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 |
|---|---|---|---|---|---|
3,512,756 | [
"https://math.stackexchange.com/questions/3512756",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | They ask me to decide if it is true or false the next sentence:
<ul>
<li>If <span class="math-container">$A$</span> and <span class="math-container">$D$</span> are simply connected subspaces with <span class="math-container">$A \cap D \neq ø$</span> then <span class="math-container">$A \cup D$</span> is also simply co... | Two halves of a circle are simply connected but not the circle. Another way to say that: a circle can be viewed as the union of two simply connected intervals which intersect in two points. For example take the circle <span class="math-container">$C$</span> centered at <span class="math-container">$0$</span> of radius ... | To help you visualize T.Aristide answer, think of a simply connected space as something with no hole, that is something you cannot hang on a needle.
If you take a sheet of paper and punch a hole in it, then it is no more simply connected.
But now if you cut this paper along a line that passes through the hole, both s... | https://math.stackexchange.com |
66,613 | [
"https://dba.stackexchange.com/questions/66613",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39554/"
] | If I use the SQL SERVER HASHBYTES() function in a script on my machine, is it guaranteed to produce the same output if run on another machine/instance?
For example, will
<code>SELECT HASHBYTES('SHA1', 'Hello World') </code>
generate the same output regardless of SQL version, processor architecture etc?
and will
... | In terms of different instances, the <code>HASHBYTES</code> should return the same values if the same script is run, regardless of the server version, processor or architecture:
I've just run the following on both SQL Server 2005 and SQL Server 2012, on completely different hardware configuration. Both have produced t... | Have similar problem with HASHBYTES. Same values from one "varchar(max)" column generate multiple hash values.
The problem is caused by capitalization and Case Insensitive collation. Because of that my values were actually different.
If you do not care about case sensitivity you can change your values to uppe... | https://dba.stackexchange.com |
45,151 | [
"https://cs.stackexchange.com/questions/45151",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/37314/"
] | input : $array[1...n]$<br>
output: permutated array<br>
Our algorithm should be probablistic and complexity should be $O(n)$.
Could you give me hint ? My weakness is probability theory and it is why I have a problem.
| First we need to define the algorithm a bit more stringently. I prefer this one.
Choose a $N$-permutation $P$ with probability $U(P)$ where $U$ is a uniform distribution of the space of $N!$ permutations on $N$ values.
I like to solve this in an inductive fashion.
First we think about how we can do this with 1 value... | I'm not exactly certain what you mean by probabilistic procedure as pertains to array permutation, and I'm going to assume you're looking for a random permutation of the array. I'm basing this off the formulation of the problem being very similar to an algorithm for that purpose.
So lets say as a person I'd like to do... | https://cs.stackexchange.com |
116,749 | [
"https://electronics.stackexchange.com/questions/116749",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/46314/"
] | I'm trying to understand something very basic about Control Theory. Let's say I have the following loop:
<img src="https://i.stack.imgur.com/oJqQo.gif" alt="Block Diagram">
If we'll relate this loop to a cart with a motor going in its single axis from X = 0 to X = 50, the controlled variable will be the engine speed ... | The control output (what you are calling the system input) and the system output are not necessarily proportional. In your example, the system is in part a integrator. This sort of thing is common. The extra pole in the system does have to be taken into account in the controller, else it can easily lead to instabili... | You need to have a goal to measure with respect to. If the goal is to simply get the cart to a certain location then you will be monitoring the location as you move along the path (like an encoder counts light ticks) and subtracting that from the total distance you intended to travel until you reach zero.
In your exa... | https://electronics.stackexchange.com |
410,009 | [
"https://physics.stackexchange.com/questions/410009",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/197531/"
] | Simply,
$dU=nC_vdT$
$dQ=nC_pdT$
Does this mean that $C_p=C_v$ for an isochoric process?
| Notation: $\delta X$ represents a small change in $X$ that is not an exact differential. $dX$ represents and exact differential. $dX_Y$ etc represent a change in $X$ during a process for which $Y$ is fixed. E.g. $\delta Q_p$ means the small change in heat during an isobaric process, for which we know $\delta Q$ is not ... | No.
Specific heats do not depend on the process and are constants(for a given material at a specific Temperature).
$C_v$ is specific heat for constant volume and $C_p$ is for constant pressure. You apply them according to these conditions. In Isochoric process only $C_v$ is relevant since it is constant volume proces... | https://physics.stackexchange.com |
285,273 | [
"https://softwareengineering.stackexchange.com/questions/285273",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/169750/"
] | I always wonder if there is any benefit of publishing programming/code related articles/tips either on ones own website or coding sites? I think it has a benefit that a programmer can have a record of his/her learning and refer them later, other than that?
As far as I can imagine, forum participation like stackoverflo... | <blockquote>
I've been wrestling with a problem in a Java project about circular references.
</blockquote>
Java's garbage collector doesn't rely on reference counting techniques. Circular references do not cause any kind of problem in Java. Time spent eliminating perfectly natural circular references in Java is time... | Granted, circular dependencies are a questionable practice from a design point of view, but they are not prohibited, and from a purely technical point of view they are not even <em>necessarily problematic</em>, as you seem to regard them to be: they are perfectly legal in most scenarios, they are inevitable in some sit... | https://softwareengineering.stackexchange.com |
13,581 | [
"https://dba.stackexchange.com/questions/13581",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5821/"
] | This is my current mySQL query:
<pre><code>SELECT e.*, MAX(m.datetime) AS unread_last, COUNT(m.id) AS unread
FROM TAB_EVENT e
LEFT JOIN TAB_MESSAGE m ON e.id=m.event_id
WHERE ( m.`read` IS NULL OR m.`read` = 0)
GROUP BY e.id
ORDER BY m.datetime DESC, e.id ASC
LIMIT 10;
</code></pre>
I get: All TAB_EVENT r... | Here is your original query from the question
<pre><code>SELECT e.*, MAX(m.datetime) AS unread_last, COUNT(m.id) AS unread
FROM TAB_EVENT e
LEFT JOIN TAB_MESSAGE m ON e.id=m.event_id
WHERE ( m.`read` IS NULL OR m.`read` = 0)
GROUP BY e.id
ORDER BY m.datetime DESC, e.id ASC
LIMIT 10;
</code></pre>
Maybe try refac... | Try joining to a subquery:
<pre><code>SELECT e.*, m.datetime AS unread_last, m.id AS unread
FROM TAB_EVENT e
LEFT JOIN (
SELECT event_id, MAX(datetime) AS `datetime`, COUNT(id) AS id
FROM TAB_MESSAGE
WHERE read IS NULL OR read = 0
GROUP BY event_id
) m ON e.id=m.event_id
ORDER BY m.datetime DES... | https://dba.stackexchange.com |
3,062,204 | [
"https://math.stackexchange.com/questions/3062204",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | So I was told that if <span class="math-container">$p,q \in \mathbb{L}^2 _\mathbb{C} [a,b]$</span> which is the set of all square integrable functions on the interval <span class="math-container">$[a,b]$</span> then:
<span class="math-container">$$(p,q) = \int^b_a{dx\ p^*(x)q(x)}$$</span>
is a scalar product.
However,... | Your part (a) is fine, assuming that you know translation is continuous.
Your part (b) is on the right track, but it assumes that <span class="math-container">$V$</span> is the continuum, whereas it should be a normed vector space. You have the right idea of separating two sets by a very small set, but you shouldn't r... | For the converse: suppose <span class="math-container">$X$</span> is not bounded. Then it contains some sequence <span class="math-container">$(x_n)$</span> such that <span class="math-container">$(\|x_n\|)\to\infty$</span> (take <span class="math-container">$x_n$</span> to be an example given by the negation of the de... | https://math.stackexchange.com |
639,545 | [
"https://electronics.stackexchange.com/questions/639545",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/321142/"
] | I am trying to figure out my screen's wattage. However, there is no wattage on the label. There are only rating values like 100-240V~, 50/60Hz, and 1.6A. How can I calculate my computer screen's wattage?
In the screen's user manual, it is written as 25W but how can this happen? I don't know the power factor and also I ... | Specs say it is 24W while on. It is 0.10A at 230V.
When sleep it takes something around 1 up to 3W.
You mismatched something anyway. 1.6A is the power supply current at 14V. 14*1.6=22.5W. Round it up and you're about 25W.
You don't need exact wattage - this is enough.
The only way to measure it correctly is to put watt... | The basic calculation is that Power = Volts * Amps. (P=VI).
So 2 Amps at 240 Volts is 480 Watts. In your case, if you are on 230V and the load (power) is 25W, the current is 25/230 = .109 Amps or 109 milliamps. At 120V it would be about double the current for the same power.
The label rating will be the expected maximu... | https://electronics.stackexchange.com |
184,383 | [
"https://softwareengineering.stackexchange.com/questions/184383",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51017/"
] | Why do I, as a developer, have to go through so much trouble developing PDF download options for my clients when everyone in the world can simply hit Ctrl+P and life is good?
The current issue I'm working on is dealing with Google Charts, so I'm not stating that offering PDF downloads in general is relatively difficul... | You dont 'have to' do anything. But if you want to ensure the PDF looks exactly the same for each person who downloads it, you need to render it yourself. Otherwise you're depending on various web browsers & print engines to render the PDF, and the results may not be that great.
And of course, you also cant as... | Web pages are not designed for print, they are designed to be rendered on a screen. As such, there's no guarantee that it will even fit within the dimensions of a standard paper size. Printing web pages to paper when they are not designed to fit on paper usually results in a mess. Giving your web application the abilit... | https://softwareengineering.stackexchange.com |
51,860 | [
"https://mathoverflow.net/questions/51860",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3634/"
] | If $\mathcal{C}$ is a category, then surely the category of simplicial
objects $s\mathcal{C}$ is not automatically a model category. What conditions
must $\mathcal{C}$ satisfy in order for $s\mathcal{C}$ to have a reasonable model structure?
| It always has a model structure using Kan's theory of Reedy categories. For a proof, see Hirschhorn <em>Model Categories and their Localizations</em> 15.3.
This is because $\Delta$ and $\Delta^{op}$ are both Reedy categories.
I will address the more general question as well:
If $C$ is any small category, the condit... | Quillen gives a couple of sets of sufficient conditions for $s\mathcal{C}$ to be a model category, in his <em>Homotopical Algebra</em> book. Notably, this includes the case when $\mathcal{C}$ is a complete and cocomplete category with a small set of projective generators. This gives model structures for categories of... | https://mathoverflow.net |
129,048 | [
"https://physics.stackexchange.com/questions/129048",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24362/"
] | According to my understanding of SR, if I travel at 0.8c relative to a line of clocks, I should see the clocks in front of me going 3 times faster than my own, and those behind me going 3 times slower than my own (Doppler effect).
OK, so what happens at my exact location? I reckon that as I look nearer and nearer to m... | I assume you used the formulae $f_o = fs\sqrt{\frac{1+v/c}{1-v/c}}$ for the clocks ahead of you and $f_o = fs\sqrt{\frac{1-v/c}{1+v/c}}$ for the clocks behind you. Those formulae do imply a singularity for the clock that is closest to you. Which equation to use?
The answer is neither. Those expressions assume the trav... | The signal from the clock moving towards you is the Doppler shifted version of the value you "know" it to be - that is, first slow it down by gamma (clock moving relative to your frame of reference), then speed it up by Doppler shift.
Ditto, with sign reversed, for clocks behind you. Now the clock moving at right angl... | https://physics.stackexchange.com |
352,011 | [
"https://softwareengineering.stackexchange.com/questions/352011",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/82383/"
] | I've got one requirement that is:
<blockquote>
When one employee starts working on a project and when he finishes working on it he must inform the system so that it can generate a report afterwards of how much hours a certain project required.
