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 |
|---|---|---|---|---|---|
52,668 | [
"https://dba.stackexchange.com/questions/52668",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/29382/"
] | Which of these queries are best for performance ? Sometimes I wonder if SHORT scripts really is the best thing to focus on. These scripts performs the same task. With left joins i can achieve what i want with just a few lines. But then I tried with a longer script, using unions. Which is the best method? Between this:
... | <blockquote>
Sometimes I wonder if SHORT scripts really is the best thing to focus on.
</blockquote>
The size of a script has little to do with how efficiently the query will execute. A more compact statement will likely consume fewer resources in terms of <em>compilation</em>, but (re)compilation is usually a rare ... | With out your entire database this is a hard question to answer. What I can say is this: you can test it your self.
If you use either SET STATISTICS TIME ON or use the patern of
<pre><code>DECLARE @StartTime DATETIME = GETDATE()
/Some Query Here/
SELECT 'Total Run Time Query 1: ' + CAST(DATEDIFF(MS,@StartTime,GET... | https://dba.stackexchange.com |
486,920 | [
"https://physics.stackexchange.com/questions/486920",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222367/"
] | The diameter of observable universe is 93 billion light years but the age of universe is only estimated to be 14 billion years. So how does light have 46.5 billion years to travel from the boundary of observable universe to us? I mean if the radius is 46.5 billion light years then that should mean light took 46.4 billi... | The farthest light we can see (the horizon) has been emited 13.8 billion years ago (minus opacity period during 300 000 first years, but that's not the point) by objects then (I mean, in CMB frame) at a distance of 13.8 billion light-years. The fact is that distance to those objects has continued to grow for 13.8 billi... | There are a few things to clarify:
<ol>
<li>the age of the universe is for the whole universe, that might be infinite in size </li>
<li>It is a misunderstanding that the diameter of the observable universe corresponds to the 13.8 billion years</li>
</ol>
Still, there is a difference/contradiction between the age of t... | https://physics.stackexchange.com |
4,474,996 | [
"https://math.stackexchange.com/questions/4474996",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/858891/"
] | First let's define a set of "normal" elements (i.e. not a set of ordered pairs):
<span class="math-container">$A=\{x\in \mathbb{N}:x>10\}$</span>
Let's call it the "first" definition. I can also define set A and its elements' properties in another way:
<span class="math-container">$\forall x(x\in... | I think this is mostly just nitpicking, because at the end of the day, as long as people understand that the indexes refer to the first and second element it is fine, but if you wish to avoid that, here is how you can do it:
<span class="math-container">$\forall x\big(x \in B \Leftrightarrow \exists y \in \mathbb{N} \ ... | Here's an option:
<span class="math-container">$\forall x(x \in B \iff \exists x_1\,\exists x_2\,( x_1\in\mathbb N)\land (x_2\in\mathbb N)\land (x=(x_1,x_2)) \land (x_1>x_2))$</span>,
| https://math.stackexchange.com |
95,816 | [
"https://electronics.stackexchange.com/questions/95816",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10731/"
] | Many capacitance values occurring in electronic circuits can be conveniently expressed in nanofarads, e.g. "a 10nF decoupling capacitor" .
However, the use of the term "nanofarads" or its abbreviation "nF" is often avoided and instead the numerically equivalent terms "10000pF" or "0.01μF" are used. The first term is t... | They don't. I'm American and I use nano for Farads like any other prefix, which is when doing so would put 1-3 digits to the left of the point.
A long time ago, nF wasn't used much for whatever reason. This wasn't a American thing as much as a long time ago thing. I've even seen pF referred to as µµF. ... | I think its just because it is a middle ground and so using just uF and pF, we can usually classify where a capacitor is being used just by that unit and then partially the value. If we were to use the nF more predominantly, it may become more difficult to discern where that is being used.
Just spit-ballin.
| https://electronics.stackexchange.com |
283,893 | [
"https://softwareengineering.stackexchange.com/questions/283893",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/61302/"
] | I am working on a colleague to refactor the following code, I am trying to turn this into a teaching experience as well.
<strong>Original Code</strong>
<pre><code>public class WidgetRepository
{
public Widget GetWidget(int id)
{
Widget widget;
if (HttpContext.Current != null)
{
... | <blockquote>
Am I justified in making the refactoring (assuming we have time allocated for cleaning up code)?
</blockquote>
Are you doing anything else in this code?
If not, this seems not worth the effort. Your peer is likely right that you aren't ever going to use other things - and that you should keep things co... | There's more than one way to skin a cat. Try again until you find a solution that resolves everyone's concerns. Part of the problem is you haven't really broken the coupling on the caching code all the way. I would start with something like this:
<pre><code>public class WidgetRepository
{
public Widget GetWidget(... | https://softwareengineering.stackexchange.com |
376,408 | [
"https://mathoverflow.net/questions/376408",
"https://mathoverflow.net",
"https://mathoverflow.net/users/136860/"
] | Is Birkhoff's pointwise/individual ergodic theorem for <span class="math-container">$L_\infty.$</span> Clearly, it is true if the measure space is finite? What about the measure space not finite?
| Here is a counter-example to the question I think you're asking. Let <span class="math-container">$X$</span> be the space of two-sided 0-1 valued sequences. Let <span class="math-container">$x$</span> the sequence with <span class="math-container">$x_n=0$</span> for all <span class="math-container">$n\le 0$</span>; <sp... | No. For the simplest counterexample take the shift on the space of one-sided 0-1 sequences <span class="math-container">$(\epsilon_1,\epsilon_2,\dots)$</span> endowed with any fully supported invariant measure (for instance, the (1/2,1/2) Bernoulli measure), and let <span class="math-container">$f$</span> be the indica... | https://mathoverflow.net |
31,743 | [
"https://quant.stackexchange.com/questions/31743",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/25883/"
] | <strong>Background</strong>
My final objective is to find a portfolio located on the efficient frontier from a choice of 100 stocks from a stock index (eg. S&P500).
This efficient portfolio will be such that its variance is the same as the stock index variance. <strong>Wrapping it up, maximizing return for a giv... | The results that you are getting from <strong>fPortfolio</strong> package are correct. And if you do not multiply your covariance matrix by 2 you will get the same result from <strong>quadprog</strong> package. So, either use <strong>fPortfolio</strong> or <strong>quadprog</strong> without 2.
"1/2" in that formula tha... | Both approach gives same results for stocks weights but different results for lamda values
Correct approach is multiplying the covariance matrix by 2 but you only need stocks weights so its the same
| https://quant.stackexchange.com |
240,999 | [
"https://math.stackexchange.com/questions/240999",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/50038/"
] | I'm totally lost on how I would integrate the following function:
$f(x) = \sqrt{4+4x^2+1/x^2}$
If anyone could even just point me to the method of integration that would be grand.
| $$4 + 4x^2 + \dfrac1{x^2} = \left(2x + \dfrac1x \right)^2$$
Hence,
\begin{align}
\sqrt{4 + 4x^2 + \dfrac1{x^2}} & = \begin{cases} 2x + \dfrac1x & x > 0\\ -\left( 2x + \dfrac1x\right) & x < 0\end{cases}\\
& = 2 \vert x \vert + \dfrac1{\vert x \vert}
\end{align}
| Compute the square root!${}{}{}{}{}$
| https://math.stackexchange.com |
314,165 | [
"https://dba.stackexchange.com/questions/314165",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/251127/"
] | I am trying to get the distinguish column depending on another column's value.
I was trying to approach with CASE function but could not get exactly what I wanted.
Condition
<ol>
<li>if ColB has only 1 then online</li>
<li>if ColB has only 2 then offline</li>
<li>if ColB has both 1 and 2 then both</li>
<li>if ColB does... | Looks like you just need conditional <code>COUNT</code>
<pre class="lang-sql prettyprint-override"><code>SELECT
t.ColA,
CASE WHEN COUNT(CASE WHEN t.ColB = '1' THEN 1 END) > 0 THEN
CASE WHEN COUNT(CASE WHEN t.ColB = '2' THEN 1 END) > 0 THEN
'both'
ELSE
'online'
END
ELSE
CASE WHEN ... | This is just another way to skin the same cat, using a conditional <code>COUNT(DISTINCT)</code> and a conditional <code>MAX()</code>:
<pre><code>SELECT
ColA
, distinguish =
CASE COUNT(DISTINCT CASE WHEN ColB IN ('1', '2') THEN ColB END)
WHEN 0 THEN 'none'
WHEN 2 THEN 'both'
ELSE
CASE MAX... | https://dba.stackexchange.com |
59,681 | [
"https://electronics.stackexchange.com/questions/59681",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/19682/"
] | I have 9 volts battery. What resistance do I need to have 5 volts. And how to calculate?
| You need to know the current you will draw, and then use Ohm's law to calculate the resistance. For example, if you draw 4 mA then the resistance will be 1000 Ohm.
However, as the current used by your circuit may vary, using a simple resistor will allow the voltage to vary: if the current drops 50%, your circuit will ... | Dropping the voltage with a resistor is impractical except for extremely low currents.
Your best bet would be a lm7805. 9v goes in 5v comes out. They are quite cheap and easy to use.
| https://electronics.stackexchange.com |
54,045 | [
"https://physics.stackexchange.com/questions/54045",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <img src="https://i.stack.imgur.com/daiFb.png" alt="enter image description here">
<strong>I have problem in understanding equation (1.23), I croped this image from Mark_Srednicki "Quantum field theory". Can anyone show me the reason for the equation (1.23)?</strong>
| The inner product of two wavefunctions $\phi$ and $\psi$ (on 1D, for simplicity) is <em>defined</em> to be the integral $\int_{-\infty}^\infty \phi^\ast(x)\psi(x)dx$, and Dirac notation assigns the symbol $\langle\phi|\psi\rangle$ to this object, in analogy to the mathematician's usual notation $\langle u,v\rangle$ for... | Because of the completeness of the eigenfunctions of the position operator you can add a factor of one in the middle of the bracket, which is the integral in the middle. The projection of a bra to the position eigenstate is simply the wave function in position space and if you change the bra with the ket in a braket yo... | https://physics.stackexchange.com |
206,739 | [
"https://stats.stackexchange.com/questions/206739",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/81809/"
] | I have two data sets (below), I want to apply the appropriate statistical test to determine the probability that the two data sets come from the same distribution. I don't believe I can use the Mann–Whitney U test because there are ties in the data.
<pre><code>data1 = c(41, 41, 29, 41, 41, 31, 31, 41, 41, 41,
22,... | Here is a possible approach to a modified version of the above problem. The modification preserves the motivation of the original problem.
<strong>Modification</strong> - $X$ and $Y$ are constrained to have $\sigma^2$ variance instead of being $\sigma^2$ sub-gaussian.
Let $E[X] = -\Delta$ and $E[Y] = \Delta $
\begin... | Sub-Gaussianity is an asymptotic property whereas expectations and the total variation are global properties. Provided the tails of the distribution are not too heavy (and any sub-Gaussian distribution has very light tails indeed), they will have negligible effect on those global properties. Thus we may modify any su... | https://stats.stackexchange.com |
61,652 | [
"https://physics.stackexchange.com/questions/61652",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23366/"
] | I am doing my first steps in spectroscopy (IFS actually) and how we can learn more about galaxies by using it. I came up with a simple question which, unfortunately, I can not answer:
How can we measure the rotational velocity of a spiral galaxy given that the galaxy is perfectly face-on?
I understand how to do so if... | Sorry, no way to directly measure that speed.
