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 |
|---|---|---|---|---|---|
581,075 | [
"https://physics.stackexchange.com/questions/581075",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/257503/"
] | I had been working on a problem recently and i stumbled upon something I did not quite get. So the relevant part of the problem is like this:
Suppose we have two conducting spheres with radii a and
b separated by a distance, r, much greater than either
radius( refer to diagram below). A total charge Q is shared between... | The friction force <span class="math-container">$F_nμ_k$</span> only applies <strong>while the body is moving</strong>, and this force's direction is opposite to the movement direction.
In your formula <span class="math-container">$a_x=g(sin\alpha-\mu_{k}cos\alpha)$</span>, you effectively subtract the friction force f... | At critical angle :
<span class="math-container">$$ \alpha_{_{th}} = 2 \arctan \left( {\sqrt{\frac {1}{\mu_{k}^2} + 1} - \frac 1\mu_{k}} \right) $$</span>
and below, toboggan will stop moving due to kinetic friction force will overcome gravity speedup. This will make <span class="math-container">$a_x = 0$</span>, so af... | https://physics.stackexchange.com |
43,996 | [
"https://mathoverflow.net/questions/43996",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4556/"
] | Given a finite subset $S$ not containing the identity element in a residually finite group $G$, does there always exist a normal subgroup of $G$ which has finite index (in $G$) and
which avoids $S$? (If $S$ is a singleton, this is of course the definition of a residually finite group.)
| Yes, take the intersection of the normal subgroups $N_1, N_2, ..., N_k$ of finite index avoiding elements $x_1,x_2,...,x_k$ of your set. It is normal and of finite index (at most the product of indices of $N_i$).
| The answer is yes. Since $G$ is residually finite, given $g\in S$ there is a finite group $F_g$ and a homomorphism $\phi_g: G\to F_g$ whose kernel does not contain $g$. Now $S$ is disjoint from the kernel of the product of these homomorphisms $G\to \prod_{g\in S}F_g$, and the target is a finite group.
More generally ... | https://mathoverflow.net |
334,769 | [
"https://softwareengineering.stackexchange.com/questions/334769",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/184339/"
] | I've been told that in functional programming one is not supposed to throw and/or observe exceptions. Instead an erroneous calculation should be evaluated as a bottom value. In Python (or other languages that do not fully encourage functional programming) one can return <code>None</code>(or another alternative treated ... | First of all, let's clear up some misconceptions. There is no "bottom value". The bottom type is defined as a type that is a subtype of every other type in the language. From this, one can prove (in any interesting type system at least), that the bottom type <em>has no values</em> - it is <em>empty</em>. So there is no... | Since there has been so much interest in purity over the last few days, why don't we examine what a pure function looks like.
A pure function:
<ul>
<li>Is referentially-transparent; that is, for a given input, it will always produce the same output.</li>
<li>Does not produce side-effects; it doesn't change the inputs... | https://softwareengineering.stackexchange.com |
27,310 | [
"https://dba.stackexchange.com/questions/27310",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5654/"
] | When doing a count (aggregate) SQL query, what can speed up the execution time in these 3 database systems? I'm sure many things could speed it up (hardware for one), but I'm just a novice DBA, so I'm sure I'll be getting a few answers here. I migrated about 157 million rows to a SQL Server database, and this query i... | Netezza is an appliance that is designed to excel at large table scans, so that's why you're getting such fast results on that system.
For your SQL Server, you can greatly speed up the row count by querying from the sys.dm_db_partition_stats DMV.
<pre><code>SELECT s.name AS [Schema], o.name AS [Table], SUM(p.row_c... | Here's a SQL Server solution that uses <code>COUNT_BIG</code> inside an indexed view. This will get you a transactionally-consistent count without the overhead of big table or index scans, and without the need for the storage required for the latter:
<pre><code>CREATE TABLE [dbo].[MyTable](id int);
GO
CREATE VIEW [db... | https://dba.stackexchange.com |
3,403,400 | [
"https://math.stackexchange.com/questions/3403400",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/460999/"
] | Let <span class="math-container">$a,b,c,d$</span> be different primes.
Do the following hold?
<span class="math-container">$(2a+b)\in \Bbb P\vee(2a+c)\in\Bbb P$</span>
<span class="math-container">$(2c+a)\in \Bbb P\vee(2c+d)\in\Bbb P$</span>
<span class="math-container">$(2b+a)\in \Bbb P \vee (2b+d)\in \Bbb P$</spa... | Recall that <span class="math-container">$g^*(s)=E[e^{-sx}]$</span> and that the Taylor series for <span class="math-container">$g^*(s)$</span> around <span class="math-container">$s=0$</span> is given by <span class="math-container">$g^*(s)=g^*(0)+\frac{\mathrm{d}g^*}{\mathrm{d}s}|_{s=0}+\frac{1}{2}\frac{\mathrm{d}^2... | Please pay attention to the fact that <span class="math-container">$T_Q^*(s)=\frac{1-\rho}{1-\rho h^*(s)}$</span> is not the moment generating function. It is the Laplace (or Laplace-Stieltjes) transform.
I will use the notation that you suggested. <span class="math-container">$\lambda$</span> - arrival rate. <span c... | https://math.stackexchange.com |
5,093 | [
"https://stats.stackexchange.com/questions/5093",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/529/"
] | I am currently working on a RandomForest based prediction method using protein sequence data. I have generated two models first model (NF) using standard set of features and the second model (HF) using hybrid features. I have done Mathews Correlation Coefficient (MCC) and Accuracy calculation and the following are my r... | I like the idea of parsimony- the smaller the number of variables in the model, the better. Unless you are driven theoretically of course. Feature selection refers to the process of choosing which variables to use in the model (getting the best combination of variables). There are lots of different options for feature ... | It just seems those two variants are equivalent; yet some better test should be made to confirm this, at least cross validation.<br>
Also if this NF and HF sets have some attributes in common, it may suggest that only this common part is useful -- I would invest some time in making feature selection.
| https://stats.stackexchange.com |
66,973 | [
"https://mathoverflow.net/questions/66973",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15603/"
] | I need to compute a large number of inverses of the following form:
$(A \Lambda_k A^\top)^{-1}$
where $A \in \mathbb{R}^{m \times n}$, $n > m$ and $\Lambda_k = \text{diag}(\lambda_1, ..., \lambda_n)$ with $\lambda_i > 0$. Is there an efficient way to do this?
In the end, I want to sample from Gaussians with me... | Now that you've provided some more information, I think I can make some useful suggestions.
First, a quick review of linear transformations of multivariate normal random vectors. If $z$ is an MVN vector with mean $\mu$ and covariance matrix $C$, and $M$ is a matrix of the appropriate size and $y=Mz$, then $y$ is MV... | You haven't really told us much about the problem.
Are you working in conventional single or double precision floating point arithmetic, or are you working in some obscure field?
Are the elements $\lambda_{k}$ positive, or could some of them be negative?
Are your matrices $A$ sparse, or are they fully dense? ... | https://mathoverflow.net |
404,174 | [
"https://stats.stackexchange.com/questions/404174",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | If <span class="math-container">$X_{1},X_{2},\ldots,X_{n}$</span> are independent random variables with common mean <span class="math-container">$\mu$</span> and variances <span class="math-container">$\sigma^{2}_{1},\sigma^{2}_{2},\ldots,\sigma^{2}_{n}$</span>. Prove that
<span class="math-container">\begin{align*}
\f... | <strong>Let's minimize the algebra.</strong> We can do this by focusing on the coefficient of <span class="math-container">$\sigma_1^2.$</span>
First, because all the variables have the same mean,
<span class="math-container">$$E[X_i - \bar X]=\mu - \mu = 0$$</span>
for all <span class="math-container">$i,$</span> imp... | I would start from
<span class="math-container">\begin{align}
\operatorname{E}(X_i-\overline X)^2&=\operatorname{E}[(X_i-\mu)-(\overline X-\mu)]^2
\\&=\operatorname{E}(X_i-\mu)^2+\operatorname{E}(\overline X-\mu)^2-2\operatorname{E}(X_i-\mu)(\overline X-\mu)
\\&=\sigma_i^2+\operatorname{Var}(\overline X)-2... | https://stats.stackexchange.com |
231,936 | [
"https://electronics.stackexchange.com/questions/231936",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10456/"
] | It's almost twice as fast charging my phone directly from the power plug compared to if I charge my phone from the computer's USB port. Why? Isn't the charge the same or is it that USB has much lower voltage, and therefore it is much less energy per time unit?
| In my opinion, it's maybe because the computer's motherboard limits the current when charging through the USB.
In details, there are two phases when charging a battery. One is constant current phase, which is fast and powerful and happened at the beginning. The other one is constant voltage phase, which is slow and ha... | USB charging on modern phones will be limited by the phone. If it detects a standard USB host port, most phones will self limit themselves to 500 mA, even if the USB port can provide more. If it detects a dedicated charging port, it will pull more. Depends on how the port is wired. Apple and the USB spent differ.
| https://electronics.stackexchange.com |
1,551,141 | [
"https://math.stackexchange.com/questions/1551141",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/255155/"
] | Given the chi-squared distribution $ \chi^2(5) $. Provide c,d such that :
$ P(c<X<d)=0,95 $ and $P(X<c) =0,025$
Any idea on how to calculate this so that both conditions hold?
| $$P(c < X < d) = P(X < d) - P(X \le c)$$
Since chi-squared is continuous, we have $P(X \le c) = P(X < c) = 0.025$
So we have
$P(c < X < d) = P(X < d) - P(X \le c) = P(X < d) - P(X < c) = P(X < d) - 0.025$
Since $P(c < X < d) = 0.95$,
$$P(X < d) = 0.025 + 0.95$$
Now we have:
... | The first thing to do would be to find $c$, using your given $P(X<c) = 0.025$. Then figure out what $P(X<d)$ is and use that to find $d$.
| https://math.stackexchange.com |
91,094 | [
"https://mathoverflow.net/questions/91094",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22025/"
] | Is every weakly compact operator from $\ell_1$ into $c_0$ extendible
to any larger space? Equivalently, is every weakly compact operator from $\ell_1$ into $c_0$ extendible to $\ell_\infty$?
| @Joaquin: This one pushed me. It is, IMO, one of the nicest problems on Banach space theory asked on MO.
The answer is no. For a counterexample, take any weakly compact operator $T:\ell_1 \to c_0$ that preserves $\ell_1^n$ uniformly for all $n$. In fact, since $\ell_1^n$ embeds isometrically into $\ell_\infty^{2^n... | <strong>Edit:</strong> it seems that I probably misunderstood the question, see Bill Johnson's comments below.
<hr>
No. The identity map factors through $\ell^2$, so it is weakly compact (no doubt one can also see that directly). If it extended continuously to $\ell^\infty$ then this would give a projection of $\ell^... | https://mathoverflow.net |
72,896 | [
"https://mathoverflow.net/questions/72896",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7206/"
] | It is known that $L\models 2^\kappa=\kappa^+$, and that for a set of ordinals $A$ we know that $L[A]\models \exists\lambda\forall\kappa>\lambda(2^\kappa=\kappa^+)$.
In this sense, there is some similarity between $L$ and $L[A]$. Both models have definable well orderings, and both models have a very nice sense of mi... | There are several issues.
<ul>
<li>First, of course, when $A\in L$ then $L[A]=L$ and
consequently $I_A=I$.</li>
<li>In any case, there will be large overlap in $I_A$ and
$I_B$, since they are both class clubs, and hence
intersect in a closed unbounded class of ordinals.</li>
<li>If $0^\sharp\in L[A]$, then every cardi... | It can also be the case that $I_A$ is a periodic (but club) subclass of $I$: by Jensen Coding one can define (necessarily by class forcing) reals $a\subset\omega$ with $0^\sharp \notin L[a]$ and that there are countable ordinals $\alpha,\beta$ so that for all $\tau\in On$ the $\tau $'th silver indiscernible for $a$ is ... | https://mathoverflow.net |
161,762 | [
"https://softwareengineering.stackexchange.com/questions/161762",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34925/"
] | (Written against GPLv2.)
