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 |
|---|---|---|---|---|---|
411,190 | [
"https://math.stackexchange.com/questions/411190",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/32707/"
] | Having
$$ f(x) = \cos(x) + \sin(10x)$$
How Can I know which is the max frequency of this signal?<br>
I need it to set the right Nyquist frequency ($2\cdot\max\text{frequency}$)
I can use Matlab if it's needed
| Denote
$$M:=\int_a^b|f_1(t)|dt<\infty.\tag{1}$$
By definition,
$$|f_{n+1}(x)|\le \int_a^x |f_n(t)|dt\quad \forall x\in[a,b],~\forall n\ge 1.\tag{2}$$
Using $(1)$ and $(2)$, by induction, it is easy to show that
$$|f_{n+1}(x)|\le \frac{M (x-a)^{n-1}}{(n-1)!},\quad \forall x\in[a,b],~\forall n\ge 1.\tag{3}$$
The co... | Here is an other way to consider the problem. You can consider the the operator
\begin{equation}
Tx(t) = \int_a^t x(t') dt' \ .
\end{equation}
Then $f_{n+1} = Tf_n$. Define
\begin{equation}
s_n(t) = \sum_{k=1}^{n+1} f_k(t) \ .
\end{equation}
Now $s_1-s_0 = Tf_1$. Note that $|Tf_1(t)| \leq ||f_1||_1$. Hence $Tf_1$ is bo... | https://math.stackexchange.com |
507 | [
"https://security.stackexchange.com/questions/507",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/254/"
] | I work in a company where security is a "fire once forget forever" concern. The administrator sets up a solution and seldom follow up and maintain it. As a result, we've got a security policy that's kind of Swiss-cheesed: full of holes.
For example:
<ul>
<li>password security policies requiring changing every xx days... | What has worked on several occasions for me is to stick the following chart in front of management:
<img src="https://i.stack.imgur.com/OOQAl.png" alt="alt text">
Run down the list of threats (left column) and ask if they believe if any of those type people described may harm the business.
If so, then you may have w... | Launching a "simulated" attack against your company's network should only be done with explicit, written permission of senior management based on an understanding of the scope of your work and agreed limitations on the results of your attack. Otherwise you risk getting yourself fired for sabotage, espionage, or just pl... | https://security.stackexchange.com |
287,124 | [
"https://softwareengineering.stackexchange.com/questions/287124",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31950/"
] | We have a legacy code base in entirely C++. Our build system is CMake. My first stab at unit testing was as follows:
<ul>
<li>Define a target (<code>LibraryA</code>). This library contains the code to test.</li>
<li>Define a unit test target per CPP test file in <code>LibraryA</code> being tested and link against <cod... | There are two options :
<ul>
<li>don't link Socket compiled binary into the libaryA, and compile libraryA with mocks. I think this is what you are trying to do : link time dependency injection.</li>
<li>use run-time dependency injection. Add interface for the Socket class, and use some kind of dependecy injection (fac... | Simple: mock libraries (mocking both .cc and .h files) and be prepared that the same library will be mocked in different ways for different tests.
| https://softwareengineering.stackexchange.com |
138,201 | [
"https://cs.stackexchange.com/questions/138201",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/126681/"
] | We have been taught that:
<blockquote>
<strong>Insertion-sort</strong> will best work if we have a <strong>small</strong> list.
<strong>Quick-sort</strong> will best work if we have a <strong>long</strong> list.
<strong>Merge-sort</strong> will best work if we have a <strong>huge</strong> list.
</blockquote>
It is not ... | Absolutely they can. The approximation algorithms give a formal guarantee that the solution won't be too bad and they quantify what this means whereas with a metaheuristic such as GA all bets are off. Really, the only guarantee you have with GA is that the solution is valid, but that's it.
Your best bet is to just impl... | Assuming P≠NP, it is known that no polynomial time approximation algorithm can always give a <span class="math-container">$1-1/e + \epsilon$</span> approximation ratio, for any positive <span class="math-container">$\epsilon$</span>.
However, this is a worst-case hardness result. In real life, instances are typically n... | https://cs.stackexchange.com |
3,620,938 | [
"https://math.stackexchange.com/questions/3620938",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/690424/"
] | How can you show that <span class="math-container">$f(x_1,x_2) = (x_1 - x_2)^4 - 5 x_1 x_2$</span> is not coercive?<br>
I somehow have to show that <span class="math-container">$\lim_{||x||\to\infty} \neq \infty$</span>.<br>
I tried expressing the function as a function of <span class="math-container">$x_1^2+x_2^2$</sp... | The hypothesis that <span class="math-container">$\wp(A)\subseteq\wp(B)$</span> says that every subset of <span class="math-container">$A$</span> is also a subset of <span class="math-container">$B$</span>. In particular, every singleton subset of <span class="math-container">$A$</span> is a singleton subset of <span c... | Here's another approach that might provide some clarity.
<blockquote>
Recall that <span class="math-container">$E\in\mathcal{P}(S)$</span> means <span class="math-container">$E\subseteq S$</span>.
Now, note that <span class="math-container">$A\in\mathcal{P}(A)$</span>. Since
<span class="math-container">$\ma... | https://math.stackexchange.com |
44,710 | [
"https://dba.stackexchange.com/questions/44710",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/24850/"
] | Good evening,
I want to know how can I use informations about MyISAM to calculate :
<ul>
<li>size of buffer,</li>
<li>size of buffer used,</li>
<li>Write ratio,</li>
<li>Read ratio,</li>
<li>and MyISAM key cache hit rate</li>
</ul>
and thank you.
| <h1>Key Buffer Size</h1>
<pre><code>SELECT variable_value INTO @KBS
FROM information_schema.global_variables WHERE variable_name='key_buffer_size';
SELECT @KBS KeyBufferSize;
</code></pre>
This should be the same number as
<pre><code>SHOW VARIABLES LIKE 'key_buffer_size';
</code></pre>
<h1>Key Buffer in Use</h1>
<... | Ronaldo anwser is very helpful, but you have to change
<pre><code>SELECT SLEEP(@SECONDS_TO_TEST);
</code></pre>
to
<pre><code>SELECT SLEEP(@SECONDS_TO_TEST) INTO @abc;
</code></pre>
for the raport to work.
| https://dba.stackexchange.com |
54,994 | [
"https://mathoverflow.net/questions/54994",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5337/"
] | Fix an algebraically closed field $k$. Why is the general curve over $k$ of genus $g \ge 3$ automorphism-free?
I am particularly interested in seeing an argument that does not go by induction and specialization to a singular genus $g$ curve.
Let's say a curve is a smooth, projective, connected $1$-dimensional $k$-s... | One way to do it is through deformation theory, provided we only consider
automorphism groups $G$ of order not divisible by the characteristic (one may of
course assume that it is cyclic of prime order). Then the
the moduli space (or just a miniversal deformation) of all curves of genus $g>1$
is smooth with tangent ... | All you need to do is write down one curve without automorphisms for every genus $g$. For $g$ of the form $(d-1)(d-2)/2$ use smooth plane curves. The automorphisms of such curves are induced by linear automorphisms of the plane, so it's easy to show that the general smooth plane curve has no automorphisms. For the gene... | https://mathoverflow.net |
313,984 | [
"https://stats.stackexchange.com/questions/313984",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/182427/"
] | I have this data in a dataframe, df:
<pre><code>>head(df)
sx rk yr dg yd sl
1 male full 25 doctorate 35 36350
2 male full 13 doctorate 22 35350
3 male full 10 doctorate 23 28200
4 female full 7 doctorate 27 26775
5 male full 19 masters 30 33696
6 male full 16 doctorate 21 28516
...
<... | <pre><code>> fit <- lm(sl ~ 0 + sx + sx:rd, data=df)
> summary(fit)
</code></pre>
This fits one regression model with separate intercepts and slopes for the two sexes (four parameters in total).
The intercepts and slopes from the above fit will be the same as you would get from fitting simple linear regressi... | Why not use these two lines rather than a single lm call?
<pre><code>lm_male <- lm(sl ~ yd, data=subset(df, sx=='male'))
lm_female <- lm(sl ~ yd, data=subset(df, sx=='female'))
</code></pre>
EDIT: I've edited the answer to make it clear I'm not asking a question about the code.
| https://stats.stackexchange.com |
108,754 | [
"https://chemistry.stackexchange.com/questions/108754",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/73990/"
] | Are there any methods out there to identify which amino acids are in a sample of protein? Perhaps using NMR?
| For a destructive technique that works with any mixture of proteins (i.e. to assess dietary questions), you could first hydrolyze the proteins into the amino acid building blocks. Then, you could separate them using chromatography (TLC, HPLC, GC), either as they are or after derivatizing functional groups to make them ... | Another technique is Shotgun mass spectrometry. For this, protein is digested with the protease (e.g. trypsin) and peptides are identified by mass / charge. Knowing the mass of peptides, the sequence of them can be found as well as the sequence of the whole protein. The last one will tell you about the exact amino acid... | https://chemistry.stackexchange.com |
224,098 | [
"https://stats.stackexchange.com/questions/224098",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/123521/"
] | <blockquote>
Suppose $X$ is uniformly distributed on $[0, 2\pi]$. Let $Y = \sin X$ and $Z = \cos X$. Show that the correlation between $Y$ and $Z$ is zero.
</blockquote>
<hr>
It seems I would need to know the standard deviation of the sine and cosine, and their covariance. How can I calculate these?
I think I need... | Since
$$\begin{align}
\operatorname{Cov}(Y, Z)
&= E[(Y - E[Y])(Z - E[Z])] \\
&= E[(Y - {\textstyle \int}_0^{2\pi} \sin x \;dx)(Z - {\textstyle \int}_0^{2\pi} \cos x \;dx)] \\
&= E[(Y - 0)(Z - 0)] \\
&= E[YZ] \\
&= \int_0^{2\pi} \sin x \cos x \;dx \\
&= 0 ,
\end{align}$$
the correlation must al... | I <em>really</em> like @whuber's argument from symmetry and don't want it to be lost as a comment, so here's a bit of elaboration.
Consider the random vector $(X, Y)$, where $X = \cos(U)$, and $Y = \sin(U)$, for $U \sim U(0, 2 \pi)$. Then, because $\theta \mapsto (\cos(\theta), \sin(\theta))$ parameterizes the unit c... | https://stats.stackexchange.com |
116,824 | [
"https://mathoverflow.net/questions/116824",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29591/"
] | Let $\mathbf C(t)$ be the field of rational functions and let $\overline{\mathbf C(t)}$ be an algebraic closure. Let $G$ be the Galois group of $\overline {\mathbf C(t)}$ over $\mathbf C(t)$.
Let $\rho:G \to GL_d(\mathbf Q_\ell)$ be a Galois representation.
Is there a useful notion of "unramified" at $x$, where $x$ i... | Yes. For $t$ a local coordinate at a pont $P$, choose an embedding $\overline{\mathbb C(t)} \subset \overline {\mathbb C((t))}$ that sends $t$ to $t$. This turns every representation of the absolute Galois group of $\mathbb C(t)$ into a representation of the absolute Galois group of $\mathbb C((t))$. Define the Galois... | I think the points of ramification are the points around which there is monodromy. A point $x$ is ramified if the element of the Galois group corresponding to a loop around $x$ has a non-trivial image under $\rho$. In your example, if $X_t$ represents the fiber above a point $t$ in the affine line and you start at $t_0... | https://mathoverflow.net |
1,096,154 | [
"https://math.stackexchange.com/questions/1096154",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/121158/"
] | I'm not familiar with Diophantine equations. I would like to solve the following equation:
$$l^2+m^2+n^2=p^3+q^3$$
where $l,m,n,p,q\in\mathbb{N}$.
I need a list of solutions where $l^2+m^2+n^2$ < 10000.
For the sake of simplicity, one can assume $l \le m \le n$ and $p \le q$.
Some numerical simulations would be u... | Quick and extremely non-pythonic python code for this. Could be done much more elegantly but this was written in a minute so don't judge. There are 9728 solutions.
<pre><code>leftside = set()
rightside = set()
lhs = dict()
rhs = dict()
for l in range(101):
for m in range(l,101):
(p,q)=(l,m)
value... | This is not an answer, but rather an extended comment to the question and the answer. It contains some visuals that may be interesting for others, so I am attaching it here.
