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 |
|---|---|---|---|---|---|
576,022 | [
"https://physics.stackexchange.com/questions/576022",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/273344/"
] | I was studying special relativity, but there is a "proof" than I don't understand:
When we need to prove time dilation, we write the Lorentz equation in form of <span class="math-container">$\Delta t= \gamma \Delta t'$</span> because we want to evaluate the time gap in the <span class="math-container">$S$</sp... | Conserning the first question, yes. The reasoning is the same, as in that post. Write the conservation of energy and momentum:
<span class="math-container">$$
\begin{align}
k + m v &= k^{'} + mv^{'} \\
k + \frac{1}{2} m v^2 &= k^{'} + \frac{1}{2} m v^{'2}
\end{align}
$$</span>
Where unprimed indices denote the ... | If the mirror is moving towards the (source) beam of photons at relativistic speeds, then yes, the laser's frequency will get blue-shifted with respect to the source's emitted frequency after it bounces off the mirror. Similar effect happens with sound waves as well.
| https://physics.stackexchange.com |
592,781 | [
"https://physics.stackexchange.com/questions/592781",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/212160/"
] | When I have an 0th order equation of motion of the form
<span class="math-container">$$
0=a(\phi)+\partial_a\partial^a\phi +\partial_\phi V(\phi),
$$</span>
can I use this equation to simplify the first order equation of motion?
Sure, if the first order has a term, containing the 0th order as a factor, it gets cancelle... | It probably isn't possible to find the function <span class="math-container">$S(T,V)$</span>, because entropy is integral of <span class="math-container">$dQ/T$</span> and from the given function <span class="math-container">$E(T,V)$</span> it isn't possible to find out how <span class="math-container">$dQ$</span> depe... | The answer is yes. There is a general relationship between energy and entropy. However, it is not like in your example.
The reason why your example does not work has been discussed extensively in another answer. Briefly, from an explicit expression for energy as a function of <span class="math-container">$T$</span> and... | https://physics.stackexchange.com |
134,886 | [
"https://dba.stackexchange.com/questions/134886",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/84795/"
] | I have a table <code>product</code> and its columns are <code>maker</code>, <code>type</code> and <code>model</code>. I want to get the makers who produce 6 product types and more than one model. Here is something I am trying:
<pre><code>select maker, type
from product
group by maker
having count(distinct type) = 6 ... | In your first query the error is produced by the attribute <code>type</code>, which is in the select clause, but not in the group by clause. This is due to the fact that there are different values of <code>type</code> for each group. So, instead of writing:
<pre><code>select maker, type from product group by maker
hav... | This is for databases with analytic function support:
<pre><code>select
maker,
type
from
(
select
maker,
type,
count(distinct type) over (partition by maker) as types,
count(distinct model) over (partition by maker) as models
from
product
)
where
types = 6
and models > 1
;
</code></p... | https://dba.stackexchange.com |
107,383 | [
"https://physics.stackexchange.com/questions/107383",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/43897/"
] | If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?
| This is due to the superposition principle: when several forces act upon a body, the net force is the sum of the individual forces: $$\vec F_{net} = \sum \vec F_i $$
However, this is only true when the relation between the force and the acceleration is <strong>linear</strong>.
Let's take the gravitational force as a... | It makes no sense for a point mass to have 2 accelerations. What you might have done is find accelerations due to 2 forces separately. You can add them as when $m= \text{constant}$,
$\vec{F}=\vec{F_1}+\vec{F_2}=m(\vec{a_1}+\vec{a_2})$
When using vectors symbol, its automatically takes care of their directions.
| https://physics.stackexchange.com |
251,104 | [
"https://dba.stackexchange.com/questions/251104",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/152218/"
] | So, I am trying to log not just the postgres user but his ID from my table (for example) Person (person_id) when he calls functions.
So far, from what I can tell I can get almost every information I need from these system tables:
<ul>
<li><code>pg_stat_activity</code></li>
<li><code>pg_stat_statements</code> if I ac... | Based on your comments, the <code>INSERT</code> could look something like this:
<pre><code>INSERT INTO log (userid, clientaddr, calltime, query)
SELECT user_id, -- function argument
a.client_addr,
a.query_start,
a.query
FROM pg_stat_activity AS a
WHERE a.pid = pg_backend_pid();
</code></pre>
The... | pg_stat_activity has application_name. You can use that to append person_id. Before every query you can run below query
<pre><code>set application_name to my_application-<person_id>;
</code></pre>
We use this way to log user_id and module from where the query was triggered. This application_name also gets logg... | https://dba.stackexchange.com |
39,253 | [
"https://mechanics.stackexchange.com/questions/39253",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4883/"
] | With temperatures below zero it's always difficult to get going even if the engine itself starts without hiccups and <strong>I'd like to know what to do better so that I don't need to wait ten minutes before the car is somewhat safe to drive</strong>.
It takes ten to fifteen minutes before the car is driveable in wint... | Get an insulating blanket for at least your windshield. You place this over the windshield at night, and it prevents frost from forming. The windscreen is the most difficult to get ice-free, so this usually reduces the time to get the car ice-free by half. These can be bought in auto supply shops.
There are also bla... | Ensure that your washer fluid is filled with appropriate temperature rated screen wash so that it does not freeze.
What I find helps is to decant a small amount of this screenwash into a Trigger Spray Bottle / Mister Trigger Bottle and keep it handy. Instead of trying to scrape the ice from the outside of the windows... | https://mechanics.stackexchange.com |
3,349,072 | [
"https://math.stackexchange.com/questions/3349072",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/94994/"
] | I want to integrate <span class="math-container">$$\int\left(\frac{y}{2}\right)^\frac{2}{3}dy$$</span>
Doing this I get <span class="math-container">$$\cfrac{3}{5}\left(\cfrac{y}{2}\right)^\cfrac{5}{3}$$</span>
But the answer is <span class="math-container">$$\cfrac{6}{5}\left(\cfrac{y}{2}\right)^\cfrac{5}{3}$$</span... | Substitute <span class="math-container">$u=\dfrac y2$</span>.
Then <span class="math-container">$du=\dfrac {dy}2$</span>, so <span class="math-container">$$\int\left(\frac{y}{2}\right)^{2/3}dy=\int u^{2/3}2du=2\left(\dfrac35u^{5/3}\right)+C=\dfrac65\left(\dfrac y2\right)^{5/3}+C$$</span>
| You are exponentiating the 1/2 as well. That's why you have an additional factor of two in the numerator.
| https://math.stackexchange.com |
66,004 | [
"https://dsp.stackexchange.com/questions/66004",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/38419/"
] | I am trying to evaluate the power spectral density <span class="math-container">$S_{xx}(f)$</span> of a cosine signal <span class="math-container">$x(t) = A\cos(2\pi f_0t)$</span>, by starting from its definition for <em>deterministic power signals</em>
<span class="math-container">$$S_{xx}(f) = \lim_{T\rightarrow\inft... | You don't need to make it so complicated as to use two variables <span class="math-container">$t$</span> and <span class="math-container">$t^\prime$</span>.
<span class="math-container">\begin{align} X_T(f) &= \int_{-T/2}^{T/2} x(t)\exp(-j2\pi ft)\,\mathrm dt\\
&= \int_{-T/2}^{T/2}\frac{\exp(j2\pi f_0t)+\exp(-... | The secret to proving the limit is to not convert the <span class="math-container">$sin$</span> to <span class="math-container">$sinc$</span>. This leaves the <span class="math-container">$T$</span> in the argument and not outside. No need to worry about the complex conjugate as the values are real. The <span class=... | https://dsp.stackexchange.com |
49,826 | [
"https://stats.stackexchange.com/questions/49826",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20735/"
] | I am working on some clustering techniques, where for a given cluster of d-dimension vectors I assume a multivariate normal distribution and calculate the sample d-dimensional mean vector and the sample covariance matrix.
Then when trying to decide if a new, unseen, d-dimensional vector belongs to this cluster I am ch... | If your samples dimensionality is less than the vector space dimensionality, singular matrices may arise. If you have less samples than $d+1$ (when $d$ is your dimensionality), this situation will even necessarily arise: $k+1$ samples span at most a $d$ dimensional hyperplane. Given such a small sample, you obviously c... | I faced this problem when trying to do KDE using <code>gaussian_kde</code> in Python where the random variables were the 784 pixels of some images. In my case the reason was that many pixels were always (in all the images) zero, so no random at all. To solve this problem I just added some small gaussian noise to the im... | https://stats.stackexchange.com |
212,426 | [
"https://security.stackexchange.com/questions/212426",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/205074/"
] | Many remote-terminal to server authentication protocols use random numbers sent by the server as a challenge that the user will encrypt and send back to the server. This way an adversary cannot perform a replay attack since the number being encrypted and sent to the server (along with other parameters) is random and un... | If you have XSS, you can perform any action on the website the user can. This can include changing the email address, adding a new user, or granting access to some resource. Whether any of these actions compromise the account depends on the web application.
For example, consider an XSS payload that changes the email a... | There are definitely more ways of hijacking a session of a victim. Think about
<ul>
<li>Session Fixation</li>
<li>Session Poisoning</li>
<li>Cross-Site-Request-Forgery</li>
<li>Cookie replay attacks</li>
<li>Man in the Middle</li>
</ul>
<blockquote>
Session Fixation
</blockquote>
At Session Fixation you are able ... | https://security.stackexchange.com |
3,516,840 | [
"https://math.stackexchange.com/questions/3516840",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/242850/"
] | Let <span class="math-container">$N(A^\top)$</span> be the left null space of <span class="math-container">$A$</span>
<span class="math-container">$N(A^\top) = \{x| A^\top x = 0\}$</span>
Let <span class="math-container">$C(A)^\perp$</span> be the orthogonal complement of the column space of <span class="math-contain... | Take the steps below<span class="math-container">$$\lim_{x \to 8} \frac{\sqrt[3]{x} -2}{x-8}
=\lim_{x \to 8} \frac{(\sqrt[3]{x} -2)((\sqrt[3]{x})^2 +2\sqrt[3]{x} + 4)}{(x-8)((\sqrt[3]{x})^2 +2\sqrt[3]{x} + 4)}$$</span>
<span class="math-container">$$=\lim_{x \to 8}\frac{x-8}{(x-8)((\sqrt[3]{x})^2 +2\sqrt[3]{x} + 4)}
=\... | The denominator is already <span class="math-container">$0$</span> in the limit. That doesn't mean the limit doesn't exist.
Recall the factorization of a difference of two cubes:
<span class="math-container">$$
a^3 - b^3 = (a-b)(a^2+ab+b^2).
$$</span>
In particular
<span class="math-container">$$
x-8 = \big(\sqrt[3] x... | https://math.stackexchange.com |
404,855 | [
"https://physics.stackexchange.com/questions/404855",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60646/"
] | Suppose we have a mechanical balance, with two identical particles kept in the two sides. Now the balance does not show any deflection.
Now, one of the particles is given some constant horizontal velocity.
Will the balance show the moving particle to be heavier (that side will move downward )or not?
(There is no fric... | Write
$$
\frac{d^2\phi}{dt^2}=-\frac{2k}{M}\phi
$$
and ask yourself: what functions do I know with the property that the second derivative if a negative multiple of the function itself? Surely the answer are the trigonometric functions, so <em>try</em>
$$
\phi(t)= A\cos(\omega t)+B\sin(\omega t) = C\cos(\omega t+ \bet... | Your differential equation looks like harmonic oscillator equation (for small oscillations) $\ddot{\theta}+\omega^{2}\theta=0$, where $\omega$ is the frequency of oscillation.<br>
If you want to prove $\omega$ is really the frequency you can try the solution $\theta(t)=A\cos(\omega t+\phi)$, where $A$ and $\phi$ are co... | https://physics.stackexchange.com |
339,384 | [
"https://softwareengineering.stackexchange.com/questions/339384",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/196142/"
] | For example, to keep a CPU on in Android, I can use code like this:
<pre><code>PowerManager powerManager = (PowerManager)getSystemService(POWER_SERVICE);
WakeLock wakeLock = powerManager.newWakeLock(PowerManager.PARTIAL_WAKE_LOCK, "abc");
wakeLock.acquire();
</code></pre>
but I think the local variables <code>powerMa... | Code is read much more often than it is written, so you should take pity on the poor soul who will have to read the code six months from now (it may be you) and strive for the clearest, easiest to understand code. In my opinion, the first form, with local variables, is much more understandable. I see three actions on t... | Some highly upvoted comments stated this, but none of the answers I saw did, so I will add it as an answer. Your main factor in deciding this issue is:
<h1>Debuggability</h1>
Often, developers spend far more time and effort debugging than writing code.
