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 |
|---|---|---|---|---|---|
476,406 | [
"https://stats.stackexchange.com/questions/476406",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/267453/"
] | The ARCH model is:
<span class="math-container">$$\left\{ \begin{align*}& X_t=\sigma_t Z_t, \ \{Z_t\} \sim IIDN(0,1) \\ & \sigma_t ^2 =\alpha _0 +\alpha _1X_{t-1}^2+\ldots+\alpha _p X_{t-p}^2 \end{align*} \right. $$</span>
After fitting such a model we can forecast <span class="math-container">$\sigma_t^2$</s... | The purpose of GARCH models is not typically to make point forecasts. When it is, even if the point forecast doesn't change over time, the width of the prediction interval will, which is generally of value for decision making.
The variance process can be of direct, independent interest, or even of more interest than <s... | Another very important application of (G)ARCH models is conditional Value-at-Risk (CVaR) estimation. At some level <span class="math-container">$\alpha$</span>, it is implicitly defined, at time <span class="math-container">$T$</span>, via
<span class="math-container">$$
P(Y_{T+1}\leq\text{CVaR}_{\alpha, T+1}\mid Y_T... | https://stats.stackexchange.com |
2,838,794 | [
"https://math.stackexchange.com/questions/2838794",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/448983/"
] | I met an interesting matrix question in a paper. My answer is ${(2S)}^{-1} - {(2S)}^{-1}({I + 4S})^{-1}$, but the answer in the paper is $ 2\times({I + 4S})^{-1}$. When I plugged in some value in $S$, I found they are equal, so why
$${(2S)}^{-1} - {(2S)}^{-1}({I + 4S})^{-1} =2\times({I + 4S})^{-1}$$
where $I$ is the ... | We can multiply on the right side by $(I+4S)$ and $2S$ on the left to get
$$I+4S-I=2S*2$$
$$4S=4S$$
This last equation is definitely true, and the steps of multiplication and simplifying are reversible as $S$ and $I+4S$ are invertible.
| We can find strong hints as to why the equation
$(2S)^{-1} - (2S)^{-1}(I + 4S)^{-1} = 2(I + 4S)^{-1} \tag 1$
holds by "unravelling" it; that is, we multiply through by $(2S)(I + 4S)$:
$(2S)(I + 4S)((2S)^{-1} - (2S)^{-1}(I + 4S)^{-1})$
$= (2S)(I + 4S)(2S)^{-1} - (2S)(I + 4S)(2S)^{-1}(I + 4S)^{-1}$
$= (I + 4S) - I = 4... | https://math.stackexchange.com |
26,083 | [
"https://mathoverflow.net/questions/26083",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4692/"
] | For example, Wikipedia states that etale cohomology was "introduced by Grothendieck in order to prove the Weil conjectures". Why are cohomologies and other topological ideas so helpful in understanding arithmetic questions?
| Why are topological ideas so important in arithmetic? In some sense KConrad is of course spot on, but let me offer a completely different kind of answer.
Why are complex functions of one variable so important in arithmetic? (Zeta function, L-functions, Riemann hypothesis, Birch--Swinnerton-Dyer, modular forms, theta s... | May I suggest that we don't have to consider cohomology to see the influence
of topology on arithmetic? Looking for rational points on curves leads to the
question of which curves have rational parameterization, and Riemann found
that the answer is topological -- the curves of genus zero. One also observes
special beha... | https://mathoverflow.net |
119,989 | [
"https://mathoverflow.net/questions/119989",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5072/"
] | For two pmf $p=\lbrace p_i\rbrace$ and $q=\lbrace q_i\rbrace$ on the same finite alphabet, we know that relateive entropy
$D(p\|q)=\sum p_i\log\frac{p_i}{q_i}$
and 1-norm
$\|p-q\|_1=\sum |p_i-q_i|$
are both measures of their distance. But it is unfortunate that relative entropy is not a norm. My question is: even so, d... | No, that is not true. Let $p^{(n)}\to q$ in $L^1$ such that $p^{(n)}$ lies in the (relative) interior of the probability simplex whereas $q$ is on the boundary (of the simplex), i.e., $q_i=0$ for some $i$. Then $D(P^{(n)}\|q)=\infty$ for every $n$.
But the other direction is true because of the Pinsker's inequality $\... | I have found a solution, but it seems not complete (will explain at the end)
$D(p\|q)=|D(p\|q)|=|\sum p_i\log p_i-\sum p_i\log q_i|=|\sum p_i\log p_i-\sum p_i\log q_i+\sum q_i\log q_i-\sum q_i\log q_i|$
$=|H(q)-H(p)+\sum(q_i-p_i)\log q_i|\le|H(q)-H(p)|+\sum|q_i-p_i||\log q_i|$.
If we denote $M_1=\max\lbrace|\log q_i|=... | https://mathoverflow.net |
105,323 | [
"https://dba.stackexchange.com/questions/105323",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/27048/"
] | I am developing a Stocks management application, the Portfolio register table has 4 columns, other than date and registry_key, and it looks like this:
<pre><code>----------------------------------------
| stock_key | user_key | units | price |
----------------------------------------
| fund_a | user_1 | 1000 | 1... | A DECIMAL(25,6) stores 25 digits, 6 of them fractional, i.e. a value up to <code>9,999,999,999,999,999,999.999999</code>
<code>10e18</code> is <code>10,000,000,000,000,000,000.000000</code>
| What is <code>DECIMAL(25,6)</code> ?
<ul>
<li>19 digits to the left of the decimal</li>
<li>06 digits to the right of the decimal</li>
</ul>
<strong><code>10e18</code> is not a 19-digit number. It's a 20-digit number</strong>
<pre><code>mysql> select 10e18 ActualValue;
+-------------+
| ActualValue |
+-----------... | https://dba.stackexchange.com |
1,560 | [
"https://quantumcomputing.stackexchange.com/questions/1560",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/1341/"
] | It is well-known that by utilizing quantum parallelism we can calculate a function $f(x)$ for many different values of $x$ simultaneously. However, some clever manipulations is needed to extract the information of each value, i.e. with Deutsch's algorithm.
Consider the reverse case: can we use quantum parallelism to ... | The exact answer depends on the exact kind of superposition you want. The answers by pyramids and Niel both give you something like
$$A\sum_{t=1}^n |\,\,f_t (x)\,\,\rangle \otimes |F_t\rangle$$
Here I've followed Niel in labelling the different functions $f_1$, $f_2$, etc, with $n$ as the total number of functions yo... | The functions $f,g,\ldots $ that you want to evaluate in different computational branches must, in order to be computable at all, be specifiable in some way (e.g. a sequence of classical logic gates). And the <em>set</em> $\{ f_1, f_2 , \ldots \}$ of the functions you wish to compute ought itself to be computable: for ... | https://quantumcomputing.stackexchange.com |
423,618 | [
"https://physics.stackexchange.com/questions/423618",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/190849/"
] | I understand that in ideal transformers, power is conserved. Because of this the product of voltage and current in the secondary winding is a constant.
This means that voltage and current are inversely related, which seems unintuitive because they are directly related by ohms law.
Shouldn't the emf induced in the sec... | <blockquote>
I understand that in ideal transformers, power is conserved. Because
of this the product of voltage and current in the secondary winding is
a constant.
</blockquote>
This isn't true. The expression of power conservation for an ideal transformer is
$$V_s\cdot I_s = V_p\cdot I_p$$
There is no requi... | Actually the emf induced per turn in both of the primary and secondary windings are equal due to the conservation of energy. Now if you increase the secondary windings with respect to the primary windings then you will get high voltage than the primary circuit for an ideal transformer. And consequently the current in t... | https://physics.stackexchange.com |
87,930 | [
"https://mechanics.stackexchange.com/questions/87930",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/60703/"
] | 2009 Subaru Legacy 2.5 EJ253 SOHC engine
My power steering pump began to squeal a few months ago and progressively increased in volume. I purchased a new pump and installed it, squealing immediatly and noticed power steering fluid oozing from the power steering pump casing where the pump is put together in two pieces f... | It's pretty clear that your issue is not the pump itself. I'd check the following:
<ol>
<li>Fluid for contamination. In fact you should flush the system whenever you change the pump.</li>
<li>Hoses and tubes for blockages. A blocked hose will prevent fluid from flowing and cause the pump to have difficulty pumping a... | Apparently the belt was not tightened enough. I tightened the belt according to the Subaru service manual but the garage I took it too tightened it way beyond the spec up to the point where the tightening bracket just touches the belt! This level of tightness has wore the belt slightly on one of the serpentine grooves ... | https://mechanics.stackexchange.com |
26,375 | [
"https://softwareengineering.stackexchange.com/questions/26375",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5826/"
] | For solo projects, do you keep your build / management tools on your local machine, or on a separate server? If the server is not guaranteed to be safer or more reliable than my own machine I struggle to see the point, but maybe I'm missing some things.
Note that I'm not debating the value of continuous integration or... | That depends, I would say.
Pro local machine:
<ul>
<li>Works without net.</li>
<li>Easier to maintain.</li>
</ul>
Pro separate server:
<ul>
<li>Some tools (continuous integration) may cause load that is annoying on your local machine.</li>
<li>You can access your tools from different machines.</li>
<li>You have a c... | I'm primarily a C/C++ guy who does telecommute projects on Linux, Mac OS X, and Windows.
All my development machines at home are on a gigabit Ethernet LAN which also includes a Linux server that doubles for source control (Perforce and git) and issue tracking/wiki (Redmine).
Why have a separate server?
<ol>
<li>The ... | https://softwareengineering.stackexchange.com |
2,507,444 | [
"https://math.stackexchange.com/questions/2507444",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/382204/"
] | I just started studying power series and I got stuck at this proving the following.
<blockquote>
Let <span class="math-container">$f(x)=\sum a_nx^n$</span> converge in <span class="math-container">$(-R,R)$</span> for <span class="math-container">$R>0$</span>
If <span class="math-container">$f(x)=0$</span> <span clas... | Notice that $\sum a_nx^n$ converges absolutely on $(-R,R)$ too, that is, $\sum |a_nx^n|$ converges for all $x\in(-R,R)$. Let's take a look at the point other than $0$. To help you understand, let's suppose $3\in (-R,R)$, and we look at $3$. (Just to ease the symbols. )
Since $\sum |a_n3^n|$ converges, the partial sum ... | <strong>Hint</strong> What happens if a particular $a_n \neq 0$?
| https://math.stackexchange.com |
1,726,704 | [
"https://math.stackexchange.com/questions/1726704",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/306462/"
] | Let $X \subset \mathbb{R}^{n}$. If $A \subset X$ is open in $X$ and $X$ is open in $\mathbb{R}^{n}$ is $A$ open in $\mathbb{R}^{n}$?
I suppose that is true but it's lack argumentation to me.
if $A$ is open in $X$ then for all $a \in A$ exists a $\epsilon > 0$ such that $X \cap B(a;\epsilon) \subset A$. If i assume... | "... because any $a \in A$ is also $a \in X$."
However, an easier way is from the definition of relatively open: $A$ relatively open in $X$ means there is an open $\hat{A} \subset \Bbb{R}^n$ such that $A = \hat{A} \cap X$. $X$ is given open (in $\Bbb{R}^n$) and the intersection of open sets is open, so $A$ is open i... | Since $X$ is open in $\mathbb R^n$, you know that such a value of $\epsilon$ exists, so let the $\epsilon$ you choose be sufficiently small that $B(a;\epsilon)\cap X\subset A$ and $B(a;\epsilon)\subset X$.
| https://math.stackexchange.com |
330,266 | [
"https://physics.stackexchange.com/questions/330266",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/154704/"
] | I'm doing a experiment that revolves around dropping an object into a container with water.
When I increase the mass of the object, will the velocity of water waves increase when the object is dropped into the container?
Will the kinetic energy coming from the object transfer its energy to the water wave, thus increa... | From the form stated, the magnitude of the field $\mathbf{E}$ is constant and the direction is radial, i.e. it is a vector normal to the sphere.
