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 |
|---|---|---|---|---|---|
50,080 | [
"https://stats.stackexchange.com/questions/50080",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20188/"
] | I have a set of real numbers. I need to estimate the quantile of a new number. Is there any clean way to do this in R? in general?
I hope this is not ultra-trivial ;-)
Much appreciated for your response.
PK
| As whuber pointed out, you can use <code>ecdf</code>, which takes a vector and returns a function for getting the percentile of a value.
<pre><code>> percentile <- ecdf(1:10)
> percentile(8)
[1] 0.8
</code></pre>
| To expand on what whuber and cwarden stated, sometimes you want to use a function in a "classical" R way (for example, to use inside a magrittr pipe). Then you could write it yourself using <code>ecdf()</code>:
<pre><code>ecdf_fun <- function(x,perc) ecdf(x)(perc)
ecdf_fun(1:10,8)
>[1] 0.8
</code></pre>... | https://stats.stackexchange.com |
42,089 | [
"https://softwareengineering.stackexchange.com/questions/42089",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4091/"
] | I seem to remember that linked lists, recursion, pointers, and memory management are all good examples of stumbling blocks - places where the aspiring programmer typically ends up spending significant time trying to understand a concept before moving on and improving, and many end up giving up and not improving.
I'm l... | My list would be:
<ol>
<li><strong>Pointers:</strong> the concept of a reference, being aware where the data is stored and the arithmetic on them are quite confusing at first.</li>
<li><strong>Linked lists:</strong> In my experience this is the first data structure with some logic operations different from arrays that... | Having taught, been taught, and studied teaching, the big three are:
<ol>
<li>Pointers.</li>
<li>Pass by value vs pass by reference. </li>
<li>Recursion.</li>
</ol>
Those are the 3 items that weed out 2/3rds of CS majors.
| https://softwareengineering.stackexchange.com |
69,342 | [
"https://cs.stackexchange.com/questions/69342",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/65278/"
] | I was wondering what the limitations to an algorithm that runs in O(n!). For example lets take an algorithm that generates all permutations of a list. Now what i am wondering is what the upper bound would roughly be for size of list. I understand that this can vary based on ram/memory. Let's say that this would be ran ... | You can certainly describe the inner workings of your project as an algorithm. It takes an input (whatever information it obtains from the browser) and produces an output, as a result of some scheme of calculations. Perhaps it needs to read inputs during the course of its calculations (depending on the first inputs, it... | In my opinion anything that is language specific would not be considered an algorithm but a solution. So in your case you came up with a javascript solution to solve your problem. I think you answered your own question when you said you could not write the pseudocode. If your solution can not be written in psuedocode t... | https://cs.stackexchange.com |
464,886 | [
"https://physics.stackexchange.com/questions/464886",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/135440/"
] | In the context of Statistical Mechanics I have to show that the following integral is zero:
<span class="math-container">$$\int \sum_{i=1}^{3N}(\frac{\partial O}{\partial q_i}\frac{\partial H}{\partial p_i}-\frac{\partial O}{\partial p_i}\frac{\partial H}{\partial q_i})\rho (P,Q)d^{3N}pd^{3N}q$$</span>
Where <span cl... | Two things that may help (following on from the comments under the question):
<ol>
<li>"The probability distribution describing the ensemble has constant value on each energy surface." This means that <span class="math-container">$\rho$</span> can be written as a function of <span class="math-container">$H$</span>, wh... | After a good night of sleep everything became clearer haha.
Between @Subhaneil Lahiri 'S answer, @LonelyProf comment and some re reading of the script by myself I could finally answer. The main things that I forgot were Liouville's theorem (<span class="math-container">$\Phi_t(P,Q)$</span> is area preserving, meaning <... | https://physics.stackexchange.com |
405,907 | [
"https://mathoverflow.net/questions/405907",
"https://mathoverflow.net",
"https://mathoverflow.net/users/380650/"
] | <span class="math-container">$$\ \int_0^{\pi} \bigl(\sin(x)\bigr)^{2n-2k+1} e^{a\cos(x)} dx , \qquad a,n,k\in\mathbb Z.$$</span>
I tried to solve this integral by parts, but I didn't get any result. I look forward to your experience.
| <span class="math-container">$$\int_0^{\pi} (\sin x)^{2n-2k+1} e^{a\cos x} dx =\int_{-1}^1 (1-\xi^2)^{n-k}e^{a\xi}\,d\xi$$</span>
<span class="math-container">$$\qquad\qquad=\sqrt{\pi }\, 2^{-k+n+\frac{1}{2}} a^{\frac{1}{2} (2 k-2 n-1)} \Gamma (-k+n+1) I_{\frac{1}{2} (-2 k+2 n+1)}(a),\;\;n-k+1>0,$$</span>
with <span... | <span class="math-container">$$\int_{0}^{\pi}(\sin x)^{2n-2k+1}e^{a\cos x}dx$$</span>
To avoid writing <span class="math-container">$n-k$</span> all the times let <span class="math-container">$v=n-k$</span>.
<span class="math-container">$$u=\cos x \implies du=-\sin x\,dx$$</span>
<span class="math-container">$$\int_{-1... | https://mathoverflow.net |
109,135 | [
"https://physics.stackexchange.com/questions/109135",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I am self-studying from a text in QM. Well defined states are mentioned several times. By and large these are consistent and seem to be readily apparent:
<ul>
<li>states of well defined energy are basis kets.</li>
<li>if $Q$ is an observable, any arbitrary ket can be represented as a linear combination of states {$q_i... | The statement you quote is correct and slightly profound till you understand it well enough that it becomes simple :-)
If a system is in an energy eigenstate, then it must exist in that state for all time -- from $t \rightarrow - \infty$ to $t \rightarrow + \infty$.
<hr>
A few comments:
<ol>
<li>Clearly, any physi... | Here are some quotes from A. Peres, "Quantum Theory: Concepts and Methods" which seem quite relevant to me, which I saw in a review on Amazon.
<blockquote>
Quantum phenomena do not occur in a Hilbert space, they occur in a laboratory". (Preface)
The essence of quantum theory is to provide a mathematical ... | https://physics.stackexchange.com |
3,591 | [
"https://quant.stackexchange.com/questions/3591",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/2478/"
] | I am hoping any answers can be threaded somewhere between "don't be naive" and starting a quasi-political flame.
Transparency is suppose to be good for markets and also a social good. The market reflecting the availability of all known information is a premise accepted by many. Why then is the disparity between acce... | On the paper you are right: the market data are close to a <em>public good</em> and could be free because of that. Nevertheless in a fragmented landscape, each trading venue is contributing specifically to the price formation process. Each of them invest that for, and it is thus not unfair to get revenue that for.
If ... | I think Lehalle answer is very good but I would like to answer in a slightly different manner, maybe from an economical point of view.
I think the real question is <em>What are market data fees charged for?</em>.
Assume the whole data was available to anybody for free, then nobody would be willing to pay for it. Ther... | https://quant.stackexchange.com |
191,939 | [
"https://security.stackexchange.com/questions/191939",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/7/"
] | Consider the following line from <code>/etc/passwd</code>:
<pre><code>sadeq:x:1000:1000:Mohammad Sadeq Dousti,,,:/home/sadeq:/bin/custom-script.sh
</code></pre>
The last part, <code>/bin/custom-script.sh</code>, shows the command/script to be run when the user logs in to the system. Currently, it's a simple Bash scri... | With the sample script you have posted, the restricted user can for example learn a whole lot about the system, like names of other users and installed programs. E.g.
<pre><code>What is your name?
> /home/*
Hi /home/foo /home/bar /home/sadeq
</code></pre>
The actual script you have may be exploitable in similar w... | Assume there is a (probably unintentional) backdoor.
The default <code>/etc/passwd</code> on Sun workstations of the early 1990s included an entry something like this:
<pre><code>games::0:0:games:/nopath:/bin/false
</code></pre>
In other words, an account named 'games' with no password. Apparently the genius who ca... | https://security.stackexchange.com |
45,361 | [
"https://physics.stackexchange.com/questions/45361",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7670/"
] | What maintains quark spin alignments in baryons?
The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed.
In contrast, the $\Delta^+$ particle (which like the proton is $uud$) and the $\Delta^0$ particle (which like the neutr... | The question is "what maintains the orientation". What maintains it is simply the angular momentum conservation. If the total angular momentum has $J^2=j(j+1)\hbar^2$ for $j=1/2$ or $j=3/2$, it obviously can't change because the whole vector $\vec J$ (including its length) is conserved. An up-spin may not spontaneously... | I can only imagine that the anti-symmetry of the wave-function maintains that order. Thus is one takes into account all the quantum numbers of the baryons, since the baryons are fermions, they obey the Fermi-Dirac statistics, and the wave-function must be anti-symmetric.
| https://physics.stackexchange.com |
429,901 | [
"https://physics.stackexchange.com/questions/429901",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/170142/"
] | What does dipole moment physically signify? I know it is the product of 2 charges and distance between them. Like momentum is the product of mass and velocity, but physically it shows the quantity of motion the larger the momentum the harder it would be to stop a moving body. I know this question has been asked, but no... | Actually, the dipole moment is a vector which is the product of the charge magnitude and the displacement vector pointing from the negative to the positive charge. An electric dipole consists of 2 equal magnitude, opposite-signed charges.
The physical significance is it gives a measure of the polarity/polarization of ... | A simple conceptual picture is that the dipole moment is a kind of average quantity which lets you describe the resultant torque from an external field.
For example, for two charges, <span class="math-container">$q$</span> and <span class="math-container">$-q$</span>, the dipole moment <span class="math-container">$\b... | https://physics.stackexchange.com |
90,443 | [
"https://cs.stackexchange.com/questions/90443",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/40972/"
] | <ol>
<li>Does $2^{n-1}$ and $2^{n}$ share the same complexity complexity class as <strong>exponential</strong> named as $O(2^n)$? So the former belongs to $O(2^n)$ even though it's one order lower?</li>
<li>What is the name of the complexity complexity class of $O(n2^{n})$?</li>
</ol>
| Consider the simply-typed $\lambda$ calculus: this is one of the simplest functional languages you can define.
It is very common to interpret it in a Cartesian closed category (CCC). Indeed, CCCs are the "ideal" categorical setting where to interpret simple types.
CCCs, being categories, admit morphisms composition a... | Your question sounds redundant to me. By definition of <strong>category</strong> whenever two morphisms with common object $f\colon A \rightarrow B$ and $g\colon B \rightarrow C$ exist, then their composition $g\circ f \colon A \rightarrow C$ <strong>must</strong> exists as another arrow in that same category. (otherwi... | https://cs.stackexchange.com |
371,728 | [
"https://electronics.stackexchange.com/questions/371728",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/166010/"
] | This is my first post here.
My wife uses a makeup mirror which has 10 x BA9s in series. Each lamp is 3W 24V and since we are in Europe they run on AC 230V nominally (reading off a multimeter is sometimes 243V and even 248V).
A few months ago one of the original bulbs burnt out and the only local replacement I found w... | Probably worse If the LEDs are only DC, and just as bad if AC in series which is non-linear.
Now the 4W lights probably are enclosed so they get hotter and reduce life from 3000h by 50% for every 10’C rise above open ambient. A Triac dimmer could solve that as well as a tiny low speed fan. You could use 12V stripLED... | Instead of using 24V lamps I would use 28V lamps if you stick with incandescent. #1873 comes into mind. But yes you can get ac rated led bulbs. and i would use the ones with the built in current limiting if you go that direction. They will state a wide range of operation (6 Volt-28 Volt AC/DC I've seen) but they cost q... | https://electronics.stackexchange.com |
261,659 | [
"https://physics.stackexchange.com/questions/261659",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/120635/"
] | I understand (or rather, I have been told, but do not understand) that a large mass can distort space by its rotation. While I am somewhat familiar with the concept of a mass distorting space and thereby creating what we experience as gravity, I haven't been able to find any explanation of how the rotation of such a ma... | Actually, the explanation as to why rotation of a mass affects the metric in principle is simple. Rotation means there is angular momentum, and angular momentum contributes to the energy-momentum-stress tensor in general relativity. If this was a nonrelativistic rotation we would say that the rotation carries kinetic e... | The bottom line is that space and mass do interact with one another. Otherwise, they would not tell one another "how to curve" and "how to move".