<em>With</em> local variables, you can:
<ul>
<li>Breakpoint on the ... | https://softwareengineering.stackexchange.com |
3,662,233 | [
"https://math.stackexchange.com/questions/3662233",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/85277/"
] | Today, during a timecut from work, I casually came up with an interesting question.
I was trying to find examples of specific functions that are commutative towards composition, that is <span class="math-container">$f \circ g=g \circ f$</span>. I tried to find a possible answer, but all my attempts lead me nowhere, w... | No nontrivial solutions exist.
Note that since <span class="math-container">$\ln$</span> is a concave function, we have for any <span class="math-container">$c \in \mathbb{R}^+$</span>
<span class="math-container">\begin{align}
\ln(x) \leq \frac{1}{c}(x-c) + \ln(c) = \frac{x}{c} - 1 + \ln(c)
\end{align}</span>
Therefo... | Alright, so let's vary the upper limits in the integrals, and write <span class="math-container">$$\log\int_1^xf(t)\mathrm dt=\int_1^x\log f(t)\mathrm dt.$$</span> Differentiating with respect to <span class="math-container">$x$</span> then gives <span class="math-container">$$\frac{f(x)}{\int_1^xf(t)\mathrm dt}=\log f... | https://math.stackexchange.com |
103,865 | [
"https://electronics.stackexchange.com/questions/103865",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15637/"
] | I'm making a program for the msp430 using energia launchpad, the first code that I had is the following:
<pre><code>// display flag
boolean flag_display = false;
void setup() {
// define ISR to activate the display
attachInterrupt(PUSH2, display_ISR, CHANGE);
}
void display_ISR() {
clean_leds();
flag_display... | I haven't worked with this processor yet but I am 100% sure there is some way to track the push button <em>transition</em> states
i.e un_pressed_button(low) - > pressed_button (high) transition
and the vice versa
If you do not want to use the flag you need to check for the
pressed_button(<strong>high</strong>) -> u... | Here is a psudo code for what i am trying to explain
<pre><code>bool prev_state
bool current state
setup{
//attach ISR
}
ISR1.subroutine{
cli(); //disable interrupts
//Print your digits to LCD
sei(); //enable interrupts
}
loop{
if(prev_state == HIGH && current_state == LOW)
{
//if this routine t... | https://electronics.stackexchange.com |
25,010 | [
"https://mechanics.stackexchange.com/questions/25010",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1743/"
] | Over the last 3 month, our 2005 Honda Odyssey has had a whining steering pump. Here's a bit of the background, from the day that it started until present.
One day in mid-October: Get a call from my other half, the car's making a loud noise. Diagnose it over the phone as the steering pump. Wife confirms puddle under th... | Reseal the pump inlet fitting. It lets air in here but will leak very little or no fluid out. It is a short plastic fitting with an o-ring seal on the pump end.
In the unlikely case that this does not resolve the symptom, next replace the inlet hose. If it is still doing it after that then reseal the pump. Honda sell... | Could also be the power steering bracket. This is an expensive fix. $1400-$2000. Had this issue with my Pilot.
| https://mechanics.stackexchange.com |
1,350,506 | [
"https://math.stackexchange.com/questions/1350506",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/251424/"
] | $$\int ^{1}_{0} \int^{1}_{y}e^{-x^{2}}\,dx\,dy$$
To solve this I know one must use change of variables, but the problem is that I do not know how to approach the actual change.
Just thinking out loud here: Could I do a change of order from $x$ in $[ y , 1 ]$ and $y$ in $[ 0 , 1 ]$ to $y$ in $[x , 1]$ and $x$ in $[0,1... | Draw out the region of integration. You should see that it is a right triangle above the line $y=x$. The integral as stated integrates from this line to the line $y=1$. To change the order of integration, integrate from the $y$-axis to the line $y=x$, from $y=0$ to $y=1$. The integral is then
$$\int_0^1 dx \, e^{-... | <strong>HINT:</strong> Draw out the region of integration. Then change the variables accordingly by fixing a $y$ value first. Then going on and finding the bounds for the $x$ values.
| https://math.stackexchange.com |
46,493 | [
"https://quant.stackexchange.com/questions/46493",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/41379/"
] | I would like someone to give me an intuitive view of conditional expectation. I mean: I have always understood it through formulas but I don't "see" what it is yet.
Thank you
| as you have an open question, let me try to give you an example in finance.
Let <span class="math-container">$(M_t)$</span> be a martingale, i.e. a fair game. Such processes, on average (their expectation), do not increase or decrease, they remain constant. As a consequence, <span class="math-container">$\mathbb{E}[M_... | An expectation is an "average" of a property measured over all the possible outcomes.
Suppose you have a die and you take the expectation of a roll. It could be 1-6 with equal chance so the expectation is 3.5.
But now give it a conditioning. <strong>A conditioning is like a filter</strong>, so that you exclude possib... | https://quant.stackexchange.com |
319,344 | [
"https://softwareengineering.stackexchange.com/questions/319344",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/229601/"
] | This may be a stupid question, sorry.
I've read about the drawbacks of global variables a lot on this site. I'm finally trying to increase my code quality for a large project that'll be reviewed by many. I understand that using global vars makes code harder to debug, since one doesn't know where the variable may be a... | Modifying a variable on one thread and reading it on another is always problematic. Modifying it on two threads is worse.
You can use atomic variables. An atomic variable would for example guarantee that readers get important_var = 0, then important_var = 5.0, then important_var = 10.0 and so on. If important_var is ... | Its not so much that globals make code harder to debug - though if you have a very large program and global state that is defined a long way from where its used, that can have an adverse effect.
The problem with global state is that its global, singular, difficult to extend.
Think of this, you have some variables tha... | https://softwareengineering.stackexchange.com |
340,024 | [
"https://softwareengineering.stackexchange.com/questions/340024",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/232250/"
] | JavaScript maps (the data type, not the array method) seem set up to accept data (key/value pairs) but not necessarily methods. At least they're not advertised that way. However, we <em>can</em> put methods onto a map instance. Intriguingly, the keyword <code>this</code> works in such methods, and returns the map itsel... | Inspired by comments from @Jules after the original question, I figured out the following: If you are using ES6, you can create a new class that extends the built-in Map data type. The constructor should pass any needed parameters to a <code>super</code> call, creating the map and placing it in <code>this</code>. Then,... | (Changing from comment to answer)
Why don't you extend <code>Map</code> with:
<pre><code>Map.prototype.speakersAreFeatured = function() {
return this.has('speakers');
};
</code></pre>
This will define it for all instance of Map.
| https://softwareengineering.stackexchange.com |
1,845,113 | [
"https://math.stackexchange.com/questions/1845113",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $A$ be an operator. An operator is called compact iff $\overline{A(B_1(0))}$ is compact.
A normed space is finite iff $\overline{B_1(0)}$ is compact.
Let $X$ be a Banach space and $Y$ a Hilbert space and consider the operator $A:X\rightarrow Y$. Let $A$ be compact, i.e. $\overline{A(B_1(0))}$ is compact.
Can you... | No, because not every set is/contains a ball, e.g. the Hilbert cube.
| A good example to think about this is to take <span class="math-container">$X=Y=\ell^2(\mathbb N)$</span>, and
<span class="math-container">$$
Ax=(x_1,\frac{x_2}2,\frac{x_3}3,\ldots)
$$</span>
Then <span class="math-container">$A$</span> is compact (it is a norm limit of finite-rank). The image of <span class="math-co... | https://math.stackexchange.com |
624,024 | [
"https://physics.stackexchange.com/questions/624024",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/293379/"
] | Writing a scifi story about a civilization with mature nanotechnology. Grain of tungsten is a proxy for a nanite.
If such a tiny thing as a nanogram of tungsten somehow got accelerated to some truly ludicrous speed, like the speed to achieve orbit, say 11km/s - would it make a sonic boom? Or would it melt into a little... | What is generally know is the mass density distribution <span class="math-container">$\rho(\vec{x})$</span>, and you can write that mass differential in terms of <span class="math-container">$\rho$</span> and a volume differential <span class="math-container">$dm=\rho(\vec{x})dV$</span>, so the center of mass is <span ... | The concept of a small particle of mass <span class="math-container">${\rm d}m$</span> existing at some location <span class="math-container">$x$</span> contributes to the mass torque by <span class="math-container">$x \, {\rm d}m$</span>
<span class="math-container">$$ x_{\rm CM} \int {\rm d}m = \int x \,{\rm d}m$$</s... | https://physics.stackexchange.com |
250,664 | [
"https://softwareengineering.stackexchange.com/questions/250664",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102302/"
] | I have a legacy application in which the UI and business logic are already reasonably well-separated. There is a proposal to separate them even further, turning the core application into a "service" (without UI) and writing a kind of "UI Server" as part of it to which various UIs (potentially in various languages, and ... | You can actually have both. Unicode supports an encoding where all characters are represented as a (variable length) sequence of 8-bit units: UTF-8.
Assuming that you refer to ASCII with your 'old-fashioned 8-bit chars', then you can almost trivially support UTF-8, because UTF-8 is a proper superset of ASCII: All char... | <blockquote>
Are there any technical reasons to reject keeping the business logic part of an application ignorant of Unicode like this?
</blockquote>
<ol>
<li>While you're reasonably certain that your system doesn't need Unicode (now), I don't see what you gain by precluding it. Unless you're using an environment wi... | https://softwareengineering.stackexchange.com |
288,227 | [
"https://physics.stackexchange.com/questions/288227",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/76385/"
] | Probably a silly question, but something that came to mind yesterday. I couldn't find anything when searching.
Why is there an Energy mass equivalence principle but not an Energy charge equivalence principle?
In other words, why do our field theories have a Gauge invariance which allow for charge conservation, but n... | You're making some category errors in the question. Energy can't be converted into mass, mass is a form that energy can take. In other words, when energy is "converted" into mass it never stops being energy. It's kind of like if I have a mass on a spring hanging vertically in a gravitational field, and I make it start ... | Both electric and color charge conservation has always been observed, whereas mass energy is observed to be interchangeable with other types of energy. While there are positive & negative electric charges, and color & anticolor charges, there are no negative masses or negative kinetic energies. Physics equation... | https://physics.stackexchange.com |
254,166 | [
"https://mathoverflow.net/questions/254166",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41130/"
] | Think of the three-sphere as given by $\lbrace|z|^2+|w|^2=1, \;z,w\in \mathbb{C}^2\rbrace$. We can regard it in terms of Hopf coordinates
\begin{align*}
z&= \cos(\theta/2)e^{i(\phi+\psi)}\\
w&= \sin(\theta/2)e^{i\psi}
\end{align*}
where $0\leq\theta\leq \pi$ and $0\leq \phi,\psi<2\pi$. Now I want to consider... | Yes, conditions 1 and 2 are equivalent (as you already noticed).
Let me start by replacing both definitions with their negations, and replace definition 2 with its $L^1$-version.
A and B below are the negations of 1 and 2 correspondingly, slightly rewritten:
A. There exists a sequence of measurable subsets $\emptyset... | I think I can answer my own question, although in a rather convoluted way. The two definitions are equivalent. Since the first definition is just the second one restricted to indicator functions, we just need to show that 1. implies 2. Assume that 2. does not hold. It follows that integration against $\mu$ is not the o... | https://mathoverflow.net |
14,517 | [
"https://physics.stackexchange.com/questions/14517",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2751/"
] | Following the news in serious "non-hype" physics blogs I`ve learnd that as things are now one needs a lot of patience and more data to learn what happens in the higgs sector.
There are already a number of good questions and discussions about what the absence of a higgs would mean for the standard model or more general... | For string theory: If the LHC sees no Higgs, then the standard model has to change (a bit or a lot), so string phenomenology will have a slightly different target to aim at.