I organized numbers from 1 to 10000 in a grid 100 x 100, and marked each number if it can be represented as a sum of three squares and/or two cub... | https://math.stackexchange.com |
151,728 | [
"https://electronics.stackexchange.com/questions/151728",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65588/"
] | I'm still new to electronics and I am trying to do a calculation. Say I have a 100 Watt bulb that runs at 120V and my source is 240V. I know the bulb will blow but my question is: if I wanted to put a resistor in the circuit how will I calculate the amount of resistance I would need?
| <ul>
<li><strong>"how will I calculate the amount of resistance I would need"</strong></li>
</ul>
<img src="https://i.stack.imgur.com/IVLcK.jpg" alt="enter image description here">
1) Calculate how much current needs to flow through the bulb at its nominal power rating.
$$I_{nom} = \frac{P}{U} = \frac{100W}{120V} =... | If you had to do this for some reason (curiosity, theoretical, etc) you can calculate the needed resistance from knowing the required voltage drop and the nominal current.
The required voltage drop is 120v, and the nominal current of a 100w bulb at 120v is: I=100W/120V , So I = 0.833A.
So a resistor to drop 120v w... | https://electronics.stackexchange.com |
308,338 | [
"https://softwareengineering.stackexchange.com/questions/308338",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/201022/"
] | From what I understand the deployment process consists of these steps.
Compiling, linking/packaging, deploying.
What does the packaging refer to? is that just a reference to packaging the object files together?
| Packaging means packaging.
<h3>Software development in a nutshell:</h3>
First, you <em>plan</em> your project. What does it need to do? How will it do it? Who will make it? And when?
Then you <em>design</em> the system. Lots of diagrams. And documentation!
Then you <em>implement</em> it. It's coding time, batman.
... | Yes. For example with a nodejs application a developer will download the various dependencies and build them from source (the one command <code>npm install</code> will do that for all dependencies, as long as none are too weird). However when deploying to the wild the developer will probably bundle up all the files h... | https://softwareengineering.stackexchange.com |
3,935 | [
"https://mechanics.stackexchange.com/questions/3935",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1252/"
] | I bought a new motorcycle (with clutch and six gears) and am learning to ride from the internet. I haven't found the answer of the following question.
How do I know when I should shift gear only by seeing the speedometer and tachometer?
| The only real rule is that you have to keep the tach between the idle speed (usually ~500 RPM) and the redline (probably around 10000 for a bike). In practice you'll usually want to find the band where the engine feels most comfortable. This is based more on sound and feel than anything. If the bike lurches or nearly s... | It's somewhat hard to explain. Keep in mind two things:
<ol>
<li>Never let your engine stall</li>
<li>Never let your tachometer red line </li>
</ol>
Engine speed for both case will vary for different vehicles. Engine speed between the red line on tachometer and idle speed is the safe region for gear shifting. But the... | https://mechanics.stackexchange.com |
927,578 | [
"https://math.stackexchange.com/questions/927578",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/175303/"
] | $(1)\quad $ How to differentiate $y=\frac 12 \sin x$?
I know that $\frac{dy}{dx}$ of $y=\sin x$ is easy to calculate: $\frac{dy}{dx} = \cos x$. But what if there is a coefficient preceding before it?
$(2)$ Another question is: Does the following equality of functions hold? $$\frac{x(x^2+1)}{x^2+1}\overset{?}{=}x$$
P... | Question $(1):\quad$ Given $y = \dfrac 12 \sin x$:
$$\frac{dy}{dx} = \frac{d}{dx}\left(\frac 12 \sin x\right) = \frac 12\cdot \frac{d}{dx}(\sin x) = \frac 12 \cos x$$
$$y = a f(x)\implies \frac{dy}{dx} = \frac{d}{dx}(a f(x)) = af'(x)$$ for all constants $a$.
<hr>
Question $(2):$
$$\frac {x(x^2 + 1)}{x^2 + 1 } = x ... | For the first part of your question, you can remove constants when differentiating:
$$\frac{\mathrm{d}}{\mathrm{d}x}\big(a\cdot f(x)\big)=a\frac{\mathrm{d}}{\mathrm{d}x}f(x)$$
You can prove this with the product rule by finding $a\frac{\mathrm{d}}{\mathrm{d}x}f(x)+f(x)\frac{\mathrm{d}}{\mathrm{d}x}a$ & noting tha... | https://math.stackexchange.com |
415,097 | [
"https://softwareengineering.stackexchange.com/questions/415097",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/373480/"
] | I'm considering HATEOAS for one of my application but for that, I need to be sure that it fits my needs. One of them is the ability to support direct links such as "https://www.webapp.com/user/1" for example. In this case, when the user lands on this page, the js code is supposed to fetch the user with ID 1. ... | From your comment:
<blockquote>
...If the SPA is only supposed to know about the root URI of the web service and only knows that the user ID is "1", how is it supposed to know the route to the "user" endpoint...
</blockquote>
HATEOAS applies to a resource and not to the entire API, so it’s fine for ... | You just include the complete absolute url in an e-mail. That is an entry point to your app.
<strong>It's a fantastic example of HATEOAS</strong>, because it allows an unknown application (email client) to continue a workflow that began in your application, essentially carrying state of that interaction through time an... | https://softwareengineering.stackexchange.com |
64,026 | [
"https://mechanics.stackexchange.com/questions/64026",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/42022/"
] | I just purchased a used black Ford F150 XL crew cab "convenience vehicle" from a dealer.
Today my friend noticed that the drivers side door handles are chrome and the passenger side door handles are matte black. I never noticed this in the showroom (shame on me).
Before I go back to the dealer and demand retribution... | Just to close this out...I discovered that someone bought and installed some type of "after market" stick on imitation chrome covers for door handles.
So either one side fell off or they never did the other side.
Grrrr.
Thanks for the replies.
| <strong>TL DR:</strong> This isn't how it's supposed to be. They should be the same from side to side ... however ...
However, stuff happens. As Solar Mike aluded to, things happen on the assembly line which can give you the wrong options. More than likely the dealership never even noticed, or maybe they did notice an... | https://mechanics.stackexchange.com |
49,822 | [
"https://cs.stackexchange.com/questions/49822",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/42721/"
] | I'm still fairly new to Turing Machines, but I've been doing some research.
I know that a Turing Machine can have an infinite tape and that it requires a finite number of states, but does it necessarily follow that a Turing Machine can have an infinite number of accept states?
I keep seeing different layouts when for... | In the <em>standard</em> Turing machine, the set of states $Q$ is finite $|Q| < \infty$. Therefore, it cannot have infinite final states. However, it may, or may not have multiple final states. This will not change the power of the machine (i.e., one final state is equivalent to $k$ final states).
| Turing machines are defined to have only a finite number of states. Since every accepting state is a state, it's impossible to have infinitely many accepting states. Being allowed to have more than one of something is not the same as being allowed to have infinitely many.
| https://cs.stackexchange.com |
120,809 | [
"https://electronics.stackexchange.com/questions/120809",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/47005/"
] | I am working on a datalogger that writes positions from GPS to serial flash W25Q64FV. I plan to write GPS data every second. I have couple of questions:
<ol>
<li>With this flash memory it is possible to write to any position from 1 to 256 bytes at once (page). Specification says the memory has 100,000 write/erase cycl... | First of all, the way flash works, in general, is that a write command can only change bits from one to zero. To return bits to one, you must erase an entire erase block. Therefore, you cannot just "write to it like a hard drive". On most flash devices, multiple writes can be made to the same block or even the same byt... | Having worked with flash and been bitten by various problems, I would suggest that it may be a good idea to design your data format in such a way that it will not be confused by <em>anything</em> that might appear in a block that was erased when power was lost. My present favored scheme is to use a rolling sequence of... | https://electronics.stackexchange.com |
69,253 | [
"https://mathoverflow.net/questions/69253",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16114/"
] | Are there any positive integer solutions to <span class="math-container">$2^n-3^m=1$</span> with <span class="math-container">$n,m>2$</span> ?
By way of justifying the question, I've found lots of info on what happens when <span class="math-container">$m=n$</span> (mostly FLT variations, Darmon + Merel,...), but I ... | Here is the proof of Gersonides [Levi ben Gershon] (1343) for $2^n-3^m=1$. It uses nothing more that arithmetic modulo $8$.
Case I: $m$ is even. Then $3^m$ is 1 mod 4, so $2^n$ is 2 mod 4, implying $n=1$ and $m=0$.
Case II: $m$ is odd. Then $3^m$ is 3 mod 8, so $2^n$ is 4 mod 8, implying $n=2$ and $m=1$.
The alterna... | The equation $p^n-q^m=k$ is a special case of the $S$-unit equation, so it has finitely many solutions by a theorem of Siegel. Using linear forms in logarithms you can get an explicit upper bound for the size of the solutions and, in principle, find all of them. In practice, the bounds may be too big in general, but I ... | https://mathoverflow.net |
1,710,558 | [
"https://math.stackexchange.com/questions/1710558",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/105670/"
] | Consider two numbers $0\leq x\leq 1$ and $0\leq y\leq 1$. Is it true that $x(1-x)=y(1-y)$ if and only if $x=y$? If not, can you give a counterexample?
| It is not true. Any pair of numbers such that $x+y=1$ will work as an example (except when both are $1/2$). This is because $x=1-y$ and $y=1-x$.
This is in fact the only way to make this happen.
| $$x(1-x) = y(1-y) \implies -x^2+x-y(1-y)=0 \implies x^2-x+y(1-y)=0\text{.}$$
By the quadratic formula,
$$x = \dfrac{1\pm \sqrt{1-4(1)y(1-y)}}{2}=\dfrac{1 \pm \sqrt{1-4y(1-y)}}{2} = \dfrac{1\pm \sqrt{1-4y+4y^2}}{2} = \dfrac{1 \pm |2y-1|}{2}\text{,}$$
so any pair $\left(\dfrac{1 + |2y-1|}{2}, y\right)$ or $\left(\dfrac{1... | https://math.stackexchange.com |
36,152 | [
"https://dsp.stackexchange.com/questions/36152",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/22692/"
] | Problem:
For an object tracking scenario with multiple objects and multiple tracks, I want to choose the "best" assignment object<->track. Therefore, I need a parameter indicating how suitable an object is for a track.
(Each object refers to a measurement and each track is a Kalman filter)
Idea:
Given the classic... | <blockquote>
Question: Which parameter is suitable to indicate how "good" the
measurement fits to the Kalman filter?
</blockquote>
To estimate a quality of association you can use <em>likelihood function</em>. The <em>likelihood</em> considers not only <em>residual</em> but also <em>uncertainty</em> and represente... | Search for radar plot to track association. There's a lot of algorithms on this subject. To your question:
The residual itself will not give you information without its associated covariance matrix
Try a chi-squared test on it. Putting a threshold on this scalar is called gating and it's a first step of plot to track... | https://dsp.stackexchange.com |
366,698 | [
"https://electronics.stackexchange.com/questions/366698",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/146255/"
] | I am in a digital circuits class. In this class we are using verilog to <strong>simulate</strong> (but not actually physically synthesize) different circuits. We have an assignment where we are supposed to simulate a circuit and one of the requirements makes it so there must be a for loop with a basic calculation in o... | When verilog is synthesized, loops are unrolled. So the code
<pre><code>always @(posedge clock) begin
isPerfectSquare = 0;
for (i=0; i<11; i=i+1) begin
if (i*i == data)
isPerfectSquare = 1;
end
end
</code></pre>
would be converted to
<pre><code>always @(posedge clock) begin
is... | In HDL the <code>for</code> loop <em>is not</em> something the hardware is <em>executing</em>. It is something the synthesis tool is generating. In your case it will just become a bunch of comparators (11 of them) or similar hardware with the input of <code>data</code> and squared numbers from <code>0</code> to <code>... | https://electronics.stackexchange.com |
200,898 | [
"https://softwareengineering.stackexchange.com/questions/200898",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/88205/"
] | Is it looked down upon or bad to write multiple variable declarations on the same line? As in:
<pre><code> boolean playMoreGames = true; int length;
boolean win; int bodyparts;
boolean contains; char blank = '-';
String word; ... | I really like the readability of that style, and might use it in a publication, but a good programming style should also be easily editable. It would be very annoying to insert or delete a declaration in the middle of the list, especially if you're accustomed to being able to do so using your editor's linewise shortcu... | Style is always different everywhere. I've never seen this style that I can recall, but that doesn't matter.