It is always said that GPL does not prohibit selling the software, as long as its source code is provided under the same license (GPL). Now, I do not understand how it is consistent with Section 2b:
<blockquote>
You must cause any work that you distribute or publish, that in
whole or ... | I am not a lawyer either, but here's how I see it:
A sales agreement is a contract between you (the <em>first</em> party) and the buyer (the <em>second</em> party). The clause you have quoted says absolutely nothing about anything that happens between the first party and the second party.
What the clause does say is... | Disclaimer: I'm not a lawyer
(section 2a)
<blockquote>
You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee.
</blockquote>
This indeed confirms that you may charge a fee in some cases. e.g. warranty protection.
Since "you" refe... | https://softwareengineering.stackexchange.com |
3,714,234 | [
"https://math.stackexchange.com/questions/3714234",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/711912/"
] | I'm trying to show that the map <span class="math-container">$\{ 0,\ldots,n-1\} \rightarrow \{0,\ldots,n-1\}$</span>, defined by <span class="math-container">$$x\mapsto x+a \text{ mod} n$$</span> belongs to <span class="math-container">$\mathcal{S_n}$</span>,where <span class="math-container">$g.c.d(a,n)=1$</span> and ... | If we set <span class="math-container">$y_n=x_n^2$</span> then
<span class="math-container">$$y_{n+1}=\frac{y_n}2+\frac c4+\frac{y_n}2\sqrt{1+\frac{c}{y_n}}=y_n+\frac{c}2+O(y_n^{-1}).$$</span>
This proves that <span class="math-container">$(y_n)$</span> grows at least linearly, so that <span class="math-container">$y_n... | You've already derived that
<span class="math-container">\begin{align}
x_{n+1}^2 - x_n^2 &= \frac 12 \left(\sqrt{1 + \frac{c}{x_n^2}} -1 \right) + \frac c4 \\
&= \frac{c}{2x_n^2} \frac{1}{\sqrt{1 + \frac{c}{x_n^2}} +1} + \frac c4.
\end{align}</span>
Taking <span class="math-container">$n \to \infty$</span> we ... | https://math.stackexchange.com |
344,150 | [
"https://stats.stackexchange.com/questions/344150",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/181051/"
] | Basically if I have binary sequence that I want to check against, and I want to determine how far other binary sequences are to this first sequence, what is the most appropriate measure to use.
The distance measures i have seen, like Manhattan etc., all give numeric values indicating ultimately the difference, not how... | Consider just a single feature column for clarity, so if the output is $y$ and the input is $x$ then $y = \text{relu}(w^Tx+b)$.
This is useful in itself: Suppose $x_1$ is the roughly speaking, the amount of cat detected and $x_2$ is the amount of dog detected. Then $w^Tx$ can compute the amount of cat minus the amoun... | No. Generally, number of filters in every layer is a hyperparameter that has different optimal value for every dataset. The same holds also for the size of the filters: Convolutions 1x1 are not so much different from convolutions 3x3; they <strong>cannot</strong> aggregate information from neighboring spatial locations... | https://stats.stackexchange.com |
50,674 | [
"https://electronics.stackexchange.com/questions/50674",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | How to calculate the Vout when the input voltage Vin is = 20V DC + 10V AC.
Here is the circuit:
<img src="https://i.stack.imgur.com/9LsuM.jpg" alt="enter image description here">
| Due to some controversy, I will work the AC component of the answer two different ways.
(1) The parallel combination of the R and C is:
\$Z_{EQ} = 100 || Z_C = 100||\dfrac{1}{j2\pi(2000Hz)(8\mu F)} = 100||(-j9.95) = (0.980 - j9.85) \Omega \$
By voltage division, the AC signal is reduced by:
\$|\dfrac{Z_{EQ}}{Z_{EQ}... | You can treat resistors, capacitors and inductors as resistors with a complex resistance (impedance):
Z = R+ j*X
<ul>
<li>resistor: R = Ohms resistance, X = 0</li>
<li>capacitor: R = 0, X = -1/(omega*C)</li>
<li>inductor: R = 0, X = omega*L</li>
</ul>
Then use common formulas for parallel and serial circuits to ca... | https://electronics.stackexchange.com |
54,075 | [
"https://dba.stackexchange.com/questions/54075",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | Made a mistake and mistyped an alter database command for tempdb.
Now the instance won't start. I can't start in single user mode using -m as it states the tempdb could not be found. I tried using:
<pre><code>net start msqsqlserver /f /t3608
</code></pre>
But then I can't actually connect to the instance at all usin... | Start SQL Server as an application, not a service, in minimal config mode, and only recovering master, from a command prompt:
<pre><code>[path to this instance]\BINN\sqlservr.exe -c -f -T3608
</code></pre>
(Add <code>-s InstanceName</code> if this is a named instance.)
Now, in a different command prompt, connect usi... | <ol>
<li>Start sql server in single user mode -
Net Start MSSQLServer /mSQLCMD /f/t3608</li>
<li>To be in single user mode sqlcmd -S. –E</li>
<li>Run the commands </li>
</ol>
Alter database tempdb modify file (name = tempdev, filename = 'E:\SQLDATA\DEFAULT\tempdb.mdf')
Alter database tempdb modify file (name = templ... | https://dba.stackexchange.com |
76,903 | [
"https://security.stackexchange.com/questions/76903",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15194/"
] | Often I read about compromise due to visit a malicious site which download some exploit to your computer. I've never seen a detailed process, all books/tutorials I read just say sentences like "once the site is visited, the target is compromised", "redirecting the user to an attacker-owned site which downloads maliciou... | Generally, most drive by browsing attacks are through browser vulnerabilities, which redirect you etc.,
but some are through PDF render engines, or in fact any input or display functionality.
These do not have to be zero-days. Many browsers have vulnerabilities - some that have been known for years and have fixes out... | Drive by exploits are a result of targeting vulnerabilities in a particular web browser. A web browser is a large piece of software with the potential for many bugs. PDF rendering, flash players, Javascript engines are all complex and have a long history of vulnerabilities.
A good mitigation is definitely keeping your... | https://security.stackexchange.com |
257,989 | [
"https://electronics.stackexchange.com/questions/257989",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/118420/"
] | I was going through a document on GMSK modulation where it is specified that it is immune to distortion from non linear amplifiers.Also it was mentioned that non linear amplifiers are more battery efficient.The exact lines are:-
"Non-linear amplifiers are more efficient in terms of the DC power input from the power ra... | When you push a non-linear amplifier transistor to <strong>extreme</strong> non-linearity, it becomes a fast switch, whose on-off cycle period is 1/f (where f is the RF carrier frequency). A switch dissipates no power when <strong>OFF</strong> (where current is zero), and it dissipates no power when <strong>ON</strong>... | All amplifiers are nonlinear, there's no such thing as a "Linear Amplifier". You can operate an amplifier in a linear region, thus the shorthand. Some terms you should be looking for are Power Added Efficiency, Saturated Output, and Quiescent current.
| https://electronics.stackexchange.com |
30,816 | [
"https://stats.stackexchange.com/questions/30816",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/770/"
] | As a non-native english speaker I was wondering which of the <strong>square</strong> or <strong>squared</strong> expression I should use. For instance in mean <strong>square</strong> error or mean <strong>squared</strong> error.
According to the Internet, it seems both forms are used indistinctly. Is one expression mo... | <strong>The conceptual uses of "square" and "squared" are subtly different,</strong> although (almost) interchangeable:
<ul>
<li>"Squared" refers to the past <em>action</em> of taking or computing the second power. E.g., $x^2$ is usually read as "x-squared," not "x-square." (The latter is sometimes encountered but I ... | Nope! Both can be used.. interchangeably :-) it's the same.
| https://stats.stackexchange.com |
912,409 | [
"https://math.stackexchange.com/questions/912409",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/71487/"
] | Let $f[a,b]: \mathbb R \rightarrow\mathbb R$ be a (Riemann) integrable function such that $f \geq0$ and $\int_{a}^{b}f = 0$. Verify with counterexamples that the sentence aforementioned conditions do not imply $f\equiv 0$.
I couldn't think of any functions except for the case when $a = b$, which is trivial. More than... | For example you can set:
$$ f(x) = \begin{cases} 0 & x \not = c \\ K & x = c\end{cases}$$
with $c \in [a,b]$ and $0 < K < \infty$ and you get, for every possible values of $c$ and $K$:
$$ \int_a^b f(x) \textrm{d}x= 0$$
The trick is that integral "doesn't see" set of null measure (points). Given a funct... | consider $f(a)= 8$ and $f(x)=0$ for every $x\neq a$, then $f$ satisfies the terms and obviously not always zero
| https://math.stackexchange.com |
77,591 | [
"https://electronics.stackexchange.com/questions/77591",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9243/"
] | <h2>Background</h2>
I have a USB webcam installed above my door that acts like a video intercom for my countryside house, but I'm worried somebody may try to cut the wires, disable it and damage the computer it's connected to while doing so. My neighbors there have much more expensive systems installed and some of the... | Most USB ports are protected against short-circuit.
You could be extra sure your computer would survive by connecting the camera to a cheap USB <em>powered</em> hub (and connecting the hub to the computer).
To be even more sure, you should open the hub and physically disconnect pins 1, 4, and 5 (if present) of the U... | Wireless would prevent somebody from electrically damaging the host computer through the cable, but if you're dealing with vandals I would suggest a decoy/dummy camera in plain sight with the real one hidden.
| https://electronics.stackexchange.com |
712,248 | [
"https://physics.stackexchange.com/questions/712248",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/310823/"
] | My reason for thinking that sand in a vacuum would be a good insulator is that heat cannot be conducted in a vacuum, and the area of contact between adjacent grains of sand is very small, which means heat would transfer between grains relatively slowly. Is this correct, or is there something I'm missing?
Also, the sand... | Simply put: If sand in vacuum had a heat conductivity close to that of vacuum, i.e., at least much closer to zero than the heat conductivity of the silicon dioxide (aka glass) it consists of, something similar would have to be true for sand in air.
But: the heat conductivity (all numbers from the German Wikipedia) of d... | Powder filled vacuum (I don't know if sand per se is used for this purpose) is in fact used in cryogenic insulation, and can be better than vacuum alone, because vacuum alone is susceptible to radiant heat transfer and also a type of heat conduction that happens because the mean free path of the remaining molecules (in... | https://physics.stackexchange.com |
53,025 | [
"https://physics.stackexchange.com/questions/53025",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/14273/"
] | I have read that there exist non-integer fractal dimensions and the images generated from these dimensions look organic and they seem to provide a new way of describing the world around us, which raises the question. How many dimensions (spatially or otherwise) do we live in? 3, 3.1, 3.5 as well as 1 time dimension or ... | Off course the Idea of having fractal dimensions in our real physical word is extremely interesting, but till now, and despite of all the experiments made, there is no evidence of such a thing (for example, in LHC there is a dedicated team of physicists that analyzing colider data for any variation that may be treated ... | The world is incredibly well-described locally by $\mathbb R^4$ and we know no experiment that would pretend the contrary.
| https://physics.stackexchange.com |
142,159 | [
"https://dba.stackexchange.com/questions/142159",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/98625/"
] | How to import <code>.sql</code> file into multiple databases at one shot.
I have tried this:
<pre><code>mysql -uroot -p -all-databases < test.sql
</code></pre>
But it asks for database name. Whatever there in <code>test.sql</code> file should reflect in all the databases/Schemas.
| Since the <code>FROM</code>, <code>WHERE</code> and <code>GROUP BY</code> clause are identical, combine them as follows:
<pre><code>SELECT
prtner_name,
COUNT(*) shipment_count,
SUM(inscan) inscan_count,
SUM(is_deliver) is_deliver_count,
SUM(is_rto) is_rto_count
FROM tbl_shipment
WHE... | Hi all query will be merge like this
<pre><code>SELECT prtner_name,
count(id) AS cnt,
SUM(inscan) AS inscan,
SUM(is_deliver) AS deliver ,
SUM(is_rto) AS rto
FROM `tbl_shipment`
WHERE `awdno` != ''
AND `prtner_name` != ''
GROUP BY `prtner_na... | https://dba.stackexchange.com |
1,134,124 | [
"https://math.stackexchange.com/questions/1134124",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | When topology is involved, we know (singular) homology is homotopy invariant. However, homology and homotopy can be discussed in much more general contexts.