For loop quantum gravity: They still can't even describe a particle moving through space, so they have bigger things to worry about than the Hig... | "The field of Higgs would be an exciting new discovery would have found the last pillar of the standard model, ie how to get the mass of elementary particles?"
But it would exclude an interesting discovery, because it would mean that the standard model, which has stood for decades as well as many precision experiments... | https://physics.stackexchange.com |
1,162 | [
"https://mechanics.stackexchange.com/questions/1162",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/91/"
] | I have a 98 Saturn sw2 with a recent problem. Two times now it has stalled while idling and when it doesn't stall it floats near 500 rpms (Usually 750 - 950). The first time, it would start and just drop down to nothing, the next was coming to a stop. These times have been remedied by using the gas pedal to regulate th... | I caved (mainly since it is dangerous to keep driving it like it is) and brought it to my local mechanic. He says it is the Idle Air Intake control. I am not going to accept this answer until I can do a test drive.
<strong>EDIT:</strong> Well my mechanic was right on the nose. The replacement worked like a charm.
| Long shot, but do you have a voltmeter? Check the voltage at the battery when the car is running, might be a faulty alternator.
<br>
<br>
There's a chance you may have developed a vacuum leak, are you handy? You can do this yourself with a bottle of brake cleaner or throttle body cleaner. Spray around the engine bay (... | https://mechanics.stackexchange.com |
43,881 | [
"https://stats.stackexchange.com/questions/43881",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/16967/"
] | I want to simulate temperature data for some "what-if" calculations. The problem is, I only have a time series of 10 actual temperature data values. I want to use temperature as an input to the simulation, so I need a way to generate a large number of temperature values that are consistent with the original 10 values... | Using your assumptions that the points came from a normal distribution with unknown mean and variance, The T distribution is the correct distribution to sample from no matter how many data points you have because it is the posterior predictive distribution of your model. You might want to check your formula though as ... | You could generate a vector of means from a normal distribution (or t if you prefer) representing your uncertainty in the mean, then generate a vector of variances from a $\chi^2$ distribution representing your uncertainty in the variance, then generate the actual observations from a normal with your vector of means an... | https://stats.stackexchange.com |
3,367,419 | [
"https://math.stackexchange.com/questions/3367419",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/702791/"
] | <blockquote>
Given a <span class="math-container">$17^\circ$</span> angle, construct a <span class="math-container">$1^\circ$</span> angle using only a compass and straightedge
</blockquote>
I've tried creating 20 seventeen angles so that there is a <span class="math-container">$360-20*17=20$</span> angle left. Howe... | Note that <span class="math-container">$17 \times 7 = 119$</span>. Can you construct a <span class="math-container">$120$</span>-degree angle?
| Construct a 60° angle and bisect twice. Subtract the result (15°) from the given 17° angle and bisect.
| https://math.stackexchange.com |
632,000 | [
"https://physics.stackexchange.com/questions/632000",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/297351/"
] | I'm looking at the lecture slide of my thermodynamics class, and have a question about the the equilibrium constant: for the reaction
<span class="math-container">$$
SO_4^{-2}+2H^+ <=> H_2SO_4.
$$</span>
The equilibrium constant is given as
<span class="math-container">$$
K(\tau)=\frac{[H^+]^2[SO_4^{2-}]}{[H_2SO_... | The trick is to use the Taylor expansion and the fact that <span class="math-container">$e^Aa^{-A}=1$</span>:
<span class="math-container">$$
e^Af(B)e^{-A} = e^A\sum_{n=0}^{+\infty}\frac{f^{(n)}(0)B^n}{n!}e^{-A}=
\sum_{n=0}^{+\infty}\frac{f^{(n)}(0)\left(e^ABe^{-A}\right)^n}{n!}=
f\left(e^ABe^{-A}\right)
$$</span>
| There's a few different ways to tackle this. One is to expand both <span class="math-container">$e^{iap_x/\hbar}$</span> and <span class="math-container">$f(x)$</span> as power series and multiply them. This will give you terms like <span class="math-container">$p_x^nx^m$</span>. Using the canonical commutation relatio... | https://physics.stackexchange.com |
1,989,255 | [
"https://math.stackexchange.com/questions/1989255",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93671/"
] | I am currently learning about generating functions and
I found an interesting one for harmonic series, $\dfrac{\log(1-x)}{x-1}$.
Is there any hope I could get a formula for $n$th coefficient out of this? The $n$th derivative looks messy...
In absence of formula, can I at least get some asymptotic information, like th... | <span class="math-container">$\newcommand{\bbx}[1]{\,\bbox[8px,border:1px groove navy]{{#1}}\,}
\newcommand{\braces}[1]{\left\lbrace\,{#1}\,\right\rbrace}
\newcommand{\bracks}[1]{\left\lbrack\,{#1}\,\right\rbrack}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\ds}[1]{\displaystyle{#1}}
\newcommand{\expo}[1]{\,\mathrm{e... | It is useful to notice that multiplication of a series $A(x)=\sum_{n=0}^\infty a_nx^n$ with the geometric series $\frac{1}{1-x}$ transforms the sequence $(a_n)_{n\geq 0}$ to a sequence of sums $\left(\sum_{k=0}^na_k\right)_{n\geq 0}$. We obtain
\begin{align*}
\frac{1}{1-x}A(x)&=\frac{1}{1-x}\sum_{n=0}^\infty a... | https://math.stackexchange.com |
28,489 | [
"https://stats.stackexchange.com/questions/28489",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3501/"
] | I am trying to use the dirmult package in R to find the parameters of the dirichlet multinomial distribution. However When I run the code, I see that it appears to be minimizing the Likelihood rather than maximizing. Here is a sample trace:
<pre><code>> foo <- dirmult(data)
Iteration 1: Log-likelihood value: -10... | It looks like it was a problem with initscalar being very far off from the correct value. Setting it to 1 seems to work much better than the default value of 30.
<pre><code>fit <- dirmult(data,initscalar=1)
Iteration 1: Log-likelihood value: -49211.1885266878
Iteration 2: Log-likelihood value: -48023.7318371376
Ite... | (I struck this paragraph now that the questioner has convinced me its inapplicable regarding <code>dirmult</code>.) <strike>Most likely it is minimizing the likelihood in the residual sums (on the log scale), but therefore maximizing the likelihood in the model. The fact that log-likelihoods behave like chi-squared st... | https://stats.stackexchange.com |
458,986 | [
"https://math.stackexchange.com/questions/458986",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/29999/"
] | Let $f_n \in L^p(B)$ be a sequence where $B$ is some ball in $\mathbb{R}^n$. Assume that $\|f_n\|_{L^p(B)} \rightarrow 0$ when $n\rightarrow \infty$, then for any $\phi \in C^\infty_0(B)$, applying Hölder we get
$$
\int_B f_n \phi \le \|f_n\|_{L^p(B)}\|\phi\|_{L^{p/(p-1)}(B)}.
$$
Thus, $\int_B f_n \phi \rightarrow 0$ ... | $\def\d{\mathrm{d}}\def\peq{\mathrel{\phantom{=}}{}}$Denote $C_n = \|f_n\|_{L_{\mathrm{w}}^p}\ (n \geqslant 1)$. For any bounded and measurable $φ$ on $B$, suppose $M = \|φ\|_{L^∞}$. For $n \geqslant 1$,\begin{align*}
&\peq \left| \int\limits_B f_nφ \,\d x \right| \leqslant M \int\limits_B |f_n| \,\d x = M \int_0^{... | Assume that $p>1$. Let $1<q<p$ and $f\in L^{p,\infty}$. Then
$$\int_B|f(x)|^q\mathrm dx=q\int_0^{+\infty}s^{q-1}\mathcal L\{t:|f(t)>s\}\mathrm dx\leqslant q\lVert f\rVert_{p,\infty}\left(\int_{1}^{\infty}s^{q-p-1}\mathrm ds+\mathcal L(B)\right).$$
In particular, the inclusion $L^{p,\infty}\to L^q$ is conti... | https://math.stackexchange.com |
272,050 | [
"https://softwareengineering.stackexchange.com/questions/272050",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/134583/"
] | Short question: Why does Java allow overriding <code>equals()</code>, why is it not final?
I am reading Effective Java 2nd edition by Joshua Bloch.
I am a bit baffled by the conclusion that
<blockquote>
There is no way to extend an instantiable class and add a value component while preserving the equals contract
</... | <code>equals()</code> is a byproduct of an attempt to improve C++ when it was created. C++ has operator overloading which allows you to perform custom operations when called with otherwise valid operators such as <, >, !=, ==, and even =.
The team made the decision (wisely so) to make equality be class method rath... | Simple argument against your logic is, what is the use of the equals method if it's modified to be a final. Then it would execute same logic against any given objects. If you want to compare A and AX in the object class what would be the logic?
Overriding of final method is allowed to be able to verify if two differen... | https://softwareengineering.stackexchange.com |
390,281 | [
"https://stats.stackexchange.com/questions/390281",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/180502/"
] | In null-hypothesis significance testing, if we were to optionally stop data collection every so often and check the p value on the data, the null hypothesis may be eventually be rejected even when it is true.
I would like to simulate some data to help myself understand this problem more deeply, but I'm having trouble... | First of all, I'd like to clear a possible misconception in the first statement of the question. In any hypothesis test, the null hypothesis may be rejected even when it is true. The probability of rejecting the null hypothesis if it is true equals the signification, usually 0.05. In wrong settings like stopping data c... | Something like this?
We check every 10 values if a t-test is significant. Here the loop in unlimited (in reality it usually isn't). In a next step we show what happens if you continue sampling (to an arbitrary total number).
<pre><code>set.seed(42) #for reproducibility
mean <- 0
sd <- 1
x <- numeric()
test ... | https://stats.stackexchange.com |
169,239 | [
"https://physics.stackexchange.com/questions/169239",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/58482/"
] | I have the following two density operators, the paper I am reading says that these two operators have same eigenvalues
<br>
$$\rho^i = \frac{1}{3} ( |0\rangle \langle 0 | +|1\rangle \langle 1 |+|2\rangle \langle 2 |+a|0\rangle \langle 1 |+a|1\rangle \langle 0 |+c|1\rangle \langle 2 |+c|2\rangle \langle 1
|),$$
$$\rh... | <blockquote>
I have the following two density operators, the paper I am reading
says that these two operators have same eigenvalues <br>
$$\rho^i = \frac{1}{3} ( |0\rangle \langle 0 | +|1\rangle \langle 1
> |+|2\rangle \langle 2 |+a|0\rangle \langle 1 |+a|1\rangle \langle 0
> |+c|1\rangle \langle 2 |+c|2... | Hints:
<ol>
<li>What happens to the density operator and its eigenvalues under a change of the orthonormal basisvectors $|0\rangle $, $|1\rangle $, $|2\rangle$ by phase factors?</li>
<li>More generally, what happens to the density operator and its eigenvalues under a unitary transformation $\rho\longrightarrow U^{\dag... | https://physics.stackexchange.com |
4,696 | [
"https://electronics.stackexchange.com/questions/4696",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1333/"
] | I am very new to electronics so please go easy on me.
Whilst I have read a couple of electronics fundementals books so far, one of the things that confuses me the most about electronics is how voltage and current is managed based on the fact that current affects the whole circuit.
Here is a very simple explanation of... | The current through each LED would not change. Each one would draw 5/330 or 15mA (I=V/R). The power supply would have to supply 4*15mA or 60mA. You didn't change the amount of current through any of the LEDs, all you did is add more of them in parallel.
Let's use a classic water analogy: you have a bucket of water ... | Ohm's law: V = R x I
As you can see, voltage is directly proportional to resistence and current. The current through an ideal voltage source is completely determined by the external circuit. The ideal voltage source does not change its voltage. So, when the resistance value decreases, the current value must increase t... | https://electronics.stackexchange.com |
144,602 | [
"https://softwareengineering.stackexchange.com/questions/144602",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51061/"
] | I'm finding it very difficult to write complex SQL queries involving joins across many (at least 3-4) tables and involving several nested conditions. The queries I'm being asked to write are easily described by a few sentences, but can require a deceptive amount of code to complete. I'm finding myself often using tem... | I'm basing most of this on just trying to get the "right" answer, so you may discover there are some performance issues. No point in speeding up an incorrect query.
