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 |
|---|---|---|---|---|---|
257,539 | [
"https://electronics.stackexchange.com/questions/257539",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7523/"
] | I have found myself reading reports of fires lately, including some that started due to high-resistance connections in electrical outlets and switches. A load on a high-resistance connection can generate enough local heat to ignite building materials, while not tripping any upstream safety devices. This is a problem th... | The other answers seem to be misinterpreting the 'thermal fuse' part of your question. A 'thermal fuse' is an electrical overload sensor that uses heat as an indicator of an electrical overload. It sounds like you are asking about a thermal cutoff like the kind included in motors to which open a circuit when the <em>... | There is a very simple reason why this is not used. The main function of the fuse or circuit braker is the overcurrent protection of the enitire wire section.
Wires with certain cross section are protected at the node where a higher cross section is distributed in many sections with smaller cross section wires. All sb... | https://electronics.stackexchange.com |
355,053 | [
"https://mathoverflow.net/questions/355053",
"https://mathoverflow.net",
"https://mathoverflow.net/users/56524/"
] | Let <span class="math-container">$1<p<\infty$</span> and <span class="math-container">$f_n$</span> be a sequence in <span class="math-container">$L^p(S^1)$</span> that converges weakly to some <span class="math-container">$f$</span>. Here <span class="math-container">$S^1$</span> is the circle so we are dealing w... | Let <span class="math-container">$A_{n,\epsilon}$</span> be the set where <span class="math-container">$|f|<\epsilon|f_n|$</span>. Now split the integral of <span class="math-container">$(|f_n|^p-|f|^p-|f_n-f|^p)\phi$</span> into an integral over <span class="math-container">$A_{n,\epsilon}$</span> and an integral o... | Here's a partial answer: For <span class="math-container">$p$</span> an even integer, it's true. Maybe someone else can see how to handle the other cases.
In this case, the desired integral can be written as
<span class="math-container">$$\left(-\sum_{k=0}^{p-1} (-1)^{k} \binom{p}{k} \int_{S^1} f_n^k f^{p-k} \phi\rig... | https://mathoverflow.net |
1,815,708 | [
"https://math.stackexchange.com/questions/1815708",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/340854/"
] | I'm currently trying to solve the following exercise:
<blockquote>
Let B be the closed unit ball in $\mathbb R^n$ together with the euclidean metric. Show that every 1-Lipschitz function $f:B\to B$ has a fixed point.
</blockquote>
I think I am supposed to use the Banach Fixed Point Theorem, but I somehow have to s... | Since <span class="math-container">$B$</span> is compact, it suffices to prove that <span class="math-container">$$\inf_{x\in B} |f(x)-x|=0 \tag1$$</span> (The infimum must be attained by compactness.)
For every <span class="math-container">$\epsilon>0$</span> the map <span class="math-container">$x\mapsto (1-\epsi... | Here's another argument I came up with, although I personally prefer the accepted answer.
Let <span class="math-container">$g(x) = ||f(x) - x||$</span>.
Since <span class="math-container">$B$</span> is compact and <span class="math-container">$f$</span> is continuous, there exists <span class="math-container">$x_0 \in ... | https://math.stackexchange.com |
874,533 | [
"https://math.stackexchange.com/questions/874533",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/139754/"
] | Why the set of functions in $C\left [ 1,-1 \right ]$ such that $f\left ( -1 \right )= f\left ( 1 \right )$ is the subspace of $C\left [ 1,-1 \right ]$?
| "May a monoid have a different neutral element than its submonoid?"
By the very definition of a submonoid, no.
But of course there are sub-semigroups which happen to be monoids w.r.t. a different neutral element, for example $(\{0\},*,0)$ inside $(\{0,1\},*,1)$.
| Consider $\mathbb N_0\times \mathbb N_0$ with componentwise multiplication. Then $\{\,(n,1)\mid n\in\mathbb N_0\,\}$ and $\{\,(n,0)\mid n\in\mathbb N_0\,\}$ are disjoint submonoids (with neutral elements $(1,1)$ and $(1,0)$, respectively).
In fact, simply consider $\{0,1\}$ with multiplication and the submonoids $\{0\... | https://math.stackexchange.com |
462,089 | [
"https://physics.stackexchange.com/questions/462089",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/121554/"
] | Why do we interpret the accelerated expansion of the universe as the proof for the existence of dark energy?
The accelerated expansion only tells us that the Einstein field equation must contain a cosmological constant, but I can put the constant on either side of the equation. Usually we put it on the right hand sid... | The accelerated expansion of the universe is not direct evidence for dark energy, i.e. a perfect fluid contribution to the stress-energy tensor with <span class="math-container">$w = -1$</span>. Dark energy is just by far the simplest thing that fits the data well.
It's simple to cosmologists because they are used to... | Occam’s Razor, the simplest solution is likely correct. The theory of Dark Energy fits all data and was obliquely postulated by Tesla. The sister of gravity is the through vacuum space acting field/force of magnetism for example which can be treated in higher dimensional math just as Dark Energy and gravity can. Spacet... | https://physics.stackexchange.com |
263,846 | [
"https://physics.stackexchange.com/questions/263846",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/116392/"
] | For massless fermion, the free propagator in quantum field theory
is
\begin{eqnarray*}
& & \langle0|T\psi(x)\bar{\psi}(y)|0\rangle=\int\frac{d^{4}k}{(2\pi)^{4}}\frac{i\gamma\cdot k}{k^{2}+i\epsilon}e^{-ik\cdot(x-y)}.
\end{eqnarray*}
In Peskin & Schroeder's book, <em>An introduction to quantum field theor... | Yes it is correct. The derivation in P&S is straightforward but I will expand on it a bit. The key observation is that
\begin{equation}
\int\frac{d^4k}{(2\pi)^4}e^{-ik\cdot(y-z)}\frac{i\gamma^{\mu}k_{\mu}}{k^2+i\epsilon}
=-\gamma^{\mu}\partial_{\mu}\int\frac{d^4k}{(2\pi)^4}\frac{1}{k^2+i\epsilon}e^{-ik\cdot(y-z)},
... | Method One:
\begin{eqnarray*}
& & \int\frac{d^{4}k}{(2\pi)^{4}}\frac{i}{k^{2}+i\epsilon}e^{-ik\cdot x}\\
& = & \frac{i}{(2\pi)^{4}}\int d^{3}ke^{i\mathbf{k}\cdot\mathbf{x}}\int dk_{0}e^{-ik_{0}x_{0}}\frac{1}{[k_{0}+(|\mathbf{k}|-i\epsilon)][k_{0}-(|\mathbf{k}|-i\epsilon)]}\\
& = & \frac{i}{... | https://physics.stackexchange.com |
143,636 | [
"https://cs.stackexchange.com/questions/143636",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/139051/"
] | I want to show, without taking a limit, that <span class="math-container">$2^\sqrt{2 \log n} \in Ω(\log^2n)$</span> and <span class="math-container">$2^\sqrt{2 \log n} \in O(\sqrt{2}^{\log n})$</span>.
I will omit what I have tried as it has not been useful.
| Note that
<span class="math-container">$$2^\sqrt{2\log n}=2^{\frac{2\log n}{\sqrt{2\log n}}}$$</span><span class="math-container">$$=\left(2^{\log n}\right)^{\frac{1}{\sqrt{2\log n}}}$$</span>
<span class="math-container">$$=n^{\frac{1}{\sqrt{2\log n}}}$$</span>
<span class="math-container">$$=\sqrt[\sqrt{2\log n}]{n}.... | To prove <span class="math-container">$2^{\sqrt{2\log n}} \in O(\sqrt{2}^{\log n})$</span>, you should note that <span class="math-container">$\sqrt{2}^{\log n} = \left(\sqrt{2}^{\sqrt{\log n}}\right)^{\sqrt{\log n}}$</span>.
To prove <span class="math-container">$2^{\sqrt{2\log n}} \in \Omega(\log^2n)$</span>, you sho... | https://cs.stackexchange.com |
160,801 | [
"https://electronics.stackexchange.com/questions/160801",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65133/"
] | I'm starting the wiring for my project and would like to solder two resistors together in series. There is good chance that the wire will be exposed to heat and gentle turbulence.
<strong>What is the best way to solder axial-lead resistors?</strong>
I have seen that twisting the metal wires from each resistor is a go... | You don't mention exactly what kind of resistors they are, but for "normal" through hole ones the best way is to first wrap one resistor's leg around the other resistor's leg, then wrap that resistor's leg around the first resistor's leg. So you end up with this:
<img src="https://i.stack.imgur.com/cRd1w.jpg" alt="en... | The preferred method, for high quality chassis wiring, is to use turret terminals staked into a G-10 (FR-4) board to capture the components, and then to make the required connections at the appropriate terminals, like this:
<img src="https://i.stack.imgur.com/AxxRX.jpg" alt="enter image description here">
| https://electronics.stackexchange.com |
167,821 | [
"https://stats.stackexchange.com/questions/167821",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/86293/"
] | My study is on the relationship of college persistence of students, perception of students on student affairs services and their academic integration. I was suggested of using mediation analysis. May I know what is the best sample size for a mediation analysis? I currently have 2,338 population.
| Yes, you need to convert the prices to have the same currency.
If the prices are cointegrated when measured in the same currency, they will not necessarily be cointegrated when measured in different currencies -- because currency exchange rates may fluctuate a lot over time.
It makes more sense to measure prices in... | Strictly speaking, no you don't have to convert. The theory of cointegration doesn't mention that you should look for a cointegration relationship between apples and apples.
If both series have a unit root and if they share a common trend on the long term, then a cointegration relationship exists between them, whatev... | https://stats.stackexchange.com |
97,965 | [
"https://physics.stackexchange.com/questions/97965",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29157/"
] | For this circuit (a and b are connected by a battery),
<img src="https://i.stack.imgur.com/CVtE3.png" alt="circuit diagram">
Will I be able to find the total resistance of the circuit by adding resistors that are in series and combining resistors that are in parallel without using the method of Kirchhoff's Voltage a... | The net resistance depends on the point where you have applied the potential difference.
Indicating the direction of current is very useful.
You can Use $[$ $($ $R_3$ series $R_4$ $)$ parallel $R_2$ $]$ to be $R_7$
Now Redraw the circuit and by naming the point with same potential as one point as I have done in my d... | Many times this kind of problems becomes very simple just by redrawing the circuit in a more standard way. Have a look at this:
<img src="https://i.stack.imgur.com/kl7wg.png" alt="These are all equivalent circuits!">
Now I think you will have no problem to solve it!
| https://physics.stackexchange.com |
22,345 | [
"https://dsp.stackexchange.com/questions/22345",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/8825/"
] | Say I am using matlab's random number generator to get an array of random numbers, which I will then, for testing purposes, find the spectral density etc. For that purpose I need to know the sampling freq., but these have been generated synthetically so I am not sure how the sampling theorem applies here.
| You do not need to know the sampling frequency in order to determine the power spectral density (PSD). The frequency variable of the PSD of a sequence is normalized by the sampling frequency. You only need the sampling frequency if you want to denormalize that relative frequency and talk about absolute frequencies in H... | The sampling rate is arbitrary- you choose it.
Usually people are simulating a real situation, like, for example, audio from a CD. Then you would choose the sample rate to be 44.1 kHz.
| https://dsp.stackexchange.com |
206,382 | [
"https://physics.stackexchange.com/questions/206382",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <blockquote>
Suppose we have a hydrogen atom, and measure the position of the electron; we must not be able to predict exactly where the electron will be, or the momentum spread will then turn out to be infinite. Every time we look at the electron, it is somewhere, but it has an amplitude to be in different places so... | The average <em>vector</em> momentum of an electron bound to an atom is exactly zero. (Otherwise, the electron would leave the atom!)
The average <em>magnitude</em> of the momentum can't be zero, because of the uncertainty principle. So Feynman is using the approximation $\vec p = \vec 0 + \Delta p \hat p$, where th... | This might be a bit helpful.