Living in $\mathsf{Ch}_\bullet(R\mathsf{Mod})$ for instance, it seems reasonable to ask whether the formalism continues to behave as it did when we had topology, ... | Homology is a representable functor on the homotopy category of chain complexes. Namely, in the homotopy category of chain complexes of $R$-modules $H_n$ is represented by $R[n]$, which you should think of as a chain complex incarnation of the $n$-sphere.
You don't get the homotopy invariance of singular homology for... | If you have a chain homotopy equivalence, then it induces isomorphisms in homology. There are various ways to see this – but here is the outline of a hands-on proof:
<ol>
<li>Show that nullhomotopic chain maps induce zero maps in homology. </li>
<li>Deduce that homotopic chain maps induce the same map in homology.</li... | https://math.stackexchange.com |
376,139 | [
"https://electronics.stackexchange.com/questions/376139",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/189744/"
] | I am trying to work out the maximum torque a motor puts out to do some stress analysis on a structure, and I have just been given the motor details from the manufacturer. They said it produces <strong>20 Nm</strong> of torque, rotates at <strong>1432 RPM</strong> and has a power output of <strong>1.8 kW</strong>. I did... | 20 Nm of torque does not coincide with maximum RPM so you can't just multiply that torque and maximum (unloaded) radians per second because that would be nonesense.
The manufacturer is most likely telling you that the motor can produce a maximum torque of 20 Nm at a significantly lower speed.
Maximum torque will be w... | Induction motors need to run very close to their “synchronous speed” which in this case is 1500 rpm. This is a 4 pole motor designed to run on 50 Hz.
As the motor slips due to losses and loads, torque goes up roughly proportional to the slip, up until the rated torque of the motor.
So your calculation of 12 N.m is co... | https://electronics.stackexchange.com |
19,978 | [
"https://physics.stackexchange.com/questions/19978",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7277/"
] | Is the curvature of space caused by the local density of the energy in that area?Could gravity be a separate phenomenon only arising from the curvature of space? For instance if the density of energy in a particular area cause that area of space to ”curve” but the effect that we understand as gravity, (causing anythi... | As understood by Einstein's general theory of relativity completed in 1915-16, gravity is indeed a manifestation of (nothing else than) the curvature of space and I have some doubts about your implicit claim that you have made this discovery "independently" of Einstein. According to the precise equations of general rel... | According to GR, in the vicinity of the Earth, for things that are not moving very fast, the gravity we experience is roughly 99.9999% due to the curvature of time and 0.0001% due to the curvature of space. Space near the Earth is extremely flat; the main effect of the Earth's mass is to cause a time dilation field, an... | https://physics.stackexchange.com |
55,477 | [
"https://chemistry.stackexchange.com/questions/55477",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/-1/"
] | Electronegativity of $\ce{H}$ is greater than $\ce{P}$, but according to my book in $\ce{PH3}$, $\ce{P}$ has oxidation number of -3. How is it possible? Is any of the data wrong?
| Here is a way to get the answer. If you place a reagent with oxidation number of H = -1 (hydride) it would produce dihydrogen gas. For example: $\ce{KH + H2O-> KOH + H2}$.
If you place a molecule with oxidation number of $\ce{H} = +1$ dihydrogen gas is NOT formed. $\ce{NH3 + H2O -> NH4+ + OH-}$. Phosphine doesn'... | Electronegativity is a mere indication of what is happening and you will find many different values for the electronegativity of H and P (and all the other elements).
If you have a look at the C-H bond, electronegativities are 2.55 for carbon and 2.2 for hydrogen, i.e. the difference is much larger than for phosphorus... | https://chemistry.stackexchange.com |
53,246 | [
"https://quant.stackexchange.com/questions/53246",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/34568/"
] | Are there rules of thumbs/models that you could use to develop intuition for when skew is cheap or expensive? From what I gather, volatility is a number that is backed out of price in a sense, "the wrong number to get the right answer". But then someone has to set the price, they have a sense of what the correct "skew"... | The bond issuer (company or government) decides the Coupon Rate once and for all (though it is less important than beginners think). But the Promised Yield to Maturity (PYTM) is going to be set in the marketplace evrey day depending on economic conditions, bond risk and PYTM available on comparable bonds. The PYTM is w... | The interest rate or rather the Yield to Maturity, Like @noob2 said, is based on market beliefs, economic conditions and comparable bond rates.
If the bond price formula was altered it’s possible to get the present value annuities formula plus the face value part on the end. This shows that the YTM acts similarly as a ... | https://quant.stackexchange.com |
22,739 | [
"https://dba.stackexchange.com/questions/22739",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | I have installed Oracle 11g R2 standard edition (server software, 2GB download from Oracle).
I found that the 'Environment Variable PATH' has not been set. Which of these directory should I use for the PATH value:-
<ol>
<li>Oracle base</li>
<li>Software location</li>
<li>Database file location</li>
</ol>
Also do I ... | As @ik_zelf mentioned, your PATH variable will need to include the "bin" directory of your Oracle software install. This will allow you to execute commonly-needed commands/utilities like "sqlplus" and "lsnrctl" without changing directories. This is typically $ORACLE_HOME/bin
Your TNS_ADMIN variable needs to be set i... | Normally you use the oraenv script to set you environment correctly for a given ORACLE_SID. The ORACLE_SID and ORACLE_HOME combinations are maintained in /etc/oratab or /var/opt/oracle/oratab which is read by the oraenv script that should be sourced (called with a .)
What oraenv by default sets does is make sure that ... | https://dba.stackexchange.com |
394,042 | [
"https://stats.stackexchange.com/questions/394042",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/234858/"
] | <blockquote>
Suppose <span class="math-container">$X_1$</span> and <span class="math-container">$X_2$</span> are independent geometric random variables with parameter <span class="math-container">$p$</span>. What is the probability that <span class="math-container">$X_1 \geq X_2$</span>?
</blockquote>
I am confused ... | It can't be <span class="math-container">$50\%$</span> because <span class="math-container">$P(X_1=X_2)>0$</span>
One approach:
Consider the three events <span class="math-container">$P(X_1>X_2), P(X_2>X_1)$</span> and <span class="math-container">$P(X_1=X_2)$</span>, which partition the sample space.
There... | Your answer, following Glen's suggestion, is correct. Another, less elegant, way is just to condition:
<span class="math-container">\begin{align}
\Pr\{X_1\geq X_2\} &= \sum_{k=0}^\infty \Pr\{X_1\geq X_2\mid X_2=k\} \Pr\{X_2=k\} \\ &= \sum_{k=0}^\infty \sum_{\ell=k}^\infty \Pr\{X_1=\ell\}\Pr\{X_2=k\}.
\end{al... | https://stats.stackexchange.com |
92,412 | [
"https://security.stackexchange.com/questions/92412",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6344/"
] | So as far as I know, when you go to a https enabled website, all the data you send to that server will be encrypted with their public key, and only the server holding the private key will be able to decrypt it.
BUT, what about the data downloaded from the server - incoming traffic? E.g. if someone could intercept inco... | An HTTPS connection encompasses both directions; server->client data is encrypted just like client->server data is.
The private key is important in securing the session key setup, and the session key is used by <em>both</em> sides to encrypt the conversation.
| short answer: yes
long answer: when using https everything is encrypted, when using http nothing is and you can do both in the same web page. most browsers warn about unsecure content in secure pages, but there is nothing to stop you from putting secure resources in unencrypted pages. It used to be common to use secur... | https://security.stackexchange.com |
526,647 | [
"https://physics.stackexchange.com/questions/526647",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/212710/"
] | (Might seem like a duplicate but is not)
The original Young's double slit experiment makes use of a single incoherent source being incident on two different slits to get two coherent sources.
The original source is incoherent.i.e There is no constant phase relation in the light being emitted.So The phase from 2s ago ... | One succes of the Dirac equation is that it correctly implies the particle g-factor to be g=2, explaining the lepton g-factor. For protons and neutrons g is very different from 2, so the Dirac equation itself cannot be applied to these.
The squared Dirac equation exhibits a spin dependent term, the relativistic gener... | The Dirac equation <em>does</em> describe composite spin-1/2 fermions - namely, baryons like the proton and the neutron. Conversely, future experiments might reveal the electron to be composite even though it's described by the Dirac equation (plus perturbative corrections).
The vertex term you describe does appear in... | https://physics.stackexchange.com |
144,593 | [
"https://dba.stackexchange.com/questions/144593",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4473/"
] | I have a list of words/phrases in a table <code>phrases</code>. I have another table with a full-text catalog indexing the <code>description</code> column.
I want to populate a table <code>results</code> with a record for each phrase, and the number of times that phrases was found in the description:
<pre><code>INSER... | Try this:
<pre><code>go
create function dbo.fn_GetCountForPhrase (@phrase varchar(500))
returns int
as
begin
declare @count int
declare @localphrase varchar(8000)
set @localphrase='"' + @phrase + '"'
SELECT @count=COUNT(*) FROM table a WHERE CONTAINS(table.description, @localphrase)
return ... | I think you can get what you need from the DMVs, including <code>sys.dm_fts_index_keywords_by_document</code> and <code>sys.dm_fts_parser</code>, something like this:
<pre><code>SELECT p.phrase, kbd.display_term
FROM sys.dm_fts_index_keywords_by_document( DB_ID(), OBJECT_ID('dbo.documentText') ) kbd
CROSS APPLY db... | https://dba.stackexchange.com |
513,999 | [
"https://physics.stackexchange.com/questions/513999",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I was taught in school that clouds are white due to the scattering of light. Since all rays are reflected it appears as white. But I am wondering about rain clouds. Why are rain clouds darker?
| This is due to the scattering of light.As the density increases scattering increase and light rays coming from sun dispersed among them. So the lower part of that clouds appear as darker but above part will be white, you can observe it on your flight, but you have to grab a window seat for a beautiful view
| Rain clouds are dark because the part of the cloud you see is <strong>in the shade</strong>.
Clouds are white because they contain tiny water droplets that scatter light of all colors equally in all directions. "Scatters light of all colors equally in all directions" <em>means</em> "white".
But if you put a layer of ... | https://physics.stackexchange.com |
164,613 | [
"https://physics.stackexchange.com/questions/164613",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/72924/"
] | If energy equals mass times the speed of light squared, what is mass times just under the speed of light? It's not energy,,,yet.
Michio Kaku said in a physics video that the faster mass goes, the heavier it gets. I'm not understanding how acceleration can both convert mass to energy and render it heavier.
I am a tota... | If the velocity is slower than the speed of light (which is always the case) the newtonian limit for small velocities is
$$E_{kinetic}=\frac{m\cdot v^2}{2}$$
and in relativity
$$E_{kinetic}=\frac{m\cdot c^2}{\sqrt{1-v^2/c^2}}-m\cdot c^2$$
The rest energy is always
$$m\cdot c^2$$
no matter what the velocity is.
| One of the insights of special relativity is that space and time are not absolute or distinct; instead of thinking of space and time, we should think of space-time. One consequence is that we should, in principle, measure space and time with the same unit. We haven't done that; we've measured time in seconds and space ... | https://physics.stackexchange.com |
106,409 | [
"https://electronics.stackexchange.com/questions/106409",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39376/"
] | I have read about fading of signals , and I have notice that the major cause of fading is multipath , but I have ask myself , what about attenuation , noise and free space loss , all of these make the power of signal be smaller , so my question is , why we emphasize on multipath when we discuss about the causes of sign... | In communication systems, <em>fading</em> refers to a specific kind of attenuation which is highly frequency and time dependent. Other types of attenuation such as loss on transmission lines, path loss in radio transmission etc. do not change rapidly with time or frequency, at least not within the bandwidth of interest... | There are no free space losses. If you had a perfect directional antenna pumping out 1 watt and a perfectly aligned identical antenna a million miles away it would receive 1 watt. Alignment will be problematic because the beam angle is so so fine. Antenna losses at either end make reception more likely to be a couple o... | https://electronics.stackexchange.com |
136,748 | [
"https://chemistry.stackexchange.com/questions/136748",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/21270/"
] | I'm looking to plate some aluminum with silver using a basic solution.
