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 |
|---|---|---|---|---|---|
314,820 | [
"https://mathoverflow.net/questions/314820",
"https://mathoverflow.net",
"https://mathoverflow.net/users/131101/"
] | Here is the generating function I'm studying.
<span class="math-container">$f=\prod^N_{j=1}\left(1+e^{i\cdot j\varphi}z\right)$</span>.
<span class="math-container">$\varphi$</span> is a phase related to a quantum optics problem.
And I want to know the analytical result of:
<span class="math-container">$\lim_{z\to ... | O. Forster "Lectures on Riemann Surfaces" (Springer) is a good starting point before taking on T. Szamuely "Galois Groups and Fundamental Groups". After all, as Szamuely writes on page 65 at the beginning of Chapter 3, parts of his exposition in this chapter were inspired by Douady and Forster.
| An English translation of the book by the Douadys is scheduled to come out with Springer early in 2020.
| https://mathoverflow.net |
173,613 | [
"https://softwareengineering.stackexchange.com/questions/173613",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/71845/"
] | I am making a paid App for Windows 8, c#. I am wondering which is better? <br>
<ol>
<li>If my application doesn't need internet connection normally but does requires internet connection for the first time to download content data. --Makes my life easier</li>
<li>Load the default data when installing. Then ask the user... | I think you can be safe in 2012 saying that "broadband internet is required to <em>fully</em> use this product" --- many other things people love and use require it.
I would probably undergo creating the default data for demo / testing / refence purposes. The fact that it shows well when a user first opens the app is ... | Yes it would be safe to assume that most of the people will have internet 90% of the time. But for a better user experience you should consider designing you app in such a way that it is still usable even if there is not internet connection.
However it totally depend on the nature of the application and since you ha... | https://softwareengineering.stackexchange.com |
282,006 | [
"https://softwareengineering.stackexchange.com/questions/282006",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/177676/"
] | I have a class which has an inner (nested) class. I have shown this relationship between the two classes in my class diagram. However, I am also using the inner class within the outer class... do I show another relationship for this or is the containment relationship enough?
| I would say no. You don't have to specify another relationship.
Inner classes AFAIK are implied to be used by their container. That's why they're an inner class. No one else needs to know about this class and no one has a use for it. This inner class is separate from it's containing object because it's different from ... | From <strong>The Unified Modeling Language User Guide</strong> (Booch, Rumbaugh, Jacobson) <em>association</em> is "a structural relationship that describes a set of links, in which a link is a connection among objects".
<em>Aggregation</em> is "a special form of association that specifies a whole-part relationship ... | https://softwareengineering.stackexchange.com |
136,239 | [
"https://dba.stackexchange.com/questions/136239",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/65778/"
] | How to grant select on all tables starting with <code>VVC_</code>?
<pre><code>grant select on VVC_* to user1
</code></pre>
| This one uses a recursive CTE. <strong>Its result is identical to the example in the question</strong>. It was a nightmare to come up with... The code includes comments to ease through its convoluted logic.
<pre><code>SET DATEFIRST 1 -- Make Monday weekday=1
DECLARE @Ranked TABLE (RowID int NOT NULL IDENTITY PRIMARY ... | Not exactly what you are looking for but could perhaps be of interest to you.
The query creates weeks with a comma separated string for the days used in each week. It then finds the islands of consecutive weeks that uses the same pattern in <code>Weekdays</code>.
<pre class="lang-sql prettyprint-override"><code>with ... | https://dba.stackexchange.com |
2,445 | [
"https://bioinformatics.stackexchange.com/questions/2445",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/1421/"
] | We all have been using samtools to convert between sam and bam files. SAM is tab-delimited file. My question resides on the ability to visualize bam files as text. Is there any way to visualize any bam file as text in linux?
Why not work only with sam files and we need to convert them to bam?
| <blockquote>
Why not work only with sam files and we need to convert them to bam?
</blockquote>
SAM is for human only, a binary format like BAM is smaller and parsed much faster by a program (and we want speed and optimize spaces for those huge files, don't we ?).
Furthermore, bam files are compressed using a meth... | bam file is a compressed sam file, comparable with zip or tar. They are binary, which means we (humans) cannot read them. So you need to unpack them (convert back to sam) to read it as a text file.
bam files are smaller than sam files, which is the reason most people like to use bam files instead of sam files.
| https://bioinformatics.stackexchange.com |
117,352 | [
"https://physics.stackexchange.com/questions/117352",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42481/"
] | What happens when the photon which hits a metal surface has energy equal to the work function of that surface?
$$\phi = hf$$
I realise the emitted electron will have no kinetic energy after escape, but then what does it do? Hover above the surface? Or does it have momentum from escaping? I also don't understand what th... | When Electron "orbits" nucleus it's trapped in potential barrier caused by nucleus:
<img src="https://i.stack.imgur.com/8Ex6j.png" alt="enter image description here">
Electron needs some energy $E_0$ to escape (overcome) that barrier ($E_0$ is same as work function $\phi$), When photon with frequency $f$ (Energy of th... | Since we are talking about free electrons being boosted out of a metal surface, It would seem like the “potential barrier” should depend on the net positive charge on the material rather than the force from “a nucleus”. But this does not seem to be the case. Perhaps someone with knowledge of quantum mechanics can comm... | https://physics.stackexchange.com |
1,253 | [
"https://electronics.stackexchange.com/questions/1253",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/333/"
] | How can I sense the touch of a hand through a thick surface? I'm working on a device that has to be completely enclosed in a 1-2" thick wooden casing (or 1-3mm thick metal) due to design requirements, so no chance of pushbuttons.
I thought we could use capacitance touch sensing, but I don't know what will work.
Any i... | If you really need to detect touch through a metal surface, you could possibly do it using 4 insulated Piezoelectric pickups. There is a technique for detecting touch that cross references the frequency detected by 4 equidistant piezo pickups. It's a technique called SAW or surface acoustic wave. It's normally used for... | It should be possible to pick up the minimal bending of the metal with a strain gauge.
I've seen them register the minuscule bending of a cm think steel bar pushed lightly with a finger. Though I don't know what quality of strain gauge and amplifier you need to achieve that. In any case it will be rather expensive (~1... | https://electronics.stackexchange.com |
406,107 | [
"https://softwareengineering.stackexchange.com/questions/406107",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/288540/"
] | I'm working on a webapp that is supposed to be "database-driven". Now, the stuff we do is a bit evolved <em>(a little configurator)</em> and I hesitate to re-read the DB on every callback, because I fear data might become inconsistent (several linked tables are involved) and possibly a lot of checking would have to be... | I understand "database-driven" to mean that the normal, ongoing operations of the application will be directed based on the state of data at the time of (or very near the time of) the operation. Meaning, as time elapses, the data will change, which will in turn affect the application's state.
If the application only c... | I think of it as data-driven vs. code driven. For example you have an application which is available in different countries, and your code looks like this
<pre><code>if (country == "Germany") {
// do this
}
else if (country == "France") {
// do that
}
</code></pre>
then you are not data-driven. Any change req... | https://softwareengineering.stackexchange.com |
95,509 | [
"https://chemistry.stackexchange.com/questions/95509",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/63045/"
] | Recently, I was telling my friends about the violent reaction that takes place when you throw potassium into water. Soon after, a friend of mine claimed that lithium would react more violently than potassium.
I disagreed with him, because potassium is more electropositive than lithium and thus more reactive.
My frien... | For the reaction,<br>
$$\ce{M -> M+ + e-}$$
the heat liberated is highest for lithium owing to its high negative $E^\circ$ value so one would think that the reaction must be most vigorous.
The reason behind the more violent reactivity of potassium rather than lithium lies in <em>kinetics</em> and not in therm... | More than 30 years ago in high school chemistry, our teacher put a flake of sodium in a beaker filled halfway with water and the sodium flitted around the beaker like a little motorboat letting out small wisps of smoke.
Once that was done he put in a small flake of potassium. It reacted much more violently. The pota... | https://chemistry.stackexchange.com |
507,181 | [
"https://physics.stackexchange.com/questions/507181",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208138/"
] | I know that slope at any point on the trajectory of a moving body gives us the direction of its instantaneous velocity.
Does it tell us anything about magnitude of the velocity at that point? I don’t think it does, but I’m not completely sure.
Slope of <span class="math-container">$y$</span> vs <span class="math-co... | <blockquote>
If there is no voltage change, then how would the capacitor become
charged?
</blockquote>
I don't follow your logic here. It's true that there is a voltage drop across a resistor <em>if there is non-zero current through the resistor</em>.
If there is zero volts across the capacitor (at some time), th... | In fact, it is the voltage across the capacitor that <em>stops</em> the charging process.
There is no problem running current through the capacitor when the voltage across it is zero. When the switch is thrown (not shown), there is a potential difference between the battery terminal and the capacitor. Charges will ... | https://physics.stackexchange.com |
680,985 | [
"https://math.stackexchange.com/questions/680985",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/129740/"
] | <blockquote>
Find, in implicit form, the general solution of the differential equation:
$$\frac{dy}{dx}= \frac{2y^4e^{2x}}{3\left(e^{2x}+7\right)^2}$$
</blockquote>
I am struggling to make any sense of this. What I have understood is that first I need to seperate the variables then integrate but I am not sure how ... | Let $y=y(x)$, then
$$
\frac{dy}{dx}= \frac{2y^4e^{2x}}{3\left(e^{2x}+7\right)^2},
$$
or
$$
-\frac{3}{y^4}\frac{dy}{dx}=-\frac{2e^{2x}}{\left(e^{2x}+7\right)^2},
$$
equivalently
$$
\frac{d}{dx}\big(y^{-3}\big)=\frac{d}{dx}\left(\frac{1}{e^{2x}+7}\right),
$$
and thus
$$
y^{-3}=\frac{1}{e^{2x}+7}+c,
$$
for some real const... | HINT:
So, we have $$\frac{dy}{y^4}=\frac{2e^{2x}dx}{3(e^{2x}+7)^2}$$
Integrate either sides by substitute $e^{2x}+7$ with $u$
| https://math.stackexchange.com |
158,306 | [
"https://stats.stackexchange.com/questions/158306",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/69213/"
] | Suppose I run a linear regression model. I am interested in generating prediction intervals. The predicted values are easy to compute, but how can I compute the standard deviations for each of the $\hat{Y}$s?
In R, I use the <code>predict.lm</code> function and use the <code>interval='prediction'</code> argument. I wo... | By fitting an lm object you obtain all the necessary components to do this. Mathematically you have estimates:
$$\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right) ^{-1} \left( \mathbf{X}^T y \right) $$
and and estimate:
$$\mbox{vcov}\left(\hat{\beta} \right) = \hat{\sigma}^2 \left( \mathbf{X}^T\mathbf{X} \right) ... | we have
$$
\hat{\beta}\pm t_{\alpha/2,n-2} \sqrt{\frac{MSE}{\sum(x_i-\bar{x})^2}}
$$
then
<pre><code> l=lm(y~x)
MSE=mean ( (l$residuals)^2)
SSX=sum ( (x-mean(x))^2 )
U= l$coefficients + qt(1-alpha/2,n-2) * sqrt(MSE/SSX)
L= l$coefficients - qt(1-alpha/2,n-2) * sqrt(MSE/SSX)
</code></pre>
| https://stats.stackexchange.com |
20,192 | [
"https://mathoverflow.net/questions/20192",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5018/"
] | I have several questions about Steinberg group and K<sub>2</sub> for symplectic group:
<ol>
<li>Can I extend the definition of Steinberg symbols to symplectic case? Will they generate the center of Steinberg group?</li>
<li>Does the center of symplectic Steinberg group coincide with K<sub>2</sub> (the kernel of $\math... | There is useful information about the symplectic analogues of the Steinberg group, the Steinberg symbols, and the $K_2$ functor in some of Michael Stein's papers from the '70's. In particular, see his papers "Generators, relations and coverings of Chevalley groups over commutative rings" and "Surjective stability in d... | Here's a small follow-up on Matsumoto's thesis, which deals essentially with
the congruence subgroup problem for Chevalley (split) algebraic groups. This
followed work by Bass-Milnor-Serre, but in turn was followed by more technical
work on nonsplit groups (Prasad-Raghunathan, in particular). In my 1980
Springer L... | https://mathoverflow.net |
83,135 | [
"https://physics.stackexchange.com/questions/83135",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12871/"
] | I'm probably missing something obvious and basic here but I can't make sense of certain usages of Observables as present in basic treatments of Quantum Mechanics that i've come across.
$$ \hat{A}|\Psi\rangle = a|\Psi\rangle $$
The above equation implies to me that a single eigenket gives a single eigenvalue of $\hat{... | <blockquote>
However Ket Vectors that are composed of superpositions have multiple possible eigenvalues. Which leads me to believe that that equation is only valid for eigenkets which are Basis States.