Therefore a moving (or rotating) mass and space will interact slightly differently. The interaction will drag with rotating mass. It may or may not be detectable depending u... | https://physics.stackexchange.com |
19,517 | [
"https://earthscience.stackexchange.com/questions/19517",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/18370/"
] | In chapter 13.1 in 'Mesoscale Meteorology in Midlatitudes' (Markowski and Richardson,2011) they use a Bernoulli equation and the hydrostatic equation and a lot of assumptions to derive an equation that predicts the height <span class="math-container">$z_{crit}$</span> at where an air parcel with an initial height of <s... | Start with the original equation. Let's first write the Hydrostatic equation:
<span class="math-container">$$\frac{\partial p}{\partial z}=-\rho g$$</span>
So let's prove that <span class="math-container">$$-g=c_p\theta\frac{\partial \pi}{\partial z}$$</span>
If we use the product rule, we observe <span class="math... | After looking back into this I found my error to lie in the long equation
<span class="math-container">$\dfrac{\partial \pi}{\partial z}=\left(\frac{1}{p_0}\right)^{\frac{R}{c_p}}\dfrac{\partial}{\partial z}\exp\left(\frac{R}{c_p}\log(p)\right)=\left(\frac{1}{p_0}\right)^{\frac{R}{c_p}}* \frac{T}{\theta}*{\frac{R}{c_... | https://earthscience.stackexchange.com |
1,264,992 | [
"https://math.stackexchange.com/questions/1264992",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/171771/"
] | Show that $\sin \dfrac{n \pi}{4}$ is divergent.
My attempt:
Consider the subsequences
$x_{4n}=\sin (n \pi)$, which converges to $0$,
and $x_{8n+2}=\sin \dfrac{2(4n+1) \pi}{4}$, which converges to $1$.
As the two subsequences converge to two different limits, the sequence is divergent.
My questions:
<ol>
<li... | A subsequence of a sequence $(f(n))_{n}$ is any sequence of the form $(f\circ g(n))_n$ where $g:\Bbb N \to \Bbb N$ is an increasing function. In your case, the defined sequences are indeed subsequences of $(x_n)_n$ taking $g(n)=4n$ and $g(n)=8n+2$ in each case.
Now, for each $n\in \Bbb N$:$$x_{4n}=\sin(n\pi)=0$$
and ... | For question 1.: Yes, and for question 2: Consider $a_n = \sin \left(\frac{n\pi}{4}\right)$, and look at $\lim \text{ sup $a_n$}$ and $\lim \text{ inf $a_n$}$ and show they are different. You can infact determine these limits.
| https://math.stackexchange.com |
1,030,255 | [
"https://math.stackexchange.com/questions/1030255",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/164795/"
] | When considering the commutative ring $R$ over itself, then this $R$-module is isomorphic to $R$, but if $I$ is an ideal of $R$, then it is a submodule, if this submodule is free too, then it is isomorphic to $R^n$, as its in $R$, thus it is isomorphic to $R$, it is a contradiction.Any mistake I made in it?
| By definition, your ideal is isomorphic to $R^n$ but this isomorphism is quite abstract and your proof shows nothing.
Counter-example : the ideal $2 \mathbb{Z}$ in $\mathbb{Z}$.
Exercise : show that your property is true if and only if $R$ is a field.
| There are rings for which every right ideal is free, and it's even possible for them to have rank more than 1. If such a ring is also commutative, it is a principal ideal domain, and all the ideals are isomorphic (as modules) to the ring.
| https://math.stackexchange.com |
31,724 | [
"https://dba.stackexchange.com/questions/31724",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1321/"
] | Can we patch Microsoft SQL server using WSUS?
Is it not recommended?
| Here's a simple query to match up foreign keys to their referenced tables/columns:
<pre><code>SELECT
o1.name AS FK_table,
c1.name AS FK_column,
fk.name AS FK_name,
o2.name AS PK_table,
c2.name AS PK_column,
pk.name AS PK_name,
fk.delete_referential_action_desc AS Delete_Action,
fk.updat... | This query nets you all of the FK relationships in the database - FK constraint name, schema/table of referencing table, referencing column name, schema/table of referenced table, and referenced column name. There will be multiple rows for a multi-column constraint.
<pre><code>SELECT
FK = OBJECT_NAME(pt.constrain... | https://dba.stackexchange.com |
21,287 | [
"https://mathoverflow.net/questions/21287",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1851/"
] | I am looking for references talking about different ways to prove flag variety $G/B$ is projective variety. Now I have some in mind:
<ol>
<li>There is a proof in Humphreys Linear algebraic groups, he first prove $G/S$ is a complete algebraic variety hence a projective variety, where $S$ is a Borel subgroup of $G$ of l... | I'm not sure this is an answer, but it got too long to be a comment! The projectivity of $G/B$ seems to me to follow from two facts: a) a homogeneous space $G/H$ is always a quasi-projective variety (which is due to Chevalley), and b) the variety $G/B$ must be complete.
The first fact clearly has nothing to do with B... | Let $V$ be an irrep for a regular dominant weight, and $\vec v$ a high weight vector.
Then the $G$-stabilizer of $k\vec v \in {\mathbb P}V$ is $B$, so the $G$-orbit is $G/B$. I guess I need a bit more thought to say why it's closed, but I'm not sure this will really be different enough from your proofs above to bear th... | https://mathoverflow.net |
35,971 | [
"https://mathoverflow.net/questions/35971",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | What is the smallest ordinal alpha which is elementarily equivalent to some smaller ordinal beta with the signature (<)?
What is the corresponding ordinal beta?
What if we instead require that beta be an elementary substructure of alpha?
| The first-order theory of well-orderings was studied in great detail in a paper of Doner, Mostowski, and Tarski, "The elementary theory of well-ordering -- a metamathematical study" [Logic Colloquium '77, edited by A. Macintyre, L. Pacholski, and J. Paris, North-Holland (1978) pp. 1-54]. In particular, their Corollary... | As far as I can see the problems are fully discussed in "The elementary theory of well orderings" by Doner, Mostowski and Tarski mentioned already by Andreas Blass. Lemma 44 covers as Andreas Blass explained the elementary equivalence and Lemma 47 there answers the part on elementary substructures.
| https://mathoverflow.net |
97,097 | [
"https://mathoverflow.net/questions/97097",
"https://mathoverflow.net",
"https://mathoverflow.net/users/112114/"
] | In Mariusz Wodzicki's paper "Cyclic homology of differential operators," the following result is mentioned: for $D_M$ the algebra of differential operators on a smooth manifold $M$ we have that $HH_n(D_M) \cong H_{DR}^{2m-n}(M)$ where $m=\dim M$. I'm having trouble finding a reference for the Hochschild Cohomology of $... | Hi,
This is an instance of a more general fact concerning deformation quantization of symplectic varieties. The general theorem is:
`Let $X$ be an symplectic manifold, and let $A_\hbar$ be any quantization of the Poisson algebra $(C^\infty(X), \{, \})$. Then we have $HH^*(A_\hbar)\cong H_{DR}^*(X)$.
See the paper:... | There are many references for this fact, which is essentially a spectral sequence argument along with the Poincare Lemma. The full proof is in section 5 of "THE HOMOLOGY OF ALGEBRAS OF PSEUDO-DIFFERENTIAL SYMBOLS AND THE NON-COMMUTATIVE RESIDUE" by Brylinski and Getzler.
| https://mathoverflow.net |
48,622 | [
"https://cs.stackexchange.com/questions/48622",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/10478/"
] | We know that Turing machines and Lambda Calculus are equivalent in power. And There are proofs for that, I'm sure.
But is there an algorithm, a systematic way for us to convert a Turing machine into a Lambda Calculus expression? Is it impossible to have such algorithm? (meaning does it go down to undecidability or NP-... | Sure there is. I'm going to assume you can figure out how to convert Haskell into the lambda calculus; for a reference, look at the GHC implementation.
Now just to be clear: a Turing Machine is a (finite) map from <code>(State, Token)</code> pairs to <code>(State, Token, Direction)</code> triples. We'll represent th... | All proofs of the equivalence of these two models of computation are <em>constructive</em>, that is they describe an algorithm for converting a program from one model of computation to the other. However, I caution you that these proofs are probably rather informal, and may not satisfy you. You may get luckier if you c... | https://cs.stackexchange.com |
741,566 | [
"https://math.stackexchange.com/questions/741566",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/140743/"
] | Show that the terms of the sequence that satisfy $a_0=2, a_1=5, a_n=5a_{n−1}−6a_{n−2}$, for all $n\ge2$, are given by the formula $a_n=2^n+3^n$.
Not sure how to go about this problem. Can someone help? Thanks
${}{}{}{}$
| First check the base case:
$$
a_2
= 5a_1 - 6a_0
= 25 - 12
= 13
= 2^2 + 3^2.
$$
Now suppose that $a_k = 2^k + 3^k$ is true for all $k \leq n-1$. Then
\begin{align}
a_{n}
&= 5a_{n-1} - 6a_{n-2} \\
&= 5(2^{n-1} + 3^{n-1}) - 6(2^{n-2} + 3^{n-2}) \\
&= 2^{n-2}(5\cdot 2 - 6) + 3^{n-2}(5\cdot 3 - 6)\\
&= ... | A proof that uses the supplied answer:
It is true for 1 and 2.
Given the first two terms,
all subsequent terms are
determined by the recurrence.
$\begin{array}\\
5(2^{n-1}+3^{n-1})-6(2^{n-2}+3^{n-2})
&=5\cdot2^{n-1}-6\cdot 2^{n-2}+5\cdot 3^{n-1}-6 \cdot 3^{n-2}\\
&=10\cdot2^{n-2}-6\cdot 2^{n-2}+15\cdot 3^{n-2... | https://math.stackexchange.com |
76,188 | [
"https://dba.stackexchange.com/questions/76188",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/46188/"
] | This is my query
<pre><code>SELECT Id, productName, Largeimagepath, Discount, Price, Image FROM tablename1 where Active =1
union
SELECT Id, productName, Largeimagepath, Discount, Price, Image FROM tablename2 where Active =1
union
SELECT Id, productName, Largeimagepath, Discount, Price, Image FROM tablename3 where ... | Typically when using <code>UNION</code> and you need to know what table a specific row comes from, you'd use a hard-coded value stored in a column similar to:
<pre><code>SELECT Id, productName, Largeimagepath, Discount, Price, Image, 'Tablename1' as Source
FROM tablename1
where Active =1
union
SELECT Id, productNam... | You can try this with <code>UNION ALL</code>
as probably you need duplicate entry too as will adding table name it will be unique and performance will be also improved
<pre>
SELECT Id, productName, Largeimagepath, Discount, Price, Image, 'Tablename1' as TableName
FROM tablename1
where Active =1
UNION ALL
SELECT Id,... | https://dba.stackexchange.com |
3,356,788 | [
"https://math.stackexchange.com/questions/3356788",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I have seen holomorphic defined two different ways. The first is that a function f is holomorphic at <span class="math-container">$z$</span> if the limit <span class="math-container">$\lim\limits_{h \to 0} \dfrac{f(z + h) - f(z)}{h}$</span> exists and the second is that it is holomorphic if there exists a complex numbe... | If the function <span class="math-container">$\psi$</span> exists, then<span class="math-container">$$\lim_{h\to 0}\frac{f(z+h)-f(z)}h=\lim_{h\to0}\frac{ah+h\psi(z)}h=\lim_{h\to0}a+\psi(z)=a.$$</span>
And if the limit<span class="math-container">$$\lim_{h\to 0}\frac{f(z+h)-f(z)}h$$</span>exists and it is equal to <spa... | If you just define <span class="math-container">$\psi (\zeta)$</span> as <span class="math-container">$\frac {f(z+\zeta)-f(z)-a\zeta} {\zeta}$</span> for <span class="math-container">$\zeta \neq z$</span> and <span class="math-container">$0$</span> for <span class="math-container">$\zeta =z$</span> you can see easily t... | https://math.stackexchange.com |
280,479 | [
"https://dba.stackexchange.com/questions/280479",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/55587/"
] | This script was make in postgres, but I don't find their way to make it in mysql
<pre><code>DO
$do$
BEGIN
IF EXISTS (SELECT FROM pg_database WHERE datname = 'example_work_db') THEN
CREATE USER example_work_srv WITH ENCRYPTED PASSWORD 'P4ssw0rd.';
GRANT CONNECT ON DATABASE example_work_db TO example_work_srv;
... | The problem was solved by someone else in the team, the differences that I see in the provided setup document are:
<ol>
<li>Login as sys@xepdb1
</li>
<li>Instead of creating new table spaces, we now rename the table spaces in Oracle XE, with the following two commands:
ALTER TABLESPACE temp RENAME TO temporary_data;
AL... | To allow the user <code>system</code> to grant privileges on objects it doesn't own, use
<pre><code>GRANT ALL PRIVILEGES TO system WITH GRANT OPTION
</code></pre>
| https://dba.stackexchange.com |
9,185 | [
"https://mechanics.stackexchange.com/questions/9185",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4152/"
] | I'm working on a 98 Dodge Ram 2500 with a Magnum 360 V8 (roller cam shaft). It had a cracked head on one side, so I purchased a pair of remanned heads from an eBay retailer. These heads are the 466/671 combination (as expected). The problem is, the heads which I pulled off are an identical set (both 466 heads - this en... | After an exhaustive search on the internet, I came to the conclusion that while the two heads have a different part number and are different in some very minor ways, I have just thrown the heads on there and done the deed. If there is a significant difference I couldn't see, there doesn't seem to be an issue with them.... | The heads are the same, left or right
When it is stated left on the vehicle it means that when you are sitting in the driver's seat, not when looking at the vehicle from the front.