My first attempt was to use sodium carbonate to make silver acetate. I sped up the process using hydrogen peroxide. I used the silver acetate as the ion source.
This simply did not work to plate any aluminum.
I concluded that this is because the alu... | <img src="https://i.stack.imgur.com/KVYhB.jpg" alt="enter image description here" />
I’m so confused now. I did this when I first started experimenting with electrochemistry (when I didn’t know what I was doing) I was using anything I had in my garage as an anode and somehow I copper plated this aluminum speed square.
... | No ! There are no method for plating aluminum. Thousands of people have tried. In vain. It is impossible to prevent the formation of a thin layer of aluminum oxide which is waterproof at the surface of the metal. The only way of preventing it is to dip a piece of aluminum in a solution of mercuric chloride. This produc... | https://chemistry.stackexchange.com |
468,343 | [
"https://math.stackexchange.com/questions/468343",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/84126/"
] | Let $\lbrace \tau_n:n\in \mathbb{N}\rbrace$ be an ascending chain of topologies on a nonempty set $X$. Then is $\bigcup\limits^{\infty}_{n=0}\tau_n$ a topology on $X$?
I have a strong notion that it may not be a topology. But I am not getting the proper counter example. Please help. I know this must be a topology if ... | This is an addendum to Asaf’s answer and Pete’s comment.
Suppose that $\tau=\bigcup_{n\in\Bbb N}\tau_n$ is <strong>not</strong> a topology on $X$. Then, as noted in Asaf’s answer, there must be some family $\mathscr{U}\subseteq\tau$ such that $\bigcup\mathscr{U}\notin\tau$, since the other requirements for $\tau$ to b... | <em>(Instead of just giving a counterexample, let's walk through the approach you should take in a situation like that.)</em>
This requires simply to verify the three axioms of topology. Let's take <em>any</em> chain of topologies, not just countably infinite. So we have $\tau=\bigcup_{i\in I}\tau_i$ which are an incr... | https://math.stackexchange.com |
214,730 | [
"https://softwareengineering.stackexchange.com/questions/214730",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/93536/"
] | I wonder if I should close any unnecessary database connection inside of my PHP scripts.
I am aware of the fact that database connections are closed implicitly when the block stops executing and 'manually' closing the connections could kinda bloat the codebase with unnecessary code.
But shouldn't I do so in order to ... | For the purpose of safe coding, you should always close database connections explicitly to make sure that the code was able to close itself gracefully and to prevent any other objects from reusing the same connection after you are done with it.
Using unset is the same as leaving the database connection open, as you're... | Yes, it of-course helps. Assume you are building an application, where clients do normal operations with your tables. Now, if the application is heavy and processing intrinsic, it is likely that your application will slow down with vast number of open connections, which will remain idle for a very long duration.
If yo... | https://softwareengineering.stackexchange.com |
26,831 | [
"https://astronomy.stackexchange.com/questions/26831",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/23550/"
] | We take observations from earth but to define radial velocity, transverse velocity and the proper motion of stars, why we consider them with respect to the sun? and then we do some corrections due to both rotational and orbital motion of the earth.
Why can't we directly consider these motions with respect to earth ins... | The Earth is a moving (actually, accelerating) platform from which we make our observations. If you want to describe the motion of a distant celestial body, then it does not make much sense to provide a geocentric velocity, because this will depend on exactly when the observations were taken (because the Earth orbits w... | We use the position of the sun (or more accurately the centre of mass of the solar system) as this gives us a very nearly inertial frame of reference. An inertial frame is one which is not changing its velocity. The surface of the Earth does not define an inertial frame.
The Earth orbits the sun and so it is moving in... | https://astronomy.stackexchange.com |
1,922 | [
"https://mathoverflow.net/questions/1922",
"https://mathoverflow.net",
"https://mathoverflow.net/users/798/"
] | One can build a projective plane from <span class="math-container">$\Bbb R^n$</span>, <span class="math-container">$\Bbb C^n$</span> and <span class="math-container">$\Bbb H^n$</span> and is then tempted to do the same for octonions. This leads to the construction of a projective plane known as <span class="math-contai... | As I recall, the Cayley projective plane is painful to build, but it is a 2-cell complex, with an 8-cell and a 16-cell. The cohomology is Z[x]/(x^3) where x has degree 8, as you would expect. Its homotopy is unapproachable, because it is just two spheres stuck together, so you would pretty much have to know the homot... | The geometric reason that there is no octonion
projective 3-space is that the Desargues theorem holds
in any projective space, and the Desargues theorem
implies that the coordinate algebra is associative.
(Essentially due to Hilbert, Grundlagen der Geometrie,
1899.)
Incidentally, the term "Cayley plane" is a misnomer,... | https://mathoverflow.net |
249,228 | [
"https://dba.stackexchange.com/questions/249228",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/191324/"
] | We have a sybase database running an application our users use which contains client info.
The situation is that address information for maybe 1000 clients or so is out of date. We were given a .csv file with updated address info, and are being asked to update the addresses in the database.
I've filtered the csv to... | Here was the solution I used. For this example, the updated info to be uploaded is in a file called updatefile.csv. The table is called multi_addresses. Columns in the file being updated in the db are the address, address_2, city, state, etc. Works well for me.
UPDATE multi_addresses, updatefile
SET multi_addresses.a... | <code>USING FILE</code> clause is used to load data from a file. The column list shows two columns to be imported from the <code>.csv</code> file.
<pre><code>LOAD TABLE clientAddress.table (client.id, address.info)
USING CLIENT FILE 'file.csv'
</code></pre>
| https://dba.stackexchange.com |
1,779,590 | [
"https://math.stackexchange.com/questions/1779590",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/293803/"
] | I need to calculate the limit$$\lim_{n \to \infty } \frac{1}{n^2} \int_0^n \frac{ \sqrt{n^2-x^2} }{2+x^{-x}} dx$$
How could I calculate this? Any hlep would be appreciated.
| <strong>Outline:</strong>
<ul>
<li>First, do the change of variable $x=ny$, to get
$
\int_0^1 f_n(y) dy
$
with $$f_n(y) = \frac{\sqrt{1-y^2}}{2+e^{-ny \ln (ny)}}.$$</li>
<li>Then, compute the pointwise limit $f$ of $f_n$ on $(0,1]$.</li>
<li>Finally, apply the Dominated Convergence Theorem to show that $\int_0^1 f_n \... | Try $u=x/n$. It'll get rid of most of the horrible places where $n$ appears. All that's left to do is figure out the limit in the denominator, where you get
$$\lim_{n\to\infty}(nu)^{-nu}$$
| https://math.stackexchange.com |
2,728,392 | [
"https://math.stackexchange.com/questions/2728392",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/221503/"
] | Is choice required to guarantee that $\mathbb R^2 := \mathbb R \times \mathbb R$ – or $\mathbb R^n := \displaystyle\prod_{k=1}^n \mathbb R$ in general – isn't the empty set $\varnothing$? If not, what's an example of a Cartesian product of two non-empty sets not guaranteed to be non-empty (without choice)?
| If $X$ is nonempty and $\kappa$ is an arbitrary cardinal, then you do not need $AC$ to prove that $X^{\kappa}$ (the cartesian power of $X$) is nonempty: since $X$ is nonempty, there exists $x_0\in X$. Then define $f\colon\kappa\to X$ by $f(i) = x_0$ for all $i\in\kappa$. This is an element of $X^{\kappa}$, so the latte... | The ability to make (and remember) <em>finitely many</em> choices during a proof is built into the rules of first-order logic. You don't need a specific set-theoretic axiom to do that.
By induction, you can then prove in general that choice functions for a family of sets you know has finite cardinality must also exist... | https://math.stackexchange.com |
192,068 | [
"https://physics.stackexchange.com/questions/192068",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/76614/"
] | I've heard that it is incredibly difficult to detect a graviton, but I don't quite understand why. With all of the knowledge I have at the present time it seems like it should be possible to create a graviton in a particle accelerator. This is how I figure: a graviton is massless, so the collision shouldn't need to hav... | You need to distinguish between the virtual gravitons that appear in a quantum field theory calculation of a gravitational interaction and real gravitons that form a gravitational wave. The sort of experiment you're describing requires the emission of real graviton i.e. the emission of a gravitational wave.
The troub... | <em>Why can't gravitons be created in traditional particle accelerators?</em>
Because gravitons are hypothetical virtual particles, proposed by particle phyicists advocating an "exchange mechanism" for gravity. This exchange mechanism is modelled using virtual particles, and it's perfectly valid for electromagnetism: ... | https://physics.stackexchange.com |
233,451 | [
"https://electronics.stackexchange.com/questions/233451",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/109694/"
] | I have a basic question about electronic ground. For example, if electrons travel from the DC battery's negative terminal through the conductive wire to the positive terminal of a DC battery with a LED as a load, how would adding ground symbol in a schematic circuit between the conductive wire of the negative terminal ... | In many (most?) circuits, the ground symbol simply indicates the point in the circuit that we will call "zero volts" - where we will place the black meter lead when measuring voltages elsewhere in the circuit.
In many circuits, this "zero volt" point is the most negative terminal of the power supply, but it could, if ... | Beware of the word "ground," since it has several conflicting definitions. The experts may be able to figure it out from syntax, but for everyone else, we can avoid much confusion by avoiding the word "ground." Use less general terms instead.
For example, "ground" can mean one or more of the following, or even a mixt... | https://electronics.stackexchange.com |
263,683 | [
"https://security.stackexchange.com/questions/263683",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/280968/"
] | I have an ESXi server that is using a self-signed certificate, and the browser gives a warning that SSL certificate cannot be trusted.
I want to put that cert into the Trusted Root Certification Authorities store.
Will that get rid of the warning message?
Also is it possible to create identical self-signed certificates... | Yes, but it is probably irrelevant.
From the connectors, at least USB is dangerous. It does not only allow many different types of possibly dangerous access like DMA, but there are also devices which, for example, emulate a keyboard and start to type malicious commands as soon as you plug them in.
But it is very unlike... | It is possible maybe, but I would rate the probability that it is indeed infected as very low. The USB is also probably the only viable attack vector. Also, I have never seen an infected projector.
This would be a highly custom attack. Which will have quite a bad cost/benefit to an attacker. To do such an attack, I wou... | https://security.stackexchange.com |
1,540,897 | [
"https://math.stackexchange.com/questions/1540897",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/256723/"
] | I am getting stuck with following problem:
Show that
\begin{align}
\dot{x} = f(x/t)
\end{align}
is equivalent to
\begin{align}
\dot{y} = (f(y) − y)/t
\end{align}
using the transformation
\begin{align}
y := x/t.
\end{align}
Any help/hint is welcomed.
| If $y=\frac{x}{t}$, we have
$$\begin{align}
\dot{y} &= \frac{\dot{x}t-x}{t^{2}} \tag{derivative of a quotient}\\
&= \frac{f\left(\frac{x}{t}\right)t-x}{t^{2}} \tag{$\dot{x}=f(x/t)$}\\
&= \frac{f\left(\frac{x}{t}\right)t}{t^{2}}-\frac{x}{t}\cdot\frac{1}{t}\\
&= \frac{f(y)}{t} - y\cdot\frac{1}{t} \tag{si... | sometimes a small transformation of a problem makes it easier to approach. here you may write the transformation as $yt=x$. then, differentiating wrt t we get (using the product rule)
$$
y+t\dot{y}=\dot{x}=f(y)
$$
and the required answer is obtained by a simple algebraic manipulation
| https://math.stackexchange.com |
697,787 | [
"https://physics.stackexchange.com/questions/697787",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/260062/"
] | I’m having some problems to identify the type of heat transfer involved in a practical experiment I’ve carried out. In my experiment, I heat a metal rod by making water vapor flow inside the rod, then I let it cool down to room temperature.