</blockquote>
The requirement itself is simple, I just want to see if I'... | Reading your question and the other answers, I am under the impression there is some confusion caused by the fact the term "event based system" often is used differently from the way it is used in your question. I am pretty sure the requirement
<blockquote>
he must inform the system so that it can generate a report... | I would say that you are better off having employees log hours against a project rather than start and stop events
Start and stop events can be come problematic when someone forgets to fill them in. Or when someone is working on more than one thing at a time. Or if they have to account for breaks.
eg. say I start wo... | https://softwareengineering.stackexchange.com |
133,441 | [
"https://physics.stackexchange.com/questions/133441",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/58309/"
] | Probably a stupid question here - I think it's a case of me not having sufficient mathematical background to follow this through. In Leonard Susskind's <em>Theoretical Minimum</em> book, he represents the ket-vector A as such:
$$
|A\rangle = \displaystyle\sum_{i} a_{i}|i\rangle
$$
Which I follow, as I do when he takes... | Note that:
\begin{equation}
\begin{aligned}
\langle j | A \rangle & = \langle j |\left( \sum\limits_{i} a_i |i \rangle \right) \\&
= \langle j| \left(a_1 |1 \rangle + a_2 |2 \rangle + a_3 |3 \rangle + \cdots + a_j |j \rangle + \cdots \right) \\&
= a_1 \underbrace{\langle j | 1 \rangle}_{=\delta_{j1} = 0}... | If you think in terms of vectors and matrices with indices, $a_i$ is a vector and $\delta_{ij}$ is the unit matrix. The summation on the right hand side of your equation represents nothing but a multiplication of the vector $a_i$ with the latter. Since free indices are preserved, the remaining object carries the index ... | https://physics.stackexchange.com |
366,577 | [
"https://softwareengineering.stackexchange.com/questions/366577",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/297157/"
] | I am not from a IT background. An idea is generated is being worked upon now. Initially we started with Waterfall methodology and now using agile. Want to understand how exactly this agile methodology works. Please don't consider my questions in a wrong way. Request for your inputs.
<ol>
<li>There is a bug found in be... | Let me start by saying, you have not specified a methodology. Agile is more of a type of way of doing things, a philosophy if you will. As such, there is no "Should do this or that".
You want to work in sprints. This means you are timeboxing your efforts and you do what you can within that timebox. Within a sprint, yo... | The thing you have to remember is that the purpose of sprints is to help you set and hit deadlines.
Essentially you are trying to work out how quickly you can program 'features'. Then you can take your list of features, multiply it by this 'velocity' and say "we should be done by this date, therefore the cost of the s... | https://softwareengineering.stackexchange.com |
698,029 | [
"https://physics.stackexchange.com/questions/698029",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208833/"
] | Consider a state vector given by
<span class="math-container">$$|\psi\rangle=a|w_1\rangle + b|w_2\rangle+c|w_3\rangle$$</span>
where <span class="math-container">$|w_1\rangle,|w_2\rangle$</span> and <span class="math-container">$ |w_3\rangle$</span> are orthonormal eigenstates of an observable operator <span class="mat... | Every self-adjoint operator <span class="math-container">$\Omega$</span> (on a finite-dimensional Hilbert space, for simplicity) can be uniquely decomposed as
<span class="math-container">$$\Omega = \sum_i \omega_i \Pi_i$$</span>
where the eigenvalues <span class="math-container">$\omega_i \in \mathbb R$</span> are all... | The postulates of quantum mechanics says that a measurement will return an eigenvalue and that there is some eigenvector with the according coefficient to match the probability of measuring that eigenvalue.
I am going to use a different normalization, let
<span class="math-container">$$
|\psi'\rangle = \frac{a|w_1 \ran... | https://physics.stackexchange.com |
204,741 | [
"https://stats.stackexchange.com/questions/204741",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/76621/"
] | I'm analyzing a data set using a mixed effects model with one fixed effect (condition) and two random effects (participant due to the within subject design and pair). The model was generated with the <code>lme4</code> package: <code>exp.model<-lmer(outcome~condition+(1|participant)+(1|pair),data=exp)</code>.
Next,... | Not a complete answer...
The difference between <code>glht(myfit, mcp(myfactor="Tukey"))</code> and the two other methods is that this way uses a "z" statistic (normal distribution), whereas the other ones use a "t" statistic (Student distribution). The "z" statistic it the same as a "t" statistic with an infinite deg... | (This answer highlights some information already present in one comment by @RussLenth above)
In situations where the difference due to "z" vs. "t" statistic is negligible (i.e. in the limit of an infinite number of observations), calling <code>lsmeans</code> and <code>multcomp</code> with the defaul... | https://stats.stackexchange.com |
206,956 | [
"https://electronics.stackexchange.com/questions/206956",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70314/"
] | PWM operation of DC relay coils in order to save power while holding is now common. This is at a frequency that is high enough to avoid chattering or audible noise and low enough to not have to worry about switching losses or exotic circuitry.
The in circuit coil inductance can be measured by looking at coil current... | This suggests to me that the relay coil may be saturating its core.
Consider this : if you are measuring the inductance in-circuit, while operating the relay, there are two important states : open and closed.
In the open state, the inductor is gapped and therefore its reluctance is relatively low. You can apply all t... | I was unable to reproduce this behavior.
I found a relay with a removable cover (stolen from my heating system!) and connected an LCR meter to the coil.
I tested the inductance of the coil with the relay open and found it to be 360 uH.
Then I manually closed the relay arm by pushing it with my finger and found the ... | https://electronics.stackexchange.com |
101,722 | [
"https://mathoverflow.net/questions/101722",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9164/"
] | Consider $Hilb_{d,g}$ the Hilbert scheme of curves in $\mathbb{P}^3$ of degree $d$ and genus $g$. Is it true that if $L$ is an irreducible component of $Hilb_{d,g}$
then there exists a curve $C \in L$ such that $C$ is irreducible? Is there some criterion under which this is true?
If the former statement is true, can w... | The Hilbert scheme is pretty horribly behaved, and positive results of this nature are quite rare.
You probably mean to ask if there exists $C\in L$ such that $C$ is both reduced and irreducible. If you don't demand reducedness, the answer is yes. For suppose $H$ is a component of a Hilbert scheme of curves in $\mat... | You may want to look at curves in three dimensional projective space. I vaguely remember, although I may be wrong, that there was a component with general member non-reduced.
| https://mathoverflow.net |
29,853 | [
"https://dsp.stackexchange.com/questions/29853",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/20349/"
] | I have short-wave digital receiver that send RP packets with IQ components over network depend of the RF frequency and passband. I need to work with the telephone passband (0.3 - 3.4 kHz). The task is:
Using ordinary notebook receive RTP packets in the real-time, extract IQ-data, build FFT, visualize it and then I nee... | The system
$$y[n]=y[n-1]+x[n]\tag{1}$$
is an ideal accumulator, i.e., it computes the cumulative sum of the input samples:
$$y[n]=\sum_{k=-\infty}^nx[k]\tag{2}$$
It is in a way analogous to a continuous-time integrator, but this doesn't mean that you will necessarily obtain an ideal integrator by transforming the d... | Your simple integrator is called a "Rectangular Rule" integrator. There are more complicated (and more accurate) integrators called "Trapazoidal Rule", "Simpson's Rule", and "Tick's Rule" integrators.
| https://dsp.stackexchange.com |
154,661 | [
"https://softwareengineering.stackexchange.com/questions/154661",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I was attempting to find a best practice for modeling the tiers in a Java EE application yesterday and couldn't come up with anything current. In the past, say java 1.4, it was four tiers:
<ol>
<li>Presentation Tier</li>
<li>Web Tier</li>
<li>Business Logic Tier</li>
<li>DAL (Data Access Layer ) which I always consid... | I believe the answer to your question will vary depending on the type of an application you are developing. Since I am more familiar with Web Based desktop (vs mobile) applications I will try to answer for this type.
The most prevalent architecture of JEE web apps these days is based on MVC (Model View Controller) des... | After doing more research, I found another answer.
In a Spring application, the services tier can combine the business logic with the data access, eliminating the need for DAO's. (Re: Apress Book: Pro Spring 3 page 50). This in effect takes the traditional 4 tiers of a J2EE application that I mentioned above into ... | https://softwareengineering.stackexchange.com |
3,901,604 | [
"https://math.stackexchange.com/questions/3901604",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/788259/"
] | I have to show, that the sequence <span class="math-container">$g(n+1) = \frac{2ag(n)}{a+g(n)^2}$</span>
is increasing for <span class="math-container">$a>0$</span> and <span class="math-container">$g(0)>0$</span>. I know that it holds for <span class="math-container">$g(n)^2<a$</span>
since <span class="math-... | See that <span class="math-container">$2^{16^x} = 16^{2^x}$</span> is <span class="math-container">$2^{2^{4x}} = 2^{2^{x+2}}$</span>
then <span class="math-container">$4x = x + 2$</span> and get <span class="math-container">$x = 2/3$</span>.
| Alternative approach
<span class="math-container">$$16^{2^x} = [2^4]^{2^x} = 2^{4 \times 2^x}.$$</span>
Since this is equal to <span class="math-container">$2^{16^x}$</span> you have
<span class="math-container">$$16^x = 4 \times 2^x \implies 8^x = 4 \implies x = (2/3).$$</span>
| https://math.stackexchange.com |
26,549 | [
"https://security.stackexchange.com/questions/26549",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6004/"
] | Some say that ignored risks as part of an organization's behavior are much worse than accepted risks.
I would like to test that axiom (in the eyes of some).
When I am handling a risk and I choose to accept it, it means that I have done risk analysis and risk control, and have chosen to accept this risk and to live wi... | Despite the gigabytes written on risk management, I don't think there is a consistent, coherent terminology for risk management. So the answer to your question is local; unless you define "ignore" differently from "accept" within your risk management program, there is no difference.
That said, I would suggest that if... | In the context you have described, there is no such thing as an ignored risk. What you have outlined is risk acceptance.
If you weigh up the risk and decide not to do anything, you are accepting that risk, not ignoring it.
| https://security.stackexchange.com |
2,206,873 | [
"https://math.stackexchange.com/questions/2206873",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/397530/"
] | <blockquote>
Prove that for $n\geq3$,$$n^3\geq3n+5$$
</blockquote>
<strong>My try:</strong>
Let $f(x)=x^3-3x-5$. Clearly $x=1$ and $x=-1$ are critical points where $x=1$ is the local minima so the function $f(x)$ is an increasing function for $x>1$ and the result follows.
Please check and if possible provide an... | Using induction:
$1)$ For $n=3$ we get $3^3\ge 3\cdot 3+5=14$
$2)$ Hypothesis: $n^3\ge 3n+5$
$3)$ For $n+1$
$$(n+1)^3=n^3+(3n^2+3n+1)\ge 3n+5+(3n^2+3n+1)\\
(n+1)^3\ge [3(n+1)+5]+(3n^2+3n-2)\quad (1)$$
but
$$3n^2+3n-2=3n(n+1)-2\ge0\text{ for } n\ge 3$$
then from $(1)$ we get
$$(n+1)^3\ge 3(n+1)+5$$
| If $n=k+3$ with $k\ge0$, then
$$n^3=(k+3)^3=k^3+9k^2+27k+27\ge3k+14=3(k+3)+5=3n+5$$
| https://math.stackexchange.com |
279,573 | [
"https://mathoverflow.net/questions/279573",
"https://mathoverflow.net",
"https://mathoverflow.net/users/99732/"
] | I am interested to know an example of a simply connected smooth projective 3-fold $X$ (over $\mathbb{C}$) satisfying the following two constraints:
<ol>
<li>$X$ has the same Betti numbers as $\mathbb{C}\mathbb{P}^{3}$ i.e. $b_{1}(X) = b_{3}(X) = 0$ and $b_{2}(X) = 1$ and all of its cohomology groups are torsion-free.<... | Let me just mention that the non-existence of such a threefold is an immediate consequence of Yau's inequality. First, as explained in the above comment, the conditions $b_2=1$ and $\mathrm{Kod}(X)\geq 0$ imply that $K_X$ is ample. Then Yau gives $c_1^3\geq \frac{8}{3}c_1c_2 $, which is equivalent by Riemann-Roch to $K... | As pointed out by dhy, the question is completely resolved in section 3 of "Uniformization of Fake Projective Four Spaces", by Sai-Kee Yeung. The conclusion is that there is no such $3$-fold.
| https://mathoverflow.net |
103,814 | [
"https://physics.stackexchange.com/questions/103814",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42559/"
] | If I sit on a chair, the first action and reaction pair force is my weight and the force acting on the earth by me. And the 2nd pair is the force acting on the chair by me and the opposite force.