I think it might be seen as pretty strange by many but again, it's subjective and really doesn't matter <strong>so long as your style doesn't get in your (or anyone elses) way</strong>.
Though I would think th... | https://softwareengineering.stackexchange.com |
96,401 | [
"https://biology.stackexchange.com/questions/96401",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/62357/"
] | My friend's argument against evolution goes like this:
It is extremely unlikely that life as we know it evolved from a random mutation process because every organism is like a machine, in that one "mistake" could render the whole machine unworkable. What makes this even more unlikely is that harmful mutations... | <blockquote>
It is extremely unlikely that life as we know it evolved from a random
mutation process because every organism is like a machine, in that one
"mistake" could render the whole machine unworkable.
</blockquote>
<strong>Garbage. Pure garbage.</strong> People in the lab know that you can induce all... | I will henceforth use the word <em>"unfortunately"</em> to describe the predicament of a person who denies evolution.
<blockquote>
Is there anything wrong with my friend's argument against evolution?
</blockquote>
<em>Unfortunately</em>, <strong>all arguments against evolution are invalid</strong>, simply due... | https://biology.stackexchange.com |
597,443 | [
"https://stats.stackexchange.com/questions/597443",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/217467/"
] | A bit of a naive question.
I understand that OLS is used for a linear regression model (for example, Wikipedia page for OLS: OLS is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables... | You are missing the definition of linear regression. By linear regression, it is meant any regression equation of the form
<span class="math-container">$$
y = \beta_0+\beta_1x_1+\beta_2x_2+\cdots+\beta_px_p + \epsilon,\tag{*}
$$</span>
where <span class="math-container">$\beta_i$</span> are the regression parameters, <... | The method of <em>least squares</em> is a nummerical method for minimizing a function. The solution to any functional form (linear or non-linear) would be <span class="math-container">$\hat{x} = (A^{T}A)^{-1}A^{T}\beta$</span>. The term OLS is often times used to describe <em>both</em> the nummerical method <em>and</em... | https://stats.stackexchange.com |
104,170 | [
"https://physics.stackexchange.com/questions/104170",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23816/"
] | I'm not entirely sure if this is correct. I have to take the time derivative of the following:
$$\frac{d}{dt}mr^{2}\dot{\phi}$$
Now, both $r$ and $\dot{\phi}$ depends on the time $t$, so I have to use the product rule to get what I want. Now, what is bothering me is, is it only one of the $r$'s I need to do, or both ... | You're almost good, you just needed to use the chain rule, which you did perhaps without knowing it. It is clearer if you write it this way perhaps:
$$ \frac{d}{dt} m r(t)^2 \dot{\phi}(t) = m\frac{d}{dr}(r(t)^2)\frac{dr}{dt}\dot{\phi}(t)+mr^2\ddot{\phi} = 2mr\dot{r}\dot{\phi}+ mr^2\ddot{\phi}$$
| For the $r^2$ you will use the power rule of differentiation:
$$\frac{d}{dt}mr^{2}\dot{\phi} =2mr\dot{r}\dot{\phi}+mr^{2}\ddot{\phi}$$
with the "2" on the first term of the right hand side being the only difference between what I wrote and what you wrote.
If you are still confused, think of it this way. Instead o... | https://physics.stackexchange.com |
61,038 | [
"https://chemistry.stackexchange.com/questions/61038",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/29678/"
] | I've noticed that in many relationships in chemistry, one variable is linearly related to the logarithm of another. Why is this the case?
For example, I carried out an experiment where the dependent variable, the amount of solute adsorbed to a surface, was almost perfectly linearly correlated (Pearson correlation coef... | Some logarithmic behaviour is built into the way the world works and some is a consequence of how we perceive things which span very large ranges.
The simplest chemical and nuclear reactions (first order ones) are, for example, inherently logarithmic. Take any first order process (like radioactive decay). The process ... | The logarithmic patterns are more a function of math than physical properties. The logarithmic identity: $\log(x^5) = 5\log(x)$ is responsible for most of your observations. If I have a property $y$ that is dependent on $x^a$ where $a$ is a constant, I can log both sides to get a relation of: $\log(y) = \log(x^a) = a... | https://chemistry.stackexchange.com |
28,739 | [
"https://chemistry.stackexchange.com/questions/28739",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/15593/"
] | So, I'm considering an Artsy Fartsy project with hard drive platters. Being mildly aware of the world around me, I've come to the conclusion that I probably shouldn't grind up modern (or any) electronics and drink it for tea. To that end, is there anything in hard drive platters that is significantly toxic, or are they... | I never opened a newer 2.5" hard disk, but I've read that these may contain glass platters.
However, I've seen and touched stacks of platters from old 3.5" hard disks - a friend of mine makes clocks from hard disk cases.
These platters have an aluminium core, on which another metallic layer, that serves as a kind of... | Discs from 3.5" drives are perfectly safe. They are made of a majority of aluminum, with hints of platinum, palladium, and other precious metals (not a lot though — the Pt coating is only a few atoms thick).
Stay away from 2.5" drives though. Their platters are made of some sort of glass, and if you put too much press... | https://chemistry.stackexchange.com |
89,744 | [
"https://physics.stackexchange.com/questions/89744",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20731/"
] | When a droplet is deposited on a surface with some surface roughness and subsequently tilted it can stick due to pinning (think of droplets on a window after rain).
What I am interested in is how/whether I can show that all the potential energy from tilting the droplet is converted in surface energy needed for the def... | Any reshaping of the droplet will require flow of water inside the droplet and there will be viscous losses. Presumably the energy would come from an increased torque on whatever motor was moving the droplet and substrate.
| If you only consider viscous dissipation within the droplet, this should indeed go to zero in the vanishing velocity limit: the (local) dissipation rate is quadratic in the velocity, so that decreasing the velocity by a factor of $\lambda$ reduces the (local and global) dissipation rate by $\lambda^2$.
Of course, the ... | https://physics.stackexchange.com |
150,571 | [
"https://mathoverflow.net/questions/150571",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13767/"
] | It is known that the 4-sphere does not have a symplectic structure. However, it does admit Poisson structures, for example the zero Poisson structure, which is quite boring. Does it have other, more interesting Poisson structures? For example, are there Poisson structures on $\operatorname{Spin}(5)$ (or $SO(5)$) such t... | Yes:
imho geometrically the most interesting one is obtained as a quotient $SO(5)/SO(4)$ where the Poisson stucture on $SO(5)$ is not the so-called standard one, but one determined by an element in the maximal torus (sometimes they are called twisted). This is the Poisson analogue of what is mentioned in Quantum symm... | If I understand your question correctly, the answer is that the zero Poisson structure on $S^4$ is the only homogeneous one. In fact, this is the only Poisson structure on $S^4$ of constant rank. To see this, note that, because the $4$-sphere does not admit an almost complex structure, it follows, in particular, that... | https://mathoverflow.net |
262,773 | [
"https://mathoverflow.net/questions/262773",
"https://mathoverflow.net",
"https://mathoverflow.net/users/105159/"
] | Let $f$ be an automorphism of the algebra of octonions. Is it true that $f$ preserves some quaternionic subalgebra? Has the statement an elementary proof?
| Seen as a map of $8$-dimensional Euclidean vector spaces, $f$ is obviously (special) orthogonal, so we can find an orthonormal basis on which is has a block diagonal form of $2\times 2$ rotation matrices, and certainly at least $u,v$ unit octonions, orthogonal to each other and both orthogonal to $1$ (=pure imaginary) ... | I would start by finding imaginary octonion $i$ fixed by $f$. This we can conclude from knowing that $f$ is orthogonal map of $R^7$ perpendicular to $1$. Now we apply argument used in Gro-Tsen answer. Each element in $SO_7$ has fixed vector.
Next I would observe that multiplication by $i$ defines complex structure on ... | https://mathoverflow.net |
1,724,280 | [
"https://math.stackexchange.com/questions/1724280",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/28012/"
] | Let $X$ be a Banach space and let $X''$ be its double dual.
Is it true that $\|x\|_X=\|x\|_{X''}$?
What I know is $\|x\|_{X''}=\sup_{\|l\|=1}|xl|$.
| clearly, the evaluation at $x \in X$ is a bounded linear form on $X^*$ : that's the natural injection $\iota$ from $X$ to its bidual $X^{**}$ defined by $\iota(x)(y) = y(x)$. and for some $z \in X$ : $$\|\iota(z)\|_{X^{**}} = \max_{y \in X^*} \frac{|y(z)|}{\|y\|_{X^*}} = \max_{y \in X^*} \frac{|y(z)|}{\max_{x \in X, \... | It is true that $$||x||_{X} =||\kappa x||_{X''}$$ where $\kappa :X\to X''$ is the canonical embedding defined by $(\kappa x ) (u) =u(x)$ for all $u\in X' .$
| https://math.stackexchange.com |
317,537 | [
"https://physics.stackexchange.com/questions/317537",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86190/"
] | Ising model consists of up spin and down spin or empty/filled space. Can we model random walk for different densities of packing through the Ising model?
| Each photon does not have its own wave function. They are entangled. By definition, there is only one wave function between them. One function describes both particles simultaneously. If you do something to one particle that alters the wave function, then that's it; the wave function is altered.
Here's an analogy: I h... | If you have two spins in an entangled state they define a wave function
$$
|\psi\rangle~=~\frac{1}{\sqrt{2}}\left(|+\rangle|-\rangle~+~e^{-i\phi}|-\rangle|+\rangle\right)
$$
in a singlet state of entanglement. What exists is the entangled state. In effect the individual spin states do not exist. A measurement of one sp... | https://physics.stackexchange.com |
83,096 | [
"https://mathoverflow.net/questions/83096",
"https://mathoverflow.net",
"https://mathoverflow.net/users/344/"
] | Recall that for any space $X$, the cohomology $H^*X$ (always, in this post, with $\mathbb{Z}/2$-coefficients) has an action of the Steenrod algebra $\mathcal{A}$; that is, a natural morphism $\mathcal{A} \otimes H^*X \to H^*X$. This is not a morphism of algebras, but $\mathcal{A}$ has a Hopf algebra structure such tha... | What I'd like to say is, to some degree, commentary and expansion on what some people have said in the comments above.
I feel that the answer to (Q1), about whether there is a "high-concept" explanation for the dual Steenrod algebra, is "no" at the current point in time. Even further, I feel like the attempt to do so... | Given two spectra $E$ and $F$, how might we get a handle on the contents of the spectrum $E \wedge F$? One thing we could try is to produce an interesting map involving $E \wedge F$ as its source or target that relates to things we already understand. Let's assume complex orientations for $E$ and $F$, so maps $u: MU ... | https://mathoverflow.net |
310,362 | [
"https://softwareengineering.stackexchange.com/questions/310362",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I am very new to programming and have this humble OOP-related question:
Can we have a module in a OOP-manner written program, that contains 2 or more OOP features? Say, both Encapsulation and polymorphism OR both inheritance and modularity, etc...
| Strictly speaking, only polymorphism is the defining feature of OOP. The other attributes are incidental, but still useful.
<ul>
<li><em>Encapsulation</em> is a feature of <em>abstract data types</em> where the externally visible interface and the implementation details are separated so that the implementation details... | OO is a paradigm - a collection of ideas/methodologies for modelling solutions to problems. You can think of OO as being "an approach to problem solving", or even a mindset.
Encapsulation and Modularity are closely related to each other. Inheritance is a prerequisite for Polymorphism. These concepts aren't mutual... | https://softwareengineering.stackexchange.com |
140,023 | [
"https://security.stackexchange.com/questions/140023",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/127746/"
] | I will be traveling through Central and South America for about half a year.
I have an agreement that I will occasionally work for my company and thus they allowed me to take the laptop from my office. My boss said I "should be careful with the laptop and the stuff I am working on, but it's not that bad if I happen to ... | Besides your friend tips consider followings:
1) enable HDD password from bios if supported. As mentioned by thePROgrammer lock boot device from bios.