</blockquote>
The equation
\begin{align}
\hat A|\Psi\rangle = a|\Psi\rangle
\end{align}
holds only for eigenvecto... | <blockquote>
As a final question is there any kind of useful interpretation of multiplying the eigenket by it's eigenvalue as appears in the above Observable Equation?
</blockquote>
This is the math that describes the idea that $ \langle \Psi \vert A \vert \Psi \rangle = \langle A \rangle$ is the <em>expectation val... | https://physics.stackexchange.com |
2,037,184 | [
"https://math.stackexchange.com/questions/2037184",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/391557/"
] | we know that $S^n = e^0 \sqcup e^n.$ Then CW decomposition of $S^n$ the following $$S^n = \bigcup\limits_{i = 0}^nX^{(n)}, X^{(0)}\subseteq X^{(1)} \subseteq \ldots \subseteq X^{(n)},$$ where $X^{(0)} = e^0, X^{(n)} = e^n, X^{(1)},\ldots, X^{(n-1)} \mbox{ are empty}.$
My question is CW decomposition of $S^n$ above rig... | Your explanation is correct. Note the binomial coefficient
\begin{align*}
\binom{n}{j}=\frac{n(n-1)\cdots(n-(j-1))}{j!}
\end{align*}
has according to the $j$ factors of $j!=j(j-1)\cdots 3\cdot 2\cdot 1$ also $j$ factors in the numerator.
<blockquote>
We obtain
\begin{align*}
\binom{j+r-1}{j}&=\binom{r-1+j}{j}\... | It is just fitting introduction of signes and inversion of a decreasing and consecutive (finite) sequence of factors. Look at the following example:
$$\binom 75=\frac{7\cdot6\cdot5\cdot4\cdot3}{5!}=(-1)^5\frac{(-3)(-4)(-5)(-6)(-7)}{5!}$$
Notice now that $(-3)(-4)(-5)(-6)(-7)=-3(-3-1)(-3-2)(-3-3)(-3-4)$ which is the n... | https://math.stackexchange.com |
2,098,338 | [
"https://math.stackexchange.com/questions/2098338",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/132898/"
] | <blockquote>
Before a bank opens, customers begin to arrive from 8 a.m. onwards. They arrive independently such that the number that arrive in any 1 minute interval is a Poisson random variable with mean $3$. A bank employee randomly checks the line-up $M$ minutes after 8 a.m, where $M$ is a binomial r.v. with $p =0.... | The book's answer is nonsense. Your calculation gives a polynomial with roots at $0,\,4,\,i$ as desired and is a very direct way to find the minimal polynomial that will have a root at all of those places. More simply, one can see this phenomenon since $x-i=0$ is a polynomial with a single root at $i$. Complex roots on... | While <em>Milo Brandt</em>'s answer is perfect, I want to give a quick demonstration that the non-real roots of a <strong>real</strong> polynomial must come in conjugate pairs. Given any complex $x$ I shall use "$x^*$" to denote the complex conjugate of $x$. Also, given any complex polynomial $f$ I shall use "$f^*$" to... | https://math.stackexchange.com |
1,726,783 | [
"https://math.stackexchange.com/questions/1726783",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/220596/"
] | Show $b_0$,.....,$b_{n-1}$ are real numbers, then for $k$ sufficiently large,
$\frac{1}{2} < 1 + \frac{b_{n-1}}{k} +$...$+\frac{b_0}{k^n} < \frac{3}{2}$.
Right now I am studying Tests of Converges of Series, so my partial solution tries this approach. please help me with my solution.
<strong>solution:</strong... | Let $M$ be the maximum of the $|b_i|$, and let $k\ge 1$. Then by the Triangle Inequality
$$\left|\frac{b_{n-1}}{k}+\cdots +\frac{b_0}{k^n}\right|\le \frac{nM}{k},$$ since $k^i\ge k$.
Thus to make our inequalities hold, it is enough to choose $k\ge 1$ so large that $\frac{nM}{k}\lt \frac{1}{2}$.
| Generalizing
André Nicolas's
answer:
As he showed,
$\left|\frac{b_{n-1}}{k}+\cdots +\frac{b_0}{k^n}\right|
\le \frac{nM}{k}
$.
For any $\epsilon > 0$,
if we choose
$k > \frac{nM}{\epsilon}
$,
then
$1-\epsilon
< 1 + \frac{b_{n-1}}{k} +$...$+\frac{b_0}{k^n}
<1+\epsilon
$,
so we can make the sum
as close t... | https://math.stackexchange.com |
124,793 | [
"https://softwareengineering.stackexchange.com/questions/124793",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25553/"
] | At work we mostly do WinForms development and it’s not a secret that it is already very outdated. I have a passion to learn new stuff like WPF, MVVM and want to use full advantages of C# 4.0. There is no way I can push my bosses to change “well-recommended” and “proven” technologies like WinForms to something else.
I... | We should all be so lucky to work somewhere that gives us 2 hours per day dedicated to self-learning! :) Don't waste that time certainly!
I wouldn't use that time for books and reading. I find myself reading books and online tutorials in my spare time at home anyway since I wouldn't need access to company resources ... | Find a business problem that needs solving - something that needs automating or a small application that will help some of the users.
Write the application using the technologies you want to learn.
You now have both learned something and have provided value to the company.
| https://softwareengineering.stackexchange.com |
450,364 | [
"https://stats.stackexchange.com/questions/450364",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/272580/"
] | When transforming variables in a linear regression, be it log, square or some form of normalization, should one then do this to every variable in the regression or is it fine to transform just one variable why and why not?
| There can't be a simple rule on this; it depends on circumstances.
At one extreme, suppose one variable is a <span class="math-container">$(0, 1)$</span> indicator (some people say dummy). Then transforming this is either impossible (e.g. the log or logit of such a variable is not defined for either one or two values... | I would say that it depends:
Many transformations are most likely to be useful on a single variable, and will depend on the distribution of such feature. For example, you might want to trim some values for a feature that has a lot of outliers, impute the ones of a feature that has missing values, log transform one th... | https://stats.stackexchange.com |
901,097 | [
"https://math.stackexchange.com/questions/901097",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/60569/"
] | How does one find equations of a variety given parametric equations (i.e. a regular map) in projective space? For example, I got stuck in finding the equations of the curve in $\Bbb{P}^2$ described by
$$\begin{align}z_0 & =u^3-v^3 \\ z_1 & =u^2v \\ z_2 &= uv^2 \end{align}$$
where $[u,v]\in\Bbb{P}^1$. I hav... | I don't know of a general method, but this case seems fairly nice: We have $v = z_1/u^2$ so $u^3 = z_1^2/z_2$. Using both of these in the first equation gives the equation for the variety in $\mathbb{P}^2$ as $$ z_0z_1z_2 = z_1^3 - z_2^3.$$
| The dimension of the space of homogeneous polynomials of degree $d$ in the $z_i$ is $(d+1)(d+2)/2$, while the dimension of the space of homogeenous polynomials of degree $3d$ in $u,v$ is $3d+1$
If you pick $d=4$ the first space is $15$-dimensional and the second is $13$-dimensional, thus there must be a nontrivial pol... | https://math.stackexchange.com |
34,442 | [
"https://stats.stackexchange.com/questions/34442",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10776/"
] | Please consider the following panel dataset:
<pre><code>comp obs industry weekDay ind10 ind15 day3 day4 day5 marketRet tweets stockRet
-----------------------------------------------------------------------------------------
1 1 15 3 0 1 1 0 0 0.10 5321 -0... | It'd be helpful if you told us what procedure you used. My answers rely on some guesses.
<strong>Question 1:</strong> If you're running the OLS regression using Analyze > Regression, then they cannot be random effects because this module does not allows it. So, they can be seen as fixed effects. If you have used Mixed... | For Q1: since weekDay and your dummy variables are not coming from random causes, I think they can be considered as fixed effects.
| https://stats.stackexchange.com |
27,579 | [
"https://quant.stackexchange.com/questions/27579",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/20507/"
] | I'm preparing a report on the different Greeks used in risk measurement, and my boss mentioned the inflation delta within the first-order Greeks (and the Inflation Vega, but I guess that if I figure out the first, I will get the latter as well).
Does anybody know what is commonly referred to as "inflation delta" of a ... | Typically one only thinks about inflation delta in the context of an inflation derivatives portfolio. Then it is the sensitivity to a 1bp change in the zero coupon inflation rate for each maturity.
As others have mentioned, regular bonds are sensitive to inflation. However we typically describe that risk as a risk... | Inflation delta is typically used in the field of fixed income and is defined as sensitivity of the the present value of cash flows to the changes in the inflation curve. In business it is used to measure the inflation risk in the portfolio relative to the liabilities.
| https://quant.stackexchange.com |
120,775 | [
"https://softwareengineering.stackexchange.com/questions/120775",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15057/"
] | I'm tasked with getting a legacy application under unit test. First some background about the application: It's a 600k LOC Java RCP code base with these major problems
<ul>
<li>massive code duplication</li>
<li>no encapsulation, most private data is accessible from outside, some of the business data also made singleto... | I believe there are two main axes along which code can be placed when it comes to introducing unit tests: A) how testable is the code? and B) how stable is it (i.e. how urgently does it need tests)? Looking only at the extremes, this yields 4 categories:
<ol>
<li>Code that is easy to test and brittle</li>
<li>Code tha... | I have a lot of experience working on legacy systems (not Java though), much larger than this. I hate to be the bearer of bad news, your problem is the size of you problem. I suspect you have underestimated it.
Adding regression tests to legacy code is a slow, expensive process. Many requirements are not well docume... | https://softwareengineering.stackexchange.com |
271,638 | [
"https://softwareengineering.stackexchange.com/questions/271638",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/94336/"
] | creating an MVC structure and pondering this...
My view has an Add button. Click it and we send off a request to the controller (using pub/sub so view doesn't really know who its talking to). Having done this the view disables its Add button until it receives a "data added" event from the controller (again pub/sub so ... | The Controller should be just as dumb as the View.
So in this case, we need to ask about responsibility.
Views are responsible for UI elements and displaying things. Controllers are responsible for connecting Views with Models and providing data for the View to display.
A Controller should be dumb about what the ... | In all likelihood, you should be doing this so that the add button doesn't get enabled again until there is something to add. That means you need client-side validation, which occurs in the View.
| https://softwareengineering.stackexchange.com |
109,298 | [
"https://mathoverflow.net/questions/109298",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16858/"
] | I'm an applied model theorist, and open image theorems are important in the mathematical structures I study (they limit the number of types of elements being realised, and therefore keep things model theoretically nice e.g. stable).
So I have some idea as to why these open image theorems should hold from a model theo... | Here's an application to independence of Heegner points. (But if you search on MathSciNet for papers that reference Serre's two results, I expect you'll find a very large number of applications.)