The uncertainty in the momentum of an electron in an atom is defined as: <span class="math-container">$(\Delta P )^{2}= \langle P^{2}\rangle-\langle P\rangle^{2}$</span>. An electron bounded by the nucleus, has an average momentum of zero, which means (<span class="math-container">$\Delta... | https://physics.stackexchange.com |
623,958 | [
"https://physics.stackexchange.com/questions/623958",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98822/"
] | Does the neutrino gas pervading the universe always have the same temperature? Does it still have the temperature as the neutrino gas that emerged from the big bang? Neutrinos don't interact, so how could the gas be cooled down (apart from space expansion)?
| The second-to-last paragraph in the question starts with
<span class="math-container">$$
p^\mu\to i\partial^\mu.
$$</span>
This implies
<span class="math-container">$$
p_\mu\to i\partial_\mu,
$$</span>
because the index on both sides is lowered using the same metric (regardless of the sign convention for the metric)... | I remember that I have also struggled with the sign of the minimal coupling term several times in the past. Therefore, I feel compassionate with your attempts to derive it.
Would you accept the non-relativistic Schrödinger equation for the bare electric field of the nucleus (i.e. without magnetic potential) as
<blockqu... | https://physics.stackexchange.com |
546,332 | [
"https://math.stackexchange.com/questions/546332",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/103518/"
] | Each item in a computer parts catalogue is given a unique code consisting of two distinct
uppercase letters followed by four distinct digits. For example, the code for a particular
keyboard is XY1702.
Suppose a sales clerk wants to order a particular item, and knows that the item code
begins with the letters DE, and th... | (Below I use the symbols $P\oplus Q\equiv(P\vee Q)\wedge\neg(P\wedge Q)$ for the propositional XOR function and $A\,\triangle\,B=(A\cup B)\setminus(A\cap B)$ for the symmetric difference operator.)
It follows immediately if you know that the regular binary XOR function $P\oplus Q$ is associative and commutative, since... | Yes, the symmetric difference is commutative. However, <strong>Symmetric Difference is not XOR.</strong> The two are similar, but they are by no means the same. XOR is a logical operation, Symmetric Difference is an operation you apply to sets.
There are several ways to attack it.
I denote symmetric difference with $... | https://math.stackexchange.com |
147,733 | [
"https://stats.stackexchange.com/questions/147733",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/74239/"
] | I need to fit a spline function to a data set. I tried with <code>bs</code>, <code>ns</code> and <code>smooth.spline</code>. In my case the curve obtained by <code>smooth.spline</code> follows the trend in data better than with the <code>bs</code> and <code>ns</code>.
However, I do not know how to
<ol>
<li>obtain the... | This fits a natural spline (linear tail restricted) using the truncated power basis. In this example, default knots (based on quantiles of the predictor) are not used; instead we specify 4 knots. The only way to get a test of goodness of fit is to postulate a richer model than this and see if it improves the model fi... | I would suggest using <code>interpSpline</code> from the <code>splines</code> package. Building on your example, you could use:
<pre><code>library(splines)
x <- 1:11
y <- c(0.2,0.40, 0.6, 0.75, 0.88, 0.99, 1.1, 1.15, 1.16, 1.16, 1.16 )
spline <- interpSpline(x,y)
plot(spline)
points(x,y)
</code></pre>
The ob... | https://stats.stackexchange.com |
5,025 | [
"https://stats.stackexchange.com/questions/5025",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1215/"
] | Suppose we have a simple linear regression model $Z = aX + bY$ and would like to test the null hypothesis $H_0: a=b=\frac{1}{2}$ against the general alternative.
I think one can use the estimate of $\hat{a}$ and $SE(\hat{a})$ and further apply a $Z$-test to get the confidence interval around $\frac{1}{2}$. Is this ok... | In linear regression the assumption is that $X$ and $Y$ are not random variables. Therefore, the model
$$Z = a X + b Y + \epsilon$$
is algebraically the same as
$$Z - \frac{1}{2} X - \frac{1}{2} Y = (a - \frac{1}{2})X + (b - \frac{1}{2})Y + \epsilon = \alpha X + \beta Y + \epsilon.$$
Here, $\alpha = a - \frac{... | You can test this hypothesis with a full versus reduced model test. Here is how you do this. First, fit the model $Z = aX + bY$ and get the residuals from that model. Square the residuals and sum them up. This is the sum of square error for the full model. Let's call this $SSE_f$. Next, calculate $Z - \hat{Z}$ where $\... | https://stats.stackexchange.com |
608,888 | [
"https://physics.stackexchange.com/questions/608888",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/278990/"
] | I am having trouble understanding the definition Hermitian and Hermitian conjugate.
An operator is Hermitian provided that: <span class="math-container">$\hat{O}^\dagger=\hat{O}$</span>
The Hermitian conjugate of the differentiation operator: <span class="math-container">$\left(\frac{\mathrm{d}}{\mathrm{d}x}\right)^\d... | <blockquote>
When we say that the heat capacity of the water is of <span class="math-container">$4186\text{ }\mathrm{J/K}$</span>, [...]
</blockquote>
But we don't say that. The value of <span class="math-container">$4186$</span> is the <em>specific heat capacity</em> <span class="math-container">$c_p$</span>:
<span cl... | In thermodynamics, heat capacity is not defined in terms of heat Q at all. The specific heat capacities at constant volume and at constant pressure are defined precisely in terms of the partial derivatives of specific internal energy and specific enthalpy with respect to temperature. These are certainly physical prop... | https://physics.stackexchange.com |
505,972 | [
"https://physics.stackexchange.com/questions/505972",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/102243/"
] | When you come from classical hamiltonian mechanics (which is based on the phase space), observables are introduced as functions <span class="math-container">$f$</span> on the phase space <span class="math-container">$(q, p)$</span>. There can't be a classical observable that isn't a function of <span class="math-contai... | In classical mechanics, any "observable" has to be a function of <span class="math-container">$x,p$</span> because we <em>define</em> <span class="math-container">$x,p$</span> to be the degrees of freedom of the system. If we experimentally find an observable that does not depend on <span class="math-container">$x,p$</... | Let's say we're working in a Hilbert space of square-integrable functions <span class="math-container">$f(x)$</span>. Indeed it's natural to talk about the operators <span class="math-container">$X$</span> and <span class="math-container">$P$</span> which act in a simple way on <span class="math-container">$f(x)$</span... | https://physics.stackexchange.com |
4,493,549 | [
"https://math.stackexchange.com/questions/4493549",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1018230/"
] | <strong>question:</strong> Let <span class="math-container">$a,b,c,d$</span> be given constants with the property that <span class="math-container">$ad-bc\neq0$</span>. If <span class="math-container">$f(x)=\frac{ax+b}{cx+d}$</span>, show that there exists a function <span class="math-container">$g(x)=\frac{\alpha x+\b... | You're trying to find the inverse function of <span class="math-container">$f(x)$</span>, so set the function equal to <span class="math-container">$y$</span> and solve for <span class="math-container">$x$</span>:
<span class="math-container">$$y = \frac{ax+b}{cx+d}$$</span>
<span class="math-container">$$ycx+yd = ax+b... | <span class="math-container">$g$</span> is the Moebius transformation corresponding to the nonsingular matrix. Then <span class="math-container">$f$</span> corresponds to the inverse matrix.
| https://math.stackexchange.com |
234,645 | [
"https://softwareengineering.stackexchange.com/questions/234645",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/59642/"
] | I've had a few programming jobs in the past where I was the only developer working on a project. After I've left, I typically get several emails a week from these companies, usually from the developer(s) who's replaced me there. These emails are usually asking for details about how things work and how I'd best go about... | You are in no way obligated to help them.
Whether or not your former employer have realized it, they have taken a low cost/high risk decision by having only one developer work on the software. That was their (perhaps uninformed) decision, and now they are paying the price - you should not.
If you feel like helping th... | Here's a potential e-mail to craft*;
<blockquote>
Sorry, I'm very busy right now with my existing contracts and not
regularly checking my e-mails. If you have a support request for a
product I used to work on, send a message to
"support@mattharrison.com", so that we can discuss setting up a
support agreement... | https://softwareengineering.stackexchange.com |
640,605 | [
"https://physics.stackexchange.com/questions/640605",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300199/"
] | It is said that internal forces do not change the state of rest to motion only external forces can change it. But in case of a gun, a gun applies force internally to the bullet inside it and the bullet changes its state from rest to motion. So how does bullet moves if internal forces do not cause motion?
| Before you can talk about internal vs external forces you must first define the system.
If the gun plus the bullet is the system, then, neglecting gravity and assuming no one is holding the gun, then there will be no external forces acting on the system. This means that the center of mass of the system will not move, t... | There is a recoil that pushes the gun back. Then, the gun holder applies force to keep the gun from moving back. So, if your system is comprised of the gun and the bullet, it is the gun holder who applies the external force. If the system is comprised of the holder, the gun, and the bullet, then it is the earth that cr... | https://physics.stackexchange.com |
18,316 | [
"https://dsp.stackexchange.com/questions/18316",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/4346/"
] | so, first let's do this for the circular correlation case (it might be easier).
let's say we have three real and periodic functions or signals $x(t)$, $y(t)$, $z(t)$ all with period $2 \pi$:
$$ x(t+2\pi) = x(t) \quad \forall t $$
$$ y(t+2\pi) = y(t) \quad \forall t $$
$$ z(t+2\pi) = z(t) \quad \forall t $$
define th... | I'm afraid your statement isn't true. This can best be seen in a suitable choice of basis, one that simplifies the cross correlation. This basis if of course the shift invariant periodic Fourier basis on your support interval.
Let's label the basis vectors $F_n$ for integer $n$. The cross correlation of two different ... | We can easily create three real, $2\pi$-periodic signals that have zero cross correlation with each other, simply by ensuring they contain no common frequency components. For example:
$$a(t) = a_1 \sin t + a_2 \sin 2t \\
b(t) = b_1 \sin 3t + b_2 \sin 4t \\
c(t) = c_1 \sin 5t + c_2 \sin 6t $$
Now, I can construct $x(... | https://dsp.stackexchange.com |
753,553 | [
"https://math.stackexchange.com/questions/753553",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/137090/"
] | Let $R$ be a commutative ring and let $0 \to L \to M \to N \to0$ be an exact sequence of $R$-modules. Prove that if $L$ and $N$ are noetherian, then $M$ is noetherian. I tried considering the pre image of the map $L \to M$ and the image of the map $M \to N$ as they are submodules of $L$ and $N$ respectively, but I coul... | Let $S_1\subset S_2 \subset S_3 \subset ... $ be an ascending chain of submodules
in $M$.
Now consider the chains $S_1\cap L \subset S_2\cap L \subset ... $
and $f(S_1)\subset f(S_2)\subset ... $ in $L$ and $N$, respectively
(here $f:M\rightarrow N$ is the second map in the exact sequence).
As $L$ and $N$ are noethe... | Let
$$0\longrightarrow L\overset{i}\longrightarrow M\overset{p}\longrightarrow N\longrightarrow0$$
be a short exact sequence of $R$-modules. Assume that $L$ and $N$ are Noetherian modules.
Let $(M_n)_{n\geq0}$ be an ascending chain of submodules of $M$.
Since $(p(M_n))_{n\geq0}$ is an ascending chain of submodules of... | https://math.stackexchange.com |
55,081 | [
"https://dba.stackexchange.com/questions/55081",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/515/"
] | I have the following table that I want to redefine:
<pre><code>create table tq84_redefinition (
id number primary key,
ts1 timestamp not null,
ts2 timestamp
);
</code></pre>
Please note the <code>not null</code> constraint on the column <code>ts1</code>.
Using <code>dbms_redefinition</code>, I specifically use... | This is a known bug (description is not public unfortunately):
<strong>Bug:4396234 ET10.2OREDEF: NULLABLE COL OF *_TAB_COLUMNS TABLE NOT UPDATED AFTER ONLINE REDEF</strong>
The NOT NULL constraints are copied as NOVALIDATE, and you have to set them to VALIDATE state manually, e.g:
<pre><code>ALTER TABLE t84_redefeni... | The <code>Not Null</code> clause of a table column definition sets a flag in <code>$sys$cols</code> and generates a <code>sys_xxxxxx</code> constraint on the column.
<code>dbms_redef</code> however just copies the <code>sys_xxxxxxx</code> constraint and omits setting the flag. It's this flag that gets decoded into t... | https://dba.stackexchange.com |
122,131 | [
"https://chemistry.stackexchange.com/questions/122131",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/84457/"
] | what was the justification for the use the cathode and anode terminology in IEF?
There is no redox taking place in IEF, just proteins interacting with an electric field
| <blockquote>
Who was responsible for this naming system and how can we change it?