2) Using a personal firewall you can decide which app can transfer data over internet (per app rules). I recommend Comodo free personal firewall.
3) not all vpns are ... | All of that info you got from your friends is very true, I have just have a few tips:
You can use proxy and vpn apps on android that will proxy all traffic through (phone traffic).
Lock your boot loader/bios!!
People seem to forget that you can simply boot (live?) another OS, and then modify/delete/view/copy all fil... | https://security.stackexchange.com |
250,277 | [
"https://softwareengineering.stackexchange.com/questions/250277",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/98876/"
] | I'm currently working on a project to replace some excel worksheets. There is a lot of industry specifics that change quite often and nobody really knows how things should be but every sure enough thinks they know how they shouldn't be.
<strong>Project Priorities:</strong>
<ul>
<li>Maintainability - The business proces... | To be honest excel spreadsheets are a better solution than the proposed database.
Maybe you could recommend a hybrid approach to your boss.
<ul>
<li>Its unlikely that you will get a new Entity (i.e. basic object type) that often so have a table for each basic object type.</li>
<li>Each Entity/Object will have a numbe... | The schema as presented is representing an object model in the database - nothing inherently wrong with that, but <strong>it hides the semantic structure of the application</strong>...
This kind of thing is common in engineering applications, especially those that originated as complex spreadsheets: everything is redu... | https://softwareengineering.stackexchange.com |
58,095 | [
"https://mechanics.stackexchange.com/questions/58095",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/40944/"
] | I hit one of those stupid orange barrels on the interstate and it left possibly deep black scuffs on the side of my car...what are some good methods or something I can buy that doesn’t cost an arm and a leg to get rid of them
| Start it and be done with it. 2.5 months sitting isn't really a big deal. You may need to charge the battery, but probably not. Just run it at idle until it warms up, check for leaks, drive it to the gas station and fill it up with fresh gas. You really shouldn't have any issues with it which weren't there before you p... | I agree with @Paulster2, save his advice to idle the motor until it warms up. Instead, minimize the time the engine is running but not yet warmed up (when the most engine wear occurs) by starting the engine and driving the vehicle. Still, don't abuse the machinery with heavy throttle application or high revs until the ... | https://mechanics.stackexchange.com |
6,418 | [
"https://cs.stackexchange.com/questions/6418",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/2827/"
] | I've been studying for an exam I have tomorrow, and I was looking through some previous sample exam questions, when I came across this problem:
<blockquote>
Give a non-regular language $L$ such that $L \cup L^R$ is regular.
</blockquote>
I've been sitting here and thinking and thinking, and I can't seem to come up ... | Hint: try to come up with a language $L$, such that $L \cup L^R = \Sigma^*$.
Hint2:
<blockquote class="spoiler">
Try to think on complements of known non-regular languages.
</blockquote>
Solution:
<blockquote class="spoiler">
Let $C = \{a^nb^n \mid n>0\}$, and define $L$ to be all the strings EXCEPT for t... | Another quick solution: use two letters ($\Sigma = \{a,b\}$) and use $b$ only as a separator, then make $L$ irregular using a counting argument in such a way that in $L \cup L^R$ the counting argument "disappears" ...
Solution:
<blockquote class="spoiler">
if $L = \{a^nba^m | n \geq m \}\;$, then $L^R =\{a^nba^m ... | https://cs.stackexchange.com |
103,084 | [
"https://math.stackexchange.com/questions/103084",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | "Some computer science majors take discrete math"
S is the domain of all college students
C(x) means "x is a computer science major"
D(x) means "x takes discrete math"
Can someone please explain why the following statement is wrong according to the TA?
There exists x in S such that C(x) implies D(x)
???
I don't un... | The statement is wrong, among other reasons, because the statement
<blockquote>
$C(x)$ implies $D(x)$
</blockquote>
is true for any $x$ that is <em>not</em> a computer science student, and for any $x$ that takes discrete math. In particular, the statement
<blockquote>
There exists $x\in S$ such that $C(x)$ impl... | Remember that $C(x)\to D(x)$ is logically equivalent to $\lnot C(x)\lor D(x)$, which in words is ‘$x$ is not a computer science major, or $x$ takes discrete math (or both)’. Your statement, therefore, can be translated into English as
<blockquote>
there is a college student who takes discrete math or is not a comput... | https://math.stackexchange.com |
156,857 | [
"https://physics.stackexchange.com/questions/156857",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/61966/"
] | I am confused with the sign we get when we want to raise or lower all indices of the totally anti-symmetric tensor of any rank. Take the metric to be mostly plus ($-+\ldots+$). Then is it
$$\varepsilon^{ijk}=\varepsilon_{ijk}$$
or
$$\varepsilon^{ijk}=-\varepsilon_{ijk}?$$
so I am confused to as which one is true.
And i... | To not confusing by these things you must know exactly what are the Levi-Civita symbols $\varepsilon$ and what are the Levi-Civita tensor $\epsilon$. Then you also need to know that the Hodge dual has no any confusion when they had defined with Levi-Civita tensor.
$$
\star H^{\mu \nu} = \frac{1}{2}\epsilon^{\mu \nu}{}... | In flat spacetime, the isomorphism between contra- and covariant components is furnished by the Minkowski metric $\eta_{\mu\nu}$. The Minkowski metric in $n$ spacetime dimensions is just $\operatorname{diag}(-1,1,\dots,1)$. Thus for all dimensions, $$\operatorname{det}\eta=-1$$
For any $n\times n$ matrix $A_{\mu\nu}$, ... | https://physics.stackexchange.com |
1,400,947 | [
"https://math.stackexchange.com/questions/1400947",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/41803/"
] | I have two hard drives. The given <code>Mean to Failure Time</code> is $100$ hours.
So if I have one hard drive, the average amount of time until it fails will be $100$ hours.
However, according to my textbook, if I have two hard drives the average amount of time until one fails is $100/2 = 50$.
I don't understand t... | (Keywords: Poisson process; exponential distribution)
The basic idea is that you have events (failures) arriving on each drive at a mean rate of 1 per 100 hours.
If a machine has two drives, then the events are arriving on <em>the machine</em> at a mean rate of 2 per 100 hours.
The mean time until one event arrive... | This is an interesting fact about exponential random variables: if $X$ and $Y$ are independent exponential random variables, say both with mean $\lambda$, the the mean of $\min \{ X,Y \}$ is $\frac{\lambda}{2}$. More generally, if they have means $\lambda_1$ and $\lambda_2$, then the mean of $\min \{ X,Y \}$ is $\frac{... | https://math.stackexchange.com |
16,331 | [
"https://engineering.stackexchange.com/questions/16331",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/11378/"
] | I know major oil pipelines do exists either underground or under the seabed. However, these usually move crude/unrefined oil from refinery to refinery. Yet we don't have refined petroleum or gas directly piped from refinery to the gas station? I mean we have done it with electricity, water, sewage, stormwater and pipe... | To begin with, gas/petrol filling stations may or may not be located at one site for a long period of time. Dealing with a disused pipeline for a closed station will be a problem. Continually extending the pipeline network will cause disruptions.
One of the main issues, is like water distribution pipelines, pipelines ... | The statement part of you questions is mostly incorrect. There are a great
number of product pipelines ( At least in the US) . There are a few stations that have pipelines to refineries or bulk plants but that is unusual. Some of the problems have been mentioned ; certainly the biggest problem would be getting the plet... | https://engineering.stackexchange.com |
406,658 | [
"https://physics.stackexchange.com/questions/406658",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Dirac equation is $$(i \gamma^{\mu} \partial_{\mu}) \psi =0. $$
a solution of Dirac equation for massless fermion case is $$\psi (x) =u (\vec{p}) e^{ip^{\mu} x_{\mu}}.$$
substitution should give
$$(\gamma^{0} p_{0}-\vec{\gamma}.\vec{p}) u(\vec{p})=0 $$
substituting and taking derivative gives zero with respect to ... | There are two issues at stake here.
First, concerning the question itself :
By definition, $\Gamma$ is the Legendre transform of $W=\ln Z$,
$$
\Gamma[\phi]=-W[J]+\phi.J,\\
\frac{\delta \Gamma}{\delta\phi_A}=J_A,
$$
where I use condensed notations $J_A$, $\phi_A$, $J.\phi=J_A \phi_A$, etc. with $A$ collecting space-ti... | The trick to compute $\Gamma^{(1,1)}$ is to compute the cross derivative
$$
\frac {\delta^2 \Gamma}{\delta\Phi^\alpha(x,t)\delta j^\beta(x',t')}.
$$
This can be done in two ways. On one hand, you know the result is $\delta_{\alpha\beta} \delta(x-x') \delta(t-t')$, because this is simply the derivative of $j^\alpha(x,... | https://physics.stackexchange.com |
341,389 | [
"https://softwareengineering.stackexchange.com/questions/341389",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/43961/"
] | There are some Tech Leads that perform code reviews for each Git pull request.
Apparently, a very good practice to be aware of the evolution of code.<br>
Basically, they expect to inspect a few lines of code differing from previous code in order to ensure "quality" easily.
As a lot of good developers know, another ... | For pull request you need already provide possible clean code. Where during review other pair of eyes can possible discover some "small" improvements:
<ul>
<li>method/classes names</li>
<li>extracting methods</li>
<li>etc.</li>
</ul>
If every pull request requires "big" amount of refactoring then you doing someth... | If you have to refactor constantly, it only means the code is in a state that needs refactoring, and nothing more. It can happen using any type of development. Generally speaking, it is a good thing if code needs less refactoring over time: it means the code is working as needed, and is well designed. This should be on... | https://softwareengineering.stackexchange.com |
632,508 | [
"https://physics.stackexchange.com/questions/632508",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/278444/"
] | I completely understand that the average energy of each degree of freedom in a thermodynamic system is (1/2)kT and that we do not consider the spin about an axis of symmetry in a polyatomic molecule as the atoms are spread out compared to the size of nucleus so the Moment of Inertia becomes significantly small for the ... | The point is that for the atoms to acquire a substantial amount of rotational energy they have to collide with other atoms in a very specific way. Of course, all atoms <strong>can</strong> have the same rotational energy as the linear energy. They can even all have only rotational energy without linear energy. Likewise... | If we avoid quantum mechanics, then spin does not exist hence it need not be considered :)
More seriously, considering spin in the basic statistical physics texts would only unnecesarily complicate the discussion - remember that these texts are designed for teaching students statistical physics rather than presenting a... | https://physics.stackexchange.com |
487,295 | [
"https://stats.stackexchange.com/questions/487295",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/163908/"
] | Sometimes, in political polls, pollsters take non-random samples from a given population, but then they apply the results of the theory of random sampling to their non-random sample. I've heard someone (not a statistician) argue that this is still valid procedure because the non-random sample obtained is one of the pos... | <strong>A particularly biased / non-representative sample is unlikely if you sample randomly.</strong>
In an ideal world you'd have a non-random sample which perfectly accurately represents the population such that the proportion of every demographic is the same in the sample as it is in the population as a whole.
This... | Play poker with your friend, bet a lot of money, and cheat to give yourself a royal flush (it beats every other hand).
“That’s cheating!”
“Nah, it’s one of the possible hands. Pay up.”
Yes, it’s about the procedure.
(Don’t actually do the poker trick, but I think it makes the point.)
| https://stats.stackexchange.com |
207,889 | [
"https://security.stackexchange.com/questions/207889",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | I'm always a little cautious about plugins I install for text editors or browsers, but can they be dangerous and cause the text editor or browser to behave in a malicious way?
For example, can a plugin for Atom or Firefox read files and delete them? Or access and send them to an unknown attacker?
How can one avoid ... | Yes they can.
Only install plugins you have verified as trustworthy, both in authorship and distribution.
| Plugins affect the way that the software behaves. So, it would be possible to write a plugin to do something malicious. And it's not just IDEs or text editors, but browsers or any software that allows plugins could be affected.
You also have to define what you mean by "malicious"? Can a plugin act as a remote access t... | https://security.stackexchange.com |
140,876 | [
"https://electronics.stackexchange.com/questions/140876",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/19869/"
] | This may seem like a dumb question, but I want to be sure. In the below datasheet, what is the DC voltage the relay can handle? I am assuming it is the <code>Contact Capacity 24 VDC, 1 A</code>.