According to newton third law, the action and reaction force must be equalI. 'm confused because how come the force acting ... | Where does the 'pairing' in your first pair come into place? I.e. what is the force counteracting the earth's gravity pull on you (in your theory)?
The relevant force pair in your example is the attractive force between your body and the earth (gravitational pull) and the repulsive force between your body and the chai... | I'm not exactly sure what you are confused about but in my experience of TAing intro physics there is a common confusion when students compare two forces that happen to be equal but are not third law pairs.
You have stated the correct third law pairs, there are two of them, the gravitation force exerted by the earth o... | https://physics.stackexchange.com |
136,900 | [
"https://softwareengineering.stackexchange.com/questions/136900",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/48185/"
] | Is it a good practice to call a method that returns true or false values in an if statement?
Something like this:
<pre class="lang-.NET prettyprint-override"><code>private void VerifyAccount()
{
if (!ValidateCredentials(txtUser.Text, txtPassword.Text))
{
MessageBox.Show("Invalid user name or passwor... | As with all these things it depends.
If you aren't going to use the result of your call to <code>ValidateCredentials</code> then there's no need (other than for debugging purposes) to store the result in a local variable. However, if it makes the code more readable (and hence more maintainable) to have a variable go w... | Why use an additional variable? I prefer use the first approach, it's more readable and simple.
| https://softwareengineering.stackexchange.com |
208,213 | [
"https://dba.stackexchange.com/questions/208213",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/105289/"
] | I need to encrypt some columns in the postgresql for privacy reasons. I would like to use the pgcrypt and encrypt the columns with an asymmetric key pair and the passphrase.
Now you can display currently executed queries. There you will see the private key and the passphrase. Is there a way to protect the executed / a... | Use parameters, then only the <code>$1</code> etc. markers are visible in <code>pg_stat_activity</code>.
| They cannot be hidden from superusers. They are already hidden from non-self, non-super users. To hide them from other sessions of the same user, you can revoke execute on function pg_stat_get_activity from public.
| https://dba.stackexchange.com |
4,180,197 | [
"https://math.stackexchange.com/questions/4180197",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/917843/"
] | Let constant <span class="math-container">$0<k<1$</span>. Prove that the <span class="math-container">$n\times n$</span> matrix <span class="math-container">$A$</span>, where its diagonal entries <span class="math-container">$a_{ii} =1$</span> and <span class="math-container">$a_{ij}=k$</span> for <span class="ma... | In general, finding the smallest such numbers would be not easy. Primes are, at times, tough to deal with. However, it can be made simpler. Rather than taking <span class="math-container">$n!$</span>, you may take the LCM of the first <span class="math-container">$n$</span> numbers.
For example, for <span class="math-c... | If it was allowed to do 2 primality test, then you could define<br />
<span class="math-container">$n = f(x)$</span><br />
where <span class="math-container">$f$</span> is either factorial or primorial, and do a primality check for <span class="math-container">$n - 1$</span> and <span class="math-container">$n + 1$</sp... | https://math.stackexchange.com |
73,025 | [
"https://dsp.stackexchange.com/questions/73025",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/55524/"
] | Assume we have:
<ul>
<li>real signal: <span class="math-container">$s(t)$</span></li>
<li>its analytic representation: <span class="math-container">$s^+(t) = s(t) + j*H(t)$</span>,
where <span class="math-container">$H(t)$</span> - Hilbert transform of <span class="math-container">$s(t)$</span></li>
</ul>
Spectrum of <... | <blockquote>
are these two methods same?
</blockquote>
no
<blockquote>
If not, how different are these (and how would you utilize)?
</blockquote>
First of all you can't be <code>"extracting 1000Hz signal"</code> . Sine waves are an interesting theoretical concept but they don't exist in practice: in order fo... | Multiplication in the frequency domain is the equivalent of convolution (digital filtering) in the time domain - one of the fundamental properties of the Fourier transform.
Using an FFT in practice to filter requires stitching together overlapping chunks and a large delay if in real-time. However in the frequency doma... | https://dsp.stackexchange.com |
653,238 | [
"https://physics.stackexchange.com/questions/653238",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/219516/"
] | In galvanic cells, electrons are used as the source of charge difference. This creates a current that we can use for a large variety of purposes (i.e. light up a bulb). When I think about this phenomenon there are several things uncertain to me.
Firstly, how does the electron flow heat up the filament of a light bulb?
... | I think you are really asking two questions.
<ol>
<li>Can positrons serve as charge carriers in electric circuits?</li>
</ol>
Theoretically, yes, <strong>if</strong> you replaced every matter particle in an electric circuit with a corresponding anti-matter particle, the circuit would work the same way (except the flow ... | This is to supplement Andrew's answer and focuses on other sub-questions. Electricity, more precisely electric current, is the flow of electric charges. Electrons are very convenient charge carriers as they move relatively easily (though not without collisions) through a lattice-like grid of nuclei in a metal (have a l... | https://physics.stackexchange.com |
14,508 | [
"https://electronics.stackexchange.com/questions/14508",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | If the pickups are just electromagnets detecting vibrations in metal strings, what effect does the guitar (size, shape, type of wood, solid body, hollow body) have on the pickups?
Most argue that the pickups are similar to microphones. However, direct contact with the pickup by material other than metal does not produ... | I think the best way to think about this is to not only think about the wire (moving guitar string) cutting through the magnetic field of the pick-ups (stationary) but also to think about the pick-ups themselves moving with the resonance of the wood that they are fixated to.
Now you must consider the frequency respons... | Of course it does not affect the "sound of the pickups", but the pickups don't have any sound to themselves anyway: they only <em>pick up</em> the sound that's coming from the guitar strings and modify it.
The sound of the strings, on the other hand, is affected quite a lot by the mechanical resonances of the guitar, ... | https://electronics.stackexchange.com |
401,852 | [
"https://electronics.stackexchange.com/questions/401852",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/134429/"
] | There is a VFD which controls an AC motor through a 0-10V control. I know that this control voltage is DC voltage.
I'm wondering would a PWM work for this application? I mean instead of 2VDC, what happens if one applies 0-10V 500Hz pulse train with 20% duty cycle? In theory this corresponds to 2VDC but since it is PWM... | They may or may not have sufficient filtering in there for whatever PWM signal timebase you can generate.
As a <strong>guess</strong>, they probably would put some filtering that would handle mains ripple on the input line so if you had a PWM timebase in the kHz it might have low enough ripple to not cause issues.
... | It would work, by adding a RC lowpass filter. But you have to tell how would you wire 10Vcc to an output and more, what is the output type. If it is a push-pull then no problem, else you might need to make an interface between yours PLC and inverter.
| https://electronics.stackexchange.com |
91,827 | [
"https://mathoverflow.net/questions/91827",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18376/"
] | <strong>Question 1:</strong> Are there any deeper applications (in any field of mathematics) of polynomials (with possibly more than one variable) over the real numbers whose coefficients are non-negative? So far I have found only some vague mentions of control theory and maybe some approximations of functions, but don... | One answer to <strong>question 2</strong> is Polya's theorem on forms positive on an orthant: Let a form (i.e. homogeneous polynomial) in several variables be given which is (strictly) positive whenever evaluated on non zero tuples of nonnegative reals. Then you can multiply it with a high power of the sum of the varia... | If you know that the coefficients are non-negative and also integral, then the polynomial can be completely determined by the values of $p(1)$ and $p(p(1))$. There might be a way to extend this to rational coefficients, but I'm not sure.
| https://mathoverflow.net |
257,839 | [
"https://math.stackexchange.com/questions/257839",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/29751/"
] | I was trying to solve the ODE
\begin{equation}
\ddot{r} r = \alpha(\dot{r}^2-1)
\end{equation}
where $\alpha$ is an arbitrary constant. There are some simple cases when $\alpha = -1 $ then you can use separation of variables to find the solution. For the initial condition when $r'(0)=1$ it also simplifies, $r(t)= t + ... | HINT:
\begin{equation}
\ddot{r} r = \alpha(\dot{r}^2-1)
\end{equation}
$$\frac{\dot{r}\ddot{r}}{\dot{r}^2-1}=\alpha\frac{\dot{r}}{r}$$
$$\frac{\dot{r}\ddot{r}}{(\dot{r}+1)(\dot{r}-1)}=\alpha\frac{\dot{r}}{r}$$
$$\frac{\ddot{r}}{\dot{r}+1} +\frac{\ddot{r}}{\dot{r}-1}=2\alpha\frac{\dot{r}}{r}$$
Then integrate both s... | Case $1$ : $\alpha=0$
Then $\ddot{r}r=0$
$r=0$ or $\ddot{r}=0$
$r=0$ or $r=C_1t+C_2$
$\therefore r=C_1t+C_2$
Case $2$ : $\alpha\neq0$
Then $\ddot{r}r=\alpha(\dot{r}^2-1)$
$r\dfrac{d^2r}{dt^2}=\alpha\left(\left(\dfrac{dr}{dt}\right)^2-1\right)$
Let $u=\dfrac{dr}{dt}$ ,
Then $\dfrac{d^2r}{dt^2}=\dfrac{du}{dt}=\d... | https://math.stackexchange.com |
549,674 | [
"https://physics.stackexchange.com/questions/549674",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/263331/"
] | I understand, at least at a basic level, that the light-difference between inside and outside, determines whether someone walking past my house can see into my room or not.
Partially-see-through materials, such as net curtains, adjust the light difference needed (make it harder to see in/out).
Is there an everyday-te... | Essentially, you can't look into a dark room form the bright outdoors (or vice versa) because the reflected light from the window is more intense and "drowns out" the light from the dark room. So people might be able to see your lights, but the rest of the room can be too dim to discern.
The strength really depends on... | The glass in a window isn't 100% see through, there is always going to be a tiny bit of reflection. When the light level on both sides are about the same, you see say, an image 90% as bright of the other side, and an image 10% as bright of the inside reflected back to you. But, say the light on your side is much bright... | https://physics.stackexchange.com |
13,151 | [
"https://stats.stackexchange.com/questions/13151",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5429/"
] | I’m doing a registry based study with almost 200 000 observations and I want to perform a competing risk analysis. My problem is that the crr() in the cmprsk package is exponentially increasing with increasing number of observations. I therefore wrote a simulation for trying different approaches; check how factors, dat... | This is not an answer in terms of computational speed, but rather a practical solution based on my experience with other types of regression models: Have you tried with a much smaller sample? I'm guessing that even with n=10,000 you might get a decent model (in terms of precision). I'd also try estimating a few such sm... | Variance estimation with the R crr() function from the cmprsk package accounts for slowing down the run time by perhaps an order of magnitude. If you call crr() and disable the variance calculation as follows:
<pre><code>crr(ftime, fstatus, cov, variance=FALSE)
</code></pre>
then the run time will be dramatically red... | https://stats.stackexchange.com |
112,579 | [
"https://softwareengineering.stackexchange.com/questions/112579",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7836/"
] | I'm working on some projects where I'd like to supply an accurate changelog with each release, but I haven't found a method for collecting the changelog that would work without hassle. The problem is mostly when the time between versions is long and each version ships with a lot of features and bug fixes, and when the ... | If you don't already have the requirement of a ticket for each change, then getting developers to create a ticket for each change important enough to end up in the change log seems reasonable.