However, you may try to guess the direction of the rotation by looking at the spiral structures. Usually the tips of the arms point in the opposite direction from the direction of rotation. But that is not a general rule, in some cases a so-called "leading structure" has b... | According to the contemporary but standard mathematics of AIAS.US, a Physics site dedicated to the revision and particularly, the rebuilding of false axioms of physics across the board; and according to my own research [largely consisting of the physical building of 3D models that mimic accordingly, the rotation and di... | https://physics.stackexchange.com |
23,453 | [
"https://softwareengineering.stackexchange.com/questions/23453",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6610/"
] | In pricing a service or product it is general practice to not merely charge for the effort spent and the costs involved + margin but from the value delivered down. As an independent consultant, how do you set the price of your work?
What is the process of determining your hourly rate as an independent software develo... | <blockquote>
In pricing a service or product it is
general practice to not merely charge
for the effort spent and the costs
involved + margin but from the value
delivered down. As an independent
consultant, how do you set the price
of your work?
</blockquote>
A combination of the above + what the market ... | Primarily the market for the work in question dictates the rates you can charge.
The work in question will be defined by the skills you're using (technical), the industry the client is in and the value the work will deliver to them, any specific knowledge which may be needed to carry out the work and any reputation ... | https://softwareengineering.stackexchange.com |
142,626 | [
"https://stats.stackexchange.com/questions/142626",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5536/"
] | What conditions must satisfy the mean and variance of a Beta distribution so that the parameters $\alpha,\beta$ are not both less than 1?
| The parameters of a $\text{Beta}(\alpha,\beta)$ distribution with mean $0\lt m\lt 1$ and variance $0\lt v\lt m(1-m)$ are
$$\alpha = m\frac{m(1-m)- v}{v},\quad \beta = (1-m)\frac{m(1-m)-v}{v}.$$
<img src="https://i.stack.imgur.com/hpqGL.png" alt="Figure 1">
<em>This shaded contour plot of $\alpha$ has contours rangin... | The mean of the Beta distribution is
$$\mu = \frac {\alpha}{\alpha + \beta}$$
We want to see whether restricting the permissible range of $\mu$, will guarantee that we will have either $\{\alpha \geq 1, \beta >0\}$, OR $\{\alpha >0, \beta \geq 1\}$.
Treating the mean as a function of the parameters we obtain
... | https://stats.stackexchange.com |
258,509 | [
"https://softwareengineering.stackexchange.com/questions/258509",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/148476/"
] | I have the follow algorithm which finds duplicates and removes them:
<pre><code>public static int numDuplicatesB(int[] arr) {
Sort.mergesort(arr);
int numDups = 0;
for (int i = 1; i < arr.length; i++) {
if (arr[i] == arr[i - 1]) {
numDups++;
} }
return numDups;
}
</code></pre>
I... | <pre><code>O(n) + O(n log(n)) = O(n log(n))
</code></pre>
For Big O complexity, all you care about is the dominant term. <code>n log(n)</code> dominates <code>n</code> so that's the only term that you care about.
| Let's reason our way through it and remember the definition of <code>O</code>. The one I'm going to use is for the limit at infinity.
You are correct in stating that you perform two operations with corresponding asymptotic bounds of <code>O(n)</code> and <code>O(nlog(n))</code> but combining them into a single bound i... | https://softwareengineering.stackexchange.com |
584,764 | [
"https://physics.stackexchange.com/questions/584764",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/192555/"
] | (Question at the bottom) The classical wave equation in 1+1D is:
<span class="math-container">$$\frac{\partial^2 y}{\partial x^2}=\frac{1}{v^2}\frac{\partial^2 y}{\partial t^2}.$$</span>
It can be solved using the following method. Let's take <span class="math-container">$a = x+vt$</span> and <span class="math-containe... | I think the answer boils down to this - for electrons that can either exist in single particle spatial wavefunctions <span class="math-container">$\phi_A(r)$</span> and <span class="math-container">$\phi_B(r)$</span>, and single particle spin states <span class="math-container">$|\uparrow\rangle$</span> or <span class=... | I suppose <span class="math-container">$|A,B\rangle = |A\rangle |B\rangle$</span> is a "2 non-identical particle state" in your notation, so that your first spin state looks symmetric. This is impossible for identical electrons, unless there is a "spatial part" of the wave function that, in this cas... | https://physics.stackexchange.com |
27,726 | [
"https://math.stackexchange.com/questions/27726",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/2219/"
] | I have known for a while that $\mathbb{R}P^1 \simeq S^1$. Indeed, visually it is easy to see why this is the case (any two antipodal points define a line through the origin)
Say we now forget everything we know, and let $F$ be a division ring and let $n \ge 0$. We definie an equivalence relation of $F - \{ 0 \}$ by $x... | First, consider the mapping
$$\varphi\colon (x,y) \mapsto \left(\frac{x}{\sqrt{x^2+y^2}}, \frac{y}{\sqrt{x^2+y^2}}\right)$$
which maps $\mathbb{R}^2-\{0\}$ to the unit circle $\mathcal{C}$.
If $(x,y)$ and $(z,w)$ map to the same point, then it follows that $x = \lambda z$ and $y=\lambda w$, where
$$\lambda = \frac{\s... | I suppose you want a <em>homeomorphism</em> between $\mathbb R\mathbb P^1$ and $S^1$. ($S^1$ does not have an algebraic structure, so isomorphism in that sense would not make sense.)
Define $\mathbb R\mathbb P^1\to S^1$ by $[a:b]\mapsto (a/\sqrt{a^2+b^2}, b/\sqrt{a^2+b^2})$ and $S^1\to \mathbb R\mathbb P^1$ by $(a,b)\... | https://math.stackexchange.com |
541,860 | [
"https://electronics.stackexchange.com/questions/541860",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/270316/"
] | I'm trying to setup a network of temperature sensors for my house connected to a Raspberry PI. I'm using Cat6 unshielded cable (data + ground running on one pair, 5v/ground running on another). To test. the lines (5v, GPIO4, Ground) from the RPI are connected to a breadboard, which has a pair of punchdown blocks pushed... | It could, depending on how it is built, and how you will short it.
If simply shorting 5V to GND, it could survive many events. Shorting 5V to data pins can damage the data pins. Shorting 5V to some other higher voltage in the circuit can damage the whole laptop.
If you like to have working USB ports and laptops, don't ... | Many USB controllers will shut down the port if it uses too much current. This affords a modicum of protection, but that's no sure thing.
A powered hub is a cheap insurance policy.
| https://electronics.stackexchange.com |
699,799 | [
"https://physics.stackexchange.com/questions/699799",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/330871/"
] | How can the Lorentz factor <span class="math-container">$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$</span> be understood? What does that mean? For example, what is the reason for the second power and square root? Why not <span class="math-container">$\frac{1}{1-\frac{v}{c}}$</span>, or what would happen if it took that form?.... | Just to add to the other answers, one might ask, "why the square root"?
The heart of it is the underlying geometry. When we ask "what is the diagonal of a square with sides <span class="math-container">$a$</span> and <span class="math-container">$b$</span>, Euclid's rules eventually land us at the concl... | The Lorentz factor can be understood as how much the measurements of time, length, and other physical properties change for an object while that object is moving.
What you have named <span class="math-container">$r^2$</span> is indeed known as <span class="math-container">$\beta^2$</span> which is the ratio between the... | https://physics.stackexchange.com |
17,991 | [
"https://earthscience.stackexchange.com/questions/17991",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/17869/"
] | Something I hear often from climate scientists, and indeed even politicians, is that we "don't understand climate change very well". And, I'm sure this is true since the climate is a complex adaptive system with thousands of dependent variables, one that we don't yet have the computational sophistication to accurately ... | We need both paleodata <em>and</em> models, in fact the relationship between paleodata and the climate at a certain time is typically evaluated through models. Paleodata does not actually measure climate observables directly (tempreture/pressure/salinity/other) but instead is (e.g.) a geochemical quantity related to on... | It is true that we don't understand climate change very well for the reasons you give in your question, namely that there are so many variables involved and some of them are unknowns. Indirect methods of assessing climate composition and temperature are reasonably accurate for the last few tens of thousands of years, b... | https://earthscience.stackexchange.com |
61,439 | [
"https://mathoverflow.net/questions/61439",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12844/"
] | Let $f∈Q[X]$ and not constant or of the form $(x−a)^n$. Suppose:
$f_1:=\frac{f}{gcd(f,D^2f)}$
and
$f_2:=\frac{f_1}{gcd(f_1,Df_1)}$
where $Df$ stands for the formal derivative.
Is it true that $gcd(f_2,Df_2)=gcd(f_2,D^2f_2)=1$ ?
| No.
Let
$$f(x)=(x-3x^3)(x+1/3).$$
Then $f''(-1/3)=0$ and
$$f_1(x)=x-3x^3.$$
Since $f_1$ and $f_1'$ have no common roots, $f_2=f_1$. But $gcd(f_2,D^2f_2)=x$.
| No. Consider polynomials which are also odd functions.
Edit: The above may be useful, but is not correct. If $f_2$ were odd, the answer might be no, but it is unclear that the relations above can ever produce an odd function. End Edit.
Edit2: Thanks to Michael Renardy for producing an odd $f_2$. End Edit2.
Gerha... | https://mathoverflow.net |
10,916 | [
"https://cs.stackexchange.com/questions/10916",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7415/"
] | In the case of LBAs (Linear Bounded Automaton), in writing a decider for the language
$\qquad A = \{ \langle M,w\rangle \mid M\ \mathrm{LBA}, w \in \mathcal{L}(M) \}$
we reject the input after a specific number (number of possible different configurations) of computation steps.
We say that the machine must be looping... | If I understand the question correctly, you are asking why are we bounding the number of configurations, rather than checking for a repeating configuration?
Well, clearly these are equivalent in the sense that in both ways you will detect a repeating configuration.
In the first method, we use the pigeonhole principle... | Because the TM, as it has an infinite tape, can get into a loop that runs off into infinity and the configuration doesn't repeat. For a minimal example, just make it move right on blank, and rewrite with 0. Start it on a blank tape, and watch it ride into the sunset.
| https://cs.stackexchange.com |
364,377 | [
"https://physics.stackexchange.com/questions/364377",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/173025/"
] | I've been doing some past-papers in order to revise for an upcoming test, and I can't seem to get my head around this question:
<blockquote>
A student stands in the middle of a balanced plank which sits on rollers on top of a
column. There is zero friction between the plank and the top of the column due to the
e... | Consider the situation:
There are at least two parallel rollers on top of a pillar.
A plank is balanced on these rollers; that is, the centre of gravity of the plank is located somewhere between the two outermost rollers.
A student stands on the centre of the plank, so the students centre of mass is located between... | The center of mass of the student plus plank <em>will</em> move, because a force is applied to the rollers to make them rotate so there is a reaction force on the student+plank system which will cause its center of mass to move slowly in the direction the student begins walking. (Student moves left, plank moves right a... | https://physics.stackexchange.com |
176,702 | [
"https://dba.stackexchange.com/questions/176702",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/127072/"
] | I need to display user-specific tables for users logged into a CMS. These tables are stored in another database with tables for the different user groups. For example User 1 to 4 should get data from Table1, User 5-12 from Table2 etc. Unfortunately I can only run one query because of the CMS plugin creating charts only... | There are basically two options with your scenario, as I understand it.