<strong>Understand the table relationships</strong> - Most will be one to many. Know the "many" table. Identify the fields required for your joins.
<stro... | <ol>
<li><strong>Indentation</strong> would be the first thing to do, if you're not doing it already. Not only it's useful with even simple queries, but it is crucial when it comes to joins and queries a bit more complex than a <code>select top 1 [ColumnName] from [TableName]</code>.
</li>
<li>Once indented properly, n... | https://softwareengineering.stackexchange.com |
3,637,631 | [
"https://math.stackexchange.com/questions/3637631",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/732532/"
] | Someone recommended Eisenbud's Section 15 to me, but I am finding it to be a little too terse. Does anyone know of a fairly self-contained introduction to the topic? I am just now finishing up a graduate level course on ring and field theory, so I am at least familiar with the basic ring theoretic concepts.
| For a longer exposition, you could try Cox, Little and O'Shea's book <em>Ideals, Varieties, Algorithms.</em>
This book contains a treatment of Grobner bases and a handful of variations on the Buchberger algorithm as it pertains to affine and projective algebraic geometry, with applications to topics like elimination t... | 2nd <em>Ideals Varieties, and Algorithms.</em> Cox, Little, and O'Shea's followup <em>Using Algebraic Geometry</em> is also a good reference that includes more advanced topics than IVA, such as Groebner bases for modules over polynomial rings, Groebner fan, and Groebner walks.
| https://math.stackexchange.com |
34,578 | [
"https://stats.stackexchange.com/questions/34578",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13397/"
] | I want to estimate the survival function $S(t_0)=1-F(t_0)$, at a specific point $t_0$ where $F$ is a continuous cumulative distribution function, based on an uncensored sample $x_1,..,x_n$ and a nonparametric estimator. So far, I am considering two estimators $\hat S(t_0)=1-\hat F(t_0)$, where $\hat F$ is
(1) Kernel d... | Kaplan-Meier is the standard non-parametric survival estimator, which I'm guessing is what you meant by empirical CDF. You can get confidence intervals by various means with it so unless you want to go down a parametric route or start looking for more interesting things about the data I would say you're done!
| Kaplan-Meier and the smoothed version of the cdf are the only two nonparametric methods that come to mind. Many time in practice parametric models such as the negative exponential or the Weibull can be reasonable to assume. In such cases the parametric fit would be preferable.
| https://stats.stackexchange.com |
148,790 | [
"https://mathoverflow.net/questions/148790",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19394/"
] | Given a $p \times p$ positive definite matrix $\Sigma$, why eigenvectors of $\Sigma$, stacked as columns of a matrix $R \equiv [r_1 \, r_2 \, \ldots \, r_p]$, optimize the following orthogonally constrained minimization problems?
$$
\mathrm{minimize}~~~~\log \det\big( I \odot (R^\mathsf{T}\Sigma R) \big)~~~~~\text{s.t.... | Your minimization problem is equivalent to
\begin{equation*}
\min_{R^TR=I}\quad\prod_{i=1}^p r_i^T\Sigma r_i,
\end{equation*}
and it can be shown (using <em>Hadamard's determinant inequality</em> and some more argumentation) that this minimum overall $p$ orthonormal tuples is achieved by choosing the $r_i$ correspondin... | Because $r_i$ is supposed to be unit norm, one can replace $r_i$ with $\frac{r_i}{\lVert r_i \rVert}$ in the objective and obtain:
$$
\mathrm{minimize}~~~~\sum_{i=1}^p \log \Big( \frac{r_i^\mathsf{T}\Sigma r_i}{r_i^\mathsf{T}r_i} \Big)~.
$$
Now, taking the derivative of this objective with respect to $r_i$ (forgetting ... | https://mathoverflow.net |
173,406 | [
"https://dba.stackexchange.com/questions/173406",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/124683/"
] | Is it possible to report an error (raise exception or anything) in merge's when-not-matched-then clause? I'm aiming for something like
<pre><code>WHEN NOT MATCHED THEN RAISE NO_DATA_FOUND;
</code></pre>
Or anything that will tell the caller that script failed.
| You can do this using a trigger.
Note: This is <em>HORRIBLE</em>, but I can't think of another way of achieving this.
Test tables:
<pre><code>create table testmerge
(
col1 number primary key ,
col2 number
);
insert into testmerge values ( 1, 1 );
create table testmerge2
(
col1 number primary key,
col2 number
);
... | My feeling doing a Merge is the same as doing a select statement, then inserting data that does not yet exist in the target table and updating data where the primary key is already there. It sounds like you are saying that all of the data should be there in advance and you are just updating some columns based on new da... | https://dba.stackexchange.com |
44,616 | [
"https://electronics.stackexchange.com/questions/44616",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10067/"
] | <img src="https://i.stack.imgur.com/LPZjr.png" alt="Circuit Diagram">
I'm wondering what are the behaviors of the inductor, L, and capacitor, C, at t = 0+
Please correct my understanding of the above circuit if I am wrong.
<ul>
<li>At t = 0, the capacitor acts like a wire. So I think that Vc must = 0 since a theoret... | You confuse the role of capacitor and inductor.
<ul>
<li>The inductor acts as a wire and the capacitor is an open circuit in static conditions</li>
<li>At t = 0- you have iC = 0, iL = 0.5A and vL = vC = 0</li>
<li>At t > 0 you have iL = -iC, vL = vC and Ic = C*vC', vL = L*iL'</li>
<li>As a consequence of vL = -L*C*vL... | I'm not sure where this "behaves like a wire" and "behaves like an open circuit" stuff comes from, but you're not the first one to bring this up, so it must be how they're teaching this stuff these days. To an old-timer like me, it doesn't seem like the clearest way to go about presenting this material.
To solve this ... | https://electronics.stackexchange.com |
1,117,003 | [
"https://math.stackexchange.com/questions/1117003",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/210137/"
] | I'm going to write down my problem verbatim:
<blockquote>
Write down the integers from $1$ to $50$ in rows of $10$ numbers each.
Mark out $1$, and then cross out all multiples of $2$ greater than $2$
(i.e., cross out, $4, 6, 8, . . . ). 3$ is not crossed out, so cross
out all multiples of $3$ greater than $3$ ... | It is known that a composite integer $a$ has a prime divisor $p$ that satisfies the inequality $p\leq a$. If you let $a=50$, then it will have prime divisor $p$ that is less than or equal to $\sqrt{50}$.The greatest among possible p's is 7. Thus in employing the Sieve you will just cross out the multiples of prime $p$ ... | $7$ is the largest integer less than the square root of $50$.
| https://math.stackexchange.com |
152,818 | [
"https://stats.stackexchange.com/questions/152818",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/77423/"
] | For my master thesis I basically want to find out, why developing countries are stagnating. Next to theoretical aspects I also want to make a regression.
I want to regress GDP or GDP growth as dependent variable on many independent variables, such as tenure of head of state, life expectancy, working hours restriction, ... | Basically, there's no ambiguity here: you must use the differences in the regression. There could be some discussion whether it's a simple difference or a log difference, but the latter is more common in the literature. If you had a cross-section, then this wouldn't matter. For a short period of time it probably doesn'... | You are interested in why countries are "stagnating"; stagnation is about a lack of growth, so, GDP growth seems logical.
A couple notes:
1. You will need data on countries that are growing at different rates.
2. If you are using data from different years for the same countries (e.g Ghana in 2011, Ghana in 2012, Ghan... | https://stats.stackexchange.com |
528,248 | [
"https://electronics.stackexchange.com/questions/528248",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/233389/"
] | Can someone clear this up for me once and for all? I feel like Thomas Edison really screwed me when he made everyone believe that current is movement of positive charges.
Do electrons go from high voltage to low voltage or from low voltage to high voltage?
| <blockquote>
I feel like Thomas Edison really screwed me when he made everyone believe that current is movement of positive charges.
</blockquote>
As we're 'clearing things up', let's be very careful in our language.
Current is the movement of charges, both negative and positive.
Current, aka Conventional Current (beca... | The electric field is defined as pointing from positive to negative. Electrons are repelled from the negative and attracted to the positive, hence they move in the OPPOSITE direction that the electric field is pointing. So I guess you could say electrons want to move from the more negative/less positive voltage to the ... | https://electronics.stackexchange.com |
206,623 | [
"https://softwareengineering.stackexchange.com/questions/206623",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/98222/"
] | I was just wondering why does Java compiler decide whether you can call a method based on the "reference" type and not on actual "object" type? To explain I would like to quote an example:
<pre><code>class A {
void methA() {
System.out.println("Method of Class A.");
}
}
class B extends A {
void m... | Your example is in some way a special case. In a non trivial program you can typically not determine the class of the object a certain reference points to better than "it is of the type the reference was declared for or a subtype of it".
The whole concept of polymorphism is based on the fact that the concrete class is... | By declaring <code>ob</code> as a <code>A</code>, you're telling the compiler that you are using an object that behaves like <code>A</code>.
Java performs strict type checking. If you tell that <code>ob</code> is an instance of <code>A</code>, then, whatever you assign to it, Java will make sure you keep to <code>A</c... | https://softwareengineering.stackexchange.com |
536,024 | [
"https://physics.stackexchange.com/questions/536024",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/237114/"
] | I have heard contradictory ideas about spacetime and the fourth dimension. Some talk as though it is spatially tangent to all other dimensions and this is where the curvature of spacetime occurs. Is this true?
| Imagine you found a spherical ball with a surface area equal to <span class="math-container">$4 \pi r^2$</span>, for some <span class="math-container">$r$</span>, but the distance between the centre of the ball and its surface was not equal to <span class="math-container">$r$</span>. In that case the 3-dimensional spac... | There isn't a notion of time being "spatially tangent." Let us take for simplicity flat Minkowski spacetime <span class="math-container">$\mathbb{R}^{1,3}$</span>. We can identify vectors tangent to a point <span class="math-container">$p \in \mathbb{R^{1,3}}$</span> with the vector in <span class="math-container">$\ma... | https://physics.stackexchange.com |
25,764 | [
"https://stats.stackexchange.com/questions/25764",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8402/"
] | I have several distributions (10 distributions in the figure below). <img src="https://i.stack.imgur.com/Tcz9b.jpg" alt="distributions">
In fact these are histograms: there are 70 values on the x-axis which are the sizes of some particles in a solution and for each value of x the corresponding value of y is the propor... | I understand you such that all distributions can potentially take on the same 70 discrete values. Then it will be easy for you to compare <em>cumulative</em> curves of the distributions (comparing cumulative curves is the general way to compare distributions). That will be omnibus comparison for differences in shape, l... | If your data are histograms, you might want to look into appropriat distance functions for that such as the "histogram intersection distance".
There is a tool called ELKI that has a wide variety of clustering algorithms (much more modern ones than k-means and hierarchical clustering) and it even has a version of histo... | https://stats.stackexchange.com |
489,557 | [
"https://electronics.stackexchange.com/questions/489557",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/175267/"
] | I just learnt, mostly by reading about something else, that magnetos are the primary sources of ignition in planes and other types of engines. The article I read said that it was important that a P-lead was working properly because if it wasn't, then moving the blade or propeller could instantly start it up, and there ... | "P-lead" is not an electrical engineering term. It appears to be exclusively a term used with aircraft magnetos. In electrical engineering, we would call the "p-lead" connection a short circuit. It provides a low resistance path that allows current to flow past an area where you want to prevent it from flowing. For an ... | So on lawnmowers the magnetos have two coils. One of them is high tension with very fine wire and a huge number of turns, the large number is required for high enough voltage to ionize air and cause a spark, which ends up being a tiny current due to high coil resistance and inductance. The spark pulse is cause by induc... | https://electronics.stackexchange.com |
196,746 | [
"https://security.stackexchange.com/questions/196746",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/187682/"
] | I haven't really understood whether firmware level infection (on either motherboard or drives) can actually be a thing without physical access, however how can one factory reset the firmware in that case?