If the change is significant enough to tell users about, then you probably want to be making that change under a ticket anyway... | <blockquote>
Feels like manual labor that could be automated.
</blockquote>
How could it be automated? There is no need to edit the changelog on each commit, but only when a feature worth mentioning is added. Does that happen so often on your software that it's a hassle to add one line to the changelog every time?
| https://softwareengineering.stackexchange.com |
634,018 | [
"https://physics.stackexchange.com/questions/634018",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/290525/"
] | I was reading about antimatter and dark energy and how Hawking Radiation can destroy black holes when I came across three theories about how the universe might end.
There are various theories regarding the end of the universe, like the Big Rip, the Big Freeze, and the Big Crunch. The first two reasons that Dark Energy ... | <blockquote>
But how can we use the kinetic energy equation when the force didn't
act over a distance in the first place? In other words, the
displacement is zero so should the work.
</blockquote>
In a collision the displacement may be very small, but the displacement is never zero. It would only be zero for a perfectl... | You're right! Real collisions actually take place over a short time (and thus a short distance). Has your teacher mentioned impulse yet?
You know from calculus that the differential form of velocity is
<span class="math-container">$$ \text{d}v = v'(t) \: \text{d}t = a(t) \: \text{d}t \text{ .} $$</span>
Using this, we ... | https://physics.stackexchange.com |
173,032 | [
"https://dba.stackexchange.com/questions/173032",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/124391/"
] | I have 3 tables:
<strong>ve_survey_questions</strong>
<pre><code>Qid | Question | CategoryId
</code></pre>
<strong>ve_survey_answers</strong>
<pre><code>AnswerID | QuestionId | Answer
</code></pre>
<strong>ve_survey_useranswers</strong>
<pre><code>id | UserId | QuestionId | AnswerId | Datetime
</code></pre>
This... | You can use a single sql:
<pre><code>SELECT q.*
FROM ve_survey_questions q
LEFT JOIN ve_survey_useranswers ua ON ua.QuestionId = q.Qid AND ua.UserId = xyz
WHERE ua.QuestionId IS NULL
</code></pre>
Replace xyz with the UserId
To show all answers of unanswered questions (for example UserId = 1):
<pre><code>SELECT a.*... | So if I'm understanding the schema right, this should work with a LEFT OUTER JOIN with a subquery:
<pre><code>SELECT q.*, ua.UserId, ua.Answer
FROM ve_survey_questions q
LEFT JOIN (
SELECT u.*, a.QuestionId, a.Answer
FROM ve_survey_useranswers u
INNER JOIN ve_survey_answers a ON u.AnswerId = a.AnswerID... | https://dba.stackexchange.com |
1,249,399 | [
"https://math.stackexchange.com/questions/1249399",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/189215/"
] | While studying the divisor sum function $\sigma(n)$ (as the sum of the divisors of a number) I observed that the following expression seems to be true always (1):
<blockquote>
$\forall\ n=5p, p\in\Bbb P,\ p\gt 5,\ if\ d(5p)=4\ then\ \sigma(5p)=3,0\ (mod\ 9)$
</blockquote>
Meaning that if the number $n=5k$ has only ... | Note that if $k=3$, then $\sigma(15) =1+3+5+15 = 24$ is congruent to $6$ modulo $9$. This is the only counterexample, as we shall show.
Note that the equation $6k \equiv 3, 6 \pmod{9}$ is equivalent to saying that $3$ divides $6k$, but $3^2$ does not. Clearly the former is true, and the latter is true for all $k \ne... | The divisors of 5k are $\{1, 5, k, 5k\}$ if and only if k is a prime number or if $k = 25$.
The divisors of $5 \times 25$ are $\{1, 5, 25, 125\}$. Their sum is $3 \pmod 9$.
Otherwise, you want to compute $1 + 5 + k + 5k \pmod 9 \equiv 6(1+k) \pmod 9$ for all prime numbers $k$ (Except $k=5$).
For $k = 0 \text{ to } 8... | https://math.stackexchange.com |
241,139 | [
"https://security.stackexchange.com/questions/241139",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/214750/"
] | Everyone knows of the common cybersecurity tips to be careful when you open links in an email. But every day we look for something on the Internet, clicking links which the search engine shows us, and we do not have the same fear. Why are the links in email considered more dangerous than links from web search results?
... | The results of a search engine are based on previously collected data, i.e. the engine does not starts to scanning the whole internet when doing a search but it looks through an index of seen and stored sites. The results are also ordered, i.e. the sites which fit the query best and which also have the highest reputati... | Let me use an analogy:
<strong>It's for the same reason we tell our children not to take sweets from strangers, but at the same time we allow them to buy some in the supermarket with their pocket money.</strong>
Or more technically: The difference is that in the first case you receive something you did (likely) not ask... | https://security.stackexchange.com |
4,468,308 | [
"https://math.stackexchange.com/questions/4468308",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <strong>If we define a relationship such as <span class="math-container">$y=x^2$</span> between the variables <span class="math-container">$y$</span> and <span class="math-container">$x$</span>, does this relation have to hold for all values of <span class="math-container">$y$</span> and <span class="math-container">$x... | <strong>Hint:</strong>
<span class="math-container">$\sin(x)= \sin(2\frac{x}{2})=\frac{2\tan(\frac{x}{2})}{1+\tan^2(\frac{x}{2})},$</span>
and <span class="math-container">$\cos(x)= \cos(2\frac{x}{2})=\frac{1-\tan^2(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}.$</span>
Try to do this in <span class="math-container">$\sin(\alph... | Let <span class="math-container">$\beta=\alpha +45^o.$</span> Then <span class="math-container">$\sin \beta=\sin \alpha \cos 45^o+\cos \alpha \sin 45^o=(1/\sqrt 2)(\sin \alpha +\cos \alpha)=(\sqrt 7)/(2\sqrt 2).$</span> And so <span class="math-container">$\cos \beta=\pm \sqrt {1-\sin^2\beta}=\pm \sqrt {1-7/8}=\pm 1/(2... | https://math.stackexchange.com |
108,258 | [
"https://physics.stackexchange.com/questions/108258",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/40023/"
] | Can anyone explain to me <em>why</em> the induced magnetic field will oppose the change in magnetic flux? Is it an energy thing?
I know that the induced emf is
$$ emf= - \frac{d\phi}{dt} $$
but my book doesn't give a satisfactory (or any) explanation as to why this is the case. I recognize that an emf source supplies ... | The trajectories are uniquely determined means that the theorem of existence and uniqueness applies (so, the differential equation has to be sufficiently regular).
Newton's principle states more: the system is fully determined by the position and the speed, that is, by $2n$ constants, where $n$ is the dimension of the... | A very simple motivation for writing $\ddot{\bf x}(t) = {\bf F}({\bf x}, \dot{\bf x}, t)$, which might shed some light, is the following. We are given ${\bf x}(t)$ and $\dot{\bf x}(t)$ and we desire to calculate ${\bf x}(t + \delta t)$ and $\dot{\bf x}(t + \delta t)$. Now, ${\bf x}(t + \delta t) = {\bf x}(t) + \dot{\bf... | https://physics.stackexchange.com |
88,804 | [
"https://physics.stackexchange.com/questions/88804",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35148/"
] | Yes, this is a homework question, but I've already failed to solve it enough times that the online system hosting it isn't going to give me any marks, so I figure it's a good time to stop hitting the wall and actually ask. The question is as below:
<blockquote>
A spectroscopist uses a spectrometer that has a grating... | So this was the answer given in the key:
<img src="https://i.stack.imgur.com/tbMl7.png" alt="enter image description here">
| $\sin \theta = (m \lambda)/d = (5 \times 1228^{-6})/(1/600) = 3.684$
$d = (1/600)\times 3 = 0.005
\lambda = (d \sin \theta) /m
= (0.005 \times 3.684)/4
= 0.004605\: \mathrm{mm}
= 4605\: \mathrm{nm}$
| https://physics.stackexchange.com |
520,505 | [
"https://math.stackexchange.com/questions/520505",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93671/"
] | I would like to show that the expression (S => P) AND (NOT S => Q) and the expression (S AND P) OR (NOT S AND Q) are equivalent.
I am not interested in any solution using truth tables or exhaustive trying of truth assignments, I find these approaches rather unilluminating.
| The following facts will get you most of the way there: $$A\Rightarrow B\equiv(\neg A)\vee B$$ $$A\wedge(B\vee C)\equiv(A\wedge B)\vee(A\wedge C)$$ $$A\vee(B\wedge C)\equiv(A\vee B)\wedge(A\vee C)$$
| \begin{eqnarray}
(S \to P) \land (\lnot S \to Q) &=& (\lnot S \lor P) \land (S \lor Q) \\
&=& (\lnot S \land S) \lor (\lnot S \land Q) \lor (P \land S) \lor (P \land Q) \\
&=& (\lnot S \land Q) \lor (P \land S)\lor (P \land Q) \\
&=&(\lnot S \land Q) \lor (P \land S)\lor ((P \land Q)\lan... | https://math.stackexchange.com |
665,437 | [
"https://math.stackexchange.com/questions/665437",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/126590/"
] | I am having a problem with my math assignment, and i'm honestly not even sure of where to begin with this one.
The question is:
<blockquote>
Let $A=\{a,b,c,d\}$, $B = \{b,d\}$ and $X = \{a,b\}$. Determine all $Y\in\mathcal{P}(A)$ such that $Y - B = X - B$.
</blockquote>
Any help would be greatly appreciated.
| Eisenstein's criterion is directly applicable with $p = 2$.
<hr>
For an alternative proof, it suffices to show that (since the degree of the polynomial is $2$) that there are no rational roots. This can be done with the rational roots theorem, or by noting that the polynomial splits over $\mathbb{R}$, and its roots a... | Well, we need a prime $p$ that divides $-4$ and $2$, but does not divide $1$, and such that $p^2$ does not divide $2.$ Can you think of any such primes?
| https://math.stackexchange.com |
212,454 | [
"https://mathoverflow.net/questions/212454",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23141/"
] | I have an idea for a possible counterexample to the noncommutative Stone-Weierstrass problem. A good answer to the following question would really help.
Let $\mathcal{A}$ be the C*-algebra of $2\times 2$ complex matrices, let $\mathcal{B}$ be the C*-subalgebra of $2\times 2$ diagonal matrices, and let $v$ and $w$ be ... | The answer to my question is no. Let $\mathcal{A} = M_2$ be the algebra of $2\times 2$ complex matrices, let $\mathcal{B}$ be the subalgebra of diagonal matrices, let $\mathcal{A}'$ be a C*-algebra which unitally contains $\mathcal{A}$, and let $\mathcal{B}'$ be a C*-subalgebra of $\mathcal{A}'$ which contains $\mathca... | This is long. I originally thought this would work but it does not separate all extensions of $f$ and $g$ (see Nik's comment).
Consider the unital embedding $\mathcal A = M_2 \subset M_4$ given by $$A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right] \mapsto A \otimes I_2 = \left[\begin{array}{cccc} a &... | https://mathoverflow.net |
601,257 | [
"https://physics.stackexchange.com/questions/601257",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/264640/"
] | I have been assigned to solve the problem: the ongoing temperature of the room <span class="math-container">$T_1 = 7$</span>; RH is 85% and I am asked to figure out how much the temperature must be increased in order that RH would drop to 70% or less.
I would like to know what I did wrong - why I could not find this se... | Comment turned answer as requested by Bill N.
This question seems to assume that the amount of water vapor in the air stays constant. Then this statement
<blockquote>
[...] Will the RH drop? Not necessarily, because the more environment's temperature, the more moisture the air can store, so boosting RH.
</blockquote>
m... | The relative humidity of air is a ratio between the maximal amount of water vapour the air can hold (before fog forms or, in technical terms, the dew point) and the amount it actually holds.
The maximum carrying capacity of water vapour of air depends on the temperature. You can just look up this value (your p<sub>sat<... | https://physics.stackexchange.com |
211,008 | [
"https://softwareengineering.stackexchange.com/questions/211008",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53322/"
] | I lead a development team and I want to release our product as often as possible (Continuous Delivery).