<ol>
<li>Dynamic SQL (see a_vlad's answer)</li>
<li>A (potentially) insanely massive <code>JOIN</code>.</li>
<li>Return "canned" data.</li>
</ol>
<strong>A massive <code>JOIN</code></strong>
For option two, you have to know the names of your tab... | as described it will not work, but You can use prepared statements for this type of operations:
<pre><code>SET @tb_name = (SELECT grouptable.tablename FROM cmsdb.usertable LEFT JOIN cmsdb.grouptable ON cmsdb.grouptable.ID = cmsdb.usertable.groupID WHERE User = 2);
</code></pre>
just keep in mind subquery above, must ... | https://dba.stackexchange.com |
305,375 | [
"https://physics.stackexchange.com/questions/305375",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/115161/"
] | I have taught myself QM using Griffiths book, and would like to move on to QFT. However, my textbook uses the Heisenberg picture of QM, and I have no idea how to use that. Are there any books that teach the Heisenberg picture of QM?
| I will always recommend Shankar's book. He not only discusses the Heisenberg picture, but also the path-integral formulation of quantum mechanics, the interaction picture, and time dependent perturbation theory, all of which will be useful in QFT.
| Razavy's text "Heisenberg's quantum mechanics" is a non-traditional but interesting presentation of the topic, emphasizing the links to classical mechanics. Another possibly more traditional text is the "Quantum Mechanics" book of Albert Messiah, which contains much less details than Razavy but emphasizes the transfor... | https://physics.stackexchange.com |
227,057 | [
"https://physics.stackexchange.com/questions/227057",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86255/"
] | For example;
Two reservoirs are at each end of a one dimensional or even two dimensional lattice.
One of the reservoirs has the temperature T < Tc. Would the lattice site have a phase transition even if the other reservoir has the temperature T > Tc?
Also as a follow up, is it possible to answer this question by st... | I've played around with this type of question quite a bit.
Your question leaves it a little undefined what you mean by the reservoirs being "at each end of [the] lattice." I will assume what you mean is that the lattice is divided into two sections, with one section being at one temperature and the other being at a d... | Following up on Nathaniel's answer, a suggestion on how to achieve an Ising model coupled to heat baths only at the boundaries: one can allow in the bulk only moves that keep the energy constant, and only at the boundaries allow energy changing moves, with rates that correspond to different heat baths at the different ... | https://physics.stackexchange.com |
288,165 | [
"https://softwareengineering.stackexchange.com/questions/288165",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/185220/"
] | How do I design a subclass whose method contradicts its superclass? Let's say we have this example:
<pre><code># Example 1
class Scissor
def right_handed?
true
end
end
class LeftHandedScissor < Scissor
def right_handed?
false
end
end
</code></pre>
Let's assume that the inheritance is necessary in... | There is nothing wrong with the design shown in the question. While one could also introduce abstract <code>Scissor</code> with two concrete subclasses, and maybe more overall clarity, it's also common to do it like shown (especially when the hierarchy is a result of years of incremental development, with <code>Scisso... | You are thinking too logically! There is no logical contradiction because class definitions are not logical propositions.
Having the Scissor base class return true does <em>not</em> correspond to saying that <em>all</em> scissors are right-handed. It just means that a scissor instance is right-handed unless the method... | https://softwareengineering.stackexchange.com |
109,867 | [
"https://cs.stackexchange.com/questions/109867",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/104917/"
] | I've seen that every comparison-based sorting algorithm must perform at least <span class="math-container">$\log_{2}(n!)=\Omega(nlog(n))$</span> comparisons on some input (<em>n</em> being the size of the input).
Why is the minimum number of comparisons <span class="math-container">$\log_{2}(n!)$</span>, and how is t... | Suppose the input array has <span class="math-container">$n$</span> elements. The goal of the sorting algorithm is to compute a permutation of <span class="math-container">$\{1,2,\ldots,n\}$</span> - the permutation needed to sort the input. Let <span class="math-container">$A$</span> be the set of these <span class="... | There are <code>n!</code> possible orderings for <code>n</code> items. Each comparison reveals only 1 bit of information, so to choose one of <code>n!</code> orderings you need to perform at least <code>log2(n!)</code> comparisons.
<code>log(n!) < C*n*log(n)</code> for some C is known from Math, so <code>log(n!) = ... | https://cs.stackexchange.com |
154,964 | [
"https://mathoverflow.net/questions/154964",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30395/"
] | From the theorem of classification of finitely generated abelian groups, we can see that every finitely generated commutative group can be considered as the additive structure underlying (at least) one unitary and commutative ring. My question is about possible generalization of
this result.
Question: Is it true that w... | As Sasha Anan'in already mentioned, there are counterexamples like $\mathbb{Z}/p^\infty = \mathbb{Z}[\frac{1}{p}]/\mathbb{Z}$ and $\mathbb{Q}/\mathbb{Z}$. The common feature of these groups is that there are divisible <em>and</em> torsion and therefore $A\otimes_\mathbb{Z}A=0$. A ring $A$ has a surjective and hence non... | No, there are many abelian groups such that only zero multiplication can be defined over them. Even if you can define a non-zero multiplication on a group, the ring obtained may have no unit, also it may not be associative, and so on. A detailed discussion of this subject can be find in L. Fuchs: (Infinite abelian grou... | https://mathoverflow.net |
526,851 | [
"https://math.stackexchange.com/questions/526851",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/73496/"
] | <blockquote>
<strong>Problem</strong>:Let $v$ and $w$ be eigen vectors of $T$ corresponding to two distinct eigen values $ \lambda _1$ and $ \lambda_ 2$ respectively
Then which of the following is true ?
$1)$ For non zero scalars $\alpha_ 1$ , $\alpha_ 2$, the vector $\alpha_ 1v + \alpha_ 2 w$ is not eige... | $Tv=\lambda_{1}v$ and $Tw=\lambda_{2}w$ with $\lambda_1 \neq \lambda_2$. Since $T$ is (presumably)
linear, $$T\left(\alpha_{1}v+\alpha_{2}w\right)=\alpha_{1}Tv+\alpha_{2}Tw=\alpha_{1}\lambda_{1}v+\alpha_{2}\lambda_{2}w.$$
Since $\lambda_{1}$ and $\lambda_{2}$ are distinct, we cannot write
this as $\lambda\left(\alpha_{... | Let $T$ act on what you're asking about. For example, what is equal to $T(\alpha_1 v + \alpha_2 w)$? You can simplify this expression.
| https://math.stackexchange.com |
29,785 | [
"https://datascience.stackexchange.com/questions/29785",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/33856/"
] | What are the benefits of having ML in JavaScript I.e. the deeplearn.js (now tensorflow) stuff, as opposed to implementing the ML steps in a python backend?
| There are a lot of services that offer free or very cheap hosting of static websites. If you are able to implement your ML model in JS this allows you to deploy your product/app/whatever easily and with low cost. In comparison, requiring a backend server running your model is harder to setup and maintain, in addition t... | JavaScript is very a popular language, especially for web developers. Machine learning in a web-native language allows additional programmers to use machine learning more easily.
JavaScript is a client-side language that allows deep learning models to predict without server-side resources.
| https://datascience.stackexchange.com |
100,178 | [
"https://math.stackexchange.com/questions/100178",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/17653/"
] | My problem says: "In the matrix $A \in M_{3\times3}$ the columns $c_1, c_2$ are linearly independent and $c_3=c_1+c_2$. Determine a basis in the $\operatorname{Null}(A)$."
Does this have an unique approach? I would solve this by choosing two independent vectors in $R^3$ and then computing the $c_3$. Is it the right ap... | The answer does depend on what you mean by "derivative". Your function $u$ appears to be a nice linear function $u:\mathbb{R}^4 \rightarrow \mathbb{R}^4$. Most of the time when one says they want to take "the derivative" of a function, $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$ at $\vec{x} = \vec{a} $ they mean they ... | You have
$$u_i(\psi)=\sum_jA_{ij}\psi_j$$
and so
$$\partial_{\psi_k}u_i(\psi)=\sum_jA_{ij}\delta_{jk}=A_{ik}$$
that is your original matrix.
| https://math.stackexchange.com |
13,824 | [
"https://dsp.stackexchange.com/questions/13824",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/7570/"
] | Given a difference equation, how do we tell if it is an IIR filter or FIR filter?
For example,
<strong>y(n) = x(n-3)+y(n-1)</strong> . Is it FIR or IIR? Can you please give me a way to figure this out?
Thanks! :)
| Non-Recursive filters are synonym to FIR filters. if you will take z transform of difference equation which is non recursive then you will find out poles for FIR can lie at only zero.Hence if the equation is non-recursive then surely it will represent a FIR filter and its z transform will have all poles at zero.for exa... | The difference equation of IIR filter is recursive, which means the current output depends upon the previous output (the output depends upon the infinite past). Your example is IIR.
On the other hand, the difference equation of FIR filter depends only upon the input. If the input is finite in duration, then the output... | https://dsp.stackexchange.com |
240,040 | [
"https://physics.stackexchange.com/questions/240040",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/105020/"
] | If we connect a wire to the main supply(240v) and if we ground it, what will happen ?? Will there be a current flow ? Will I get a huge electricity bill at the end of the month ??
Also if we connect a bulb in middle of the wire, will it light ?
Thanks
| Assuming you have the electric network common e.g. in Europe, the current will flow through the wire into earth. The current will depend on the soil humidity and wire termination; it may or may not be sufficient to light a bulb.
With very good (and bulky) termination, the current may be so high that the circuit break... | When you connect your wire to ground you will create a circuit via earth.
The current that flows depends mainly on the impedance of the earth and earthing arrangement (also on the impedance of the wiring and any other conductive return paths). If the main earth of the suppy point is a at a local transformer the curren... | https://physics.stackexchange.com |
266,845 | [
"https://electronics.stackexchange.com/questions/266845",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/128101/"
] | So I have learned that in order to shorten christmas lights, you need a resistor. And unless you get a very very big resistor (which is expensive and hard to find, or use a heatsink, or string many together to up the wattage a lot), it will get very hot and you can't let it touch anything.
I don't know what I am missi... | The strings are designed to use bulbs whose voltages sum to equal the supply voltage. So a string that uses 20 bulbs for a 120V power source will use bulbs designed to operate at 6 volts. And a string that uses 50 bulbs for a 120V source will use bulbs designed to operate at 2.4V. When you are making hundreds of tho... | Bulbs can be manufactured to any desired voltage.
I'd assume the strings use different voltage bulbs. Did you measure the voltage across each bulb when it's in it's string and lit?
Incandescent bulbs also don't have a rigid threshold of "working" vs "not working". The bulbs in one string might be overdriven with a vo... | https://electronics.stackexchange.com |
455,625 | [
"https://electronics.stackexchange.com/questions/455625",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/205758/"
] | Please bear with me, if this is a stupid question.
I obtained a linear actuator of a family of linear actuators, here are the specs
<pre><code>| Bipolar linear actuator | 04 | 12 |
|-------------------------|--------|----------|
| Operating voltage | 4 VDC | 12 VDC |
| Current / phase | 0.2... | This will depend on your specific motor driver a little, however if you can set a current limit on the driver, you can use the lower voltage device with a higher supply voltage, your driver will get a little hotter depending on the method it uses, but it also will give your actuator a higher maximum torque and higher t... | Usually modern stepper drivers are designed to control the current to the coils by rapidly switching on and off so that the current through the coil is at a predetermined value (which should be selected to be within the motor specifications). A sense resistor allows the current to be measured. By using a higher supply ... | https://electronics.stackexchange.com |
43,642 | [
"https://chemistry.stackexchange.com/questions/43642",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/24609/"
] | Consider an nitrogen atom with 7 protons and 7 electrons. How can an nitrogen anion <span class="math-container">$\ce{N^-}$</span> exist? Shouldn't the 7 electrons in valence shell repel the extra one?
What force does hold the extra one electron in the valence shell? There isn't an extra proton in the <span class="math... | One reason cations and anions exist is due to the stability of a full or half-full valence shell. The stability from those electronic configurations means that the atom or molecule does not require protons to "hold" the extra electron.