Is there, in particular, a way to be sure it was reset to a clean version, without interference from a malicious ... | <blockquote>
I haven't really understood whether firmware level infection (on either motherboard or drives) can actually be a thing without physical access
</blockquote>
It's possible because you can update the firmware on many boards without actually needing physical access. The common case is to use the EFI Capsu... | You can use Hasleo EasyUEFI Professional to Delete, Backup, Restore, Rebuild the EFI system partition. And you can use Diskpart to assign a letter to it and explore it. But the letter assignment will be removed on reboot.
| https://security.stackexchange.com |
65,952 | [
"https://security.stackexchange.com/questions/65952",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/11679/"
] | I recently tried to use Fiddler2 from a third-party vendor Telerik. While decrypting the HTTPS traffic of my network, it asked me to install its own root certificate in my Windows operating system:
Take a look at the below screenshot:
<img src="https://i.stack.imgur.com/FueX5.jpg" alt="enter image description here">
... | It's safe as long as you understand the implications.
Fiddler acts as a proxy / man in the middle to intercept and decrypt traffic between you and the target.
For SSL sites, it does this by dynamically generating an SSL certificate with the name of the target. The problem is that your browser will not trust certific... | The way that I understand that Fiddler (And similar proxyies such as Burp or OWASP ZAP) work is that each installation generates a unique root certificate which it then uses to generate certificates on the fly when you have it assigned as a proxy, so you can intercept and modify traffic flowing over this connection (th... | https://security.stackexchange.com |
187,756 | [
"https://physics.stackexchange.com/questions/187756",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/82503/"
] | A question asks you to determine the relationship between true weight and apparent weight when an elevator that has descended from the 50th floor is coming to a halt at the first floor.
I believe that as the elevator is coming to a halt, the acceleration is decreasing (close to zero), and so this downward acceleration... | First and foremost, I assume you've been in an elevator? Don't you feel heavier (your feet have to push a little harder) when the elevator stops at the first floor (i.e. stops after going downward)? So it should be intuitive that your apparent weight would be greater than your true weight.
However, when in doubt, dr... | If you are in a non-inertial reference frame inside the elevator that is accelerated in the upward direction, then you experience a pseudoforce downwards (we assume downwards is positive) ($F_{pseudo}=0-(-ma)=ma$. So the apparent weight is N=mg+ma and the apparent weight increases.
| https://physics.stackexchange.com |
2,140,355 | [
"https://math.stackexchange.com/questions/2140355",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/280080/"
] | Let $f(z)$ de defined by
$f(z)=2z/(z+1)$ for $z\not=0$
and $f(z)=1$ for $z=0$.
So I want to assume the function is continuous at $z=0$ and then come to a contradiction. So i have $|2z/(z+1)-1|<\epsilon$ which makes:
$|z-1|/|z+1|<\epsilon$ and i do not really know what to do here. Any help will be appreciated. ... | By the triangle inequality $|1+z|\geq |1|-|z|=1-|z|.$
$$\text {So }\quad |z|<1/3\implies |1+z|\geq 1-1/3\implies |1+z|^{-1}\leq 3/2\implies $$ $$\implies |z(1+z)^{-1}|=|z|\cdot |(1+z)^{-1}|=$$ $$=|z|\cdot |1+z|^{-1}\leq |z|\cdot 3/2\leq (1/3)(3/2)=1/2.$$
$$\text {Therefore }\quad0<|z|<1/3\implies |f(0)-f(z... | By a simple change of variables $w := z+1$ we have $f(w) = 2(w-1)/w = 2 - 2/w$, so your function has no hope of being continuous at this point - it has a pole there.
To finish your argument, make the same change of variables, and then note that as $w \to 0$, you can make paths that blow up any way you want in the comp... | https://math.stackexchange.com |
205,985 | [
"https://mathoverflow.net/questions/205985",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1946/"
] | A first-order structure $M$ is <em>Leibnizian</em>, if any two distinct
elements $a,b\in M$ satisfy different $1$-types; that is, if there
is some formula $\varphi$ such that $M\models\varphi(a)$ and
$M\models\neg\varphi(b)$. Thus, a Leibnizian model is one in which
you can distinguish any two elements by properties ex... | $\newcommand\Z{\mathbb{Z}}\newcommand\P{\mathbb{P}}$Here is a simple account of a large class of examples.
<strong>Theorem.</strong> With probability one, the structure
$\langle\Z,<,A\rangle$ is Leibnizian and has no definable
elements, where $<$ is the usual order on the integers and
$A\subset\Z$ is a unary pre... | Here is a different example.
For any irrational $a$, put $\mathcal M_a=\langle\mathbb Q,<,M,I_a\rangle$, where
\begin{align*}
M(x,y,z)&\iff y=\frac{x+z}2,\\
I_a(x)&\iff a<x<a+1.
\end{align*}
In $\mathcal M_a$, we can define the interval $(a,a+1/2)$ by the formula
$$I_a(x)\land\forall u,v\,\bigl(I_a(u... | https://mathoverflow.net |
12,222 | [
"https://security.stackexchange.com/questions/12222",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/8092/"
] | Having a debate with a coworker about the merits & faults of public key authentication with ssh.<br>
I'm basically wondering what all the possible merits and faults are, especially in regards to passwordless private keys.
In our environment, ssh is not accessible to the outside world. Meaning that you would have t... | This is a typical defence-in-depth question. Why do I need X if I already have Y and Z in place?
The common answer is that your security is usually as good as its weakest link. In your case, your one and only security mechanism appears to be your VPN. This is your strongest and weakest link. In your opinion it is enou... | There are two main ways for an attacker to obtain the private key file:
<ul>
<li>By compromising the client machine, in which case the attacker can usually obtain the password as well.</li>
<li>By compromising a backup of the client machine, or stealing that machine.</li>
</ul>
If you're comparing private key authent... | https://security.stackexchange.com |
16,616 | [
"https://dba.stackexchange.com/questions/16616",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6173/"
] | I was taught not to use the name <code>Id</code> for the identity column of my tables, but lately I've just been using it anyways because it's simple, short, and very descriptive about what the data actually is.
I've seen people suggest prefixing <code>Id</code> with the table name, but this just seems to make more wo... | Here's a summary of all the answers about the advantages obtained from the convention to not use a common name for all primary keys:
<ul>
<li>Less mistakes, since the identity fields are not named the same
You cannot mistakenly write a query that joins on <code>B.Id = B.Id</code> instead of <code>A.Id = B.Id</code>, be... | The table name prefix has very good reasons.
Consider:
<pre><code>TableA (id int identity, stringdata varchar(max))
TableB (id int identity, stringdata varchar(max))
</code></pre>
We want to <code>DELETE</code> from <code>TableA</code> records that exist in both tables. Easy enough, we will just do an <code>INNER ... | https://dba.stackexchange.com |
652,164 | [
"https://physics.stackexchange.com/questions/652164",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | The weak equivalence principle is (from the Weinberg book)
<blockquote>
<em>At every space-time point in an arbitrary gravitational field it is possible to chose a 'locally inertial coordinate system' such that, within a sufficiently small region of the point in question the laws of motion of freely falling particles t... | It is not possible that both the input voltage and current are given as constant. Therefore this answer assumes that:
<ul>
<li>The 12V power supply is a stable DC power supply such as a car-battery.</li>
<li>The current of 2A mentioned in the question is the <em>measured current</em>.</li>
</ul>
Under these assumptions... | As far as I know, there is no simple yes-or-no answer to this question. The theory of electrodynamics uses Maxwell's equations to calculate forces on charges and magnetic moments, it has nothing to do with the motion of bodies or gravity, for which their mass (having weight in some gravitational field) is important. Th... | https://physics.stackexchange.com |
89,229 | [
"https://mathoverflow.net/questions/89229",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11661/"
] | I apologize if this is a trivial question. If $X$ is a smooth irreducible codimension two subvariety of projective space $\mathbb P^n$, then does there always exist a smooth irreducible codimension one subvariety $Y \subset \mathbb P^n$ with $X \subset Y$ ?
| For $n = 3$ this is always true. It is also true when $X$ is a complete intersection.
Suppose $n ≥ 4$, and suppose that $Y$ exists; then by a well known result of Lefschetz $X$ is a hyperplane section of $Y$, and so $X$ is a complete intersection. Now, for $m = 4$ there are subvarieties of $\mathbb P^4$ that are not c... | The obvious thing to do is to choose $H$ a general hypersurface containing $X$. In other words, choose a general global section of $I_X \otimes O_{P^n}(k)$ for $k \gg 0$.
Certainly $H$ is smooth away from $X$ by Bertini. I don't see why it should be smooth along $H$ though (unless of course, $X$ is a complete inte... | https://mathoverflow.net |
185,889 | [
"https://dba.stackexchange.com/questions/185889",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/97323/"
] | I have the following query that is used to define a view in MySQL. But the query takes forever to complete even if I perform the query outside the view. I have a feeling that the inner select is what's slowing things down, but i have no idea how to optimize it further. HELP PLEASE!
<pre><code>SELECT DISTINCT
`t... | Yes, the subselect is slowing you down. This is because it has to execute that query for every single row of the outer query. The bigger the outer table, the more times you have to run that same query again.
By moving it out to a join you will only have to execute it once.
<pre><code>SELECT DISTINCT
`table1`.`... | If you don't need to check the column for <code>NULL</code> before counting it, leave it out. That is: <code>COUNT(col2)</code> --> <code>COUNT(*)</code>
<code>tbl1</code> needs either of these:
<pre><code>INDEX(col1, date)
INDEX(date, col1)
</code></pre>
PLEASE do not have an alias (<code>tbl1</code>) the same as... | https://dba.stackexchange.com |
257,806 | [
"https://stats.stackexchange.com/questions/257806",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/120380/"
] | I wanted to rephrase an earlier question to try and be less vague. I'm essentially looking for help understanding basic Bayesian inference.
Let's say I want to predict the transfer rate of a high school in its first year of existence. To do this I feel like the ideal set up would be looking at it from a Bayesian persp... | Apparently, whatever this "transfer rate of a high school" thing is, it seems to be a result of a binomial process and you are trying to find a model for each students "chance of a transfer", which I'll call <span class="math-container">$\theta$</span>. Now the KISS approach would be to assume an identical <span class=... | Your idea is to learn about the transfer rate for a school for which you as yet have no data from a collection of related schools for which you do have data. This is a great idea and the Bayesian approach is the right way to go. In the Bayesian framework, your "willingness to learn" amounts to an assertion of prior dep... | https://stats.stackexchange.com |
11,345 | [
"https://dsp.stackexchange.com/questions/11345",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/5808/"
] | I'm trying to create a digital filter from a first order analog filter with transfer function
$$H(s)=\frac{1}{1+\tau s}$$
with time constant $\tau=.1\text{s}$, and sampling rate $f_s=1000\text{Hz}$.
Applying the bilinear transform in Matlab however appears to yield a filter with the a different 3dB point than expect... | The expected 3dB frequency is wrong because of radian conversion. With $s=j\omega$,
$$H(j\omega) = \frac{1}{1+\tau j\omega} $$
and $20\log_{10}|H(j\omega)|\approx-3$
when $\omega=\omega_{3dB}=\frac{1}{\tau}$. However $\omega=2\pi f$, so
$$f_{3dB}=\frac{\omega_{3dB}}{2\pi}=\frac{1}{2\pi\tau}.$$
With $\tau=0.1\text{s}$,... | I was able to play around with the frequency warping parameter to get a result close to what you're looking for. The parameter value didn't turn out to be what I expected it to be, but I got a decent shape out of it anyway:
<pre><code>[numd,dend]=bilinear(num,den,fs, 470);
</code></pre>
<img src="https://i.stack.imgu... | https://dsp.stackexchange.com |
163,658 | [
"https://softwareengineering.stackexchange.com/questions/163658",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/63418/"
] | Since programming languages initially only used lines of code executed sequentially, and it evolved into including functions which were one of the first levels of abstraction, and then classes and objects were created to abstract it even further; what is the next level of abstraction?
What's even more abstract than cl... | I think you have some misconceptions about the history of computing.