</blockquote>
Michael Faraday was responsible for the terms anode and cathode more than hundred years ago.
All the confusion regarding the nomenclature will vanish if you do not associate electrostatic signs with these two terms. One ... | The good mnemonic tool to remember is :
<ul>
<li><strong>Anode</strong> = anabasis, electrons would be going upwards from the electrode to the wire = <strong>oxidation</strong>, ( Xenophon, Anabasis, 404BC, "The journey upwards(to north))</li>
<li><strong>Cathode</strong> = cathabasis(the journey downwards), electron... | https://chemistry.stackexchange.com |
373,950 | [
"https://softwareengineering.stackexchange.com/questions/373950",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/308427/"
] | I'm quite new to microservices and I'm studying what is the best approach when it comes to microservice inter communication and fallback scenarios.
For example:
if service <strong>A</strong> is calling service <strong>B</strong> to get a particular data.
Case:
<ol>
<li>What if service <strong>B</strong> is not avai... | There's no general answer for this. When you are using (micro-)services, you are building a <em>distributed system</em>. Distributed systems are massively more complex than a monolithic system exactly because we have to think about such things like partial failures and maintaining consistency – it's great that you imme... | <blockquote>
What if service B is not available? How should it reflect on the Front end?
</blockquote>
I'm not sure what you mean by 'front end'? Is that service A?
At any rate, if service A calls service B, and service B fails, there are two classes of cases. If the error was 4xx, then you should service A should f... | https://softwareengineering.stackexchange.com |
3,276,511 | [
"https://math.stackexchange.com/questions/3276511",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/254604/"
] | <blockquote>
Let <span class="math-container">$f:[a,\infty)\to \mathbb{R}$</span> be two times differentiable.
If <span class="math-container">$\lim_{x\to \infty} f(x)=f(a)$</span> then there exists <span class="math-container">$x\in [a,\infty)$</span> such that <span class="math-container">$$f^"(x)=0.$$</span>
</block... | Suppose <span class="math-container">$f''(x) \neq 0$</span> for all <span class="math-container">$x$</span>. Since any derivative has IVP it follows that <span class="math-container">$f''(x) >0$</span> for all <span class="math-container">$x$</span> or <span class="math-container">$f''(x) <0$</span> for all <span... | <strong>Higlights</strong> - Try to fill in details:
Assume <span class="math-container">$\;f\;$</span> isn't constant (otherwise the claim is trivially true), then <span class="math-container">$\;f\;$</span> must either decrease from <span class="math-container">$\;a\;$</span> and then increase towards <span class="m... | https://math.stackexchange.com |
291,782 | [
"https://math.stackexchange.com/questions/291782",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/8140/"
] | How do I show the following formula is true?
$$
\lim_{N\to\infty} p_{\hat{\mu}}(x) = \delta(x-\mu)
$$
when
$$
p_{\hat{\mu}}(x) = \frac{\sqrt{N}}{\sqrt{2\pi\sigma^2}}\exp\left(-\frac12\frac{N}{\sigma^2}(x-\mu)^2\right).
$$
It involves the probability density function for the <em>sample mean</em> of independent, ident... | This illustrates that $\delta$ is not a function, but a <em>functional</em>: it does not reside in the world of functions but in operators <em>on</em> functions. By definition, you have that $\int_{-\infty}^\infty f(x)\delta(x-\mu)=f(\mu)$ for all nice functions $f$ (continuous and compactly supported), so what you rea... | Alternatively, what you want to prove is equivalent to showing that $\hat{\mu}$ converges in probability to $\mu$. That is, for every $\epsilon > 0$,
$$\lim_{n \rightarrow \infty}{P(|\hat{\mu}-\mu|>\epsilon) = 0}$$
This follows from the law of large numbers.
| https://math.stackexchange.com |
368,117 | [
"https://math.stackexchange.com/questions/368117",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/37174/"
] | <blockquote>
Prove that sign$(\sigma \tau)$ = sign$(\sigma)$sign$(\tau)$ for any permutations $\sigma, \tau \in S_n$.
</blockquote>
I think the two thing's I'm trying to show are:
<ul>
<li>If sign$(\sigma)$ = sign$(\tau) = \pm 1 \implies$ sign$(\sigma \tau)$ = $1$</li>
<li>Wlog, if sign$(\sigma) = 1$, sign$(\tau) =... | sign is defined as 1 or -1 depending on whether the number of transpositions you can write a permutation in is even or odd.
if $\sigma$ is written as $k$ transpositions and $\tau$ is written as $t$ then $\sigma \tau$ is $k+t$ transpositions.
This proves that $\text{sgn}(\sigma)\text{sgn}(\tau)=\text{sgn}(\sigma\tau)$... | <ul>
<li>Let $\pi\in S_n$ and set $\Delta=\prod_{1\leq i\leq j\leq n}(x_i-x_j)$.</li>
<li>Set $\Delta^{\pi}=\prod_{1\leq i\leq j\leq n}(x_{(i)\pi}-x_{(j)\pi})$.</li>
<li>Show that $\Delta^{\pi}=\text{Sgn}(\pi)\Delta$.</li>
<li>Show that for $\pi,\phi\in S_n$, $\text{Sgn}(\pi\phi)=\text{Sgn}(\pi)\text{Sgn}(\phi)$ by sho... | https://math.stackexchange.com |
344,751 | [
"https://softwareengineering.stackexchange.com/questions/344751",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/266383/"
] | Let's say that I have a JSON file like at example below.
How would I go about finding all possible values of item combination <strong><em>time sums</em></strong> that exist between let's say <code>00:03:04</code> to <code>00:25:55</code> without finding every single permutation combination that exists and adding them ... | <blockquote>
what makes it difficult for say the visual C++ compiler on windows to generate a linux binary executable file?
</blockquote>
Other than an unwillingness to do that on Microsoft's part, absolutely nothing. The obstacles aren't technical.
Development toolchains are just programs that take input and prod... | Yes, if you have all of the info about your target platform then it should not matter what platform you're actually running on.
There's two problems that tend to crop up:
<ol>
<li>People don't focus on it because it's a less common scenario. Often the only thing you cross compile is a compiler so you can then stop cr... | https://softwareengineering.stackexchange.com |
274,300 | [
"https://physics.stackexchange.com/questions/274300",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/122366/"
] | Average velocity:
$$v_{\rm avg,1}=\frac{v_{\rm final}+v_{\rm initial}}{2}$$
and average velocity:
$$v_{\rm avg,2} =\frac{\rm total\;displacement}{\rm time \;taken}=\frac{\Delta x}{\Delta t} $$
What is the difference between them and when do we use them?
| Your first way of calculating an average velocity is inaccurate and really should be avoided.
Only the second method is accurate. This is a consequence of the underlying <em>calculus</em> of kinematics.
When a object travels (e.g. but not necessarily on a straight line) its velocity is not required to be constant. In f... | Taking the average of the initial velocity and final velocity is not necessarily, you are assuming a linear change in the velocity which is not the general situation. So only the second formule specifies the average velocity.
| https://physics.stackexchange.com |
351,325 | [
"https://mathoverflow.net/questions/351325",
"https://mathoverflow.net",
"https://mathoverflow.net/users/119645/"
] | It's known that order topology is completely normal, so the lexicographic ordering on the unit square is also completely normal. It's also known that the lexicographic ordering on the unit square is not metrizable. I am interested in whether it is perfectly normal. (A space is <em>perfectly normal</em> if for any two d... | As Nate Eldredge points out in the comments, the book <em>Counterexamples in Topology</em> states that this space is not perfectly normal, but does not provide a proof. Here is the idea for a proof.
A <em>perfectly normal</em> space is a normal space in which every closed set is a <span class="math-container">$G_\delt... | It is a known fact that any perfectly normal (countably) compact space <span class="math-container">$X$</span> is ccc. The proof is what you would try: start with an uncountable cellular family <span class="math-container">$\mathcal{U}$</span>, choose a point <span class="math-container">$p_U \in U$</span> for each <sp... | https://mathoverflow.net |
113,483 | [
"https://softwareengineering.stackexchange.com/questions/113483",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29270/"
] | I want to code my next work project in a language I'm unfamiliar with (python). I can think of plenty of reasons from my point of view why its a good idea (not least of all because it sounds fun). However my manager will probably ask me why. I'm a little stumped on the advantages from his point of view.
<strong>EDIT<... | I would rather choose a language that is better for the task I have to accomplish. Which kind of <em>project</em>? This would not only be of benefit for your company but also for you (choosing the wrong tool can cause trouble later).
If Python is something that could enter in your company/group strategy and you want t... | Shouldn't you approach it from the point of "what should I do that is best for the company" rather than "what do I want to do and how can I convince them of its value."?
| https://softwareengineering.stackexchange.com |
1,941 | [
"https://cardano.stackexchange.com/questions/1941",
"https://cardano.stackexchange.com",
"https://cardano.stackexchange.com/users/137/"
] | I'm guessing it means remove the token from circulation, permanently. In a real-world example that would be akin to literally throwing cash into a fire? What are the technical details involved in the process?
<s>Furthermore, how does this all work in token conversion?</s>
Edit: will ask above as a separate question.
| One way in which Tokens/ADA can be burned is by sending them to a contract which has a deadline for extracting them. Once the deadline is passed, the validation script will never be able to validate and thus burning them. It would be wise to make the deadline the current slot so that there would be no chance of Tokens/... | One way to burn a token would be to send it to a script address where the validator always fails. One of the simplest validators in Plutus would look something like this...
<pre><code> mkValidator :: Data -> Data -> Data -> ()
mkValidator _ _ _ = error ()
</code></pre>
Since any UTxO belonging to a script a... | https://cardano.stackexchange.com |
114,268 | [
"https://mathoverflow.net/questions/114268",
"https://mathoverflow.net",
"https://mathoverflow.net/users/26798/"
] | Let $X = \prod _{s \in S} \Omega_s$, with $\Omega_s$ finite and all the same, $S$ countable. Let $\mu_1$ and $\mu_2$ be two probability measures on the product space (not necessarily the product measure). Let $C$ be a coupling between the two measures and let's define,
$$
rift(C) = sup_{s \in S}\lbrace \mbox{ } C \mb... | Here is what seems to me a good beginning, if the argument can be carried all the way.
We have that $dist(\mu_1,\mu_2):=\inf_c \sup_s f(s,c)$,
where $f(s,c):= c( \{ (\omega^1,\omega^2) \in X\times X : \omega^1_s \neq \omega^2_s \} )$.
Then for any indices $ \{ s_i \}$ for $i$ from $1$ to $r$, we have
$\sup_s f(s,... | For any specific coupling $C$, the left hand side can be bounded by the probability that $\omega^1_s \ne \omega^2_s$ for some $s\in I$, where $I$ is the set of indices on which the cylinder $A$ is defined. This is a most $r$ times $rift(C)$.
| https://mathoverflow.net |
24,503 | [
"https://cs.stackexchange.com/questions/24503",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16959/"
] | There is a complete binary tree with its leaves as components of some system
<img src="https://i.stack.imgur.com/xSP4r.jpg" alt="enter image description here">
The values from one node to another gives propagation time for a signal to propagate from one junction to another
For the signal to arrive at the leaves at ex... | You can do a lot better than a total delay of 36. In fact you can get a total delay of half that. The idea is to recursively adjust the delays from bottom up.
In your example, I'll count the edges in the bottom level starting at the left at what I'll denote by edge 1, then edge 2, and so on up to the rightmost edge at... | As the tag suggests, this is a classic greedy algorithm. Some notations:
<ul>
<li>$ancestor(i, c)$ denotes the ancestor on the $i$-th level (root $R$ is at level 0)</li>
<li>$delay(c)$ denotes the propagation delay from $R$ to component $c$ (without addition of any delays)</li>
<li>$M = \max_{i} {delay(c_i)}$. In this... | https://cs.stackexchange.com |
299,912 | [
"https://electronics.stackexchange.com/questions/299912",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/128206/"
] | "A student tried to make an AC generator consists of a coil of one turn, and cross sectional area of (<span class="math-container">\$7.54 × 10^{-3} m²\$</span>), and rotates in magnetic flux density (<span class="math-container">\$2.5 × 10^{-2} T\$</span>), and when it was taken out of the magnetic flux in <span c... | It is not a description of a practical generator:
<ol>
<li>The magnetic field is weaker than the field of a typical refrigerator magnet.</li>
<li>There is no indication of a mechanism to sustain the magnetic field or maintain its direction.</li>
<li>The coil of wire is initially described as rotating, but then describ... | I think you (and unfortunately, us) are taking this question far to serious. This is a question of scale.
