<br>
$\cos A * 2* \sin \frac{C-B}{2} \cos \frac{B+C}{2} + 2* \sin (B-C) \cos A=0$<br>
$... | You are very close to answer.
<ul>
<li>cross multiply.</li>
<li>subtract 1 from both side.</li>
<li>take b-c common from Numerator.</li>
<li>It's done!! :)</li>
</ul>
| https://math.stackexchange.com |
260,386 | [
"https://security.stackexchange.com/questions/260386",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/201889/"
] | Scenario: a user enters his password incorrectly x times, so his account is locked for y minutes.
<em>Should I revoke all his refresh tokens?</em>
Problems:
<ul>
<li>user is logged out of all devices, not just the one he's on currently (where he entered the wrong password)</li>
<li>attacker can log out any user (from a... | The answer is easy, please don't do this, otherwise this would be a built-in denial-of service.
If an attacker knows a user name it would be possible to run a script that every x minutes performs a set of requests using an arbitrary password just to trigger this function which erases all the user's refresh tokens.
This... | Another strategy: block the IP address for a failed login attempt (for x minutes).
Unless that user is up to no good, there's no reason that IP address should be communicating with your service anytime soon, because it represents a blocked user.
| https://security.stackexchange.com |
725,936 | [
"https://physics.stackexchange.com/questions/725936",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/67907/"
] | It looks like to me that whenever we need to describe something we start from observations which lead to a theory. All theories seem to rely on laws:
<ul>
<li>theory of classical mechanics
<ul>
<li>Newton's laws</li>
</ul>
</li>
<li>theory of relativity
<ul>
<li>special relativity
<ul>
<li>Einstein's postulates</li>
</... | The relationship between thermodynamics and mechanics (whether Newtonian or quantum or general relativity) is subtle. It is like the relationship between momentum conservation and Newton's Laws of motion. Or, a better comparison, it is like the relationship between translational invariance and Newton's Laws.
To explain... | Your question is not written very well. Anyway...
<strong>Thermodynamics is a physical theory</strong>
I can't agree with you if you really mean the thermodynamics is not a physical theory. Let's focus here on classical thermodynamics, the one studied in high school and in the first years at the university, and see why... | https://physics.stackexchange.com |
30,073 | [
"https://quant.stackexchange.com/questions/30073",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/6889/"
] | Where can I find the Credit default swap index that JPMorganChase bank puts out? I am able to find some indices for Europe but none for the US.
thanks
| Amazingly, there are several different methods for computing bond forward price β the underlying ideas are the same (forward price = spot price - carry), but the computational details differ a bit based on market convention.
Let's start with the basics. Assume between now ($t_0$) and the forward settlement date $t_2$,... | Some financial terms to begin with:
<ol>
<li><strong>Dirty Price</strong>: It is equal to the sum of clean price and the accrued interest since last coupon payment. Say you hold a semi-annual bond (Purchased on 1st January and received a coupon on 1st July). Now if you price this bond on 1st September, then its price w... | https://quant.stackexchange.com |
66,577 | [
"https://security.stackexchange.com/questions/66577",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/54291/"
] | We are a small startup. One of our products is a B2B web service, accessible through its <code>https://service.example.com</code> canonical URL.
For testing purposes, that service also runs on different testing/staging/integration environments, such as <code>https://test.service.example.com</code> , <code>https://inte... | Using the same certificate does not in any way affect the fundamental security of the connection that is established using it.
The only possible "weakness" introduced by using the same certificate is that if that certificate expires or is leaked all your sites will be affected. Since this certificate is on multiple se... | There are two weaknesses with this model.
1) Information leakage. Including the dev/qa/etc URLs in the certificate allows one to more easily find these environments. Often they are less secure then the actual production environment since it is used to test the code. If you have other controls in place to limit acce... | https://security.stackexchange.com |
12,624 | [
"https://electronics.stackexchange.com/questions/12624",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3741/"
] | I'm experiencing a lot of noise in an RS485 network I've put together using ST485 chips. The cable lengths are very short (<1m total cable length), I'm properly biasing the A and B signals and I've tried both with and without a terminator (seems to make no difference), and I'm only running at 19200 baud.
I suspect... | I'm guessing that the pulsed current draw on the +12v supply is what is putting the noise into the RS-485 signals. For debugging purposes, try disconnecting the LEDs. If your noise issues go away then you know that it's that pulsed 1 amp current. Assuming that's the case, then your job will be to reduce the current ... | A 3.8% error is too high, change your crystal or use a baud rate that has a smaller error. It won't be causing your noise problem, although noise will have more effect than if the error was smaller.
| https://electronics.stackexchange.com |
266,153 | [
"https://softwareengineering.stackexchange.com/questions/266153",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/130282/"
] | Since the <em>Garbage Collector</em> is part of the language implementation (not OS, etc.), does the compiler has to attach the GC to the final executable? Or is it like a dependency that has to be already available on the target machine?
If it's attaching the GC, then should I think of it as a <em>Wrapper</em> around... | <blockquote>
does the compiler has to attach the GC to the final executable? Or is it like a dependency that has to be already available on the target machine?
</blockquote>
This depends on the language implementation and the target platform.
It's possible that the GC gets linked into the executable, it's also poss... | In D the standard runtime that gets linked in during compilation includes the implementation of the GC.