In many cases, we have to implement a feature that takes longer to implement than the time between releases. I still want people to commit their code on a daily basis (Continuous Integration).
Many times implementi... | I take a different view from the other answers on here already. I agree with you that you want to integrate changes from developers as soon as possible, and to keep testing the combined mix of code.
However, I do not agree that its right to ship code developed this morning, just because we are releasing this afternoo... | There are two problems here: one is implementing half a feature; the other is keeping the shipping product working during continuous development.
<strong>Implementing half a feature</strong>
A strong overarching design will help with this. This lets you implement the feature with its boundaries clearly defined--e.g.,... | https://softwareengineering.stackexchange.com |
291,496 | [
"https://electronics.stackexchange.com/questions/291496",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/141713/"
] | I have a cordless handheld vacuum cleaner (Electrolux Rapid ZB4103) which is powered by 3 rechargeable AA NiMH batteries (1.2V 1300mAh) connected in series and stacked (glued?) in a pyramid to fit within the case. The batteries are typically recharged by placing the vacuum unit on a changing base (base output is 8V 200... | 1) Yes, charging should be safe enough.
2) Slow charging rarely generates enough heat to be troublesome, though relying solely on hot-melt is not a good idea, bundle them with cable ties as well.
Be aware that not all NimH batteries are equal in discharge current ratings. The batteries you are replacing appear to be ... | 1) Yes, since the newer cells are of a quality brand and have the same or higher capacity than the old ones, and the nominal voltage is the same. I'd say that's "safe enough". (Take it from a random person on the Internet.)
2) Possibly. Is there a temperature sensor in the circuit somewhere? Holding the cells tightly ... | https://electronics.stackexchange.com |
41,356 | [
"https://dba.stackexchange.com/questions/41356",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/15907/"
] | I am trying to write a simple system function so that the <code>dbo.</code> prefix is NOT required to access the function. I have found an example of this for SQL Server 2000 but when I run
<pre><code>EXEC SP_CONFIGURE 'ALLOW UPDATES', 1
RECONFIGURE WITH OVERRIDE
go
create function system_function_schema.trim
(@... | Using system_function_schema was an undocumented and unsupported process in SQL 2000. As of SQL 2005, it is no longer possible.
By design, UDFs require that the schema be included in the function call.
There is one exception: calling the function like a procedure doesn't actually require the schema, but also wouldn't... | For functions it's tricky. You can probably create a function and then create a synonym for it in Model (if you want the function for any new databases that are created as they will inherit Model objects).
Create a function in master database:
<strong>Note</strong>: You have to first create <code>system_function_sche... | https://dba.stackexchange.com |
538,429 | [
"https://math.stackexchange.com/questions/538429",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/77862/"
] | <blockquote>
Prove if $S_1,S_2$ are compact, then their union $S_1\cup S_2$ is compact as well.
</blockquote>
The attempt at a proof:
Since $S_1$ and $S_2$ are compact, every open cover contains a finite subcover. Let the open cover of $S_1$ and $S_2$ be $\mathscr{F}_1$ and $\mathscr{F}_2$, and let the finite subco... | HINT: You’re starting in the wrong place. In order to show that $S_1\cup S_2$ is compact, you should start with an arbitrary open cover $\mathscr{U}$ of $S_1\cup S_2$ and show that it has a finite subcover. The hypothesis that $\mathscr{U}$ covers $S_1\cup S_2$ simply means that $S_1\cup S_2\subseteq\bigcup\mathscr{U}$... | Suppose you have an open cover of $S_1 \cup S_2$. Since they are separately compact, there is a finite open cover for each. Then combine the finite covers, this will still be finite. Hence the union is compact,
| https://math.stackexchange.com |
732,526 | [
"https://physics.stackexchange.com/questions/732526",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/132400/"
] | First
<span class="math-container">$ \rho = 0 $</span> inside the conductor
from
<span class="math-container">$\nabla \cdot E = \rho / \epsilon_0 $</span> if E=0 then <span class="math-container">$ \rho $</span> should be 0 too
I got this concept but Why E=0 inside a conductor?
Why E=0 inside a conductor?
from em gri... | As usual in Thermodynamics, any statement about interactions between a system and its surroundings requires careful identification of what the system is and what the surroundings are.
In the case of a fluid in a variable-volume container, the natural choice is to consider the fluid as the thermodynamic system and the o... | P external
Think about free expansion in vacuum
there is no work in vacuum
For a free expansion into a vacuum, a gas does no work because there is no resistance on the gas as P=0.
| https://physics.stackexchange.com |
725,185 | [
"https://math.stackexchange.com/questions/725185",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/119569/"
] | <span class="math-container">$A$</span> is a <span class="math-container">$n \times m$</span> matrix with known real elements and <span class="math-container">$b$</span> is a known real <span class="math-container">$n$</span>-dimensional vector.
I would like to find all <span class="math-container">$x$</span> such that... | You want to minimize
<span class="math-container">$$
|Ax-b|^2 = (Ax-b)^t (Ax-b) = x^t A^t A x - 2 x^t A^t b + |b|^2
$$</span>
derive to obtain
<span class="math-container">$$
2 A^t A x - 2A^t b = 0
$$</span>
which gives
<span class="math-container">$$
x = (A^t A)^{-1} A^t b.
$$</span>
| The vector x is given by $$x=(A^{T}A)^{-1}A^{T}b$$ As suggested by commentators, read up on least-squares approximations.
| https://math.stackexchange.com |
151,109 | [
"https://mathoverflow.net/questions/151109",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23534/"
] | Considering parameter of $S^1$ as $t$, we define.
$$ev_t: C^\infty(S^1, \mathbb R^n)\to \mathbb R^n$$
$$ev_t(\gamma):=\gamma(t)$$
I am looking for a possible topology on $C^\infty(S^1,\mathbb R^n)$ which makes $ev_t$, an open map.
| The (compact) $C^\infty$-topology makes $ev_t$ an open map. Namely, any open neighborhood $U$ of $f$ is described by: You may deviate from $f$ uniformly by a positive constant for a chosen finite set of derivatives and still stay in $U$; no conditions on the derivatives outside this set.
So for the 0-th derivative you ... | I suspect it will suffice to find a topology for whicg $ev_1$ is an open map. (In any reasonable topology, loop reparametrization should define a self-homeomorphism of $C^{\infty}(S^1,\mathbb{R}^n)$.)
For a Lie group $G$, $$LG:=C^{\infty}(S^1,G)$$ is its loop group. We find that $$ev_1:LG\rightarrow G$$ is a surjectiv... | https://mathoverflow.net |
284,641 | [
"https://physics.stackexchange.com/questions/284641",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/31840/"
] | Can one use a thermometer with $\pm$5 mK accuracy to measure a temperature difference of 2 mK (the measurement is near 100 mK temperature on a sample on an ADR)? Using the same thermometer, I am thinking to measure temperature of the sample, heat the sample slightly, measure temperature again, and take the difference. ... | Yes, of course you can do it. The 'accuracy' is from a calibration, after all, and your temperature-difference determination establishes a short-term new calibration. If the apparatus were to have hysteresis (the meter pointer is sticky), or if there were interfering signals (the power supply ripple dominating
an el... | I do not think that you will have a problem measuring a temperature difference of $2$ mK but as to the accuracy you will achieve you need to give/get more information about the type and calibration method of your thermometer.
Suppose that the reading you got on your thermometer was $105.32$ mK' (the K-primed showing i... | https://physics.stackexchange.com |
149,287 | [
"https://electronics.stackexchange.com/questions/149287",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/59850/"
] | I want to ask if there is differences between this two circuits:
<img src="https://i.stack.imgur.com/cpaG8.png" alt="enter image description here">
I ask this questions becouse in different schematics like this:
<img src="https://i.stack.imgur.com/1Ix7t.png" alt="enter image description here">
There is two decoupli... | Decoupling caps need to be physically close to the pins they are decoupling. This also means every power pin needs its own decoupling cap. Since the values of all your decoupling caps are the same and are small, what you see is probably due to the IC having more than one power pin. This is common with large digital ... | The basic idea is that they are in parallel, however they are possibly located at many different places on the PCB, but not always.
Some schematics will show several capacitors all together in one place, and you don't really know where they are physically located. This is very common on VCC and other power lines. ... | https://electronics.stackexchange.com |
86,947 | [
"https://mathoverflow.net/questions/86947",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2191/"
] | For a (bounded) double complex (of abelian groups or vector spaces) one can consider two spectral sequences that converge to the cohomology of the totalization: one can first compute either the cohomology of rows, or the cohomology of columns. Suppose that one of these spectral sequences degenerates at $E_1$ (i.e. the ... | There is a basic way to see whether things like this should be true. Any bounded double complex of vector spaces over a field $k$ is (noncanonically) the direct sum of complexes of the following two sorts:
<b>Squares:</b> $$\begin{matrix} k & \rightarrow & k \\ \uparrow & & \uparrow \\ k & \righ... | Let $E,F$ be the two spectral sequences of the double complex and for simplicity assume they are in the first quadrant. If $E_1$ degenerates, say, $E_1^{i,j}=0$ for $j>0$ then you know that $F$ converges to $E_2$, i.e. $F_2^{\;i,j} \Rightarrow E_2^{i+j,0}$.
In general, I don't think much can be said about the prop... | https://mathoverflow.net |
377,725 | [
"https://softwareengineering.stackexchange.com/questions/377725",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/314162/"
] | I am writing applications in C++ using an sqlite database. Suppose I have a simple user system with a user database.
<strong>User Class</strong>
<pre><code>class User {
private:
void LoadFromDatabase(uint32_t id);
public:
std::string name;
uint32_t age;
void SayHello();
... | Look at this approach :
<pre><code>class User {
private:
UserRow userRow;
void LoadFromDatabase(uint32_t id); // init userRow
public:
std::string GetName(){return userRow.name;}
// implement setName in an analogous manner
uint32_t getAge(){return userRow.age;}
... | You could say that your User objects actually are row objects, since they already have the same information. Like you have done now, You have only created an unnecessary abstraction layer which doesn't provide anything useful.
| https://softwareengineering.stackexchange.com |
598,501 | [
"https://stats.stackexchange.com/questions/598501",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/299851/"
] | (<strong>Background:</strong> I am researching a economics problem and for the research, I need to know the general theory of multinomial distribution problems. This question is just an example to understand the general problems)
There is a fair dice. Let's say <span class="math-container">$X$</span> is the number you ... | There are less common estimators that we can use and might want to use under some circumstances. For instance, if we estimate the parameters of a linear model by minimizing something other than square loss (sum of squared residuals), we might wind up with the square loss increasing as we add parameters, since the optim... | The question is a bit vaguely formulated (how is one increasing the number of variables?, what sort of loss function is your model trying to minimize?). In the following result, I try to state a set of precise conditions under which the answer to your question is "yes". I then discuss why my result is true un... | https://stats.stackexchange.com |
135,802 | [
"https://electronics.stackexchange.com/questions/135802",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/56877/"
] | I'm designing a small system in VHDL using the datapath and contorller method. Is it okay if I design registers that don't have a clock input (load data on the rising edge of the load signal) as they are being controlled by the control unit which is going to be running on the same clock signal; just to use less wiring.... | You "can" do it but it would be highly discouraged. The correct thing to do is to learn how to design your logic so that everything (or at least large separate partitions of the logic) run on a common clock rail. Then learn to use clock enables to allow the "load", "clear", "increment", and "shift" type operations to h... | Caveat: this answer assumes you are targeting an FPGA implementation, not an ASIC. Also, my knowledge is more in Verilog than VHDL.
Your code example is just fine. It is just a register with the clock input connected to the net named <code>load</code> and with an asyncronous reset feature. (Assuming I understand the V... | https://electronics.stackexchange.com |
173,314 | [
"https://softwareengineering.stackexchange.com/questions/173314",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66910/"
] | I have to sort a set of 100000 integers as a part of a programming Q. The time limit is pretty restrictive, so I have to use the most time-efficient approach possible.