Spin a coil in a magnetic field or spin a magnet in a coil and all you get is 1.5V.
Although you can get into the theory, it is NOT practical because the generator does not have the capability of an AAA 1.5V bat... | https://electronics.stackexchange.com |
26,734 | [
"https://mechanics.stackexchange.com/questions/26734",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/15147/"
] | With motorcycles, what are the parts that most frequently get damaged and therefore have to be exchanged most frequently?
I'm asking this question because I am looking to buy a motorcycle that I would like to maintain and repair myself. One factor for deciding for a specific model will be the availability of spare par... | As @JPhi1618 says "Handlebars, levers, footpegs, and the exhaust are the most commonly damaged parts for a new rider when they lay the bike down", additionally anything made of plastic is also likely to break in such an event.
However if you mean things that wear out and you can maintain yourself then all bikes will s... | I'm assuming you're asking about parts availability. If you're looking at Honda CBs stick to the more common models that were made for long periods and you won't have trouble finding consumable parts, old spares from parted out bikes and aftermarket new parts. Also there's tons of people out there using these bikes eve... | https://mechanics.stackexchange.com |
526,746 | [
"https://math.stackexchange.com/questions/526746",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/9718/"
] | Let $0 \to A \stackrel f\to B \stackrel g\to C \to 0$ be short exact sequence of modules ($f:A \to B$, $g:B \to C$). Suppose that there exists $\alpha: B \to A$ and $\beta: C \to B$ such that $g \beta = id_C$, $\alpha f = id_A$. How can I prove that $f \alpha + \beta g = id_B$?
| The claim is not correct (see below). However, the following is true: Assume that we have the short exact sequence, as well as some $\beta : C \to B$ with $g \beta = 1_C$. Then there is a unique $\alpha : B \to A$ with the desired properties:
The morphism $\beta g - 1_B$ has the property that $g(\beta g - 1_B) = g - g... | Very Big Hint: Proceed in two parts.
<ol>
<li>Show that, if $y\in B$ satisfies the two equations $g(y) = 0$ and $\alpha(y)=0$, then $y=0$.</li>
<li>Let $y=(f\alpha + \beta g)(x) - x$.</li>
</ol>
(I believe that Martin is right; this seems to require that $\alpha\beta=0$.)
| https://math.stackexchange.com |
26,465 | [
"https://astronomy.stackexchange.com/questions/26465",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/20370/"
] | Assume two black holes collide head-on. In other words, they were not orbiting one another before the collision. I know this is unlikely. Further assume that their sizes and distance from Earth are similar to past collisions detected by LIGO.
My understanding is that detectable gravitational waves are caused by mas... | There are two issues: Would there be gravitational waves to be detected and would LIGO detect them.
On the first issue, gravitational waves are quadrupolar, and a cylindrically symmetric system will not produce any. (Specifically, the second time derivative of the quadrupole moment of an isolated system's stress–energ... | The waveform of binary inspiral was about 100ms with a peak for every rotation, about 10 waves/rotations were measured, ranging from 30 to 200Hz. The average female voice has a fundamental frequency of about 200hz, to have some idea, and a typical pitchfork is about 440Hz.
The waveform for a head on collision would ab... | https://astronomy.stackexchange.com |
2,327,738 | [
"https://math.stackexchange.com/questions/2327738",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/454930/"
] | Use the Comparison Test to determine for what values of $p$ the integral: $\int_{8}^{\infty} \frac{1}{x^p} \ ln(x) \ dx$ converges. (Use interval notation.) $$\\$$
This is what I have so far:
I'm comparing to $\frac{1}{x}$, which diverges.
I'm unsure of what to do next. I know it starts to converge from 2.
I would... | For any $p > 1$ choose $a$ such that $0 < a < p-1$.
We have
$$\frac{\ln x}{x^p} = \frac{\ln x^a}{ax^p} < \frac{x^a}{ax^p} = \frac{1}{ax^{p-a}}$$
Since $p-a > 1$ we have convergence for any $p > 1$.
The integral diverges if $p \leqslant 1$ by an easy comparison: $\ln x / x^p > 1/x^p$
| Note that for $x>1,\ln { x } <x$ so $$\\ \int _{ 8 }^{ \infty }{ \frac { \ln { x } }{ { x }^{ p } } dx<\int _{ 8 }^{ \infty }{ \frac { dx }{ { x }^{ p-1 } } dx } } \\ \\ \\ \\ \\ \\ $$ and RHS converges when $p-1>1$ or $p>2$
| https://math.stackexchange.com |
5,505 | [
"https://biology.stackexchange.com/questions/5505",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/1609/"
] | Why is the secondary antibody conjugated to the enzyme in ELISA, instead of the primary antibody? Wouldn't it be easier to conjugate the enzyme to the primary antibody?
| Making an antibody-enzyme conjugate isn't trivial. By using a primary/secondary set-up you can use the same well-characterised conjugate in combination with many different primary antibodies (as long as these primaries are all raised in the same species). There is also the possibility of some amplification: for example... | Another reason that secondary antibodies are used is to look for the production of antibodies by a test animal. Follow me for a second with an example that I think will make it clear.
<strong>Our Purpose:</strong>
We have identified a protein (call it 'V_Entry') that is vital for Ebola to infect human cells.
We wonde... | https://biology.stackexchange.com |
496,556 | [
"https://stats.stackexchange.com/questions/496556",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/298218/"
] | I have just started learning Markov chain and I am clueless about how to solve this problem
A man rolls a boulder up a 40 meter-high hill. Each minute, with probability 1/3 he manages to roll the boulder 1 meter up, while with probability 2/3 the boulder rolls 1 meter down. If the man is currently half-way towards the ... | It would be overkill to solve this problem using Markov Chain theory: but the <em>underlying concepts</em> will help you frame it an a way that admits a simple solution.
<h3>Formulating the problem</h3>
The most fundamental concept is that of a <em>state:</em> we may model this situation in terms of 41 distinct positio... | Imagine that the hill-climbing journey consists of 41 states, one for each meter possible, so states <code>0, 1, 3, ...., 40</code>. The transition probability matrix then becomes a 41x41 matrix, representing the different probabilities of going from one state to another. It looks like the following:
<pre><code> 0 ... | https://stats.stackexchange.com |
74,597 | [
"https://dba.stackexchange.com/questions/74597",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/45132/"
] | OK, here's a challenge for you guys.
I am tasked with setting up reporting for two companies being run as a single company. For reasons I won't get into, they are implicitly split but (for our purposes) are run identically. They each have two software implementations for which I have access to the databases.
What i... | Some other ideas:
<ul>
<li>Use readily available tools to compare two databases after a change is deployed (you can automate this perhaps, depending on your existing deployment process), and synchronize them</li>
<li>Automate the deployment of changes such that changes to procedures always occur against both databases... | Assuming you can use Stored Procedures for the queries, you could create a single database for the purpose of version control of the queries in question.
Each Stored Proc could then check with the version_control database to see if the stored proc is the latest version, and refuse to run if it is not the latest versio... | https://dba.stackexchange.com |
239,905 | [
"https://electronics.stackexchange.com/questions/239905",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/107683/"
] | I have an application where the maximum DC current is 160A. However in reality the actual current flow never exceeds 40A. I want to measure the current with an ADC (like one found on the Arduino or a higher resolution ~16 bit ADC). I originally wanted to use a hall effect sensor, specifically the ACS770ECB-200U-PFF-T.
... | I'd recommend the ACS722 10AU sensor. However, you will likely not get the accuracy you want from a Hall effect device. A shunt resistor is always more accurate, but that comes at the cost of BOM lines and potentially more expensive amplifiers/current shunt's (at least at the very good sensitivities/very high currents)... | As a designer, you get to set the dynamic range. This comes at a cost of sensitivity, because the wider the range the less gain you will need. Noise and ADC resolution sets a lower limit in a system to what can be measured, so when you increase the dynamic range and lower the gain, you will get lower sensitivity per bi... | https://electronics.stackexchange.com |
72,417 | [
"https://dba.stackexchange.com/questions/72417",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11209/"
] | Is there a method to point mysql to a credentials file instead of entering account passwords directly in scripts?
Example:
<pre><code>mysqldump --opt --credfile /etc/mysql_creds mydatabase > output.sql
</code></pre>
/etc/mysql_creds
<pre><code>username=myuser
password=ToPsEcReT
</code></pre>
| It would be better to store the credentials in a config file, and load them as an extra-defaults file:
<pre><code>$ mysqldump --defaults-extra-file=mycred.cnf ...
</code></pre>
The config file is the same format as /etc/my.cnf or ~/.my.cnf
<pre><code>$ cat mycred.cnf
[mysqldump]
user = myuser
password = xyzzy
</code... | Just figured out how to do this:
<blockquote>
mysqldump --opt --user=myuser --password=`cat /etc/secure/mysqlpasswd`
mydatabase > output.sql
</blockquote>
| https://dba.stackexchange.com |
638,686 | [
"https://math.stackexchange.com/questions/638686",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/33907/"
] | Suppose we color an $n\times n$ square board using $n$ colors exactly $n$ times each. Prove that there is either a column or a row containing at least $\lceil \sqrt n \rceil$ different colors. A friend of mine gave me this problem and I managed to solve it, but I would like to know if there is a neater way.
Regards.
| Each color, since it is used $n$ times, is found in at least $2\sqrt{n}$ distinct lines (i.e., rows and columns). (If it is found in $r$ rows and $c$ columns, then $r c \ge n$; hence $r+c \ge 2\sqrt{n}$.) Adding these up, the number of distinct (color, line) pairs is at least $2n\sqrt{n}$. By the pigeonhole principl... | Here is another solution I found: Suppose each column contains less than $\lceil \sqrt n\rceil$ different colors. Then that means The number of times a color is repeated per column is at least $n-\lceil \sqrt n \rceil$ So the number of times a number is repeated columnwise through the hole board is at least $n^2-n\lcei... | https://math.stackexchange.com |
14,241 | [
"https://physics.stackexchange.com/questions/14241",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4485/"
] | If a person has a good grounding in classical mechanics, electrodynamics and special relativity, is Einstein's 1916 paper a recommended way of learning about the subject?
After looking through it briefly, I like what I see because he explains all about tensors from first principles. On the other hand, I'm not too sure... | No. It is not a good starting point. If nothing else, modern notation is very different from Einstein's original notation. Old notation left a lot to be desired about separating tensors from tensor components, if nothing else.
There has also been a lot of new insight into topology, surface charges, the action pri... | Yes.
Some of the commentary may be outdated, but you can gain a lot of perspective. What problem was he solving, where did he come from, what was the thinking at the time, what was the available data, etc. You also get a good, short, concise introduction to the subject, and older scientific papers tend to be more read... | https://physics.stackexchange.com |
11,167 | [
"https://scicomp.stackexchange.com/questions/11167",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/7753/"
] | <pre><code>double trap(double func(double), double b, double a, double N) {
double j;
double s;
double h = (b-a)/(N-1.0); //Width of trapezia
double func1 = func(a);
double func2;
for (s=0,j=a;j<b;j+=h){
func2 = func(j+h);
s = s + 0.5*(func1+func2)*h;
func1 = func2;
}
return s;
}
</cod... | Mathematically, your expression is equivalent to:
$$I = h \left(\frac{1}{2}f_1 + f_2 + f_3 +...+f_{n-1} + \frac{1}{2}f_n \right) + O\left(\frac{(b-a)^3 f''}{n^2} \right)$$
So you could implement that. As it was said, the time is probably dominated by the function evaluation, so to get the same accuracy, you can use a... | Chances are that the evaluation of the functions is the most time consuming part of this computation. If that's the case, then you should focus on improving the speed of func() rather than trying to speed up the integration routine itself.