<pre><code>Micro 1A SPDT Relay
(275-0240) Specifications Faxback Doc. # 45621
Contact Form: ....... | What's given as the "Contact Capacity" on the data sheet is the amount of current the contacts can break and achieve their life expectancy with the specified open-circuit voltage across them when the break happens.
The voltage is higher for AC because even if the contacts open up at the AC peak when they're passing 1... | A 0.15 mm contact gap with dry air will arc over at ca. 500 V. What the relay needs to "handle" is really the current that it needs to stop and the inductance of the circuit. (A big inductor can generate the needed 500 V and maintain an arc for a while, however small the voltage that was used to build up a current in t... | https://electronics.stackexchange.com |
213,382 | [
"https://physics.stackexchange.com/questions/213382",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95991/"
] | When an object is not moving and we affected it by some force does the given velocity cause the motion or is the motion caused by the acceleration?
Let us say that we have an object that is not moving so to make it move we apply some force which means we have just applied an initial velocity that is clear to me the ob... | My answer will assume the reader knows some calculus, but I will try to explain the concepts in an intuitive manner as well.
Most of the question is about what we call "kinematics", that is the study of the motion of objects under the assumption the velocity/acceleration is known. Kinematics of point masses (in one di... | To add to Matt S's answer, it helps to understand that velocity $v$ is the <em>rate of change of displacement</em> $x$, or mathematically:
$v=\lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}=\frac{dx}{dt}$.
Similarly, the acceleration $a$ is the <em>rate of change of velocity</em> $v$, or mathematically:
$a=\lim_{\De... | https://physics.stackexchange.com |
2,388,763 | [
"https://math.stackexchange.com/questions/2388763",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/283057/"
] | <blockquote>
Solve the ordinary differential equation $x'' + 186(x')^2$ = constant.
</blockquote>
It is an exercise from textbook. I have no idea to solve the ODE. Can anyone give me some hints? Thank you in advance!
| As a not so obvious substitution set $y=e^{186x}$ then
$$
y''(t)=e^{186x(t)}\,186(x''(t)+186x'(t)^2)=186\,c\,y(t)
$$
which now is a standard linear differential equation of second order.
| Hint let $x'=u $ so we have $x''=u' $ the new equation is $u'+186u^2=c $ . Now you can see its variable separable differential equation. $\frac {du}{dx}=c-186u^2$ hence $\int \frac {du}{c-186u^2}=x+d $ . From here we can integrate lhs and then again put $u=x'$ to solve the next differential equation. Note that here $d ... | https://math.stackexchange.com |
3,998,345 | [
"https://math.stackexchange.com/questions/3998345",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/732778/"
] | Segment <span class="math-container">$BC$</span> is the shortest side of noniscosles triangle <span class="math-container">$ABC$</span>. Points <span class="math-container">$K$</span> and <span class="math-container">$L$</span> lie respectively on sides <span class="math-container">$AB$</span>, <span class="math-contai... | Let <span class="math-container">$S,T$</span> be points of tangency to circle inscribed in triangle <span class="math-container">$ABC$</span> respectively on sides <span class="math-container">$AB$</span> and <span class="math-container">$AC$</span>. It is clear that <span class="math-container">$AK+AL=SA+TA$</span>, m... | Note: The condition that <span class="math-container">$BC$</span> is the shortest side, or that <span class="math-container">$ABC$</span> is non-isosceles, are not necessarily. They might have been introduced to avoid signed lengths and degenerate cases (parallel lines, gradient = 0, etc).
Set this up on the coordinate... | https://math.stackexchange.com |
457,717 | [
"https://physics.stackexchange.com/questions/457717",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214901/"
] | If I leave a glass of water out on the counter, some of the water turns into vapor. I've read that this is because the water molecules crash into each other like billiard balls and eventually some of the molecules at the surface acquire enough kinetic energy that they no longer stay a liquid. They become vapor.
Why i... | From a thermodynamic point of view, at fixed pressure, the vaporization takes place when the temperature exceeds the temperature of change of state <span class="math-container">$ Tc (P ) $</span>
Within the liquid, the pressure that is to be taken into account is the hydrostatic pressure. This pressure is a little gre... | There's a fundamental difference between a liquid changing to a gas at the surface vs. in the bulk: the formation of new surface area, which costs energy.
Net evaporation from the surface is spontaneous whenever the relative humidity is less than 100% because energy fluctuations enable surface molecules to detach int... | https://physics.stackexchange.com |
197,814 | [
"https://mathoverflow.net/questions/197814",
"https://mathoverflow.net",
"https://mathoverflow.net/users/66607/"
] | Let $f(x)=\frac{1}{\sin(\pi x)}$ for $x\in (0, 1)$ and let
$\Gamma=\left\{(x,f(x)): x\in (0, 1)\subset \mathbb{R}^2\right\}$ be its graph.
For any set $X\subset \mathbb{R}^2$ and $\lambda>0$ and $\mathbf{v}\in \mathbb{R}^2$, let $\lambda X+\mathbf{v}=\left\{\lambda \mathbf{x}+\mathbf{v}: \mathbf{x}\in X\right\}$.
... | No, your partition of $\mathbb R^2$ into curves is not a foliation in the sense you provide. To see this, you only have to notice that any neighborhood $U$ of $(0 , y_0)$ disconnects some curves and does not others. Being given a rectifying chart $(\psi , U)$ and a strict subdomain $U'\subset U$ with smooth boundary, ... | Wanted to add a picture of the foliation but could not place the image into a comment (can it be done?) so put it in an answer
<img src="https://i.stack.imgur.com/JjJYf.jpg" alt="a sketch of the foliation">
(just a sketch of it)
| https://mathoverflow.net |
72,940 | [
"https://stats.stackexchange.com/questions/72940",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31563/"
] | I read that the $Cov(\hat{\beta})=\sigma^2(Z'Z)^{-1}$, where $\hat{\beta}=(Z'Z)^{-1}Z'y$. However, I have yet been unable to find a proof of this fact online. Could anyone please provide a proof and/or a reference?
| A good reference is Greene, <i>Econometric Analysis</i>. You should be able to pick up an older version (sixth edition or before) online for relatively cheap. Seventh is not noticeably better than sixth. I am changing your notation $Cov(\hat{\beta})$ to
$V(\hat{\beta}_{\textrm{OLS}})$, but I mean the same thing by ... | This is the expression for the <em>conditional</em> variance-covariance matrix of the estimator. For the model $$Y=Z\beta + U, \; E(U\mid Z) =0,\; E(UU'\mid Z) = \sigma^2I$$
we have
$$\operatorname {Cov}(\hat\beta \mid Z)=\operatorname {Cov} \left[(Z'Z)^{-1}Z'y\mid Z\right]$$
$$=\operatorname {Cov} \left[(Z'Z)^{-1}Z... | https://stats.stackexchange.com |
648,313 | [
"https://electronics.stackexchange.com/questions/648313",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/138681/"
] | I have a design where I measure 0-24 VDC on an STM32 ADC using a divider to translate the input voltage down to 0-3 VDC through a 10.5 kΩ and 1.5 kΩ divider. What would the be the best way to implement a TVS solution with this configuration?
I've looked through numerous specs for devices around the 24 V mark to place d... | You already have 10k in series with the input. Therefore, a pair of Schottky diodes to clamp the outout of the divider to the supply voltage levels of the ADC is adequate. These two Schottkies can be had in a single package such as the BAT54S.
| The TVS leakage current will affect your measurement if you place it in the 0-3 VDC point. 24 VDC is the simple solution.
You could also split your 10.5 kOhm resistor and place it in the middle of the divider, but from standard ESD protection (or defib) perspective there is no need. In fact often just having a high eno... | https://electronics.stackexchange.com |
2,616,755 | [
"https://math.stackexchange.com/questions/2616755",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/416286/"
] | let $(X, \Sigma, \mu)$ be a measure space
$f_n \to f$ in $L^1$ norm means that : $f_n \in L^1$ for ever $n$ and $\int_X |f_n-f|d\mu \to 0$
almost everywhere convergence means that $f_n \to f$ pointwise except for a set of points $J$ which is negligible. meaning $\mu(J) = 0$
<blockquote>
I'm still new to meas... | You have already give the difference However there some couples of implication to each other
<strong>First</strong> if the convergence in norm holds true <strong>then the converseof the Lebesgue Convergence Dominated theorem</strong> says there is exist a subsequence $(f_{n_j})_j$ of $(f_n)_n$ that convergence almost... | Let $f_n = 2^n \cdot 1_{\left(\frac{1}{2^n}, \frac{1}{2^{n-1}}\right]}$, $f_n$ pointwise converge to $f \equiv 0$. But $\int |f_n - f| d\mu = 1$, so no convergence in $L^1$.
| https://math.stackexchange.com |
60,313 | [
"https://mathoverflow.net/questions/60313",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13127/"
] | I'm trying to solve the equation
$(1-|x|^2)T = 0$,
where $T$ is a tempered distribution. I know how to do this (it is a common exercise) in dimension $1$. How can I solve it in higher dimensions?
Thank you very much.
| The solution is the direct product of $\delta(|x|-1)$ and any distribution on the sphere.
| This is not a different answer. I only give here the details of Michael Renardy's solution.
Theorem. A tempered distribution $T$ on $\mathbb{R}^n$ solves $(1-|x|^2)T=0$ if and only if for some distribution $V$ on the unit sphere $S^{n-1}=\{x \in \mathbb{R}^n : |x|=1 \}$, we have $T(\phi)=V(\phi_{|S^{n-1}})$, for ever... | https://mathoverflow.net |
31,004 | [
"https://scicomp.stackexchange.com/questions/31004",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/13202/"
] | <strong>Some Background</strong>
I am working on a C++ translation of a SLATEC routine, <code>R1UPDT</code>, which performs a Givens rotation:
<span class="math-container">$$r = \frac{1.0}{\sqrt{a^2 + b^2}}$$</span>
Usually, this equation is put in a slightly different form, depending upon whether <span class="math-... | If you have constants that will not change before runs, declare them in a header file:
<pre><code>//constants.hpp
#ifndef PROJECT_NAME_constants_hpp
#define PROJECT_NAME_constants_hpp
namespace constants {
constexpr double G = 6.67408e-11;
constexpr double M_EARTH = 5.972e24;
constexpr double GM_EARTH = ... | Another alternative that may be in line with your train of thought is to use a namespace (or nested namespaces) to properly group constants. An example might be:
<pre><code>namespace constants {
namespace earth {
constexpr double G = 6.67408e-11;
constexpr double Mass_Earth = 5.972e24;
constexpr d... | https://scicomp.stackexchange.com |
64,854 | [
"https://electronics.stackexchange.com/questions/64854",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22165/"
] | I know that if I use vias on high speed traces that I need to reduce the inductance effect of the via. So I will put ground vias next to these vias to help returning current. I have seen a picture about using ground vias that has confused me. Here is the first picture:
<img src="https://i.stack.imgur.com/oRm63.jpg" al... | This is my understanding, based on very little knowledge:
The the return current for the high speed part of the signal will take the path of least inductance. This means travelling along whichever plane is closest to the track. (In fact, it will travel on the <em>side</em> of that plane closest to the track).
When yo... | I believe the last picture is when you are applying a signal that is referenced to the power plane. This is not uncommon. See the signal return path (in yellow on the right) is returning via the power-plane and this informs me that it is this type of signal i.e. referenced to the power-plane.
There is a little confusi... | https://electronics.stackexchange.com |
25,426 | [
"https://electronics.stackexchange.com/questions/25426",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7656/"
] | I want to reduce the level of sound in a speaker (i think 6Ω 30w rms). I wonder if it is that simple to put a potentiometer in one of the cables.
If this can do the trick, how do I calculate the resistance needed?
| That's a way, but it's better suited for eadphones, as the resistance will consume a power comparable to the speaker, so you need a fairly high power resistor.