Recall that $d\mathbf{S}$ is a vector whose magnitud is the area of the surface and points outwards. Therefor $\mathbf{E}\cdot d\mathbf{S}=EdS$ (where the scalar product in $... | Nevermind, I figured it out (that was a really dumb question):
$\int_{S_R}{d\textbf{S}\dot{}\textbf{E}}$ is the same as $\int_{S_R}dS \ \textbf{E}\dot{}\textbf{n}$ (where $\textbf{n}$ is the unit vector pointing away from the sphere). Because $\textbf{n}=\frac{\textbf{r}}{||\textbf{r}||}$ the dot product becomes $\frac... | https://physics.stackexchange.com |
4,089,123 | [
"https://math.stackexchange.com/questions/4089123",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/26632/"
] | Find a harmonic function on <span class="math-container">$|z|<1$</span> with value 1 on an arc of <span class="math-container">$|z|=1$</span> and zero on the rest.
Of course, if allow the arc with value <span class="math-container">$1$</span> to be the whole <span class="math-container">$|z|=1$</span> circle it woul... | Originally a comment but expanded to an answer - another way to express the required <span class="math-container">$u$</span> is as follows:
Let <span class="math-container">$0 \le \alpha \le 2\pi$</span> the length of the arc in question (where the function needs to go to <span class="math-container">$1$</span>) and fo... | So we want a complex power series, with radius of convergence <span class="math-container">$1$</span>, and such that on the unit circle it is sometimes 0 and sometimes 1. There is really only one way to construct this, because the power series coefficients need to be precisely the Fourier coefficients of your function ... | https://math.stackexchange.com |
575,183 | [
"https://physics.stackexchange.com/questions/575183",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/197434/"
] | Suppose that <span class="math-container">$|a\rangle$</span> is a vector in Hilbert space <em>H</em>.
Is the projector <span class="math-container">$|a\rangle\langle a|$</span> "always" an operator on <em>H</em>?
Also, what is the condition under which <span class="math-container">$|a\rangle\langle a|$</span>... | Yes, it is always an operator. The inner product is defined for all vectors in a space, so <span class="math-container">$|a\rangle\langle a|\psi\rangle$</span> is always well-defined. It is also always Hermitian, since its eigenvalues are only <span class="math-container">$\langle a|a\rangle$</span> and <span class="ma... | Yes. For any vector <span class="math-container">$\psi$</span> in the Hilbert space, the projector <span class="math-container">$P_\psi$</span>, which eats a vector <span class="math-container">$\phi$</span> and spits out <span class="math-container">$\langle\psi,\phi\rangle \psi$</span>, is bounded (with operator nor... | https://physics.stackexchange.com |
932,731 | [
"https://math.stackexchange.com/questions/932731",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/176122/"
] | <blockquote>
If $b=log_3(x),$ what value of $x$ satisfies $log_b(log_3(x^2))=3?$
</blockquote>
I just started learning this topic by myself. I wanted to know if my working is correct. If not can someone help me with this solution?
$log_b(\frac{(log(x^2)}{log(3)})$
$=$ $log_b(log(x^2))$
$=$ $log_b(2log(x))$
$=$ $... | Let's start with $\log_b (\log_3(x^2)) = 3$. It can be written as $\log_3(x^2)=b^3 \Rightarrow 2 \log_3 (x) = b^3 \Rightarrow 2b=b^3 \Rightarrow b(2-b^2)=0 \Rightarrow b=\sqrt{2}$ and not the negative root because $b$ has to be positive. A base cannot be negative. Thus we get: $\sqrt{2}=\log_3 (x) \Rightarrow x= 3^{\sq... | The question should be, I believe, what value <strong>of</strong> $\;b\;$ satisfies the given equality, as $\;x\;$ has no role given that $\;\log_3x=b\iff 3^b=x\;$:
$$\log_b\left(\log_3x^2\right)=3$$
$$\log_b\left(2\log_3x\right)=3$$
$$\log_b\left(2b\right)=3$$
$$\log_b2+\log_bb=3$$
$$\log_b2=2\iff b^2=2\iff \ldot... | https://math.stackexchange.com |
505,799 | [
"https://electronics.stackexchange.com/questions/505799",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/251063/"
] | When there are three amplifiers that are cascaded to produce higher gain:
<ul>
<li>The source resistance should be lower than input impedance of first amplifier</li>
<li>The output impedance of first amplifier should be lower than input impedance of second amplifier</li>
<li>The output impedance of second amplifier sho... | [I discuss Noise Voltage versus Noise Figure at end of this answer.]
simply stated
<ul>
<li>matching will cost you 6dB per interface on the voltage levels
</li>
<li>I once lead a team doing RF design on silicon; we concluded there was no need to match over our 500 micron distances on the silicon
</li>
<li>I guided the ... | For practical purposes, the answer depends very much on the frequency band that you're working with, and on the length of your transmission lines = whether TML properties need to be considered at all, at those frequencies.
My first experiences as a DIY has been with audio circuitry. The classic is a phono preamp, follo... | https://electronics.stackexchange.com |
174,803 | [
"https://electronics.stackexchange.com/questions/174803",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/78419/"
] | I want to replace the onboard AMS1117-5.0 (broken) with a LM7805.
However, the pinout is different between the two voltage regulators; AMS1117: Gnd, Vout, Vin vs LM7805: Vin, Gnd, Vout.
I would like to know what is the best practice of how to approach this? Line-up the Vin and cross the Vout and Ground pins and add s... | Why do you need to change over to a 7805? If you're gonna be bending pins up and using jumper wires, you're cruisin' for a bruisin'. A quick look at the data sheets leads me to believe there is no good reason to switch, other than the possibility that this is all you've got on hand?
If it must be done, here's how I'd ... | The two devices may not be interchangeable in the target circuit (not shown). The drop-out voltage for the AMS1117-5.0 is typically only 1.1V at a load current of 0.8 amps. The LM7805 drop-out voltage is specified as typically 2V at 1A load current. You may not find the replacement works correctly.
I think you need to... | https://electronics.stackexchange.com |
243,125 | [
"https://physics.stackexchange.com/questions/243125",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/111162/"
] | My understanding of relativity explains that the presence of mass warps space-time so that light travelling through the warp follows at straight line but the warp itself is curved and therefore the light seems to an outside observer (non-local reference frame) to be travelling in an arc.
If the mass is sufficiently la... | If we consider the thought experiment where we take the classic 2 dimensional plane curved in a graphic representation of the curvature of space-time, copy it and arrange the copy so the lowest points of the gravity wells are aligned. These copies can be arranged any way you like, as long as the low point, or gravity ... | The presence of matter doesn't warp spacetime. You could make a shell of matter and the spacetime on one side could be perfectly flat no matter how close to the shell you get.
Spacetime warps naturally. A wave of warped spacetime could propagate through a universe that is everywhere devoid of matter and always was and... | https://physics.stackexchange.com |
651,028 | [
"https://physics.stackexchange.com/questions/651028",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86968/"
] | My question is related to what is the physical content of infinitesimals. In mathematics the infinitesimals as hyperreals (Robinson 1960) are introduced as numbers greater than 0 but smaller than any real number. Can a physical quantity in real nature increase with a such infinitesimal number?
This must be outside phys... | Numbers, by themselves, do not have any physical content whatsoever. Physics is about creating models that accurately predict the outcome of experiments. So the physical content is in the model, not the numbers used by the model.
That said, the most successful models that we have developed, the ones that produce the be... | The existence of planck length and plank time seems to show ourselves that the world is discrete....
So i think we can answer "no" to your question...
Everything in nature appears to be quantized at fundamental level
| https://physics.stackexchange.com |
575,172 | [
"https://physics.stackexchange.com/questions/575172",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/172936/"
] | I don't understand the following statement from my notes:
<em>"A fourth active neutrino is not allowed by the invisible width of the <span class="math-container">$Z$</span>-boson to which it would contribute as much as one active neutrino, <span class="math-container">$Z \to \nu_\alpha \bar{\nu}_\alpha$</span>.&qu... | The Z boson coupling to all fermions is predicted by the Standard Model, and does not depend on what family the fermion is in. Because the mass of all neutrinos is much, much lighter than the mass of the Z, they all have the same partial decay widths, which can be determined using precision electroweak measurements. Th... | Your question is quite obscure, but I'm starting a placeholder answer, to avoid a garland of comments in a clarificatory conversation.
The full width of the Z is about 2.5 GeV, of which the visible leptonic and hadronic (quark) decays observed add up to 1.9 GeV or so; so the invisible width is the rest, about 0.5 - 0.6... | https://physics.stackexchange.com |
312,986 | [
"https://physics.stackexchange.com/questions/312986",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/85765/"
] | We are familiar with Newton's law of gravitation:
$$\textbf{F} = \frac{-GMm}{r^2} \hat{\textbf{r}},\tag{1}$$
which leads to a gravitational field strength relation:
$$\textbf{g} = \frac{-GM}{r^2} \hat{\textbf{r}}. \tag{2}$$
In terms of vector calculus we can write this in the form:
$$\nabla\cdot\textbf{g} = -4\pi ... | <em>Yes,</em> the Newtonian gravitational field ${\bf g}$ is also required to be rotation-free $\nabla \times {\bf g} = 0$. This also follows from the existence of a Newtonian gravitational potential.
| You can show that if there exists a scalar potential for the field, it will also be curl-free. So the relation is required, but stating it separately is redundant, as it is a consequence of the existence of the potential.
| https://physics.stackexchange.com |
8,952 | [
"https://quant.stackexchange.com/questions/8952",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/5168/"
] | I am trying to find out what is the purpose of "repeating groups" in FIX and what exactly do they represent? Are they all related to the same order and if so, why do you need repeated tags? If they aren't related to the first order wouldnt it be easier to send in a separate message? Is it just all orders at that exact ... | Repeating groups are a way for FIX to represent arrays. A "number of" field prepends the repeating group to alert the recipient how many elements to expect.
For example, Arca uses <code>TradingSessionID</code> (tag 336) to identify pre-open (<em>P1</em>), primary (<em>P2</em>), and post-close (<em>P3</em>) market hour... | No, it doesn't have to do with time frames. It's a protocol feature designed to enable something akin to <em>nested data</em>, whether for more compact data transmission, or just to allow one to adhere to rules of semantic sense.
Take market data requests, for example, <em>i.e.</em> retrieving the current market depth... | https://quant.stackexchange.com |
1,266,110 | [
"https://math.stackexchange.com/questions/1266110",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/30379/"
] | What is the most motivating way to introduce LCM of two integers on a first elementary number theory course? I am looking for real life examples of LCM which have an impact. I want to be able to explain to students why they need to study this topic.
| A real life example of finding LCM is adding two fractions together:
$$\frac14+ \frac16 = \frac3{12} + \frac2{12} = \frac{5}{12}$$
How do you know what the common denominator is? Well, it's the LCM of all of the denominators.
| Alice hit the bulls eye 43 times in 57 attempts; and Bob hit it 48 times in 61 attempts. Who has a good record? Ideally to make them comparable both should have made an equal number of attempts. So we scale them up by maintaining hit rate by expressing the success count for the same number of hits; this requires a com... | https://math.stackexchange.com |
16,447 | [
"https://electronics.stackexchange.com/questions/16447",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | After removing the dead CCFLs from an LCD monitor, I noticed something odd. Although both wires go to different ends of the tube and presumably carry identical currents, they are visibly and internally different sizes. Everything I know about electronics tells me the current is the same in all parts of a circuit for a ... | It's because the pink wire is at a high potential with respect to the rest of the system. The distance between two conductors at which bad things start happening is related to the potential difference between them, so the thicker insulation is to force the conductor to stay further away. The ground wire doesn't need it... | I guess ground wire does not need thick insulation. So every penny saved :-)
| https://electronics.stackexchange.com |
704,134 | [
"https://physics.stackexchange.com/questions/704134",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/332933/"
] | I am reading Jackson's <span class="math-container">$Classical$</span> <span class="math-container">$Electrodynamics$</span> and there are two forumlas which cause some problems for me. What happens is that if I combine those formulas in a certain way, I can deduce some absurd results. Let me explain:
The formulas in q... | You are making a mauntain out if a molehill. Remember that in
<span class="math-container">$$
\nabla \left\{\int d^3x'\frac{\rho(x')}{|x-x'|}\right\}
$$</span>
the <span class="math-container">$\nabla$</span> is <span class="math-container">$\nabla_x$</span> a derivative wrt to <span class="math-container">$x$</span> n... | The mistake appears to be in the step
<span class="math-container">$$ -k\nabla\int \frac{\rho(A\textbf{x}')}{|A\textbf{x}-A\textbf{x}'|} d^3 x' = -k\nabla\int \frac{\rho(\textbf{x}')}{|\textbf{x}-\textbf{x}'|} d^3 x'. $$</span>
Let <span class="math-container">$f(\textbf{x})=1/|\textbf{x}|.$</span> We can write
<span ... | https://physics.stackexchange.com |
284,581 | [
"https://electronics.stackexchange.com/questions/284581",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/130553/"
] | I have the question "For the circuit shown"
<img src="https://i.stack.imgur.com/UAlhX.jpg" alt="enter image description here">
Find the value of the supply voltage V.