Recall also that nitrogen has three (or five) valence electrons, rather th... | Something to consider: does N become an anion all by itself? No. It gets those electrons from a much less electronegative atom. When it does that it generates an anion and a cation. They attract each other. Potential energy decreases (energy is released) and that "released" energy drives the REACTION.
A... | https://chemistry.stackexchange.com |
607,177 | [
"https://math.stackexchange.com/questions/607177",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/112825/"
] | Given a quadrilateral $ABCD$, prove that the quadrilateral formed by its midpoints, $EFGH$, is a parallelogram.
| <img src="https://i.stack.imgur.com/nF3sH.png" alt="enter image description here">
Since EH is a midline of triangle ABD, $EH \parallel BD$. Likewise, $FG \parallel BD$ looking at triangle BCD. Therefore $EH \parallel BD \parallel FG$. Similarly you can show $EF \parallel HG$.
| <strong>Hints:</strong> Let vectors $a,b,c,d$ go from an (arbitrary but fixed) origin to points $A,B,C,D$. Then
<ol>
<li>Express the vectors from the origin to the midpoints $E,F,G,H$, using $a,b,c,d$.</li>
<li>Conclude that $\vec{EF}=\vec{HG}$.</li>
</ol>
| https://math.stackexchange.com |
107,513 | [
"https://security.stackexchange.com/questions/107513",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/93917/"
] | If I exchange https packets between a server and an Android client, is it easy for the user of the client to get whatever is in the encrypted traffic? Should I consider all such traffic unsafe if the safety is dependent on the user not being able to somehow read what's in the https packets?
| I don't quite understand what is your usage model where the security depends on the user of the app itself not able to know the HTTPS traffic.
But I believe if your app has no certificate pinning built in, and your client do not properly check the TLS connection (similar to how an end user click "Add Exception..." whe... | I would not say it would be easy for the user to get this information but it is possible. I would consider this traffic unsafe on the client end. If you are encrypting this traffic it will be harder for people other than the client to access. The client needs to be able to decrypt the information to access it so yes th... | https://security.stackexchange.com |
24,209 | [
"https://stats.stackexchange.com/questions/24209",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9177/"
] | I am trying to propose Gibbs sampling with the density below,
$$p(y_1,y_2,y_3)\propto \exp [-({{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{\theta}_{12}{y_1}{y_2}}+{{\theta }_{13}{y_3}{y_1}}+{{\theta }_{23}{y_2}{y_3}})]$$
where, $({{y}_{1}},{{y}_{2}},{{y}_{3}})\in R_{+}^{3}$ and ${{\theta }_{ij}}=i+j$
How do I find the full condi... | There you go-
Gibbs Sampler:
The burning period is to reach some stationarity in the samples
<pre><code>burning_period=5000
iterations=1000
y=matrix(nrow=(burning_period+iterations),ncol=3)
a=matrix(nrow=iterations,ncol=3)
y[1,1]=0.5 #Initial Sample
y[1,2]=0.6
y[1,3]=0.2
for(i in 2:(burning_period+iterat... | The full conditional distributions can be found by fixing the values of the two "other" variables, then combining all the terms that you can combine and seeing what you get:
$p(y_1|y_2,y_3) \propto \exp\{-(1+\theta_{12}y_2+\theta_{13}y_3)y_1\}$
which is evidently an exponential distribution with parameter $1+\theta_... | https://stats.stackexchange.com |
425,404 | [
"https://math.stackexchange.com/questions/425404",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/34371/"
] | Consider a linear optimization problem such that the RHS of the constraints depends on a parameter $a$, as in $$Ax=b+ae_j$$
Here $e_j$ is a unit vector in the direction of $x_j$.
Suppose that for some $a_0\in[\alpha,\beta]$ we have solved the problem using the tableau version of the simplex algorithm, and that the val... | Hint: The optimal z-row is represented in matrix-notation as follows: $z^*=c_BB^{-1}b + (c_N - c_BB^{-1}A_N)x_N$. So what it means that the objective value is not altered by the addition of $ae_j$ is that $c_BB^{-1}b=c_BB^{-1}(b+ae_j)$. Now see whether this means that $y^T$ is affected by the addition of $ae_j$ or not.... | The problem with one parameter in objective function is solved by Simplex method, and dual problem is converted to the problem with one parameter in constrict, and is solved by Dual Simplex method. I have improved Simplex method and Dual Simplex method to solve parametric linear programming problem.
| https://math.stackexchange.com |
106,501 | [
"https://softwareengineering.stackexchange.com/questions/106501",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6827/"
] | I feel weird when I'm editing code in an IDE that does not have line numbers in the text editor.
The questions I have are:
<ol>
<li>Are line numbers visually excessive, particularly when a find by line function exists in your IDE of choice?</li>
<li>What are the uses of showing line numbers?</li>
</ol>
| <strong>Anything that aids communication is a plus.</strong>
<ol>
<li>It doesn't take up much space so no, it's not excessive if you or any of your colleagues find it useful to discuss the code. </li>
<li>Even if you don't do pair programming, it is useful for "over the shoulder" code reviews if you don't use tools li... | Displayed line numbers are essential for paired-programming. There is no faster way to direct your pair's eyes to the code you are thinking about.
By extension, line-numbers are also extremely useful for code-reviews, both formal and informal.
| https://softwareengineering.stackexchange.com |
19,496 | [
"https://mathoverflow.net/questions/19496",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2389/"
] | Hello all, it is well-known by transcendence results or Galois theory that famous geometric problems such as trisecting an angle or "squaring the circle" (i.e. given a disk of radius 1 construct a square of equal area) are not solvable by compasses-and-ruler only
constructions.
On the other side, it is equally well-... | Well, for trisection it's very simple. You could divide angle into $2^n$ parts, then just take $\lfloor\frac{2^n}{3}\rfloor$ parts. Of course it could be made as close to one third as you want, but might be hard to do.
For circling the square - draw the $2^n$-gon, then a rectangle with sides $a_n \cdot 2^n$ and $R/2$... | You can get approximate trisections using the geometric series $$\frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + \cdots = \frac{1}{3}$$ Geometrically, take your angle and halve it; take the bottom half and halve it again; take the top half of <i>that</i> and halve it again, etc.
| https://mathoverflow.net |
266,959 | [
"https://stats.stackexchange.com/questions/266959",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/116165/"
] | In maximum likelihood estimation for the parameter, mean $\mu$ of multivariate normal distribution, I end up with the following result:
$\mu_{MLE} = \dfrac{1}{n}\sum_{i=1}^n x_i$
The way I understand the above equation is the following way below, but I am wondering if the above equation means the following equation:
... | It's just linear algebra. Let's take a concrete example where $n=3$. Then ${\bf \mu} \in \mathbb{R}^{3 \times 1}$.
$$\Sigma_{MLE} = \dfrac{1}{3}\sum_{i=1}^3(x_i-{\bf \mu})(x_i-{\bf \mu})^T = \frac13 \left( \begin{array}{c} x_{1} - \mu \\ x_{2} - \mu \\ x_{3} - \mu\end{array} \right)\left( \begin{array}{ccc} x_{1} - \... | <blockquote>
I can't see how this part,
$\dfrac{1}{n}\sum_{i=1}^n(x_i-\mu)(x_i-\mu)^T$, works and produces the
covariance matrix.
</blockquote>
I think it is mostly the mathematical notation that confuses you. I, myself, interpret in this notation system:
$\Sigma_{MLE} =: E[(X-\mu)(X-\mu)^T] = \frac1n \left( \... | https://stats.stackexchange.com |
326,293 | [
"https://physics.stackexchange.com/questions/326293",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21068/"
] | So I have been recently reading about chaotic motion in the solar system. Some research articles particularly emphasize on sensitivity to initial conditions as a prime governing factor behind the rise of a chaotic situation. But what does that physically mean for let's say our solar system? I may be asking a really que... | An easier to understand example of chaos is a frictionless billiard table. Suppose you have several perfectly spherical billiard balls in a perfectly straight line. Suppose you shoot the end ball perfectly straight toward the next ball. All the balls will bounce off each other. The end ball bounces off the table and re... | If you imagine a single sun with a single satellite, the orbital dynamics can be described quite simply. That's because the sun is only exerting a gravitational field on the satellite and the satellite is only exerting it's gravity on the sun. So they'll orbit about their gravitational center. When you introduce a seco... | https://physics.stackexchange.com |
152,884 | [
"https://electronics.stackexchange.com/questions/152884",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/66140/"
] | I want to use my oscilloscope to check the cleanliness of the output a high-voltage power supply (electrophoresis type, up to 3000 volts DC).
I built a 100:1 voltage divider (out of 2 resistors - roughly 700k and 7k ohms), hooked up the scope to the "1x" output of that (to protect the scope from HV damage), then turne... | There are a couple of things going on here.
First of all, many isolation transformers do NOT isolate the ground terminal on the load side; they simply connect it through to the ground on the supply side. I've never understood this reasoning, but there it is. This means that the input ground of your scope <em>is still ... | I have a couple of power supplies intended for electrophoresis use and they have a ground fault indicator. In the case of my power supplies, this fault indicator trips when there is <em>either</em> a missing AC ground OR if the power supply negative terminal is connected to earth ground.
So check your supply for both... | https://electronics.stackexchange.com |
452,549 | [
"https://physics.stackexchange.com/questions/452549",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/183014/"
] | I am a little confused over the terminology of the rest frame. Say a photon collides with a massive particle then from the rest frame of the massive particle would it be the photon or the particle that has momentum?
i.e. in the rest frame of the massive particle is it the photon that travels to the particle or the par... | Choosing a photon in this example could result in a dangerous example but, in your sentence the answer is that from the rest frame of the massive particle the photon has momentum.
You see, in general momentum is (for massive particle) how much force you have to apply in one second to put to rest (in your frame) the in... | In the rest frame by definition the momentum vanishes. In the particle rest frame only the photon moves. However, before and after the collision, it will have different rest frames. It is better to work in the combined rest frame as this remains the same. In this frame <span class="math-container">$\hbar \vec k + m \ve... | https://physics.stackexchange.com |
747,607 | [
"https://physics.stackexchange.com/questions/747607",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222990/"
] | I'm currently doing Introductory QFT and was confused about the origin of the additional terms in the covariant derivate. My understanding is as follows:
If we begin with the Dirac Lagrangian describing a free fermion:
<span class="math-container">\begin{equation}
\require{cancel}
L = \bar{\psi}(i\cancel{\partial}-m)\p... | The increase in velocity for the longer pendulum does, while increasing the total dampening force, not increase the damping constant. This can easily be shown by analyizing the mechanical problem.
Damping that leads to <span class="math-container">$e^{-kt}$</span>-like decay of the oscillations is due to friction force... | It was a good idea, but a pendulum in water will behave differently than a pendulum in air. Looking in section <span class="math-container">$2$</span> of your link, Reynolds number is given by
<span class="math-container">$$Re = \frac{\rho L |v|}{\mu}$$</span>
The derivation that follows is valid for sufficiently low R... | https://physics.stackexchange.com |
79,244 | [
"https://dsp.stackexchange.com/questions/79244",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/-1/"
] | I am wondering if SDRs (software defined radios), e.g. HackRF, RTL-SDR, or USRPs, are, in essence, just oscilloscopes you can plug to a computer to get the data from it. If not, what are the main differences between such devices ?
| All the three devices you mention have mixers, so that's what you wouldn't find in an oscilloscope usually. The amplifiers are optimized for weaker signals, and typically, the quality of ADCs in expensive oscilloscopes is higher than in SDRs – because if you're limited by noise and interference, a high-resolution ADC h... | That depends on how much your definition of "just an oscilloscope" limits functionality. There's probably enough hardware in a high-end O-scope to make at least a receive-side SDR.