Depending on the properties of func(), it's also likely that you could get a... | https://scicomp.stackexchange.com |
77,325 | [
"https://electronics.stackexchange.com/questions/77325",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25870/"
] | All the resistors available come with a finite amount tolerance. This is undesirable particularly in highly sensitive systems. While we can use resistors with the least tolerance available, I want to know if there are any methods (something like designing a special setup to bring down the tolerance) using which we can ... | Tolerance is a statistical abstraction which tells us how much variation to expect from a sample of resistors of a given type. A single resistor doesn't have tolerance: it has a value, which deviates to some extent from the stated value (and of course varies with temperature). We cannot change (manually or otherwise) ... | While you cannot change the tolerance of the resistors <strong>you can select</strong> a value within the tolerance.
If you were to purchase say 1000 resistors and <strong>accurately measure their resistance values</strong> you may be able to find a few resistors that are closer to the actual value required. These s... | https://electronics.stackexchange.com |
16,886 | [
"https://chemistry.stackexchange.com/questions/16886",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/3743/"
] | So I created a DC power supply of 15 V (special transformator connected to the net) and I have a graphite anode and stainless steel cathode. When I put them in a beaker next to each other in water, the electrolysis takes place as I see gas bubbles. However, when i put them in another container that consists of two beak... | Fine copper powder can be prepared using thermal decomposition of copper citrate (can be prepared by mixing dirt cheap citric acid, three equivalents of a base like potassium hydroxide and copper sulphate). I once made pyrophoric (!) copper powder using this technique. There are mentions of preparation of iron powder s... | Regarding the suggestion in the comments above: Concentrated sulfuric and nitric acids produce $\ce{SO2}$ and $\ce{NO2}$ gases, respectively, as they oxidize metals. This is a common way of dissolving many metals, but you need to do it somewhere where you won't breathe them in.
When you're actually electroplating, you... | https://chemistry.stackexchange.com |
375,512 | [
"https://physics.stackexchange.com/questions/375512",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/179232/"
] | If an object under a constant force , say gravity. Collides with another object with no external force acting on it. Will the momentum of the system right before and after the collision be the same if the collision is instantaneous?
Assume that the collision is vertical.
| The Impulse-momentum theorem is
$$\Delta \vec{p}=\int \vec{F}\cdot d\vec{t},$$
where the quantity on the right is the impulse, and $\vec{F}$ is an external force (or a sum of external forces). So if you want to know when momentum is conserved, $\Delta \vec{p}=0$, you want to know when the impulse will vanish. This can ... | Yes. If the collision is instantaneous (contacct time <span class="math-container">$t=0$</span>) then the external force <span class="math-container">$F$</span> imparts no impulse <span class="math-container">$Ft=\Delta p$</span> during the collision. So momentum <span class="math-container">$p$</span> is conserved dur... | https://physics.stackexchange.com |
133,276 | [
"https://cs.stackexchange.com/questions/133276",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/104887/"
] | <strong>Problem</strong>
Given a set of intervals with possibly non-distinct start and end points, find all maximal gaps. A gap is defined as an interval that does not overlap with any given interval. All endpoints are integers and inclusive.
For example, given the following set of intervals:
<span class="math-containe... | The key to prove your algorithm is correct is to find enough invariants of the loop, step 4 so that we apply use mathematical induction.
<hr />
Let <span class="math-container">$I_1, I_2, \cdots, I_n$</span> denote the sorted intervals. When the algorithm has just finished processing <span class="math-container">$I_i$<... | I'd like to propose a quite simple algorithm as well. The idea is this: we're going to place open and close parentheses on the number line at the boundaries of each interval. For example, for the intervals <span class="math-container">$(1,5), (2,7), (9, 10)$</span>, the number line would look like this:
<pre><code>1 2 ... | https://cs.stackexchange.com |
111,252 | [
"https://physics.stackexchange.com/questions/111252",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44837/"
] | I've heard it said many times that you're more likely to burn food on an electric stove than a gas one, but I can't tell a difference. This seems to me to be a fallacy perpetuated by the natural gas industry, and I would expect the issue to just be people are not sure how to accurately adjust the system they're not use... | In my opinion there is no physical reason. To cook food the same energy is needed, and to burn it too. It is behavioral differences because of the form of heat:
One is aware of the dangers of gas and is much more careful in turning it off on time, when food just starts to smell "singed". Electric : we may turn it off ... | It is easier to regulate a gas stove. If you turn off or turn down the flame, the heats source is immediately reduced.
Turning off an electric stove leaves the element still hot. It continues to heat the pan.
In an oven, you don't often turn the heat up or down. In an electric oven the element heats by radiation. T... | https://physics.stackexchange.com |
79,491 | [
"https://cs.stackexchange.com/questions/79491",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/75377/"
] | Let's consider the language over $\{0,1\}$ containing such words $w$ that:
$$w = m_1m_2..m_n $$ where $m_i$ has length $n$. (so $|w|=n^2$) and $$m_1 + m_2 + .. + m_n \mod 3 = 0$$
($m_i$ we interpret as binary encoded number).
Prove, that the language is $NC^1$ class.
<hr>
The first problem is: How to decide whe... | you have to use the fact that $2^n\mod 3 = n\mod 2 + 1$:
<ul>
<li>2 mod 3 = 2</li>
<li>4 mod 3 = 1</li>
<li>8 mod 3 = 2</li>
<li>16 mod 3 = 1</li>
<li>32 mod 3 = 2</li>
</ul>
and so on.
The solution then for an $n$ bit number is to use $n$ processors, the $i$th processor will calculate $f_0(i) = i\mod 2 +1 * w[i]$ ... | The most direct way to show that this is in $\mathsf{NC}^1$ is through a "divide and conquer" approach.
First, we show how to compute $m\bmod{3}$ in $\mathsf{NC}^1$. The idea is to write $m = 2^h m_h + m_\ell$, where $m_h,m_\ell$ have roughly the same number of bits, compute $m_h,m_\ell \bmod{3}$, and combine the resu... | https://cs.stackexchange.com |
407,402 | [
"https://electronics.stackexchange.com/questions/407402",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/204729/"
] | I am using LTC3624-3.3 regulator, with components as in the datasheet app notes - 12 V Vin, burst mode, 10 uF at in, 47 uF at out, 2u2 inductor rated at 2.3 A...
At no load, voltmeter says 3.34 V. Good. But with 47 ohm resistor across output (i.e. 70 mA load), Vout drops to 3.20, and at 10 ohm - 330 mA, to 3.05 V. Thi... | While moving things on the workbench with regulator loaded, I noticed that the voltage across resistor is swinging few hundred millivolts (I noticed that before, but I thought it was regulator instability). Checking the hookup wires, it turned out one had insufficiently crimped pins, which sporadically added few ohms t... | Because it's working on no (or very light) loads it can be assumed that your problem lies in one of these areas (despite what you may think you have done): -
<ul>
<li>Input supply (12 volts) is not capable of supplying the current that the load needs - measure the input voltage when adding loads.</li>
<li>Inductor cho... | https://electronics.stackexchange.com |
340,761 | [
"https://physics.stackexchange.com/questions/340761",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/159175/"
] | Can we calculate average velocity when we just know the distance covered? For example, when a car moves with a certain acceleration for a distance $u$ then it moves with a constant velocity for a distance $2u$ and at last it deaccelerates for a distance $3u$.
I tried to solve it by taking the intervals of time $T_0$ ... | The two statements are independent and not at all contradictory. Specifically:
<ul>
<li>For all subshells (but keeping the subshell fixed), as you increase the nuclear charge $Z$, the energy becomes more negative.</li>
<li>For a fixed nuclear charge $Z$, as you look at the different subshells of the same atom, the $s$... | Let me break it down for you .The statements quoted in that article talk about two types of energies:
The one which is due to the nucleus of an atom, and the other which is the energy lost by the electron when it starts coming towards a nucleus.
When an electron is away from a nucleus it has zero influence over it(by... | https://physics.stackexchange.com |
51,865 | [
"https://datascience.stackexchange.com/questions/51865",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/63219/"
] | I am using 3 features <code>(x1, x2, x3)</code> for binary classification. All my feature values are in 0 to 1 range (unit range).
I obtained how important each feature was in classification as follows (i.e. feature importance)
<pre><code>x1 --> 0.1
x2 --> 0.5
x3 --> 0.7
</code></pre>
It is clear that featu... | Generally speaking moving from a classification space to a ranking space is not straight forward. In classification problems there is no meaning to order between labels. This means that your suggested equation might not represent the order between labels at all.
This is somewhat dependent on the feature space and cl... | Why don't you try getting weights using ahp and then do ranking using topsis or vekor?
| https://datascience.stackexchange.com |
11,659 | [
"https://astronomy.stackexchange.com/questions/11659",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/8047/"
] | I'm researching high altitude photography and want to know a schedule for taking pictures of the moon.
Preferably I want a picture of the (full) moon on the horizon.
How would I go about scheduling such an event from a high altitude location?
| There was a object, apparently flying above you, that you couldn't identify. By definition this is an unidentified flying object. However this does not imply that it was an extra-terrestrial spacecraft.
UFO reports can be explained by a combination of:
<ol>
<li>Not recognising a known natural object, such as Venus, o... | Most likely a satellite. They look exactly like stars, but they glide across the sky smoothly.
Airplanes may have multiple light sources, some blinking lights, and you can definitely perceive how low it seems to be: An airplane somewhat seems to come from the horizon and disappear the same way, while a satellite "see... | https://astronomy.stackexchange.com |
373,930 | [
"https://mathoverflow.net/questions/373930",
"https://mathoverflow.net",
"https://mathoverflow.net/users/74343/"
] | A classic result in graph theory tells us that any planar graph must have at least one vertex with valence no bigger than 5. On the other hand, there exist examples of planar graphs that are 5-regular (e.g. the skeleton of the icosahedron). My question is, is there a planar graph <span class="math-container">$G$</span>... | The conjecture follows quickly from <strong>Brodkey's Theorem</strong>: Let <span class="math-container">$G$</span> be a finite group and <span class="math-container">$p$</span> a prime. Suppose that Sylow <span class="math-container">$p$</span>-subgroups of <span class="math-container">$G$</span> are abelian. If <span... | Now that I understand things better, let me also give a direct proof (using essentially the same idea as Brodkey's theorem).
Let <span class="math-container">$P,Q,R$</span> be Sylow <span class="math-container">$p$</span>-subgroups of <span class="math-container">$G$</span>, let <span class="math-container">$N=N_G(P\ca... | https://mathoverflow.net |
1,804,851 | [
"https://math.stackexchange.com/questions/1804851",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/331405/"
] | We have randomly taken $21$ integers from $1$ to $2046$.
Show that we can take $a$, $b$ and $c$ from the previous $21$ integers in a way such that the following inequality holds
\begin{equation}
bc<2a^2<4bc \end{equation}
<strong>My Attempt</strong>:
I have found $3$ triplets of such integers, but I do not... | Let the 21 numbers be $x_1<x_2<\ldots <x_{21}$.
It is not possible to have $x_{k+2}\ge 2x_k+1$ (or equivalently $x_{k+2}+1\ge 2(x_k+1)$) for all $k$ as that would lead to $2047 \ge x_{21}+1\ge 2^{10}(x_1+1)\ge 2^{11}=2048$. Thus we find $k$ such that $x_{k+2}\le 2x_k$. With $b:=x_k$, $a:=x_{k+1}$, $c:=x_{k+... | Let set $S$ be the set of integers from $1$ to $2046$, we split $S$ to $S_i$s like this:
$$S_1=\{1,2,3\}\\S_i=\{s\in\mathbb{Z}\,|\,2^{i}\le s\lt2^{i+1}\}\quad (2\le i\lt10)\\
S_{10}=\{1024,1025,\dots,2046\}$$
So we have $10$ sets in total, by Pigeonhole principle there's a set which has at least $\lceil\frac{21}{10}\r... | https://math.stackexchange.com |
160,560 | [
"https://electronics.stackexchange.com/questions/160560",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/60051/"
] | Imagine this: A rod is attached at one end to a rotating shaft. So, as the shaft rotates from 0 to 90 degrees back-and-forth (in the xy plane), so does the rod. My goal is to measure the instantaneous acceleration of the rod while its moving. I have a few 3-axis accelerometers, but I feel like I'm really confused. I gu... | Let me guess the location of the accelerometer.
<blockquote>
My goal is to measure the instantaneous acceleration of the rod while its moving.