How the GC does the inspection of the program state depends on implementation. There is a stop-the-world type that uses a system call to suspend all program threads and lets the GC thread inspect the program withou... | https://softwareengineering.stackexchange.com |
19,039 | [
"https://dba.stackexchange.com/questions/19039",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/115/"
] | Was designing a table a <code>customer_phone_numbers</code> table a while back, which only purpose was to allow us to store as many phone numbers as a user wanted to have on file. I originally came to the conclusion that <code>customer_id</code> + <code>phone_number</code> was unique, but then it occurred to me, it is ... | There are probably ways to solve this (e.g. an instead of trigger rather than an explicit constraint, or a clever filtered index if on 2008+), but why?
As an example, you can do this with two filtered indexes in 2008+:
<pre><code>CREATE TABLE #cpn(c INT, pn VARCHAR(32), x VARCHAR(8000));
CREATE UNIQUE INDEX x ON #cp... | Just throwing it out there: you could instead put your PK on { CustomerID, PhoneType }. You'd be storing a little context on what each phone number means, which could be useful.
If you make PhoneType a free-text string rather than an FK to a PhoneTypes dimension table, you allow an indefinite number of phone numbers ... | https://dba.stackexchange.com |
11,683 | [
"https://cs.stackexchange.com/questions/11683",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7934/"
] | I was working on proving this one and I've solve one direction as follows :<br>
to prove that $P \subseteq PCP(0,logn)$ I said :<br>
let $M$ be deterministic polynomial TM that accepts $L \in P$ ,we want to show that we can there exists a proof system which consists of prover and deterministic polynomial verifier that ... | As Kaveh points out, any problem in $P$ by definition can be solved in polynomial time by a Turing Machine, so it in effect produces its own proof and checks it, hence $P = PCP[0,0]$ and the inclusion you want to show is trivial.
What's more interesting is to show that $PCP[0,O(\log n)] \subseteq P$ (and hence equal).... | The verifier is a polynomial-time machine, it can solve a problem in $\mathsf{P}$ by itself (without needing to check the certificate/proof sent by prover at all). Also no need for any randomness.
| https://cs.stackexchange.com |
349,674 | [
"https://math.stackexchange.com/questions/349674",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/43217/"
] | I was able to prove the original statement, but I'm stuck on the converse.
If $a = b$ or $a = -b$, then $a\mid b$ and $b\mid a$. This holds true for $a = b = 1$, but I'm not sure how to proceed. I mean, it seems to be true.
| Yes, indeed, the converse is true, that is, we can show that $$(a\mid b \;\;\text {and}\;\;b\mid a )\implies a = \pm b$$
If $a\mid b$, then $b = ma$ for some integer $m$. And if $b\mid a$ then $a = nb$ for some integer $n$...so...
$$b = ma = m(nb) = mn( b) \implies mn = 1 \implies m = n = \pm 1 \;\implies a = \pm b$$... | I'm assuming you're talking about division in $\mathbb{Z}$. If so, then the original statement is false. -7 and 7 divide each other ($-7$ times $-1$ is $7$, and $7$ times $-1$ is $-7$), but they certainly are not equal.\
As for the converse you mentioned, if $a = b$, then there exists an element, namely $1$, such th... | https://math.stackexchange.com |
121,787 | [
"https://chemistry.stackexchange.com/questions/121787",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/81326/"
] | I understand most of the theory behind TLC and that different volatile solvents have different polarities and cause the 'spotted' substances to move at different rates, but what is the point of creating mixtures and then using them in different ratios? How could the results change if I changed the ratios?
For example,... | Chromatography is really an empirical science. The fluid mechanical side and the adsorption phenomenon is somewhat well understood but choosing mobile phases is essentially based on trials, sadly to date. If someone has given you a ratio, say 8:2, it means someone must have tried it and they found that this mobile phas... | I can give a very pictorial answer that doesn't require the use of actual pictures nor typesetting and might useful for beginners.
It is all about the misconception, encountered even in chemists with a relative experience in successful experiments, that solubility of the compounds in a mixture is a key factor for the... | https://chemistry.stackexchange.com |
363,888 | [
"https://physics.stackexchange.com/questions/363888",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/117144/"
] | I want to consider the Poincare group $\text{ISO}(1,3)$ as the symmetry group of four-dimensional Minkowski spacetime $\mathbb{R}^{1,3}$. Within the Poincare group, there is a <em>normal</em> subgroup isomorphic to $\mathbb{R}^{1,3}$ consisting of translations. The Lorentz transformations, which here I will call $\ma... | This is simplest to appreciate in the Euclidean case. The first transformation not only translates but also rotates the original vector.
Thus, when the second transformation is done, it acts on this already rotated (and translated) vector.
In the case of the Euclidean group in the plane $E(2)$ (just because the alg... | Well, using your definition (never mind what any of it means for now): several conclusions can be drawn. First, let <span class="math-container">$1$</span> denote the identity of the <span class="math-container">$k$</span> group, and <span class="math-container">$(k,k') β¦ kk'$</span> the product operation for that grou... | https://physics.stackexchange.com |
118,640 | [
"https://softwareengineering.stackexchange.com/questions/118640",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/38221/"
] | I am writing a wiki article and wondering what is the proper way to write a directory scheme?
I am doing something like
<pre><code>main folder
- sub folder
- sub folder
...
</code></pre>
But I'm stuck after that.
Any help?
| <pre><code>root
- sub1
- sub1a
- sub1b
- sub2
- sub3
</code></pre>
keep the indention consistent ( I used 2 spaces ) and use a <code><pre/></code> or <code><code/></code> block in your html
you can try and make it look more like a tree control with a <code>|</code> if you want to stick to AS... | I find the output of the <code>tree</code> command very readable. Here's an example that uses Jarrod's directory structure:
<pre><code>root
βββ sub1
βΒ Β βββ sub1a
βΒ Β βββ sub1b
βββ sub2
βββ sub3
</code></pre>
| https://softwareengineering.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.