| https://mechanics.stackexchange.com |
2,743,750 | [
"https://math.stackexchange.com/questions/2743750",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/472288/"
] | I'm trying to figure out my mistake here.
Find the Derivative of $$\frac {x^2}{x-1}$$
Now I want to simplify this and use the product rule instead of the quotient rule:
$$(x^2)(x-1)^{-1}$$
Use the product rule:
$$[\frac {d}{dx}x^2](x-1)^{-1}+[{\frac {d}{dx}(x-1)^{-1}]}(x^2)$$
Simplify left side:
$$\frac {2x}{x-1}$$
Si... | Note that
$$\frac {2x}{x-1}-\frac {x^2}{(x-1)^2}=\frac {2x(x-1)-x^2}{(x-1)^2}=\frac {x^2-2x}{(x-1)^2}$$
| This line is not correct
$$\frac {2x-x^2}{(x-1)-(x-1)^2}$$
It should be
$$\frac {2x}{(x-1)}-\frac {x^2}{(x-1)^2}=\frac {2x(x-1)-x^2}{(x-1)^2}=\frac {x^2-2x}{(x-1)^2}$$
| https://math.stackexchange.com |
147,784 | [
"https://dba.stackexchange.com/questions/147784",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/104289/"
] | I have a table with the following format:
<pre><code>id description1 description2
123 null abcd
123 zyxw abcd
124 null efgh
124 vuts efgh
125 null ijkl
126 null mnop
</code></pre>
Basically, I want S... | <pre><code>SELECT id,
description1 = MAX(description1),
description2 = MAX(description2)
FROM dbo.MyTable
GROUP BY id
ORDER BY id;
</code></pre>
| With Teradata, I was able to solve this with:
<pre><code>SELECT id, description1, description2 FROM dbo.MyTable
QUALIFY ROW_NUMBER() OVER (PARTITION BY id ORDER BY description1 nulls last) = 1
</code></pre>
However, since I didn't specify Teradata and Andy's generic answer works great, it's definitely the best!
| https://dba.stackexchange.com |
412,124 | [
"https://softwareengineering.stackexchange.com/questions/412124",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/206728/"
] | I regularly review the technical debt tickets from my backlog, to prioritize them and remove those which are no longer relevant (fixed by some other development, obsolete...) Among those with high priority, we take 2 or 3 in each sprint, and this way our codebase is healthy for the moment.
The problem is that all those... | I would say that there isn't a single best answer for this problem. You've got a few overall strategies, you would probably be best doing all of them. But the information should never be deleted, but it can be transformed.
<strong>Keep them in the issue tracker with the rest of the project</strong>
For high priority or... | You are considering deleting the records of genuine problems with the codebase because the product owner wants a shorter backlog?
For me, the only reason to delete (close) an item in the backlog is because you decide it will <em>never</em> be implemented, not because it won't be implemented for a while. Also, in an agi... | https://softwareengineering.stackexchange.com |
1,516 | [
"https://dba.stackexchange.com/questions/1516",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1074/"
] | I've set up a Data Source Connection to the Adventure Works DW database using the service's credentials.
I'm creating a dimension using the <code>DimDate</code> table. To simplify things, I'm using only the <code>Calendar Quarter</code>, <code>Calendar Year</code>, <code>Day Number of Month</code>, <code>English Mont... | I've often found errors reported from SSAS indicating a duplicate key value in the dimension. When I've reviewed the source data, the duplicates aren't found. While I can't shed light on why this error is popping up in the dimension, I can offer a solution that bypasses the error and allows the cube to finish deployi... | I feel you're treating the symptoms and not the cause by suppressing errors.
<blockquote>
I set the attribute Relationships to <code>Date Key -> Day Number Of Month -> English Month Name-> Calendar Quarter -> Calendar Year</code>
</blockquote>
If that data looks like:
<pre>"16062000"--> 6 --> "June" --... | https://dba.stackexchange.com |
37,475 | [
"https://softwareengineering.stackexchange.com/questions/37475",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7693/"
] | It continue to astounds me that, in this day and age, products that have years of use under their belt, built by teams of professionals, <strong>still</strong> to this day - fail to provide helpful error messages to the user. In some cases, the addition of just a little piece of extra information could save a user hou... | While there are plenty of examples of bad error messages that simply should not be, you must keep in the mind that it isn't always possible to provide the information you'd like to see.
There is also the concern over exposing too much information, which may lead developers to error on the side of caution. (I promise ... | Developers are not the right people to write error messages.
They see the application from the wrong angle. They are extremely aware of what went wrong inside the code, but are often not approaching the software from the point of view of trying to accomplish something. As a result, what's important information for t... | https://softwareengineering.stackexchange.com |
294,213 | [
"https://math.stackexchange.com/questions/294213",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/48726/"
] | This is what I've been able to do:
Base case: $n = 1$
$L.H.S: 1^3 = 1$
$R.H.S: (1)^2 = 1$
Therefore it's true for $n = 1$.
I.H.: Assume that, for some $k \in \Bbb N$, $1^3 + 2^3 + ... + k^3 = (1 + 2 +...+ k)^2$.
Want to show that $1^3 + 2^3 + ... + (k+1)^3 = (1 + 2 +...+ (k+1))^2$
$1^3 + 2^3 + ... + (k+1)^3$
$ ... | HINT: You want that last expression to turn out to be $\big(1+2+\ldots+k+(k+1)\big)^2$, so you want $(k+1)^3$ to be equal to the difference
$$\big(1+2+\ldots+k+(k+1)\big)^2-(1+2+\ldots+k)^2\;.$$
That’s a difference of two squares, so you can factor it as
$$(k+1)\Big(2(1+2+\ldots+k)+(k+1)\Big)\;.\tag{1}$$
To show th... | Consider the case where $n = 1$. We have $1^3 = 1^2$. Now suppose $1^3 + 2^3 + 3^3 + \cdots + n^3 = (1 + 2 + 3 + \cdots + n)^2$ for some $n \in \mathbb N$. Recall first that $\displaystyle (1 + 2 + 3 + \cdots + n) = \frac{n(n+1)}{2}$ so we know $\displaystyle 1^3 + 2^3 + 3^3 + \cdots + n^3 = \bigg(\frac{n(n+1)}{2}\bigg... | https://math.stackexchange.com |
95,662 | [
"https://dba.stackexchange.com/questions/95662",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/61676/"
] | I have a column which is unique and when I add <code>Αγάθη</code> and <code>Αγαθή</code> (which are different) it says <code>#1062 - Duplicate entry 'Αγαθή' for key 'word'</code>. My collation is set to <code>utf8_general_ci</code>. Is there any better collation?
| Of the several <code>utf8</code> collations available:
<pre><code>mysql> SELECT * FROM information_schema.collations WHERE character_set_name = 'utf8';
+--------------------------+--------------------+-----+------------+-------------+---------+
| COLLATION_NAME | CHARACTER_SET_NAME | ID | IS_DEFAULT | IS... | Try using the <code>utf8_bin</code> collation, e.g. this will show its effect:
<pre><code>SELECT _utf8 'Αγάθη' = _utf8 'Αγαθή' COLLATE utf8_bin;
</code></pre>
| https://dba.stackexchange.com |
21,850 | [
"https://electronics.stackexchange.com/questions/21850",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4545/"
] | <strong>The Question:</strong>
<em>When is using latches better than flip-flops in an FPGA that supports both?</em>
<strong>Background:</strong>
It is a well-known principle that level-sensitive transparent latches should be avoided in FPGAs, and edge-sensitive flip-flops should be used exclusively. Most FPGA archit... | Your question is basically, "when do you know you need latches?" Which, as you implied, is a subjective question. Expect more opinion than fact as answers. That being said, here is my opinion:
I, like you, often find better ways to use flip-flops thus avoiding latches. The resulting logic is often more elegant and r... | Flip flops are often preferable to latches because they have only four race conditions/constraints:
<ol>
<li>setup time between a change to the data input and a following active clock edge, and </li>
<li>hold time between a clock edge and the next change to the data input; </li>
<li>minimum active clock pulse duratio... | https://electronics.stackexchange.com |
108,078 | [
"https://dba.stackexchange.com/questions/108078",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/61057/"
] | I have a date of birth column to which I need to compare the current date and return the difference as age. Currently I am using the following query :
<pre><code>DECLARE @DateOfBirth date = '2000-07-27'
DECLARE @CurrentDate date = '2015-07-25'
SELECT
@Age = DATEDIFF(YEAR, @DateOfBirth, @CurrentDate)
</code></pre... | Subtract one from each other in YYYYMMDD format, and divide by 10000 using integer division (which rounds down).
So:
<pre><code>(YEAR(@CurrentDate) * 10000 + MONTH(@CurrentDate) * 100 + DAY(@CurrentDate)
- YEAR(@DateOfBirth) * 10000 - MONTH(@DateOfBirth) * 100 - DAY(@DateOfBirth)
) / 10000
</code></pre>
20150725-200... | I have taken Robs method, and turned it into a function, and written a test script for it.
I can no longer find any mistakes.
<pre><code>CREATE or alter FUNCTION dbo.CalcAge
(
@DOB date, /* birthday */
@Today date /* either today or the day you want to calculate the age for */
)
RETURNS TABLE
AS
RETURN
(
-- fr... | https://dba.stackexchange.com |
18,545 | [
"https://stats.stackexchange.com/questions/18545",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2912/"
] | I have noisy time series which I need to segment into those portions with a zero mean and those portions without a zero mean. Finding the boundaries as accurately as possible is important (clearly where the boundary precisely lies is a bit subjective). I think a cusum variant could be adapted to do this but as cusum is... | This is a simple situation; let's keep it so. <strong>The key is to focus on what matters:</strong>
<ul>
<li>Obtaining a useful description of the data.</li>
<li>Assessing individual deviations from that description.</li>
<li>Assessing the possible role and influence of chance in the interpretation.</li>
<li>Maintain... | I think that whuber's answer is straightforward and a simple one for a non-time series person like me to understand. I base mine on his. My answer is in R not Stata as I don't know stata that well.