</blockquote>
I will assume it's on the extremity of the rod. There would be 2 forces acting on your accelerometer:
<ul>
<li>gravity</li>
<li>centrifugal force</li>
</ul>
I thin... | You certainly can do this. Kionics app note AN019 `Using two tri-axis accelerometers for rotational measurements' outlines exactly what you are talking about. This method essentially exploits, from the rigid body planar kinematics of a rotating disk, that the linear acceleration
\$ a = r\dot\theta\$. (\$\dot\theta\$ be... | https://electronics.stackexchange.com |
299,924 | [
"https://softwareengineering.stackexchange.com/questions/299924",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/200330/"
] | If there is Employees repository and I have to get Employee that has a greatest salary - where to put filtering that represents business rule for that?
I can get all Employees and filter them out in Domain Model, but that does not seem as efficient as SQL Query in repository. What patterns come into play?
| The business logic is not the query that returns the Employee with the greatest salary -- databases are great at that and you should let the database do that for you via the repository. The business logic is what you do after you retrieve the most highly compensated employee.
| Since a salary, its presentation and database computation is quite natural and has no strict domain, I would not call it business logic here. It's just an <code>ORDER BY</code> query for the database.
Let me give you another example with business logic:
If you would like to have the most "profitable" employee and the... | https://softwareengineering.stackexchange.com |
168,883 | [
"https://mathoverflow.net/questions/168883",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1832/"
] | To my knowledge, usually there are two ways to construct supercuspidal representations over p-adic fields. The first is via theory of types (for GL(n) and classical groups), notably by Bushnell, Kutzko, Stevens etc. The other is the construction given by Yu,Jiu-Kang (for more general groups).
Both constructions are ve... | There are certainly links between the two; a good place to start would be looking at the theory for $GL_2$ and $SL_2$. Henniart's appendix to Breuil-Mezard's <em>Multiplicités modulaires et représentations de $GL_2(Z_p)$ et de $Gal(\bar{Q_p}/Q_p)$ en $l=p$</em> makes explicit the construction for $GL_2$ via strata, and... | In complement to the other answers I would like to add the following.
There are of course some links between both construction. For instance for ${\rm GL}(N)$ Yu's construction amounts to Howe's construction (cf. his Pacific Journal paper) based on admissible pairs. On the other hand the Bushnell and Kutzko construct... | https://mathoverflow.net |
40,513 | [
"https://mechanics.stackexchange.com/questions/40513",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7132/"
] | I assume that a timing light functions by some kind of inductive pickup and the signal is amplified by power from the battery and turned into a flash at the bulb.
But I was wondering, is it picking up the strength of the current in the wire, or the voltage, and will the strength of the flash vary according to the stre... | A timing light works like a camera flash.
Inside the timing light there is a section that steps up battery voltage. That high voltage is applied across a gas discharge tube bulb filled with xenon gas. The tube is long enough that the high voltage won't arc over.
The pickup detects when the plug fires in an inductiv... | Most timing lights have a magnetic pickup that will 'detect' current flowing through the spark plug wire. This triggers the strobe to flash. The signal is not amplified, it closes a switch. I do not think the brightness of the light is dependent upon how much current flows through as the light is powered from the ba... | https://mechanics.stackexchange.com |
259,486 | [
"https://mathoverflow.net/questions/259486",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Let $G=(V,E)$ be a simple, undirected graph. A <em>clique decomposition</em> is a set ${\cal C} \subseteq {\cal P}(V)$ such that
<ol>
<li>$\emptyset \notin {\cal C}$,</li>
<li>$C\in {\cal C}$ and $x\neq y \in C$ imply that $\{x,y\}\in E$ (that is every member of ${\cal C}$ is a clique),</li>
<li>$\bigcup {\cal C} = V$... | Easy answer to the first question: for $n \gg 0$, we have $f(n) > 1$ or $f(n) < -1$. Hence $f(n)$ is divisible by some prime number $p$, so $n$ is a root mod $p$.
| Let $d$ be the degree of $f$. There are at most $2d$ integers $m$ such that $|f(m)|=1$. Pick any other integer $n$ and then an arbitrary prime factor $p$ of $f(n)$.
| https://mathoverflow.net |
136,348 | [
"https://physics.stackexchange.com/questions/136348",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | When the water first hits your body, it feels warmer than when it streams down towards your feet. I realize that part of this is due to the water cooling down by dissipation to the surrounding as it falls. But as the water loses gravitational potential energy shouldn't it also gain kinetic energy (heat)? Is the dissipa... | Even assuming all of the energy it gains is turned into thermal energy (heat) it's just too small to worry about.
$$\Delta KE = mg \Delta h$$
Let's assume it falls $2m$.
$$\Delta KE = mg (2m)$$
Given that energy, we can compute the heating of the water.
$$ Q = m C_p \Delta T$$
$$ \Delta T = \frac{Q}{mC_p}$$
$C_p$ for... | Temperature doesn't rise as an object falls. Temperature is just the average kinetic energy of the individual particles within an object, but their individual velocities is random. A water droplet falling is an ordered falling that you can consider as a form of work, and you feel it as the splattering on your feet.
| https://physics.stackexchange.com |
370,159 | [
"https://mathoverflow.net/questions/370159",
"https://mathoverflow.net",
"https://mathoverflow.net/users/160714/"
] | Let <span class="math-container">$X=(X_t)_{t\in I}$</span> (<span class="math-container">$I\subset\mathbb{R}$</span> an interval) be a stochastic process with continuous sample paths and such that <span class="math-container">$X_t$</span> admits a continuous Lebesgue density <span class="math-container">$\chi_t\in C(\m... | No, this is false even when <span class="math-container">$G$</span> is abelian and finite. For instance take
<span class="math-container">$$G = \langle (1,2), (3,4), (5,6), (7,8) \rangle \le \mathrm{Sym}_8.$$</span>
Define <span class="math-container">$x_1,x_2,x_3,x_4,y_1,y_2,y_3,y_4$</span> as indicated by
<span class... | No, <span class="math-container">$G$</span> need not equal <span class="math-container">$\langle x_1, \dotsc, x_k, y_{k + 1}, \dotsc, y_n\rangle$</span>.
Let <span class="math-container">$G$</span> be any group generated by two involutions <span class="math-container">$a, b$</span>. Let <span class="math-container">$k ... | https://mathoverflow.net |
7,726 | [
"https://mechanics.stackexchange.com/questions/7726",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3766/"
] | My 2007 Daihatsu has failed the national car test on emissions. The readings at 3500rpm are:
<pre><code>Lambda: 1.10 (normal range 0.97 - 1.03)
CO: 0.02% volume (normal range below 0.20%)
HC: 11ppm (normal range below 200ppm)
</code></pre>
To me, this sounds like the exhaust has a hole - which seems likely as it's ra... | Thanks for your advise, Allan. Got the car up on the lift, and was greeted with a nice large hole in the exhaust - large enough to fit two fingers into, and one of many. The botched weld job didn't help, either.
<img src="https://i.stack.imgur.com/hUCZf.jpg" alt="Hole in the exhaust">
<img src="https://i.stack.imgur.... | Do not put your bare hand over the tailpipe, it will get burnt. If you cannot hear an exhaust leak, puff puffing, you can pressurise the exhaust system with a rag over the tailpipe to make an exhaust leak more pronounced and tracible. The downside to this is that you can destroy the catalytic converter, so it is really... | https://mechanics.stackexchange.com |
323,569 | [
"https://electronics.stackexchange.com/questions/323569",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/159736/"
] | I am using Eagle 7.6 to route a four layer board. While routing a trace, I would like to either add a via at the end of a trace or place a via mid-trace without changing the the current layer. I believe this is done with the spacebar in V8 but I don't have that.
The application is to 'pin' ground and power traces to t... | All you have to do is hold down SHIFT while clicking the left mouse button with the ROUTE command active. That specifically places a via, not just end the current route segment as it would without SHIFT.
Do HELP ROUTE and read the whole page carefully.
| Assuming Eagle 7.6 and 7.3 are similar.
What I usually do is use the Via GUI button to place a via(Looks like 3 stacked discs with the top and bottom discs green). I then right click on the via I just placed and rename the via to the same name as the trace I want it to connect to(So rename the via to the same name as... | https://electronics.stackexchange.com |
222,528 | [
"https://softwareengineering.stackexchange.com/questions/222528",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/112969/"
] | Which one is considered better:
<ul>
<li>having a directive that interacts with services directly</li>
</ul>
or
<ul>
<li>having a directive that exposes certain hooks to which controller may bind behaviour (involving services)? </li>
</ul>
| A directive is best (as a rule-of-thumb) when it's short (code-wise), (potentially) re-usable, and has a limited a scope in terms of functionality. Making a directive that includes UI and depends on a service (that I assume handles connection to the backend), not only gives it 2 functional roles, namely:
<ul>
<li>Cont... | Allow me to disagree with Michal Charemza answer.
Although his answer is theoretically correct, it is not very practical for the real world.
I am saying that because I used to think like that and tried to enforce it on a large real world app that myself and my team are building and it just became too troublesome.
Th... | https://softwareengineering.stackexchange.com |
62,043 | [
"https://mathoverflow.net/questions/62043",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5031/"
] | This is a re-post on a previous question I asked. My first question was too vague to warrant detailed responses. Really, I have two specific questions to ask.
1) Let $\sigma = (A; \{0,1\}; +, \times)$ be a signature. Form the language $L(\sigma)$ over $\sigma$. Let $T$ be the theory of commutative rings and let $M$ b... | EDIT: At the bottom, I'll explain how, if you have a ring $R$ and a subset $A$ of $R$, how you can construct a theory such that any model of that theory contains a copy of $R$ such that the copies of elements of $A$ are units.
First, let me comment on a couple issues with the approach you're taking. Then I'll try to ... | General first-order model theory may be too general for treating localizations and analogous concepts. As Amit explained, one can express the notion of "a ring that contains a copy of $R$ and inverses for all members of $A$", but the universal property of localizations is not expressible in first-order logic. Neverth... | https://mathoverflow.net |
52,405 | [
"https://mechanics.stackexchange.com/questions/52405",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/36060/"
] | I replaced the radiator and thermostat on my 98 Subaru Forester but still when I drive it the temperature gauge reads over the hot line the heater doesn't work but the coolant doesn't seem to be circulating to where its supposed to be. It spills back into the reservoir tank (plastic tank attached to the radiator) then ... | I would start by verifying your water pump is operating. You could clamp a piece of clear hose in-line on one of the pipes and most likely verify this.
Attempt Grounding out your temperature sensor and verify if your gauge is working correctly, after doing this use an ohm-meter / Digital Multimeter and check the resis... | The first thing that comes to my mind, is that the water pump is not working. If the water isn’t circulating, the water in the engine will boil and cause the loss of water that you are experiencing.
Because the water isn’t circulating, the heater will also not receive hot water, so it will blow cold.
| https://mechanics.stackexchange.com |
86,104 | [
"https://datascience.stackexchange.com/questions/86104",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/106565/"
] | I'm doing some research for the summarization task and found out BERT is derived from the Transformer model. In every blog about BERT that I have read, they focus on explaining what is a bidirectional encoder, So, I think this is what made BERT different from the vanilla Transformer model. But as far as I know, the Tra... | The name provides a clue. BERT (Bidirectional Encoder Representations from Transformers): So basically BERT = Transformer Minus the Decoder
BERT ends with the final representation of the words after the encoder is done processing it.
In Transformer, the above is used in the decoder. That piece of architecture is not th... | BERT (Bidirectional Encoder Representations from Transformers) is a deep learning model that was developed by Google in 2018. It is based on the Transformer architecture, which was introduced in the same year in the paper "Attention Is All You Need".
The main difference between BERT and the vanilla Transforme... | https://datascience.stackexchange.com |
743,346 | [
"https://math.stackexchange.com/questions/743346",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/141166/"
] | I would like to write two expressions.