The first abstraction (in 1936) was, in fact, Alonzo Church's Lambda Calculus, which is the foundation for the concept of high-order functions and all of the functional languages that followed. It directly inspired Lisp (the second oldest high-level ... | For many, the purest form of code abstraction in the current era of binary programming is the "higher-order function". Basically, the function itself is treated as data, and functions of functions are defined, much as you would see them in mathematical equations with operators defining the result of their operands and ... | https://softwareengineering.stackexchange.com |
1,675,185 | [
"https://math.stackexchange.com/questions/1675185",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/186998/"
] | I think the domain is all real except $(0,0)$, because this point anulates the denominator, but what about with the fact that the limit exists when $(x,y)$ tends to $(0,0)$?
| The domain of $f$ is all real numbers except when $\sqrt{x^2+y^2} = 0$. But, this occurs when $x^2 + y^2 = 0$ which, in turn, occurs only when $x=y=0$. Therefore,
$$ \text{Domain}(f) = \mathbb{R}^2 \setminus \{ (0,0) \} $$
| It can be made continuous, with domain $\mathbb{R}^2$, by defining $f(0,0)=0$, but the domain of the given function excludes $(0,0)$.
| https://math.stackexchange.com |
132,247 | [
"https://mathoverflow.net/questions/132247",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15728/"
] | I have a question about some quotient groups of the lower central series of a free group.
When there's a free group $F = \langle x_1,\cdots, x_n, y_1, \cdots, y_m\rangle $,
let $A$ be the subgroup generated by elements of the forms $[x_i, a]$ in $F_{k+1}/F_{k+2}$, with $1\leq i\leq n$ and $a\in F_{k}/F_{k+1}$;
and ... | I don't believe so.
I will associate my commutators on the left, so that $[a,b,c]=[[a,b],c]$; and use $[x,y]=x^{-1}y^{-1}xy$; I'm not sure it matters, but that's what I'm used to.
Say $k=2$; in $F/F_{4}$, the Hall-Witt identity becomes
$$ [r,s,t][s,t,r][t,r,s]\equiv 1\pmod{F_{4}}.$$
Now consider the case where $a_1... | Not necessarily. By the Jacobi Identity, in $F/F_4$ we have for example
$[x_1,[x_2,y_1]][x_2,[y_1,x_1] = [y_1,[x_1,x_2]]^{-1}$.
For your second question, the rank of $A$ is clearly at most $n$. For $k=2$, you could choose $a_i=x_i$, so it could be anything between 0 and $n$. For $k>2$, the relation above shows tha... | https://mathoverflow.net |
459,601 | [
"https://physics.stackexchange.com/questions/459601",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9435/"
] | I had a coworker bring up time reversibility during a lunchtime conversation the other day and how physical systems would behave. Sparing the unimportant details of the conversation, his position was that: if you were to break an egg it would unbreak by running the clock backward.
I've never studied this, but my knee-... | The uncertainty principle isn't quite relevant here. Quantum physics is unitary, which means you can un-do everything by running it backward — provided you include the whole system (not just the egg) in the quantum model, including whatever physical entities are used to make measurements. The uncertainty principl... | <strong><em>tl;dr</em>-</strong> It depends on how perfectly you "<em>reverse time</em>"; a perfect reversal would unbreak the egg, while imperfect reversals might not. Any system in which information is conserved, i.e. in which earlier states can be perfectly predicted from later states, can describe a perfect time ... | https://physics.stackexchange.com |
493,719 | [
"https://electronics.stackexchange.com/questions/493719",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/220456/"
] | I am going through analog electronics.
I have seen many designs but I have a few questions below :
My Questions :
I understand that resistors are used to limit current in some places. And in other places, resistors are used to pull up/pull down the voltage and make sure that node is in a defined voltage state instea... | Selecting a resistor depends on the circuit/block in question. As you already mentioned, different applications demand different requirements.
For example, here are a few things to consider:
<strong>Pull up / down</strong>
Small resistors (aka "strong" pull up/down) are used when some nodes must be held at a given... | Generally by limiting current flow resistors are altering voltage levels. Now, you can halve a voltage by using two resistors as a divider network, with input voltage at the top, ground at the bottom and tapping off between the resistors. However, choosing the value is not quite so simple. You might think that to reduc... | https://electronics.stackexchange.com |
23,778 | [
"https://security.stackexchange.com/questions/23778",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15505/"
] | Our company schedules Security Training courses for our personnel.
In order for us to test them, we develop code such as keyloggers which we email to our personnel to detect stupid personnel, and of course we want to know whether our antiviruses detect this code.
We send keyloggers by email to all personnel and renam... | No, anti-malware packages will not detect <em>every</em> form of keylogger. They will detect known ones by hashing, and some may detect certain keylogger-like behaviour via heuristic analysis.
However, I <strong>strongly</strong> advise you against this. First off, it's insulting to your employees. If I found out my e... | No, not every keylogger will be found.
Just like viruses, Anti-Virus-Softwrae can only detect stuff they know and/or detect "strange" behaviour.
And: Hardware-Keylogger will most likely not be detected at all.
| https://security.stackexchange.com |
3,615,122 | [
"https://math.stackexchange.com/questions/3615122",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/734735/"
] | <blockquote>
Let <span class="math-container">$V=P_n(F)$</span> (the vector space of polynomials with coeffficients in R of degree at most n), and let <span class="math-container">$c_0,c_1,...,c_n$</span> be distinct scalars in F. show that there exist unique polynomials <span class="math-container">$p_0(x),...,p_n(x... | <span class="math-container">$$x^2+y^2+xy=1/2 \implies \frac{(x+y)^2+(x-y)^2}{2}+\frac{(x+y)-(x-y)^2}{4}=\frac{1}{2}$$</span>
<span class="math-container">$$\implies \frac{3}{2}(x+y)^2+\frac{(x-y)^2}{2}=1$$</span>
<span class="math-container">$$\implies \frac{(\frac{x+y}{\sqrt{2}})^2}{1/3}+\frac{(\frac{x-y}{\sqrt{2}})^... | Let <span class="math-container">$\sqrt{2}x = u+v$</span> and <span class="math-container">$\sqrt{2}y=u-v$</span>. Then the resulting expression is
<span class="math-container">$$3u^2 + v^2 = 1$$</span>
which is the standard form of an ellipse and since the transformation is a pure rotation, the shapes of the objects... | https://math.stackexchange.com |
1,449,204 | [
"https://math.stackexchange.com/questions/1449204",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/52694/"
] | The group $\Bbb A_\Bbb Q/\Bbb Q$ of adeles mod rationals is:
<ol>
<li>Isomorphic to the solenoid</li>
<li>Isomorphic to the group $\Bbb A_\Bbb Z/\Bbb Z$</li>
<li>Dual to the rational numbers</li>
</ol>
This raises the question of the structure of the individual groups $\Bbb Q_p / \Bbb Q$ of p-adic numbers mod rationa... | The key is in the dots. It is tough to get a handle on an infinite thing, so usually, it would be a process:
<blockquote>
<ol>
<li>Start with $x_1=5$ </li>
<li>Calculate $x_2=5+6/x_1$ </li>
<li>Calculate $x_3=5+6/x_2$ </li>
</ol>
</blockquote>
Carry on; what is the limit of $x_n$?<br>
Suppose $x_n=6+y... | I really dislike the equality $$\sum _{n=1}^{\infty }n=-\frac {1} {12}.$$ It is much better to write it as $$\zeta(-1)=-\frac1{12},$$ where $\zeta$ is Riemann's zeta function. And $$\sum _{n=1}^{\infty }n=+\infty$$ is absolutely true.
And for the original question, the method is valid only when the expression has a ... | https://math.stackexchange.com |
5,252 | [
"https://electronics.stackexchange.com/questions/5252",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1610/"
] | Let me start off by saying that I know just enough about electronics to be dangerous (how to solder, follow a simple schematic, and check for connectivity problems and usually figure out what each wire is for).
I've installed a cruise control kit in my car, and I want to use a set of Honda steering wheel controls inst... | I assume by switching, you mean logic level translation. That is, you want to step 5V up to 12V.
The simplest solution would be a set of 5V SPST relays, connecting the coil to the switches and the NO (normally open) to the 12V and the output to the cruise control system.
If you want a cheaper and better solution you co... | The potential safety issue is the current, not the voltage. You can use a resistor to limit the current so a short won't cause irritating fires. The control switches may not be expected to pass a significant amount of current but you can measure that with a multimeter.
| https://electronics.stackexchange.com |
1,661,466 | [
"https://math.stackexchange.com/questions/1661466",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/315587/"
] | I can't seem to be able to get the correct signs for this derivative.
$\frac{d}{dx}(4x^5\tan(\frac{-1}{x}))$
Here's my work:
$= (4x^5)'\tan(\frac{-1}{x}) + 4x^5(\tan(\frac{-1}{x}))'$
$= 20x^4\tan(\frac{-1}{x}) + 4x^5(\tan(\frac{-1}{x}))'$
$= 20x^4\tan(\frac{-1}{x}) + 4x^5(\frac{-1}{x})'\sec^2(\frac{-1}{x})$
$= 20x... | Hint $sec(-\theta)=sec(\theta)$ thats the only mistake.
| Wolfram Alpha is using odd-even angle identities to turn $+\sec^2(-1/x)$ into $-sec^2(1/x)$ (and appears to do the same thing to the tangent function when I plug thd equation into Wolfram Alpha myself). This isn't really necessary, and so your answer is correct; doing so just removes a $-$ sign, making the expressio... | https://math.stackexchange.com |
238,629 | [
"https://mathoverflow.net/questions/238629",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15197/"
] | Suppose $Y$ is a 3-manifold and the boundary $\Sigma:=\partial Y$ is non-empty. Let $G$ be a Lie group with trivial center. Let $\overline {\mathcal A}_{flat}(\Sigma)$ and $\overline {\mathcal A}_{flat}(Y)$ denote the gauge equivalence classes of flat connections on the trivial bundles $\Sigma \times G$ and $Y \times G... | Another good reference is Chris Herald's paper. Legendrian cobordism and Chern-Simons theory on 3-manifolds with boundary. Comm. Anal. Geom. 2 (1994), no. 3, 337–413.
It is an easy exercise with Poincare duality to see that the image of the map in cohomology (so at the level of "Zaraski" tangent spaces)
$$
H^1(Y;ad_\... | For the case of compact $G$, see Proposition 3.27 in: Freed, Daniel S. <em>Classical Chern-Simons theory. I.</em> Adv. Math. 113 (1995), no. 2, 237–303.
For the case of complex reductive $G$, see Theorem 61 in: Sikora, Adam S. <em>Character varieties.</em> Trans. Amer. Math. Soc. 364 (2012), no. 10, 5173–5208.
| https://mathoverflow.net |
35,420 | [
"https://electronics.stackexchange.com/questions/35420",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8769/"
] | <img src="https://i.stack.imgur.com/izkxp.png" alt="Schematics of figure 1-36">
The question asked is the following: <img src="https://i.stack.imgur.com/GYz3Y.png" alt="image of question being asked">
The book says that the correct answers are: \$V_{limit}\$ = 0V, \$V_{diode}\$ = 5V.
I don't get why it ended up like... | No current is right, because your circuit is interrupted, and you need a closed circuit to get current flowing.
<img src="https://i.stack.imgur.com/PSrww.png" alt="enter image description here">
And when there's no current through the resistor there won't be a voltage drop across it neither, per Ohm's Law: Voltage ... | "Fails open" is not fail to open. "Fails open" means that it blows up and becomes an open circuit, so in this case there would be the full 10V across its terminals, with 0V across the limit resistor. I don't see how anyone can get 5V.
If it "failed to open" it would presumably remain as a working diode with 0.7V or so... | https://electronics.stackexchange.com |
1,212,451 | [
"https://math.stackexchange.com/questions/1212451",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/227423/"
] | I'm attempting to find a recurrence relation and the first few terms of a power series solution for the differential equation:
<span class="math-container">$$(1-x^2)y'' - 2xy' + \lambda y = 0$$</span>
Where <span class="math-container">$\lambda$</span> is some integer.