I wonder if the question is actually asking us to look at whether the absolute year on year increase is the same in t... | https://stats.stackexchange.com |
4,309,872 | [
"https://math.stackexchange.com/questions/4309872",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/649670/"
] | Let there be functions <span class="math-container">$$f(x)=x, if\ \ x\in \mathbb{Q},$$</span> <span class="math-container">$$f(x)=0, if\ \ x\not\in \mathbb{Q}$$</span> and <span class="math-container">$$g(x)=1,if\ \ x\neq 0,$$</span> <span class="math-container">$$g(x)=0,if\ \ x=0.$$</span> Consequently, <span class="... | This example doesn’t satisfy the hypotheses in the theorem you provided. In particular, the part that says
<blockquote>
…and <span class="math-container">$f(x)\neq u_0$</span>, for all <span class="math-container">$x$</span> near on <span class="math-container">$x_0$</span>.
</blockquote>
In your example, <span class="... | Your "composite function" limit theorem is probably <span class="math-container">$(1)$</span>, which is immediate from the sequence-based characterisation of continuity, i.e. <span class="math-container">$(2)$</span> below. Your function <span class="math-container">$f$</span> is nowhere continuous except at ... | https://math.stackexchange.com |
1,530 | [
"https://electronics.stackexchange.com/questions/1530",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/424/"
] | More components are only available in SMD packages.
For hobbyist assembly the options are to buy breakout boards or
solder SMD.
Since components are usually packaged in a couple of SMD
package types I am trying to put together a set of guidelines
for choosing packages that are compatible with hobbyist
skills and too... | 0603 isn't too bad to solder by hand (I won't do 0402 or smaller though).
SOT23 is probably a good guideline (for diodes too, not just transistors); there are some SOT323s that are smaller that are a pain.
I would avoid certain SOT23-6 parts because it can be very difficult to determine which way the package is suppo... | As far as my skills, to add a point of data. Using a $40 soldering iron, and lots of flux (I have a 'pen' with the liquid kind inside), and the occasional desoldering braid.
Easy: 0805 passives , 0.7mm pitch ICs
Doable if careful, but have ruined a couple: 0603, 0.5mm pitch ICs
Haven't tried smaller than those yet, ... | https://electronics.stackexchange.com |
22,143 | [
"https://stats.stackexchange.com/questions/22143",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5464/"
] | So I want to find the long run probability of getting two heads in a row when flipping a fair coin many times. I know this answer should be 1/6 (expected number of flips to get 2H in a row is 6) but I'm trying to figure out how to use a Markov chain to solve this.
I think my transition matrix should be (3x3):
<pre><c... | The response above by Xi'an addresses a different question than the one you are asking, I believe. He answers the question of the probability of 'HH' in a given <strong>pair</strong> of flips. This is slightly different than flipping until you get two heads in a row since the sequence 'THHT' would not register as two h... | Your analysis is almost correct, but you made a mistake in the Markov construction: first, you need four states, not three, because $(H,T)$ is not the same as $(T,H)$: the former cannot be followed by $(H,H$). (And you confuse the probability of seeing $(H,H)$ in the sequence of flips with the number of flips required ... | https://stats.stackexchange.com |
92,447 | [
"https://electronics.stackexchange.com/questions/92447",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25721/"
] | Say I have a gyro that outputs degrees/second, and I take the euclidean magnitude of the x,y, and z rotations:
$$
\text{magnitude} = \sqrt{x^2 + y^2 + z^2}
$$
Is this actually useful? Is magnitude now "total degrees/second"? Or does the weirdness surrounding non-commutative addition of rotations come into play?
| <i>Think</i> back to basic geometry and what the individual X, Y, and Z output values of the gyro actually mean.
One way to look at them is as the components of the rotation vector. This vector is parallel to the axis of rotatation with the magnitude being the speed of rotation. The square root of the sum of the squ... | The gyroscope sensor reports instantaneous angular velocity - the tiny rotation occuring from t to t+dt. This is a vector. Actually, pseudovector - it misbehaves around mirrors but that's not relevent here. You add angular velocities like normal. Pythagoras give the magnitude of this - how many radians per second ... | https://electronics.stackexchange.com |
40,747 | [
"https://security.stackexchange.com/questions/40747",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15010/"
] | I have no idea if Linux is more secure than windows.
I think Linux is more secure but I want to know what is going at kernel level. Somebody told me that Linux have only one main kernel and has it root password on it. Is it true? I Google it and I found many confusing answers :
<ol>
<li>Linux does not run .exe (execu... | In <em>some</em> areas, it has better approaches to security. Overall, pretty much the same. If you behave insecurely, you'll get compromised, Windows or Linux. It's just that there are more people using Windows than Linux, so it's a less desirable target for opportunistic attackers.
A determined attacker coming after... | <ul>
<li>Linux does not make distinctions on files based on file extension as Windows does. </li>
</ul>
Any file can be executable if it has the user has permissions to execute said file, so it's possible to embed malicious code an any kind of file that could be processed.It the file itself is executable or if the go... | https://security.stackexchange.com |
612,152 | [
"https://electronics.stackexchange.com/questions/612152",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/309427/"
] | Problem as follows:
I have a reference voltage that must not be loaded and a separate load that must be driven at a minimum of the reference voltage, but must be adjustable from the reference point to 10V. The reference voltage ranges from 0-6V
Solution as I imagine so far:
Using a linear voltage regulator with the GN... | No. According to the data sheets, the ground pin current of the MIC5209 can be up to 25 mA, and the LT3080 control pin up to 30 mA.
If I understand your proposal correctly, this doesn't satisfy your requirement to keep the reference voltage free from additional loads.
| "<em>Problem: I have a reference voltage that must not be loaded</em>"
"<em>Solution: Using a linear voltage regulator with the GND tied to the reference voltage.</em>"
The linear regulator itself has an operating current which it will flow from its Vin and out through its GND.
So your reference vol... | https://electronics.stackexchange.com |
149,502 | [
"https://security.stackexchange.com/questions/149502",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/137466/"
] | Imagining I want to develop a website to intentionally harm its visitors, what kind of attacks can I do ? I figure a typical CSRF attack would work, but could I steal cookies from another website that isn't mine? What else could I do?
I'm developing a system that allows third-party html/javascript code and I need to p... | Javascript is an engine executing code client side. If you allow third party <em>uncontrolled</em> javascript in your site, that means that potentially visitors of your site may execute arbitrary code in your browser.
Damages can come at various levels:
<ul>
<li>simplest and lightest: simply play with the browser. As... | Generally speaking, I think your best bet is to install Kali linux on VM and test your website and webserver for vulnerabilities. If you patch it up enough to make Kali testing negative, you'll be safe against the majority of potential hacking.
Having a closer look into <strong>Nikto web scanner</strong> and then per... | https://security.stackexchange.com |
210,092 | [
"https://dba.stackexchange.com/questions/210092",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/153745/"
] | I had asked this question in serverfault.Later, i came to know about this site.
I have percona xtrabackup installed in my ubuntu client machine. My local machine IP address is 192.168.0.100. The database that i need to backup is in 192.168.0.200. Is it possible to do the backup of remote server in local server using p... | Mostly yes, but with small correction. You can get the stale data if they aren't replicated yet to another node (replication happens almost at the same time, but still could be delayed because of garbage collection, etc.). You can get strong consistency by tuning consistency levels...
The comment is about point 3c - ... | You cannot accomplish 3a (in sync replication) because Cassandra doesn't do that. You can use the write consistency <code>ALL</code> (as you mention in 3b) which will eagerly attempt to write to all replicas. Even if the write says it fails it still may have worked (just the nodes didn't respond in time).
About point ... | https://dba.stackexchange.com |
1,582,890 | [
"https://math.stackexchange.com/questions/1582890",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/193752/"
] | I was trying to solve a bigger exercise and I thought of the following
<blockquote>
<strong>Conjecture</strong>
Let <span class="math-container">$f:\Bbb R^n\to \Bbb R^m$</span> be continuous in <span class="math-container">$\Bbb R^n$</span>. Then <span class="math-container">$f$</span> is bounded in every bounded inter... | If $f:\mathbb{R}^n\to\mathbb{R}^m$ is continuous and $A\subset\mathbb{R}^n$ is any bounded set, then $f(A)$ is bounded. This follows from the fact that a continuous image of a compact set is compact: if $A$ is bounded, then $\overline{A}$ is closed and bounded and hence compact, so $f(\overline{A})$ is compact and hen... | Another, more "analytic" proof is this:
Consider the function $g:\mathbb{R}^n\to \mathbb{R}$ given by $g(x)=\Vert f(x)\Vert$, which is a composition of continuous functions, so it is continuous . We easily see $f \text{ bounded on }I\Leftrightarrow g \text{ bounded on }I$
To prove $g$ bounded on $I$, first, assume $... | https://math.stackexchange.com |
587,535 | [
"https://physics.stackexchange.com/questions/587535",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Suppose two bodies collide inelastically, does the total loss in kinetic energy get converted into potential energy associated with the deformation? Or does the energy also transform into other forms like sound or light?
| So you aren't doing the same thing as your teacher here.
Notice how in what your teacher did they have <span class="math-container">$\Vert d \mathbf r \Vert =ds$</span>, so they did not say that
<span class="math-container">$$\frac{d\mathbf r}{dt}·\frac{d\mathbf r}{dt} = \left(\frac {dr}{dt}\right)^2 $$</span>
this wou... | Yes, <span class="math-container">$\vec v=\frac{ds}{dt}\hat{t}$</span>
So, <span class="math-container">$$ d\vec{v}\cdot d\vec {v}=(d^2s\hat t +ds\,d\hat t)\cdot(d^2s\hat t+ds\,d\hat t)=(d^2s)^2+(ds)^2$$</span>
But <span class="math-container">${dv}^2=(d^2s)^2$</span>
| https://physics.stackexchange.com |
1,817,530 | [
"https://math.stackexchange.com/questions/1817530",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/346302/"
] | I have to verify if the statment:
$$I-X(X^TX)^{-1}X^T=((I-X(X^TX)^{-1}X^T)^2$$
is true or not. (I do not get to demonstrate).
Any help or hint will be very useful for me. Thanks a lot!
| First let me warn everyone who reads this that $X$ is <b>not</b> supposed to be a <b>square</b> matrix; it is a matrix with typically many more rows than columns. Its columns must be linearly independent since otherwise $X^T X$ is not invertible.
Let $H= X(X^T X)^{-1} X^T$. Then
$$
H^2 = \Big( X (X^TX)^{-1} X^T \Big... | $P_X = X(X^{T}X)^{-1}X^{T}$ is known as the <strong>projection matrix</strong> onto $\mathcal{C}(X)$, the column space of $X$. Note that since $r(X^TX) = r(X)$, if $X$ is a $n \times p$ matrix, $X$ needs to have rank $p$.
Your statement is equivalent to showing that $I - P_X$ is idempotent.
Observe
$$(I - P_X)^2 = (... | https://math.stackexchange.com |
186,496 | [
"https://electronics.stackexchange.com/questions/186496",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/57453/"
] | It says it is an ambient light sensor, but is it a phototransistor? Something else? It has Vcc and Vout pins. Bonus points if you include a data sheet.
<img src="https://i.stack.imgur.com/dktIO.jpg" alt="back of package">
| No.
The insulation in the 12V switch is not designed to withstand 120V (really 170V).
| No. You can't use that switch.
The switch would heat up a lot and sometimes can cause an electric shock if you touch it.
This is because the insulation would be provided for the specified voltage and current.
| https://electronics.stackexchange.com |
1,369,903 | [
"https://math.stackexchange.com/questions/1369903",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/225132/"
] | A number when divided successively by $4$ and $5$ leaves remainder $1$ and $4$ respectively. When it is divided by $5$ and $4$, then the respective remainders are:
$1,2$
$2,3$
$3,2$
$4,1$
I thought of picking a number, say $9$, which satisfies the given conditions, and the answer it gave me was option $D$. But ... | $$N=4a+1, a=5b+4\implies N=4(5b+4)+1=20b+17$$
$$N=5(4b+3)+2, 4b+3=4(b)+3$$
| Lets assume number is n
So n is of the form $4k+1$.
and k is of the form $5p+4$.