I know that the equation for voltage is V = IR.
However, I am not sure what the values for I and R should be ?
| Since they are in parallel, they all have the same voltage across them.
So the V would be 3*20 = 60V
This voltage is the same for the other 2 resistors. So I1 would be 60/10 = 6A
I3 would be 60/60 = 1A
| Hint - ignore R1 and R3 to find V. Pretend they are not there. Now can you see the simplicity of the basic problem?
It is a bit of a trick question in that there is too much irrelevant information contained. Focus on what you know and ignore the superfluous visual noise.
Once you have V, the unknown currents are eas... | https://electronics.stackexchange.com |
185,906 | [
"https://electronics.stackexchange.com/questions/185906",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/78518/"
] | Suppose I have an IGBT transistor rated for 60A, that has junction temperature range of -55 to 175C. What happens if I do not exceed max current, but I do exceed max temperature? The characteristics in the datasheets don't seem to have any changes around max temperature limit, so what is the problem? I would like to se... | As you may know, semiconductor devices are fabricated doping a very pure silicon (or other, less common, semiconductor materials) substrate using various kinds of ions. Doping different zones of the semiconductor with different types and concentrations of dopants produces the different kinds of semiconductor devices yo... | The most dominant effect limiting the temperature range for the use of a transistor is intrinsic conductance.
An undoped semiconductor has some electron-hole pairs. The number of free carriers depends on the temperature and can be calculated with the fermi distribution. Following this an undoped silicium will be a fai... | https://electronics.stackexchange.com |
226,717 | [
"https://security.stackexchange.com/questions/226717",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/129883/"
] | My textbook for CompTIA Security+ has the following practice question:
<blockquote>
In which one of following PKI Trust Models is the root NOT a single point of failure?
<ul>
<li>Single CA</li>
<li>Hierarchical CA</li>
<li>Online CA</li>
<li>Self-signed</li>
</ul>
</blockquote>
Now, I immediately dis... | The way the question is worded, there is a root. Therefore, you should have dismissed self-signed because there is no root in self-signed. That's the "obviously wrong" option (using the 4-option model of obviously wrong, 2 almost right, and right/more right).
Online CAs include the idea of redundancies and a distribu... | The online root cert is in your trusted certificate store.
So if the issuing CA cert is trusted by the root then you trust the issuing CA.
As such, the Root can be offline and the certificate chain is still trusted
| https://security.stackexchange.com |
484,902 | [
"https://math.stackexchange.com/questions/484902",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93268/"
] | Have been working on this for the past 2 hours and still not getting any where. Any help will be much appreciated!
Consider the following argument
1) p<br>
2) p v q<br>
3) q → (r → s)<br>
4) t → r
∴¬s → ¬t
Analyze the validity of the argument. If it is valid, show the proof with the inference rules & logica... | Proceed methodically: Suppose the premisses are true and conclusion false. So
<blockquote>
<span class="math-container">$1.\quad p \quad \Rightarrow \quad T$</span>
<span class="math-container">$2.\quad p \lor q \quad \Rightarrow \quad T$</span>
<span class="math-container">$3.\quad q \to (r \to s) \quad \Rightarrow \q... | It is false, since you can instantiate p=1, q=0, r=1, s=0, t=1, that verify all the premises but not the conclusion.
Moreover notice that the assumption 2 is useless, since it is direct consequence of assumption 1.
| https://math.stackexchange.com |
584,510 | [
"https://physics.stackexchange.com/questions/584510",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/259384/"
] | My textbook says that we can't apply the Parallelogram Rule of vector addition for two parallel vectors. Why can't we apply the rule?
| Suppose you have two particles 1 and 2 interacting with each other. Force on 1 by 2 is <span class="math-container">$F_{12}$</span> and force on 2 by 1 is <span class="math-container">$F_{21}$</span>. From Newton's third law it follows that <span class="math-container">$F_{12} = - F_{21}$</span>. Now let's calculate th... | If the sum of the internal torques was not zero, then the system could undergo spontaneous angular acceleration in violation of conservation of angular momentum (and energy).
| https://physics.stackexchange.com |
209,633 | [
"https://dba.stackexchange.com/questions/209633",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/153231/"
] | I did ask same question on stackoverflow, but no response, hence I thought database experts will help me to solve this.
I have following table similar to Oracle <code>user_sequences</code>.
I have logic of sequence prefix/suffix something, but for simplicity, I'm skipping as matters less here.
<pre><code>create tabl... | Possible solution.
Each thread which will obtain the values from "sequence generator" have some <code>customer_id</code> value it will use when ask for next value. Additionally, it generates some random and unique (guaranteed!) value when starting (if all threads works in one OS instance, it can be thread's PID, for e... | I was able to solve this problem by just combining suggestions of @Akina and @RickJames , thank you both for thier support.
<pre><code>create table my_seq(
min_value integer,
Max_value integer,
last_value integer,
increment_by tinyint,
customer_id integer)ENGINE = InnoDB;
</code></pre>
Here <code>ENGINE=InnoDB</code>... | https://dba.stackexchange.com |
31,396 | [
"https://engineering.stackexchange.com/questions/31396",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/3734/"
] | The concrete slab (?) supporting the swimming pool (≈ 10 x 10m x 1m) of my building has clearly a 'belly':
<img src="https://i.imgur.com/S1Q6uW4.jpg" alt="concrete slab belly">
I'm not sure whether this was built this way or evolved over time, however, my best guess is that after 25 years the heavy load of the swimmi... | <ul>
<li>What is the technical term for this?</li>
</ul>
Bending downwards is called <strong>sagging</strong>. (Technically "sagging" isn't moving downwards; it's bending in a shape that looks like the mouth on a smiley face).
One thing you'll see with concrete structures is <strong>creep</strong>. This is where unde... | That will fail eventually, concrete supports compression easily but not tension (something Barnes Wallis used to break the dams).
Get this inspected by a professional.
One wonders if the situation has been exacerbated by increasing the level of water in the pool - is the level what the designer originally designed fo... | https://engineering.stackexchange.com |
152,351 | [
"https://softwareengineering.stackexchange.com/questions/152351",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/41464/"
] | I manage a small team of developers on an application which is in the mid-point of its lifecycle, within a big firm. This unfortunately means there is commonly a 30/70 split of Programming tasks to "other technical work". This work includes:
<ul>
<li>Working with DBA / Unix / Network / Loadbalancer teams on various ta... | It sounds like you are placing too much effort on having well rounded <em>individuals</em> and not enough effort on having a well rounded <em>team</em>.
There is nothing wrong with being good at something--in fact, that is probably why he was hired! You should be thankful to have someone who is good at programming to ... | You are catching some heat here in the other answers for your decision to "do something" about this guy, but I fully get what you are saying. If the other team members "would all prefer to be coding, rather than doing these more mundane tasks" then they are going to be annoyed that you are <strong>rewarding the bad per... | https://softwareengineering.stackexchange.com |
1,759,736 | [
"https://math.stackexchange.com/questions/1759736",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/274536/"
] | <blockquote>
Let $f : [0,1] \to \mathbb{R}$ be a continuous function such that
$$\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$$
Determine all such functions $f$.
</blockquote>
So far, I've managed to show that $\int_0^1\!{f(x)^t\, \mathrm{dx}}$ is constant ... | Note that
$$\int_0^1 f(x)^2 (1 - f(x))^2 \; dx = \int_0^1 \left(f(x)^2 - 2 f(x)^3 + f(x)^4\right) \; dx = 0$$
so $f(x)(1-f(x))$ must always be $0$. Since $f$ is continuous, the only solutions are $f(x)=0$ and $f(x)=1$.
| Calculate the difference of first and second integral then second and third.
$$\int_0^1f^2(x)-f^3(x)dx=0$$
$$\int_0^1f^3(x)-f^4(x)dx=0$$
Subtract both equations:
$$\int_0^1f^2(x)-2f^3(x)+f^4(x)dx=0$$
$$\int_0^1f^2(x)\left[1-2f(x)+f^2(x)\right]dx=0$$
$$\int_0^1f^2(x)(1-f(x))^2dx=0$$
Look at the integrand it consists ... | https://math.stackexchange.com |
28,860 | [
"https://stats.stackexchange.com/questions/28860",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6845/"
] | I have downloaded the sample codes from kaggle for the randomForest benchmark <em>[URL?]</em> and there's this part that I don't understand.
<pre><code> appendNAs <- function(dataset, cols) {
append_these = data.frame( is.na(dataset[, cols] ))
names(append_these) = paste(names(append_these), "NA", sep = "_")
... | You somehow have to model the the missingness (NAs). You can either model the variables that contain NAs in order to impute values, or you can include NA indicator values that become a part of your overall model.
When you think about it that way, simply choosing the median of a variable to fill in its NAs is probably ... | In many cases, the presence of NA is non-random, and can be used as a predictive variable in its own right. For example, knowing whether survey participants chose to disclose a certain fact can be as important as the fact itself. Imputation discards this information, which can reduce predictive performance.
| https://stats.stackexchange.com |
402,310 | [
"https://math.stackexchange.com/questions/402310",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/79454/"
] | Vector math is something I find very interesting. However, we have never been told the link between vectors in physics (usually represented as arrows, e.g. a force vector) and in algebra (e.g. represented like a column matrix). It was really never explained well in classes.
Here are the things I can't wrap my head aro... | Physicists tend to emphasize a geometric interpretations of vectors, which mathematicians need not do. This is because one of the main uses of vectors in physics is to talk about the geometry of some system, while vectors in general can be used in more abstract senses (and perhaps with no geometric interpretation at a... | You can represent a vector as an arrow in cartesian coordinates by drawing an arrow from (0,0) to the vector (row vector) for example <3,2> taken as a point on the plane (3,4). In other words, your first bullet point is correct.
Vector normalization is the process by which one takes an arbitrary vector (a, b) and c... | https://math.stackexchange.com |
587,115 | [
"https://electronics.stackexchange.com/questions/587115",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/296038/"
] | I have received several parts from a PCB manufacturer which should have been inspected to IPC-A-600 Class 2 but were instead inspected to IPC-A-600 Class 3.
I believe I have received PCBs inspected to a higher degree of accuracy, meaning potentially less defects. But I'd like to know the potential negative impacts of e... | I very much doubt there's a significant downside to class 3 inspection when you specified class 2. After all, class 3 is for critical equipment so your boards were inspected to tighter tolerances, etc. I obviously was not a party to your conversation with the manufacturer but I think that what you are interpreting as... | It could be that your contractor's production line is tuned for construction and testing to Class 3, and for some reason it's less trouble and/or less expensive for them to simply bill you for Class 2 and build and test to a higher spec than to build and test to Class 2.
| https://electronics.stackexchange.com |
583,154 | [
"https://physics.stackexchange.com/questions/583154",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167278/"
] | Point electric dipoles are usually introduced as two charges <span class="math-container">$\pm q$</span> at a distance <span class="math-container">$d$</span>, then taking the simultaneous limit <span class="math-container">$d \to 0$</span> and <span class="math-container">$q \to \infty$</span> keeping the product <spa... | <blockquote>
is there a sensible way to introduce a point electric dipole with well defined electrical and mechanical properties?