My current code -
<pre><code>#include<cstdio>
#include<algorithm>
using namespace std;
int main() {
int n,d[100000],i;
for(i=0;i... | For maximum efficiency you only want to do the sort once, so version 2 is definitely not the way to go.
An alternative to just storing the numbers in an array in the order they are read and then sorting, is to use a data structure that will sort itself as each number is added, such as a (red/black) binary tree or a sk... | If you want to sort time-efficient and it is guaranteed that your elements are numbers, then go for <code>Radix-Sort</code>. It is sorting your Dataset in <code>O(a*n)</code>, a is the length of the longest/biggest number.
10 would get you a=2, 200 would get you a=3, 2*10^(100) would get you a=1000 and so on.
Quicksor... | https://softwareengineering.stackexchange.com |
290,936 | [
"https://softwareengineering.stackexchange.com/questions/290936",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/151374/"
] | I started working on a website,for tracking and rating watched anime/manga/etc. and recommendations, and it should also have an API, for providing the info about series and other things.
On similar sites, I have noticed that, to use an API, one typically needs a token/auth of sorts, and there are certain usage limits,... | Having a public API for data access from your site is about making the data available in a convenient, supported, well-defined and always-up-to-date manner. It is a way for a site owner to say 'here is data I collect and own, but I want you to be able to use it so I'm making it available. Oh, and I promise not to chan... | Token-authorized APIs are used for lots of reasons.
<ul>
<li><strong>Controlling access to restricted information.</strong> Since a token usually maps somehow to an authorized identity, the site can restrict programmatic access to data exactly as it would to interactive access via the web UI. Tokens also prevent p... | https://softwareengineering.stackexchange.com |
4,543,126 | [
"https://math.stackexchange.com/questions/4543126",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1102102/"
] | <span class="math-container">$20$</span> people that A, B and C belong to are to be randomly seperated in groups of 4. I have a few questions about this problem:
Q1: What is the probability, that A, B and C place in the same group?<br />
My intuition would be, that the person A has a <span class="math-container">$4/20=... | <span class="math-container">$\require{cancel}$</span>
Your first answer is correct, but your second isn't.
What I consider the simplest approach is given below.
Consider <span class="math-container">$20$</span> slots in <span class="math-container">$5$</span> groups of <span class="math-container">$4$</span>,
<span cl... | To avoid using comments, to heavily, I add my views in an answer.
Q1) I am ok with already, twice, given answers.
Q2) I am in agreement with true blue anil. Although I failed to find his elegant way of modeling it, my inelegant reasoning lead to the same result. And so did the monte-carlo simulation I ran.
Q3) I unders... | https://math.stackexchange.com |
2,264,247 | [
"https://math.stackexchange.com/questions/2264247",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | X is a cauchy sequence implies that |xn-xm|<ε for n,m>N
I've tried breaking this up into the different case for xn, xm greater than or equall to zero, but I am struggling with when xn and xm have different signs.
The best thing I could come up with was that if X is cauchy sequence the only time two consecutive m... | What you want is the <em>reverse triangle inequality</em>, which states
$$\bigl| |a|-|b|\bigr| \leq |a-b|$$
For a quick proof using the triangle inequality, we have that
\begin{align}
|a| & = |a+b-b| \\
& \leq |a-b|+|b|
\end{align}
so $|a|-|b| \leq |a-b|$. Symmetry gives us the other inequality $|b|-|a| \leq |... | You lose a <em>ton</em> of meaning when you leave out quantifiers. Don't do that.
A sequence $\{x_n\}$ is Cauchy if : <strong>for every</strong> $\epsilon > 0$ <strong>there exists</strong> $N \in \mathbb N$ with the property that <strong>for every</strong> $n,m \in \mathbb N$, $n,m \ge N$ implies $|x_n - x_m| &l... | https://math.stackexchange.com |
252,161 | [
"https://mathoverflow.net/questions/252161",
"https://mathoverflow.net",
"https://mathoverflow.net/users/95838/"
] | I am trying to understand whether some non trivial explicit estimate is known about the following
$$\sum_{n \leq x} \mu(n) \chi(n)$$
as a function of $x$.
Here $\chi$ is a Dirichlet character modulo $q$ and $q > (\log x)^2$ (for example).
| Estimating this sum is much the same as estimating the error term in the prime number theorem for arithmetic progressions. See Exercises 7-8 in Section 11.3 of Montgomery-Vaughan: Multiplicative number theory I (Cambridge University Press, 2006). (Your sum is denoted by $M(X,\chi)$ in this book, as introduced by (11.39... | Explicit estimates for the Moebius function are much harder than for the prime counting function. Ramare (From explicit estimates for the primes to explicit estimates for the Moebius function, Acta Arithmetica 157, (2013), 365-379) has shown how to translate estimates for primes to estimates for the Moebius function, a... | https://mathoverflow.net |
255,451 | [
"https://physics.stackexchange.com/questions/255451",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/117091/"
] | I was reading about damped simple harmonic motion but then I saw this equation:
$$-bv - kx = ma$$
$b$ is the damping constant. Then it said by substituting $dx/dt$ for $v$ and $d^2x/dt^2$ for $a$ we will have:
$$
m\frac{\mathrm d^2x}{\mathrm dt^2}+b\frac{\mathrm dx}{\mathrm dt}+kx=0
$$
Then it says the solution of ... | The differential equation you quote is fairly standard in university physics/engineering course but definitely requires some calculus to solve. As a first step, if you know how to differentiate products and chains, you can substitute the given solution into the differential equation and verify that it is indeed a solut... | This is a linear and homogeneous differential equation. That means you can produce new solutions by adding other solutions together and multiplying solutions by a constant. That means they form a vector space. I'll try to avoid over complicating things for you, but the idea is that there is an infinite number of soluti... | https://physics.stackexchange.com |
359,079 | [
"https://softwareengineering.stackexchange.com/questions/359079",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/285737/"
] | When creating a Set in Java, what's the difference between the following? Which one should I use, and why?
<pre><code>Set< T > set = new HashSet<>();
HashSet< T > set = new HashSet<>();
</code></pre>
| In object-oriented programming, there is a concept of "programming to an interface." The idea is you do not really care which type of set you use, only that it fulfills the contract of the <code>Set</code> interface (or <code>List</code>, or <code>Map</code>).
Your examples do not really show the benefits of the first... | The answer from @Snowman is right for the general case. It is most of the time correct to code to an interface, for the reasons he stated.
There are cases however, where you don't want that, as the underlying implementation can make a big difference to performance.
Consider the case of a <code>List<E></code> w... | https://softwareengineering.stackexchange.com |
113,177 | [
"https://softwareengineering.stackexchange.com/questions/113177",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35740/"
] | Well, I know that there are things like malloc/free for C, and new/using-a-destructor for memory management in C++, but I was wondering why there aren't "new updates" to these languages that allow the user to have the option to manually manage memory, or for the system to do it automatically (garbage collection)?
Some... | Garbage collection requires data structures for tracking allocations and/or reference counting. These create overhead in memory, performance, and the complexity of the language. C++ is designed to be "close to the metal", in other words, it takes the higher performance side of the tradeoff vs convenience features. Othe... | Strictly speaking, there is no memory management at all in the C language. malloc() and free() are not keywords in the language, but just functions that are called from a library. This distinction may be pedantic now, because malloc() and free() are part of the C standard library, and will be provided by any standard c... | https://softwareengineering.stackexchange.com |
255,503 | [
"https://mathoverflow.net/questions/255503",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7458/"
] | The proof by Cauchy induction of the arithmetic/geometric-mean inequality is well known. I am looking for a further theorem whose proof is much neater by this method than otherwise.
| A nice proof by Cauchy induction can be given for the identity
$$ \|A^n\|=\|A\|^n, $$
which holds for a bounded, self-adjoint operator $A:H\to H$ on a real Hilbert space $(H,\langle\cdot,\cdot\rangle)$. Here $\|\cdot\|$ denotes the operator norm.
Indeed, the inequality $\|A^n\|\le\|A\|^n$ is trivial by submultiplicati... | Assume that $f$ is a function defined in a certain interval $\Delta$ and you want to prove that $$\sum_{i=1}^n f(x_i)\geqslant nf(a),\,a=\frac1n \sum x_i,\tag 1$$ where the numbers $x_i$ in $\Delta$ are arbitrary or satisfy some additional condition U. Example of U would be '$x_i+x_j\leqslant 2b$ for $i\ne j$.' Then Ca... | https://mathoverflow.net |
522,456 | [
"https://physics.stackexchange.com/questions/522456",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <img src="https://i.stack.imgur.com/g7yTf.jpg" alt="An object applying force on another">
<strong>Refer to the diagram shown above</strong>
<strong>Question</strong>
Assume a system of two objects (<span class="math-container">$1$</span> and <span class="math-container">$2$</span>) which are applying force on one an... | As pointed out in the comments, your argument cannot be applied to systems with more than 2 interacting bodies. For <span class="math-container">$N$</span> bodies, you will arrive at
<span class="math-container">$$\sum_i^N\sum_{j\neq i}^N\mathbf F_{ij}=0$$</span>
which does not specify <span class="math-container">$\ma... | I would like to rephrase this question into the following form:
Is three laws the minium, or is a system of two axioms also possible?<br>
I think the answer to that is yes.
Of course, implicitly you are already using the axioms in the form I describe below, I'm only making it explicit.
<br>
First let me propose a f... | https://physics.stackexchange.com |
39,002 | [
"https://stats.stackexchange.com/questions/39002",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | Apart from some unique circumstances where we absolutely must understand the conditional mean relationship, what are the situations where a researcher should pick OLS over Quantile Regression?
I don't want the answer to be "if there is no use in understanding the tail relationships", as we could just use median regres... | If you are interested in the mean, use OLS, if in the median, use quantile.
One big difference is that the mean is more affected by outliers and other extreme data. Sometimes, that is what you want. One example is if your dependent variable is the social capital in a neighborhood. The presence of a single person with ... | There seems to be a confusion in the premise of the question. In the second paragraph it says, "we could just use median regression as the OLS substitute". Note that regressing the conditional median on X <em>is</em> (a form of) quantile regression.
If the error in the underlying data generating process is normall... | https://stats.stackexchange.com |
74,837 | [
"https://mathoverflow.net/questions/74837",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17656/"
] | hi, does anyone know a good book or some lecture notes on the theory of frechet manifolds ?
| There is the book by Kriegl and Michor called "Convenient setting of global analysis" published by the AMS. It goes much beyond Fréchet and really gives a big panorama. However, it is not easy reading and requires really some work. But I guess that is due to the subject...
| You could try
<blockquote>
Hamilton, Richard S. (1982). "The inverse function theorem of Nash and Moser". Bull. Amer. Math. Soc. (N.S.) 7 (1): 65–222. doi:10.1090/S0273-0979-1982-15004-2
</blockquote>
And there's a paper by Milnor on infinite dimensional Lie groups which could be useful.
| https://mathoverflow.net |
1,737 | [
"https://stats.stackexchange.com/questions/1737",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | I want to calculate a summary of a variable in a data.frame for each unique combination of factors in the data.frame. Should I use plyr to do this? I am ok with using loops as opposed to apply() ; so just finding out each unique combination would be enough.
| While I think <code>aggregate</code> is probably the solution you are seeking, if you are want to create an explicit list of all possible factor combinations, <code>expand.grid</code> will do that for you. e.g.