So $n=4(5p+4)+1=20p+16+1=20p+17$.
n could be 37,57,77 etc, starting from submitting p=1,2,3 and so on.
Now, rewrite $20p+17$ as $15p+5p+15+2=15(p+1)+5p+2$.
Clearly, if you divide this by 5 the remainder is <strong>$2$</strong>, and q... | https://math.stackexchange.com |
160,031 | [
"https://electronics.stackexchange.com/questions/160031",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11453/"
] | I am restoring a stereo amplifier circa 1985 (specifically the Technics SU-Z55). Part of that is replacing the electrolytic capacitors on the mainboard due to some audio popping and general age. There are 6 capacitors on this board that are electrolytic but have no polarity strip on them or negative marking on the PCB.... | I would say that these are indeed non-polarized caps. You would want to replace them with similar capacitors. Do NOT replace them with ceramic caps.
Ceramic caps are great for many purposes but not in the audio path. Among other problems, they suffer from piezo electric sensitivity and their value can vary greatly de... | The slashed capacitor symbol with a + is apparently a Japanese variant symbol for an electrolytic; you can see it on the schematic for C1 and C13. It definitely seems reasonable to think that without the + it signifies a non-polar electrolytic.
| https://electronics.stackexchange.com |
431,358 | [
"https://physics.stackexchange.com/questions/431358",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208031/"
] | When I look at a first surface mirror with a thermal camera I don't see the temperature of the mirror but the temperature of the reflected objects. It is like if a polished metallic surface don't lose infrared light due to is own thermal agitation. Whatever the temperature of the mirror ( without being altered ), I can... | An interesting consequence of thermal equilibrium is that objects that don't <em>absorb</em> much thermal radiation also don't <em>emit</em> much thermal radiation. If you put two objects, one black and one white, in an isolated box and let them reach thermal equilibrium (same temperature), the black object will emit m... | I would imagine that it is because light is a form of electromagnetism, as in, the infrared light the camera is detecting is the light being reflected off of the mirror, as the mirror's personally emitted temperature is simply a reflection of the thermal agitation of the object it is reflecting.
| https://physics.stackexchange.com |
78,300 | [
"https://electronics.stackexchange.com/questions/78300",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22783/"
] | Since I2C, SPI, etc all communicate bits in some serial fashion, is there an equivalent name to refer to the type of communication/protocol that occurs on the TX/RX pins (associated with UART) of a micro-controller other than "Serial" regardless of whether its voltages are TTL (3.3V,5.0V) level or RS-232?
| The best answer is "TTL-Level RS-232-Style serial communications" <sub>Sometimes with additional specifiers (parity, no parity | 7/8/whatever bits per byte | 1/2/1.5 stop bits, etc...), but those options are defined in the standard.</sub>.
<sub><sup>RS-232, EIA-232 and TIA-232 are all the same protocol, in general. T... | The communications protocol used by UARTs is peculiar to UARTs, and so it is called "UART communication".
| https://electronics.stackexchange.com |
29,651 | [
"https://dsp.stackexchange.com/questions/29651",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/16107/"
] | Basically I couldnt find proof for this anywhere though it's a very simple and basic equation.
| The signum function is defined by
$$\text{sgn}(t)=\begin{cases}-1,&t<0\\0,&t=0\\1,&t>0\end{cases}$$
Using the half-maximum convention, the unit step function is defined by
$$u(t)=\begin{cases}0,&t<0\\\frac12,&t=0\\1,&t>0\end{cases}$$
From these two definitions it should be obviou... | Its simple actually,
By neglecting the t = 0 in sgn(t),
sgn(t) =
<span class="math-container">\begin{cases}-1,&t<0\\1,&t>0\end{cases}</span>
Add 1 to sgn(t),
sgn(t) + 1 =
<span class="math-container">\begin{cases}0,&t<0\\2,&t>0\end{cases}</span>
Now we can compare sgn(t) + 1 and u(t) easily,... | https://dsp.stackexchange.com |
14,849 | [
"https://dba.stackexchange.com/questions/14849",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7118/"
] | I did not ready about this but found out after trying to restore a database from remote server and it wont restore if the database did not exist before. What I would do is
<ol>
<li>create a .bak file (backup the database)</li>
<li>Copy the .bak file to the remote server using shared folder</li>
<li>Run restore in SQL... | No, for a restore you don't have to have the database existing already (be mindful though to not have the <code>with replace</code> option set in your <code>restore database</code> command).
The below statement would create a new database from the backup:
<pre><code>RESTORE DATABASE [YourNewDbName]
FROM DISK = N'C:... | No, a database does not need to exist already in order to restore a backup. The error you received was probably because you copied some restore command from somewhere and it had options that prevented it from working successfully. It will be easier to help you sort out the issue if you post the actual <code>RESTORE</co... | https://dba.stackexchange.com |
1,495,109 | [
"https://math.stackexchange.com/questions/1495109",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/271393/"
] | I think that this is pretty basic, but I just can't seem to figure it out. I've tried all of the approaches that I can think of, and I can't seem to find the expression for the Nth sum. The Sum is given by:
$$\sum_{n=1}^\infty \frac{1}{(a^n+1)}$$
And I have to find the values of $a>0$ that makes this sum converge... | If $a = 0$ or $a = 1$ the series is obviously divergent.
If $a>1$ we write
$$\frac{1}{a^n+1} = \frac{1}{a^n}\frac{1}{1+a^{-n}}\le\frac{1}{a^n}.$$
This shows that the series converges for $a>1$.
If $0<a<1$ we have that the sequence $a^n$ is decreasing, so that $\tfrac{1}{a^n+1}$ is bounded below and the se... | Hint: Try to split it into two cases:
<ul>
<li>$ 0 < a\le 1$. Think of the divergence test. </li>
<li>$a >1$. Then $a^n > 1^n = 1$. Then try to use comparison test. </li>
</ul>
| https://math.stackexchange.com |
726,719 | [
"https://physics.stackexchange.com/questions/726719",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/306551/"
] | Faraday's Law of Induction tells us that a changing magnetic flux induces an EMF in the conductor, causing an electric current to flow.
By Lenz's Law, we get the <strong>direction of induced EMF</strong> which turns out to be in the opposite direction of the changing magnetic flux. But why is it in the opposite directi... | Besides the answer "because that's how the maths works", there is a conservation of energy argument.
Consider a dipole magnet, which you drop through a metal tube. As it falls, it creates a changing magnetic field, and that induces a current in the tube to oppose the changing magnetic field.
What do you obser... | Actually the Lenz law is connected to <strong>energy conservation</strong> (one of the most fundamental "law" of nature).
So let us suppose you have a fixed conducting loop and a movable magnet. If you move the magnet towards the loop and <strong>suppose the induced current was the other way round</strong> th... | https://physics.stackexchange.com |
312,381 | [
"https://softwareengineering.stackexchange.com/questions/312381",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23470/"
] | This is my scenario, I have this interface:
<pre><code>public interface hitTheDataBase
{
public void insertMe(String [] values);
public void modifyMe(String [] values);
public DataTable selectMe();
}
</code></pre>
And I have these two classes that implement the interface:
<pre><code>public Class hitSqlSe... | When your software updates are deployed, is there any reason why you could not upgrade your schema as well? A change to the software which requires a change to the database schema implies that the schema should change on the target system.
Backward compatibility with older versions of a database schema is typicall... | This is what happens if your database schema doesn't match an application version. Any application that gets the new col3 code, should have the database updated along with it.
If you're going to go to the trouble of checking if a column exists in a table, just create it during the update to the newer version.
| https://softwareengineering.stackexchange.com |
32,691 | [
"https://physics.stackexchange.com/questions/32691",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10786/"
] | I had a college student build an overclocked PC using phase-change technology. (This is essentially an air-conditioning unit with the evaporator attached directly to the motherboard.) He said that cold temperature made the CPU more stable at higher clock speeds (5.5 GHz) by affecting how the atoms and electrons behav... | Temperature certainly affects semiconductors.
As someone who is not specialized in semiconductors, I can think of at least two microscopic effects at play here. The first is that at lower temperatures there are less phonons (quantized vibrations of the atomic lattice). The effect of phonons is to scatter the electrons... | I am not really an expert on solid state physics, and I'm prepared to look an idiot here - but I don't think it's the low temperatures that help.
By overclocking a CPU 5.5 GHz you are almost doubling the power consumption and hence the dissipation. A large reduction in the temperature of the cold site of the heat... | https://physics.stackexchange.com |
518,882 | [
"https://physics.stackexchange.com/questions/518882",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21146/"
] | This is a question about the approach of Weinberg in "The Quantum Theory of Fields" to the irreducible unitary representations of the Poincare group in Chapter 2.
Let <span class="math-container">$U(\Lambda,a)$</span> be such a representation. Weinberg shows that from it one is able to obtain the generator of translat... | Both <span class="math-container">$p^2$</span> and the sign of <span class="math-container">$p^0$</span> are invariant under infinitesimal Poincaré transformations (we're really looking at representations of the Poincare algebra or rather projective representations of the connected component of the Poincaré group here)... | Following the answer by @ACuriousMind I believe I got the point and decided to post a version which is a little bit more expanded with what I understood.
Let <span class="math-container">$f(p)$</span> be some function defined in momentum space. We can define the function acting on the momentum operators <span class="m... | https://physics.stackexchange.com |
45,850 | [
"https://security.stackexchange.com/questions/45850",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/31325/"
] | I notice that in <code>/usr/share/wordlists</code> in Kali Linux (former Backtrack) there are some lists. Are they used to bruteforce something? Is there specific list for specific kind of attacks?
| Kali linux is a distribution designed for penetration testing and computer forensics, both which involve password cracking. So you are right in thinking that word lists are involved in password cracking, however it's not brute force.
Brute force attacks try every combination of characters in order to find a password,... | One of the better basic wordlists in Kali is <code>/usr/share/wordlists/rockyou.txt.gz</code>. To unzip simply run <code>gzip -d /usr/share/wordlists/rockyou.txt.gz</code>.
Be sure to add "known weak" passwords that are used by the organization you are testing. I like to add these "additional" custom passwords to ... | https://security.stackexchange.com |
31,389 | [
"https://dsp.stackexchange.com/questions/31389",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/7555/"
] | <pre><code>t = 0:0.001:1;
y1 = 400 * sin(2*pi*20*t);
y2 = 200 + 400 * sin(2*pi*20*t);
plot(t,y1)
hold on
plot(t,y2,'-g')
grid on;
rms_y1 = sqrt(mean(y1.^2))
rms_y2 = sqrt(mean(y2.^2))
</code></pre>
In the above MATLAB code there are two signals <code>y1</code> and <code>y2</code>.
<code>y1</code> is a sinusoidal si... | RMS values don't simply add up. The RMS value of $N$ discrete samples $x[n]$ (assuming $0\le n<N$) is
$$x_{RMS}=\sqrt{\frac{1}{N}\sum_{n=0}^{N-1}x^2[n]}\tag{1}$$
Now if you have $y[n]=x[n]+c$ with some constant $c$, the RMS value of $y[n]$ is
$$\begin{align}y_{RMS}&=\sqrt{\frac{1}{N}\sum_{n=0}^{N-1}y^2[n]}\\&... | Your intuition is wrong.
If your <code>y2</code> was more like:
<pre><code>y2 = 200*sign(sin(2*pi*20*t)) + 400 * sin(2*pi*20*t);
</code></pre>
then your intuition would be correct.
The issue is that adding a constant value to the sinusoid <em>adds</em> to the sinusoid's RMS value when the sinusoid is positive (and ... | https://dsp.stackexchange.com |
298,783 | [
"https://physics.stackexchange.com/questions/298783",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/139293/"
] | Imagine you have two slightly different liquids, or a couple of underwater streams facing eachother. Can there be any friction between them?
Thanks in advance!
| Yes. But we use a different name for it, <strong>Viscosity</strong>.
| I think that friction and viscosity are slightly different, but I may be wrong. However, they are very closely linked. The friction of a fluid is also known as 'Fluid-friction'. The higher the viscosity of a liquid the higher the friction between the two.