</blockquote>
Partly. We have a few options:
<ul>
<li><strong>Finite moment of inertia</strong>: For finite <span class="math-container">$d$</span>, the electric dipole moment is <span class... | See, when we are talking about point dipoles we have usually pictures of polar molecules in our mind where <span class="math-container">$d \approx 1 \overset{°}{\text{A}}$</span> and charge separation <span class="math-container">$q \approx 10^{-10}~\textrm{esu}$</span>. So, their dipole moment is very small.
When an ... | https://physics.stackexchange.com |
156,855 | [
"https://cs.stackexchange.com/questions/156855",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/149100/"
] | Is there a 2SAT instance of variables <span class="math-container">$(a,b,c,d,e,f,g)$</span> that has exactly the solution set <span class="math-container">$S=\{ (1,0,0,0,0,0,0),(0,1,0,0,0,0,0),(0,0,1,0,0,0,0),(1,1,0,1,0,0,0),(1,0,1,0,1,0,0),(0,1,1,0,0,1,0),(1,1,1,1,1,1,1) \}$</span>? It sounds plausible, but other than... | Your proof doesn't work. First of all you can't choose your favorite decomposition of <span class="math-container">$s$</span>: the pumping lemma just ensures that such a decomposition
<strong>exists</strong> so your argument needs to work for all possible decompositions.
Nevertheless, even with your decomposition it is... | First of all, you don't get to pick the decomposition. So one decomposition you'd need to handle is <span class="math-container">$x = \varepsilon$</span>, <span class="math-container">$y = 00$</span>, <span class="math-container">$z = 0^{2p-2}$</span>. Now if we pump <span class="math-container">$y$</span> for <span cl... | https://cs.stackexchange.com |
49,219 | [
"https://astronomy.stackexchange.com/questions/49219",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/46037/"
] | After the death of the universe’s first generation of stars, the clouds from which new stars form will include elements heavier than hydrogen. In the formation of a protostar from such a cloud, do heavier elements sink down toward the center? If so, does this sinking dilute the concentration of hydrogen at the protos... | No. The diffusion process you describe does not take place to any significant extent in regions that are thoroughly mixed by convection.
Protostars are fully convective and as such have a uniform composition.
| There is no gravitational separation of elements as such for a self-gravitating system (held together by <span class="math-container">$1/r^2$</span> forces only). At all phases during star formation (and afterwards) you can assume the virial theorem to hold, by which the average kinetic energy = -1/2x average gravitati... | https://astronomy.stackexchange.com |
6,248 | [
"https://mathoverflow.net/questions/6248",
"https://mathoverflow.net",
"https://mathoverflow.net/users/987/"
] | I've been attending a series of lectures on Cryptography from an engineering perspective, which means that most of the assertions made are supplied without proof... here's one that the lecturer couldn't recall the reason for, nor original source of.
Given an unfactored $n=pq$, computing $\phi(n)$ is as hard as finding... | While I cannot immediately see an easy way to find Φ(n) from (t-u)Φ(n), assuming t-u is also of "cryptographic size" of course, an attacker will probably not have to.
Depending on how RSA-like the cryptosystem is, knowing a multiple of Φ(n) might well be enough to decrypt. After all, given the public expon... | If you know an even $m$ such that $a^m \equiv 1 \mod n, (a,n)=1$, e.g. a multiple of $\phi(n)$ then there is a standard probabilistic algorithm to factor $n=pq$. Write $m = 2^rs$ with $s$ odd. Pick a random $a$ and compute $a^s, a^{2s}, a^{4s},\ldots$. If $a^s \ne 1 \mod n$, then at some point in the calculation, you f... | https://mathoverflow.net |
138,769 | [
"https://stats.stackexchange.com/questions/138769",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/68744/"
] | I am running some imputations using the mice package in R. During this process I need to use the as.mids function. However, it seems that as.mids change the values of my subsequent analysis - but I hope I am just doing something wrong.
An example:
Let's say I first impute 5 datasets.
<pre><code>imp1 <- mice(myDat... | There is indeed a bug somewhere in <code>as.mids</code>.
I used <code>as.mids</code> to convert a stacked dataset of 10 imputations, and then got a list of imputations from it. Weird stuff would happen. Once I randomly got <code>NA</code>s from a value. Other times it started changing values in my final imputation.... | I also discovered this bug in mice.
My analysis: <code>as.mids</code> assumes that the <code>.imp</code> column is coded as a factor, and therefore subtracts <code>1</code> from the max to get the right number of imputations. But if it is not a factor – subtracting <code>1</code> will lose the last imputation. Furthe... | https://stats.stackexchange.com |
191,941 | [
"https://softwareengineering.stackexchange.com/questions/191941",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11462/"
] | Have you ever had this feeling that your code is bad, the whole project is a mess, and you just want to step off? On your daily job you can explain this feeling away with your coworkers, asshole boss, or something like this. But with side/pet projects there is really no excuse.
For example I'm currently maintaining my... | Don't hate. 2nd tier programmers hate. Craftsmen look at code without bringing ego into it. Code is not a reflection of who you are. It is a means to an end. Try to learn from your past mistakes and try not to repeat them but you can't do that if all you are thinking about is how shitty of a coder you are. So don't be ... | From what you're saying, it sounds like you have accumulated techincal debt.
I think everyone has thought "did I write that". I suggest the following for doing what you can to improvide it:
<ul>
<li>Refactor where at all possible</li>
<li>Make sure your naming is consistent</li>
<li>Format the code to make it more re... | https://softwareengineering.stackexchange.com |
671,073 | [
"https://physics.stackexchange.com/questions/671073",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/282151/"
] | I take a ball smaller than the mouth of the bottle and blow into the bottle (The bottle is horizontal).
When I blow I create a <em>low pressure</em>, outside the bottle at the mouth and there is high pressure inside the bottle so it pushes the ball out. But you said that the increased air speed results in low pressure.... | Bernoulli's principle states that <span class="math-container">$p + 1/2$$\rho$$v^2$</span> + <span class="math-container">$\rho$$gh = const.$</span>
This equation is strictly for incompressible (const. density) fluids, but it simplifies the problem . So the air you blow into the bottle has to come back out through the ... | I think this is better understood by imagining the velocity field of the flow than through pressure. Yes, at some level pressure is what causes it to move, but it is simpler just to say that the ball is swept along with the motion of the air.
When you blow into the mouth of the bottle, you tend to form a jet that is mo... | https://physics.stackexchange.com |
444,257 | [
"https://physics.stackexchange.com/questions/444257",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214597/"
] | What happens with the object when it absorbs a photon by not reflecting it. Does its mass grow or its heat grows?
| Consider that
1) Photons are massless particles
2) When an object is in thermal equilibrium, it absorbs as much radiation as it radiates itself (otherwise, its temperature would fluctuate). Absorbing the photon would then mean emitting some other radiation, called thermal radiation in this context.
Read about black... | Also note that if the photon is absorbed, it means that there has been an electronic energy transition, whose energy difference is equal to the photon energy. The electron now is in a higher energy state. Thus higher temperature (kinetic energy).
The photon will only be absorbed if there’s any possible energy transiti... | https://physics.stackexchange.com |
385,158 | [
"https://physics.stackexchange.com/questions/385158",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/184227/"
] | If you put something like a penny in a jar in space and brought it back to earth would the penny still float like in space?
| <blockquote>
would the penny still float like in space?
</blockquote>
Your main misunderstanding is in thinking that, in space, things float because they are in vacuum. Instead, things "float" because the gravitation of the earth is counterbalanced by the movement of the spacecraft in orbit. When you bring them back... | If you bottled up some air in some region of space outside of earths atmosphere where space doesn't have much air in it and bring it back down, the bottle would implode at some point as you brought it down because of the pressure difference of the inside and outside air. The air becomes thicker as you move the bottle d... | https://physics.stackexchange.com |
66,970 | [
"https://stats.stackexchange.com/questions/66970",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28884/"
] | <img src="https://i.stack.imgur.com/nGx8c.png" alt="Question for interpretation">
The way I interpreted this question was that $H_0: \mu \ge 10, H_a: \mu < 10$. But the answer for this question set up a hypothesis of $H_0: \mu = 10,H_a: \mu>10$. Shouldn't it be the first way?
| If "the claim" is "that it takes <em>at least</em> 10 years", and you want to test this, then that is your alternative hypothesis. The null hypothesis negates the alternative. Thus:<br>
$$
H_0: \mu\le10 \\
H_a: \mu>10
$$
A way to think about these things is that the alternative hypothesis is what the researcher r... | I am bit confused with gung's interpretation. Please correct me if I am wrong.
Since the claim is that it takes 'at least 10 years', then we should state this claim as mu>=10, and the other hypothesis should be the complementary of this one, so it is mu<10.
To my understanding, the claim of 'mu>=10' has to be the... | https://stats.stackexchange.com |
339,211 | [
"https://electronics.stackexchange.com/questions/339211",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/134757/"
] | In his book "Modern Operating Systems", Tanenbaum makes a statement about processors speed that I can't understand:
<blockquote>
According to Einstein’s special theory of relativity, no electrical signal can propagate faster than the speed of light, which is about 30 cm/nsec in vacuum and about 20 cm/nsec in copper ... | The limit he gives is predicated on an assumption of the entire chip being in a single clock domain. Large chips have used multiple clock domains for years though.
From a practical perspective, frequency limits on high-end CPUs <em>mostly</em> depend on the ability to deliver and dissipate power. With sufficient cool... | The chip itself can be any size (within tech limits), but propagation time is an issue already. Very big chips such as high cell count FPGAs frequently have multiple clock sources, so the local propagation distance can be made small. Synthesis and route/place tools will warn of timing violations, and the propagation ti... | https://electronics.stackexchange.com |
36,311 | [
"https://softwareengineering.stackexchange.com/questions/36311",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1338/"
] | I tend to keep my objects consistent during their lifetime. In some cases, setting up an object requires multiple calls to different routines. For example, a connection object may operate in this way:
<pre><code>Connection c = new Connection();
c.setHost("http://whatever")
c.setPort(8080)
c.connect()
</code></pre>
pl... | I believe I understand what you are trying to get at, and there are a few different approaches you can use. Inconsistent states do create a problem in multithreaded re-entrant applications.
<strong>Dependency Injection Approach</strong>
Probably the least amount of work with the greatest return on investment would b... | How about passing values to initializer?
<pre><code>Connection c = new Connection("http://foo", 80);
c.connect();
</code></pre>
I, personally, use this approach when coding with ruby (and rails) as well as Objective-C (and Cocoa).
<strong>Update:</strong> I try to pass all the non default values in object initialize... | https://softwareengineering.stackexchange.com |
652,178 | [
"https://electronics.stackexchange.com/questions/652178",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/331779/"
] | Somehow LEDs with a lower forward voltage than the source with a 100 Ω resistor tend to blow up every time the switch is turned on. How can I understand forward voltage better?
| I don't know if 330 mA is sufficient to drive the sensors. But I question how you plan to read soil resistance by measuring current, where that current is already being regulated to 330 mA. The current sensors will always read 330mA * 15 mOhms = 4.95 mV until the soil resistance exceeds the ability of the 5V source to ... | U2 is sensing the current generated by U1 and the MOSFETs so it's not going to work.
Soil resistance is pretty high so it should be measurable with much less than 1mA, and it is preferable to use AC to avoid probe corrosion. So the simplest solution would be a RC oscillator with the soil acting as the frequency setting... | https://electronics.stackexchange.com |
145,875 | [
"https://electronics.stackexchange.com/questions/145875",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/36884/"
] | My project is a data logger board which must mount a PIC of some kind to provide USB and Ethernet as a means to communicating with the board. I can develop this system into two products a low-end version which provides 10Mbps (10BaseT) and a more featured one which must provide 100Mbps (100BaseT) for compliance with LX... | Subsampling does not necessarily mean resampling previously sampled data, although it often gets implemented that way in practice.