The alternative is to use a power transistor, and then you would need only a circuit to bias it, and that can be generated also with a voltage divider, with th... | You can use pure resistance to reduce sound level to a speaker.<br>
But the power levels you suggest are significant and would require somewhat expensive components if implememted with passive resistance. It will help the specification a lot if you can precisely specifiy what you need.<br>
What is the maximum RMS Wat... | https://electronics.stackexchange.com |
382,824 | [
"https://softwareengineering.stackexchange.com/questions/382824",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/322268/"
] | I have a <strong>MySQL</strong> database and I am working with <strong>Core PHP</strong>.
What is the best practice in terms of accessing the database? Should I
<ol>
<li>create functions in MySQL and access them in my PHP-code <strong>OR</strong></li>
<li>write inline queries from code directly?</li>
</ol>
Let me k... | The essential factor in your calculation is scalability.
You can scale your database by creating a cluster or splitting out the queries from the commands.
You can scale your webserver by spinning up more instances and load balancing across them.
Usually it's much cheaper and easier to scale your webserver.
Therefor... | By default, you should actually prefer to use SQL stored procedures because of a laundry list of performance improvements the RDBMS can give you. You also win in security by removing direct table access and allowing access only in very controlled ways.
You also get to write less PHP code, which is a boon in itself...
| https://softwareengineering.stackexchange.com |
308,479 | [
"https://softwareengineering.stackexchange.com/questions/308479",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/160523/"
] | This question is about applying rules of my application that confuse me.
My controller is using service and the service is using repository.
<pre><code>public class CommentController: ApiController{
[HttpPost]
public bool EditComment(Comment comment){
commentService.Update(comment);
}
}
public c... | I would
<ul>
<li>create a seperate PermissionService that implements methods like <code>isUserAllowedTo(user, PermissionService.Permissiontype.Update, PermissionService.Topic.COMMENT, additionalContextRelevantParameters)</code> </li>
<li>and call the <code>PermissionService</code> methods in the controller, where nec... | First, take some time to consider what the comment service is actually responsible for. This will depend on your specific requirements, and possibly even your own best judgment.
If the comment service's responsibility is limited <em>to updating any given comment</em>, then what you have written is well. In this case,... | https://softwareengineering.stackexchange.com |
305,635 | [
"https://softwareengineering.stackexchange.com/questions/305635",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/208475/"
] | I want to map an integer (let's say 32bits) to a valid path.
The integer is an autoincrement value stored in the database.
I also don't want at any case any folder to have more than N subfolders.
That is because in WIN-NTFS (for example) after a specific number (around 1000) things are going really slow.
So I devised... | Development techniques change and improve all the time, so if you are undertaking a rewrite, it's unlikely that you'll want to simply copy the current code's structure. So I'd suggest you can rule out the <strong>Functional clone (dev view)</strong>, <strong>Forensics</strong> and <strong>Path analysis</strong> approac... | A rewrite has to offer value to the users. That's a must. If you simply declare that an app is too hard to maintain, there's too much technical debt, et cetera, your sponsors will look at you and ask, "Well who made it that way?" And that's a good question. Why write a check to the same team who screwed it up last time... | https://softwareengineering.stackexchange.com |
935,441 | [
"https://math.stackexchange.com/questions/935441",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/86565/"
] | Is it true that the extension $\mathbb{Q}(\sqrt [n]{3})/\mathbb{Q}$ is the splitting field of some polynomial over $\mathbb{Q}$? My guess is no. But I can not prove it. Some observations I made are as $[\mathbb{Q}(\sqrt [n]{3}):\mathbb{Q}]=n$ any element of $\mathbb{Q}(\sqrt [n]{3})$ will satisfy a polynomial (irreduc... | It is not the splitting field since it is not Galois. Such fields contain all the conjugate roots, $\zeta_n\sqrt[n]{3}$
| Hint: If $K$ is a splitting field of some polynomial over $F$, and if some other irreducible polynomial over $F$ has a zero in $K$, then this other polynomial splits over $K$.
| https://math.stackexchange.com |
106,440 | [
"https://softwareengineering.stackexchange.com/questions/106440",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36141/"
] | I have my undergraduate final year project coming up and am very interested in lexers, parsers, compilers and so on. I would like to use the DLR (.NET 4.0 dynamic language runtime) for my undergraduate final year project, but am struggling to find a reason to use it!
A domain specific language would be an idea, but mo... | It obviously depends on your code review process but personally I'd say the functional completeness of the requirement is more within the remit of the QA / Test team than the code reviewer.
That's not to say that a code reviewer shouldn't be able to pick up on problems with the functionality where they find them (assu... | If the reviewer spots any problem he should definitely mention them (especially if he is the SME).
But when I receive code that needs to be reviewed I am concentrating at the function level. I see my primary job as reviewer is to make sure the code is readable and <strong>maintainable</strong> in the future (if I spot... | https://softwareengineering.stackexchange.com |
2,612,000 | [
"https://math.stackexchange.com/questions/2612000",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/514257/"
] | <blockquote>
Given the function:
<span class="math-container">$$f(x) = \cos(\sin(x))$$</span>
Calculate the periodicity of <span class="math-container">$f(x)$</span>.
</blockquote>
I understand it equals <span class="math-container">$\pi$</span> but how would a solid answer look like?
Thank you.
| If $r(x)$ has period $k$, then $r(s(x))$ has a period less than or equal to $k$
$$r(x)=\cos x, \ s(x)=\sin x$$
For $s(x)$ period as $2 \pi$, $r(s(x))$ has period less than $2 \pi$. So,
checking for half-period i.e., $\pi$,
$$\cos(\sin (x+\pi))=\cos(\sin (-x))=\cos( \sin x)$$
For the fundamental period check,
$$f(x... | Basically, a function $f(x) $ has a period of $L$ if: $$f(x+L) = f(x) $$
Now, note that the period of $\sin x$ is $2\pi$, where it is negative for half of the time. And since $\cos(-x) =\cos x$, we obtain: $$\text{ Period of} \cos(\sin x) = \frac12\left[\text{Period of} \sin x \right] = \pi$$
| https://math.stackexchange.com |
40,907 | [
"https://stats.stackexchange.com/questions/40907",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/16557/"
] | I keep seeing this in class and I don't understand why we add the log in there from time to time. For example we have regression model 1: $$1:\hat Y=-14.37+.321X_1+.043X_2-.0051X_3+.0035X_4$$ and then it says that we reestimate the model using the log form of $X_3$ and $X_4$ to get model 2: $$2:\hat Y=-36.30+.327X_1+.0... | There are two sorts of reasons for taking the log of a variable in a regression, one statistical, one substantive.
Statistically, OLS regression assumes that the errors, as estimated by the residuals, are normally distributed. When they are positively skewed (long right tail) taking logs can sometimes help. Sometimes ... | Taking logs will make certain forms of relationship that look curved look linear or more nearly linear. Think of introducing new variables, $X_5 = \log(X_3)$ and $X_6 = \log(X_4)$ and then your model is linear in $X_1, X_2, X_5$ and $X_6$.
Sometimes these transformations are obvious from subject-matter consideration... | https://stats.stackexchange.com |
51,385 | [
"https://cstheory.stackexchange.com/questions/51385",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/66448/"
] | Suppose that we have a stream of numbers <span class="math-container">$x_1,x_2,\ldots$</span> such that we wish to track the median of the values observed so far.
This task is easy to do with <span class="math-container">$O(\log n)$</span> update time (where <span class="math-container">$n$</span> is the current number... | If you can maintain the median of <span class="math-container">$n$</span> objects in <span class="math-container">$O(1)$</span>, then you can sort a sequence <span class="math-container">$x_1, \dots, x_n$</span> in <span class="math-container">$O(n)$</span>:
<ul>
<li>first you compute a value <span class="math-containe... | The question's title presupposes the wrong answer. Median can in fact be maintained in <span class="math-container">$O(1)$</span> time. Here is the counter example disproving the title's fallacious claim of “How to show that the median cannot be maintained in <span class="math-container">$O(1)$</span> time?”.
The giv... | https://cstheory.stackexchange.com |
210,644 | [
"https://mathoverflow.net/questions/210644",
"https://mathoverflow.net",
"https://mathoverflow.net/users/58443/"
] | My question, put simply, is: When did mathematicians/number theorists begin viewing questions in number theory through a geometric lens?
For example, was it before Grothendieck introduced schemes to generalize the notion of covering spaces and algebraic curves to include primes in rings? Today we call p-adic fields l... | Treating number and function fields on the same footing or (for instance) the idea that ramification in algebraic number theory and in the theory of covering of Riemann or analytic surfaces are two incarnations of the same mathematical phenomenon are classical ideas of the German school of the second half of the 19th c... | <ul>
<li>Minkowski, H.
On geometry of numbers. (Ueber Geometrie der Zahlen.) (German) JFM 23.0208.04
Naturf. Ges. Halle LXIV. 13 (1891).</li>
</ul>
| https://mathoverflow.net |
108,338 | [
"https://softwareengineering.stackexchange.com/questions/108338",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36721/"
] | My friend and I are relatively new TDD and have a dispute about the "Obvious Implementation" technique (from "TDD By Example" by Kent Beck). My friend says it means that if the implementation is obvious, you should go ahead and write it - <strong>before</strong> any test for that new behavior. And indeed the book says:... | I agree with your interpretation - it is still Red Green Refactor, only with the Refactor bit left out ;)
So, write a failing test first, then implement the obvious solution instead of slowly building up a design of "the simplest possible" one.
| <blockquote>
Do you know a book or blog post saying just that?
</blockquote>
I would argue that Beck's book says just that.
He goes on to say
<blockquote>
However, by using only Obvious Implementation, you are demanding perfection of
yourself. Psychologically, this can be a devastating move.
<strong>What if ... | https://softwareengineering.stackexchange.com |
494,206 | [
"https://electronics.stackexchange.com/questions/494206",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/233228/"
] | I have made a PMDC motor. The resistance of the coils is 0.25 ohms. But the commutation system is very resistant. It adds more 0.85 ohms to the armature resistance. So, the total resistance becomes 1.1 ohms through the commutation system.
The motor needs 14.80 volts and 5.75 amperes to work properly, using the same com... | Assuming you can overcome (with zero resistance using slip rings or some other magical method) the 0.85 ohm resistance in the commutation, this reduces the effective motor resistance from: -
<span class="math-container">$$\dfrac{V}{I} = \dfrac{14.80}{5.75} = 2.574\Omega$$</span>
To....
2.574 ohms - 0.85 ohms = <stro... | You haven't allowed for the back EMF in the voltage calculation.
There are 3 sources of voltage drop opposing the supplied voltage :
<ul>
<li>I (5.75A) * R (0.25 ohms) in the winding, = 1.43V.</li>
<li>I (5.75A) * R (0.85 ohms) in the commutator/brush, = 4.88V.</li>
<li>Back EMF which is speed dependent, and currently... | https://electronics.stackexchange.com |
191,920 | [
"https://softwareengineering.stackexchange.com/questions/191920",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27116/"
] | I have an event(s) controller:
<pre><code>class Event extends CI_Controller{
public function index(){
}
public function foo(){
}
//Shouldn't be able to use this method unless logged in
public function bar(){
}
}
</code></pre>
And I'm trying to organise my code so it's fairly tidy and straigh... | I am a Software Development Engineer in Test, and have been at 2 separate companies. Currently I work for Microsoft.
Broadly speaking, Bryan Oakley is correct: you write software that tests software.