The big difference: An oscilloscope lets you see a waveform. A <em>basic</em> oscilloscope just needs to collect a series of s... | https://dsp.stackexchange.com |
566,864 | [
"https://electronics.stackexchange.com/questions/566864",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10282/"
] | I'm looking to sample a signal using an ADC at very low rates - perhaps once every minute. What's the best practice for anti-aliasing filtering in this situation?
Obviously, trying to construct a first-order passive filter at the Nyquist frequency produces absurd component values. Do I use some higher-order (probably... | <blockquote>
THE ANSWER IS GIVEN: 6V
</blockquote>
And that answer is wrong. As drawn, the + input of the opmap is <strong>grounded</strong>
The voltages 1V, 2V, 3V <strong>do nothing</strong>.
The rest of the circuit will have as solution <span class="math-container">\$V_O\$</span> = 0 V as that is the only valid solu... | Either it’s a dumb drawing or a trick question.
Disconnect erroneous gnd on Vin+ and recompute.
| https://electronics.stackexchange.com |
629,365 | [
"https://physics.stackexchange.com/questions/629365",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/238871/"
] | According to the ideal gas law:
<span class="math-container">$pv = nRt $</span>
My question is, why is the volume <span class="math-container">$v$</span> independent of the volume of individual components of the gas, i.e. molecules? As the sizes of individual molecules increase, should the volume of the gas itself not ... | For an ideal gas at ambient pressure and temperature, the actual volume occupied by the molecules is so much smaller than the volume occupied by the gas molecules as they zoom about at high speed and bounce off the container walls and one another that it can be ignored, and the resulting approximations derived from the... | The equation you mention stems from a model known as the “perfect gas” model.
In this model, the molecules of gas are approximated by material points, with a given mass, no size and a given (average) momentum (or speed or kinetic energy). In this model the molecules do not interact with each other. So basically, in thi... | https://physics.stackexchange.com |
131,830 | [
"https://mathoverflow.net/questions/131830",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27398/"
] | Let $j:\mathbb{A}^{n}\rightarrow\mathbb{A}^{n}$ an open immersion over a field $k$. Is it an isomorphism?
| If $U \cong \mathbb A^n$ is the image of $j$, then the long exact sequence of a pair shows that $\mathbb A^n \setminus U$ has no cohomology in any degree, which is only possible if $U = \mathbb A^n$.
More generally (using heavier machinery), no variety $X$ is isomorphic to a Zariski open subset $U \subsetneq X$. The s... | Let $U \cong \mathbb{A}^n$ be the image of $j$ and let $\Delta = \mathbb{A}^n \setminus U$. Since $U$ is affine, $\Delta$ is purely codimension $1$, so $\Delta$ is the zero locus of some $f \in k[x_1, \ldots, x_n]$. But then $f$ is a unit on $U$, contradicting that $U \cong \mathbb{A}^n$.
| https://mathoverflow.net |
44,642 | [
"https://quant.stackexchange.com/questions/44642",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/19004/"
] | I'm trying to build a convertible bond pricer. In my case a convertible bond is a complex derivative with call, put and conversion price reset clauses, and all of the clauses are triggered in a path-dependent fashion. For example, the call clause might be:
<blockquote>
In 30 consecutive trading days,
if the closi... | The usual approach to deal with path dependency in finite differences/lattices solvers is to capture the path dependency trough one or more auxiliary variable(s) that make the problem non path dependent in the augmented space, and to discretize along these auxiliary variable(s).
For instance that's easily done for as... | If you are asking whether it is possible to price path-dependent American options in tree based models, the short answer is yes. You simply construct your tree/grid and evaluate the rules in each node (analogous to what you would do in your MC simulations). These rules can be arbitrarily complex. Note, however, that yo... | https://quant.stackexchange.com |
368,443 | [
"https://mathoverflow.net/questions/368443",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34538/"
] | The computation below (part 1) shows that if two finite groups of order at most <span class="math-container">$100$</span> have the same (ordered) list of conjugacy class sizes, then they also have the same (ordered) list of (irreducible) character degrees.
<strong>Question</strong>: Is it true in general?<br />
If so, ... | SmallGroup(128,227) and SmallGroup(128,731)) are counterexamples.
<pre><code>gap> S:=List([227,731],n->SmallGroup(128,n));;
gap> for g in S do L:=List(ConjugacyClasses(g),c->Size(c));; Sort(L);; Print(L); od;
[ 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8 ]
... | Here is a general comment related to my answer to a previous MO question. If <span class="math-container">$\chi$</span> is a complex irreducible character of a finite group <span class="math-container">$G$</span>, and <span class="math-container">$\chi$</span> takes a root of unity value at <span class="math-container"... | https://mathoverflow.net |
419,190 | [
"https://softwareengineering.stackexchange.com/questions/419190",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/86669/"
] | I'm implementing a stack-based virtual machine in C.
The following variables are used by pretty much every function:
<ul>
<li>memory array</li>
<li>various pointers to memory offsets</li>
<li>program counter</li>
<li>stack</li>
<li>stack pointer</li>
<li>frame pointer (less so)</li>
</ul>
Ordinarily, I'd avoid the use ... | <strong>Usage of globals is a matter of scope of the program "around" them.</strong>
If this "stack-based virtual machine" is the whole program, and the statement <em>"...variables are used by pretty much every function"</em> is literally true (and not an exaggeration), then making those v... | Since the entire purpose of your program is to emulate a system with a hardware-defined, unalterable set of globally available resources, modelling these as a fixed set of globally available resources is perfectly fine; it reflects the structure of the domain object accurately.
Of course, you might still want to encaps... | https://softwareengineering.stackexchange.com |
49,783 | [
"https://electronics.stackexchange.com/questions/49783",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2191/"
] | I have a small 3 year-old 6V 1.2Ah SLA battery that is used in a solar powered burglar alarm sounder box. The sounder recently stopped operating and the battery shows a voltage of about 4V so I am recharging it (using a charger designed for this purpose). I will clean the solar cell and replace the unit's 9V PP3 batter... | It sounds like both batteries are likely end of life, but testing them is a great way to determine if there is useable life remaining. I'm assuming that you don't consider the burglar alarm to be mission-critical, as using a marginal battery in applications that really need reliable power is a bad idea.
First, measur... | Measure the time you can have a 6 V say 10 W lamp connected before you hit 6 or 6.1 V. This will give you the useful Ah of the battery.
You might also want to measure the self discharge rate by simply measuring the battery voltage(preferably under load) after 5 days and 30 day, that will give you at least a somewhat o... | https://electronics.stackexchange.com |
525,112 | [
"https://physics.stackexchange.com/questions/525112",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/174412/"
] | Since textbooks say work is <strong>act transfer of energy</strong>, it led me to think of the following assumption:
<strong><em>Work is being done on the the atoms in the wall, in contact with the hands, when we push (hard) on the wall.</em></strong>
When we push the wall, energy is being transferred <strong>as h... | <blockquote>
Work is being done on the the atoms in the wall, in contact with the
hands, when we push (hard) on the wall.
</blockquote>
At the macroscopic level the wall is considered a rigid body, and since the wall as a whole is not displaced, no work is done.
On the microscopic level you are doing work pushing... | Friction is a red herring here. You can do work on an object by pushing on it, even if there is no friction.
When you push on a spring, you do work by compressing the spring. The spring deforms (shortens) and the work that you do to deform the spring is stored as potential energy in the spring. The spring pushes back ... | https://physics.stackexchange.com |
174,992 | [
"https://softwareengineering.stackexchange.com/questions/174992",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/16411/"
] | I've been following the convention of adding created and modified columns to most of my database tables. I also have been leaving the modified column as null on record creation and only setting a value on actual modification.
The other alternative is to set the modified date to be equal to created date on record creat... | With <code>modified = created</code> if you want the latest modifications with never edited ones included you can rely on the modified column. However if the modified column is initialized with null you have to do a <code>COALESCE(modified, created)</code> which would perform worse.
With <code>modified = created</code... | I think you've summed them up already.
The big pro for initially having the last modified date equal to the created date are that your code is a lot simpler. Simpler code is good as it's easier to maintain.
The only con I can think of right now is that if you need to check to see if the record has been modified your ... | https://softwareengineering.stackexchange.com |
14,402 | [
"https://dba.stackexchange.com/questions/14402",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7200/"
] | I need to keep track of deleted items for client synchronization needs.
In general, is it better to add a <em>tombstone table</em> and a trigger that tracks when a row was deleted from the server database - basically adding a new row to the tombstone table with the data from the deleted item - or to keep the items in... | In general it is better to know the specific requirements and not make design decisions based on what works best in most situations. <strong>Either</strong> could be preferable. Here are some specifics to gather:
<ul>
<li>How fast do deletes need to be? </li>
<li>How fast do un-deletes need to be?</li>
<li>How ofte... | Maybe you should combine the two methods on purpose. Why ???
Let's use that table (MySQL-dialect)
<pre><code>CREATE TABLE mydata
(
id int not null auto_increment
firstname varchar(16) not null,
lastname varchar(16) not null,
zipcode char(5) not null,
...
deleted tinyint not null default 0
KE... | https://dba.stackexchange.com |
580,201 | [
"https://math.stackexchange.com/questions/580201",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/110993/"
] | This might sound retarded for your standards.
But the higher x gets, the higher $\log_{10}(x)$ gets, right?
Does the same principle apply for $\log_{2}(x)$ ?
And by that matter if I have the following expression:
$$n! \leq n^n$$
Does $\leq $ hold?
$$\log_{2}(n!) \leq \log_{2}(n^n)$$
| Yeah the logarithm is a strict monotone increasing function, so if
$$a\leq b \implies \log(a) \leq \log(b)$$
This is true for the natural logarithm and hence for all logarithm with base greater 1.
The derivative of the logarithm is $\frac{1}{x}$ and hence for $x>0$ always positive. So in fact if $a,b$ are strictly... | This is true if the base of the log is larger than $1$.
Think of it this way. If $a > b$ then $\frac{a}{b} > 1$. Now we have reduced it to a single special case (proved below). Applying the log to both sides gives $\log_c \left( \frac{a}{b} \right) > 0$. This simplifies to $\log_c a - \log_c b > 0$, and so... | https://math.stackexchange.com |
436,939 | [
"https://softwareengineering.stackexchange.com/questions/436939",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/99398/"
] | I have a class called SomethingProvider that contains:
<pre><code>private static string convertMapA(string convertA)
{
switch (convertA?.ToUpper())
{
case "NONE":
case "TEST":
case "MEHTEST":
return "None";
... | Personally I prefer having temporary variables with explicit names (but don't abuse them either).
For me:
<pre class="lang-cpp prettyprint-override"><code>void foo()
{
int const number_of_elements = (function_1() + function_2()) / function_3(); // Or more complex expression
write(number_of_elements);
}
</code>... | I think there are two key factors here:
<ul>
<li>How complex is the expression?</li>
<li>How meaningful is the intermediate variable?</li>
</ul>
Take an example where we have three elements to get a final price:
<pre><code>total = price + tax - discount;
</code></pre>
An intermediate variable used only once is probably... | https://softwareengineering.stackexchange.com |
570,457 | [
"https://stats.stackexchange.com/questions/570457",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/353919/"
] | In a 2-stage stacked classifier the first model takes the input data and outputs feature vectors, which are then fed into a second model as input. The second model learns the mapping between the output of the first model and the data labels.
But what mapping does the first model learn? It is given the input data, but h... | In the common stacked classifier setup, the base learners train using the true labels; they do not receive feedback from the second model. And generally, they don't produce feature vectors, just a single prediction; it is those predictions from several base learners that produces the feature vector for the second mode... | Yes, it is possible, but you need a single model that does that.