It really refers to sampling at a rate (either in space or time) that's lower than the Nyquist criterion would indicate. It usually follows some sort of low-pass or bandpass filter that re... | In image processing it often means <em>chrominance subsampling</em>, meaning that color information is in lesser resolution than the luminance (greyscale) data.
Sometimes, perhaps, it also could mean other things such as resampling to a lower resolution, for example to make it easier to calculate initial vectors in mo... | https://electronics.stackexchange.com |
8,747 | [
"https://dba.stackexchange.com/questions/8747",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/3914/"
] | Well after learning DBMS as a subject i got so many questions in mind. Normalization is one of them. As i learnt it there was a lot more confusion and i found that whatever we do in normalization process we can do it by general common sense also. Even while making projects also people are not used to follow it. So is i... | To answer your question, yes normalization is needed.
Common sense is a relative term and is open to interpretation. RDBMS's have been around since the 1970's. Normalization has been put into use on countless projects over the past 30 years, much to the benefit of the applications being developed.
The most comple... | Every rule, every process, every pattern that is taught in programming courses is an effort to try to "institutionalize" common sense. If all of your developers have perfect common sense at all times and are clear-headed and insightful, then you don't need to follow anybody's rules, processes or patterns.
<em>However... | https://dba.stackexchange.com |
23,264 | [
"https://datascience.stackexchange.com/questions/23264",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/201/"
] | I have a dataset with 19 columns and about 250k rows. I have worked with bigger datasets, but this time, Pandas decided to play with my nerves.
I tried to split the original dataset into 3 sub-dataframes based on some simple rules. However, it takes a long time to execute the code. About 15-20 seconds just for the fil... | The concept to understand is that the conditional is actually a vector. So, you can simply define the conditions, and then combine them logically, like:
<pre><code>condition1 = (df.col1 == 10) & (df.col2 <= 15)
condition2 = (df.col3 == 7) & (df.col4 >= 4)
# at this point, condition1 and condition2 are ... | Have you timed which line of your code is most time consuming? I suspect that the line <code>df = df[~df.isin(df1)].dropna()</code> would take a long time. Would it be faster if you simply use the negation of the condition you applied to obtain <code>df1</code>, when you want to filter away rows in <code>df1</code> fro... | https://datascience.stackexchange.com |
56,737 | [
"https://mathoverflow.net/questions/56737",
"https://mathoverflow.net",
"https://mathoverflow.net/users/450/"
] | A justly celebrated theorem by Ehresmann states that a proper smooth submersion $\pi: X\to S$ between smooth manifolds is locally trivial in the sense that every point $s\in S$ downstairs has a neighbourhood $ U$ such that $\pi ^{-1} (U) $ is $S$-diffeomorphic (=fiber preserving diffeomorphism) to $U\times F$ for some... | Here is a variant of Jason's example with a proof that it is not even topologically locally trivial. Let $T$ be a (complex) manifold that admits a morphism $\phi$ onto $\mathbb P^1=\mathbb P^1_{\mathbb C}$ (or $S^2$ if you prefer) and there exists a point $a\in T$ with $b=\phi(a)\in \mathbb P^1$ such that $\{a\}=\phi^{... | If you drop the properness hypothesis, there are easy counterexamples. For instance, begin with A^1 with coordinate t, and with A^2 with coordinates x and y. Consider the projection p_1: A^1 x A^2 --> A^1, (t,(x,y)) --> t. Now remove the closed subset C = Z(x(x-t),y) as well as the disjoint closed set which is the s... | https://mathoverflow.net |
3,802,548 | [
"https://math.stackexchange.com/questions/3802548",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/572331/"
] | Let <span class="math-container">$\alpha$</span> be the differential 1-form defined by <span class="math-container">$$\alpha = xdy-ydx+zdt-tdz$$</span> and let <span class="math-container">$$i: S^3 = \{(x,y,z,t) \in \mathbb{R}^4 | x^2+y^2+z^2+t^2=1\} \longrightarrow \mathbb{R}^4$$</span> be the inclusion map. I need to... | For any <span class="math-container">$p=(x, y, z, t)$</span> in <span class="math-container">$\mathbb S^3$</span>, the vector
<span class="math-container">$$ v =(y, -x, t, -z)= y\frac{\partial}{\partial x}-x\frac{\partial}{\partial y} + t\frac{\partial}{\partial z}-z\frac{\partial}{\partial t}$$</span>
is in <span clas... | Now <span class="math-container">$i^*\alpha$</span> is a differential, so in polar coordinates it should have
<span class="math-container">$d\theta$</span>s, <span class="math-container">$d\phi$</span>s and <span class="math-container">$d\gamma$</span>s in it. On the sphere
<span class="math-container">$$x=\cos\theta$$... | https://math.stackexchange.com |
2,167,592 | [
"https://math.stackexchange.com/questions/2167592",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/393599/"
] | I need to find all solutions to:
$$\cosh(z) = -1.\,\text{Taking $z=x+iy$, I have the following identities:}$$
$$\cosh(z) = \cosh(x)\cos(y)+i\sinh(x)\sin(y)$$
and
$$\cosh(z) = \frac{1}{2}\left(e^z+e^{-z}\right)$$
Can anyone help please?
| Use the second condition to reduce the problem down to
$$e^z+e^{-z}=-2$$
Add $2$ to both sides:
$$e^z+2+e^{-z}=0$$
Noticing that $e^z+2+e^{-z}=(e^{z/2}+e^{-z/2})^2$, this reduces to
$$e^{z/2}+e^{-z/2}=0$$
Or,
$$e^{z/2}=-e^{-z/2}=e^{\pi i-(z/2)}$$
Hence, we can equate the exponents after accounting for the perio... | $$\cosh(z) = \cosh(x)\cos(y)+i\sinh(x)\sin(y)=-1$$
then
$$\cosh(x)\cos(y)=-1~~~;~~~\sinh(x)\sin(y)=0$$
the second shows $y=k\pi$ or $x=0$. With the first,
if $x=0$ then $\cosh x=1$ so $\cos y=-1$ shows $y=2k\pi+\pi$ that is $z=(2k\pi+\pi)i$.
if $y=k\pi$ then $\cos y=\pm1$ so $\cosh x=\pm1$ shows $x=0$ that is $z=(k... | https://math.stackexchange.com |
187,181 | [
"https://stats.stackexchange.com/questions/187181",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/80438/"
] | For a linear regression model I tried on a dataset, when I fitted OLS, the output is as follows:
<pre><code>fit = lm(price ~., data = art)
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 2.326e+03 8.863e+02 2.625 0.008777 **
# temp_s... | As @RichardHardy says, Ordinary Least Squares (OLS) can be used when you can reasonably assume that your data is homoscedastic. Weighted Least Squares (WLS) can be used when your data is heteroscedastic (but uncorrelated) and Generalised Least Squares (GLS) accounts for correlation and heterscedasticity.
When you c... | Given the regressand ($y$) and the regressors ($x$'s), OLS will by costruction yield the lowest in-sample residual standard error among the linear estimators. After all, OLS <em>minimizes</em> the residual standard error (hence the term "<em>least</em> squares"). You should not be getting a smaller error from WLS than ... | https://stats.stackexchange.com |
64,250 | [
"https://physics.stackexchange.com/questions/64250",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24375/"
] | If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture.
Can you please explain?
| Imagine a heavy chord raised off the ground between two blocks. Rather than consider all of the mass pieces of the rope, and the forces on them, we can simplify the problem a little bit by considering a slightly different one.
The chord can be represented by a heavy ball (in the middle of the chord) connected by two ... | This is a statics problem.
Assume the cable is static, perfectly straight and horizontal.
Pick any point on the cable and <em>the sum of the forces on that point must equal zero.</em>
There is a force, due to gravity, "downward".
So, there must be an equal, opposing force "upward". This upward force must come from... | https://physics.stackexchange.com |
530,744 | [
"https://stats.stackexchange.com/questions/530744",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/309128/"
] | within the framework of an exercise, I have 2 factors: a <code>type of animal</code> & a <code>database</code>
<pre><code>M <- as.table(rbind(c(22000, 2300, 42009,106000), c(380,30,7,260)))
dimnames(M) <- list(Databases=c("database1","database2"), Animals=c("Bird","Dog"... | By inspection, it is pretty clear that <code>Cat</code> is
under-represented in the second database. Let's see
how that plays out in a chi-squared test of your
<span class="math-container">$2\times 4$</span> contingency matrix.
<pre><code>db1 = c(22000, 2300, 42009, 106000)
db2 = c( 380, 30, 7, 260)
M... | A <span class="math-container">$\chi^2$</span>-test would be the obvious choice, especially since you do not seem to have a problem with small cell counts.
| https://stats.stackexchange.com |
463,154 | [
"https://stats.stackexchange.com/questions/463154",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/283012/"
] | I am training an SVM on highly imbalanced data. I have rectified this issue and my ML pipeline works just fine. I have allocated 70% of my dataset for training, however this takes an infeasible amount of time to compute. I read posts about how performance doesn't necessarily grow with the amount of data and sometimes t... | SAT score is discrete, but it is not a count. Not all discrete variables need to be counts. SAT score is an interval variable. Typically, SAT score is treated as a continuous variable in regression models.
| First, for those who don't know, the SAT is a common test in American high schools and is used in college admissions. Scores are integers ranging from 0 to 800.
Now, to the meat of the question: SAT scores aren't really counts - they are computed from the number of right and wrong answers, but the computation is not s... | https://stats.stackexchange.com |
338,393 | [
"https://softwareengineering.stackexchange.com/questions/338393",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30315/"
] | I have to develop a logging system for my project which has multiple features. I am stuck at a choice. I could either make a centralized database and front end for everything. Or I could have one log table for each feature and a common front-end none the less.
Centralized seems like the way to go but it has its disadv... | For the most flexibility, do a combination of both: a single centralized table and individual tables that handle data specific to a particular action or process.
Have one central table to log all basic actions. This could be an individual entry 'Account Payable - Add' or a batch 'Payroll Process.' There could be separ... | I am no expert in logs or database. I would use a logging system like logstash for this, but to answare your question, using a single table with indexes on functionality and level is the best choise, since indexes will give you speed, while having one table will give you flexibility.
For example you could query all err... | https://softwareengineering.stackexchange.com |
557 | [
"https://quant.stackexchange.com/questions/557",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/42/"
] | In my firm we are beginning a new OMS (Order Management System) project and there is a debate whether we use Quickfix or we go for a professional fix engine? Because there is a common doubt that QuickFix is not enough fast and obviously we will not get any technical support. I heard that in BOVESPA it has been used fo... | In order <strong>to answer your question</strong> (for you) <strong>you would need something to compare to</strong>. You would need numbers to know if it is slower/faster, how much, and if it will impact your system overall. Also knowing your performance goals could narrow down the options.
<strong>My advice</strong> ... | How fast do you need? Have you measured round-trip times from the exchange and determined that you need a better solution?
I wouldn't call QuickFix <em>quick</em>; it has a lot of unnecessary overhead (temporary objects, temporary strings, nested functions, etc). But I've used it in projects before without too much tr... | https://quant.stackexchange.com |
58,779 | [
"https://softwareengineering.stackexchange.com/questions/58779",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1525/"
] | So I've got to work with this set of code here for a re-write, and it's written by people who speak both English and French.
Here's a snapshot of what I'm talking about (only, about 4000 lines of this)
<pre><code>function refreshDest(FormEnCours,dest,hotel,duration) {
var GateEnCours;
GateEnCours = FormEnCour... | This isn't going to be that helpful, but I only see two options.
<ol>
<li>Learn French</li>
<li>Refactor</li>
</ol>
I am strongly in favor of the second option. It prevents someone from having to deal with the same issue in the future. It also increases the consistency throughout the code base to a certain style of c... | <blockquote>
<blockquote>
about 4000 lines of this
</blockquote>
</blockquote>
You can probably fix this in a 2 hours with Goggle translate + Search and replace.