Let $E/\mathbb{Q}$ be an elliptic curve with no CM, and let $\Phi:X_0(N)\to E$ be a modular parametrization. (Wiles et.al. ... | Well, this isn't explicitly diophantine, but here goes:
If $f$ is a level one weight $k$ eigenform with rational coefficients, the image of the attached Galois representation
$\rho_f:G_{\mathbb{Q}}\rightarrow GL_2(\hat{\mathbb{Z}})$
is open in the subgroup $G$ defined by demanding
$det(G)\subset \hat{\mathbb{Z}}... | https://mathoverflow.net |
554,121 | [
"https://math.stackexchange.com/questions/554121",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/58742/"
] | let $a,b,c\ge 0$,and such $abc=1$,show that
<blockquote>
$$a^2+b^2+c^2+8(ab+bc+ac)+3-10(a+b+c)\ge 0$$
</blockquote>
<strong>My solution: Without loss of generality,assume that</strong>
<blockquote>
$a=\max{(a,b,c)}$, since $abc=1$,we have
$a\ge 1$,
we will show that
$$f(a,b,c)\ge f(a,t,t)\ge 0, t=\sqrt{... | Let $f(x) = x^2+\dfrac8x + 1 - 10x + 16 \log x$ for $x > 0$.<br>
Then the given inequality is $f(a)+f(b)+f(c) \ge 0$, and it is sufficient to show $f(x) \ge 0$.
We note $f'(x) = \dfrac{2(x-2)^2 (x-1)}{x^2}$.<br>
Thus for $x < 1, f'(x)<0$ and for $x > 1, f'(x) \ge 0$. Hence $\forall x >0, \; f(x) \ge f(... | Let $a+b+c=3u$, $ab+ac+bc=3v^2$ and $abc=w^3$.
Hence, our inequality is a linear inequality of $v^2$, which says that
it's remains to prove the last inequality for an extremal value of $v^2$,
which happens for equality case of two variables.
Let $b=a$ and $c=\frac{1}{a^2}$.
Hence, we need to prove that
$$(a-1)^2(... | https://math.stackexchange.com |
94,212 | [
"https://softwareengineering.stackexchange.com/questions/94212",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/97214/"
] | I'm working on a small webservices project (java, axis2..). There is a lot of existing code, the code is divided into many layers, from the first layer where the request in interpreted to a few layers down to the dao layer. In the dao layer I'm seeing some validation code interspersed in a few places. The project conta... | I think DAOs are for persistence. If I wanted to ensure integrity at the database level I'd do it in the database itself, but validation and binding should be completed long before data reached the DAO.
An incoming request to your web service should be validated and bound when it reaches the web service.
| I usually go for this architecture, it's very standard and served me well countless times:
<ul>
<li>A common library with POCO and interfaces defined.</li>
<li>A data access layer based on a common interface so it is interchangeable. It will map the database tables to the POCO.</li>
<li>A business layer which will req... | https://softwareengineering.stackexchange.com |
47,302 | [
"https://softwareengineering.stackexchange.com/questions/47302",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | In my IB Computer Science class I am routinely asked by... pretty much everyone how to do X or implement Y. I'm the only person with any significant programming experience in the class and I do not necessaries mind teaching people about programming but so many of the questions could be simply solved by doing a little i... | <blockquote>
Build a fire for a man and he will be
warm for a night, set a man on fire
and he will be warm for the rest of
his life.
</blockquote>
As a development manager I encounter this issue a lot with the more novice programmers. It is very frustrating when you help them with an issue and they seem to kee... | Firstly, if you're showing them software patterns, stop doing that.
Seriously. For awhile, anyway.
Software patterns, plugins and libraries give students the impression that all programming is about is stitching together bits of code, and makes them lazy, because they don't think for themselves.
Anyway, the single ... | https://softwareengineering.stackexchange.com |
159,697 | [
"https://mathoverflow.net/questions/159697",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11317/"
] | Let $K$ be a field and $A$ the associative unital $K$-algebra of all $n\times n$ upper triangular matrices with entries in $K$. What is $\dim_K$ of its hochschild homology $HH_k(A;A)$?
Is there any software to compute Hochschild homology?
| Sasha's argument is pretty technological. You can really do this almost by hand, though.
Let $A$ be the algebra in question, let $r$ be its Jacobson radical (that is, the subspace of strictly upper triangular matrices), and let $E$ be the subalgebra of the diagonal matrices in $A$ (which is a complement to $r$) Notice... | This is the same as Hochschild homology of the derived category of $A$-modules. The derived category has a semiorthogonal decomposition into $n$ components equivalent to the derived category of $K$-modules each. Hochschild homology is additive for semiorthogonal decompositions. Thus $HH_\bullet(A) = K^n$, everything si... | https://mathoverflow.net |
13,284 | [
"https://earthscience.stackexchange.com/questions/13284",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/12153/"
] | I need to do this for a planet that has uniform density, and a planet that has two layers. For the first part, I was given that the density was 550 kg/m³, so I made one column in an Excel spreadsheet that gave mass as a function of radius, then made another column that plugged that $M$ value into $g = \frac{GM}{r^2}$. ... | As long as we deal with a spherically symmetric planet, the mass of the shell above you does not influence the observed gravity; the little mass close by exactly cancels the large amounts of mass far away (you would float inside a planet if it looked like a pingpong ball and had all its mass centered on the surface!), ... | For each point as you descend into your planet you have a balance between gravity due to a solid sphere below you and "counterbalanced" by the gravity due to a hollow sphere of the planet above you. This last is what is interesting because you are located at a point on the inside surface of the hollow sphere and need ... | https://earthscience.stackexchange.com |
476,913 | [
"https://physics.stackexchange.com/questions/476913",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/230507/"
] | When do we use the word pressure instead of force?
I think pressure and force are same.
Please explain without including the formula.
In the example of nail penetrating into the wall whereas if we invert the nail and then it will be hard to penetrate this example doesn't help me. I think here there is only requirement ... | I'll give you a short but better example.
Consider a plain circle made of clay. It will have a certain weight, whatever it is. Weight is the force that pushes it downwards.
If you put that circle on a water surface, it might float.
Now, take the circle and convert it into a sphere with your hands. Now the sphere doe... | Pressure is the amount of force per unit area
<span class="math-container">$$
P = \frac{F}{A}. $$</span>
Let's say you push on a balloon with a lot of force, it might be that the balloon is very flexible and does not pop. If you push with your hand the force you push with is spread out over the surface of your hand.
I... | https://physics.stackexchange.com |
128,716 | [
"https://mathoverflow.net/questions/128716",
"https://mathoverflow.net",
"https://mathoverflow.net/users/112109/"
] | During courses on geometry it is sometimes necessary to draw a triangle on the blackboard that can easily be recognized as a <em>general triangle</em>. It must not be rectangular and must not have two or more equal angles. Further all angles should be less than $\pi/2$. Has anybody optimized this old problem of geometr... | The book by "Humor in der Mathematik" by Friedrich Wille (from the 1970s or 1980s) contains the tongue-in-cheek theorem "Up to similarity, there is a unique general triangle". (Google book search for "Friedrich Wille" "Allgemeines Dreieck")
"General" is defined as "all angles must differ from each other, and from 9... | Since the question is reopened, I convert my comments into an answer.
The "general triangle" must have angles 75,60,45 degrees (as in Carl Dettmann's comment above), and so there is only one such triangle up to similarity. Here is a "psycho-mathematical" proof. 1) The triangle should not be obtuse (otherwise it is no... | https://mathoverflow.net |
101,634 | [
"https://softwareengineering.stackexchange.com/questions/101634",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4057/"
] | I've always felt lucky to work in a small programming team. I think the most I've worked with is 11 programmers. What is it like working on a project with hundreds of developers? Thousands? What does scale and what doesn't?
EDIT: Thanks for all the responses! There seem to be very few positives:
<ul>
<li>possible ... | I find bureaucracy scales really well.
Other than that, not a whole lot. Large projects have large teams because there's no other way, not because it's more efficient (per developer). You pay a cost as soon as you add a second person to the mix in terms of inefficiency (ie knowledge transfer and communication).
Lar... | Communication is what I have found to be the biggest thing that starts to degrade as the size of the team grows. It becomes harder to get communication out, and harder to ensure that everyone is still on the same page. I work indirectly on a team of about 75 developers, we use a common code base, but many of the 75 b... | https://softwareengineering.stackexchange.com |
91,472 | [
"https://electronics.stackexchange.com/questions/91472",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29873/"
] | <strong>How does a system bus work?</strong>
I don't understand how can a circuit avoid input/output issues with a bus. I included an image to better explain my thinking.
<img src="https://i.stack.imgur.com/NoY43.png" alt="enter image description here">
The circuit has 2 general purpose registers connected to a syst... | Instead of AND gates you need to use tristate drivers. These drivers go to a high-impedance state when they are not enabled, which allows some other device on the bus to control the bus signal voltages. Presumably, the control logic allows only one register output to be enabled at any given time.
Logisim calls these d... | Joe Hass covers the traditional way, replacing the AND gates with tristate logic. This is the way things were done with TTL chips in the 1970s and it is still quite common at the PCB level.
However inside an FPGA, tri-state buffers are no longer supported (except at the external pins) since about the start of this cen... | https://electronics.stackexchange.com |
91,874 | [
"https://chemistry.stackexchange.com/questions/91874",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/59983/"
] | Using the formula $C_1V_1 = C_2V_2$ I am supposed to calculate the molarity of dilutions.
The original solution is $\pu{0.100 M}$ at $\pu{10 mL}$. I diluted it by mixing a $\pu{7.50 mL}$ stock solution with $\pu{2.50 mL}$ water, and made another one by mixing a $\pu{5 mL}$ stock solution with $\pu{5 mL}$ water.
... | You're mixing up the terms and formulae. Instead of rote learning the formulae, remember that the <strong>moles of the solute will remain the same in a solution - before and after dilution.</strong>
With that in mind, let's inspect your $\pu{7.5ml}$ stock solution. Before dilution, it had $\pu{7.5ml}\times\pu{0.1M}$ m... | It should be $7.5\cdot0.1=(7.5+2.5)\cdot C$ then find the value of C which is the concentration of 1st solution....for the 2nd one similarly, $5\cdot 0.1=10\cdot C$ then similarly calculate concentration....
| https://chemistry.stackexchange.com |
1,130,575 | [
"https://math.stackexchange.com/questions/1130575",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/190848/"
] | If I got the invertible matrix $A$, I can calculate the inverse matrix $A^{-1}$, so that $A \cdot A^{-1} = E$, where $E$ is the identity matrix.
Wikipedia says that not only $A\cdot A^{-1} = E$ must be fulfilled, but also $A^{-1} \cdot A = E $. Can someone explain to me why this is not a contradiction to the fact that... | The inverse of a matrix is <strong>defined</strong> as the matrix that satisfies both relationships.
For square matrices $A$ and $B$,
$$
B\mbox{ is the inverse of }A:=B\mbox{ such that } AB{}={}BA{}={}I\,.
$$
Incidentally, this also means that $A$ is the inverse of $B$.
| They are inverses of each other by definition,
therefore $AA^{-1} = E$ holds
now take $A= (A^{-1})^{-1}$ then $A^{-1}(A^{-1})^{-1} = E = A^{-1}A$ also holds as they are inverses of each other
commutativity of matrix multiplication holds in certain cases for example $AE =EA$ where $E$ is the identity matrix
| https://math.stackexchange.com |
149,492 | [
"https://mathoverflow.net/questions/149492",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3319/"
] | Suppose I have a smooth manifold with a tangent bundle, and I have a connection. If this connection is curvature-free, is it guaranteed to be torsion-free? (I am not assuming a metric, just a finite-dimensional smooth manifold.)
I know that in general curvature-free connections do not exist, and that in general torsi... | Many manifolds have curvature-free (i.e., flat) connections on their tangent bundles. For example, any orientable $3$-manifold $M$ is parallelizable, i.e., its tangent bundle is trivial, so it carries a flat connection (in fact, many flat connections). However, nearly all of these connections will have torsion. In f... | Special examples of Robert Bryants answer are Lie groups.