On the one hand, I think it sounds reasonable to argue that both the heat trans... | It depends on the dimensions and thermal properties (thermal conductivity, density, heat capacity) of the rod. If the rod wall is very thin and has a high thermal conductivity, then the convective transport to the fluid stream will dominate. But if the rod wall is very thick and/or has a low thermal conductivity, the... | When only fluids are involved, then convection. Conduction happens between the material surface and an individual fluid particle, but then that particle is immediately replaced by another and a new convective transfer takes place. This repeating process is what we call convection.
| https://physics.stackexchange.com |
357,355 | [
"https://physics.stackexchange.com/questions/357355",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/120250/"
] | Electron flow in Cathode Ray Tube?
In a TV CRT, electrons from the cathode go pass the anode and strike the TV screen to produce the picture. It seems that, in order to for the system to work, the electrons hitting the screen must be redirected back to the anode to complete the electrical circuit.
I'll like to known ... | In the big cathode ray tubes that used to be used in television receivers, the inside of the glass walls leading up to the screen were coated with graphite, and the coat connected to the eht (extra high tension) supply, whose other end was (directly or indirectly) connected to the cathode, so that electrons landing on ... | TV picture tubes and a CRO most CRO tubes, the phosphor on the screen and the inside of the tapered part of the tube are coated with aluminium, which is evaporated on. The electrons can pass through aluminium to the phosphor. Then they are then collected by the coating and returned through the EHT laed, which is clippe... | https://physics.stackexchange.com |
10,350 | [
"https://stats.stackexchange.com/questions/10350",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1763/"
] | I am working on insurance data in which a customer has a field named <code>customer_no_dependent</code> (customer's number of dependent). Its coming out to be a significant variable( just that it has $p<0.0001$).
This variable has almost 20% missing values. For imputation, I thought to determine proxy indicators f... | First of all: it is not clear from your explanation whether or not you have done multiple imputation. If not: please do so: single imputation could be worse than simple complete case analysis, and can both lead to severely biased results.
Next, if I understand correctly, your problem is that you don't know which varia... | I don't know if you have SAS experience, but I've used SAS PROCs MI and Mianalyze to perform (and then synthesize) multiple imputations in several different models. Building the "imputation model" (this yields non-biased estimates of missing data, incorporating the uncertainty one finds in non-missing data) is probably... | https://stats.stackexchange.com |
619,841 | [
"https://electronics.stackexchange.com/questions/619841",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/309878/"
] | A proportional, integral, and derivative (PID) controller can feature three terms.)
We sometimes see only two of the terms in use. For example, the derivative is disregarded for a PI controller. While I know what each of the three terms do, I am not sure about the situations that warrant their removal and the control i... | If you start with a PID and:
<ul>
<li>remove the D action: the controller won't respond quickly to quick changes in the input. This is sometimes desired if the input is noisy and you don't wont the output to be that jerky. Sometimes D action is needed for a quick reaction.</li>
<li>remove the I action: the controller m... | The P term is the term which provides the main drive to drive the process in a direction which reduces the error signal. Integral response is inherently slow and so the proportional term is needed to speed the response of the system to a change in the set point.
The integral term responds to what has happened in the pa... | https://electronics.stackexchange.com |
99,478 | [
"https://mathoverflow.net/questions/99478",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23758/"
] | Does someone knows a good reference for the following result?
"A topological group is Hausdorff if and only if the identity is closed."
I have seen proofs in lecture notes of courses on the web, but I would like a reference in a book or an article, in order to refer to it.
| You could find a routin proof in the book "Topological Ring" written by Seth Warner. In this book at page 21 in Theorem 3.4 you could see the following Proposition:
Theorem: Let $G$ be a topological group. The following statements are equivalent:
<ol>
<li>{$0$} is closed.</li>
<li>{$0$} is an intersection of the nei... | You can probably find this result in a million places, one of which is N. Bourbaki, <i>General Topology</i>, Part 1, Chapter 3, Section 1.2, p. 223, Proposition 2.
| https://mathoverflow.net |
1,106,157 | [
"https://math.stackexchange.com/questions/1106157",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/168398/"
] | So the question is as follows. Prove that there is no meromorphic function $f$ such that at every $z\in \mathbb{C}$ we have $f(z)=f(z+1)$ and $f(z)=f(z+i)$ with only simple poles at the points $m+ni, m,n \in \mathbb{Z}$.
So, this looks like a holomorphic map from the torus to the Riemann sphere. Since the map is cont... | Consider $R = \{z \in \mathbb{C} \mid \operatorname{Re}(z), \operatorname{Im}(z) \in \left[-\frac{1}{2}, \frac{1}{2}\right]\}$. By the periodicity of $f$,
$$\int_{\partial R}f(z) dz = 0.$$
However, by the residue theorem,
$$\int_{\partial R}f(z) dz = 2\pi i\operatorname{Res}(f, 0).$$
As $f$ has a simple pole at $0... | Assume for a contradiction that such a meromorphic function <span class="math-container">$f\colon\mathbb{C}\rightarrow\mathbb{C}$</span> existed.
Let <span class="math-container">$\Gamma\colon= \mathbb{Z}+\mathbb{Z}i$</span> denote the Gaussian integers.
Consider the holomorphic mapping <span class="math-container">$F\... | https://math.stackexchange.com |
3,380,592 | [
"https://math.stackexchange.com/questions/3380592",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/560190/"
] | Given the linear equations, over the field of <span class="math-container">$5$</span>, so only numbers <span class="math-container">$0,1,2,3,4$</span> "exists" :
<span class="math-container">$$\left(\begin{matrix}
2 & 1 & 3 \\
3 & 2 & 2 \\
3 & 0 & 2 \\
\end{matrix} \right|
\lef... | Let <span class="math-container">$a, b\in \Bbb R$</span>.
Pick <span class="math-container">$n\in \Bbb N$</span> and for <span class="math-container">$0\le i\le n$</span>, let <span class="math-container">$x_i=a+i\frac{b-a}n$</span> (so <span class="math-container">$x_0=a$</span>, <span class="math-container">$x_n=b$</... | Let <span class="math-container">$x \neq y$</span> and w.l.o.g <span class="math-container">$x<y$</span> and <span class="math-container">$n \in \Bbb{N}$</span>
Then take the partition <span class="math-container">$P$</span> of <span class="math-container">$[x,y]$</span> such that <span class="math-container">$P=\... | https://math.stackexchange.com |
201,334 | [
"https://security.stackexchange.com/questions/201334",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/196613/"
] | If my laptop is locked, can a thumb drive be able to still infect my computer, or create a backdoor, or any other security risk if it's plugged into it. If so what are some example
| Well technically yes, once somebody has a physical access virtually anything is possible. An example might be that you are running old version of windows with autoplay still on by default. Somebody then simply inserts the thumb drive with malicious autoplay data and there goes your security even though the computer is ... | There are all sorts of opportunities to really impact a laptop or any physical machine if an attacker has direct access. A user can change the SAM database and provide themselves root/administrative access, or they could copy all your files out, they could use a Linux USB bootable device to embed an application script ... | https://security.stackexchange.com |
380,549 | [
"https://softwareengineering.stackexchange.com/questions/380549",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/318591/"
] | First of all I am going to give you a brief explanation of what i am after doing. I want to write a program that applies filters to an image using a strategy design pattern. I have read some documentations about the pattern and decided to use it like this.
First I will create an Interface called FilterStrategy which h... | I would implement a parent class for your filters eg <code>FilterBase</code>
This FilterBase would implement the read, write, convolution and display methods. Then when your classes BeautifulFilter and UglyFilter inherit from it, they would be able to access the methods themselves.
| <blockquote>
Here is what I am asking. BeautifulFilter and UglyFilter has many common methods such as read image, write image, convolution and display...
</blockquote>
So far this sounds fine.
<blockquote>
and there also some methods that are used by only one of the filters above.
</blockquote>
And here's whe... | https://softwareengineering.stackexchange.com |
639,039 | [
"https://physics.stackexchange.com/questions/639039",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/271783/"
] | Clouds are present in the troposphere . So the radiation from the Sun first needs to pass this layer of the atmosphere to come down which means that the clouds above are constantly being radiated from the Sun in daytime with <em>higher intensity</em> than what reaches down the earth but if that's true <strong>why don'... | <strong>Light from the sun heats the earth’s surface, which in turn heats the atmosphere</strong>.
The atmosphere is made up of air and water vapour etc (when that vapour is thick enough we get clouds). The light coming from the sun is reflected back into space by clouds, and some light completely passes through them (... | I assume you mean to ask Why cloud don't evaporate?
First,
<h3>How clouds are formed?</h3>
Assuming a hot sunny day with clear sky, water on surface of a water body evaporates. Assuming still air evaporated water remains at same site.
Till now it is in gaseous state.
Now, As Sun is going down condition for condensation... | https://physics.stackexchange.com |
128,860 | [
"https://softwareengineering.stackexchange.com/questions/128860",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8784/"
] | How does one prevent users from creating erroneous input sets, when there is no practical way to vet the input?
<h3>The scene</h3>
I modify a small ERP package written in Visual FoxPro. One part of the package concerns itself with printing truck manifests and invoices to be sent with the drivers on their delivery rout... | This is easy, if they leave everything blank you prompt that this will print everything, however, the DEFAULT selection in that prompt MUST be to cancel.
If they enter values, print whatever they asked for.
This way, they won't accidentally blaze through the form and print everything. They'll blaze through and print... | It sounds to me like you've got a requirement to fix something, but every time you propose a solution (and there are plenty of good ideas in your list) it gets shot down.
This is the point where you need to push back. You don't need a vague idea that "this is wrong; fix it." What you need is a spec. Ask the people ... | https://softwareengineering.stackexchange.com |
561,762 | [
"https://physics.stackexchange.com/questions/561762",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/267101/"
] | When calculating a part of the trace for the partition function of the fermionic Ramond-sector in light-cone coordinates, I'd like to understand how we get to the result <span class="math-container">$\left(\frac{\theta \left[1/2;0\right](0,\tau)}{\eta (\tau)} \right)^4$</span>.
My problem is that I get a global <span c... | Thank you for your answer. I fortunately already found the mistakes in my computation:
<ol>
<li>From the second to the third line I simply misinterpreted the identities for the <span class="math-container">$\theta$</span>-functions.
</li>
<li>I forgot the <span class="math-container">$\sqrt{2}$</span> contribution, whi... | <strong>First, I'm going to work out the calculation to help you be clear about getting the desired result and how similar computations are performed in the literature.</strong>
The character of the evolution operator for a free fermion in the Ramond sector on the torus is: <span class="math-container">$$Tr_{R}[q^{L_{0... | https://physics.stackexchange.com |
34,816 | [
"https://scicomp.stackexchange.com/questions/34816",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/35606/"
] | I have an X value that can go from 0.0000001 to infinite.<br>
I want, if this value is less than 0.8, get 0.8<br>
And if that value is equal to or more than 0.8, get 0
How would you do that using only min and max functions (and of course basic +-/x operations) ?
I ask this because I have to calculate this inside a ... | I have kind of an answer, but it might not be useful depending on what you want to use it for.
Let <span class="math-container">$t$</span> be some large parameter, <span class="math-container">$\text{min}(\text{max}(t*(0.8-x),0),0.8)$</span> will approximate the function you seek very well. It will only be incorrect f... | The trick is noticing that <span class="math-container">$|x| = \max(x, 0) - \min(x,0)$</span>. With that, it's easy to get to the function you asked for,
<span class="math-container">$$f(x) = \mbox{0.4}\left(1-\dfrac{x-0.8}{\max(x-0.8,0)-\min(x-0.8,0)}\right)$$</span>
| https://scicomp.stackexchange.com |
410,292 | [
"https://softwareengineering.stackexchange.com/questions/410292",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/310910/"
] | Is there a standard on db alter scripts (both data and ddl), should they be re-runnable if so what are the reasons for making them re-runnable.