<blockquote>
the first model takes the input data and outputs feature vectors, which are then fed into a second model as input
</blockquote>
This sounds like a description of a standard two-layer neural network. A neural network is an example of such a mo... | https://stats.stackexchange.com |
470,246 | [
"https://stats.stackexchange.com/questions/470246",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/151384/"
] | No matter how much I google, I cannot find the answer to this simple question.
Say you do 10-fold, repeated (5x) CV logistic regression with elastic net regularization.
For alpha you try <code>seq(0,1,length=10)</code>, and for lambda you try <code>seq(0.1, 0.5, length = 5)</code>
It tries lots of combinations of a... | For consistency, by the weak law of large numbers <span class="math-container">$\bar X_n \stackrel{\text p}\to \frac 1\lambda + \theta$</span> and <span class="math-container">$X_\min \stackrel{\text p}\to \theta$</span> so by Slutsky
<span class="math-container">$$
\bar X_n - X_\min \stackrel{\text p}\to \frac 1\lamb... | Although you are also asking about the estimator <span class="math-container">$\hat{\lambda}$</span>, I am going to note some things about <span class="math-container">$\hat{\theta}$</span>. In this particular case it is quite easy to obtain the <em>exact</em> distribution of this estimator. Since you have a series o... | https://stats.stackexchange.com |
22,749 | [
"https://softwareengineering.stackexchange.com/questions/22749",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5826/"
] | If you're doing a solo project - would you use CI tools to build from a repository? I've used Hudson and Cruise Control in a team environment, where it's essential to build as soon as anyone checks anything in.
I think the value of version control is still obvious, but do I need to build after every commit, seeing as ... | Well I'm planning to use an continuous integration tool on a project and I'm the unique developer. The need comes because
<ol>
<li>One goal is to make it cross-platform, and having an integration tool helps you implicitelly (basic) check your app on several platform once you've pushed your changes in the integration ... | After a brief contemplation I would suggest that it might even be <em>more</em> important for a solo developer than for a team.
At the most basic level a CI server demonstrates that you can build your application from scratch from committed source - combined with a decent set of tests it should demonstrate that you ca... | https://softwareengineering.stackexchange.com |
21,633 | [
"https://dsp.stackexchange.com/questions/21633",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/14792/"
] | I know that frequency mixer $y(t)=x(t)cos(\omega_ct)$ is a nonlinear system since its output has frequency components that are not present in the input. To prove its nonlinearity, it shuldd be shown that the system either violates scaling or additivity. However, I could not do that. Can someone please help me?
| If the system is nonlinear then if $y_1(t)$ is the response to the signal $x_1(t)$, and $y_2(t)$ is the output given input signal $x_2(t)$ then the response to the signal
$$x(t)=a_1x_1(t)+a_2x_2(t)\tag{1}$$
with arbitrary constants $a_1$ and $a_2$ will generally <em>not</em> be equal to
$$y(t)=a_1y_1(t)+a_2y_2(t)\t... | The system is linear but time-variant, because
$$
x(t-t_0)\cos(\omega_\mathrm{c}t) \neq y(t-t_0)\quad\text{for }\omega_\mathrm{c} \neq k2\pi
$$
which can be seen by comparing the above equation with
$$
y(t-t_0) = x(t-t_0)\cos(\omega_\mathrm{c}t - \omega_\mathrm{c}t_0)
$$
Therefore, a frequency mixer is <em>no</em> line... | https://dsp.stackexchange.com |
130,675 | [
"https://electronics.stackexchange.com/questions/130675",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/53375/"
] | I have effectively three sets of variables to put in two locations. Sets 1 and 2 are never used together, so they can occupy the same space. Set 3 needs to be unique.
I know I can use a union of structs to get what I want, but that's a lot of data to force into the same area, and it makes the names unnecessarily com... | As @george-herold said, it is pretty pointless to estimate noise in a circuit, unless, I'd add, you're a circuit engineer who wants to check how much noise your circuit induces in a system. What one generally wants is minimize the impact of noise on a system.
This said, noise sources include almost anything in electro... | Main sources digital parts that use a lot of power
<ul>
<li>FPGAs</li>
<li>uC and uP</li>
<li>DSPs</li>
</ul>
Analog parts of note
<ul>
<li>Switching power supply</li>
<li>RF transmitters</li>
<li>Motor drivers</li>
</ul>
| https://electronics.stackexchange.com |
60,708 | [
"https://dsp.stackexchange.com/questions/60708",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/45147/"
] | i'm pretty new to the topic and I'm trying to understand how to determine the stability of a process. I'm giving this discrete-time stochastic system:
<span class="math-container">$$
\cases{ s_t = 2s_{t-2} + 3w_{t-2} \\
y_t = s_t + v_t \\
w_t = wn(0, q) \\
v_t = wn(0, r) \\
w_t \perp v_t
}
$$</span>
where <span class=... | You're right, the given <span class="math-container">$x[n]$</span> is clearly periodic. You can show this by simply checking if
<span class="math-container">$$x[n]\stackrel{?}{=}x[n+N]\tag{1}$$</span>
is satisfied for some positive integer <span class="math-container">$N$</span>.
For the given <span class="math-cont... | I think you're missing a critical component in your drawing/calculation
Hint: Look at the exponent
EDIT: Yep I was wrong, my bad
| https://dsp.stackexchange.com |
14,998 | [
"https://quant.stackexchange.com/questions/14998",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/5190/"
] | I intend to calculate the daily return on my investment in forex.
Assume a trader invests $\$$40 at a leverage of 100:1, so in total he is trading $\$$4000 worth of currency, and assume the position is open from Dec 4 to Dec 6. Also the trader has enough money to cover potential drawdowns.
In order to calculate the da... | Use your total wealth allocated to the trades as denominator. Total wealth allocated would include all collateral. In this way you (or your broker) make sure that the denominator is always positive. Presumably this would also reflect what you really want to track. The only problem that remains is what amount of your we... | My suggestion would be to use the actual (leveraged) position value, rather than the cost you paid to open the position. Then if you want, you can multiply the return on the position by your leverage, so you might see something like this (if I understood your question correctly):
<pre><code>Date PnL Begin ... | https://quant.stackexchange.com |
316,385 | [
"https://physics.stackexchange.com/questions/316385",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75734/"
] | I have a question which reads:
Let \begin{bmatrix}
{E_0} & 0 & A \\
0 & E_1 & 0 \\
A & 0 & E_0
\end{bmatrix}
be the matrix representation of the Hamiltonian for a three-state system with basis states $|1>, |2> \mbox{and } |3>$.
a. If the state of the s... | Your reasoning is perfectly correct. Here it is in a complete form.
Let us write the Hamiltonian in the following way to make things clearer
$$ \hat{H} = E_0(|1 \rangle \langle 1|+|3 \rangle \langle 3|) + E_1|2 \rangle \langle 2| + A(|1 \rangle \langle 3| + |3 \rangle \langle 1|) $$
It is then straightforward to se... | Actually I believe both answers are correct. I can't seem to find anything wrong with either. Certainly a. is correct since the hamiltonian in the time operator should just be replaced by the eigenvalue, seen simply if we expand the matrix exponential.
For b, there is nothing wrong with expressing our time dependent... | https://physics.stackexchange.com |
7,816 | [
"https://cogsci.stackexchange.com/questions/7816",
"https://cogsci.stackexchange.com",
"https://cogsci.stackexchange.com/users/6350/"
] | I've recently become aware of this - I kinda knew I was always doing it, but just now it got me self conscious and thinking about it:
When crossing paths with a stranger, you are supposed to be friendly and smile at them, acknowledge them through a nod, and so on.
This is particularly the case in many service indust... | Since this (excellent) question has been around for a while without any answer, I thought I'd give my two cents.
I think we do this as a gesture of <em>respect</em> to the other person. We may fear that if we don't acknowledge them at all, it will come off as rude or arrogant. Maybe we fear that if we don't even look... | I suspect that it's rooted in primal responses to seeing a human being you are not expecting to see. This would in part explain the gender difference.
If you've ever seen two cats unexpectantly try to walk past each other, you'll get the problem here: what if the 'unexpected other' perceives you as a threat and attac... | https://cogsci.stackexchange.com |
153,827 | [
"https://dba.stackexchange.com/questions/153827",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/9525/"
] | <ol>
<li>Go to a random table in the Object Explorer</li>
<li>Expand it down to indexes</li>
<li>Right-click on an index - it takes around <em>10 seconds</em> to come up</li>
</ol>
If I attempt to create a <code>DROP & CREATE INDEX</code> script off the context menu, it takes a similar amount of time.
I've looke... | I fixed this by changing my authentication method from "Windows Authentication" to "SQL Server Authentication".
I have no idea why.
Before this change i had to wait up to 1 minute for context menu's to appear.
After change context menus are instant.
| I notice this every now and again after I've had SSMS (2012) open for over a week or more and I've been running things like activity monitor / replication monitor / AO Dashboards
Check opening another instance of SSMS to see if it takes the same length of time, if it is significantly shorter then have both closed (I'm... | https://dba.stackexchange.com |
61,995 | [
"https://electronics.stackexchange.com/questions/61995",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15600/"
] | I am done a google search on this and have come up blank. What I have is a signal/sound being fed through a wire that ranges from (0-9V). When the volume is low, and i need 1 or 2 leds to light up, when it's high, more leds should light up. How would I solve this problem?
Since my signal fluctuates between 0 and 9V, I... | An electronic VU meter is show below so you have an idea how to "rectify" the audio before it goes into the chip.
<img src="https://i.stack.imgur.com/XD9c5.gif" alt="enter image description here" />
I have circled the input where you connect your audio signal and the output is circled where you feed the recti... | Aside from Andy's option, you could always go with the LM3915. Or the internal setup of the LM3915. It's just a bunch of comparators. You could even use op amps as comparators, if you wire them correctly.
<img src="https://i.stack.imgur.com/M42ac.png" alt="enter image description here">
Or you could use opamps.
<img ... | https://electronics.stackexchange.com |
123,553 | [
"https://cs.stackexchange.com/questions/123553",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/118795/"
] | How would we solve the knapsack problem if we now have to fix the number of items in the knapsack by a constant <span class="math-container">$L$</span>? This is the same problem (max weight of <span class="math-container">$W$</span>, every item have a value <span class="math-container">$v$</span> and weight <span class... | You can transform this problem into an instance of Knapsack. Let <span class="math-container">$n$</span> be the number of items, <span class="math-container">$V$</span> be the maximum value of an item and suppose that each item weighs at most <span class="math-container">$W$</span> (otherwise it can be discarded).
To ... | Define a matrix <span class="math-container">$M$</span> of size <span class="math-container">$n \times W \times L$</span>. The entry <span class="math-container">$M[i][j][k]$</span> denotes the maximum value of the knapsack when exactly <span class="math-container">$k$</span> items are chosen from <span class="math-con... | https://cs.stackexchange.com |
93,227 | [
"https://softwareengineering.stackexchange.com/questions/93227",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7702/"
] | I'm currently working on a project with a new programmer. How do I help him speed up his work? He often asks me questions, and I pair programmed with him in backbone.js (a part of the project).
Now I want him to handle the project himself so I can concentrate on other things to speed up the process. He doesn't want to... | Say "<strong>I'm a bit busy right now, you can ask on stackoverflow.com if you're really stuck.</strong>" Eventually he will hopefully get the clue. Also, next time he comes to your desk say
<strong>"Hmm I don't know, let's Google that and see..."</strong>
or
<strong>"Let's check the API docs."</stro... | Much like is required on stackoverflow.com when questions are asked, say <strong><em>"show me what you have so far"</em></strong>. If that is a big fat <strong>nothing</strong>, send him packing, with some hints on what to search for of course, until he has something concrete to ask about.
| https://softwareengineering.stackexchange.com |
2,572,036 | [
"https://math.stackexchange.com/questions/2572036",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/67576/"
] | I have a function $f:\mathbb{C}\to\mathbb{C}$ that is analytic on $A = \{s\mid \mathfrak{R}(s)\geq1\}$ and does not vanish on $A$.