On any Lie group, the left trivialization of the tangent bundle corresponds to a flat connection whose torsion is essentially the Lie bracket, whereas the right trivialization corresponds to another connection without curvature whose torsion is essentially the n... | https://mathoverflow.net |
1,789,016 | [
"https://math.stackexchange.com/questions/1789016",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/332193/"
] | Our professor gave two examples of spaces of sequences one of which is Banach and the other not:
Consider the space of sequences $X$, where only finitely many terms are non-zero, with the norm defined as $||x|| = \sup \{\frac{|x_n|}{n} : n \in \mathbb{N}\}$. This is apparently a normed space but not Banach.
However, ... | For $X$, take $x_n=(1,1,1,\dots, 1, 0, 0, \dots)$, where the last $1$ is in the $n^{th}$ position. Then for any $n<m\in\mathbb{N}$, $||x_n-x_m||=\frac{1}{n}$ which goes to $0$ as $n\to\infty$, so $(x_n)$ is Cauchy. On the other hand, if $z\in X$ (thus only finitely many non-zero entries), you can find a $N\in\mathbb... | HINT.-Put $$a_n=\sum_{k=1}^n\frac 1k$$ Then $x_n=(a_1,a_2,...,a_n,0,0,0,...)\in X$ and the sequence $\{x_n\}$ is Cauchy but it is not convergent because$$\sum_{k=1}^{\infty}\frac 1k$$ is divergent. Hence $X$ is not Banach.
$Z$ is just a quite known Banach space of bounded sequences.
| https://math.stackexchange.com |
7,657 | [
"https://electronics.stackexchange.com/questions/7657",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1129/"
] | I am looking for a cheap way to get +24V DC max 3A from computer power supply. I prefer easy soldering solution like DIP, and standard components that do not need to be purchased over internet. Any ideas, please?
| You can open the supply and look for the TL431 chip. There will be two resistors forming a voltage divider from the 5V rail to the 2.5V that the TL431 compares against. If you calculate the right resistor values, you can set this divider to output half the voltage it currently does. Then you can get the output up s... | I am not sure you can get 3A out of it, but there are both +12V and -12V leads in ATX. You have -12V on blue wire, 0V on black, and +12V on yellow. So it's 24V betweeen blue and yellow.
If you need +24V from black wires, you'll have to arrange a boost converter and draw about 6A from the 12V. You'll likely want to us... | https://electronics.stackexchange.com |
102,752 | [
"https://softwareengineering.stackexchange.com/questions/102752",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29082/"
] | What is the general workflow when I want to add a feature to an open source application I didn't originally write? How do I get to know the code? How do I find the spot that needs to be changed or added? How do I actually make the change without breaking anything else? How do I test that everything is still working?<br... | There's some protocol, everybody more or less desumes it with time, but here it is, unrolled.
<ul>
<li>You download the distributed source.</li>
<li>You start navigating the code by yourself a little
<ul>
<li>If it's a compiled program, you learn <strong>now</strong> how to compile it.</li>
<li>If you fail compiling ... | <h2>Typically.</h2>
If it was a random OS project, you would most likely fix minor bugs here and there.
Eventually you would submit a a bunch of changes, as a "patch".
Usually you would get commit rights if your stuff is good.
I'm talking generally and as vague and nonspecific as possible due to the question
| https://softwareengineering.stackexchange.com |
226,978 | [
"https://physics.stackexchange.com/questions/226978",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75191/"
] | The elastic potential energy is defined as
<span class="math-container">$$V\left ( x \right )=\frac{1}{2}kx^{2}.$$</span>
Then suppose the point <span class="math-container">$x=x_{0}$</span> is the point of a local minimum.
We know that any potential about a local minimum can be approximated reasonably well.
Quoting fr... | First addressing a part of the question: shifting the potential energy <em>does</em> obviously change the potential energy; it just doesn't change the behavior of the system at all. Explanations for the classical and quantum cases follow.
<hr>
In classical mechanics, the behavior of a system doesn't change when the p... | because F=-dV/dx, adding a constant C to V doesnt change the force
| https://physics.stackexchange.com |
154,352 | [
"https://cs.stackexchange.com/questions/154352",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/113436/"
] | I am reading an algorithm book.
Any comparison sort must make <span class="math-container">$\Omega(n\log(n))$</span> comparisons in the worst case to sort <span class="math-container">$n$</span> elements.
Can we create a decision tree for any comparison sorting algorithm even if it is very complicated for <span class="... | In general, a decision tree would enumerate all possible permutations <span class="math-container">$(N!)$</span> for given input of <span class="math-container">$N$</span> elements, out of which only <span class="math-container">$1$</span> would be desirable.
A sorting algorithm doesn't generate all possible permutatio... | The procedure below can be used to explicitly build the decision tree of any comparison-based algorithm:
<ul>
<li>generate all permutations of the array <span class="math-container">$[1, 2, \cdots n]$</span>.
</li>
<li>for every permutation, run the algorithm and note the outcomes of every comparison, together with the... | https://cs.stackexchange.com |
672,090 | [
"https://physics.stackexchange.com/questions/672090",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275029/"
] | The first Maxwell equation:
<span class="math-container">$$\vec\nabla \vec E(\vec r)=\frac {\rho(\vec r)}{\epsilon_0} .$$</span>
But why both variables in the electric field and in the charge density are of the same letter, in this case <span class="math-container">$\vec r$</span>. If we are in some volume/space and we... | ... ''<em>which is the point in which we want to find the value of the electric field generated by the charge distribution</em>''... But then you must have a function <span class="math-container">$\:f[\rho(\mathbf r'),\mathbf r]\:$</span> that provides the information of how the charge density <span class="math-conta... | The equation relate the divergence of the electric field in the point <span class="math-container">$\vec{r}$</span> with the charge density in the same point <span class="math-container">$\vec{r}$</span>.
Maybe you are getting confuse with the Coulomb law applied to a charge distribution.
| https://physics.stackexchange.com |
63,060 | [
"https://security.stackexchange.com/questions/63060",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/45908/"
] | Google, Facebook, Twitter, and several other services still knows the older passwords which we used on our accounts. At times, I can not <em>reuse</em> the same password as I have. Then with Google, if I type an old password by mistake, it tells me when I last changed my password. I think this could be more or less of ... | <strong>Security:</strong>
It might sound like a security hole to you. But trust me, It is one of the strongest security pattern.
It prevents you from avoiding you to create an old password of yours even in your hurry times. It is really necessary for you
not to re-create your old passwords, since there is always a ch... | Nothing is 100% secure, however, this feature of keeping old-passwords protects you from using the passwords which are known to other unauthorized people.
Let's say you have a password 123, someone got hold of it, and then you changed it. Sometime later you realized that you are in need of changing the password again... | https://security.stackexchange.com |
85,365 | [
"https://mathoverflow.net/questions/85365",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16046/"
] | Let $S:=k[X_1,\ldots,X_n]$ be a polynomial ring over a field $k$, with its natural grading, and let $\mathfrak{p}$ be a <em>homogeneous</em> prime ideal of $S$. Also, let $M:=\bigoplus_{i} M_i$ be a finitely generated graded $(S/\mathfrak{p})$-module. Write $\mathcal{F}_P$ for the coherent sheaf on $\mathrm{Proj}\:\:\:... | The ranks are the same. Since $M$ is a finitely generated $(S/\mathfrak{p})$-module you can write down a finite presentation of $M$ by twisted (in the sense of twisting the grading) copies of $S/\mathfrak{p}$:
$$ \oplus_j (S/\mathfrak{p})(-b_j) \stackrel{\Phi}{\longrightarrow} \oplus_{i=1}^k (S/\mathfrak{p})(-a_i) \... | The ranks are the same: $\mathscr F_A$ is the pull back to $\mathrm{Spec} S/\mathfrak p\setminus\{\text{vertex of the cone}\}$ of $\mathscr F_P$.
| https://mathoverflow.net |
47,908 | [
"https://math.stackexchange.com/questions/47908",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11203/"
] | Statement of the problem: Prove that if $A_1 \supseteq A_2 \supseteq A_3 \cdots$ are all finite, nonempty sets of real numbers, then the intersection $\bigcap_{n=1}^{\infty} A_n$ is also finite and nonempty.
My solution: $\bigcap_{n=1}^{\infty} A_n = \emptyset.$ Then at least one $A_n$ is disjoint from the rest - cont... | That the intersection is finite follows because it is contained in $A_1$, which is finite, and a subset of a finite set is always finite.
<strong>Note:</strong> What follows was written before the condition not to use induction was added to the problem.
One possibility to show the intersection is nonempty is to do it... | Since the intersection is a subset of a finite set (namely $A_1$) we know that it is finite.
The simplest way to prove that the intersection is non-empty is to use the theorem that any nested sequence of compact sets is non-empty (which generalizes the nested interval property of closed intervals).
This proof is sur... | https://math.stackexchange.com |
2,044,926 | [
"https://math.stackexchange.com/questions/2044926",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/80708/"
] | Let $p$ be a prime, $n\in \mathbb{N}$ and $f=x^{p^n}-x-1\in \mathbb{F}_p[x]$ irreducible .
Let $a\in \overline{\mathbb{F}}_p$(=algebraic closure of $\mathbb{F}_p$) is a root of $f$.
I want to show that $\mathbb{F}_p(a)$ contains all the roots of $f$.
$$$$
If $a\in \mathbb{F}_p$ then $a^p=a$ and then
$a^{p^n}=... | Let $|F_p(a)|=g$. Then as $F_p(a)^\times$ is a group of order $g-1$, all elements of $F_p(a)$ satisfy $x^g-x=0$. Because $F_p$ is a field, this polynomial, which has all distinct roots as its derivative is identically $-1$ has distinct roots in the algebraic closure, in particular, all elements of $F_p(a)$ are roots of... | Hint:
For any $\;t\in\Bbb F_p\;$ , we have that
$$(a+t)^{p^n}-(a+t)-1=a^{p^n}-a-1+t^{p^n}-t=0$$
| https://math.stackexchange.com |
9,507 | [
"https://dba.stackexchange.com/questions/9507",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5244/"
] | I am using informix...
I dont know how i did it, but there are two procedures with the same name in my database. When i try to remove them with a
<pre><code>DROP PROCEDURE myProc;
</code></pre>
then i get a error message
<pre><code>ERROR: Routine (add_adr_trigger_row) ambiguous - more than one
routine resolves to ... | This happens when you have 2 or more procedures, with the same name, but with different numbers of input parameters.
For example, you have created 2 procedures:
<pre><code>CREATE PROCEDURE myProc(param1)
...
CREATE PROCEDURE myProc(param1, param2)
...
</code></pre>
To delete the second one, you have 2 options:
The ... | If you are aware that this might be a problem in the future, you can create your procedure with a SPECIFIC name, which must be unique across all procedures in the database.
If you aren't aware that it will be a problem when you create the procedure, then you can't officially go back and add a specific name, and you do... | https://dba.stackexchange.com |
113,370 | [
"https://physics.stackexchange.com/questions/113370",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46790/"
] | I know this is an already answered question, but I couldn't make head or tail of it, and it's bugging me. I know I'm probably asking a silly question, but please bear with me as I'm 14 and this is my first post.
I saw this perturbation while studying up a bit of linearised gravity:
$$g_{\mu\nu} = \eta_{\mu\nu} + h_{... | Note that:
$$
h^{\mu \nu} = \eta^{\mu \rho}\eta^{\nu \lambda} h_{\rho \lambda}
$$
Therefore, up to first order, we have:
\begin{equation}
\begin{aligned}
g^{\mu \nu}g_{\nu \sigma} & = (\eta^{\mu \nu} - h^{\mu \nu})(\eta_{\nu \sigma} + h_{\nu \sigma}) \\&
=\eta^{\mu \nu}\eta_{\nu \sigma} + \eta^{\mu \nu}h_{\nu \... | If you have $g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$, with $|h_{\mu\nu}|\ll 1$ a perturbation, $\eta_{\mu\nu} = \text{diag}(-1,1,1,1)$, then you can simply perform a Taylor expansion to obtain the inverse, $$g^{\mu\nu} = \eta^{\mu\nu} - h^{\mu\nu}+ \mathcal{O}(h^2),$$ where the indices of $h^{\mu\nu}$ are raised by $\... | https://physics.stackexchange.com |
157,171 | [
"https://mathoverflow.net/questions/157171",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2039/"
] | Let $h$ be an additive cohomology theory. If we want to compute $h^*(X)$ for an infinite CW-complex $X$, a standard method is to use the Milnor sequence
$$ 0 \to \mathrm{lim}^1_k h^{n-1}(X^{(k)}) \to h^n(X) \to \mathrm{lim}_k h^n(X^{(k)}) \to 0, $$
where $X^{(k)}$ is the $k$-skeleton of $X$. If $h$ is singular cohomo... | For our CW-complex I'm going to take $X = \Bbb{CP}^\infty$ (as a based space), whose skeleta are $\Bbb{CP}^n$. The cohomology theory will be more difficult to construct.