There would be friction as the particles would bump and rub aga... | https://physics.stackexchange.com |
8,352 | [
"https://cogsci.stackexchange.com/questions/8352",
"https://cogsci.stackexchange.com",
"https://cogsci.stackexchange.com/users/6875/"
] | I find that things you learn in school are much easier to learn than before you take the course. For example, there is a mathematical theorem that seems unnerving when I self studied calculus, but the same theorem appeared to be so much easier when I actually learned it in school.
Why is it easier to learn something w... | I'm not sure what you mean by harder, because I find things about the same, if not easier(thanks internet), after leaving school and understanding how our memory works.
I think you're noticing the difference between a teacher and a book. A teacher will draw pictures, use gestures, tone of voice, and answer any questio... | A bad teacher would explain things in a manner that's harder to digest, when compared to a good teacher. However, in general, for any teacher, even a tutor, it is easier to concentrate because the prefrontal cortex is reminded continuously of the goal (of learning). This is called goal-directed behavior. Learning alone... | https://cogsci.stackexchange.com |
31,199 | [
"https://quant.stackexchange.com/questions/31199",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/25456/"
] | Somewhat embarrassingly I'm stuck with something very elementary.
I want to find the conditional probability of a stock movement (GBM):
$$\mathbb{P} \big( S_t \geq b \vert S_s \leq b) $$
for $ t > s$. My main problem is to determine what $\mathbb P(S_t \geq b, S_s \leq b\big)$ equals.
| By a certain algebraic manipulation, what you need is the probability $P(W_t \ge a, W_s \le c)$, which can be computed as below:
\begin{align*}
P(W_t \ge a, W_s \le c) &= P(W_t-W_s \ge a-W_s, W_s \le c)\\
&=E\big(E\left(1_{W_t-W_s \ge a-W_s} 1_{W_s \le c} \mid W_s \right)\big)\\
&=E\big(1_{W_s \le c}E\left(... | <strong>Hint</strong>
Let
$$dS_t=\mu S_tdt+\sigma S_t dW_t\,.\tag 1$$
Set $x_t=\ln S_t$, By application of Ito's lemma we have
$$x_t=x_0+\left(\mu-\frac 12 \sigma^2\right)t+\sigma W_t\tag 2$$
thus
$$x_t\sim\mathcal {N}\left(x_0+\left(\mu-\frac 12 \sigma^2\right)t\,,\,\sigma^2 t\right)\tag 3$$
on the other hand
$$\ma... | https://quant.stackexchange.com |
19,605 | [
"https://mechanics.stackexchange.com/questions/19605",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/11366/"
] | I've read gasoline engines use sparks to ignite the mixture, but diesel engines use just compression which can't be done in gasoline engines due to high compression ratios which can cause engine knocking, but if that was true gasoline? It can then be put in diesel engines and will ignite properly because diesel engines... | You can run gasoline in a diesel motor, but it causes problems. As mentioned elsewhere, when you compress the fuel/air mixture enough, it gets really hot then ignites. With diesel, this is ok, because the fuel burns (relatively) slowly, so it doesn't need to be timed very well.
Gasoline, on the other hand, burns reall... | I would say there are two major reasons.
First, the seals and o-rings used in diesel engines can't tolerate the chemical composition of gasoline. They are designed to tolerate the chemical composition of diesel only.
Second, the kind of pressure needed to inject diesel can't be tolerated by gasoline. The Chevy Dura... | https://mechanics.stackexchange.com |
57,640 | [
"https://stats.stackexchange.com/questions/57640",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20307/"
] | I have some EEG data sets that I am testing against two classes. I can get a decent error rate from LDA (the class-conditional distributions aren't Gaussian, but have similar tails and good enough separation), and so I want to plot the ROC of the LDA predictor against data sets from other subjects.
Here is a typical g... | A perfect ROC "curve" will be shaped with a sharp bend. The performance you have there is very near perfect separation. In addition, it looks like you have a scarcity of points making the curve.
| Although this question was asked about 3 years ago, I find it useful to answer it here after coming across it and getting puzzled by it for some time. When your ground truth output is 0,1 and your prediction is 0,1, you get an angle-shape elbow. If your prediction or ground truth are confidence values or probabilities ... | https://stats.stackexchange.com |
210,926 | [
"https://softwareengineering.stackexchange.com/questions/210926",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23475/"
] | The big question I have in my mind: how many developers are brownfield ("enterprise") compared to greenfield (all new code, from the ground up).
I'm constantly reading breathless articles about the latest technology, only to find out that It Just Won't Work On Our Enterprise Software codebase. People aren't ready for... | It is a well-known fact that most software development effort is spent maintaining existing software, not writing new software.
Why? Because the first version of a program is only written once. Every subsequent version builds on the original, and steady revenue comes from steadily maintaining, promoting and upgradi... | In terms of revenue, pure Green Field development is probably close to 0.0% of revenue generated from development.
<strong>Why?</strong>
Development is almost always building on earlier code, doing rewrites of part of a design, bringing out new and improved version 4.0 etc... I can think of very few commercial situat... | https://softwareengineering.stackexchange.com |
12,973 | [
"https://ai.stackexchange.com/questions/12973",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/26584/"
] | When describing tensors of higher order I feel like there is an overloading of the term <em>dimension</em> as it may be used to describe the order of the tensor but also the dimensionality of the... "orders"?
Assume one describes the third-order tensor produced by a convolutional layer and wants to refer to its width ... | <strong>Ambiguity in Terms</strong>
You are correct that there is something like overloading occurring in tensor terminology in posts and in software libraries. Confusing jargon often appears when those without the mathematical background use mathematical terms. You rarely find this confusion when reading NASA, Cambri... | By definition, tensors can be of any order (usually named differently if the order is less than three). So, I use <span class="math-container">$d_i$</span> to indicate the dimensionality of the <span class="math-container">$i$</span>th facet.
Unless you have three or four-order tensors which each facet has a very spec... | https://ai.stackexchange.com |
141,653 | [
"https://electronics.stackexchange.com/questions/141653",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/41188/"
] | From what I understand, matching a load to a transmission line means that no signal is reflected from the load, which means that at the two sides of the connection point between the load and the transmission line the impedance is the same, the load impedance. I tried to test my understanding with the following example:... | When you match to complex valued loads the matching for zero power reflection states that the impedance seen from your complex-valued load (\$100+50j\$) has to be its complex conjugate (\$100-50j\$).
This is because that way we would be satisfying the max. power theorem, and, at the same time, getting rid of the imagi... | Your calculations look good and your confusion is justified. It's matched, so why isn't the reflection coef. zero?
Most of the time, the reference impedance is 50ohms or at least positive real. Most books assume Zo is postive and purely real, but don't specifically say so. This leads to the common expression for refle... | https://electronics.stackexchange.com |
468,041 | [
"https://electronics.stackexchange.com/questions/468041",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18643/"
] | Induction motors do not have magnets in them, instead the magnetic field the outer coils generate creates electricity, and subsequently magnetic field, in the inner coil. This means those motors need no brushes as the inner coil is not connected to anything.
I was wondering, purely academically, if you could prime the... | <blockquote>
The manufacturer always specifies voltage in a certain frequency range. Why is this parameter important?
</blockquote>
Because these are the parameters the transformer has been specifically designed for.
As depicted, this transformer's primary input of 10-40v @100kHz will produce X to 5v/3A at the outp... | The 500V is a voltage used for insulation test between different coils, not voltage over a single coil.
Otherwise the transformer works best in the frequency and voltage range it is designed for. If the volt × second is higher then the core starts to saturate.
| https://electronics.stackexchange.com |
2,134 | [
"https://mechanics.stackexchange.com/questions/2134",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1120/"
] | Drain oil, add new oil... find oil everywhere. It spills, the funnel is full of it when I'm done and drips forever, and I'm pouring kitty litter all over the driveway. If I had a proper garage this would be simple, but as a shade-tree guy, I never quite figured it out.
Any answers about things like draining the oil fi... | Oil changes are a boring job!
As Hasen says, a larger size oil catch pan is the only real solution. Before you start, try and estimate the direction of flow. If the drain plug is on the side of the sump (oil pan), the oil will begin to flow horizontally, curving down with gravity, and hit the ground around 9-12" out f... | As a fellow driveway warrior I feel your pain. I have a good experience with getting a large diameter oil container. If your car has its oil filter in a tough location you are just gonna have to live with some mess. But large easy to grab container helps.
If I wanted to spend the cash I would shoot for a remote oil fi... | https://mechanics.stackexchange.com |
394,258 | [
"https://physics.stackexchange.com/questions/394258",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/72517/"
] | What is the precise meaning of "projector", "projection" and "projection operator"? I always thougth those two terms are synonyms, but I have seen both used in a quantum optics paper where the former is not the same as the latter. There the projector was defined as $(I_S|0)$ and the projection operator as
$\begin{pmatr... | Usually, people will use all of these words interchangeably, to mean what your source calls a "projection operator". As for what your source means, note that
<ul>
<li>a linear transformation is a linear map <span class="math-container">$T: V \to W$</span> for vector spaces <span class="math-container">$V$</span>, <spa... | They are the same thing. In quantum mechanics, one usually defines a projection operator as $$\hat{P} = |\psi\rangle\langle\psi|$$
This operator then acts on quantum states (vectors) $|\Psi\rangle$ as
$$\hat{P}|\Psi\rangle = |\psi\rangle\langle\psi|\Psi\rangle = \langle\psi|\Psi\rangle|\psi\rangle$$
This is exactly th... | https://physics.stackexchange.com |
109,417 | [
"https://cs.stackexchange.com/questions/109417",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/105398/"
] | I'm looking for an algorithm name to change the order of the levels of a tree. I've done something that works but there's a lot of code and the <span class="math-container">$ O(n) $</span> is very bad.
Here's an example, let say there are 3 levels. Each level representing something in a hierarchy <code>project > bu... | Casting of primitive datatypes works in a very simple way:
<blockquote>
Under the hood, values don't have types. Casting does absolutely nothing.
</blockquote>
As a simple example, let us consider casting 65 to an ASCII character, thus obtaining the symbol <code>A</code>. What happens under the hood? Absolutely not... | <blockquote>
How does the casting of primitive datatypes works?
</blockquote>
The restriction "primitive datatype" is not enough:
Casting from a 16-bit integer to a 32-bit integer works differently than casting between integer types of the same size. And casting between integer and floating-point types is even more... | https://cs.stackexchange.com |
36,297 | [
"https://security.stackexchange.com/questions/36297",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/26282/"
] | I'm looking for a pattern to store a config file containing sensitive information in a semi trusted hosting environment. Semi trusted in this case meaning I trust them in general, but not with this info (passwords).
In this case I'm writing a simple daemon to watch a folder for changes, and push those changes to a d... | If you're worried about the admins actively snooping on your application, there's nothing you can do except never use their system with any sensitive data. Whatever your program does to decrypt or retrieve credentials, they can also do. For the same reason, you need to trust them not to allow administrative access to t... | <strong>Don't waste your time on this. There's nothing you can do.</strong>
You're placing your data on a server that is not yours, and people managing this server can have access to your data.
Let's say you found the best way to store database credentials securely. Your server admin has a DBA account that can access ... | https://security.stackexchange.com |
275,146 | [
"https://dba.stackexchange.com/questions/275146",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/210960/"
] | I need to connect to a remote Oracle DB, so I requested to open the firewall on the port 1521 to the DB and the replica.
<pre><code>[root@ansible-test ~]$ telnet <oracle_db_active> 1521
Trying <oracle_db_active>...
Connected to <oracle_db_active>.
Escape character is '^]'.
^CConnection closed by fore... | I end up finding the answer :)<br />
On my test server on the same network as the DB I made a tcpdump and I notice that my connection started on the primary IP and the DB reply through the secondary IP. There was a request on the DNS server in the middle.