Once done, Get your self a beer and add it to your "Black Book of War stories" with proper embellishments.
| https://softwareengineering.stackexchange.com |
136,237 | [
"https://chemistry.stackexchange.com/questions/136237",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/78670/"
] | What is the difference between <span class="math-container">$$\Delta Q$$</span> and <span class="math-container">$$\mathrm dQ$$</span> in thermodynamics? I think one is used when the change is very small and the other with bigger changes, but I am not sure.
| This is not about mere arbitrary notation. It is about fundamental concepts in classical thermodynamics, and the notation flows from these concepts.
So: q and w are not state functions; rather, they are path-dependent. Hence their differential forms are inexact rather than exact. The dyet, <span class="math-container"... | It is rather mathematical than chemical question, as it applies to any continuous and differentiable quantity, not limited to chemistry.
<span class="math-container">$\Delta Q$</span> would be macroscopically measurable exchange of thermal energy. But the convention is we use <span class="math-container">$Q$</span> is ... | https://chemistry.stackexchange.com |
85,836 | [
"https://mathoverflow.net/questions/85836",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20272/"
] | Let <span class="math-container">$R$</span> be a Noetherian ring. By the Hilbert Basis Theorem the polynomial ring <span class="math-container">$R[x_1, \ldots , x_n]$</span> is also a Noetherian ring. What can we say about the number of generators of an ideal <span class="math-container">$I$</span> of <span class="math... | Nothing. Assume $R=k$, a field, for specificity. Then $k[x_1]$ is a principal ideal domain, as you know, but $k[x_1,x_2]$ has ideals with unbounded number of generators. Specifically, $(x_1,x_2)^n$ is minimally generated by $n+1$ elements for all $n$. One can get higher rates of growth by adding more variables.
| Perhaps I should mention that within certain classes of ideals (for example ideals with the same integral closure or radical or some other closure) people do certainly study the minimal number of generators.
For integral closure of ideals (working locally and assuming that the residue field is infinite), then that min... | https://mathoverflow.net |
3,093,811 | [
"https://math.stackexchange.com/questions/3093811",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/301884/"
] | Suppose I have a function <span class="math-container">$$f(x,y)=0$$</span> and suppose I want to find <span class="math-container">$\frac{dx}{dy}$</span> then I think I can get it by doing <span class="math-container">$$\frac{dx}{dy}=\frac{df}{dy}\frac{dx}{df}.$$</span> But I do not understand why do we need to put a n... | The exact rule is
<span class="math-container">$$\frac{\partial f(x,y)}{\partial x}dx+\frac{\partial f(x,y)}{\partial y}dy=0\implies\frac{dy}{dx}=-\dfrac{\dfrac{\partial f(x,y)}{\partial x}}{\dfrac{\partial f(x,y)}{\partial y}}.$$</span>
<hr>
E.g., with <span class="math-container">$$x^2+y^2-1=0$$</span>
<span clas... | <span class="math-container">$f$</span> is a function of <em>two</em> variables. It does not make sense to write <span class="math-container">$\frac{df}{dy}$</span>.
If <span class="math-container">$f(x,y)=0$</span>, the derivative of the implicit function <span class="math-container">$x(y)$</span> is given by:
<span... | https://math.stackexchange.com |
194,676 | [
"https://mathoverflow.net/questions/194676",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20883/"
] | Assume $F, G : \mathbf C \to \mathbf D$ be functors. Denote by $\widehat{\mathbf C} = \mathrm{Fun}(\mathbf{C}^{\mathrm{op}}, \mathbf{Set})$ the category of presheaves of sets on $\mathbf C$. Then, $F$ and $G$ induce "restriction" functors, obtained by composition with $F$ and $G$:
\begin{align*}
\mathrm{Res}_F, \mathrm... | You can recover $F$ from $\mathrm{Res}_F$; this is an exercise in using the Yoneda lemma. Let $H_A$ denote the presheaf represented by an object $A$ of $\mathbf C$ or $\mathbf D$. Then for $A\in \mathbf{C}$ and $B\in\mathbf{D}$ we have $$\operatorname{Hom}_{\mathbf D}(FA,B)=H_B(FA)=\mathrm{Res}_FH_B(A).$$
By Yoneda... | If $\mathcal{C}$ and $\mathcal{D}$ are small then $Res_F$ is right adjoint to $F^>:=Lan_{Y_D\circ F} Y_C$ where $Y_C: \mathcal{C}\to \mathcal{C}^>, Y_D: \mathcal{D}\to \mathcal{D}^>$ are the Yoneda immersion's infact:
$\mathcal{D}^>(F^>(P), Q)=\mathcal{D}^>(\varinjlim_{X\in \mathcal{C}\downarrow F}h... | https://mathoverflow.net |
184,387 | [
"https://dba.stackexchange.com/questions/184387",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/56050/"
] | First, I want to list databases with a specific table:
<pre><code> SELECT name
FROM sys.databases
WHERE CASE
WHEN state_desc = 'ONLINE'
THEN OBJECT_ID(QUOTENAME(name) + '.[dbo].[TB_INF_CLI]', 'U')
END IS NOT NULL
</code></pre>
Then, I want to use the <code>database_name</code> insid... | Although you said you do not like sp_msforeachdb because of multiple result sets, you can use a temp table to avoid it. The following code should work for you
<pre><code>-- return indexes on a table [dbo].[TB_INF_CLI] across all dbs
--drop table ##t
create table ##t (dbname varchar(100), tblname varchar(100), idxname... | If you want to assemble the statement at runtime, you're locked into Dynamic SQL as far as I know. I don't like sp_MSforeachdb as well because it's undocumented and I've ran into bugs with it, so here's an alternative that doesn't require its use:
<pre><code>DECLARE @cmd nvarchar(max) = N'';
SELECT @cmd = @cmd + N'
... | https://dba.stackexchange.com |
242,482 | [
"https://security.stackexchange.com/questions/242482",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/247843/"
] | I stumbled into this recently for a specific project I had in mind. I thought HTTPS would prove that a given content actually came from the origin, by having its contents always signed before transfer. But actually, after the initial handshake, all communications are only secured through an agreed-upon symmetric encryp... | TLS is a two-party communication protocol, and HTTPS is not much more than HTTP over TLS. Its threat model considers only two participants (the client and the server) and its goal is to secure the communication against attackers who might read or modify the data that is exchanged. Non-repudiation does not fit in this t... | <blockquote>
I thought HTTPS would prove that a given content actually came from the origin, by having its contents always signed before transfer.
</blockquote>
Since "content" is sent in both directions, providing non-repudiation would require some cryptographic identity capable of signing on <em>both</em> s... | https://security.stackexchange.com |
139,408 | [
"https://electronics.stackexchange.com/questions/139408",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43765/"
] | characteristic impedance of a transmission line depends on frequency of transmission as can be seen by its expression.
What will be the characteristic impedance of TL if my signal has two frequency components?
What will be its expression?
| Above about 1MHz, normal cable characteristic impedance is fairly contant with frequency as per the equation: -
\$Z_0 = \sqrt{\dfrac{L}{C}}\$ where L and C are inductance and capacitance per unit distance.
The theoretically correct equation for all frequencies is: -
\$Z_0 = \sqrt{\dfrac{R+j\omega L}{G + j\omega C}}\... | You will have two different impedances, one at each frequency. The impedances could be almost the same, depending on the frequencies. Generally these sort of systems are analyzed under the assumption of superposition, only considering one single frequency at a time. If you have a nonlinear transmission line, then th... | https://electronics.stackexchange.com |
212,596 | [
"https://physics.stackexchange.com/questions/212596",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95575/"
] | I have a couple clarifying questions:
(A) in $E=kq/r^2$ for the area between a sphere inside another spherical shell, the sphere inside is considered a point charge. However, the sphere inside has a radius of say $.1 \text{ m}$, if I wanted to find the E-field at the radius value of the inner sphere, would i plug in .... | (A) When using Gauss' law for spherically symmetric systems, $r$ is evaluated at the radius of the Gaussian surface. I understand where the confusion comes from, because in the "standard" equation for the electric field, the distance $r$ is defined as the distance between the point where you're measuring the field an... | For (C), the work done BY the electric field is given by: W = −Δ
However for the work done by an EXTERNAL AGENT in an electric field, it is given by W = Δ
| https://physics.stackexchange.com |
218,604 | [
"https://mathoverflow.net/questions/218604",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31310/"
] | Is it true that the number of carries, when calculating the sum of a finite set of finite positive integers, is constant (i.e. independent of their permutation and the order in which the additions are carried out)? Carries are computed in base 2, so that 1+3 is $01_2+11_2=100_2$, which involves 2 carries: the least si... | In base $b$,
let $G_n$ be the set of $n$-digit integers, thought of as the integers mod $b^n$. Then we have an exact sequence
$$0\rightarrow G_1\rightarrow G_n\rightarrow G_{n-1}\rightarrow 0$$
For $n-1$ digit numbers, the leftmost
carry digit is the two-cocycle associated to this group extension and therefore sat... | For any base $b$, if we add $a$ and $c$ with $k$ carries, then $S_b(a+c)=S_b(a)+S_b(c)-(b-1)k$, where $S_b$ denotes the sum of digits. Since the resulting sum is independent of the order of addition, the total number of carries is independent as well.
| https://mathoverflow.net |
649,311 | [
"https://physics.stackexchange.com/questions/649311",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/306089/"
] | I've looked around quite a bit and can find no definitive explanation of which units to use when utilizing the inverse square (or cube) law. I can find the top level explanation: if you double the distance between a radiative source and the target, the energy is cut by 4, all over the place. But this is a top level e... | It depends on whether you are calculating the <em>ratio</em> of the values of a quantity at two different distances - in which case the unit of distance does not matter since all you need is the ratio of the distances - or whether you are calculating the <em>absolute value</em> of a quantity at a given distance, in whi... | There is a way similar to your method 2), using areas. The surface area of a sphere is <span class="math-container">$4\pi{r}^2$</span>, so if you do a <span class="math-container">$\pi r^2$</span> for the earth and divide by <span class="math-container">$4\pi{r_s}^2$</span> where <span class="math-container">$r_s$</sp... | https://physics.stackexchange.com |
228,093 | [
"https://softwareengineering.stackexchange.com/questions/228093",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/60189/"
] | Is it a good practice to put bug numbers in the file itself inside a header comment?
The comments would look something like this:
<pre><code> MODIFIED (MM/DD/YY)
abc 01/21/14 - Bug 17452317 - npe in drill across in dashboard edit mode
cde 01/17/14 - Bug 2314558 - some other error description
</code></pre>
It... | I've seen this done before, both manually by authors and automatically by scripts and triggers integrated with version control systems to add author, check-in comment, and date information to the file.
I think both methods are pretty terrible for two primary reasons. First, it adds clutter and noise to the file, espec... | There is exactly one case where I would do this, namely as part of a warning for future programmers: "Don't call function <code>foo()</code> here directly; this has caused bug #1234, namely ...", and then a short description of the bug follows.
And if the code has changed in a way that there is no temptation to call <... | https://softwareengineering.stackexchange.com |
2,053 | [
"https://security.stackexchange.com/questions/2053",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/33/"
] | If I were to run more than one VPN clients on my machine, simultaneously, what risks would be involved?
E.g. are there technical conflicts, such that it wouldn't work right?
Could there be address resolution conflicts?
More scary, can traffic from one network cross over, via my machine, into the other network?... | I've used VPN client software on Mac OS X that hijacks the default route to send all traffic through the tunnel (actually, if memory serves me correctly, that was Cisco's). If two such clients were installed, or even one and a sane client, then the answer to the question "where will this packet go?" will be timing and ... | On a quite fundamental level, a VPN emulates a "private network" whose purpose is to be isolated from the Internet at large. The "V" means that such isolation is performed cryptographically rather than physically; however, the model is still "separate cables". If your machine is part of two VPN simultaneously, then the... | https://security.stackexchange.com |
68,844 | [
"https://physics.stackexchange.com/questions/68844",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21817/"
] | Since any source of light will have a finite duration, the light emited won't have a particular frecuency. It will be a sum of different frequencies (infinite, I think) if we apply Fourier's series (integral).
Would this mean that any photon's frequency will have some uncertainty or something like the photon emitted w... | If you look at it from the quantum mechanical point of view you might invoke the energy-time uncertainty relation, which for a foton might become:
$\Delta\omega\Delta t \geq \frac{1}{2}$.