For any $k \geq 1$, let $E_k$ be the spectrum which is the homotopy fiber of the map
$$
Sq^{2^k} \cdots Sq^8 Sq^4 Sq^2: \Sigma^2 H\Bbb{Z}/2 \to \Sig... | Take $X$ to be the Moore space for the group $\mathbb Z[\frac1p]$ in dimension $n$ (realized by a telescope of $n$-spheres mapping to each other vie the times-$p$ map), and take $h^*$ to be ordinary cohomology with coefficients in $\mathbb Z$.
The universal coefficient theorem gives you a sort exact sequence
$$
0\long... | https://mathoverflow.net |
150,993 | [
"https://cs.stackexchange.com/questions/150993",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/149932/"
] | It is possible to have this logical consequence?
<span class="math-container">$$
\forall x (p(x) \vee q(x)) \models \forall x p(x) \vee \forall x q(x)
$$</span>
| The statement <span class="math-container">$\forall x (p(x) \vee q(x))$</span> does not imply <span class="math-container">$\forall x p(x) \vee \forall x q(x)$</span> because there exist a domain, a propositional function p(x) and a propositional function q(x) for which <span class="math-container">$\forall x (p(x) \ve... | Take the structure <span class="math-container">$\mathfrak{A} = (\{a, b\}, =)$</span> and <span class="math-container">$p(x) \equiv x = a$</span>, <span class="math-container">$q(x) \equiv x = b$</span>. Then <span class="math-container">$\mathfrak{A} \models \forall x (p(x) \vee q(x))$</span> but <span class="math-con... | https://cs.stackexchange.com |
23,120 | [
"https://security.stackexchange.com/questions/23120",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15389/"
] | I am an outsourcing person, not a programmer. My website is a shopping website (think eBay). My website will need a user suspension feature, in case a user violates the terms and conditions. The problem is to detect users who create a second account. Here are ways I've thought of:
<ul>
<li>IP address tracking</li>
<li... | There is no way to prevent multiple registrations.
I have two suggestions to offer
<ol>
<li>Make multiple registrations undesirable, for example by charging a fee.</li>
<li>Outsource the identity problem to someone else, for example my using Facebook or Google login instead of rolling your own.</li>
</ol>
| No - given that most users come in from large ISPs, their IPs are not fixed for all time - the names they give to you certainly aren't fixed
Security is not a black and white issue - though it seems too many don't seem to understand that - it's an issue of making the cost of defeating it not worth the reward
In the... | https://security.stackexchange.com |
1,455,008 | [
"https://math.stackexchange.com/questions/1455008",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/267950/"
] | Given equation is $x^5-10a^3x^2+b^4x+c^5=0$ which has 3 equal roots. What I know is that since its a 5th degree equation therefore it must have 5 roots out (of which 3 are equal).
Aim is to establish the relationship between the constants $a,b$ and $c$.
Options given are:
1) $6a^5+c^5=0$.
2) $b^4=15a^4.$
I have to ... | Let $$f(x) = x^5 - 10a^3x^2 + b^4x + c^5 = (x - m)^3g(x)$$ where $m$ is the repeated root, and $g(x)$ is some second-order polynomial.
Then, differentiating and substituting $x = m$,
$$5x^4 - 20a^3x + b^4 = (x - m)^3g'(x) + 3(x - m)^2g(x)$$
$$5m^4 - 20a^3m + b^4 = 0$$
Differentiating another time, and similarly sub... | Let $t$ the triple root and consider the coefficients $r,s$ of the quadratic factor so one has the polynomial $(x-t)^3(x^2+rx+s)$. The equality of corresponding coefficients gives $$r-3t=0$$ $$s-3tr+3t^2=0$$ $$-3ts-t^3+3t^r=-10a^3$$ $$3t^2s-t^3r=b^4$$ $$-t^3s=c^5$$ Solving easily this system we have a parameterizat... | https://math.stackexchange.com |
119,020 | [
"https://softwareengineering.stackexchange.com/questions/119020",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/9267/"
] | Can you use Google Analytics to track visitors/downloaders for a Google Code project?
I've searched google for an answer but I get results about Google Analytics as a Google Code project itself and not for applying it to a Google Code project for visitor/download data.
| You can use Analytics to track visits and views of Code projects but not downloads as far as I know.
If you look under your project's Administer tab, you'll see towards the bottom that there is a box into which you an enter an Analytics tracking code. That's all there is to it.
| Trick to using GA to track downloads is to use javascript to fire off an event (or a pageview) when someone clicks the download link.
No idea how much javascript one can push into a google code page.
| https://softwareengineering.stackexchange.com |
37,303 | [
"https://quant.stackexchange.com/questions/37303",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/30915/"
] | Suppose the value of an option is given by $v(s_0)$ where $s_0$ is the current price of the underlying asset and $v:\mathbb{R}_+\to\mathbb{R}_+$.
It seems that the literature is mostly focused on getting an estimate of $v(s_0)$. My question is whether there is any benefit from estimating the whole function $v$ instead... | Some numerical methods, e.g. finite difference schemes, enable you to compute the entire function $s \mapsto v(s)$ at once. This can be useful as no additional pass is required to compute the delta and the gamma.
| Ciao,
Of course it would be amazing to know the future (i.e. the whole trajectory of the price process) and it would be really usefull for hedging (it makes the hedging itself a trivial problem). However I think you have to think about that everything in the future depends on stochastic variables and that the only pla... | https://quant.stackexchange.com |
2,510 | [
"https://stats.stackexchange.com/questions/2510",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/603/"
] | For the more mathematically minded,
we have $x \in \mathbb{R}^2$ and the function $h(x)$ defined as:
$h(x)=\alpha_1x_1^2+\alpha_2x_2^2+\alpha_3x_1+\alpha_4x_2+\alpha_5x_1x_2+\alpha_6$
and the vector of alpha's is <strong>known</strong> and further guaranteed to be such that $h(x)$ is a general
elliptic paraboloid ... | The $L^2$ distance between $g$ and a polynomial approximation will be finite if and only if the polynomial approximation behaves asymptotically like $g$, which means it behaves asymptotically like $h$, which implies it must equal $h$. Therefore $h$ is the unique $L^2$ approximator.
Thus:
(1) Yes; the global approxim... | Note that $h(x)$ itself is a polynomial in $x_1$ and $x_2$ and $g(x)$ is what I would call a <em>truncated polynomial</em>.
The region where $h(x)$ is negative, $g(x)$ will be zero. You can approximate this region where $h(x)$ is flat by a non-constant polynomial (non-constant because you also need to approximate the... | https://stats.stackexchange.com |
23,329 | [
"https://electronics.stackexchange.com/questions/23329",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1317/"
] | I have just had a frustrating experience with an NPN transistor that came from a pack of 15 "switching transistors" from Radio Shack. The specs on the packaging say "Typical hfe: 200" but when I measure and calculate the values from an actual operating circuit it looks like the hfe is more like 8. (If I am calculating ... | No problem at all. The transistor 'degrades' to being a simple diode which receives some modest (I assume!) current from your controller.
| Typically, disconnecting the collector from a transistor will be harmless, but that isn't always the case. Consider an NPN transitor with the emitter tied to ground through a 5ohm resistor and the base tied to a "rigid" 10-volt supply and the collector either attached to a "rigid" 15-volt supply or disconnected. With... | https://electronics.stackexchange.com |
222,208 | [
"https://softwareengineering.stackexchange.com/questions/222208",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4091/"
] | I'm looking at a very large (5-6 digit LOC), very complex, code-base, full of interacting bulky, interdependent, views and stored procedures (multiple 4-5 digit count silos).
The source SQL has been touched many times, by many different people, and no formatting constraints have been enforced. This led to wildly diffe... | Agree to a sensible coding standard for future work, and fix the problem SQL as needed during refactoring. Leave intact all of the code that is working that otherwise doesn't need to be touched.
| <blockquote>
what is a sane standard to conform to for formatting [SQL] ?
</blockquote>
Something that you can express in programmatic form, so that you can send a text file to a program and know if the format is "standard" or not.
Ideally, the rules you care about will be the kind you can automatically impose on a... | https://softwareengineering.stackexchange.com |
519,435 | [
"https://physics.stackexchange.com/questions/519435",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249539/"
] | In <em>The Universe in a Nutshell</em> chapter 4, Hawking explains the warping of spacetime according to general relativity.
Near a massive but ordinary star, spacetime is warped such that the light emitted from the star appears to move slower when near the star, and appears to "speed up" to the constant speed of ligh... | It is possible to have a simultaneous eignfunction of <span class="math-container">${\hat L}^2$</span> and one other component of the angular momentum. Typically this is taken to be <span class="math-container">${\hat L}_z$</span>, but it could just as well be the <span class="math-container">$x$</span> or <span class=... | The reason is quite simple:
The operators <span class="math-container">$\hat{L}^2$</span> and <span class="math-container">$\hat{L}_z$</span> have common eigen-functions
because they commute with each other, i.e. <span class="math-container">$[\hat{L}^2,\hat{L_z}]=0$</span>.
The operators <span class="math-container"... | https://physics.stackexchange.com |
20,239 | [
"https://softwareengineering.stackexchange.com/questions/20239",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8029/"
] | I guess most people have been in this situation.
The initial project planning begins. The requirements are outlined. After architectural review and sorting through APIs/Frameworks the fitting technology is picked. The development starts.
And then it starts. As soon as you need to do some supposedly simple supporting ... | Prototype, Prototype, Prototype!!
If your team is not familiar with a particular framework then prototype something in it to evaluate where the pain points are.
Matt Raible (Java Web framework comparator guy) suggests working with a framework for one week if possible.
Prototyping includes investigating the community... | Managing external dependencies is the bane of many an IT project. Many years ago the experienced programmers I worked with always made sure they had control over their dependencies - Usually by insisting that source code licenses were bought.
Personally, that has not been my approach. I tend to be of the under promis... | https://softwareengineering.stackexchange.com |
284,743 | [
"https://softwareengineering.stackexchange.com/questions/284743",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/72595/"
] | I learned that it's good practice to declare variables before they are used. For example:
<pre><code>function myFunction() {
var i;
var j;
}
</code></pre>
Does the same thing go for object properties, and is there a usual way/best practice for doing it? Because sometimes we don't know values of all properties whe... | There are two aspects to the <code>const</code> in C++:
<ul>
<li>logical constness: When you create a variable and point a <code>const</code> pointer or reference to it, the compiler simply checks that you don't modify the variable via the <code>const</code> pointer or reference, directly or indirectly. This constness... | When using the qualifier const as inthe case below:
<pre><code> const int value=67;
</code></pre>
We are telling the compiler that we promise not to change the value of the variable "value". As such the compiler will merely replace instances of "value" with the actual value we initialized it with.since the compiler r... | https://softwareengineering.stackexchange.com |
43,895 | [
"https://mechanics.stackexchange.com/questions/43895",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/13160/"
] | While I was driving my car suddenly the left control arm suddenly broke off (the car has had a curb accident on that side before) and the cv-joint de-attached from the transmission and the car was not moving anymore while in gear. But something I noticed is the vehicle speedometer was relative to the RPM; as the car wa... | If the ECU would calculate speed from RPM, how would it calculate speed when the car is in neutral or during shifting?