The only web pages I could find are telling me how to do it, but i want to know why to do it?
| The reason you want to have re-runnable scripts is the same reason you want idempotent operations in any other situation in IT: to avoid <em>state</em>.
By "state", here we mean that the state of the world influences what the outcome of an operation will be. Idempotent operations have the same effect no matter what th... | The idea of such a script is to take the database from one "known state" to another "known state". You don't want to end up in some "half-way house", which would be even <em>more complicated</em> to sort out.
Some cases are easier to handle than others.
If, for example, you are adding a column to a table, then you... | https://softwareengineering.stackexchange.com |
430,277 | [
"https://physics.stackexchange.com/questions/430277",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/192515/"
] | Centrifugal force for the observer in a rotating frame is a force as real as the force of gravity. However I know that gravitational force is an interaction between a mass and another. And the agent responsible is called graviton if I am not mistaken.
Centrifugal force on the other hand feels like gravity but no one i... | <blockquote>
Are there any fundamental interactions behind centrifugal force?
</blockquote>
Actually, there is no centrifugal force and therefore there is no physical interaction or agency behind it.
Imagine a bead on a frictionless rotating rod. The bead appears to accelerate radially relative to the rod, but, sin... | The force you feel in a centrifuge is due to the time rate of change of your velocity vector, which you experience as an acceleration. You get the same feeling in a car when you hit the gas, and in that case what is changing is the magnitude of your velocity vector and not its direction. In the centrifuge case, what is... | https://physics.stackexchange.com |
498,514 | [
"https://physics.stackexchange.com/questions/498514",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/239807/"
] | When current flow through a wire, this generates a magnetic field around the wire, this field tends to circle around the wire and called electromagnetic field.
When current flow though a straight wire does it create a magnetic dipole ?
If yes, Where are these dipoles (by drawing) ? I didn't see any site draw the dipo... | When you run current through a wire, a circular magnetic field is created around the wire. It does not have poles but the magnetic field does have a direction (tangent to the circle. Keep in mind you have to use the right hand rule to find the direction).
So it does not create poles
| Unless you are talking about a transient flow from one charged region to an oppositely charged region, current can only flow in a loop.<br>
Any loop of current will produce a field that resembles the classical magnetic dipole field at a distance. Separated electric charges produce an electric dipole field. Flowing el... | https://physics.stackexchange.com |
3,654,132 | [
"https://math.stackexchange.com/questions/3654132",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/422626/"
] | I encountered the following, deceptively simple looking integral -
<span class="math-container">$$ \lim_{n \to \infty} n^{\frac{3}{2}} \int_0^1 \frac{x^2}{(1+x^2)^n} dx. $$</span>
My goal was to hopefully somehow use the Lebesgue dominated convergence theorem; I've tried every elementary bound that I can think of to... | By the change of variable <span class="math-container">$y = n^{1/2} x$</span> you get
<span class="math-container">$$
n^{3/2} ∫_0^1\frac{x^2}{(1+x^2)^{n}}\,\mathrm{d}x = ∫_0^{n^{1/2}}\frac{y^2}{(1+n^{-1}y^2)^{n}}\,\mathrm{d}y \underset{n\to\infty}{⟶} ∫_0^\infty y^2e^{-y^2}\,\mathrm{d}y
$$</span>
by dominated convergenc... | For large <span class="math-container">$n$</span> the integrand decreases rapidly away from <span class="math-container">$x=0$</span>, so instead of integrating from <span class="math-container">$0$</span> to <span class="math-container">$1$</span> we may integrate from <span class="math-container">$0$</span> to <span ... | https://math.stackexchange.com |
72,717 | [
"https://security.stackexchange.com/questions/72717",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/20657/"
] | I have an API written in nodejs and I have a frontendapp written in angularjs. I want my API to be called only through my frontendapp and not from any other source.
e.g. I have an endpoint called myhost.com/posts/id and when the method is delete it deletes the posts. I dont want an attacker to access this end point an... | I believe that this is not possible in a failsafe way, unfortunately. Let me explain why.
You want your frontend app to have a way to identify itself to the API. In other words, you want authentication.
But authentication requires the existence of some kind of unique, secret data that the frontend app can use to dist... | A good way to start is to prevent connections to the API application from anything except valid client addresses, in your case, your angularjs server.
Additional security would be gained by implementing a revocable shared API key between each angularjs instance and your API, so you can revoke permissions from compro... | https://security.stackexchange.com |
1,194,967 | [
"https://math.stackexchange.com/questions/1194967",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/207504/"
] | <blockquote>
Show that given $\epsilon>0$ there is a $\delta>0$ such that $\left|\frac{1}{1+x^2}-{1}\right|<0$ whenever $|x|<\delta$.
</blockquote>
| First write
$$\left|\frac{1}{1+x^2}-1\right|=\left|\frac{x^2}{1+x^2}\right|$$
Note that $1+x^2>1$ implies that $\frac{1}{1+x^2}<1$. Using this inequality reveals
$$\left|\frac{1}{1+x^2}-1\right|=\left|\frac{x^2}{1+x^2}\right|<x^2$$
So, for all $\epsilon>0$,
$$\left|\frac{1}{1+x^2}-1\right|=x^2<\e... | <strong>hint</strong>: $\left|\dfrac{1}{1+x^2}-1\right| = \dfrac{|x|^2}{1+x^2} < |x|^2$
| https://math.stackexchange.com |
2,342,046 | [
"https://math.stackexchange.com/questions/2342046",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/287583/"
] | Let $f$ be a real valued function as below:
$f(x) = \begin{cases} 1 &\text{if } x \text{ belongs to Cantor set } \\ 0 &\text{otherwise }. \end{cases}$
I know that $f: \mathbb{R} \rightarrow \mathbb{R}$ is continuous on every $ x \in \mathbb{R}\setminus C$ but what can we say about $f: \mathbb{R} \rightarrow ... | It is differentiable on $\mathbb{R}\setminus C$ using the same argument why it is continuous on $\mathbb{R}\setminus C$.
By construction of $C$, you know that for each point $x\in\mathbb{R}\setminus C$ exists an open neighbourhood $U$ of $x$ such that $U\subset\mathbb{R}\setminus C$. On this neighbourhood is $f$ consta... | $C$ is closed therefore $\mathbb R \setminus C$ is open. Let $x \in \mathbb R \setminus C$. Then there exists an open set $U$ such that $U \subseteq \mathbb R \setminus C$. Now, $f \equiv 0$ on U. Hence $f$ is differentiable at $x$.
| https://math.stackexchange.com |
247,710 | [
"https://math.stackexchange.com/questions/247710",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/16753/"
] | If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use?
For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is important especially since I am trying to couple this with a limit toward infinity.
| You could define the notation recursively as a sequence of functions.
Let $f_{n+1}(x) = f(f_n(x))$ for $n \geq 2$ with $f_1(x) = f(x)$.
Sequence notation of this type is so generic that the reader will be forced to consult your definition, which will avoid any possible misinterpretation.
| In the course I took on bifurcation theory we used the notation $$f^{\circ n}(x).$$
| https://math.stackexchange.com |
5,691 | [
"https://mathoverflow.net/questions/5691",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1841/"
] | The exercise is the following:
<blockquote>
Let $A$ be a valuation ring, $K$ its field of fractions. Show that every subring of $K$ which contains $A$ is a local ring of $A$.
</blockquote>
Does anyone know what is meant by "to be a local ring of a valuation ring"?
| Let B be the subring of K containing A. I am going to prove that B is the localization of A at a prime ideal $P\subset A$, which seems a reasonable interpretation of the statement that B is a local ring of A.
First B is a local ring [by Atiyah-MacDonald Prop 5.18 i)] ; let $M_B$ be its maximal ideal.
Similarly let $M_... | I believe it just means "a localisation of A".
| https://mathoverflow.net |
1,137,842 | [
"https://math.stackexchange.com/questions/1137842",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/213710/"
] | How you integrate
$$\frac{1}{x\sqrt{1+x^2}}$$
using following substitution? $u=\sqrt{1+x^2} \implies du=\dfrac{x}{\sqrt{1+x^2}}\, dx$
And now I don't know how to proceed using substitution rule.
| If <span class="math-container">$u=\sqrt{1+x^2}$</span> then <span class="math-container">$u^2 = 1+x^2$</span>, so <span class="math-container">$x^2= u^2-1$</span>. Then you have
<span class="math-container">\begin{align}
& \int \frac 1 {x\sqrt{1+x^2}} \,dx = \int \frac {x} {x^2\sqrt{1+x^2}} \,dx \\[8pt]
= {} &... | Use $x=\tan\theta$, $dx=\sec^2\theta\,d\theta$
$\tan^2\theta+1=\sec^2\theta$
$$\int\dfrac{\sec^2\theta\,d\theta}{\tan\theta\sec\theta}=\int\dfrac{\sec\theta\,d\theta}{\tan\theta}=\int\dfrac{d\theta}{\sin\theta}=-\ln|\csc\theta+\cot\theta|+C$$
| https://math.stackexchange.com |
189,362 | [
"https://physics.stackexchange.com/questions/189362",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/83602/"
] | What is the slowest speed at which a vehicle driven off a cliff can clear the cliff without catching its underside between the wheels?
In the usual frictionless vacuum, this would appear to depend on the vehicle's clearance and its wheelbase. The front axle responds to gravitational attraction as soon as it clears the... | This problem is an example of the wave-particle duality (which is a simplistic model of a complex quantum interaction). Everything can be considered as a wave or a particle, although the higher the energy (that is the larger the particle's mass) the smaller the wave length. So, a low energy photon (like a radio photo... | There is simply no such thing as an electron that "goes from place to place". That electrons are little hard balls is simply an implicit assumption that we carry over from the macroscopic into the microscopic world. It's also a false assumption.
The best way to think of an electron is in form of quantization and conse... | https://physics.stackexchange.com |
351,495 | [
"https://mathoverflow.net/questions/351495",
"https://mathoverflow.net",
"https://mathoverflow.net/users/151671/"
] | I am looking for a function <span class="math-container">$\phi(x)$</span> such that
<span class="math-container">$\mathbb{E}_{x\sim\mathcal{N}(0,1)}[\phi(x)^2] = \mathbb{E}_{x\sim\mathcal{N}(0,1)}[\phi'(x)^2]$</span>.
Obvious solutions are <span class="math-container">$\phi(x) = x$</span> and <span class="math-contai... | In fact, every reasonable function can be made into an example by adding an appropriate constant.
I'll write <span class="math-container">$Z$</span> for a standard Gaussian random variable. Recall the Gaussian Poincaré inequality:
<blockquote>
<strong>Theorem.</strong> For every <span class="math-container"... | A family of such functions is given by
<span class="math-container">$$\phi(x)=\phi_c(x):=e^{t_cx+cx^2}$$</span>
for all real <span class="math-container">$x$</span>, where <span class="math-container">$c\in[-\frac{1+\sqrt2}2,\frac{-1+\sqrt2}2]$</span> and <span class="math-container">$t_c=\pm\sqrt{1 - 8 c + 12 c^2 + 1... | https://mathoverflow.net |
68,650 | [
"https://electronics.stackexchange.com/questions/68650",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18033/"
] | Can someone please give me tips on how I could prove that the transfer function of the multiple feedback filter below is
\$
T(s) = \dfrac{ -\dfrac{1}{R_1 R_2 C_1 C_2 } } {s^2 + s\dfrac{1}{C_1} \left( \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} \right) + \dfrac{1}{R_2 R_3 C_1 C_2} }
\$
I just can't figure out... | You must use the basics of your ideal opamp assumptions and derive the KVL and KCL equations for Vout/Vin.