So I've assumed a solution <span class="math-c... | For the differential equation $(1-x^{2}) y'' - 2 x y' + \lambda y = 0$ it is seen that if $y$ is of the form $\sum a_{n} x^{n}$ the following holds.
\begin{align}
y(x) &= \sum_{n=0}^{\infty} a_{n} \, x^{n} \\
y'(x) &= \sum_{n=0}^{\infty} n \, a_{n} \, x^{n-1} \\
y''(x) &= \sum_{n=0}^{\infty} n(n-1) \, a_{n}... | You have $$y = \sum_{n=0}^\infty a_nx^n$$ $$y' = \sum_{n=0}^\infty n a_nx^{n-1}$$ $$y'' = \sum_{n=0}^\infty n(n-1) a_nx^{n-2}$$ $$(1-x^2)y'' - 2xy' + \lambda y =y'' -x^2y''-2xy' + \lambda y =0$$ Now, replace $y,y',y''$by their expression for the last right hand side. So, $$\sum_{n=0}^\infty n(n-1) a_nx^{n-2}-\sum_{n=0... | https://math.stackexchange.com |
55,238 | [
"https://quant.stackexchange.com/questions/55238",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/47614/"
] | I have a portofolio with 30 indexes and I want to calculate the annulised returns and volatility because I want to compare it with another portofolio with different number of indexes (but same time period)
My data are time series with 3 month frequency from 2009-12-31 to 2020-3-31.
I know that the general formula is: <... | I think all the previous answers have small mistakes:
Given that you have derived the return over the period of interest, i.e. in your case 2009-2020 we can then:
<ol>
<li>Compute the return at the granularity level of your data i.e:</li>
</ol>
<span class="math-container">$r_{quarterly}=(1+r_{total_{period}})^{\frac{1... | If you compute total return as:
<span class="math-container">$$R_{2009-12-31 \rightarrow 2020-3-31} = \frac{P_{2020-3-31} + D_{2020-3-31}}{P_{2009-12-31}}-1$$</span>
Where <span class="math-container">$D_{2020-3-31}$</span> are all the dividend paid in that period. Then you can do the following:
<ol>
<li>First note tha... | https://quant.stackexchange.com |
57,729 | [
"https://electronics.stackexchange.com/questions/57729",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18888/"
] | I need to connect 20-25Volts 1MHz digital input to Arduino. Are there any possible ways to do it? I think, using optocoupler will be useless because of high frequency. Any other ways to solve it?
| The fixed-on time is the time during which no current regulation is done (other than absolute current limiting). This allows for faster acceleration at the beginning of each pulse, if the motor is not in inertial motion already.
Fixed-on time ends early if current reaches desired value before time-out, and this is th... | This answer is in large part to have enough space to discuss the points made in the currently-checked answer. (I've seen many good answers from Anindo, but this one is wide of the mark, I think!)
Background: To make a stepper motor advance from one position to the next, the controller changes the voltages across the s... | https://electronics.stackexchange.com |
33,125 | [
"https://electronics.stackexchange.com/questions/33125",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3966/"
] | My MCU runs a SPI bus with about 4 devices. I'd like to extend this bus to be off board as well i.e. have some PCBs connect to the "main" board and extend the functionality. The "pad to pad" distance would be:
trace length of main board + Cable length + trace length on the extending board
3" + 6" + 3" = about 12"
I... | Rule-of-thumb says you have to calculate transmission line effects in if your connection length is longer than 1/10th of the signal's wavelength.
<img src="https://i.stack.imgur.com/JJ4V1.gif" alt="enter image description here">
Transmission lines will cause reflections where they show a sudden change in impedanc... | For such a short bus, I'd try putting a small resistor in series with anything driving a line. That's not the theoretical ideal way taking transmission line theory into account, but a pragmatic approach that I think will work well enough for your case. Try 47 Ω for starters and see what that does. If that help... | https://electronics.stackexchange.com |
168,231 | [
"https://physics.stackexchange.com/questions/168231",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70777/"
] | In Cohen-Tannoudji's Quantum Mechanics book the tensor product of two two Hilbert spaces $(\mathcal H = \mathcal H_1 \otimes \mathcal H_2)$ was introduced in (2.312) by saying that to every pair of vectors $$|\phi(1)\rangle \in \mathcal H_1, |\chi(2)\rangle \in \mathcal H_2$$ there belongs a vector $$|\phi(1)\rangle \o... | $|\phi(1)\rangle \otimes |\chi(2)\rangle $ is a cumbersome notation to write ket corresponding to $\psi$ function $\phi(\mathbf r_1)\chi(\mathbf r_2)$, where $\mathbf r_i$ refers to coordinates of the $i$-th subsystem. That's why the order of factors in $\otimes$ product does not matter; the resulting ket corresponds t... | You are correct in that the tensor product does not commute in general. The ordering of vectors in some tensor product, say
\begin{equation*}
|\psi\rangle\otimes|\phi\rangle\otimes|\xi\rangle \equiv |u\rangle
\end{equation*}
implicitly refers to how the resulting Hilbert space is defined via the tensor product. To the ... | https://physics.stackexchange.com |
2,038,713 | [
"https://math.stackexchange.com/questions/2038713",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/248602/"
] | How can I show that the global minimum of $4x^2-12x+y^2+2y+10$ is $0$ at $(3/2,-1)$?
I know that at $(3/2,-1)$ is a critical point and I can display that it's not a maximum. But I cannot figure out whether this is enough to conclude it being a minimum or whether I need to show some inequalities of the form $f(x,y)>... | Note that $4x^2-12x+y^2+2y+10=(2x-3)^2+(y+1)^2$.
| The function is strictly-convex which you can prove using the definition:<br>
$f(\lambda x + (1-\lambda)y) < \lambda f(x) + (1-\lambda)f(y)$. Such functions have only a unique minimum, and indeed the point you have is a unique minimum.
In general distinguishing minima/maxima and saddle points can be done by lookin... | https://math.stackexchange.com |
213,456 | [
"https://physics.stackexchange.com/questions/213456",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95608/"
] | Why is centrifugal force considered fictitious, when it's the one that feels real to us when we are moving in a circle? I understand the explanation regarding the reference frames: if our body is the reference frame, and it is rotating, a fictitious centrifugal force needs to be made up to cancel the centripetal force ... | The reason we feel that we are pushed outwards is due to inertia. Inertia is the resistance to movement. It is measured by mass. When we have more movement, it makes it harder to get us moving.
In a car that is on a curve, for example, our inertia makes us want to keep on going forward. Going forward in this case wou... | Suppose you're in a fast car and you stomp on the accelerator. You feel pressed into the back of the seat. In which direction are you accelerating? Forward, obviously, but you feel a force pushing against your back. Now you turn a corner. Your seatbelt, and maybe the door next to you, press against your side. In which ... | https://physics.stackexchange.com |
105,835 | [
"https://mathoverflow.net/questions/105835",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1310/"
] | Has anyone defined what it means for a modular operad to be Koszul, or what the Koszul dual of a modular operad is? In particular, is it meaningful to say that a modular operad is quadratic? Merkulov, Markl and Shadrin (Wheeled PROPs, graph complexes and the master equation) give a definition for wheeled properads, whi... | Here are two answers to this question based on different interpretations of the meaning of ``Koszul.''
One reasonable way to define things is that Koszul duality depends not only on algebraic data (operad, modular operad, algebra, whatever) but also on a presentation of the algebraic data. This is both elegant and a b... | With due thanks to Daniel for pumping my thesis, it does not really deal with operads, modular or otherwise. Judging by your question, you probably already have some basic references, like Loday and Vallette's monograph (available online) on Algebraic Operads, which deals in particular with Koszulness for general oper... | https://mathoverflow.net |
3,091,832 | [
"https://math.stackexchange.com/questions/3091832",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/639364/"
] | This is an exercise from a sequence and series book that I am solving.
I tried manipulating the number to make it easier to work with:
<span class="math-container">$$111...1 = \frac{1}9(999...) = \frac{1}9(10^{55} - 1)$$</span>
as the number of <span class="math-container">$1$</span>'s is <span class="math-container... | The number is composite.
We have
<span class="math-container">\begin{align*}
\underbrace{11\ldots111}_{55 \text{ times }} = \frac{1}{9} \cdot (10^{55} - 1) \\
= \frac{1}{9} \cdot ((10^{5})^{11} - 1) \\
\end{align*}</span>
Also, note that <span class="math-container">$x^{m} - 1$</span> is divisible by <span class="ma... | You can see with some very quick "in your head" maths that this is a composite number. Since 55 is 5 times 11 we can take a number that is 11111111111 (eleven ones) and divide the original by it using standard long division. Its easy to see that the result will be 100000000001000000000010000000000100000000001.
Similar... | https://math.stackexchange.com |
4,262,066 | [
"https://math.stackexchange.com/questions/4262066",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/915356/"
] | I would like to prove (or disprove) the following limit:
<span class="math-container">$$\lim_{n \to \infty}\frac{c}{n}\sum_{j=1}^{n}\bigg(1-\frac{bc}{n}\bigg)^{2(n-j)}\stackrel{?}{=}\frac{1}{2b}(1-e^{-2bc})$$</span>
for <span class="math-container">$b,c>0$</span>. After using the results on the geometric series I go... | Let us do this explicitly, let us break down all the definitions, since <span class="math-container">$G$</span> is a transitive action, we have that there is a single orbit, that is given <span class="math-container">$x,y\in A$</span> there is some <span class="math-container">$g\in G$</span> such that <span class="mat... | Here are two approaches:
<strong>Fancy approach</strong>: Prove <span class="math-container">$G_{g\cdot\alpha}=gG_{\alpha}g^{-1}$</span>. Then in your scenario you get <span class="math-container">$G_\beta=G_{g\cdot\alpha}=gG_\alpha g^{-1}=g\{1\}g^{-1}=\{1\}$</span>.
<strong>Direct approach</strong>: You just need to s... | https://math.stackexchange.com |
285,522 | [
"https://mathoverflow.net/questions/285522",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Let $a, b \in {\cal P}(\omega)/\mathrm{(fin)}$ with $a<b$. Do we have ${\cal P}(\omega)/(fin)\cong [a,b]$?
| The answer is yes.
Without loss of generality, we may choose representatives for $a$ and $b$ such that $a \subseteq b$ when construed as elements of $\mathcal{P}(\omega)$ (by taking arbitrary representatives, and changing these as needed at the finitely many indices where the subset relation may not already hold).
No... | Suppose $a<b$ in $\mathcal P(\omega)/\text{fin}$. Pick representatives $A,B\in\mathcal P(\omega)$ for these equivalence classes mod fin, and, by modifying $A$ by finitely many elements if necessary (which doesn't change the equivalence class), arrange that $A\subseteq B$. The strict inequality $a<b$ implies that ... | https://mathoverflow.net |
23,921 | [
"https://electronics.stackexchange.com/questions/23921",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/665/"
] | I built up a LM317 power supply which is working great.
I have moved it into a large case as I am now powering it off 240VAC (fused) down to 18VAC then rectified into the power supply. Which is going well. I also put a much bigger heat sink on it (1.4C/W). The plan is to set up another one in there as well and have du... | I think a good starting answer is
(1) - It would stop the case from becoming live if something shorted to the case would it not? :-)
(2) BUT, not only stop it becoming live, but also provide the intended means of operating the provided protection equipment if a phase to case fault occurred.<br>
aka "blowing the fu... | Yes. 110% definately! Infact depending on where you are you are probably required to do it by law.
| https://electronics.stackexchange.com |
23,201 | [
"https://stats.stackexchange.com/questions/23201",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9340/"
] | I have a task that is specific to inventory management that is currently driving me crazy. To summarize the problem: We regularly must monitor inventory settings to ensure that they represent true demand, to ensure that we are not overstocking nor understocking. The standard procedure is to schedule reviews, where high... | That's a familiar problem from a previous life!
First, you're not going to be able to do exactly what you want, which is to come up with a probability that the observations could have come from a specified distribution etc. This is because you don't have a well-specified alternative distribution, one which the data... | Look at the <code>ks.test</code> function for one option of comparing data to a given continuous distribution (with predefined parameters). Look at the <code>vcd</code> package for tools to examine discrete distributions.
| https://stats.stackexchange.com |
41,628 | [
"https://cs.stackexchange.com/questions/41628",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/30872/"
] | I'm a student reading a book on threads. And I got when I got to non-deterministic and parallel programs, I got a bit confused. I hope you can help me out.
I understand the difference between concurrency and parallelism. I get that concurrent programs are non-deterministic depending on the precise timing of events. "... | The book is using the term <em>non-deterministic</em> in two different ways. In concurrent computations and parallel computations the <em>order</em> in which the computations occur is non-deterministic. The final <em>result</em> however may (or may not) be deterministic.