The speed usually is derived from the RPM of the output shaft of the transmission (to the differential). This way, one gets an average of the speed of the left and right wheels.
The key to your obser... | Somewhere there is a signal that measures rotating speed on the driveline, downstream of the torque converter. It is typically somewhere inside the transmission housing. Because of how a torque converter operates, engine RPM would not be a totally great indicator for vehicle speed.
Typically auto manufacturers use... | https://mechanics.stackexchange.com |
19,592 | [
"https://cstheory.stackexchange.com/questions/19592",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/214/"
] | Let $x_i \in \{-1,0,+1\}$ for $i \in \{1,\ldots,n\}$, with the promise that $x = \sum_{i=1}^n{x_i} \in \{0,1\}$ (where the sum is over $\mathbb{Z}$). Then what is the complexity of determining if $x = 1$?
Notice that trivially the problem lies in $\cap_{m \geq 2}{\mathsf{AC}^0[m]}$ because $x \equiv 1\bmod{m}$ iff $x ... | Here is a modified version of the Euclidean algorithm that is stable.
When considering the equation
$$ax + by = c \quad (1)$$
we may w.l.o.g. assume that $a, b, c \ge 0$, $b \ge 1$ and $b \ge a$. From now on we will only consider such equations. Moreover, we will set $d = \gcd(a,b)$.
We call a solution $(x,y)$ <stron... | One way to solve this might be through an application of the Chinese remainder theorem and some kind of Hensel lifting.
Let's fix a constant <span class="math-container">$\alpha$</span> with the property that <span class="math-container">$2^\alpha 3^\alpha 5^\alpha > 2^{129}$</span> and <span class="math-container">... | https://cstheory.stackexchange.com |
16,965 | [
"https://physics.stackexchange.com/questions/16965",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6134/"
] | When I open my blinds, there is light enough to read a book outside while the lamp is on inside.
So when I close my blinds, does the light that otherwise will escape, stay inside and thus being lighter inside?
| Microcanonical ensemble means an isolated system with defined energy. The system may be found only in microscopic state with the adequate energy, with equal probability.
Canonical ensemble means a system attached to the "temperature reservoir", which may supply/take infinite amount of energy. The system may be found i... | The canonical ensembles is the collection of a large number of essentially independent system having the some temperature. Volume and the some number of identical particles. The individual system of this ensembles are seperated by rigid impremeable and conducting walls.
| https://physics.stackexchange.com |
244,713 | [
"https://dba.stackexchange.com/questions/244713",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/186488/"
] | I am creating partition tables in postgreSQL. And the partition is on date column so its nearly high in number to show in schema. I want to show only my parent table for other users.
I tried many searches but this kind of concept is not explained anywhere.
This is my hierarchy,
<pre><code>Master_table
child_01_2013
... | If all you want is to remove the partitions from the schema view, you could simply move the partitions to another schema:
<pre><code>ALTER TABLE child_01_2013 SET SCHEMA otherschema;
</code></pre>
Everything will continue to work as before, but the visual clutter will be gone.
| I don't know for dbvisualizer. For pgAdmin4 (tested on version 4.11) the partitions already show up in a folder under the main table in the object tree. Unless you open the folder, you aren't going to see them. You can even hide that folder altogether from the pgAdmin4 preferences setting, if you want.
| https://dba.stackexchange.com |
110,310 | [
"https://security.stackexchange.com/questions/110310",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/96606/"
] | Which is the safest way to do <strong>home banking</strong>, given that I do use Windows on a tablet, I do connect to both <em>private and public networks</em> and I cannot use a Linux live distro right now?
I've been thinking about these methods so far:
<ol>
<li>using a <strong><em>safe environment</em></strong> pro... | Strictly speaking, both are insecure compared to USB boot etc. However, every layer of security drops the probability of generic attacks succeeding. Using a VM with incoming network connections disabled should be immune to the vast majority of malware on the host. You could disconnect the USB keyboard from the host and... | A virtual machine can't protect the guest OS from the host (without specialized hardware features to support it). You will not gain any security from running Linux in a VM if Windows gets infected, and if your VM gets infected then that's still the environment you intended to use for security sensitive things that's ne... | https://security.stackexchange.com |
124,648 | [
"https://softwareengineering.stackexchange.com/questions/124648",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22712/"
] | I've seen a lot research articles and tech blogs that boast the benefits of software testing. I've convinced on that. But since all the software testing research are conducted by large software companies, I do not believe they really apply to startups. Since startups have different needs and constraints compared to lar... | There is always a conflict between what should be done and what we realistically have time for. Yes many startups forgo test driven development and automated testing to shave some time off to get a project up and running.
The social networking sites and mobile app companies are the big bubbles now, and they are <stro... | Software testing isn't a religion. It's just a very good idea.
You say you don't have the manpower to write tests right now? OK, fine. 6 weeks from now, are you gonna have the manpower to find the bug that's crashing your application, which would have been found immediately if you had proper tests in place?
Too much ... | https://softwareengineering.stackexchange.com |
10,656 | [
"https://physics.stackexchange.com/questions/10656",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3805/"
] | Person A in reference frame A watches person B travel from Star 1 to Star 2 (a distance of d). Of course, from person B's reference frame, he is at rest and is watching Star 2 traveling to him.
Now we know from the principle of relativity, each one will measure the other one’s clock as running slower than his own.
... | Everything you have said describing the situation in your question is correct; Person A and Person B disagree about how much time elapses on person A's clock between the two events. (The first event is Person B leaving Star 1 and the second event is Person B arriving at Star 2) This is not a logical contradiction. I... | Layman's answer here. First we need to clean up the thought experiment a bit.
In relativity texts it's common for these kind of thought experiments to use observers stationed at the points in question, so that the travel delay of light can be ignored. As part of the setup of the thought experiment Person A would have ... | https://physics.stackexchange.com |
223,006 | [
"https://softwareengineering.stackexchange.com/questions/223006",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/111969/"
] | There seem to be quite a few ways of communicating between directives. Say you have nested directives, where the inner directives must communicate something to the outer (e.g. it's been chosen by the user).
<pre><code><outer>
<inner></inner>
<inner></inner>
</outer>
</code></pre... | My preference is for defining a <code>&</code> attribute in the directive scope primarily because I view the <code>scope: {}</code> definition of a directive as its API. It's much easier to look at a scope attribute definition to see what information the directive needs to function properly than it is to scour lin... | My opinion:
Services are the preferred way of sharing behaviour/data across modules/directives/controllers. Directives are isolated things that can be nested or not. Controllers should stick to being a viewmodel as much as they can, ideally no business logic should end up in there.
So:
When you start wiring them tog... | https://softwareengineering.stackexchange.com |
3,623,289 | [
"https://math.stackexchange.com/questions/3623289",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/658285/"
] | I have to prove that <span class="math-container">$O_2(\mathbb R)=\{A \in GL_2(\mathbb R):|\det(A)|=1\}$</span> is a normal subgroup of <span class="math-container">$GL_2(\mathbb R)$</span>.
I tried to go on with the definition of normal subgroup but I don't really know how to use it in this case. I've also tried with... | You can do it using the definition. Just take <span class="math-container">$A \in \text{SL}_2(\mathbb R)$</span> (that is, a <span class="math-container">$2 \times 2$</span> real matrix <span class="math-container">$A$</span> such that <span class="math-container">$\operatorname{det} A = 1$</span>) and <span class="mat... | If you can use homomorphisms, then <span class="math-container">$A \mapsto |\det(A)|$</span> is a group homomorphism
<span class="math-container">$GL_2(\mathbb R) \to \mathbb R^\times_+$</span> whose kernel is the set in question.
| https://math.stackexchange.com |
174,901 | [
"https://dba.stackexchange.com/questions/174901",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/105289/"
] | I need to set the time of a timestamp in SQL.
My results need to be between yesterday at 7 o'clock and today at 7 o'clock.
Here is the query
<pre><code>WHERE created_at BETWEEN
?::timestamp - INTERVAL '1 day' AND ?::timestamp
ORDER BY created_at DESC
</code></pre>
The value is:
<pre><code>2017-05-30
</code>... | You can use <code>current_date</code> (without a time) and then add the 7 hours:
<pre><code>WHERE created_at BETWEEN (current_date - 1) + time '07:00:00'
AND current_date + time '07:00:00'
</code></pre>
<code>(current_date - 1)</code> is "yesterday"
Alternatively you could use an interval:
... | Since you didn't give any sample data, I based it on create date on databases.
<pre><code>select name, datediff(day, create_date, getdate()) DaysDiff from sys.databases
**where DATEDIFF(DAY, create_date,getdate()) > 1**
</code></pre>
You'll need to evaluate days difference, something like:
<pre><code>where DATEDI... | https://dba.stackexchange.com |
723,425 | [
"https://physics.stackexchange.com/questions/723425",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/342528/"
] | According to my understanding, an oscillating pendulum is not at equilibrium, since its momentum and velocity changes with time. Now my question is that we say that the pendulum at its resting position or equilibrium position is in stable equilibrium. But if we apply even a small force to the pendulum or displace the p... | A mechanical equilibrium position means that no resulting force is acting on the system. Therefore, if we put the system at the equilibrium position at rest, it will remain there forever.
Stable equilibrium means something more. If we slightly displace a system from a stable equilibrium position with a small velocity, ... | Equilibrium means that the state will remain unchanged until disturbed. That is true for the pendulum at rest. A small disturbance from a stable equilibrium requires energy. There is then a force returning the system to the rest position, but, unless there is some friction, when the system returns there it still has th... | https://physics.stackexchange.com |
400,238 | [
"https://physics.stackexchange.com/questions/400238",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/124796/"
] | I am trying to calculate the capacitance between a circular plate of radius $r$ and infinite ground plane, where the circular plate is tilted at an angle $\theta$ to the ground plane. The aim is to better understand capacitive displacement sensors, and an analytical result would be better than a numerical one for that.... | Let's start with the small-angle approximation $\sin\theta\rightarrow\theta$. We get
$$C=\epsilon_0\frac{2}{d}\int_{-r}^rdx\frac{\sqrt{r^2-x^2}}{1+(\theta/d)x}.$$
You say that $d\ll r$: this is important in the sense that it's useful for analyzing any typical parallel-plate capacitor, where we want to ignore the frin... | Here's another approach that I like more: you could use the method of images. Keep the first circular plate tilted at $\theta$, above the infinite conducting plane; replace the infinite conducting plane with another circular plate <em>below</em> it and tilted at angle $-\theta$. The charge distribution on the new plate... | https://physics.stackexchange.com |
382,338 | [
"https://math.stackexchange.com/questions/382338",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/76098/"
] | As an application of the Fourier transform, show that
there does not exist a function $I\in L^1(R^d,m)$ such that
$f*I = f$ for all $f\in L^1(R^d,m)$.
| This is usally answered in the context of Grothendieck's Galois Theory (where $G$ is a profinite group, for example the etale fundamental group of a scheme, and we only consider finite continuous $G$-sets). See Lenstra's notes on Galois theory for this. I only mention this as a background, the rest of this answer expla... | If $G$ acts transitively on $S$ and $s\in S$, we get a bijection $G/G_s\to S$, $gG_s\mapsto gs$, so the examples from your first bullit point are precisely the cases with transitive action.
| https://math.stackexchange.com |
366,161 | [
"https://softwareengineering.stackexchange.com/questions/366161",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/227030/"
] | In one of my projects, I had to name some variables and functions that belong to the person using my app. I named them <code>userCard</code>, <code>getUserInventory()</code> and so on. I named them like that cause there were variables and functions that belonged to other persons, like <code>opponentCard</code>, <code>g... | I ended up using <strong>own</strong> as prefix.
So variables and functions belonging to the user are named like <code>ownCard</code>, <code>ownUser</code>, <code>getOwnInventory()</code>. Variables and functions belonging to others are unchanged (<code>opponentUser</code>, <code>opponentCard</code>, <code>getAllyInv... | It seems your app is a competitive multi-player game and you want to discriminate between "just any user" on the one hand and "the user on this end of the app" on the other hand.