Beyond that, it depends on your level of experience, the scope of your responsibilities, and the type of software tha... | "Developer in test" usually means that you are in the QA department or in a QA role, but the focus is on writing automated tests rather than on creating and running manual test cases. Thing of it as writing software to test software. It can be a particularly challenging career choice because it takes both programming s... | https://softwareengineering.stackexchange.com |
122,944 | [
"https://stats.stackexchange.com/questions/122944",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2798/"
] | This strikes me as a simple question, but in re-visiting how the Naive Classifier works I started wondering if there is <strong>any</strong> probabilistic model that under certain independency assumptions obtains:
$p(Y | a,b) = p(Y|a) \cdot p(Y|b)$
This could be used, for example, to build a classifier that gets the... | The equation in the question only happens in the trivial case where both $p(Y|a)$ and $p(Y|b)$ are point masses on a single $Y$ value. If it were true, then $\sum_Y p(Y|a) p(Y|b) = 1$. However, consider the following bound:
$$
\sum_Y p(Y|a) p(Y|b) \leq \sum_Y p(Y|a) \max_{Y'} p(Y'|b) = \max_{Y'} p(Y'|b)
$$
For the LH... | Sure, if $a$ and $b$ are assumed to be non-interacting events yielding independent information about $Y$ and $Y$ has a uniform prior, then this is the only reasonable way of combining information. Geoff Hinton calls this a <em>product of experts</em>. One caveat, if $Y$ doesn't have a uniform prior, then you'll doubl... | https://stats.stackexchange.com |
3,990,902 | [
"https://math.stackexchange.com/questions/3990902",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | In the proof of Theorem 46.8 Munkres Topology following is claimed (not exact copy but exact interpretation)
<blockquote>
If A is any compact subset of a metric space Y and V is any open subset of Y containing A then there is a <span class="math-container">$\epsilon>0 $</span> such that the <span class="math-contai... | As Brian M. Scott stated, the function <span class="math-container">$f: A \to \mathbb R$</span> sending <span class="math-container">$x$</span> to <span class="math-container">$d(x, Y \setminus V)$</span> is continuous on <span class="math-container">$A$</span> and <span class="math-container">$A$</span> is compact, so... | A direct proof which does not relyy on the continuity of the distance function (a handy fact though that is..):
If <span class="math-container">$A \subseteq V$</span> for each <span class="math-container">$a \in A$</span> find <span class="math-container">$r_a>0$</span> such that <span class="math-container">$B(a,2r... | https://math.stackexchange.com |
10,958 | [
"https://stats.stackexchange.com/questions/10958",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1763/"
] | I am trying to increase my model accuracy by taking into account interaction effect of relevant variables.
I am choosing variables to interact based more on the common sense than on trying every combination.
So far most interaction effects with good p value ( p<.0001) and chi-square have resulted in an increase of... | "True positives", like proportion classified correctly, requires arbitrary and information losing categorization of the predicted values. These are improper scoring rules. An improper scoring rule is a criterion that when optimized leads to a bogus model. Also, watch out when using P-values in any way to guide model... | No it should not. e.g. for logistic regression, which appears to be the case here, it may be that the greater p-value (I'm assuming you mean the right kind of p-value here, like from a likelihood ratio test) comes from increasing the odds for (correctly predicted) observations that are already relatively extreme (e.g. ... | https://stats.stackexchange.com |
212,602 | [
"https://softwareengineering.stackexchange.com/questions/212602",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/67068/"
] | I'm programming a plugin for a software under GPL v2. I'm using an unique name for my plugin, but I'm considering to rename it. I would like to take another plugin's name which has been abandoned and isn't currently being developed.
Am I allowed to take up that name without asking for permission from the author before... | This is not so much a copyright/licensing issue as a trademark issue.
The name of a program/library/plugin is not substantive enough to claim copyright on, but it can be protected under the trademark laws.
As long as the author of the abandoned plugin has not registered a trademark on the plugin's name, you can publis... | The name of the project is not covered by the GPL, the license applies only to the project's code.
Now, without knowing the actual project, it's impossible to tell if you are allowed to use its name or not. For all we know, the name may be trademarked. Nevertheless, if you are set on using the name, the <em>proper</e... | https://softwareengineering.stackexchange.com |
383,079 | [
"https://physics.stackexchange.com/questions/383079",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/183133/"
] | Suppose the quantum system has state
$$a|0_A\rangle|0_B\rangle + b|1_A\rangle|1_B\rangle.$$
I want to prove that system $A$ has reduced density matrix of $a^2|0_A\rangle\langle 0_A| + b^2 |1_A\rangle\langle 1_A|$ when $0_A\rangle$ and $|1_A\rangle$ are orthogonal (and assume that $0_B\rangle$ and $1_B\rangle$ are orth... | The partial trace $\mathrm{Tr}_B$ is defined as:
<ul>
<li>a linear map $\mathrm{Tr}_B:\mathcal{L}(\mathcal H_A\otimes \mathcal H_B) \to \mathcal{L}(\mathcal H_A)$ that goes from the space $\mathcal{L}(\mathcal H_A\otimes \mathcal H_B)$ of linear operators on $\mathcal H_A\otimes \mathcal H_B$ to the space of linear op... | Let's assume that the states $|0\rangle,|1\rangle$ are normalized. Let's also assume $|a|^2+|b|^2 = 1$ so that $|\psi\rangle = a |0_A 0_B\rangle+ b |1_A 1_B\rangle$ is normalized (this is all done so that $\rho$ is properly normalized).
We have then
$\rho = |\psi\rangle\langle\psi|= |a|^2 |0_A 0_B\rangle \langle 0_A 0... | https://physics.stackexchange.com |
300,994 | [
"https://softwareengineering.stackexchange.com/questions/300994",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/201812/"
] | I have been getting my head around monads in functional programming and seem to see some commonality between Perl's default variable <code>$_</code> and FP monads.
Is this true? Are there similarities, if not why not - perhaps this'll allow me to grok monads once and for all by understanding why the use of <code>$_</... | I understand why you see a similarity between monads and the <code>$_</code> variable:
<ul>
<li>a monad encapsulates a value in some context, and allows operations to be performed on that value.</li>
<li>the <code>$_</code> variable refers to the current context. Operations can use this context.</li>
</ul>
So the com... | Well, I don't know Perl, but that code reminds me of the <code>State</code> monad. So here's my attempt at mimicking it in Haskell:
<pre><code>{-# LANGUAGE OverloadedStrings #-}
import Control.Monad
import Control.Monad.Trans
import Control.Monad.Trans.State
import Data.Text.Lazy (Text)
import qualified Data.Text.La... | https://softwareengineering.stackexchange.com |
78,524 | [
"https://softwareengineering.stackexchange.com/questions/78524",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11099/"
] | As a Master's project, I am designing a simple operating system. It is being designed to run in 16-bit Real Mode on an x86 architecture. Ideally, I would like to develop this OS in C++, and only using assembly where necessary. Thus far, I have a boot loader written in assembly, that loads a kernel that is a mix of C... | The <code>new</code> keyword hands off the actual allocation to <code>operator new</code>, which behaves rather similar to <code>malloc</code>: it gets memory from somewhere. The compiler will then do all the constructor magic. Therefore, the C++ compiler will expect the C++ runtime lib (or your code) to provide an imp... | Many of the advantages of C++ over C have nothing to do with runtime support, and in those cases there's really no difference between code written in C and code written in C++. Templates, for example, don't do anything at runtime. They do nothing you couldn't do with a lot of extra typing. C++ is a very reasonable l... | https://softwareengineering.stackexchange.com |
298,399 | [
"https://softwareengineering.stackexchange.com/questions/298399",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/100972/"
] | Wikipedia explains:
<blockquote>
<strong>A dependency is</strong> an object that can be used (<strong>a service</strong>). An injection
is the passing of a dependency to a dependent object (a client) that
would use it.
</blockquote>
But studying AngularJS's DI implementation, I noticed it includes many differen... | <strong><em>Everything</em></strong> fits into the Dependency injection pattern.
When ol' Wirth was proclaiming that every Pascal program should begin with
<pre><code>PROGRAM ProgramName(INPUT,OUTPUT)
</code></pre>
it was dependency injection that he had in mind, albeit in a very rudimentary form, and we did not e... | A Dependency is any piece of logic your code depends on. Its inversion of control because the alternative method of implementing the logic would be
<pre><code>dependency.Logic(myObject)
</code></pre>
vs
<pre><code>myObject.Logic(dependency)
</code></pre>
the first requires that dependancy knows about and has access... | https://softwareengineering.stackexchange.com |
421,844 | [
"https://softwareengineering.stackexchange.com/questions/421844",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/302331/"
] | I'm wondering how to effectively test a lexer (tokenizer).
The number of combinations of tokens in a source file can be huge, and the only way I've found is to make a batch of representative source files and expect an specific sequence of tokens for each of them.
| Your grammar probably has some rules for each token on how it can be produced (for example, that a <code>{</code> signifies a BLOCK_START token, or that a string-literal token is delimited by '"' characters). Start writing tests for those rules and verify that your lexer produces the correct token in each case.
On... | <ul>
<li>If you're writing the lexer yourself, this seems like an ideal case for test-driven development.
While “the number of combinations of tokens in a source file can be huge,” the number of branches in your source code is finite. The idea is that before you add a feature in your code—for instance an edge case to h... | https://softwareengineering.stackexchange.com |
57,627 | [
"https://math.stackexchange.com/questions/57627",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/12864/"
] | Everyone knows the rules of zero divisors like
$$\forall \alpha,\beta\in\mathbb{R}\;:\;\alpha\cdot\beta = 0\Rightarrow\alpha=0\vee \beta=0.$$
But how can I prove it for $\mathbb{Z}$? My first try was this one: For $\alpha\cdot \beta=0$ and $\alpha\neq 0$ let
$$0=\alpha^{-1}\cdot 0=\alpha^{-1}\cdot (\alpha\cdot\beta)=(\... | The rules you provide are incorrect: your fifth "rule" currently reads:
$$a\cdot b = a\cdot c \Rightarrow b=c.$$
This is not a valid rule of multiplication in $\mathbb{Z}$: after all, $0\cdot 1 = 0\cdot 0$, but we do not have $1=0$.
The correct cancellation rule is:
$$\Bigl(a\cdot b = a\cdot c \land a\neq 0\Bigr) \Rig... | Hint: Show that $\mathbb{Z}$ has characteristic 0 and note that 1 generates $\mathbb{Z}$ as an additive group.
| https://math.stackexchange.com |
194,818 | [
"https://mathoverflow.net/questions/194818",
"https://mathoverflow.net",
"https://mathoverflow.net/users/62826/"
] | Let $A$ be an integrally closed domain whose quotient field is $K$, $L$ be a finite Galois extension of $K$, and $B$ be the integral closure of $A$ in $L$. Let $M_A$ be a maximal ideal of $A$, and $M_B$ be a maximal ideal of $B$ that lies above $M_A$ (that is, $M_B\cap A = M_A$). Denote by $F_A$ the field $A/M_A$, and ... | Let $k$ be the field with $2$ elements. Let $R = k[t_i, x_i; i \in \mathbf{N}]$. Let $\sigma : R \to R$ be the order $2$ automorphism sending $t_i$ to $t_i$ and $x_i$ to $x_i + t_i$. Let $S \subset R$ be the fixed elements under the action. Then $R$ and $S$ are normal domains and $R$ is integral over $S$. In particular... | As pointed out above, the answer of Count Dracula is also valid, mutatis mutandis, if one desires counter-examples where the field extensions are of characteristic $p>2$. It turns out that it can also be adapted to provide an example where the characteristic of the base field extension is $0$, and is $2$ for the re... | https://mathoverflow.net |
514,767 | [
"https://electronics.stackexchange.com/questions/514767",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/225429/"
] | I have two brands of broken HDMI cables that I need to join to make them longer.
Can't join them by color, because they are completely different. Plus, one of the cables has all the wires, the other floats some of the pins.
So,
<strong>What are the most fundamental pins to transmit audio and video between PC and TV ?</... | Unfortunately, they are all important. Including cable shields. Except maybe the UTIL and CEC lines if you don't need the features they provide.
| Aside from what Justme wrote (accept their answer, it's correct and the critical point here):
HDMI's data lines are really high-speed. That's easy to imagine: assume you have 1920×1200 px screen you want to feed at 60 fps. That makes 138.24 million pixels a second. Each of these have 8 bit on each color channel, and th... | https://electronics.stackexchange.com |
47,883 | [
"https://physics.stackexchange.com/questions/47883",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/573/"
] | I place a flammable gas (natural gas) inside a metal container and energize the container (apply AC current). Do I have any concerns at this point. I understand for combustion to occur I have to have oxygen available. I also know that some gasses combust underwater (torch welding). I assume it's because oxygen is a... | The far I know is "Safety first!"
Since you're playing with fire, then even if the risk level were 0, there should be no need to try.