If you recall ideal opamp assumption "1", the inverting terminal voltage is equal to the non-inverting terminal voltage, and so that node, where R2 and C2 connect, is at ground (they call it "virtual" since its a... | Tips:
(1) The voltage across C2 is -Vout. Thus:
\$I_{C_2} = -sC_2 V_{out} \$
(2) The voltage across R2 is:
\$V_{R_2} = I_{C_2}R_2 = -sR_2C_2 V_{out}\$
(3) Due to the virtual ground: \$V_{C_1} = V_{R_2} \$
This should give you a good start.
| https://electronics.stackexchange.com |
86,240 | [
"https://dsp.stackexchange.com/questions/86240",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/65062/"
] | I have been working with digital signals for quite some time and this fencepost-error issue when taking a simple example of sample frequency and sample spacing always trips me up (and I must say drives me completely crazy):
<span class="math-container">$f_s$</span>: sampling frequency, number of samples per second
<spa... | This is the way I look at it; the duration of a discrete-time signal is <span class="math-container">$N/f_s$</span>. In your first example, with four samples, the duration is one second.
Perhaps one intuitive way to see this is to consider one sample as "capturing" the value of the signal in a time interval, ... | Thanks for the great answer, thats very helpful. I've put some further thoughts below.
Equivilently, you can image the samples as covering [0.125, 0.375, 0.625, 0.875] (i.e. middle of the range [0 - 25, 0.25 - 0.5, 0.5 - 0.75, 0.75 - 1]).
This is similar to classic fencepost issue e.g. counting from 1 to 5. We say [1, ... | https://dsp.stackexchange.com |
123,969 | [
"https://cs.stackexchange.com/questions/123969",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/93561/"
] | It's conceptually simple to state what an "unordered pair" is supposed to be in set theory. Yet, in homotopy type theory I have trouble formalizing this. A first naive try in agda syntax:
<pre><code>data UPair (A : Type ℓ) : Type ℓ where
mkpair : (x y : A) → UPair A
uswap : ∀ a b → mkpair a b ≡ mkpair b a
</code><... | The type of unordered pairs in a type <span class="math-container">$A$</span> is defined to be <span class="math-container">$$\sum_{(X:\mathcal{U})}\sum_{(H:\|X\simeq \mathsf{bool}\|)}A^X.$$</span> In other words, an undordered pair in <span class="math-container">$A$</span> is simply a map <span class="math-container"... | The <em>set</em> of unordered pairs of <code>A</code> can be defined using a higher-inductive type with set-truncation, just as you suggested, somewhat like this (I am writing this off the top of my head without verifying it in Agda, but you'll get the point):
<pre><code>data UPair (A : Type ℓ) : Type ℓ where
mkpair... | https://cs.stackexchange.com |
321,307 | [
"https://stats.stackexchange.com/questions/321307",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9355/"
] | My understanding of the multinomial likelihood, with four states, ${A}$, ${B}$, ${C}$ and ${D}$ is that it can be expressed as:
$Likelihood = \frac{N!} {nA! nB! nC! nD!} P(A)^{nA} P(B)^{nB} P(C)^{nC} P(D)^{nD}. $
where
${N}$ = number of trials.
${nA}$ = number of trials resulting in State ${A}$
${nB}$ = number ... | From the previous comments if I understand the model structure, the log of the likelihood is given by
$$\log{L}=-\log ((n-n_a-n_b-n_c)!)+\log (n!)-\log (n_a!)-\log (n_b!)-\log (n_c!)+$$
$$2 (n-n_a-n_b-n_c) \log (1-p)+2 n_a \log (p)+(n_b+n_c) \log (1-p)+(n_b+n_c) \log (p)$$
where $n_a$, $n_b$, and $n_c$ are the known ... | I agree with you that there is no round-off issue.
But your answer is different from 80 because there's no reason to believe one should get the same value that minimizes a similar likelihood equation but modified with different values of $N$ and therefore $nD=N-nA-nB-nC$ - especially non-integer values of $N$. Even r... | https://stats.stackexchange.com |
123,150 | [
"https://stats.stackexchange.com/questions/123150",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/60244/"
] | $X\sim \Gamma(p,a)$,find the two dimensional moment generating function of ($X, \ln X$)
What I have done is
$$M_{(X,lnX)}(t_{1},t_{2}) = E(e^{t_{1}x+t_{2}lnx}) = E(e^{t_{1}x}x^{t_{2}}) = \int\int e^{t_{1}x}x^{t_{2}}f_{X,lnX}(x_{1},x_{2})dx_{1}dx_{2}$$
I need help to find the joint distribution of $X$ and $\ln X$.
| The gamma distribution is an exponential family and $(x, \log x)$ are the expectation parameters, so just write it in exponential family form and you have the density function of $(x, \log x)$.
$$\begin{align}
f_X(x) &= e^{\eta^\intercal T(x) - g(\eta)} \\
\implies \int_{x\in\mathbb R} f_X(x) &= 1 \\
t &= ... | The bivariate random variable $(X,\ln X)$ does not have a <em>joint density</em>
and so you cannot use a double integral as you have indicated in your question. Instead,
the law of the unconscious statistician gives
$$M_{(X,\ln X)}(t_{1},t_{2})=E[e^{t_1X+t_2\ln X}]
=E[e^{t_1X}X^{t_2}]
=\int_0^\infty e^{t_1x}x^{t_2} \c... | https://stats.stackexchange.com |
332,303 | [
"https://softwareengineering.stackexchange.com/questions/332303",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/247898/"
] | How can I manage my code to exactly wait for a certain amount of time (say 10s), if <strong>all</strong> * <em>time functions</em> on the system are not reliable and return immediately ?
<pre><code>Sleep(10000); // Do not sleep for 10s and execute directly the next function
MyFunction();
</code></pre>
The solution sh... | In my experience, as far as interviews go, the exact (language specific) implementation doesn't actually matter and many will simply let you write it out in pseudo code. If they do require you to write it in a specific language the interviewer will usually be more than happy to help you out with the specific syntax, bu... | You would roll your own data-structure when:
<ol>
<li>You are learning to code, and need the experience (re)writing a "known" solution.</li>
<li>You have a very specialized use-case and have done enough research to determine that a pre-built solution is not available for you. (This is relatively rare because EVERYONE... | https://softwareengineering.stackexchange.com |
514,168 | [
"https://physics.stackexchange.com/questions/514168",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247438/"
] | From classical mechanics we know that centrifugal inertial force, acting on an electron in a circular orbit of radius <span class="math-container">$R$</span> in relatively slow motion (<span class="math-container">$v \ll c$</span>), can be expressed in terms of its kinetic energy <span class="math-container">$K$</span... | In perturbation theory of QFT, we often (possibly implicitly) Taylor expand the action
<span class="math-container">$$ S[\phi]~=~S[\phi_0] ~+~\underbrace{\left. \frac{\delta S[\phi]}{\delta \phi^{\alpha}}\right|_{\phi_0}}_{=0}\eta^{\alpha}~+~\frac{1}{2}\left. \frac{\delta^2 S[\phi]}{\delta \phi^{\alpha}\delta \phi^{\be... | If you write a general potential as a function of the field and you expand in Taylor series you have a linear term but if you want to have some global minimum of the potential at the field value zero then you have to ensure that there is no linear term. This is the best I can do.
| https://physics.stackexchange.com |
110,076 | [
"https://softwareengineering.stackexchange.com/questions/110076",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27417/"
] | My team is composed of 4 developers; all seasoned and skilled. One of them is a wordy, well intended chap who insists on defining the technical solution to our stories before we put down our estimates with Planning Poker. He refuses to estimate if he doesn't have a rough idea of the agreed technical solution (which sou... | He seems to like things being defined formally, so a timer would be a good idea, since planning poker is defined as having set amounts of time for people to speak.
He's got the wrong idea about estimation too, everyone estimates <strong>against the story</strong> and <strong>not the implementation</strong>, which is w... | You team member sounds an analyst personality. Analysts need lots of information to make a decision. The timer idea is best, but be aware, he is going to caveat the hell out of anything he gives. Work with him to explain that it's just an early estimate based on the problem NOT the solution. If he wants to ask ques... | https://softwareengineering.stackexchange.com |
523,079 | [
"https://electronics.stackexchange.com/questions/523079",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/182852/"
] | I stumbled across some information about an opamp on the Texas Instruments Site, the OPA1604 and in the datasheet it says:
<blockquote>
These devices also feature completely independent circuitry for lowest crosstalk and freedom from interactions between channels, even when overdriven or overloaded.
</blockquote>
I wou... | It's not normally a big factor in selection so distributor parametric searches don't allow for it, you might find some analog IC manufacturer that includes it, I don't think AD does.
It's normally not very important in circuit design, the only time I've seen it become at all significant is when one amplifier in the pac... | You will always have HEAT interactions. Even if the layout of each front_end diffpair is the legendary cross_coupled quad, the metallization will have imbalances; given aluminum has about the same specific heat and thermal conductivity of silicon, there will be thermal interactions. The thermal timeconstant of 1mm (1,0... | https://electronics.stackexchange.com |
53,266 | [
"https://softwareengineering.stackexchange.com/questions/53266",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13846/"
] | I have a Maven project consists of around 100 modules. I have reason to decompose the project to so many modules, and I don't think I should merge them in order to speed up the build process.
I have read a lot of projects by other people, e.g., the Maven project itself, and Apache Archiva, and Hudson project, they all... | What part of your maven build is taking the longest? You may find that javac is your main bottleneck. Perhaps it's the unit test execution, try running your tests in parallel. Without more details it's really hard to give a useful answer. How big are the projects?
Are the builds fairly parallelizable? If you are usi... | This comparison is meaningful only if they are building exactly the same project. If not, maybe you should try building a Make file to build the same project that you are building with Maven.
| https://softwareengineering.stackexchange.com |
178,927 | [
"https://softwareengineering.stackexchange.com/questions/178927",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/73457/"
] | I have a little problem with the terms module and component.
In my mind, a module are bundled classes, which are only accesable via a well defined interface. They hide all implementation details and are reusable. Modules define modules on which they depend.
What is the difference to components? I looked it up in some ... | The terms are similar. I generally think of a "module" as being larger than a "component". A component is a single part, usually relatively small in scope, possibly general-purpose. Examples include UI controls and "background components" such as timers, threading assistants etc. A "module" is a larger piece of the who... | The generic meaning of <em>module</em> is a group of reusable code, not tied to one specific program. This could be everything from an entire set of GUI libraries down to a single class.
The generic meaning of <em>component</em> is a module with the additional restriction of substitutability using a specific interfac... | https://softwareengineering.stackexchange.com |
1,951,601 | [
"https://math.stackexchange.com/questions/1951601",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/166180/"
] | I need to prove that if $f(t) = \int_0^t |sin s| \ ds$, then $f(10\pi) = 5f(2\pi)$, using the change of variable theorem. That's what I did:
$$f(10\pi) = \int_0^{10\pi} |\sin s| \ ds $$
take $s = 5x$, then $s^{-1}(0) = 0$ and $s^{-1}(10\pi) = 2\pi$, $ds = 5dx$, therefore
$$f(10\pi) = \int_0^{10\pi} |\sin s| \ ds = 5... | $\newcommand{\braces}[1]{\left\lbrace\,{#1}\,\right\rbrace}
\newcommand{\bracks}[1]{\left\lbrack\,{#1}\,\right\rbrack}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\ds}[1]{\displaystyle{#1}}
\newcommand{\expo}[1]{\,\mathrm{e}^{#1}\,}
\newcommand{\ic}{\mathrm{i}}
\newcommand{\mc}[1]{\mathcal{#1}}
\newcommand{\mrm}[1]... | <strong>HINT:</strong>
Show that
$$\int_{2k\pi}^{2k\pi+2\pi}|\sin(s)|\,ds=\int_0^{2\pi}|\sin(s)|\,ds$$
for all integer $k$ by making a change of variable.
| https://math.stackexchange.com |
280,672 | [
"https://physics.stackexchange.com/questions/280672",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/90762/"
] | Given an observable $A$ and a system in the state represented by the vector $|\psi \rangle$, after the measurement is the system in the state $A |\psi \rangle$?
| According to the Born rule, measuring $A$ could give you any of its eigenvalues $\lambda_i$ as a result, with probabilities
$$ p_i = \left| \left< \psi | a_i \right> \right|^2. $$
According to the Copenhagen interpretation the system is then found to be in the corresponding eigenstate $\left| a_i \right>$.
| There are a lot of factors you haven't considered before asking this question.