All users are players or contestants or participants. I would avoid the generic term user altogether, it has more of a professional feel to ... | https://softwareengineering.stackexchange.com |
200,797 | [
"https://physics.stackexchange.com/questions/200797",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62755/"
] | Many times I see plots for expected/measured "event rates", but what's the motivation for this? Why not generate/use plots for expected/measured event numbers/counts instead?
| Actual number of events measured will depend on how long an experiment is run, the efficiency of a detector, the size or thickness of a target, the intensity of an incoming beam among other things. Each of these is unique to a given experiment.
Science is done with the expectation of reproducibility, so these factors ... | Because rate is often the right observable to report.
The <em>number</em> of event depends on how long you observe, but to within statistics (corrected) rates can be compared between similar experiments without correction.
| https://physics.stackexchange.com |
230,083 | [
"https://mathoverflow.net/questions/230083",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31310/"
] | In the case of undirected, connected graphs the name for the maximal cycle-free subgraph of minimal weight is called Minimum Spanning Tree, and the efficient algorithms for their calculation are well known.
Questions:
<blockquote>
<ul>
<li>is there a name for maximally directed-cycle-free subgraphs of minimal a... | Here is the story behind these notes, and a redirect to <A HREF="https://spencerthughes.files.wordpress.com/2012/06/allard-on-the-first-variation-of-a-varifold.pdf" rel="noreferrer">On the First Variation of a Varifold</A>, W.K. Allard (1972).
<IMG SRC="https://ilorentz.org/beenakker/MO/Almgren.png"/>
a quote from: <... | I just bumped into your post after doing some google search to find a bibtex entry for Almgren's notes.
I have a copy of them: I could copy it and send it to you (or maybe scan it and share it via dropbox). However before getting to the combinatorial arguments you would have to go through quite a lot of material. I a... | https://mathoverflow.net |
45,787 | [
"https://dba.stackexchange.com/questions/45787",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/16613/"
] | <strong>Scenario:</strong> Lets say I have several tables for a software ticketing system: Developer, Supervisor, TicketType, TicketStatus and a Ticket table to join them on. Assume I have done my inner joins and now have a complete table listing all assigned Ticket info.
<pre><code>Id|TicketName|TicketStatus|Develop... | Dynamic SQL is another option. I would try both this method and @a1ex07's method and see which runs faster for you.
<pre><code>CREATE PROCEDURE WorkAssignmentReport @Category varchar(25)
,@---Name varchar(25)
,@Stats varchar(25)
... | I'd do something like
<pre><code>WHERE (@Category IS NULL OR [TicketType].Name LIKE @Category)
AND (@ReportName IS NULL OR [Ticket].Name LIKE @ReportName )
AND ....
</code></pre>
Thus, if a particular parameter is null, <code>@Param IS NULL</code> will be true, and filter on this field won't be used...
I hope I un... | https://dba.stackexchange.com |
15,521 | [
"https://physics.stackexchange.com/questions/15521",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5265/"
] | I was letting my mind freewheel, and it occurred to me that hair, containing keratin, is a polymer. It is also capable of acquiring and maintaining a charge as happens, on occasion, when brushed.
So ...
<ol>
<li>Can hair be used as a dielectric in a capacitor?</li>
<li>Do any capacitors/manufacturers use hair as an ... | Anything that is an insulator works as a dielectric--- you might as well substitute "insulator" for "dielectric", as they are essentially synonyms. The object doesn't need to get charged easily by static friction--- that's an incidental surface property. The dielectric properties are determined by the polarizability of... | Exactly you can use any insulator as dielectric.<br>
you can use the your finger or nails or any body part as an dielectric.<br>
because those are insulators and my classmate did the same in their lab xam when there is an shortage of capacitors in lab.
| https://physics.stackexchange.com |
459,575 | [
"https://physics.stackexchange.com/questions/459575",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222206/"
] | Apparently bound states in quantum mechanics require energy states to be discrete. That means energy in such systems is quantized, right? However, say that we have a superposition of energy eigenstates. Using the superposition principle, I say that their average is a possible state, since we also say that there's the s... | This can be understood from a purely classical perspective, and it's a notion which appears in the discussion of almost any discrete variable. <strong>The expectation value is not <em>necessarily</em> an allowed state</strong>. For instance, even with a fair die, the expectation value is 3.5 (since it's the average of ... | No. It is a good thought but no. In short, you are correct that we can prepare states whose <em>average</em> energy takes on any value between the lowest and highest energy state. But this is different than creating a state which is "between" the energy eigenstates.
Let <span class="math-container">$|n\rangle$</span> ... | https://physics.stackexchange.com |
403,927 | [
"https://mathoverflow.net/questions/403927",
"https://mathoverflow.net",
"https://mathoverflow.net/users/113402/"
] | There are a variety of characterizations of spin structures on the tangent bundle of a manifold. Two facts about them:
<ol>
<li>Spin structures on <span class="math-container">$TM$</span> are an affine space over <span class="math-container">$H^1(M; \mathbb{Z}/2\mathbb{Z})$</span>, but in general there's no canonical w... | Is the theorem true? There is an non-natural bijection. There is no natural bijection.
A link exterior is homotopy-equivalent to a <span class="math-container">$2$</span>-complex, so a trivialization of the tangent bundle over the <span class="math-container">$2$</span>-skeleton is simply a map:
<span class="math-con... | The unique spin structure on <span class="math-container">$S^3$</span> restricts to a spin structure on <span class="math-container">$S^3 \setminus L$</span>, and so provides a basepoint to the affine space of all spin structures on the latter.
| https://mathoverflow.net |
344,184 | [
"https://softwareengineering.stackexchange.com/questions/344184",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/265586/"
] | I am coming more from the web development angle. We build a module, test it and then deploy it. Some people call this last step (deploy) as 'release'. What's the difference? or are they the same things?
| I don't think the terms release" and "deployment mean exactly the same, thing I'm not sure they should be used interchangeably like that.
From a web development perspective:
Deployment refers to getting your program to a running state on a server. It doesn't need to be the <em>production</em> server. You can <em>depl... | Creating a release consists of compiling a program (Usually an application or a library) and incrementing the version number of what you just compiled in your source control system. There might be additional steps to your release process like sending out emails to those that might be interested.
After you created a ... | https://softwareengineering.stackexchange.com |
26,025 | [
"https://mathoverflow.net/questions/26025",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6334/"
] | Hi people!
This my first question, here. I don't sure if it has a trivial answer, or not.
Let G a group, N normal subgroup in G. In which cases there is a subgroup in G isomorphic to G/N?
TIA
| Assuming you're looking at the case where the isomorphism is induced by the quotient $G \to G/N$ (as per George McNinch's comment), then this should be if and only if the sequence
$$ 0 \to N \to G \to G/N \to 0$$
splits. i.e. there is a section $\sigma : G/N \to G$. This is then seen to be equivalent to $G$ being isomo... | You have to be careful! Of course in split extensions it is trivial that $G/N$ is isomorphic to a subgroup of $G$.
On the other hand there are examples of extensions
$$1\rightarrow N\rightarrow G\rightarrow G/N\rightarrow 1$$
that are not split but nevertheless there is a subgroup $H\le G$ with $H\cong G/N$.
An exampl... | https://mathoverflow.net |
207,649 | [
"https://mathoverflow.net/questions/207649",
"https://mathoverflow.net",
"https://mathoverflow.net/users/74175/"
] | Consider three independent, normally distributed RVs: $YA \sim N(a,\sigma ^{2}),$ $%
YB\sim N(b,\sigma ^{2})$ and $YC\sim N(c,\sigma ^{2})$.
What is the probability that $YA$ is the maximum?: $$\Pr (YA>YB \;\;\mbox{and} \;\;YA>YC)=IA=\int_{-\infty }^{\infty }\Phi (\frac{Y-b}{%
\sigma })\Phi (\frac{Y-c}{\sigma }... | Let $H\mathbb{Z}$ denote the spectrum for cohomology with coefficients in $\mathbb{Z}$, so your spectrum is $H\mathbb{Z}\wedge M_k(G)$. Let $$0\to\bigoplus_I\mathbb{Z}\stackrel{f}{\to}\bigoplus_J\mathbb{Z}\to G\to 0$$ be a presentation of $G$. Then we can explicitly construct a Moore space $M_k(G)$ as the cofiber of ... | In case you are curious, here is a more concise but higher level argument.
The homotopy groups of the spectrum $H\mathbb Z \wedge M_k(G)$ agree with the homology groups of $M_k(G)$, which is just a $G$ in degree $k$. So the spectrum $H\mathbb Z \wedge M_k(G)$ is equivalent a shift of $HG$.
These are all standard fact... | https://mathoverflow.net |
654,496 | [
"https://electronics.stackexchange.com/questions/654496",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/151621/"
] | I want to design a PCB with few "low dropout linear voltage regulators", which would be used to power some sensors we are building. None of the parts on the PCB is expected to do any high speed switching. The sensor is on a separate board, and the power from the PCB is routed through SMA cables to the sensor.... | In commercial smartmeter, the microcontroller and ADC are not isolated from mains, so voltage sensing is done with a simple voltage divider.
In your case I would absolutely not recommend this option because it requires the whole circuit to be at mains potential, which is quite dangerous if you work on it. It also makes... | One solution is not to care which line is phase and which is neutral. Pick one of the two incoming wires, and call it ground for the purposes of your design.
Don't make any connection between your circuit and the protective Earth wire. Don't allow anyone to touch any part of the circuit while it is plugged in.
If the... | https://electronics.stackexchange.com |
392,905 | [
"https://softwareengineering.stackexchange.com/questions/392905",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/96641/"
] | Take the following instance for example:
<strong>CreditCardApplication</strong> class
<pre><code> public class CreditCardApplication
{
public int Id { get; set; }
public string FirstName { get; set; }
public string LastName { get; set; }
public int Age { get; set; }
public d... | Constructors should not do work. The initialization of a new object should happen very quickly, and making database calls, or interacting with any resource outside of the current process, can take considerably longer.
Instead, your constructor should either require the data from the database as separate arguments, so ... | When you instantiate the object CreditCardApplicationEvaluator, it needs to be ready to evaluate applications. We must think of the failure case where you can't pull this data from the database. So if you put the db call for those constants in the constructor, it might never return, so you will never instantiate your o... | https://softwareengineering.stackexchange.com |
286 | [
"https://physics.stackexchange.com/questions/286",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/119/"
] | Does anyone have an intuitive explanation of why this is the case?
| This is a note on why angular velocities are vectors, to complement Matt and David's excellent explanations of why rotations are not.
When we say something has a certain angular velocity $\vec{\omega_1}$, we mean that each part of the thing has a position-dependent velocity
$\vec{v_1}(\vec{r}) = \vec{\omega_1} \times... | Defining properties of vectors are that you can add them and multiply them by constants. These both make sense for angular velocities. On the other hand, adding rotations doesn't make sense. What you can do with two rotations is compose them: first rotate one way, then rotate another. This operation doesn't look like a... | https://physics.stackexchange.com |
51,688 | [
"https://chemistry.stackexchange.com/questions/51688",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/30399/"
] | I'm looking to purchase a sofa, but have been bombarded with all kinds of internet info about the toxicity of certain materials used to make sofas. For example, polyurathane foam is labeled as toxic--is this true? Is something like a blend of cotton/polyester and polyurethane toxic?
| The popular procedure to experimentally isolate caffeine is sublimation.
Slowly heat a teaspoon of coffee or tea from 150°C to 250°C. Let the sublimated caffeine precipitate at a watch glass cooled with ice. The resublimated caffeine forms white needles that can be identified under a microscope.
The sublimation tempe... | I did this in a practical lesson in chemistry. We filtered the coffee (1.2um filter paper), concentrated it 10x using distillation and then extracted the caffeine into an equal volume of chloroform in a separatory funnel. After evaporating the solvent, we were left with fairly white powder.