I made the same test on my <em>ansible-test</em> server and foun... | I once had a similar scenario like the one you are having. I deployed Oracle Connection Manager on RedHat 6. Everything configured through ansible. Everything was working on my Vagrant Oracle Linux during development, but once deployed to RedHat I had these ORA- messages. Everything was correct, but I never found the r... | https://dba.stackexchange.com |
141,715 | [
"https://physics.stackexchange.com/questions/141715",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62278/"
] | A conservative force $\vec{F}$ is <em>apparently</em> defined as the gradient of a potential energy $U$:
$$\vec{F} = -\nabla\ U$$
I am curious if this definition was originally used to describe a conservative force in relation to potential energy or the other way around.
Where does this relation come from, and how i... | Here is one take on how to understand the relation between force and potential energy, which I think is the closest modern version of how it would have been seen originally. Let's take as the conditions for a force to be conservative
$$\nabla \times \mathbf{F} = 0$$
and $\mathbf{F}$ is a function of position only (t... | We can start at the relationship: $W=-\Delta U$, which is work done by a conservative force.
<strong>The math</strong>
A (conservative) force $F$ will do this work on an object when doing a displacement $\Delta x$, and $W=F \Delta x$. In the general case, the force might be different at different points as the object... | https://physics.stackexchange.com |
13,728 | [
"https://physics.stackexchange.com/questions/13728",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/329/"
] | It is well-known even among the lay public (thanks to popular books) that string theory first arose in the field of strong interactions where certain scattering amplitudes had properties that could be explained by assuming there were strings lurking around. Unfortunatelly, that's about as far as my knowledge reaches.
<... | in the late 1960s, the strongly interacting particles were a jungle. Protons, neutrons, pions, kaons, lambda hyperons, other hyperons, additional resonances, and so on. It seemed like dozens of elementary particles that strongly interacted. There was no order. People thought that quantum field theory had to die.
Howev... | Well I believe the original clue was Regge trajectories. It was observed that if you plotted mass squared vs. angular momentum for strongly interacting resonances, they tended to follow straight lines. This could be explained as the spectrum of rotating strings connecting massless particles.
| https://physics.stackexchange.com |
422,808 | [
"https://softwareengineering.stackexchange.com/questions/422808",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/73722/"
] | I am brain storming on how to create a type system for a programming language, and what the compiler will do with the typing information. Here is what I have found, followed by the main question, which is if I can represent more complicated "validations" as types somehow.
First, it seems there is a difference... | Yes, types are just constraints. Any general type system has <code>top</code> which means “this value can be anything” and <code>bot</code> (bottom) which is so constrained that no value can satisfy it.
That’s literally chapter one of any type theory book.
What can be determined at compile time depends on your operatio... | You might want to look into refinement types, which are types with programmer-specified restrictions along the sort you mentioned.
The main thing that determines if you don't need a runtime check is if you are casting from a subtype to a parent type. <code>fibonacci</code> is a subtype of <code>int</code>, for example,... | https://softwareengineering.stackexchange.com |
2,755,621 | [
"https://math.stackexchange.com/questions/2755621",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/478267/"
] | I am teaching the normal distribution as a continuous random variable and my students have just learned binomial distribution. Wondering what would be a good idea to explain the transition from discrete to continuous where, instead of histogram, we now find the probability as area under the curve?
Would appreciate any... | Fix the mean of the binomial, some $M$, and then let $p = M/n$ and consider the sequence of distributions $$\mathcal{B}(n,p) = \mathcal{B}(n,M/n).$$
You will converge to a continuous distribution, you can show this by the sequence of pdfs.
Another way is to fix any distribution $\mathcal{D}$, even discrete, and find ... | I think the best way for an introductory probability course to make the transition from discrete to continuous begins by explaining the Poisson process, first showing that the number $X_t$ of arrivals before time $t$ is so distributed that
$$
\Pr(X_t=x) = \frac{(\lambda t)^x e^{-\lambda t}}{x!}.
$$
Then let $T_x$ be th... | https://math.stackexchange.com |
146,503 | [
"https://security.stackexchange.com/questions/146503",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/70868/"
] | I have a lot of information to backup, this includes accounts passwords, personal files, images and a lot more. So I was thining about backing up everything using a cloud service like Dropbox, Google Drive or OneDrive.
My question is: Is this secure? Are these services always going to keep my files "forver"?
| "The cloud" is marketing-speak for "other people's servers", so I will use that term instead.
When you move your data to other people's servers, you need to be aware that they have direct access to your data. When they are not trustworthy, they are able to steal your data. Read the privacy policy of the people you giv... | YMMV.
When you say <em>secure</em>, it could mean many things. Would I trust a service with my passwords, unencrypted? No.
Will they never delete my files? Yes - your files are safe in this way forever.
| https://security.stackexchange.com |
253,599 | [
"https://mathoverflow.net/questions/253599",
"https://mathoverflow.net",
"https://mathoverflow.net/users/56462/"
] | I have a 3 dimensional abelian variety whose formal group law breaks into a formal summand where one of the pieces is one-dimensional.
I am desperately wondering how to compute the $p$-series of this one-dimensional formal group law without finding an explicit model of the abelian variety.
<hr>
Here is the set up ... | I don't know how to do this purely with invariant differentials. One
of the main reasons is that, in order to solve this problem, you need
to construct an "algebraic" lift of this variety from the complex
numbers to a much smaller number field. This lift isn't necessarily
unique and different choices will give you diff... | It seems the elliptic curve $$\mathbb{C}/\mathbb{Z}[\sqrt{-7}]$$ is a subvariety of this Abelian variety. The one-dimensional formal group law can most likely be computed for this elliptic curve.
| https://mathoverflow.net |
128,737 | [
"https://security.stackexchange.com/questions/128737",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/116184/"
] | I am a software engineer from Bucharest and I've created an audio based encryption and authentication application called WaveCrypt. It basically allows users to encrypt (AES) their files with an WaveKey - a unique audio fingerprint that can be obtained from an Wave file (thus the name of the application. I've chosen th... | If you use some "natural" sound, you have lots of redudancy in it and this reduces the key strength (this may or may not be critical to your application).
Because you cannot reproduce your sound key, you'll have to store it (in a passphase-locked key store). With this condition, a randomly generated strong key is alw... | A very interesting idea.
I suppose that malware could indeed obtain a very hard to reproduce key like this, however there could be some issues :
<ul>
<li>the target's microphone is muted</li>
<li>there is a very low amount of sound in the room - no sound is captured</li>
</ul>
I would suggest to have a fallback me... | https://security.stackexchange.com |
378,968 | [
"https://softwareengineering.stackexchange.com/questions/378968",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/316087/"
] | Let's say I have a function that calculates a sensor output, all values are >=0, but also I have to detect some error situations like "NO_POWER" which I encoded with value "-65500". On my application there are classes that only care for the real output value (regardless if an error is present) and other classes that ne... | First of all, I assume that using exceptions to signal those errors is out of the question (either because you do not wish to use exceptions, or those errors are considered part of the "normal" flow of the program for one reason or another).
I would strongly suggest the second approach. If you were to use a <code>-655... | The other approach would be boost::optional or (if your compiler supports it) std::optional. An optional may or may not have a value. I don't know if this would work as well for you as the struct, but it's less to get wrong.
| https://softwareengineering.stackexchange.com |
15,486 | [
"https://mathoverflow.net/questions/15486",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78/"
] | Recall that a <em>group</em> is an associative, unital monoid $G$ such that the map $(p_1,m) : G \times G \to G\times G$ is an isomorphism of sets. Here $p_1$ is the first projection and $m$ is the multiplication, so the map is $(g_1,g_2) \mapsto (g_1,g_1g_2)$.
My question is a basic one concerning the definition of ... | You can always do this. Take any $b$ and define $d = p_2 b$. Then $b' = (p_1, d)$ is equivalent to the original $b$. To see this note that
$$(p_1, m) \circ b = (p_1b, m \circ (p_1 b, d)) \simeq id = (p_1, p_2) $$
The first component shows $p_1 b \simeq p_1$. We use this transformation $\times id$ to show that
$b \... | I think the answer is no, but cannot give a counterexample off hand. What is true is that there will be an equivalent monoidal category such that the corresponding functor $b$, does have the property. Any 2-group is equivalent to a strict 2-group (which can be assumed to come from a crossed module). What would be an in... | https://mathoverflow.net |
422,034 | [
"https://physics.stackexchange.com/questions/422034",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/203640/"
] | I was reading the definition of heat capacity and it says that
$$\Delta Q = C \ \Delta T$$
(introduction to statistical physics - K. Huang)
So my question is that, if we consider an isothermal process, becuase temperature remains the same, $\Delta Q$ would be zero. And $\Delta U= \Delta W$ by the first law, but thats... | Suppose you take an ideal gas as your system.
Then according to the equipartition theorem its total internal energy would be $\frac{1}{2}k_B T$ per degree of freedom per molecule. So if $f$ is the number of degrees of freedom then the total internal energy of your $N$ molecule ideal gas system would be $$\frac{f}{2}NK... | In freshman physics, they did us a disservice by incorrectly teaching us that heat capacity is defined by $Q=C\Delta T$ (or $Q=mC\Delta T$, where C is the heat capacity per unit mass) (or $Q=nC\Delta T$, where C is the heat capacity per mole). This definition works fine as long as no work is done. However, when work... | https://physics.stackexchange.com |
3,889,379 | [
"https://math.stackexchange.com/questions/3889379",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/74378/"
] | <blockquote>
Let <span class="math-container">$G$</span> be a finite abelian group, and let <span class="math-container">$n$</span> divide <span class="math-container">$|G|$</span>. Let <span class="math-container">$m$</span> be the number of solutions of <span class="math-container">$x^n=1$</span>. Prove that <span ... | By the fundamental theorem of finite abelian groups we may choose a <span class="math-container">$G$</span> subgroup <span class="math-container">$G_n$</span> of size <span class="math-container">$n$</span>. Lagrange's theorem gaurantees <span class="math-container">$G_n\leq\ker(\varphi_n)$</span> where <span class="ma... | Let <span class="math-container">$p$</span> be a prime and assume <span class="math-container">$p^k\|n$</span>. If one of the factors in the product representation of <span class="math-container">$G$</span> is <span class="math-container">$C_{p^r}$</span> for some <span class="math-container">$r\ge k$</span>, then this... | https://math.stackexchange.com |
2,263,768 | [
"https://math.stackexchange.com/questions/2263768",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/442955/"
] | I'm trying to figure out whether the following optimization problem is convex, but I haven't found the proper answer yet. I have not much experience in convex analysis so I hope I can get some insight from you. The following objective function arises from a practical data mining problem we are trying to solve.
The pr... | Suppose that $\{x,y\}$ is linearly dependent. Then either $x$ is a multiple of $y$ or vice versa. Without loss of generality, assume that $x = cy$. Then
$$\lambda x = \phi(x) = \phi(cy) = c\phi(y) = c\mu y = \mu (cy) = \mu x$$
Thus, we have that $\mu x = \lambda x$. Since $x\neq 0$, it follows that $\mu = \lambda$.
| You may want to see a proof that can be generalized to more than two vectors.
Consider $\alpha x+\beta y=0$. Then
\begin{align}
\varphi(\alpha x+\beta y)&=0 \\
\mu(\alpha x+\beta y)&=0
\end{align}
which become
\begin{align}
\alpha\lambda x+\beta\mu y&=0 \\
\alpha\mu x+\beta\mu y&=0
\end{align}
Subtract... | https://math.stackexchange.com |
93,544 | [
"https://mathoverflow.net/questions/93544",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18238/"
] | [EDIT]: After getting a very nice answer by Kevin Buzzard I realize that my question was a little bit too vague and I try to restate it more precisely.
As the title says, I would like to understand an isomorphism of Hida from a more geometric perspective than what I normally read. What bothers me is that there are two... | I am not sure what your criteria would be for a proof to be given a geometric interpretation, but the reason why weights "disappear" when we take the inverse limit on the level stems from the contraction property of Hecke operators (at $p$), or informally from the fact that Hecke operators at $p$ diminish the level.