Consider the following example:
<pre><code>t... | Take matrix-matrix multiplication which can be done in parallel. Initially one node (thread, computer, or whatever), call it N0, divides the two matrices into blocks, and distribute those blocks to the other nodes. All nodes now compute the product of their matrix blocks, and send the result back to N0. Finally N0 cons... | https://cs.stackexchange.com |
533,046 | [
"https://physics.stackexchange.com/questions/533046",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/254995/"
] | Not sure if this is a trivial question or not. But I am essentially asking is if for instance we have a phone that emits "x" amounts of frequency and is pointed towards like a cell. If I add 10 more phone does the cell now experience now 10 times as much frequency or is that not true?
| Signal strength of a phone is a measure of how much electromagnetic energy (of a particular range of frequency) is passing through it’s antenna. The frequency of the radiation is a fixed property of the emitter. What is changing is the amount of energy passing through. This scales with the number of emitters, provided ... | When you add more sources, you have more photons emitted, but each one has the same frequency and energy as with one source. Classicaly, you have an electromagnetic wave with the same frequency but larger amplitude (assuming the waves from various surces don't have a destructive interference).
| https://physics.stackexchange.com |
4,019 | [
"https://mechanics.stackexchange.com/questions/4019",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1539/"
] | Asked a local mechanic for the charge of repairing a puncture and he says he'd charge a certain amount for simply taking a piece of rubber tube and sticking it over the puncture, or if I would pay him a little bit extra, he'd use a pressing machine to apply a bit of heat to the patch of rubber tube and press it onto th... | These ways to repair tires can work - the air pressure inside the tire does hold the patch to the body of the tire - but the question you want to ask yourself is:
Are you willing to trust your life to a weaker tire when a small amount of money will get you a brand new tire?
I would <strong>always</strong> go with the... | <strong>This is a standard patching technique for car and motorcycle tires</strong>
Three components of a good tire repair include the following
<ul>
<li>Pressure</li>
<li>Heat</li>
<li>Vulcanizing glue</li>
</ul>
The combination of the three ensure that the patch is broken down by the vulcanizing glue as well as pa... | https://mechanics.stackexchange.com |
30,965 | [
"https://electronics.stackexchange.com/questions/30965",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9344/"
] | I have two questions on semiconductors that I hope someone will be able to help me with.
<ol>
<li>I have been told that a semiconductor is classed as N-Type when it's donor density is greater than its acceptor density and that it is classed as P-Type when its acceptor density is greater than it's donor density. So far ... | Non-organic semiconductors are used in crystalline form. The definition of a crystal is not that it looks like a gem, though that is a common result, it's that the constituent atoms are arranged in a regular pattern known as a lattice. A crystal of silicon forms a diamond-cubic lattice structure like this:
<img src=... | <blockquote>
So far so good, but I have also been taught that trivalent atoms are acceptors and pentavalent atoms are donors.
</blockquote>
I think the key thing here is that each nucleus has a set of available "states" for electrons available around it, whether the atom provides electrons to fill those states or no... | https://electronics.stackexchange.com |
136,350 | [
"https://cs.stackexchange.com/questions/136350",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/132827/"
] | I am trying to model a problem to enable me to use Dijkstra's Shortest Path algorithm. Given are a set of vertices <em>V</em>, and a set of vertices <em>X</em> ⊂ <em>V</em>.
Between these vertices are given a set of edges where:
<ul>
<li>edge(<em>u</em>,<em>v</em>) with <em>u</em> ∈ <em>V</em> \ <em>X</em> being weight... | I assume that you want to show that the language <span class="math-container">$L$</span> <strong>does</strong> satisfy the Pumping Lemma, as it indeed is regular. In words your language consists of all strings that have length at least 4 and contain two consecutive symbols that are the same. The position of a pair of e... | It suffices to show that the language is regular.
The language <span class="math-container">$L_1$</span> of all words on <span class="math-container">$\{0,1\}^*$</span> with at least two identical consecutive symbols is regular (since it can be described be the following regular expression: <span class="math-container"... | https://cs.stackexchange.com |
89,177 | [
"https://mathoverflow.net/questions/89177",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13464/"
] | I'll call a polynomial in $z_1,..,z_N$ cyclic if it is invariant under cyclic permutation of the indices. I hope that's standard terminology.
I have N complex numbers $(z_1,...,z_N)$. I want to be able to compute what they are up to cyclic permutation, given the value of some set of cyclic polynomials. For example, if... | Actually, if $N>2$, it's impossible to find $N$ "cyclic polynomials" as you desire. That's the same as asking if the cyclic invariants are a polynomial ring, which is impossible by the Chevalley-Shepard-Todd theorem
I suspect in general, the right thing to look at is the sum of the $z_i$'s and all monomials in $p... | So you have a cyclic group acting on complex affine space, and the situation at the level of function fields is clear enough: by basic Galois theory the extension of rational functions is a cyclic extension of degree n. It is a Kummer extension, even: write down a linear combination of the indeterminates with nth roots... | https://mathoverflow.net |
105,934 | [
"https://mathoverflow.net/questions/105934",
"https://mathoverflow.net",
"https://mathoverflow.net/users/26080/"
] | Imagine that we're trying to define the expression
$$\int_U f(x)dx$$
in a rigorous way.
Assume that $f:X \rightarrow \mathbb{R}^{\geq 0}$ where $(X,\mu)$ is a measure space, and suppose that $U$ is a measurable subset of $X$. That most typical approach to making this integral rigorous is the method of Lebesgue, whereby... | Linearity of this integral is very mysterious. Moreover, the definition of the product measure <em>using</em> integration, i.e. $\mu \otimes \lambda (M) =\int \int I_M(x,y) d\mu(x) d\lambda(y)$,
is very easy (up to a technical problem concerning measurability) and can be understood without
knowing Caratheodory's constr... | I'm not sure I buy Jochen's comment that product measure can be so easily defined using integration --- it seems like you're going to have to do some work to show that his double integral is well-defined for every set $M$ in the $\sigma$-algebra generated by the measurable rectangles.
The real problem may be that you ... | https://mathoverflow.net |
22,468 | [
"https://softwareengineering.stackexchange.com/questions/22468",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1023/"
] | What are some data structures that should be known by somebody involved in bioinformatics?
I guess that everyone is expected to know about lists, hashes, balanced trees, etc, but I expect that there are domain specific data structures. Is there any book devoted to this subject?
Thanks,
Lucian
| If you want to be good at working on embedded systems, then yes, you need to think like a EE some of the time. That is generally when you are writing code to interface with the various peripherals (serial busses like UART, SPI, I2C or USB), 8 and 16-bit timers, clock generators, and ADCs and DACs. "Datasheets" for mi... | @tcrosley's answer is excellent. You do not need to be an electrical engineer, but knowing the basics helps.
I don't think you need to fear being "too low on the software stack". I've had to solve many very interesting problems as an embedded engineer. You mention a list of tasks you enjoyed:
<ul>
<li>Concurren... | https://softwareengineering.stackexchange.com |
30,798 | [
"https://dba.stackexchange.com/questions/30798",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/14786/"
] | Query:
<pre><code>Select *
from `t_event`
where `create_user_id`=7
and (`event_create_date`)=('2012-12-18 00:00:00')
and `event_type_cd`=11
and `domain_id` =602
and `job_id` =1
limit 1
</code></pre>
Table structure:
<pre><code>mysql> show create table t_event\G
*************************** 1. row **************... | I would suggest that you indexes to job_id assuming there are many events for the same job and event_date assuming that there are many events on the same date assuming that there are queries which use these columns for filters.
However see answer by @ypercube below which has a better explaination for indexes
PS: Upd... | Your query has 5 equality conditions in 5 different columns:
<pre><code>select *
from t_event
where create_user_id=7
and event_create_date = '2012-12-18 00:00:00'
and event_type_cd = 11
and domain_id = 602
and job_id =1
limit 1 ; -- why is this for?
</code></pre>
<hr>
Now you have 2... | https://dba.stackexchange.com |
843,661 | [
"https://math.stackexchange.com/questions/843661",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/92619/"
] | a.Let $E$ be a non-zero Banach space and show that for every $x\in E$ there is $\phi \in E^*$ such that $||\phi ||=1$ and $|\phi (x)|=||x||$
b. Let E and F be Banach spaces,let $\pi: E\to F $ be a bounded linear map and let $ \pi^*:F^* \to E^* $ be the induced map on dual spaces. Show that $||\pi^*||=||\pi||$.
No ide... | b) $$ \|\pi \| = \sup_{x \neq 0} \dfrac{\| \pi(x) \|}{\| x \|} = \sup_{x \neq 0}\sup_{\phi \neq 0} \dfrac{ | \phi( \pi(x))| }{\|x\| \|\phi \|} = $$ $$ \sup_{x \neq 0}\sup_{\phi \neq 0} \dfrac{ | \phi( \pi(x))| }{\|x\| \|\phi \|} = \sup_{x \neq 0}\sup_{\phi \neq 0} \dfrac{ | (\pi^* \phi)(x)| }{\|x\| \|\phi \|} = \sup_{\... | To do (a), try applying the Hahn-Banach extension theorem.
| https://math.stackexchange.com |
134,987 | [
"https://cs.stackexchange.com/questions/134987",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/113831/"
] | <span class="math-container">$$T(n)=2^n+4T(\frac{n}{2})$$</span>
I have started substitution for:
<span class="math-container">$$T(\frac{n}{2})=2^{\frac{n}{2}}+4T(\frac{n}{4})$$</span>
<span class="math-container">$$T(\frac{n}{4})=2^{\frac{n}{4}}+4T(\frac{n}{8})$$</span>
<span class="math-container">$$...$$</span>
<spa... | It's not easy to give a full explanation without knowing your axioms and rules, however, <span class="math-container">$A \land \neg A$</span> is a contradiction, and it is by exploiting that, that you can prove whatever you like.
First, let <span class="math-container">$\top = A \lor \neg A$</span>.
We know that "... | Think of it this way.
There are no elements of the empty set <span class="math-container">$\emptyset$</span>. Moreover, for all sets <span class="math-container">$A$</span>, <span class="math-container">$\emptyset \subseteq A$</span>.
But what does subset actually mean? <span class="math-container">$A \subseteq B$</spa... | https://cs.stackexchange.com |
390,727 | [
"https://physics.stackexchange.com/questions/390727",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/169443/"
] | This is a problem I came across: Imagine there is a glass test-tube with a small hole of radius ‘r’ at the bottom of the tube. Now this tube is lowered into a water-filled beaker; upto what depth ‘d’ can you lower the test-tube into the water before water starts filling into the test-tube through the hole? Given that t... | The force acts on every element of a 3d object.
Take for example a 3d charged object. The charges can be distributed any way at all. They could be uniform, or not. One side could be positively charged, the other negative. And so on.
That 3d object has an element of charge existing at every point. (More precisel... | A vector field defines a situation where the magnitude and direction of vectors are a function of location only. We can best understand this on a rotating rigid body where the linear velocity of each particle $\boldsymbol{v}$ depends on its location $\boldsymbol{r}$.
$$ \boldsymbol{v} = \boldsymbol{\omega} \times \bol... | https://physics.stackexchange.com |
678,449 | [
"https://physics.stackexchange.com/questions/678449",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/319911/"
] | I'm reading about chain reactions in pressurized water reactors. All is good and clear. U-235 splits, releases 2 or 3 neutrons, if the reactor is supercritical then reaction will continue. Part of the neutrons will escape the reactor, some will be slowed down to split some more U-235.
But what happens with all the capt... | If you know how a certain gate acts on a certain basis then you can write your initial state as a linear superposition of states in that basis and use the fact that gates are linear operators.
For some given constant <span class="math-container">$\alpha,\beta,\gamma,\delta$</span>, you can write a linear combination li... | If the initial qubits are entangled, then the answer could be different. So I'll assume they're not entangled. Then the initial state is:
<span class="math-container">$$
|00\rangle + |01\rangle - |10\rangle - |11\rangle
$$</span>
Applying <span class="math-container">$CNOT(a,b)$</span> flips the second bit whenever the... | https://physics.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.