It was probably impure, cont... | https://chemistry.stackexchange.com |
4,355,736 | [
"https://math.stackexchange.com/questions/4355736",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11210/"
] | I would like to know how to calculate fractions in the field <span class="math-container">$\mathbb Q(\sqrt 2,\sqrt 3)$</span>, for example:
<span class="math-container">$$\frac{A+B \sqrt 2+C \sqrt 3 + D \sqrt 6}{E+F \sqrt2+G \sqrt3 + H \sqrt6}$$</span>
Couldn't this be done with techniques from linear algebra?
Clearly ... | You can use base <span class="math-container">$\frac 12\sqrt 6+\frac 12\sqrt 2$</span>, and a vertical row of <span class="math-container">$\sqrt 2$</span>. That's what I normally use here.
If you want to do divisions, you do this by taking the three conjugates, and multiplying them together, and then multiply that by... | In general if you extend field <span class="math-container">$F$</span> as <span class="math-container">$F[\sqrt p]$</span>, then you can construct inverse by doing the following:
<span class="math-container">$$
\frac1{a+b\sqrt p} = \frac{a-b\sqrt{p}}{a^2-b^2p} = (a^2-b^2p)^{-1}(a-b\sqrt p).
$$</span>
You can consider <... | https://math.stackexchange.com |
217,922 | [
"https://mathoverflow.net/questions/217922",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | I'm playing with exponential sums...
If $q$ is an odd prime and $a$ an integer such that $q \nmid a$, then the following formula for the Gaussian sum is known
$$\sum_{x=0}^{q-1} e_q(ax^2) = \left(\frac{a}{p}\right) i^{\left(\frac{q-1}{2}\right)^2} \sqrt{q} ,$$
where $e_q(z) := \exp\left(\frac{2\pi i z}{q}\right)$ and ... | Yes, this is standard. More generally, we have the following
<strong>Theorem.</strong> Let $p$ be an odd prime, and let $a_1,\dots,a_k\in\mathbb{F}_p^\times$. Then the number of solutions of the equation $a_1x_1^2+\cdots +a_kx_k^2=1$ in $\mathbb{F}_p$ equals
\begin{align*}
p^{k-1}-\left(\frac{a_1\dots a_k}{p}\right)p^... | I just want to share a character-free proof - very accessible and too long for a comment (also - probably not original). Of course, it's just a restatement of a character-full proof.
Let $\vec{v} \in \mathbb{R}^{\mathbb{F}_q}$ be the vector whose $i$'th coordinate is the number of solutions to $x^2 \equiv i \mod q$. T... | https://mathoverflow.net |
150,523 | [
"https://cs.stackexchange.com/questions/150523",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/146262/"
] | I get that it depends from the number of probes, so by how many times the hash code has to be recalculeted, and that in the best case there will only be one computation of the hash code and the complexity will be O(1) and that in the worst case the hash code will be calculated a number of times equal to the size of the... | Define the <em>load factor</em> of a hash table with open addressing to be <span class="math-container">$n/m$</span>, where <span class="math-container">$n$</span> is the number of elements in the hash table and <span class="math-container">$m$</span> is the number of slots. It can be shown that the expected time for ... | Implementations will typically store the hash value inside the table - this will save lots of hash value calculations.
For the hash value of the key being looked up, it depends on the caller how often that value is calculated. Hash values can be cached. I might have an object with a name, address, and age. And name obj... | https://cs.stackexchange.com |
39,577 | [
"https://cstheory.stackexchange.com/questions/39577",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/5191/"
] | Base conversion is the problem of converting an integer between representations in two fixed bases. Without loss of generality consider the case of relatively prime bases. I think it's easier to imagine a single type of machine that can handle all cases even though the bases are fixed, so consider a base-$b$ number as ... | Base conversion can be done in time $O(M(n)\log n)$, where $M(n)$ is a bound on the time complexity of multiplication of two $n$-bit integers. (We assume that $M(n)$ satisfies usual regularity conditions: it is monotone, and $2M(n)\le M(2n)$.)
The standard divide-and-conquer algorithms are described e.g. in Brent&... | I think I just figured it out, and maybe this means it is too obvious to be an appropriate question for this site, but I'll post my solution here anyway (maybe it is wrong).
Given a number $n$ in the source base, write it as $n = a^2+b$, with $a$ and $b$ also represented in the source base. We don't even require $b &l... | https://cstheory.stackexchange.com |
17,915 | [
"https://cstheory.stackexchange.com/questions/17915",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/10526/"
] | I would like to ask you a question about (denotational?) semantic of program. After defining program as a transition system, and the semantics as a transition function: $$next: States \rightarrow States$$
the author stated that the meaning of program is the solution of the equation:
$$ P = next \circ P $$
which is give... | "Meaning", or "semantics" to use the more technical term, is only the understanding you wish to associate with the
text of the program. It can be a mathematical function that specifies
abstractedly what the program computes (denotational semantics), or it
can be a formal description of how the computation is conducted... | In this case, I guest that "meaning" is "semantics". You can consider the set $\mathcal{P}$ of all partial functions $States \to States$ and the function $Next \colon \mathcal{P} \to \mathcal{P}$ defined by: $$Next(P) = next \circ P$$ for all $P \in \mathcal{P}$. On $\mathcal{P}$ with the ordering by function extension... | https://cstheory.stackexchange.com |
870,174 | [
"https://math.stackexchange.com/questions/870174",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/164958/"
] | If I have $6$ children and $4$ bedrooms, how many ways can I arrange the children if I want a maximum of $2$ kids per room?
The problem is that there are two empty slots, and these empty slots are not unique.
So, I assumed there are $8$ objects, $6$ kids and $2$ empties.
$$C_2^8 \cdot C_2^6 \cdot C_2^4 \cdot C_2^2 =... | Looks right, given some assumptions. Let's build it up a different way to check your work.
We're basically interested in two patterns of putting kids into rooms. Those are all kids paired with one empty, 2-2-2-0, and two pairs and two solo sleepers, 2-2-1-1. Any other arrangement either breaks the 2 kids max rule or ... | Only possible distributions are (2,2,2,0) and (2,2,1,1).
So, total ways=$^4C_1*^6C_2*^4C_2+^4C_2*^6C_2*^4C_2*2=1440$
$\\$
If you do not want to leave any room empty as an added requirement, the only pattern possible is (2,2,1,1), so the answer is 1080. hence, OP is right!
| https://math.stackexchange.com |
720,088 | [
"https://physics.stackexchange.com/questions/720088",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/245835/"
] | I have a question that result equation is how it has derived.
When we have a following equation,
<span class="math-container">$$\frac{\mathrm dr}{\mathrm dt}=\frac{\delta r}{\delta t}+\omega \times r.$$</span>
<span class="math-container">$\omega$</span> is angular velocity, <span class="math-container">$r$</span> is p... | It depends on the detailed set-up of the thought experiment. However, if you assume the travelling twin's periods of acceleration are negligibly short, then there are three inertial frames to consider, namely the frame of the Earth, the frame of the outbound twin and the frame of the returning twin. In that set-up, the... | Different people use the word "frame" in a great variety of ways. The answer to this (and to your other questions about frames) depends on what <strong>you</strong> mean by the word "frame". Since you haven't told us that, there's no way to answer your question.
At every event in spacetime, there ... | https://physics.stackexchange.com |
42,204 | [
"https://dsp.stackexchange.com/questions/42204",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/29571/"
] | I recently introduced myself into the field of CS, but I do not understand why some people try to find deterministic measurement matrices?
If I am correct, gaussian random matrices are very powerful with their properties. They are easy to create, their reconstruction power is very good (having a low RIP constant) and s... | As far as I know there are two reasons:
<ul>
<li>In sensing part: For practical implementation, usage of random matrices
is hard, so people try to come up with simpler matrices that are fixed,
this is thought to be helpful for designing efficient hardware.</li>
<li>In reconstruction part: To find deterministic matrices... | The sampling matrix needs to be known to both during compression and during reconstruction. This typically means having to keep the entire matrix on both sides. This may be very prohibitive for sensor systems, which often have quite limited memory. A non-random matrix may be stored with a fewer number of parameters, a... | https://dsp.stackexchange.com |
228,127 | [
"https://math.stackexchange.com/questions/228127",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/47807/"
] | Events $A$ and $B$ are independent. We know their probabilities, $P(A)=0.7, P(B)=0.6$. Compute $P(A \cup B)$? Can this be solved somehow?
| Yes.
If $v$'s are orthonormal then
$$\left[\matrix{v_1^\top \\ v_2^\top}\right]\left[\matrix{v_1 & v_2}\right]=\left[\matrix{1 & 0 \\ 0 & 1 }\right]$$
and if the $u$'s are defined for some matrix $(a,b,c,d)$
$$\left[\matrix{a & b \\ c & d}\right]\left[\matrix{v_1 & v_2}\right]=\left[\matrix{u_... | Let all of them be $N \times 1$ vectors. Clearly $U=VX$ for some $2\times 2$ matrix $X$. Given $U^{H}U=I$. Hence $(VX)^{H}VX=I$ implies $X^{H}X=I$. In a similar manner, using $V^{H}V=I$, you can prove Note that $XX^{H}=I$. Hence $X$ is a orthogonal matrix. Multiplication by any orthogonal matrix is a rotation.
| https://math.stackexchange.com |
12,526 | [
"https://electronics.stackexchange.com/questions/12526",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2824/"
] | Hi
I want my circuit to be able to switch on and off several 230V AC circuits. I was wondering if relays are my only option. It starts to get a bit expensive if you need a few. Originally I was going to use a 5V dc relay to switch the devices on and off
| You may find relays with a 12 or 24V coil cheaper. You may consider triacs (thyristors) but it is hard to beat the price (and simplicity) of a relay.
| If you need fast switching (up to 50-60Hz), you can take a look at solid state relays. They don't produce a "click" like mechanical ones, but this feature comes with a price...
| https://electronics.stackexchange.com |
151,736 | [
"https://cs.stackexchange.com/questions/151736",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/150888/"
] | Problem statement- Given a sorted array, print out the pair of elements of the array that have a sum of K, where K is a whole number.
The solution to the above problem goes like this:
<blockquote>
With using the Two Pointers pattern, and Pointer 1 pointing to the beginning of the array and Pointer 2 pointing to the end... | Let me make the following suggestion: <em>get rid of asymptotic notation</em>.
Here is how to do that. Your recurrence relation is really the following:
<span class="math-container">$$
T(n) = \begin{cases}
1 & \text{if } n = 1, \\
T(n-1) + f(n) & \text{otherwise},
\end{cases}
$$</span>
where <span class="math-c... | Formaly, for all <span class="math-container">$n>N$</span>,
<span class="math-container">$$T(n-1)+c_0n\le T(n)\le T(n-1)+c_1n$$</span>
If we expand the right inequality,
<span class="math-container">$$T(n)\le T(n-1)+c_1n\le T(n-2)+c_1n+c_1(n-1)\le\cdots \le T(N)+c_1\sum_{i={N+1}}^ni\\
=T(N)+c_1\frac{n^2+n-N^2-N}2.$$... | https://cs.stackexchange.com |
21,087 | [
"https://mathoverflow.net/questions/21087",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1176/"
] | Call a subset of $\mathbb{N}$ <em>primitive-recursively enumerable (p-r.e.)</em> if it is empty or an image of a primitive recursive function. I feel like a lot must be known about the poset of such sets ordered by inclusion, but I am unable to dig up references. Concretely, I would like to know whether there exists a ... | Yes, take 2-extraspecial group $2^{2n+1}$, plus or minus should not matter. It has $2^{2n}$ irreducible representations of degree 1 and one of degree $2^n$. So your $K_G$ is about 2 while $d(G)=2^n$.
| Let b(G) be the maximum degree of an irreducible character of the finite group G.
This answer is mostly to address the solvable, but not nilpotent case. I already up-voted the other two excellent answers: Jim Humphreys mentioned how the groups of Lie type behave (showing that K<sub>G</sub>≈q<sup>2N</sup> can be enorm... | https://mathoverflow.net |
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