<pre><code>> expand.grid(height = seq(60, 80, 5), weight = seq(100, 300, 50),
sex = c("Male"... | See <code>aggregate</code> and <code>by</code>. For example, from the help file for <code>aggregate</code>:
<pre><code>## Compute the averages according to region and the occurrence of more
## than 130 days of frost.
aggregate(state.x77,
list(Region = state.region,
Cold = state.x77[,"Frost"] > 130)... | https://stats.stackexchange.com |
359,549 | [
"https://physics.stackexchange.com/questions/359549",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/162666/"
] | On Hyperphysics, it says that the threshold index of refraction $n_t$ for some incident angle $\theta_i$ is (in radians);$$
n_isin\theta_i=n_tsin\frac\pi2
$$
but isn't $sin\frac\pi2$ equal to one?
so would this be the correct equation for the threshold index of refraction?$$
n_isin\theta_i=n_t?
$$
or displaying it as a... | Short answer: yes.
Long answer:
You start with Snell's Law $n_i\sin\theta_i = n_r\sin\theta_r$ and set the angle of refraction $\theta_r = \pi/2$ (as total internal reflection occurs when the refracted wave would not leave the medium). That is why you are left with $n_i\sin\theta_i = n_r$. The angle of refraction woul... | The critical angle is precisely the one that <strong>separates</strong> total and partial reflection. Consequently, it is only one value and it must be a equality, and not an inequality.
You are right, you get that equation when $\sin \theta_r=1$. That's because it means that the reflected ray exits at $90º$ from the ... | https://physics.stackexchange.com |
117,780 | [
"https://stats.stackexchange.com/questions/117780",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1381/"
] | I have a vector, $k$, that determines allocation to five pools.
I'd like to set priors on these probabilities, and I can provide informative priors on a few of the ratios, e.g.:
$$ \frac{k1}{k2} \sim \text{beta}(6,1)$$
$$ \frac{k1}{k3} \sim \text{beta}(2,12)$$
$$ \frac{k1+k2+k3}{k4+k5} \sim \text{beta}(50,1)$$
$$ \fr... | Let's do this by arithmetic:
Subtract $1$ from the value and range, and work with $7.1/8$. That is the same as $3.55/4$.
Add $1$ back in and you have $4.55$.
There is a strong assumption in there about how people would have answered had the scale been different, which you make and are responsible for and which th... | The best way is to use a linear transformation. Basically you use 2. First convert the 9 point scale to a 0-1 interval and then convert it to a 5 point interval. This isn't dissimilar to the method used by random number generators, they often start by generating a random number from 0-1 and then transforming it to the ... | https://stats.stackexchange.com |
81,248 | [
"https://dba.stackexchange.com/questions/81248",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | Can the following be setup in Oracle11.2 for password authentication?
<ol>
<li>A new, non temp password should be atleast 24 hours old before it can be changed. System admin and authorized help desk personnel may change passwords of any age. </li>
<li>Users will change temporary passwords including system administrat... | For single table you can use
<pre><code>sp_spaceused MyTable
</code></pre>
For all tables in a database you can use it with <code>sp_msforeachtable</code> as follwoing
<pre><code>CREATE TABLE #temp (
table_name sysname ,
row_count INT,
reserved_size VARCHAR(50),
data_size VARCHAR(50),
index_size VARCHAR(50),
unused... | If you don't want to write a script, you can also open the much underused 'Object Explorer Details' in SSMS (Shortcut key F7).
<img src="https://i.stack.imgur.com/zqWwB.png" alt="Top Level of Object Explorer Details">
From the Top-Level, open the Tables folder to get a list of all the tables in your database.
You ma... | https://dba.stackexchange.com |
117,926 | [
"https://security.stackexchange.com/questions/117926",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/104685/"
] | If someone adds a password to the bios of a computer and make it so that when booting the computer it prompts for the password, is there any way to bypass or overide that protection?
| Take out the CMOS battery, which is on the inside of the computer on the mother board. Wait for 20-30 seconds (less time may be needed, but the exact time varies). This is normally a button battery. Put the battery back, boot, and there should be no more BIOS password.
| If you know the brand of the motherboard, you can find the right software to reset it. I had used it long time ago. However, you may need to boot it from A: drive if there is any :-) , otherwise you may use a CD drive. Another way is to short the clear CMOS jumper on the motherboard itself if one is present.
Besides... | https://security.stackexchange.com |
131,470 | [
"https://physics.stackexchange.com/questions/131470",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57434/"
] | For example if a body in motion experiences time dilation, why does it see a body at rest slow down relative to it? wouldn't it make more sense if the body at rest has a faster clock relative to it?
| No, since by the principle of relativity: A body in constant velocity motion cannot determine whether <strong>it</strong> is in motion in a certain direction or whether everything else is in motion in the other direction. No physical experiment can determine this hence for all purposes a body in motion will simply clai... | "How do we know that clocks slow down relative to each other?"
Experimentally. This has been observed many times in the lab. The same answer is true for ANYTHING in physics and science in general. We only know that it is true, because we have experimental evidence for it.
| https://physics.stackexchange.com |
707 | [
"https://earthscience.stackexchange.com/questions/707",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/10/"
] | Cloud forcing is still one of the major uncertainties of radiative forcing in climate modeling because there are so many uncertainties in it (and parametrizations). But also because the timescale of cloud development are much shorter than the timescale that climate models are run at.
So I'm curious: are clouds much ea... | The answer to this question depends on what process one is interested in simulating well. As you know, short/mid-range weather prediction models and climate models have very different applications and goals.
Because the short range weather prediction model is typically of much higher resolution than climate models (~1... | It is also challenging to get clouds, rain etc. right in weather forecasts. Compared to climate applications the advantage in weather forecasts is that cloud information from the initial conditions can improve the cloud representation in the model. Unfortunately that information does not last that long in the model due... | https://earthscience.stackexchange.com |
26,634 | [
"https://electronics.stackexchange.com/questions/26634",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8125/"
] | I recently got my hands on some miniature DIP relays, and would like to prototype a circuit with them on a solderless breadboard. Unfortunately, these relays have standard 100 mil pin spacing, but 200 mil between rows, rather than the more usual 300 mil. Obviously I can't just put them in at a right angle... is any ada... | Best bet is usually some DIY if you have not got too many.
Use 200 mil centre sockets if available or socket strips,
<img src="https://i.stack.imgur.com/LFuxJ.jpg" alt="enter image description here">
or cut a socket in two and solder two strips onto a piece of veroboard/vector board/whatever you call board with co... | Solder wires to the relay pins and stick the other ends of the wires into the breadboard. After all, <b>it's a breadboard</b>, meaning it's for one-off testing. Geesh, sometimes people get so hung up in the process they forget the original intent.
| https://electronics.stackexchange.com |
95,503 | [
"https://mathoverflow.net/questions/95503",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17047/"
] | Smooth vector fields are in a one-to-one relationship with flows $\Phi: D \subseteq M\times \mathbb{R} \rightarrow M$,
$$X_m = {\frac{d}{d t}}_{t=0} \Phi(m, t),$$
and by the symplectic form also with 1-forms
$$X \longleftrightarrow \; - \iota_X \omega. $$
The following is well known (e. g. Abraham Marsden, Propositio... | The diffeomorphisms which are generated by (time-dependent) Hamiltonian vector fields are said to be Hamiltonian diffeomorphisms. Hamiltonian diffeomorphisms form a subgroup of the group of symplectic diffeomorphisms (actually, they are a subgroup of the connected component of the identity).
As you observe, locally t... | Given a symplectic vetor field, you may try to build a hamoltonian function the following way. Fix some point P. For any point Q, choose some curve from P to Q, and define H(Q) to be the flux of the vector field across the chosen curve (infinitesimal symplectic area swept by the curve when you push it by the flow durin... | https://mathoverflow.net |
5,286 | [
"https://electronics.stackexchange.com/questions/5286",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1616/"
] | I just bought my first analog oscilloscope (GoldStar OS-7020A) and noticed it has a port on the front labeled "ground". What exactly is this port for?
I thought it might be for plugging in a ground clip for probes that don't have one included, but there are two channels and only one ground port, so I'm not sure. Is it... | Most oscilloscopes have a safety ground. This connects to the earth ground on the plug and also to the case. The thinking is if you wire it up wrong worst case you trip the GFI/RCD instead of shocking yourself or damaging the instrument.
As an oscilloscope is usually a bench instrument it is not isolated from the main... | That terminal is the <em>case-ground</em> of the oscilloscope.
Assuming your oscilloscope is using a three-pin plug, it is connected through the device's power-cord to ground.
It's generally used for controlling your ground-current routing, when you are trying to make high-precision measurements, which normally invo... | https://electronics.stackexchange.com |
64,682 | [
"https://electronics.stackexchange.com/questions/64682",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22214/"
] | Does anyone know whether two circuit L293D can built above themselves that it allows flow high current?
| Here's what the L293 output stage looks like: -
<img src="https://i.stack.imgur.com/zPkHR.jpg" alt="enter image description here" />
I didn't see anything in the product pdf that says that they can be "effectively" paralleled but it's quite possible there was some small print somewhere or I was being stupid. ... | Recommended or not, soldering one of these chips atop another was in fact common practice back in the day.
Today there are many other alternative parts which it would be worth considering instead.
| https://electronics.stackexchange.com |
87,558 | [
"https://security.stackexchange.com/questions/87558",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/32204/"
] | As I send this question as a request to yahoo's server, the information in the request will be encrypted with yahoo's public key (which is available for everyone). Then the information will arrive at the server. There it will be decrypted with yahoo's server private key. Will Yahoo's server send me a response
<br>
afte... | That's not quite what happens. As public/private key encryption is more expensive than symmetric encryption, its use is minimal. During the SSL handshake, the client and server agree upon a shared symmetric key that they use for bulk encryption. The remainder of the communication then occurs using this symmetric key. T... | You are not connecting to public web sites with a certificate of your own. The server does have a key pair in its certificate. Therefore, yahoo can't identify you; but you can identify yahoo. Setting up an encrypted link is actually unrelated to the certificates.
A simplified way to think of SSL is: 1) identifica... | https://security.stackexchange.com |
385,031 | [
"https://physics.stackexchange.com/questions/385031",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/153368/"
] | I am unable to reproduce the calculation of the sunset diagram for $\phi^4$ theory in Pierre Ramond's Fied Theory a Modern Primer. This is the second edition chapter 4.4. He starts with eq. (4.4.19)
\begin{equation}
\Sigma(p) = \frac{\lambda^2 (\mu^2)^{4-2\omega}}{6} \int \frac{d^{2\omega}\ell}{(2\pi)^{2\omega}} \frac{... | Silly me, it is the 't Hooft Veltman regularisation scheme explained 5-6 pages earlier. I guess that's what happens when you start reading a section in the middle of the book.
| <span class="math-container">$$
I(p)=\int\frac{d^D p_1}{(2\pi)^D}\frac{d^Dp_2}{(2\pi)^D}\frac{1}{(p_1^2+m^2)(p_2+m^2)[(p+p_1+p_2)^2+m^2]}.
$$</span>
<span class="math-container">$$
I(p)=-\int\frac{d^D p_1}{(2\pi)^D}\frac{d^Dp_2}{(2\pi)^D}\frac{1}{2D}(p_1^\mu\frac{\partial }{p_1^\mu}+p_2^\mu\frac{\partial }{p_... | https://physics.stackexchange.com |
2,835,209 | [
"https://math.stackexchange.com/questions/2835209",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I know that the tangent is on the form $y=ax+b$ but how should I show this one:
Let $f:\mathbb{R}→\mathbb{R}$ be a differentiable function.
Consider a sample point $(x_0, f(x_0))$.
(a) determine the tangent line at $f(x_0)$, i.e. the straight line $l(x)=ax+b$, that passes through $f(x_0)$ with slope $a = f'(x_0)$.
(... | What do we know about the tangent line at the point $(x_0, f(x_0))$? We know it has slope $f'(x_0)$ and it passes through the point $(x_0, f(x_0))$. Remember the point-slope form of the equation of a line? $y-y_0 = m(x-x_0).$
Alternatively, you could start with $y=mx+b$ and plug in the slope and the know point
$$f(x... | The tangent line has a common point $l(x_0) = f(x_0)$ and the slope in common with $f$: $l’(x) = f’(x_0)$.