<ul>
<li>For each $t$ outputs <code>1,2,3,4,5,6,7,8</code> for $t=0,1, \ldots, \infty$.</li>
<li>For each $t$ outputs <code>1+2+3+4+5+6+7+8</code> for $t=0,1, \ldots, \infty$.</li>
</ul>
I have thought about
$$\sum_{t=0}^{\infty} n \qquad 1 \leq n \leq 8$$
but how do I get $n$ t... | For the first expression try,
$$t\mod8 + 1$$
(In a programming language that would be $(t\%8)+1$)
For the second, try
<pre><code>c=t%8 + 1
n = c*(c+1)/2
</code></pre>
$$c(c+1)/2$$ is a well known formula for the sum of the first c natural numbers.
| <strong>For the series:</strong>
I am uncertain about what you mean, but...
$$\sum_{n=1}^{8} n = 1 + 2 +3 +4 + 5+ 6+ 7 + 8$$
In a summation, the variable and its starting value goes on the bottom of the sigma, and the ending value goes on top (so here we let <em>n</em> go from 1 to 8). What then happens is that we e... | https://math.stackexchange.com |
618,365 | [
"https://physics.stackexchange.com/questions/618365",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/290865/"
] | Suppose an object (aeroplane be better) having 1m/s² acceleration, started its journey from north pole towards south pole. Crossing south pole it reached north pole again.
So, here displacement is 0 meter (as the initial point and the final point are the same). If we neglect the frictional force of air... can we say <s... | It is not zero, because the work done by a force is defined by a line integral. The work done by the force that accelerated the object is
<span class="math-container">$$W=\int_{\vec{r}_0}^{\vec{r}_f}\vec{F}\cdot d\vec{r},$$</span>
being <span class="math-container">$\vec{r}_0$</span> the point where the force began to ... | There are two types of work.<span class="math-container">`</span>the work done by a conservative force is path independent ,and work by nonconservative is path dependent.so the work done need not be always zero.
| https://physics.stackexchange.com |
47,723 | [
"https://softwareengineering.stackexchange.com/questions/47723",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/14951/"
] | I have developed a unique website but do not have a lot of fund to protect it with trademark or patents. I'm looking for suggestions so that when my supervisor gets my codes, some laws restrict anyone from copying it and claim their work. I'm in the middle of thinking, making the application a commercial one or never a... | Check with a lawyer. Odds are surprisingly high that the university <b>already</b> legally owns the source code. However in the USA universities are generally fairly willing to license your code back to you. So if you want to, say, build a startup using the website you have built, you probably will be able to. But ... | Be aware that no license can <em>physically prevent</em> someone from taking your code, copying and reselling it. The only thing a license does is announce your intention to sue anybody who tries to violate it.
That means if you cannot afford a lawyer to write a good license for your agreement, then you likely cannot ... | https://softwareengineering.stackexchange.com |
210,248 | [
"https://softwareengineering.stackexchange.com/questions/210248",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/86698/"
] | I have just landed a role as a C#/Asp.Net developer at a large software house. I have previously worked at a much smaller software house for about two years but it was a varied/mixed role there, and here the asp.net applications we have are a factor of 10 or so larger.
As seems to be the norm, I have been given the ta... | It depends. But IMHO, it should take about a month to know your way around, and up to six months to be normally productive.
An interesting exercise, if you have time, etc: Take a part of the application, and reprogram it in another language, if you know any. Or, try reading all of the source code that you can, and wr... | The answer to this question is completely subjective. The length of time it takes a developer to come up to speed can depend on:
<ol>
<li>the developer's level of knowledge and professional experience</li>
<li>the level of complexity of the application(s) or the level of documentation for the same</li>
<li>the abilit... | https://softwareengineering.stackexchange.com |
93,727 | [
"https://softwareengineering.stackexchange.com/questions/93727",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29032/"
] | Many of my Java books are 5 - 10 years old. Does it still help to read them, or should I use something within 2 years.
| If the books is about <em>the language itself</em>, lose it and get a new one.
If the book is about <em>programming as a subject</em> (art, subject, discipline, techniques, whatever), then it definitely is worth reading. The best programming books I have were written over 10 years ago.
| It depends on the book and on what you want to learn from them and on you.
There are goods reasons to read old books:
<ul>
<li>If they teach concepts better than their new equivalents.</li>
<li>If they teach general principles rather than specific technologies.</li>
<li>If the technology they teach hasn't changed ver... | https://softwareengineering.stackexchange.com |
132,740 | [
"https://physics.stackexchange.com/questions/132740",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57632/"
] | The stature and design of the human body. Is it possible that the best physical structure belongs to a human being? If not. What are the flaws in it and what improvements could be done?
Is there actually a perfect physical design in terms of strength and agility?
| As was stated in the comments, your question can't be answered precisely. Here's my reactions, I hope it could help you :
From a biological (evolution) point of view, a creature can be considered as "good" or "bad" only <strong>in a given environment</strong>. It means that there can't be a "best creature", because yo... | Humans weren't designed, they evolved in a series of small incremental modifications that each at the time imparted a little overall survival advantage. Such a method results in a effective design, but not necessarily a optimal one.
This process is ongoing, and there are still modifications that could be made that wo... | https://physics.stackexchange.com |
6,723 | [
"https://mechanics.stackexchange.com/questions/6723",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3472/"
] | This is my first question in mechanics.stackexchange.com. I am a computer programmer and work in Location based services. Along with GPS monitoring, I want to give the clients , a proper manipulation of the fuel level in their vehicles.
<h3>Current method that we implement</h3>
We take the fuel wire (from the fuel gaug... | I'd also go with calibrating the existing sensor, but I'd do it the other way around to mac.
Start with an empty tank and measure the voltage. add a known volume of fuel, measureagain. repeat until the tank is full. This will give you a series of reference points, and obviously the smaller the volume you add each time... | It sounds like you just don't know the characteristics of the output of the fuel level sender in the vehicle--perhaps learning more about that sensor would solve your problem.
In terms of an alternate solution that does not use the fuel level sender, if the vehicle is a modern one with electronic fuel injection, then ... | https://mechanics.stackexchange.com |
157,242 | [
"https://math.stackexchange.com/questions/157242",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/18240/"
] | Here's a nice question I heard on IRC, courtesy of "tmyklebu."
Let $A$, $B$, and $C$ be $2\times 2$ complex matrices. Define the commutator $[X,Y]=XY-YX$ for any matrices $X$ and $Y$. Prove
$$[[A,B]^2,C]=0.$$
| Assuming that the density of the region is uniform, the $y$ coordinate of the center of mass is given as $$y_c = \dfrac{\int_R y dx dy}{\int_R dx dy}$$
The region, $R$, you are interested in i.e. the semi-annular plane as shown below.
<img src="https://i.stack.imgur.com/tnSIh.png" alt="enter image description here">
C... | We want to find the moment of the region about the $x$-axis, and divide by the area of the region. The area is no problem, it is basic geometry, so we deal with the moment. (But we must not forget to divide at the end!)
The easiest way is to note that the moment is the moment of the upper half of the circle $x^2+y^2=4... | https://math.stackexchange.com |
366 | [
"https://cs.stackexchange.com/questions/366",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/98/"
] | I wrote
$\qquad \displaystyle \sum\limits_{i=1}^n \frac{1}{i} = \sum\limits_{i=1}^n \cal{O}(1) = \cal{O}(n)$
but my friend says this is wrong. From the TCS cheat sheet I know that the sum is also called $H_n$ which has logarithmic growth in $n$. So my bound is not very sharp, but is sufficient for the analysis I need... | What you are doing is a very convenient abuse of notation.
Some pedants will say that what you write is nonsense, as $\mathcal{O}(f)$ denotes a <em>set</em> and you cannot do arithmetic operations on them the way you are doing.
But it is a good idea to ignore those pedants and assume that $\mathcal{O}(f)$ stands for ... | What you wrote is perfectly correct. The $n$th harmonic number is indeed in the set $O(n)$.
<em>Proof:</em> $\sum_{i=1}^n \frac{1}{i} \le \ln n + 1 \le 2n = O(n)$. $\square$
The upper bound $O(n)$ isn't <em>tight</em>, but it's correct.
| https://cs.stackexchange.com |
51,670 | [
"https://electronics.stackexchange.com/questions/51670",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3353/"
] | I've been able to hook up a Futaba S3003 servo directly to my Arduino and it works perfectly. However, when I power it with an external 6 volt DC power supply (instead of the Arduino's onboard 5V) it fails to work.
I'm assuming I need to translate the 5v "language" of the Arduino to the 6v "language" that the servo no... | The servo on the external 6V source may be failing to work becasue you failed to interconnect the GND of the MCU board to the GND of the external supply.
| Here's how I have mine wired, same scenario:
<img src="https://i.stack.imgur.com/sdxqV.png" alt="enter image description here">
You won't need the mosfet / diode deal if you don't need to power it off completely.
| https://electronics.stackexchange.com |
3,390,645 | [
"https://math.stackexchange.com/questions/3390645",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/713865/"
] | Mainly I need to get the real fundamental system of solutions of <span class="math-container">$y^{vi}+729y=0$</span>.
As well, I'm stuck in getting the solution for <span class="math-container">$4y''+36y=\operatorname{cosc}(3x)$</span>. Basically because I don't know how to operate it with the <span class="math-contai... | The reason for your fallacy is that you assumed that <span class="math-container">$x*S +x =S$</span>.
The reason you cannot argue that they are equal is because for <span class="math-container">$x \gt1$</span> , the series is diverging and each term is bigger than the previous. Hence the sum of these two series will n... | Yes, because you need to have <span class="math-container">$S$</span> finite to write that equality. If <span class="math-container">$S=\pm\infty$</span> (which holds for <span class="math-container">$|x| \geq 1$</span>), then that equation does not make sense.
| https://math.stackexchange.com |
528,858 | [
"https://electronics.stackexchange.com/questions/528858",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/262795/"
] | I'm just wondering what logic gate has two inputs and only outputs <code>HIGH</code> if one of the inputs is <code>HIGH</code>. Here's a truth table:<br>
<pre><code>|-----------|-----------|-----------|
| A | B | OUT |
|-----------|-----------|-----------|
| 0 | 0 | 0 | ... | This is an <strong>XOR</strong> gate. It outputs HIGH when an odd number of inputs are HIGH.
| It's an 'Exclusive OR Gate' (XOR Gate). It outputs a 'high' only when an odd number of its inputs is 'high'.
It's unlike an 'OR' gate which outputs a 'high' with one or more of it's inputs being 'high'.
| https://electronics.stackexchange.com |
32,421 | [
"https://cs.stackexchange.com/questions/32421",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/12532/"
] | This statement is Theorem 1.1 (page 39) of <em>Computability, Complexity and languages</em> by Martin Davis:
<blockquote>
If function $h$ is obtained from the (partially) computable functions $f$, $g_1$, $g_2$, ..., $g_k$ by composition then $h$ is (partially) computable.
</blockquote>
What I understand from this t... | The theorem should be read as "If you compose computable functions, you get a computable function; if you compose partial computable functions, you get a partial computable function."
Note that, perhaps confusingly, partial computable is a larger class of functions: every computable function is partial computable. On... | This is a confusion about terminology:
<ul>
<li>A function $f : A \to B$ is <strong>total</strong> if it is defined everywhere on $A$.</li>
<li>A function $g : A \to B$ is <strong>partial</strong> if it is defined on a subset $A' \subseteq A$, called the <strong>domain</strong> of $g$.</li>
</ul>
Cruicially, there is... | https://cs.stackexchange.com |
75,226 | [
"https://electronics.stackexchange.com/questions/75226",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25259/"
] | I'm using Atmega328 as a master in SPI communication with a single slave. Is there a way to avoid using the SS (slave select) pin for SPI? That pin can also be used for PWM output, which I would like to use.
| Whether or not you can tie a SPI slave's "select" input permanently active depends on both the specific slave and the overall system design. Some slaves rely on edges on their select inputs for things like flow control and/or byte alignment.
In some systems, in which the master and slave are always reset together (e.g... | ATmega is a master here, as you yourself said.
Let's take a look at what the datasheet says about slave select pin:
<code>SS: Slave Select input. When the SPI is enabled as a Slave, this pin is configured as an input regardless of the set-
ting of DDB2. As a Slave, the SPI is activated when this pin is driven low. Wh... | https://electronics.stackexchange.com |
2,194,177 | [
"https://math.stackexchange.com/questions/2194177",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/365976/"
] | This question is from a book provided by my basic math class.
For $f$: $\mathbb Z^+ \rightarrow \mathbb Z^+$, where $f(x) = \sqrt n$
Is it a function?
My first thought was that as $x\in \mathbb Z^+$, for all positive integers, there will be exactly one assignment of $x$ to an image $y \in \mathbb Z^+$.