If $\mid \psi \rangle$ is an eigenstate of the A operator, it will leave the system unchanged (upto a constant, which is the eigenvalue). If this is not the case, the wavefunction $\mid \psi \rangle$ can be represented in terms of the eigen... | https://physics.stackexchange.com |
52,498 | [
"https://dba.stackexchange.com/questions/52498",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/29994/"
] | Evaluating MySQL's slow query log with pt-query-digest from the Percona Toolkit, I need to group queries by transaction. As it seems, the easiest way to do this is to group by the Innodb_trx_id attribute.
However, my logs don't include this attribute. I tried with vanilla MySQL, MariaDB and Percona Server -- so I figu... | The extended fields that Percona added are not available in stock MySQL.
The only other option is to add a comment to your SQL query in your app. The comments are added to the log, and pt-query-digest can parse fields out of comments with the <code>--embedded-attributes</code> option.
It's a bit tricky to discover th... | MySQL Slow log is completely a separate entity from innodb_trx information which you get from Information_Schema <code>innodb_trx</code> table.
MySQl slow log logs all slow running queries specified while enabling it, it does not matter whether queries are within TRANSACTION or not slow log will record all slow runni... | https://dba.stackexchange.com |
277,097 | [
"https://softwareengineering.stackexchange.com/questions/277097",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/172173/"
] | I'm new to a small company that's pretty much run by one guy. He knows all the ins and outs of the system which is quite large. We have a database with about 300 different tables. I'm struggling to keep track of where everything in the database is and what relates to what. What methods can be used to manage large datab... | For the database that I am responsible for I do the following:
<ul>
<li>expose all metadata in views so you can see groups of related tables in a more human readable fashion</li>
<li>every view/table has a comment, every column has a comment. Yes, it's a pain but it helps new people</li>
<li>every function/procedure/t... | What have worked for me is:
<ul>
<li>Plot a giant physical model of the database.</li>
</ul>
You must use a tool like Sybase Power Designer and reverse-engineer the model. There are also free tools that could be used. Once there you must find a plot service and have it plotted in big format. Then put it on the wall. ... | https://softwareengineering.stackexchange.com |
102,310 | [
"https://electronics.stackexchange.com/questions/102310",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38428/"
] | My understanding of a D flip flop is that when the clock is high and D=1, it sets Q to 1. If D=0, Q is set to 0. So it is like a set to 1 if D=1 and reset to 0 otherwise.
The table repeatedly given in my book is:
<pre><code>D CLK Q QN
0 High 0 1
1 High 1 0
x 0 (last Q) (last QN)
x 1 (last Q) (last QN)
</code></pre>... | You mention that the table looks like a T flip flop. Is it possible you are interpreting the table incorrectly?
I believe the "QN" column represents "Q NOT", where the "Q" column is the value of Q resulting from the specific input. In this case, the table correctly represents the behavior of a D flip flop.
| "My understanding of a D flip flop is that when the clock is high and D=1, it sets Q to 1."
Not exactly. The D-FF is edge triggered, so when the clock transitions from low to high whatever is on the D input will be clocked to the Q output. If the clock is just high, then the Q output will not change no matter what t... | https://electronics.stackexchange.com |
277,193 | [
"https://softwareengineering.stackexchange.com/questions/277193",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/161992/"
] | So, I've looked at some similar questions asked here in regards to how these three should be used in naming. Usually, the answer is something along the lines of "it's conventional" and "just be consistent". I'm wondering if that's the same answer for my question.
I have an interface <code>StatSet</code> defined as
<p... | Any of the above seem logical. Immutable, Unmodifable and ReadOnly all are acceptable choices. It is important however, that you stick to a convention. If some of your classes are 'Immutable' while others are 'ReadOnly', this could imply that there is a difference, which could confuse a consumer of your public code.
I... | <strong>Naming your object immutable/read-only/unmodifiable seems superfluous.</strong>
It seems strange to me that you need to use immutable, read-only, unmodifiable or whatever else in the class name if the class already acts as immutable.
That's something that you should describe using keywords/class structure but... | https://softwareengineering.stackexchange.com |
290,409 | [
"https://electronics.stackexchange.com/questions/290409",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/100269/"
] | I was studying the CC, CB and CE Amplifier. And I have found a sentence somewhere that,
"Maximum power transfer occurs when load impedance is equal to source impedance."
As much as I understand impedance is something that opposes current. But, what are this load impedance, output impedance, input impedance? I mean ... | To give a mathematical definition, if we were to excite the input of a two-port with a sinusoidal current source
$$i_{in}(t) = I_0 + I \sin(\omega t)$$
with \$I\$ small enough to not cause any nonlinear behavior, we'd find
$$v_{in}(t) = V_0 + V_i \sin(\omega t) + V_q \cos(\omega t)$$
Then we could define
$$R_{in}... | Input impedance is the impedance that is "seen" by a device when connecting to a circuit's input. For example if I connect a source to the input of any of the amplifiers you just mentioned, the input impedance would be Vin/Iin
The output impedance on the other hand is the impedance seen when looking into the circuit f... | https://electronics.stackexchange.com |
540,909 | [
"https://physics.stackexchange.com/questions/540909",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214011/"
] | My professor was showing us how to derive the ground state wavefunction for the quantum harmonic oscillator. He begins with the annihilation operator acting on the lowest energy eigenvector:
<span class="math-container">$$a|E_0\rangle = 0$$</span>
Then he projects the equation onto the position eigenvector:
<span c... | It is just how the operators work in the position basis. I will show how it works for the position operator. The momentum operator can be handled similarly
First, we know that matrix elements of the position operator in the position basis are given by <span class="math-container">$\langle x|\hat X|x'\rangle=x'\delta(x... | The way to "pull out" the operator is to write it formally in ket notation, so that it acts naturally on kets. For example (in natural units with <span class="math-container">$\hbar=1$</span>)
<span class="math-container">$$\mathbf P = -\int d^3\mathbf x | \mathbf x \rangle i \nabla \langle \mathbf x|.$$</span>
Then yo... | https://physics.stackexchange.com |
689 | [
"https://mathoverflow.net/questions/689",
"https://mathoverflow.net",
"https://mathoverflow.net/users/349/"
] | Could someone give an overview, or just some examples, of "finiteness conditions" for simplicial sheaves/presheaves and/or simplicial schemes? Any answer or comment about this would be interesting, but I am interested in particular in the following two things:
1) I once heard Toen say something about this, and that on... | I don't know what Toën was talking about, but I suspect that it was about finiteness conditions for Artin stacks: the problem is that the usual finiteness conditions we look at for schemes (like the notion of constructibility for l-adic sheaves) do not extend to stacks in a straightforward way, which gives some trouble... | I don't understand much about this issue, but
Section 6.5 of Lurie's book on higher topos theory treats some related issues.
One natural condition is to bound above the homotopy groups of the simplicial sheaf,
ie to ask for it to be n-truncated for some n (homotopy sheaves bigger than n vanish).
The issue discussed b... | https://mathoverflow.net |
3,255,090 | [
"https://math.stackexchange.com/questions/3255090",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/623343/"
] | Let <span class="math-container">$T(X)$</span> be an efficient estimator (its variance equates the Cramer-Rao bound) of the parameter <span class="math-container">$\theta$</span>. A theorem in my course states that it is the only maximum likelihood estimator of <span class="math-container">$\theta$</span>. <br>
The pro... | Note that any subgroup of a cyclic group is characteristic. So in <span class="math-container">$\Bbb Z_6$</span>, the subgroups <span class="math-container">$\{0,3\}$</span> and <span class="math-container">$\{0,2,4\}$</span> are characteristic but their union is even not a subgroup!
| Let <span class="math-container">$G$</span> be a group and <span class="math-container">$H,K$</span> subgroups of <span class="math-container">$G$</span>. Then <span class="math-container">$H \cup K$</span> is a subgroup of <span class="math-container">$G$</span> if and only if <span class="math-container">$H \subseteq... | https://math.stackexchange.com |
379,153 | [
"https://mathoverflow.net/questions/379153",
"https://mathoverflow.net",
"https://mathoverflow.net/users/158328/"
] | Consider a set <span class="math-container">$V$</span> of <span class="math-container">$n$</span> vertices, and three degree sequences <span class="math-container">$a_i$</span>, <span class="math-container">$b_i$</span> and <span class="math-container">$c_i$</span> such that <span class="math-container">$c_i = a_i+b_i$... | The answer to this question is <em><strong>No</strong></em>.
Let us assume <span class="math-container">$V = \{1,2,3,4,5,6\}$</span> and consider degree sequences <span class="math-container">$a = [3,2,2,1,0,0]$</span>, <span class="math-container">$b = [1,0,0,3,2,2]$</span> and <span class="math-container">$c = a+b = ... | I think your property is true and can be shown recursively depending on the size <span class="math-container">$n$</span> of the graph.
<h2>Existence</h2>
For <span class="math-container">$n=2$</span> well one of the sequences has to be (0,0), so the other one is equal to <span class="math-container">$c$</span>: it work... | https://mathoverflow.net |
70,168 | [
"https://mechanics.stackexchange.com/questions/70168",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/51388/"
] | I recently purchase an 07 Honda shadow spirit and it has chrome exhaust, could anyone tell me how I could paint them black, thank you
| Since you have a scan tool, check the fuel trims to see if the ECM is adding fuel to compensate for a vacuum leak. ECM can add up to 25% more fuel, which would indicate a fairly large leak in the intake. Also check the O2 sensor reading to make sure it's switching rapidly between rich and lean.
| Check the rubber intake hose for cracking. I had several tears in mine that were causing a major vacuum leak in the intake and triggering the P0171 code. The reason for the cracking was the cycles of the rubber bending back and forth during acceleration and deceleration combined with engine heat and so on. Prior to rea... | https://mechanics.stackexchange.com |
671,245 | [
"https://physics.stackexchange.com/questions/671245",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/316304/"
] | <strong>The Device:</strong>
Imagine a physical system involving two circular rings of distinct inner and outer radii, but equal in inertia. The smaller ring is superimposed inside the inner radius of the larger ring. These two rings have negligible thickness and are allowed to freely rotate about an axis going through... | The description is super-complicated, so I could be misunderstanding the setup. But I believe that the mistake is here:
<blockquote>
The whole two-ring, rod and plate system is NOT moving translationally because no force had acted through it's center of mass.
</blockquote>
It doesn’t matter if a force acts through the ... | "<em>Okay, so you are suggesting that my statement of the whole system not moving is wrong. And, that it is in fact moving in the opposite direction of the balls in accordance with Newton's Laws so that there is not net change in momentum. And once the balls collide with the plate, the system stops entirely. That'... | https://physics.stackexchange.com |
688,459 | [
"https://physics.stackexchange.com/questions/688459",
"https://physics.stackexchange.com",
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] | I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION, page: 67 and they use perturbation method to approximate:
<span class="math-container">\begin{equation} T = \frac{kV + g}{gk}(1-e^{-kT}) \end{equation}</span>
they first expand <span class="math-container">$-e^{-kT... | Let's consider a sligthly more simple example. Let's say I have <span class="math-container">$h(k)=f(k)g(k)$</span>. I want to calculate <span class="math-container">$h(k)$</span> to first order. I can come up with two ways to do this. One way is to just Taylor expand <span class="math-container">$h(k)$</span> in the u... | I don’t have that textbook but I guess what authors want to derive is your last equation, <span class="math-container">\begin{equation}T = \frac{2V}{g}+(\frac{T^2}{3}-\frac{2V^2}{g^2})k+O(k^2).\ \ \ (1) \end{equation}</span>
This equation is equivalent to your first self-consistent equation, <span class="math-container... | https://physics.stackexchange.com |
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