Which says that for very short times the uncertainty on the frequency can become very large.
| I don't think it is a combination of different photons. I think the uncertainty of the frequency is lower if the duration is longer.
| https://physics.stackexchange.com |
82,055 | [
"https://chemistry.stackexchange.com/questions/82055",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/38636/"
] | <blockquote>
Calculate the number of atoms of oxygen present in $\pu{1.3 mol}$ of $\ce{H_2SO_4}$
</blockquote>
1 mol has $6.02\times 10^{23}$ atoms
So $\pu{1.3 mol}$ must have $1.3 \times 6.02 \times 10^{23} = 7.826 \times 10^{23}$ atoms
<hr>
Since there are 4 oxygen atoms out of 7 atoms in total in $\ce{H_2SO_4... | The key about the unit <em>mole</em> is that it does not reference which type of entity is specified. Using the mole only makes sense if you define what you are using the mole for. This could be:
<ul>
<li>protons</li>
<li>atoms</li>
<li>ions</li>
<li>molecules</li>
<li>formula units of an ionic or metallic solid</li>
... | There are 1.3 mol of the entire acid molecule, so there are four as many moles of oxygen as there are of the acid, because one acid contains four oxygens.
$4×1.3=5.2$ and 5.2 times Avogadro's constant is (about) $3.1×10^{24}$ atoms.
Your error is in dividing by seven, which is neither conceptually nor mathematically ... | https://chemistry.stackexchange.com |
219,272 | [
"https://physics.stackexchange.com/questions/219272",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17338/"
] | I don't know the connection between how forming a new bond with oxygen then changes the density of states to transform the metal into an insulator. It seems like a very powerful transformation.
| Metals are good conductors of electricity because the outer (valence) electrons of the metal atoms are only loosely bound to the nucleus and form molecular orbitals known as the <em>conduction band</em>. Electrons can move more or less freely through the conduction band and so metals conduct electricity generally well.... | It's because valence electrons are bounded. For example, consider Si and SiO2. While Si is semiconductor, SiO2 is insulator because it has no free valence electrons. BTW, many metal oxides ARE NOT in fact insulators - for example ZnO, Fe3O4 are all conductors. But it's true that oxides of metals have lower conductivity... | https://physics.stackexchange.com |
183,013 | [
"https://physics.stackexchange.com/questions/183013",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/80827/"
] | Let $$\langle x'|p'\rangle = N \exp(\frac{ip'x'}{\hbar})$$ be the overlap between position and momentum space, where $N$ is a normalization constant to be determined.
We can then compute $N$ by
$$
\langle x'|x''\rangle = \int \mathrm{d}p'\langle x'|p'\rangle \langle p'|x''\rangle\\
\rightarrow \delta(x'-x'')=|N|^2 \i... | You're close, but you seem to be saying that $\exp(ikx) = \delta(x)$, which is not true, and you're missing a $2\pi$. The correct identity is
$$\int dk\ e^{ikx} = 2\pi \delta(x)$$
Therefore, with a change of variables $p=\hbar k$:
$$\int dp\ e^{ipx/\hbar} = \hbar \int dk\ e^{ikx} = 2\pi\hbar$$
| You can express the dirac-delta-function as:
$$\delta(x-x')=\frac{1}{2 \pi}\int dp e^{i p (x-x')}$$
(simply fourier-transform the dirac-function)
compare it with your expression and you get the factor.
p.s Your last line from intermediate step is wrong.
| https://physics.stackexchange.com |
195,142 | [
"https://electronics.stackexchange.com/questions/195142",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88943/"
] | Why do we also use magnetometers when building IMUs, that is why don't we simply and only use gyroscopes and accelerometers?
I also would like to know how does a magnetometer work as a 3-axis device?
Furthermore, how are the three sensors working together?
| Accelerometers can itself measure the inclination, they have a slow response. Gyros measure angle rate change, fast response, but the problems for gyros is the zero drift and it has to be compensated for any usable application.
While at steady state, a filter is used such that accelerometers track and eliminate t... | There is also Mahony's Algorithm, besides many versions of Kalman Filters can use magnetometers readings to correct gyro bias and long therm drift.
The Mag readings are used in a similar manner to those from Accelerometers
| https://electronics.stackexchange.com |
84,180 | [
"https://mathoverflow.net/questions/84180",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13731/"
] | I have the following question:
For a given two-dimensional Riemann surface $C$,
<ol>
<li>Is there a way to classify all topologically distinct
three-dimensional compact manifolds $M$ whose boundary is $C$,
i.e., $\partial M =C$?</li>
<li>Is there always a three-dimensional compact manifold
$M$ such that $\partial M =... | <ol>
<li>When you say "Riemann surface", do you mean "topological surface"? Does the Riemann surface structure have any significance?</li>
</ol>
I assume below that you mean "two-manifold"
<ol>
<li>Well, any three manifold contains a handlebody of your favorite genus, so this question is at least as hard as classifyi... | (1) Consider the case where C is a sphere. For any such manifold, we can just add a 3-dimensional ball to get a closed compact 3-fold. So in this case it's just the classification of closed compact 3-folds.
For the torus, it's slightly more compact. One can again add a donut, so the problem includes the classification... | https://mathoverflow.net |
12,286 | [
"https://physics.stackexchange.com/questions/12286",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3066/"
] | Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The observers don't know the exact color (state) of their balls, they know only the probability of having one or another color, un... | Quantum entanglement is different from the "classical entanglement" in the following way:
<ul>
<li>In your example, each ball has only one property of interest, namely "color $\in$ {white, black}".</li>
<li>In the traditional examples of quantum entanglement, each ball (particle) has <strong>two</strong> properties of... | It is somewhat analogous, but the analogy fails because of Bell's theorem. Bell uses a similar analogy with "Bertlmann's socks", when you see one sock is white, and assuming they match, you learn the other is white instantly.
But let us say Bertlmann has three feet, and tries to wear three matching socks, but he doesn... | https://physics.stackexchange.com |
396,411 | [
"https://electronics.stackexchange.com/questions/396411",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/174733/"
] | If a laptop forced to drag out more current than the power supply can provide at the given voltage (i.e. 20 volts), the voltage does decrease, usually approximately anti-proportionally if I am correct.
For a 100W (20V 5A) power supply, it is U[V]=(20×5)/I[A] starting at 5 ampères:
<ul>
<li>5A 20V</li>
<li>6.25A 16V (... | <blockquote>
Which one is the reason for the drop of the voltage?
</blockquote>
This question is a conceptual mix-up. Nothing happens "naturally" without getting out of specifications. Power supplies are not "constant power supplies", they are either "constant voltage", or "constant current". It is difficult to desi... | Laptop chargers seem to use the flyback principle. That is: The voltage in the output capacitor is observed. Every time it seems to be too low (there's a drop treshold well below 1V, say 100mV) a new current pulse is injected to the output capacitor to rise the voltage back to the acceptable level.
Injecting a pulse i... | https://electronics.stackexchange.com |
40,248 | [
"https://softwareengineering.stackexchange.com/questions/40248",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1338/"
] | Imagine to have this code:
<pre><code>class Foo:
def __init__(self, active):
self.active = active
def doAction(self):
if not self.active:
return
# do something
f=Foo(false)
f.doAction() # does nothing
</code></pre>
This is a nice code; I actually have (not in Python) a global active variable ... | I believe both have their place; depending on where the on/off logic should reside.
I would use the first <em>more encapsulated</em> case if the check should be local to Foo, e.g. if it was a connection state for the internals of Foo for example.
The second <em>external check</em> case makes more sense if the caller ... | Your first example is valid OO, and could be used for many things like being sure a connection is open, etc. I'm not sure if it has a name.
The second example is ok. Not really a pattern in my mind, just a condition check before performing an action. (Well, I guess Sequence, Selection, Iteration is a pattern.)
Both m... | https://softwareengineering.stackexchange.com |
21,587 | [
"https://dba.stackexchange.com/questions/21587",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7104/"
] | Recently updated my machine from Mac OS X Lion (10.7.4) to Mountain Lion (10.8) and I think it borked my PostgreSQL installation. It was installed originally via Homebrew. I'm not a DBA, but hoping someone can tell me how to troubleshoot this.
I am unable to connect (but was able to before pre-Mountain Lion):
<pre><c... | I found that I had an extremely similar problem, namely that postgres was opening a socket in <code>/var/pgsql_socket_alt</code> where none of my software expects to look, but the solution to my problem was not only a problem with my <code>$PATH</code>.
I had to create the directory <code>/var/pgsql_socket</code>, cho... | A plausible and typical explanation would be that the <code>psql</code> that comes with homebrew is in <code>/usr/local/bin/psql</code> which is different from the one that would be in your $PATH, like <code>/usr/bin/psql</code> (bundled with OS X).
You may want to try with the full path:
<code>$ /usr/local/bin/psql ... | https://dba.stackexchange.com |
32,158 | [
"https://stats.stackexchange.com/questions/32158",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12531/"
] | I have a series of daily log returns and I am looking to fit them to an AR() process.
Any suggestions?
| The key question is "have the test examples in the final cross-validation been involved in selecting <strong>any</strong> aspect of the model"; if the answer is "yes" then the performance estimate is likely to be biased. If the answer is "no" then it is probably unbiased.
For example nested cross-validation is fine (... | There is a difference between repeated cross-validation and nested-cross validation. The latter is useful for determining hyper-parameters and selecting features.
I've seen a couple of recent papers about the bias-variance implications of repeated cross-validation. Rodriguez and Lozano (IEEE T.PAMI 2010) test on ar... | https://stats.stackexchange.com |
332,567 | [
"https://softwareengineering.stackexchange.com/questions/332567",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/248279/"
] | For example, if I have a method
<pre><code>public void method(Pair<String, Object> pair){
...
}
</code></pre>
Should I create the method
<pre><code>public void method(String str, Object obj){ this.method(new Pair<>(str, obj); }
</code></pre>
if it is <strong>not</strong> to maintain an existing API?... | The second approach is hiding the dependency on <code>Pair</code>, which may or may not be desirable.
To decide which one is better, you'd have to know what is more likely for the user of that method: to have a <code>Pair</code> object already constructed or to have its individual pieces, because that's when the diffe... | I always focus on how code is used. You'd like to go from using:
<pre><code>foo.method(new Pair(str, obj));
</code></pre>
To using:
<pre><code>foo.method(str, obj);
</code></pre>
To which I say: <code>foo</code> and <code>method</code> are terrible names! At least I know what a <code>Pair</code> is.
By which I me... | https://softwareengineering.stackexchange.com |
2,105,390 | [
"https://math.stackexchange.com/questions/2105390",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/343408/"
] | Integral related to Pythagoras theorem
Triangle ABC is a right angle triangle, where Angle $ABC=90^o$.
$h$ is perpendicular to the hypotenuse AC and meet at angle ABC.
Where $a$ and $b$ are two small sides
How can I Show that h can be represented in term of this integral $(1)$
<blockquote>
$${2\over \pi}\int_{0}... | Hint: Observe if you have a right triangle with legs $a, b$ and $h$ is as specified, then we see that
\begin{align}
\text{Area} = \frac{a\cdot b}{2} = \frac{h\cdot \sqrt{a^2+b^2}}{2} \ \ \Rightarrow \ \ h^2 = \frac{a^2b^2}{a^2+b^2}.