However, th... | The expression
$$
f : \mathbb{Z}^+ \rightarrow \mathbb{Z}^+, \quad f(n) = \sqrt n,
$$
does not describe a function.
This is because the expression is erronerous: first it is stating that $f$ is a function from $\mathbb{Z}^+$ to $\mathbb{Z}^+$, but $f(2) = \sqrt 2$ is not an element of $\mathbb{Z}^+$.
<hr>
<strong>Y... | I think we have to make the distinction between the domain of definition of $f$ and the fact that $f$ is a function because it assigns at most $1$ image element for any input.
For instance $f_1 : \mathbb R\to\mathbb R,\quad f(x)=\sqrt x$.
Is $f_1$ a function ? You could say yes but domain is not $\mathbb R$ but $\ma... | https://math.stackexchange.com |
355,700 | [
"https://physics.stackexchange.com/questions/355700",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56477/"
] | Suppose that the shape of a fish pond is irregular, so we can't use any simple math formula, e.g. width $\times$ length $\times$ depth, to find its volume.
I'm wondering if, there's a good way of estimating its volume? For example, one can estimate the size of a molecule using an oil film. Reversely, one can also esti... | Probably the most accurate way is to use a radioactive tracer as is used to measure blood volume but . . . . . . .
Or you use some inert chemical compound.
Look up effect on pond life, both plant and animal) of a low concentration of common salt in pond water.<br>
A concentration of less than 5 parts per thousand... | For a fairly exact measurement, I would take some harmless chemical that's easy to detect, and pour a certain volume in and let it dissolve/diffuse completely. Then, measure it in ppm, do the necessary calculations, and get your volume.
| https://physics.stackexchange.com |
284,544 | [
"https://mathoverflow.net/questions/284544",
"https://mathoverflow.net",
"https://mathoverflow.net/users/116515/"
] | Let $X$ be a compact metric space. Say that two compact subsets $E,F\subset X$ are <em>parallel</em> if
$$ dist(x,F) = dist(y,E)$$
for all $x\in E$ and $y\in F$. Here $ dist(y,E) = \inf\{d(y,z):z\in E\}.$
The overall question I would like to understand is the following:
<blockquote>
Let $X$ be a compact (Hausdorff,... | The answer to this problem is affirmative (at least for covers).
<strong>Definition.</strong> A family $\mathcal C$ of subsets of a topological space $X$ is called
$\bullet$ <em>lower semicontinuous</em> if for any open set $U\subset X$ its $\mathcal C$-star $St(U;\mathcal C):=\bigcup\{C\in\mathcal C:C\cap U\ne\empty... | If $(E_t)_{t\in T}$ is a partition of a metric space $(X,d)$ into parallel compact subsets, then the metric $d$ induces a quotient metric $\hat d$ on the index set $T$. This metric is defined by $\hat d(t,s)=\inf\{d(x,y):x\in E_t,\;y\in E_s\}$ for $t,s\in T$.
It is easy to show that the quotient map $q:X\to T$ (defin... | https://mathoverflow.net |
2,545,459 | [
"https://math.stackexchange.com/questions/2545459",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/492423/"
] | <strong>Question:</strong> If $n \in \mathbb{Z}$ and $n^5 − n$ is even, then $n$ is even.
<strong>My solution:</strong> By counter example, let $n = 3$, then $3^5 - 3 = 240 =$ even, but $3 =$ odd.
However, if I use direct proof on this, it will be:
Suppose $n \in \mathbb{Z}$ and $n^5− n$ is even, then $n^5 − n = 2a$... | The prime factorization of $8!$ is
$$
8!=2^7\cdot3^2\cdot5\cdot7.
$$
We want the three factors $a,b,c$ to be roughly the same, so both should be approximately $(8!)^{1/3}\approx 34$. This suggests one factor could be $2^5$, another factor could be $5\cdot 7$, and then the remaining factor of $2^2\cdot 9$. This gives $... | Note that $8! = 40320$. Note that if $a < b < c$, then $a,b,c$ must be very close to the cube root of $40320$, which you can easily estimate to be between $30$ and $40$, since $3^3 = 27 < 40 < 4^3 = 64$, so we can predict the first digit easily.
Therefore, the desired numbers have to be somewhere around t... | https://math.stackexchange.com |
714,580 | [
"https://physics.stackexchange.com/questions/714580",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/291933/"
] | I'm trying to calculate the derivative of the Lagrangian <span class="math-container">$$\mathcal{L}=\frac{1}{2}\partial_\mu\phi\,\partial^\mu\phi-\frac{1}{2}m^2\phi^2$$</span> with respect to the metric tensor <span class="math-container">$g_{\mu\nu}$</span>, with the convention <span class="math-container">$(+, -, -, ... | This is just elaborating a little more on the 'behind the scenes', since OP's confusions seem to be resolved in the comments already.
<hr />
Consider the following simplified situation. Let <span class="math-container">$f_1,f_2:\Bbb{R}^2\to\Bbb{R}$</span> be two functions defined as <span class="math-container">$f_1(x,... | I want to summarize the answer given by @peek-a-boo in a physicists friendly way:
The identity <span class="math-container">$g_{\alpha\beta}g^{\beta\delta}=\delta_{\alpha}^{\delta}$</span> is actually a relation between the metric tensor <span class="math-container">$\mathbf{g}$</span> and its inverse <span class="math... | https://physics.stackexchange.com |
658,894 | [
"https://physics.stackexchange.com/questions/658894",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300178/"
] | I was reading about the angular momentum of rigid bodies, and I cam across the following problem.
Imagine a solid sphere is rolling down over an inclined plane without slipping, and I was trying to find the angular momentum of this body.
I found the following formula : <span class="math-container">$L = I\omega + mvr = ... | The formula you mention is for general motion of an object that is both rotating and translating. Let <span class="math-container">$\mathbf{r}$</span> be the position of a point in the object and <span class="math-container">$\mathbf{r}_{\text{CM}}$</span> be the position of the center of mass of the object. We define ... | The confusion arises because the <span class="math-container">$r$</span> in <span class="math-container">$I\omega=\frac{2}{5}mvr$</span> is the distance to the center of the rolling sphere. The <span class="math-container">$r$</span> in the second term <span class="math-container">$mvr$</span> is the distance to some f... | https://physics.stackexchange.com |
708,601 | [
"https://physics.stackexchange.com/questions/708601",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/333588/"
] | If the angular momentum of a particle is conserved and it is also 0, then is it true that the particle moves along a line? If so, how can we derive the equation for the trajectory from both the above fact and knowledge of initial position?
(This question was inspired by the fact that if angular momentum is conserved an... | Yes, if the angular momentum of a particle is conserved and it is zero, the particle must move along a straight line.
Indeed, by using the triple product identity, we have
<span class="math-container">$$
{\bf r} \times ( {\bf r} \times {\bf v} ) = ( {\bf r} \cdot {\bf v} ) {\bf r} - r^2 {\bf v}.
$$</span>
Therefore, if... | The angular momentum is defined relative to a chosen point. For it to be zero, the velocity vector of the center of mass of a non-rotating rigid object must be directed toward that point.
| https://physics.stackexchange.com |
316,565 | [
"https://dba.stackexchange.com/questions/316565",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/260282/"
] | I have the following request, using pg_trm and gin index:
<pre><code>SELECT
email,
first_name,
last_name
FROM external_patient
WHERE PGP_SYM_DECRYPT(cat_name::bytea, 'SUPER_AES_KEY') ILIKE $2
OR PGP_SYM_DECRYPT(cat_name::bytea, 'SUPER_AES_KEY') % $1
ORDER BY... | You can add your decrypted column to the SELECT and wrap that into a derived table:
<pre><code>select email, first_name, last_name
from (
SELECT email,
first_name,
last_name,
PGP_SYM_DECRYPT(cat_name::bytea, 'SUPER_AES_KEY') as cat_name_decrypted
FROM external_patient
) t
WHERE cat_name... | I would add a new column (or 3) with a hash of the search. It take up some space but you only decrypt once.
<pre><code>ALTER TABLE external_patient
ADD COLUMN cat_name_hash TEXT;
UPDATE external_patient
SET cat_name_hash = SHA256(LOWER(email || first_name || last_name));
SELECT
email,
first_name,
last_name, ... | https://dba.stackexchange.com |
4,557 | [
"https://dba.stackexchange.com/questions/4557",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1910/"
] | I've heard all kinds of horror stories around gremlins living in database triggers, and--worse--systems being brought down by the addition of a trigger that caused a chain of cascading ones.
I'm considering implementing a strict policy about the use of database triggers. For separation of concerns, the initial thought... | Sounds like we hold similar views on trigger usage but I'm very interested to hear the opposite opinions from other DBAs. Personally, I view them as a last resort and have only implemented triggers where there is no other option. The exception being INSTEAD OF triggers against views.
Triggers are often the only option... | Overall, triggers have a silent and hidden impact on your data modification performance.
I have seen environments where cascading errors were caused by updating other tables from within a trigger and the updated tables had triggers.
As far as auditting is concerned, a trigger may be used, but if you have the Enterp... | https://dba.stackexchange.com |
306,910 | [
"https://dba.stackexchange.com/questions/306910",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/245910/"
] | We have a DB view that has many tables having "location" field common in most tables, requirement is we need to provide restricted access to users based on location field, e.g. a US user can see/query only data that has location as US.
how we can create such user in DB with this restricted access?
Thanks..
| Your use case is of the simplest kind, so you'd likely see very similar performance regardless if you used a RDBMS or NoSQL system.
But here are the things you should actually consider when deciding on a database system:
<ol>
<li>Do you have a well structured schema?
Answer: Yes, it appears you do when you're able to d... | Your example give is non relational data, which often leads to nosql been a good fit. Each row would be a document within a nosql dB, having all 'rows' in a document would mean bringing a huge document each time. This would make adding new data very quick too. Also you'll probably break size limits of the document. Thi... | https://dba.stackexchange.com |
115,891 | [
"https://mathoverflow.net/questions/115891",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25947/"
] | Let $f$ be an entire function of order $ρ<\infty$. Assume that $f$ does not vanish identically on $\mathbb{C}$. Then, we know that $f$ has a Hadamard's product formula
$$ f(s) =e^{g(s)}s^{r}\prod _ {k=1}^{\infty}\frac{s _ {k}-s}{s _ {k}} e^{s/s _ k} $$
the integer $r$ is the order of vanishing of $f$ at $s=0$, the... | (1) It seems your formula for the Hadamard product is only correct for $\rho<2$; more generally the exponent of $e^{s/s_k}$ contains a power series in $s$ of order $q={\rm Int}\;\rho$; see for example Eq. 1 in these <A HREF="http://www.math.harvard.edu/~elkies/M259.06/prod.pdf" rel="nofollow">lecture notes</A>.
(2)... | The statement of the question must be corrected.
First, as Carlo pointed out, the Hadamard representation as in the question
is not valid for all functions of finite order.
The correct Hadamard representation is
$$f(z)=z^me^{P(z)}\prod_{n=1}^\infty \left( 1-\frac{z}{z_n}\right)
\exp\left(\frac{z}{z_n}+\ldots+\frac{1}{q... | https://mathoverflow.net |
210,373 | [
"https://math.stackexchange.com/questions/210373",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/40094/"
] | How do I show the following?
$$\frac{n!}{(k+1)!(n-(k+1))!}=\frac{n-k}{k+1}\frac{n!}{k!(n-k)!} \text{ for } k=0,1,\ldots,n-1$$
| It’s just algebra:
$$\begin{align*}
\frac{n-k}{k+1}\cdot\frac{n!}{k!(n-k)!}&=\frac{(n-k)n!}{(k+1)k!(n-k)!}\\
&=\frac{(n-k)n!}{(k+1)!(n-k)!}\quad\text{since}(k+1)!=(k+1)k!\\
&=\frac{\color{red}{(n-k)}n!}{(k+1)!\color{red}{(n-k)}(n-k-1)!}\quad\text{since}(n-k)!=(n-k)(n-k-1)!\\
&=\frac{n!}{(k+1)!(n-k-1)!}... | $$\frac{n!}{(k+1)!(n-(k+1))!}=\frac{n!}{(k+1)k!(n-k-1)!}=\frac{n!}{(k+1)k!\frac{(n-k)!}{n-k}}=\frac{n-k}{k+1}\frac{n!}{k!(n-k)!}$$
| https://math.stackexchange.com |
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