Intuitively, I would expect this to mean that $f$ has an analytic logarithm on $A$, but I am not sure if that is true.
I know that it has a holomorphic logarithm on $\{s\mid\mathfrak{R}(s... | Yes, because you can take $B$ to be the union of $A$ and a family of open disks with center on the imaginary axis, so that $B$ is simply connected.
Why is $B$ simply connected? Note that $z+x\in B$ for all $z\in B$ and $x>0$. So given a closed curve in $B$ you can shrink it to a point by first pushing it to the ri... | Yes, it is true. In fact, if $A\subset\mathbb C$ is open and connected, then $A$ is simply connected if and only if every analytic function $f\colon A\longrightarrow\mathbb C$ has an analytic logarithm. See, for instance, theorem 2.2 in John B. Conway's <em>Functions of One Complex Variable I</em>.
| https://math.stackexchange.com |
187,291 | [
"https://security.stackexchange.com/questions/187291",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/179788/"
] | Is it possible to hack an Android device while the victim is using vpn?
I've tried hacking my Android device on WAN and it worked but when I connected my cellphone to a vpn network it seemed that the session was unable to be opened . Now I'm wondering if there is a way by which Android devices can be hacked while they ... | Use an old version of pyjwt (0.4.3) where this exception wasn't implemented yet.
<pre><code>pip install pyjwt==0.4.3
</code></pre>
| When running your program, it reports the line that throws the exception:
<pre><code> File "/some-path/site-packages/jwt/algorithms.py", line 151, in prepare_key
'The specified key is an asymmetric key or x509 certificate and'
jwt.exceptions.InvalidKeyError: The specified key is an asymmetric key or x509 certific... | https://security.stackexchange.com |
14,466 | [
"https://quant.stackexchange.com/questions/14466",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/1733/"
] | I am working with data for an exotic currency, that has been re-denominated a couple of times during the twenty years of data that I have.
What is the best way of 'normalising' the data, so that I can work with the data, although it contains two 'switch over' dates on which the currency was re-denominated?
| How is this different than a reverse stock split? If you just want the same scale for all the data, you'd just have to update the historic data using the reverse split ratio.
| why not run the same time series 3 times, once for each data set?
| https://quant.stackexchange.com |
51,782 | [
"https://chemistry.stackexchange.com/questions/51782",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/-1/"
] | Whats the difference between chemical processes and chemical reactions?
Ive heard that the chemical industries only uses chemical processes to produce new substances, but isnt that also what happens when a chemical reaction occurs? I couldn't find a lot on this topic online except for the wikipedia aricles that only ma... | According to IUPAC:
<blockquote>
<strong>Chemical reaction</strong>
A process that results in the interconversion of chemical species.
Chemical reactions may be elementary reactions or stepwise reactions
(It should be noted that this definition includes experimentally
observable interconversions of conformers.) Detecta... | While a reaction is a kind of process in the broader sense of that word, in the chemical industry the term process usually refers to an <em>engineered system for producing a chemical product</em>, including one or more reactions, the equipment, the feedstocks, the separation methods, etc. An example of how a process is... | https://chemistry.stackexchange.com |
3,047 | [
"https://engineering.stackexchange.com/questions/3047",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/602/"
] | All these processes sound like structural change caused by heating.
| <strong>Annealing</strong> is a heat-treatment process for stress-relief of a material. Annealing facilitates reduction of internal stresses and total elastic energy stored in inter-atomic bonds within a treated material. The term is used for appropriate heat-treatments of metals, ceramic glasses, and high-performance ... | Knowing the context here might be useful. These terms have nothing to do with each other.
<em>Annealing</em> is warming a metal, usually steel, to give it a soft, easy shaped type of crystalline structure.
<em>Curing</em> is the process of letting a metal sit to work out internal stresses that may have formed during ... | https://engineering.stackexchange.com |
2,109,384 | [
"https://math.stackexchange.com/questions/2109384",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/249111/"
] | I have the following expression:
$$x + \sin(x)=0 $$
I have to demonstrate that this expression has a single root.
What can I do
| The derivate of $f(x)=x+\sin(x)$ is $f'(x)=1+\cos(x)$ which is non-negative and $0$ only for isolated points.
Hence, $f(x)$ is strictly increasing, therefore it can have at most one root.
Since $f(0)=0$, $0$ is the only root.
| Peter's answer is perfect.
And for the sake of curiosity, if you are searching for a root near the origin, for example, then you can use Taylor expansion for the sine:
$$\sin(x) \approx x - \frac{x^3}{6} + \mathcal{O}(x^3)$$
hence
$$x - x + \frac{x^3}{6} = 0$$
$$x^3 = 0$$
Which means $x = 0$. Three solutions, but... | https://math.stackexchange.com |
387,375 | [
"https://electronics.stackexchange.com/questions/387375",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/173446/"
] | In many datasheets and application guides there is always an equation for ripple current, because it is fundamental to the operation of a buck or boost converter, but I never see a direct equation for ripple voltage.
I know the ripple comes from the finite capacitance that needs to discharge the load current during th... | <blockquote>
I suspect the equation is a second order (since the derivative of the
capacitors voltage depends on the derivative of the inductor current)
</blockquote>
This is fundamental to understanding the ripple voltage. The inductor and capacitor form a 2nd order low-pass filter with an input that can be assum... | Quite likely <strong>all</strong> the discrete and the parasitic Cs and Ls interact, and cause ripple/ringing. Thus you should expect "ripple" at 150MHz because of 10nH (0.010uH) interacting with 100pF Cout of onchip power FETs.
And all other possible LC resonators may be a problem, depending upon the amount ... | https://electronics.stackexchange.com |
194,728 | [
"https://dba.stackexchange.com/questions/194728",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/141817/"
] | One of the things that I spend a lot of time when i start some proyect is to understand the relationships of the database provided, and the results of update or delete some foreign key
what is your way of learn a database structure? maybe you draw on paper? or some software
| Well, I did not spot a likely cause of the 30GB, but there are some issues to address:
<strong>Observations:</strong>
<ul>
<li>Version: 5.7.19-17-log</li>
<li>64 GB of RAM</li>
<li>Uptime = 23d 17:12:41</li>
<li>You are not running on Windows.</li>
<li>Running 64-bit version</li>
<li>You appear to be running entirely... | Things to do in my.cnf/ini to improve response time after your research,
could be add, change or lead with # to disable
<pre><code>thread_cache_size=100 #from 50 to Ver 8 suggested CAP to minimize thread creation overhead
read_rnd_buffer_size=128K #from 262144 default to reduce RD per second
innodb_io_capacity=1500... | https://dba.stackexchange.com |
542,454 | [
"https://math.stackexchange.com/questions/542454",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/103695/"
] | There are two tangent lines on $f(x) = \sqrt{x}$ each with the $x$-value $a$ and $b$ respectively.
I need to prove that $c$, the $x$ value of the point at which the two lines intersect each other, is equal to $\sqrt{ab}$, the geometric mean of $a$ and $b$.
I have been trying many different ways of doing this questi... | The two points of tangency are $(a, \sqrt{a})$ and $(b, \sqrt{b})$. If either of $a$ or $b$ is $0$ then the result holds trivially, so assume $ab \neq 0$.
Because the curve is a parabola, the intersection of the tangents, $(x_0, y_0)$, has $y_0=(\sqrt{a}+\sqrt{b})/2$. That's because projecting perpendicularly onto the... | The tangent line at $(a,\sqrt{a})$ has equation $y=\frac{1}{2\sqrt{a}}x+\frac{\sqrt{a}}{2}$.
The tangent line at $(b,\sqrt{b})$ has equation $y=\frac{1}{2\sqrt{b}}x+\frac{\sqrt{b}}{2}$.
Set $\frac{1}{2\sqrt{a}}x+\frac{\sqrt{a}}{2}=\frac{1}{2\sqrt{b}}x+\frac{\sqrt{b}}{2}$ and solve for $x$.
| https://math.stackexchange.com |
640,902 | [
"https://physics.stackexchange.com/questions/640902",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/232790/"
] | In every book or pdf I read about the path integral, I see:
<span class="math-container">$$
\begin{array}{ccl}
\langle q_2,t_2|\hat{q}(t_1)|q_0,t_0\rangle & = & \displaystyle{\iint} dq_3dq_4\langle q_2,t_2|q_3,t_1\rangle\langle q_3,t_1|\hat{q}(t_1)|q_4,t_1\rangle\langle q_4,t_1|q_0,t_0\rangle\\
& = &\di... | The structure of the interior of the sun has been extensively studied by the technique of <em>helioseismology</em> and the findings are consistent with a model in which that structure is relatively simple.
Helioseismology yields structural information on length scales of order ~tens of thousands of kilometers and thus ... | We cannot compare the complexity of objects; we can only compare the complexity of our models for these objects.
And when we talk about models, the complexity of a model increases when our understanding of the object increases. Given enough resources and motivation, we can research an object forever.
Observations and r... | https://physics.stackexchange.com |
564,829 | [
"https://electronics.stackexchange.com/questions/564829",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/285423/"
] | I am looking at using a centre tap transformer with a 12mH secondary to drive a 50W 40kHz ultrasonic transducer (4100pF 10-20Ohm resonance impedance) for cleaning applications.
The input voltage is 12V at the centre and 0V either side of the primary alternated to switch up the output for ~270VAC out of the secondary.
M... | The air gap is for energy storage, i.e. used mostly in flyback converters (where it's used as two inductor on the same core, not as a transformer).
For ultrasonic transducers you are actually looking at an <em>impedance matching</em> transformer (and you usually have to match it to the transducer for best efficiency, t... | Normally, a forward (normal, ideal, power supply, impedance matching) transformer would be designed without an airgap to minimise energy storage in the core, and a flyback transformer would use an airgap for maximising the core energy storage.
However, for driving an ultrasonic transducer for cleaning applications, whi... | https://electronics.stackexchange.com |
4,008,509 | [
"https://math.stackexchange.com/questions/4008509",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | After multiplying it out I get: <span class="math-container">$\ f(x,y)=x^2y+xy^2-6xy-2x^2-2y^2+8x+8y-8$</span>
Where I would take the partial derivative
with respect to x and set to zero: <span class="math-container">$\ y^2+2xy-6y-4x+8=0$</span>,
with respect to y and set to zero: <span class="math-container">$\ x^2+2x... | Since both <span class="math-container">$x^2-6x-4y$</span> and <span class="math-container">$y^2-6y-4x$</span> are equal to <span class="math-container">$-2xy-8$</span>, you have <span class="math-container">$x^2-6x-4y=y^2-6y-4x$</span>, or <span class="math-container">$x^2-y^2=2(x-y)$</span>. Therefore, <span class="m... | Just don't multiply out. The partial derivative with respect to <span class="math-container">$x$</span> (note that <span class="math-container">$(y-2)$</span> is constant in this case) using the product rule for <span class="math-container">$(x-2)(x+y-2)$</span> is
<span class="math-container">$$f_x(x,y) =(y-2)(x+y-2+... | https://math.stackexchange.com |
700,219 | [
"https://physics.stackexchange.com/questions/700219",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/331061/"
] | I can't understand the direction of tension. Why is the direction of tension at the ends of a string away from the object or block of mass? Can someone tell me what happens internally in a string? ps: string is massless
| <blockquote>
I can't understand the direction of tension. Why is the direction of tension at the ends of a string away from the object or block of mass?