Regarding theoretical analysis, not only oxygen to be mixed with gas, but also at some limits known as flammability limits or explosive limits. Explosion or firing takes place if the ox... | The Natural gas flammability limit is 4% to 17% , if there is little to no oxygen it will not result in a flame.
| https://physics.stackexchange.com |
60,794 | [
"https://mathoverflow.net/questions/60794",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14124/"
] | For any manifold $M$, the unordered configuration space of $k$ points is obtained as a quotient of ordered configuration space of $k$ points by the group action of symmetric group on $k$ letters. Does it induce some relation between the cohomology algebras of the two spaces?
| If $F_n(M)$ denotes the ordered configuration space and $C_n(M)$ the unordered configuration space, the quotient map gives a map
$$H^*(C_n(M)) \longrightarrow H^*(F_n(M)).$$
If one takes rational coefficients, then this induces an isomorphism
$$H^*(C_n(M);\mathbb{Q}) \longrightarrow H^*(F_n(M);\mathbb{Q})^{\Sigma_n}$$
... | This is an expansion to Oscar's answer. The cited result on the cohomology with rational coefficients is an application of the Transfer Theorem:
<blockquote>
Let $G$ be a finite group, $X$ a topological manifold and $F$ a field with
$\mbox{char}\,F = 0$ or $\mbox{char}\,F \nmid o(G)$, then
$$H^*(X/G; F) \cong H... | https://mathoverflow.net |
7,490 | [
"https://mathoverflow.net/questions/7490",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2040/"
] | Let R be a normal noetherian domain.
What is the difference between a finitely generated reflexive module and a finitely generated projective module?
Can anybody recommend any references or make any suggestions about this?
<hr>
Finitely generated projective modules can be identified with idempotents matrix...
F... | Well, the answer is well known of course. For a finitely generated module over a commutative normal Noetherian domain TFAE
<ol>
<li>M is reflexive </li>
<li>M is torsion-free and equals the intersection of its localizations at the codimension 1 primes </li>
<li>M satisfies Serre's condition S2 and its support is Spec ... | This is not an answer to your question, but I found it a few days ago looking for something else and did strike me as quite curious... :
According to E. E. Enochs [A note on reflexive modules. Pacific J. Math. Volume 14, Number 3 (1964), 879-881.] a free module of infinite countable rank over a discrete valuation ring... | https://mathoverflow.net |
480,520 | [
"https://electronics.stackexchange.com/questions/480520",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/242158/"
] | I am designing PCB library for a component whose Package is DIP-16. I have already footprint of this Package in other components. Can I use them interchangeably in the new component in terms of their size? Are their size the same?
Thanks for your contribution.
| <h2>Almost yes but No.</h2>
<img src="https://i.stack.imgur.com/THEFg.jpg" alt="enter image description here"><img src="https://i.stack.imgur.com/PlQwh.jpg" alt="enter image description here">.
Please check datasheet for each part. There will be slight differences which you will be able to accept or adjust.
| Mostly yes.
The vast majority of 16 pin DIPs have a 0.1 inch lead pitch and a 0.3 inch width (measured from the Center of one row of pins to the centre of the other row)
You do see the occasional special component though, for example I have used some high isolation optocouplers, which came in a package that was like ... | https://electronics.stackexchange.com |
258,159 | [
"https://mathoverflow.net/questions/258159",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22810/"
] | I'm trying to understand how the six functor philosophy applies to representation theory. Consider the category of classifying stacks $BG$ (assume $G$ discrete for simplicity). To every stack we can assign a triangulated category $D(BG)=D(BG,k):= D(Rep(G))$ the (perhaps bounded) derived category of the abelian category... | Allow me to answer not in stacks but rather in spaces (which may be appropriate if the answer is about getting intuition; e.g. for $B\mathbb{Z}/2\mathbb{Z}=\mathbb{RP}^\infty$ there is probably nothing that cannot be said without stack language). The main point I want to make is that setting up the dictionary is more s... | I assume all groups are discrete and ignore Q3.
Also I assume that π comes from a group homomorphism from H to G.
By Poincaire-Verdier duality π<sup>!</sup> is the same as π<sup>*</sup>. Both of these are identified with restriction.
Then π<sub>*</sub> is the right adjoint of restriction, hence is what I... | https://mathoverflow.net |
594,358 | [
"https://electronics.stackexchange.com/questions/594358",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/294994/"
] | Let's say I have diode or a polarized capacitor in my circuit.
How do PCB manufacturers know how to orient the part on the PCB?
When I create the part in Altium for example, I just make up which pin is pin 1 and which pin is pin 2. As long as the schematic matches the PCB, it won't throw an error at me.
In other words... | <blockquote>
In other words, is there something that relates the pins on the schematic and the pads on the PCB to the real-life leads of the component?
</blockquote>
None, just like there is no standard of whether the anode and cathode in a diode symbol or footprint should be pin 1 or pin 2. It's all up to you to use t... | <blockquote>
I have not seen on diode datasheets where it says "pin 1 should be the
cathode, pin 2 should be the anode"
</blockquote>
It is because you are looking in the wrong place. The datasheets define the pin function of the specific part. The orientation (called "zero orientation") of the pin... | https://electronics.stackexchange.com |
544,719 | [
"https://physics.stackexchange.com/questions/544719",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/209916/"
] | Suppose I have a box on the floor. I lift this box up, being very careful to make sure it rises with a constant upward velocity. (Yes, I will need to accelerate it to start, but assume I do that quickly.) Now, as this box rises with this constant velocity, it gains potential energy, but how? From my understanding, the ... | Your reasoning is completely right. The kinetic energy of the box is <span class="math-container">$mv^2/2$</span>, so if <span class="math-container">$v$</span> is constant, the energy doesn't change. You do positive work <span class="math-container">$W$</span> on the box by pushing it up, while gravity does negative w... | It’s true that there is no net work done. But this just implies that there is no change in kinetic energy, which is true since velocity is constant. The main point here is that the force that you apply is a non-conservative force and work done by non conservative force is change in total energy. Since this work is posi... | https://physics.stackexchange.com |
241,426 | [
"https://dba.stackexchange.com/questions/241426",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/171862/"
] | Hope you're doing well.
Since I'm new to Oracle database and PL/SQL it's a bit difficult for me to understand complicated queries and now I'm trying to figure out what this procedure exactly does.I think it tries to find a specific expression but I do not understand the way it tries to do that
This is the procedure bo... | I have a different approach to the same.
Adding the answer on top of the correct answer, <strong>just to reduce the manual work</strong>.
The following query will directly identify the number of rows in each table which is matching the criteria.
<pre><code>select table_name, column_name,
to_number(xmlquery('/ROWSE... | Firstly, you need to try to run:
<pre><code>select 'select count(*) from ' || table_name || ' where ' || column_name || ' like ''%05510%''' col_name
from user_tab_columns t
</code></pre>
Does it produce a list of queries?
What is the purpose of each query? >> Each query will serve for one column within one table. A... | https://dba.stackexchange.com |
260,313 | [
"https://stats.stackexchange.com/questions/260313",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/141559/"
] | I know the following results:
$\frac{RSS}{\sigma^{2}} \sim \chi^{2}_{n-r}$ where $r = rank(X)$ and $k$ is the degrees of freedom. Then, for any $c \in \mathbb{R^{p}} $, and when X has full rank, i.e. $rank(X) = p$, $\frac{\mathbf{c}^{T}\hat{\beta}-\mathbf{c}^{T}\beta}{\sqrt{\mathbf{c^{T}(X^{T}X)^{-1}\mathbf{c}\frac{RS... | If you wonder where did the extra $1$ come from. We have
$$E(\hat{Y}_* - Y_*)^2 = Var(\hat{Y}_*) + E(E(\hat{Y}_*) - Y_*)^2 = Var(\hat{Y}_*) + E(Y_* - x_*\beta)^2 = Var(\hat{Y}_*) + \sigma^2$$
Let's denote $Z = Y_* - \hat{Y}_*$. From Fisher's Theorem we know that $\hat{Y}_*$ is normally distributed, then so is $Z$. No... | Prediction intervals are wider because there is that extra uncertainty due to the new random observation. See <strong>Hahn and Meeker's Statistical Intervals</strong> text published by Wiley for clear derivations and discussions of the various types of statistical intervals including Bayesian credible regions.
| https://stats.stackexchange.com |
616 | [
"https://scicomp.stackexchange.com/questions/616",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/536/"
] | I have a set of files consisting of randomly selected points from a dataset, each file belonging to a particular class. Each row in these files contains the coordinates in n-space of the point. I'd like to compare the distributions in n-space of each of these files - and am inspired by the K-S test for comparing hist... | I like aeismail's answer, but I'm going to provide an alternative perspective.
In optimization, it's impossible to really learn the field without understanding real analysis. Even before you tackle numerical issues, you need to understand notions of convergence of sequences, because you are going to prove in classes t... | HPC is a blend of mathematics, computation, computer science, and applications. You need to be able to understand all of them to be truly successful in the long run. However, you do not necessarily need to achieve the same level of proficiency in all of them.
In the computation versus mathematics argument, for an eng... | https://scicomp.stackexchange.com |
548,556 | [
"https://electronics.stackexchange.com/questions/548556",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/253935/"
] | I'm about to start placing components on my very first 4-Layer PCB (wrapping up schematic and MCU software tested on 2-layer pre-prototype, all runs surprisingly ok, but still 2 layer meh). I've studied a lot of materials, videos from Robert Feranec and Rick Hartley on grounding. While a lot of stuff there is really co... | I agree with some comments in the answers above, but not completely so I'll offer another perspective:
As was mentioned above, Hartley is talking about passing EMI compliance with fast data rate applications. You'll have fast enough rising/falling times to generate a lot of noise but unless you care about passing EMI, ... | <ol>
<li>Ground pour is a generally a good starter move, nice way to separate potentially interfering signals, but not necessary. Make sure you stitch to your main reference plane with vias. Consult with your board house, but it can help with very high aspect ratio traces which can overetch. Don't waste a whole layer w... | https://electronics.stackexchange.com |
294,640 | [
"https://mathoverflow.net/questions/294640",
"https://mathoverflow.net",
"https://mathoverflow.net/users/121594/"
] | Let $f:X\to Y$ be a finite etale Galois morphism of varieties over $\mathbb{C}$. Let $C$ be a smooth quasi-projective connected curve in $X$.
<blockquote>
<blockquote>
Is $f(C)$ a smooth curve?
</blockquote>
</blockquote>
| No. Just take two points in <span class="math-container">$X$</span> that map to the same point <span class="math-container">$p$</span> in <span class="math-container">$Y$</span>; then a general curve in <span class="math-container">$X$</span> containing these two points will have image with a node at <span class="math-... | If you want an explicit counterexample, take a smooth genus $2$ curve $C$ and embed it in its Jacobian $X:=J(C)$. Choose a point $\alpha$ of order $2$ in $C$ and let $f \colon X \to Y$ the quotient map by the translation $x \mapsto x+ \alpha$.
Then $f$ is a degree $2$ isogeny of abelian surfaces and, setting $C':= C... | https://mathoverflow.net |
4,625,778 | [
"https://math.stackexchange.com/questions/4625778",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1143264/"
] | <blockquote>
Show that for <span class="math-container">$b>1$</span>, <span class="math-container">$\int_0^\infty {\log x\over x^b-1}\ dx = {\pi^2\over b^2\sin^2(\pi/b)}$</span> using <span class="math-container">$PV\int_0^\infty{1\over x^b-1}\ dx = -{\pi\over b}\cot(\pi/b)$</span>.
</blockquote>
Consider a region <... | Substituting <span class="math-container">$x \mapsto x^{a}$</span> for <span class="math-container">$a > 0$</span>, we get
<span class="math-container">$$ \mathrm{PV}\!\int_{0}^{\infty} \frac{1}{x^b - 1} \, \mathrm{d}x
= \mathrm{PV}\!\int_{0}^{\infty} \frac{a x^{a-1}}{x^{ab} - 1} \, \mathrm{d}x $$</span>
This and us... | If one wishes to use contour integration, then one may proceed as follows.
First, let <span class="math-container">$I(b)$</span> be given by the integral
<span class="math-container">$$I(b)=\int_0^\infty \frac1{x^b-1}\,dx$$</span>
Next, enforcing the substitution <span class="math-container">$x^{1/b}\mapsto x$</span> r... | https://math.stackexchange.com |
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