Here $l’(x) = a$, and $l(x_0) = a x_0 + b = f(x_0)$.
This results in $l(x) = f’(x_0) (x-x_0) + f(x_0)$ which I remember by the first order Taylor expansion of $f$ around $x_0$.
| https://math.stackexchange.com |
3,308,586 | [
"https://math.stackexchange.com/questions/3308586",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/17341/"
] | Is it possible to define a similar form of Argand's formula but for quaternions?
In the sense
<span class="math-container">$$ \cos(nA)+i\cos(nB)+j\cos(nC)+k\cos(n) =(\cos(A)+i\cos(B)+j\cos(C)+k\cos(D))^{n}, $$</span>
where <span class="math-container">$A, B, C, D$</span> are the angles of the quaternion with respec... | A unit quaternion can be written as
<span class="math-container">$$q=\cos t+(bi+cj+dk)\sin t$$</span>
where <span class="math-container">$b^2+c^2+d^2=1$</span>. Then
<span class="math-container">$$q^n=\cos nt+(bi+cj+dk)\sin nt.$$</span>
This just follows from the usual complex case: there's an isomorphism between
<span... | Since @LordSharktheUnknown discussed the trigonometry, I'll answer your later questions. Do you want <span class="math-container">$w:=z_1/z_2$</span> to satisfy <span class="math-container">$z_1=z_2w$</span> or <span class="math-container">$z_1=wz_2$</span>? It matters, which is why we don't usually write such expressi... | https://math.stackexchange.com |
702,481 | [
"https://physics.stackexchange.com/questions/702481",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/106906/"
] | I have two questions concerning Wigner's transformation law for irreps of the Poincare group:
<span class="math-container">\begin{equation}
U[\Lambda,\vec{a}]\vert p,\sigma\rangle=e^{ip\cdot a}D_{\sigma'\sigma}[\Lambda;p]\vert \Lambda p,\sigma'\rangle
\end{equation}</span>
<strong>Question 1:</strong> <em>Should this t... | (1) The value in calories that you've taken is very likely in food calories (<span class="math-container">$\text{Cal}$</span>), because <span class="math-container">$1\,900\,\text{cal}$</span> a day is too little for an average human. The conversion is:
<span class="math-container">$$1\,\text{food calorie (Cal)} = 1\,0... | <blockquote>
energy consumption in watts
</blockquote>
watt is unit of power, which is joule/second, i.e. energy/time.
1 kcal is 4184 J. 1900 kcal is 7.949.600 J.
1 day has 24 hours or 1440 minutes or 86400 seconds.
7.949.600 J/day equals 92 J/second or 92 W. This number is close to basal human metabolism rate.
If you ... | https://physics.stackexchange.com |
25,006 | [
"https://mechanics.stackexchange.com/questions/25006",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/9164/"
] | Many of the European manufacturers of cars and motorcycles publish their ICE power numbers to reflect kW rather than HP.
<strong>Is there a reason for this?</strong>
<strong>What is the conversion for kW to HP?</strong>
| Wikipedia has this nice table:
<pre><code> PS hp kW
1 PS = 1 0.98632 0.735499
1 hp = 1.01387 1 0.74570
1 kW = 1.35962 1.34102 1
</code></pre>
Finally, this are all different measures of power.
PS an hp are both a measure of t... | <em>It's like asking why do certain countries drive on the left side of the road and other on the right side?</em>
<strong><em>kW is part of the SI system of units. Horsepower is a legacy from the imperial units system.</em></strong>
kW stands for kilo-watt - a measure of power, or energy per unit time, named after t... | https://mechanics.stackexchange.com |
9,415 | [
"https://mathoverflow.net/questions/9415",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1358/"
] | In "Random Matrices and Random Permutations" by Okounkov it says, "It is classically known that every problem about the combinatorics of a covering has a translation into a problem about permutations which arise as the monodromies around the ramification points." Apparently, this is called the "Hurwitz encoding" but I ... | <strong>What it means for a covering of a sphere to be branched:</strong> Let $f:X \to Y$ be a map of Riemann surfaces. We are particularly interested in the case that $Y$ is $\mathbb{CP}^1$; in this case, $Y$ has the topology of a sphere. At most points $y$ in $Y$, there will be a neighborhood $V$ of $y$ so that $f^{... | What do you mean by a covering?
It sounds like you're talking about the action of the fundamental group of the base space on $\pi_0$ of the fibre, for a covering space. Or some variant of it for a branched covering space.
Take a look in Hatcher's Algebraic Topology textbook in Section 1.3, "Representating Coveri... | https://mathoverflow.net |
424,565 | [
"https://electronics.stackexchange.com/questions/424565",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70761/"
] | I'm trying to switch an analog audio line from its given channel to analog ground when a specific line goes low (in this case, the DACs charge pump goes low when it shuts down).
Would a tri-state buffer degrade or in anyway impact the AC signal going from the A side to the Y side?
| Any digital logic part will seriously distort an analog audio signal.
A digital gate will only output either a logic High or a logic Low, with nothing in between, while an analog signal must smoothly vary between its positive and negative peaks.
| No, there are specialised "analogue switch" ICs for this.
| https://electronics.stackexchange.com |
293,106 | [
"https://electronics.stackexchange.com/questions/293106",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/141256/"
] | I'm wondering whether to use an isolated CAN transceiver or not. A few of the nodes in the vehicle use a TI ISO1050 which has an isolated power supply and run GND and 5 V with CAN-Low and CAN-High signals so they have a common ground. I wanted to use a TI SN65HVD232 because of the reduced package size and no need ... | The issue is not whether <em>your</em> system is critical, but whether there are <em>any</em> critical functions that will fail if the bus is disabled (made unavailable for any communication) by a fault on your "non-critical" device.
A bus means that all devices share a common channel of communication. If your device ... | If you want just for datalogging, then I presume this data logging device is a computer or handheld device that has its own power supply. In such case the galvanic isolation between these two separate systems seems the right way to go. without galvanic isolation you can face a risk of destroying all devices on CAN bus,... | https://electronics.stackexchange.com |
2,310,339 | [
"https://math.stackexchange.com/questions/2310339",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/449209/"
] | $\forall set\; A,B,C\;\;$Let $a=card(A),\;\; b=card(B),\;\; c=card(C)$
<strong>Claim</strong>
prove $(ab)^c = a^cb^c$
<hr>
We need to show that $(A\times B)^C \approx A^c \times B^c$.
Thus let $\pi_A:A\times B\rightarrow A\;$ $\pi_B: A\times B \rightarrow B$ be the projections.
then the function: $$\phi:(A\tim... | Just writing that doesn't show the function is invertible; one could just as easily say that the inverse of the function sending $x$ to $x^2$ is the inverse of the function sending $x^2$ to $x$, even though $x\mapsto x^2$ (defined on $\mathbb R$) is not invertible.
Here's the inverse: let $g:A^C\times B^C\to (A\times... | The prescription for the inverse is:$$\langle f,g\rangle\mapsto\{\langle c,\langle f(c),g(c)\rangle\rangle\mid c\in C\}$$
Written as a set of ordered pairs it is:$$\psi:=\{\langle\langle f,g\rangle,\{\langle c,\langle f(c),g(c)\rangle\rangle\mid c\in C\}\rangle\mid f\in A^C\wedge g\in B^C\}\subseteq (A^C\times B^C)\ti... | https://math.stackexchange.com |
146,987 | [
"https://dba.stackexchange.com/questions/146987",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4514/"
] | I need to consolidate several older instances to SQL Server 2016 Enterprise on a single VM. Since all of the databases are third party vendor systems, they are a sprawling mess of <em>SQL Agent jobs</em>, <em>custom roles</em>, <em>dynamically created users</em>, and demands for doing installs/upgrades with <em>SA acce... | Perhaps others can add more info but I'd say first ensure that sharing a server is fully supported by the vendors you want to clump together, and get that in writing.
Then consider how important it is for these apps to maintain different instance level settings such as memory/processor/MAXDOP/Parallel threshold/Supp... | Obviously an opinion here, but...
Personally, I think separate instances is definitely the way to go. We have several servers at my work like that. You have so much more control of stuff, especially server related objects like linked servers, etc. Being able to restart one instance and leave the others alone is a va... | https://dba.stackexchange.com |
958,586 | [
"https://math.stackexchange.com/questions/958586",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/115078/"
] | My attempt at integrating <span class="math-container">$\cos^3(x)$</span>:
<span class="math-container">$$\begin{align}\;\int \cos^3x\mathrm{d}x &= \int \cos^2x \cos x \mathrm{d}x
\\&= \int(1 - \sin^2 x) \cos x \mathrm{d}x
\\&= \int \cos x dx - \int \sin^2x \cos x \mathrm{d}x
\\&= \sin x - \frac {1}{... | If you let $u = \sin x$, then $du = \cos x \ dx,$ and
$\int \sin^2x \cos x \ dx $ becomes $$\int u^2 du = \frac{1}{3} u^3 + C.$$
Then you substitute $u=\sin x$ back in.
| Notice that applying the chain rule to $\frac{1}{3}\sin^3(x)$ yields $\sin^2(x)\cos(x)$. Indeed you have $\int\sin^2(x)\cos(x)\,dx=\int\sin^2(x)\,d(\sin(x))=\frac{1}{3}\sin^3(x)+c$
| https://math.stackexchange.com |
160,141 | [
"https://physics.stackexchange.com/questions/160141",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/63535/"
] | I am asking whether the following Lagrangian for a point moving in a conservative field, can be correct :
$L(r, v, \omega) = \frac {mv^2}{2} + \frac {I \omega^2}{2} - U(r)$.
$r$ is the distance between the equipotential surface on which the movement begins and the equipotential surface on which the movement ends, $v... | The answer to the title of this question, "Can a conservative field produce a torque?" is yes. For example, a non-uniform gravity field (e.g., the Earth's gravity field) results in a gravity gradient torque on an object with a non-spherical mass distribution. This torque is sometimes problematic for artificial satellit... | I'm not sure about the notation, so there will be a bit of guessing here. I assume $v = \dot r$, so the kinetic term can be interpreted to be that of a point moving on a plane, described by polar coordinates. Now take any radial potential, which by the rotational symmetry generates a central field. Let us consider Kepl... | https://physics.stackexchange.com |
37,570 | [
"https://mathoverflow.net/questions/37570",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4643/"
] | Let $X$ be a smooth projective variety over $\mathbb{C}$.
And let $L$ be a big and nef line bundle on $X$.
I want to prove $L$ is semi-ample($L^m$ is basepoint-free for some $m > 0$).
The only way I know is using Kawamata basepoint-free theorem:
Theorem. Let $(X, \Delta)$ be a proper klt pair with $\Delta$ effecti... | Here is a simple example of a linear space and 2 disjoint convex sets such that there is no linear functional separating the sets. Note that the notions of convexity and linear functional <em>do not</em> require any norm or whatever else. You can introduce them, if you want, but they are completely external to the prob... | Take $K_1$ to be a proper dense subspace and $K_2$ the translate of $K_1$ by a vector not in $K_1$.
| https://mathoverflow.net |
19,064 | [
"https://security.stackexchange.com/questions/19064",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10074/"
] | I've resisted the idea of password managers for a long time. Bringing together passwords for all your online accounts in one place that is only protected by difficult-to-remember master password doesn't sound like a good idea to me.
However, I've been doing lots of password resets lately. I try to vary my passwords as... | It certainly is more <strong>convenient</strong>. But i doubt it would be more secure.
For one thing, such a setup introduces another point of failure compared to the master password solution. The attack surface would be larger as there would be another target (Google), to compromise instead of just your password man... | I think your reasoning is sound. You would get much stronger passwords, and if anything, I believe <em>that</em> is worth more than the added risk of using a password vault.
The alternative – being a human password vault – is neither feasible nor very secure (unless your mind is amazing). With passwords getting cracke... | https://security.stackexchange.com |
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