</blockquote>
I too had many misconceptions about tension and used to struggle with it. Now, this is how I treat it:
Tension is no 'extra force' that you need to learn... | Tension force lies in <strong>electromagnetic</strong> category of the four fundamental forces.
When you try to stretch a string more than its length, you are actually trying to increase the intermolecular spaces between the atoms of the string. Atoms contain charged particles (initially in equilibrium) and when you di... | https://physics.stackexchange.com |
127,717 | [
"https://mathoverflow.net/questions/127717",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33163/"
] | Let me detail the title of the question. I'm trying to give students an intuition of what the class number is.
Let $K=\mathbb{Q}(\sqrt{-d})$, with $d>0$ a square-free integer, be a quadratic imaginary field. Let $\mathcal{O}_K$ be its ring of integers. It is of the form $\mathbb{Z}[\tau]$ with $\tau=\sqrt{-d}$ or $... | This is an interesting question that I've wondered about myself, so I can't really answer it properly but I'll make a couple elementary observations. First, for a lattice in ${\mathbb Z}[\tau]\subset{\mathbb C}$ to be an ideal just means that multiplication by $\tau$ takes the lattice to itself. For example, for the ... | I think that showing the lattices $(1, \sqrt{-5})$ and $(2, 1+\sqrt{-5})$ is a good idea. As Felipe Voloch says, not all lattices are ideals, but the fact that these lattices are ideals can be shown visually: You just need to check that $\sqrt{-5} I \subset I$ and, of course, multiplication by $\sqrt{-5}$ means multipl... | https://mathoverflow.net |
5,194 | [
"https://physics.stackexchange.com/questions/5194",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1093/"
] | How is the speed of light calculated? My knowledge of physics is limited to how much I studied till high school. One way that comes to my mind is: if we throw light from one point to another (of known distance) and measure the time taken, we could know the speed of light. but do we have such a precise time measuring to... | From Wikipedia:<br>
Presently, the speed of light in a vacuum is defined to be exactly 299,792,458 m/s (approximately 186,282 miles per second). The fixed value of the speed of light in SI units results from the fact that the metre is now defined in terms of the speed of light.
Different physicists have attempted to m... | The title of your question is about <em>calculating</em> the speed of light ($c$), but the body asks about <em>measuring</em> $c$. Others have answered you on the measurement issue, but I'd like to include a bit about the calculation of $c$ from principles.
Light, as an electromagnetic phenomenon, is described by Maxw... | https://physics.stackexchange.com |
476,627 | [
"https://physics.stackexchange.com/questions/476627",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/230543/"
] | The naming of doped semiconductors as "n-type" <em>(for donor-doped)</em> and "p-type" <em>(for acceptor-doped)</em> is ubiquitous. But I am having a hard time digging up where this naming tradition comes from and how it has come to be so widely accepted. From my perspective, there is nothing intuitive about this choi... | I want to supplement Eagle's answer.
Long before people deliberately doped semiconductors, physicists were studying samples of crystalline germanium.
While playing with these crystals, some seemed to act as if they had a few n or negative carriers in them, and others seemed to have p or positive carriers in them.
At fi... | For semiconductors, <strong>n</strong>-type mainly refers to <strong>N</strong>egative electrons which are the major charge carriers, whereas <strong>p</strong>-type refers to <strong>P</strong>ositive, indicating holes which are the majority charge carriers (in this case), and can be thought of as positive.
In short,... | https://physics.stackexchange.com |
57,295 | [
"https://electronics.stackexchange.com/questions/57295",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16948/"
] | My plan is to ultimately develop an Autonomous Faraday Cage. The project seems very straight forward; however, I am unsure on how to effectively control the cage (turn on and off).
I have constructed a prototype Faraday Cage at home. From my research on these cages, my first theory was that an un-grounded cage with no... | The following is just a guess. I could be completely wrong.
You can't disable a cage, but you might be able to make a switchable "leak" in the cage.
Imagine this, you have a cage with two antennas. One antenna on the inside, one on the outside. The two antennas are connected with a wire. Where the wire goes throu... | Your analysis of the cage is not right: it doesn't generate its own field, it acts as an antenna or inductor, absorbing all the emitted RF energy. The energy is dissipated as an eddy current within the cage.
So far as I know you can't electrically disable a Faraday cage.
| https://electronics.stackexchange.com |
4,521,243 | [
"https://math.stackexchange.com/questions/4521243",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/727256/"
] | Compute the indefinite integral
<span class="math-container">$$\displaystyle \int\tan^{8}{x}dx$$</span>
My Attempt:(proposed solution)
<span class="math-container">$$\displaystyle \tan{x}=z\Rightarrow dz=(1+\tan^{2}{x})dx$$</span>
<span class="math-container">$$\displaystyle dx=\frac{dz}{1+z^{2}}$$</span>
<span class="... | Notice that :
<span class="math-container">$$\int \tan^n x \mathrm{d}x + \int \tan^{n - 2} x \mathrm{d} x = \int (1 + \tan^2 x) \tan^{n - 2} x \mathrm{d} x = \int \tan' x \tan^{n - 2} x \mathrm{d} x = \dfrac{\tan^{n - 1} x}{n - 1}$$</span>
| Let <span class="math-container">$X = \int \tan^8 xdx $</span>
<span class="math-container">$\to$</span> <span class="math-container">$\int \tan ^ 6 x (\sec ^ 2 x - 1)d$</span> <span class="math-container">$= \int(\tan x)^6d(\tan x)-\int \tan^4x(\sec^2x-1)dx$</span>
<span class="math-container">$=\tan^7x/7-\int(\tan x)... | https://math.stackexchange.com |
218,846 | [
"https://physics.stackexchange.com/questions/218846",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98365/"
] | If I have the energy per atom <span class="math-container">$e=7.37 $</span> eV, how can I estimate the energy of the single covalent bond in the diamond?
| The first method is giving the correct answer. In writing the work done by the force, you are assuming that the force $F$ itself is constant throughout the extension. However, this is not true. While extending the spring in a quasi-static way, the force $F$ must always match exactly the spring force at that time. This ... | If you use a constant force along the path, the spring will move past the position where $F=kx$, because it will reach that point at some speed. Thus it is incorrect to use the force method in the way you used it, because at maximal extension $v=0$ but $a\neq0$. The energy method as you used it will give the correct an... | https://physics.stackexchange.com |
238,563 | [
"https://softwareengineering.stackexchange.com/questions/238563",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/63589/"
] | In my current code I have felt the desire multuple times to have helper methods that generate a collection of objects and return them as a map of string to object, with the string being some unique id like the objects label. Many of my objects have gaurenteed unique labels since these labels are used via restful inter... | The decision depends on many things:
<ul>
<li><strong>Is the caller method aware(at code-time) of the map's structure?</strong><br>
When I say "code-time" I mean that when you write the code you have a specific structure in mind(compared to compile-time and runtime). If you don't, and the method should be able to hand... | <blockquote>
Should methods returning a hashmap of string to object be avoided?
</blockquote>
Yes, if you're using a statically typed language, <code>object</code> should be avoided. It means that you have to cast to do anything meaningful with the result, which means you have to modify any handling code when you ad... | https://softwareengineering.stackexchange.com |
178,136 | [
"https://softwareengineering.stackexchange.com/questions/178136",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54388/"
] | It might be obvious, but I am not sure.
Should the analyst who interview the client, gather and analyse requirements then give an estimate, also specifies how many and with how much experience developers should be required to develop it?
Maybe I'am not so sure on how I go about this allocation thing, maybe this is ju... | If your organization isn't very big, then you won't have enough programmers to choose from and you should give the work to the programmer who is least busy. They can tell you if an assignment is beyond their technical abilities or their ability to meet the artificial deadline you have probably set for them.
If your o... | At best I would think the analyst can make recommendations on team makeup if there is no team currently, but whoever the Developer Manager/Lead is should be making the decision based on the velocity (or other metric of tracking) of the people he is working with. This assumes that there is already a working development ... | https://softwareengineering.stackexchange.com |
241 | [
"https://mathoverflow.net/questions/241",
"https://mathoverflow.net",
"https://mathoverflow.net/users/83/"
] | The <em>slope</em> of a vector bundle $E$ is defined as $\mu(E) = \deg(E)/\mathrm{rank}(E)$. Then a vector bundle $E$ is called <em>semistable</em> if $\mu(E') \leqslant \mu(E)$ for all proper sub-bundles $E'$. It is called <em>stable</em> if $\mu(E') < \mu(E)$.
I've heard that moduli spaces of stable and semistabl... | I believe "nice" here means "is a quasi-projective variety."
As for why, the reason is geometric invariant theory, which is roughly a way of looking at moduli problems, or actions of groups (which is roughly the same thing) and picking out a subset of the quotient (which itself is only nice as a stack) which is a qua... | Since I can't comment yet, I'll have to recommend this in an answer:
The book by Huybrechts and Lehn: "The Geometry of the Moduli Space of Sheaves" might be worth a look. I really liked the parts that I read.
| https://mathoverflow.net |
1,505,305 | [
"https://math.stackexchange.com/questions/1505305",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/270494/"
] | I'm trying to find the limit of $n!^{1/n^2}$ as $n$ goes to infinity.
What I've done so far is:
I know that $n < n^2 < n! < n^n$ for large $n$,
and I know that $n^{1/n^2} = 1$, but I'm not sure how to find the limit of $n^{n^{1/n^2}}$.
| Hint: $n!^{1/n^2} \le (n^n)^{1/n^2}=n^{1/n}.$
| One more way: $t=e^{log t}$ and then compare the sum over $ \log n$ to the integral. The limit is 1.
| https://math.stackexchange.com |
481,535 | [
"https://physics.stackexchange.com/questions/481535",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/189721/"
] | It's obvious that for every particle velocity is smooth i.e it cannot undergo sudden finite change in its position in infinitisiminal time.
Similarly any particle's velocity cannot undergo a change instantaneously (Infinite acceleration can't happen, intuitively).
Does this pattern apply to higher time derivatives of... | Typically these higher derivatives are assumed to be smooth.
The key question will be what <em>causes</em> a discontinuity in the n-th derivative. If you focus on classical mechanics, the forces on an object boil down to the positions of particles in the system, which are continuous. This means there would need to b... | In order for jerk to be non-zero, the acceleration <span class="math-container">$a=\frac{\mathbf{d}v}{\mathbf{dt}}$</span> must be time-dependent:
<span class="math-container">$$a=\frac{\mathbf{d}v}{\mathbf{dt}}=f(t)\tag{1}$$</span>
That's because the derivative of any number, <strong>no matter how large</strong>, is... | https://physics.stackexchange.com |
283,083 | [
"https://mathoverflow.net/questions/283083",
"https://mathoverflow.net",
"https://mathoverflow.net/users/86048/"
] | Let $(X_t)_{t\in\mathbb{R}\geqslant 0}$ be a Markov Jump Process on a discrete state space $S\cup \{0\}$, with $0$ an absorbing state. If $T_0$ is the hitting time of $0$, I want to prove that
$$ \mathbb{P}_x(T_0<+\infty)=1$$
knowing these facts:
1) For some (finite) neighbourhood of $0$, say $C$, $\mathbb{P}_x... | <blockquote>
What I don't understand is why the exactly the same terms should appear in both sums.
</blockquote>
The Galois action on CM points is described in adelic terms via the fundamental theorem of complex multiplication (or Shimura's explicit reciprocity law) so identifying the terms appearing in the right-ha... | Thank you Olivier for this great answer, I wish I could be one of your students ;-) !
Though I still not quite fully understand the adelic setting, here is some "classical" explanation I found, using the theory of ideals in orders of imaginary quadratic fields. I guess this is supposed to be a very well-known result b... | https://mathoverflow.net |
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