A... | As you've spotted, there are two ways to do $p$-adic modular forms. The point is that at some point you take a limit of classical modular forms, and there are a whole host of modular forms which may have e.g. very big weight but whose $q$-expansions are $p$-adically very close 1. Multiplication by such a gadget can com... | https://mathoverflow.net |
1,599,368 | [
"https://math.stackexchange.com/questions/1599368",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/59553/"
] | This was a question in a maths contest, where no calculator was allowed. Also, note that only a (>,< or =) relationship is being searched for and not the value of the numbers itself.
<blockquote>
Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$ ?
</blockquote>
<hr>
<strong>What I've done:</strong... | Starting with:
$$\sqrt[2015]{2015!}\mid\sqrt[2016]{2016!}$$
<hr>
Raise each side to the power of $2015\cdot2016$:
$$2015!^{2016}\mid2016!^{2015}$$
<hr>
Divide each side by $2015!^{2015}$:
$$2015!^{1}\mid2016^{2015}$$
<hr>
Write it explicitly as:
$$\underbrace{1\cdot2\cdot\ldots\cdot2015}_{2015\text{ terms}}\m... | Look at the function:
$$y(x)=\sqrt[x]{x!}=\left(\Gamma(x+1)\right)^{1/x}$$
It's a monotonically strictly increasing function, as:
$$y'(x) = \frac{1}{x}\left(\Gamma(x+1)\right)^{1/x-1}\Gamma'(x+1)>0,\forall x>1$$
$\blacksquare$
As a side note:
$$\lim_{x\to\infty}y(x)=\frac{1}{e}x$$
So you can expect the RHS to be... | https://math.stackexchange.com |
138,680 | [
"https://electronics.stackexchange.com/questions/138680",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52570/"
] | I'm trying to interface with an LCD display (HD44780). I came across a tutorial on the internet to send characters and strings to the display. Everything went well and it works fine but I have no idea why a pointer is used. I'm not quite familiar with pointer in C. I know that thay can hold addresses of variables etc. ... | C language does not have a native string format, so instead, strings are implemented as character arrays. The <code>string_to_lcd</code> function receives a pointer to the memory location where the first character of the string is.
By conventions in C strings are terminated with a null character (0x00).
<strong>Edit<... | This is a well commented source code, at least it already gives the functions' main function in brief.
In C language, there is a data type "array", when you need display some "words" or "character strings" on the display, you can present this in C language as a "characters array". And you can use a "pointer" to point ... | https://electronics.stackexchange.com |
70,088 | [
"https://dba.stackexchange.com/questions/70088",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/41591/"
] | I have two schema. Schema1 and Schema2
How would I transfer all the tables from schema1 to schema2?
| Execute this for all of the tables:
<pre><code>alter schema2
transfer schema1.table1;
</code></pre>
To programmatically get the statements to execute:
<pre><code>declare
@SourceSchemaName sysname,
@DestinationSchemaName sysname,
@AlterStatements varchar(max);
set @SourceSchemaName = 'NewSchema';
set @De... | Assuming destination schema is empty:
<pre><code>DECLARE @sql NVARCHAR(MAX) = N'';
SELECT @sql += N'
ALTER SCHEMA Schema2 TRANSFER Schema1.'
+ QUOTENAME(t.name) + ';' FROM sys.tables AS t
INNER JOIN sys.schemas AS s
ON t.[schema_id] = s.[schema_id]
WHERE s.name = N'Schema1';
PRINT @sql;
-- EXEC sp_executesq... | https://dba.stackexchange.com |
222,146 | [
"https://security.stackexchange.com/questions/222146",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/222658/"
] | In the backend I am currently working on I have a servlet (call it <code>S</code>) and a WebSocket endpoint (call it <code>E</code>). <code>S</code> needs to communicate with <code>E</code>, yet, as of now, any WebSocket client may connect to <code>E</code>.
My question is: how should I name the URI of <code>E</code>... | While I agree with the previous answer that naming should not be considered a strong security control, I would suggest that you avoid naming things in an overtly obvious manner (i.e. "ThisServerHostsMyCrownJewels.company.local" :) )
In terms of how to allow only 'S' to talk to 'E', that is a technical question for whi... | Naming should have nothing to do with security, as security by obscurity should not be your goal. Instead you should find a way to authenticate the user (using a passphrase, a challenge...)
| https://security.stackexchange.com |
506,422 | [
"https://electronics.stackexchange.com/questions/506422",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/255762/"
] | I'm working on logging GPS values(from u-blox Neo 6m GPS module) to an SD card using an Arduino Pro Mini.
The code I'm working with works without any flaw when we connect the Arduino to the laptop with a USB cable
(power source is from the USB port.)
Once I run my program, all the GPS coordinates along with other data ... | I had a similar problem with CR2032 in one of my very first projects! CR2032 simply can't supply enough current, its voltage falls into unusable as soon as you pull anything significant to power the MCU (I had STM32 blue pill and it pulled single CR2032 nominal 3.2V almost immediately down to borderline 2.65V with full... | A CR2032 battery, or many in series, could perhaps power up the Arduino.
Saving data to the SD card can take bursts of current up to 300 mA depending on the SD card make/model/speedgrade.
One CR2032 battery manufacturer says the maximum current drawn from battery is 10mA, so it might be possible to parallel up to 30 ba... | https://electronics.stackexchange.com |
42,022 | [
"https://mathoverflow.net/questions/42022",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5210/"
] | Let $A$ be a C*-algebra. Suppose that $P:A \rightarrow A$ is a contractive completely positive projection. Does the range $P(A)$ is completely order isomorphic to a $C^*$-algebra?
In the case where the answer is false:
Is it true in supposing, in addition, that the range $P(A)$ is an operator system, $A$ unital and $... | Yes. $P(A)$ is abstractly a C$^\ast$-algebra $B$ under the Choi-Effros product: $a\circ b := P(ab)$; and $P(A)$ is completely order isomorphic to $B$. See (the proof of) Theorem 3.1 in [M.-D. Choi and E. G. Effros; Injectivity and operator spaces. J. Functional Analysis 24 (1977), 156-–209]. Moreover, there is a surjec... | I would add to Taka's answer, since the Choi-Effros paper is not widely available online, that the nontrivial parts of the proof are to show the "C$^*$-identity" $\|x\|^2=\|x^*x\|$, associativity, and to check the completeness of $P(A)$.
Indeed, the algebra $(P(A),+,\circ)$ is a $*$-algebra, normed with the norm inhe... | https://mathoverflow.net |
638,699 | [
"https://physics.stackexchange.com/questions/638699",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/244756/"
] | After a star becomes a White dwarf, it resists gravitational collapse mainly due to the electron degeneracy pressure. If the mass of the white dwarf is greater than the Chandrasekhar limit, the degeneracy pressure cannot resist the collapse any longer and is doomed to become a neutron star or a black hole. Why can't th... | The basic problem is that for a sufficiently massive star, the electrons become relativistic. The fine details of this calculation are rather complicated, but you can get a qualitative sense of the argument as follows:
For non-relativistic fermions at zero temperature, it is possible to show that the total energy of <... | An alternative: As the white dwarf mass increases, the electrons become ultra-relativistic. Hydrostatic equilibrium is not possible for ultra-relativistic degeneracy pressure.
Hydrostatic equilibrium requires:
<span class="math-container">$$\frac{dP}{dr} = - \rho g \ . $$</span>
Working just with proportionalities, non... | https://physics.stackexchange.com |
446,985 | [
"https://physics.stackexchange.com/questions/446985",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75502/"
] | What difference does it makes if the same experiment is conducted with a transparent box? I mean what is the significant of the opaque box in the original thought experiment? Can't we observe the radioactive decay in progress? Isn't this experiment about the probabilistic nature of particle decaying?
| The idea is that Schrodinger's cat must be perfectly isolated from all outside influence. That's why it's imagined as being put in a box to begin with, as opposed to say the guy (Schrodinger?) watching it just turning his back. By definition, a transparent box is one which admits a particular outside influence - namely... | Not knowing the decay time, we can use a transparent box and a lot of cats to get a statistics of the mean decay time. After this experiment we could open a opaque box using the statistical evaluated time and after a lot of cats we will get the result, that in 50% the cat is death.
For the description of the situation... | https://physics.stackexchange.com |
3,264,384 | [
"https://math.stackexchange.com/questions/3264384",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/679045/"
] | <span class="math-container">$\log_2 3\cdot\log_3 4\cdot\log_4 5\cdots\log_{2019} 2020=x$</span>
Find the largest natural number which is less than <span class="math-container">$x$</span>.
| It is not that it is possible to express...etc., it is just that that's the way we have to check continuity of <span class="math-container">$\;F\;$</span> at <span class="math-container">$\;a\;$</span> . In fact, we have that
<span class="math-container">$$F(x)=\begin{cases}f(x),&x\neq a\\{}\\0,&x=a\end{cases... | You have an assumption that <span class="math-container">$f $</span> has a limit <span class="math-container">$0$</span> at <span class="math-container">$a$</span>, so when you define <span class="math-container">$F $</span> to be equal <span class="math-container">$f$</span> near <span class="math-container">$a$</spa... | https://math.stackexchange.com |
402,941 | [
"https://physics.stackexchange.com/questions/402941",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/171780/"
] | I am taking a course on Quantum Mechanics and last class we saw the coherent states of the harmonic oscillator, namely states $ | \lambda \rangle $ such that $$ a | \lambda \rangle = \lambda | \lambda \rangle $$ and we saw how they represent the classical situation when $ \lambda \to \infty $.
The professor also told ... | Today I went back with my professor and asked this same question. Here goes my version of his answer. Apparently the answer is yes. Every quantum system has some set of coherent states that reproduce what we would wait in the classical limit.
In the case of the harmonic oscillator these are the eigenstates of the ann... | Coherent states are eigenstates of annihilation operator. If you can reduce/transform a particular problem to a simple harmonic oscillator problem, then by construction itself there will be coherent states.
In the context of the hydrogen atom problem, hereby we consider only the angular momentum part of the problem. I... | https://physics.stackexchange.com |
2,906,958 | [
"https://math.stackexchange.com/questions/2906958",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/346515/"
] | Is trivial show that $I \subseteq R$, but i'm stuck proving that $R\subseteq I$.
If i take a $x\in R \implies x\in \sqrt{I} \implies \exists n \in \mathbb{N}; x^n\in I$
But, how i can show that $x \in I$ ?
| Figured out that applying De L'Hospital provides a brutally fast proof (assuming $f$ is continuous at $x_0$) :
$$\lim_{x \to x_0}\frac{f(x) - f(x_0)}{x-x_0} = \lim_{x \to x_0} \frac{[f(x) - f(x_0)]'}{(x-x_0)'}=\lim_{x\to x_0} \frac{f'(x)}{1}=c \implies f'(x_0) = c$$
| Assuming $f$ is continuous at $x_0.$ It is equivalent to show $g'(0)=c$ where $g(x)=f(x+x_0)-f(x_0).$ That is, to show $\lim_{x\to 0}\frac {g(x)}{x}=c.$
We have $\lim_{x\to 0}g'(x)=c$ and $\lim_{y\to 0}g(y)=g(0)=0.$
Since $\lim_{x\to 0}g'(x)=c,$ there exists $x_1>0$ such that $g'$ is bounded on $(0,x_1).$ ... | https://math.stackexchange.com |
12,919 | [
"https://astronomy.stackexchange.com/questions/12919",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/6760/"
] | The materials inside a neutron star are densely packed (extremely close to each other) and as time goes by say about an <strong><em>eon</em></strong> later, most of the neutrons would eventually tunnel into each other and voila! the neutron star becomes black hole? sound suspicious to me but can it happen?
| <blockquote>
The materials inside a neutron star are densely packed (extremely close to each other) and as time goes by say about an eon later, most of the neutrons would eventually tunnel into each other
</blockquote>
Based on what ?
The material's collapse was <em>halted</em> from an astonishingly high speed coll... | <blockquote>
Would all neutron stars inevitably collapse into black holes due to quantum tunnelling?
</blockquote>
Not to my knowledge. Where did you hear that? I don't think it's true, because if it was you could make the same claim about any massive body.
<blockquote>
The materials inside a neutron star are de... | https://astronomy.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.