\end{align}
One can show that the integral
\begin{align}
\frac{2}{\pi}\int^\infty_0 \... | Let
$$ I=\int^\infty_0 \frac{dx}{(a^2+b^2x^2)(b^2+a^2x^2)}.\tag{1}$$
Changing variable from $x\to\frac1{x}$ gives
$$ I=\int^\infty_0 \frac{x^2dx}{(a^2+b^2x^2)(b^2+a^2x^2)}.\tag{2}$$
So $a^2$(1)+$b^2$(2) gives
$$ a^2I+b^2I=\int^\infty_0 \frac{dx}{b^2+a^2x^2}=\frac{\pi}{2ab}$$
and hence
$$ I=\frac{\pi}{2ab(a^2+b^2)}.$$
S... | https://math.stackexchange.com |
47,797 | [
"https://datascience.stackexchange.com/questions/47797",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/56922/"
] | I am working on a CNN model. As always, I used batches with epochs to train my model. When it completed training and validation, finally I used a test set to measure the model performance and generate confusion matrix. Now I want to use Cross Validation to train my model. I can implement it but there are some questions... | <blockquote>
<strong>Question 1: Why do most CNN models not apply the cross-validation technique?</strong>
</blockquote>
<span class="math-container">$k$</span>-fold cross-validation is often used for simple models with few parameters, models with simple hyperparameters and additionally the models are easy to optimi... | The previous answer already got accepted, but I am answering this question just to make sure that things are clear. I will go one step deeper which can be helpful to advanced people.
First of all, cross validation is a model selection mechanism that is used mainly to select hyperparameters. Changing hyperparameters wi... | https://datascience.stackexchange.com |
8,292 | [
"https://mechanics.stackexchange.com/questions/8292",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1865/"
] | I have a manual shift honda civic.
How would I or the motor mechanic know that the clutch pads need replacing?
Would they check it during oil change? Certainly you don't open the transmission box to check the clutch pads during an oil change.
How long would they usually last under normal usage? Do they even wear out... | The life of the clutch all depends on how it's driven. A clutch driven in the hills of San Francisco is not going to last nearly as long as one driven on the plains of Texas. Yes, the pads do wear out over time. It usually isn't hard to tell when they start to go. You will notice more slippage when taking off from a st... | You will feel any of the following
<ul>
<li>"Slippage"</li>
<li>Engaging the clutch will be very high on the clutch pedal. </li>
<li>Squishy clutch</li>
<li>A foul smell</li>
<li>Trouble changing gears</li>
</ul>
A test that I do is to find a nice stretch of road, and go into 1st. Get the revs up really high, and jum... | https://mechanics.stackexchange.com |
43,380 | [
"https://mechanics.stackexchange.com/questions/43380",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/26868/"
] | I have a 2010 Audi A4 2.0T Quattro. Here are the facts:
<ol>
<li>I had an oil change several months ago performed by a shop that is quite familiar with this kind of car and has a very good reputation.</li>
<li>About a month after the oil change, my Audi suddenly complained that it was very low on oil. I should add a q... | It's a known problem that Audi had a manufacturing defect between 2009 - 2011 on ALL 2.0T Petrol engines. They ALL use oil and to fix it you need to pull the whole engine out and do a complete rebuild with new pistons, piston rings, gaskets etc. I did this a year ago on my 2010 one in NZ and it cost $8000. Audi is awar... | Using the dip stick if you actually did see that the oil was low, then definitely there is a problem, There is a possibility that the piston rings may be leaking oil into the combustion chamber thus burning oil along with gas. Piston rings are like rubber seals around the piston that block the oil getting in to the com... | https://mechanics.stackexchange.com |
142,357 | [
"https://cs.stackexchange.com/questions/142357",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/139680/"
] | This seems to be my first ever question :)
Given that adjacency lists store all the necessary information with regards to the endpoints of an edge, we could even store a weight alongside that.
I don't understand why we would ever want to use an Edge List in a way that would be more useful than the above mentioned Adjac... | Any primitive operation that can be done with edge list, also can be done in adjacency list, but the main difference between them is time complexity of the primitive operations, for example, when you want find all adjacent vertices to some vertex <span class="math-container">$v$</span> the time complexity is <span cl... | <blockquote>
Is that something we can't accomplish with some other representation?
</blockquote>
Edge list and adjacency list represent the same thing so if you can do something with one, you can do it with the other. In the worst case, you will have to convert one to the other.
<h2>Storage</h2>
When it comes to space,... | https://cs.stackexchange.com |
139,372 | [
"https://physics.stackexchange.com/questions/139372",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46740/"
] | My textbooks at the moment don't really explain the underlying theory of circuits. All I do is apply the rules I was taught when I solve these problems. I don't get why electrons need to have a closed loop in order to want to flow.
The circuit I'm analysing right now is an RC circuit. The battery in the circuit is rem... | Your question has two parts.
First addressing why electron needs a closed loop to flow-
Consider a wire which is not closed for e.g in the diagram.
Here Due to the electric field(marked in green) the electrons move to the right.But after some time the electrons accumulate in the right forms their own electric field w... | Why does current need a closed loop to flow? Not in every case you need a closed circuit.
A good example that current in an open "circuit" can flow is the antenna rod. A generator generates an alternating current and the electrons in the rod moves and there is an electric flow.
| https://physics.stackexchange.com |
345,417 | [
"https://physics.stackexchange.com/questions/345417",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/161071/"
] | Can I replace the derivative operator in the Dirac equation with momentum?
$$ (i\gamma^\mu\partial_\mu - m)\psi(x) = 0 $$
$$ (\gamma^\mu p_\mu - m) \tilde{\psi}(p) = 0$$
| If we posit a solution to the Dirac equation of the form,
$$\psi = u(\vec p)e^{-ip\cdot x}$$
then one finds that the four-component spinor $u(\vec p)$ must satisfy the equation,
$$(\gamma^\mu p_\mu -m) u(\vec p) = 0$$
and we call such a solution a positive frequency solution. Furthermore, we can also make the subst... | Short answer: yes you can!
Long answer: in the Dirac equation those derivatives are actually the covariant derivatives of a 4 component coordinate vector denoted usually by $X:(x_0,x_1,x_2,x_3)$. So if we want to be consistent, that momentum which you want to obtain by considering that $-i\hbar d/dx_i\to p_i$ is the <... | https://physics.stackexchange.com |
81,012 | [
"https://mathoverflow.net/questions/81012",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13284/"
] | This should be rather standard so I hope somebody with a good background in probability theory would give me a quick solution or a reference.
We are given a threshold positive integer $T>0$. Let $a_1=1$ and for all $k$ with probability one half set $a_k=3a_{k-1}$ or else $a_k=2a_{k-1}$. We will stop the process at ... | From the way you ask, I conclude that you can prove that the limit exists (which by itself is by no means trivial), so I'll just show how to compute it under this assumption.
Let $v(t)$ be $\frac 1t$ times the expectation in question if we stop after we exceed $t>0$ (not necessarily an integer). Then $v(t)=\frac 1t... | I think it is possible to find the result using renewal theory. Indeed, the process $(\ln(a_i))$ is a random walk with i.i.d. increments ($\ln(2)$ or $\ln(3)$ with probability $1/2$). The renewal theorem will tell you the structure of the walk when it jumps over a large time (here $\ln(T)$). More precisely when $T \to ... | https://mathoverflow.net |
156,616 | [
"https://dba.stackexchange.com/questions/156616",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/55822/"
] | I have a series of update statements that follow a general pattern: one update aggregates values from another table (or sometimes multiple tables), the next update produces a rank based on the aggregated values. This process is repeated 23 times for a total 46 update statements. Each update couplet takes 30-40 seconds ... | <h2>Debunking</h2>
If you are doing all your updates in the same transaction, each of them will have to work an increasingly bigger set of (physical) tuples. See the following example:
<pre><code>CREATE TABLE explode (id integer, something text);
INSERT INTO explode SELECT i, md5(i::text) FROM generate_series(1, 10... | The following query should perform much better than the original and, importantly, should return the <em>correct</em> result:
<pre><code>WITH union1and2 As (
Select int_id, injurycrash, false As aggressive_driverfault, ...
From crashes_bike1
Union All
Select int_id, injurycrash, aggressive_driverfault,... | https://dba.stackexchange.com |
47,596 | [
"https://cs.stackexchange.com/questions/47596",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/34905/"
] | According to CLRS,
<blockquote>
When the edges of the graph are static—not changing over time—we can
compute the connected components faster by using depth-first search.
</blockquote>
However, I tried to do some runtime analysis, and in a graph $G(V, E)$ on which we have to answer $Q$ connectivity queries.
DFS w... | Your running time analysis of Union-Find is incorrect. To use Union-Find for this situation, we need to perform $V$ MakeSet operations, $E$ Union operations, and $2Q$ Find operations. Each operation takes $O(\alpha(V))$ amortized time. Therefore, the total running time for the Union-Find-based algorithm will be $O(\... | When the graph is dynamic, union-find can update the list of connected components in time $O(\alpha(V))$ per vertex or edge, whereas it is not clear how to run DFS progressively. So we can complement the statement you quote by
<blockquote>
When the edges of the graph are dynamic – changing over time – DFS is not a g... | https://cs.stackexchange.com |
2,931,034 | [
"https://math.stackexchange.com/questions/2931034",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/597218/"
] | I will buy a car or take a vacation.
I will buy a car.
Therefore, I will not take a vacation
What is this form called? Is it valid or invalid?
I understand the form to be
"P or Q.
P.
Therefore ~Q."
But what is this form called?
| Observe that <span class="math-container">$$\begin{align}0.162162162\ldots &= 0.162 + 0.000162 + 0.000000162 + \cdots\\ &= 0.162(1 + 0.001 + 0.000001 + \cdots)\\ &= 0.162(1 + {1\over 1000^1} + {1\over 1000^2} + \cdots) \\ &= 0.162\left[\sum_{n=0}^\infty\left({1\over 1000}\right)^n\right]\\ &=0.162\l... | <span class="math-container">$$.162162162... = .162+.162(10^{-3})+.162(10^{-6})+...$$</span>
<span class="math-container">$$ = \frac {.162 }{1-0.001} = \frac {162 }{999} = \frac {6 }{37} $$</span>
| https://math.stackexchange.com |
88,759 | [
"https://physics.stackexchange.com/questions/88759",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29955/"
] | Let $T$ be the time-ordering operator which orders operators $A_1(t_1), A_2(t_2), \ldots$ such that the time parameter decreases from left to right:
$$T[A_1(t_1) A_2(t_2)] = A_2(t_2) A_1(t_1) \text{ if } t_2 > t_1 \text{ and }= A_1(t_1)A_2(t_2) \text{ otherwise. } $$
The time $t_i$ does not have to be a physical ... | Hint
$\int_0^t \int_0^{t_1} dt_1 dt_2 \, a(t_1) a(t_2) = \frac{1}{2!} \int_0^t\int_0^t dt_1 dt_2\, \mathcal{T}\{ a(t_1) a(t_2) \}$
and so forth. You can see this by noting that the (square) integration region in the second integral can be split up into two triangular integration regions like in the first integral.... | Hints to the question (v1):
<ol>
<li>Recall that the operator time ordering is symmetric
$$\tag{1}T[A_1(t_1)\ldots A_n(t_n)]~=~T[A_{\pi(1)}(t_{\pi(1)})\ldots A_{\pi(n)}(t_{\pi(n)})], $$
where $\pi\in S_n$ is a permutation. (Here we assume for simplicity that all operators are Grassmann-even. Else there will be additio... | https://physics.stackexchange.com |
2,812,122 | [
"https://math.stackexchange.com/questions/2812122",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/568291/"
] | <blockquote>
For any real numbers $x$ and $y$ satisfying $x^2y + 6y = xy^3 +5x^2 +2x$, it is known that $$(x^2 + 2xy + 3y^2) \, f(x,y) = (4x^2 + 5xy + 6y^2) \, g(x,y)$$<br>
Given that $g(0,0) = 6$, find the value of $f(0,0)$.
</blockquote>
I have tried expressing $f(x,y)$ in terms of $g(x,y)$. But seems that some ... | first we shall see that:
$\frac1n\sum_{\omega:\omega^n=1} \omega^{-\alpha}f(\omega) = \frac1n\sum_{\omega:\omega^n=1}\omega^{-\alpha }\sum_{j}a_j\omega^j = \frac1n\sum_{\omega:\omega^n=1}\sum_{j}\omega^{j-\alpha }a_j =$
$ = \frac1n\sum_{j}\sum_{\omega:\omega^n=1}\omega^{j-\alpha }a_j$
I'm leaving for you to think w... | This formula comes from Thomas Simpson's Series Multisection Theory. Speak in the concrete，
a multisection of the series of an analytic function
<span class="math-container">$$f(z) = \sum_{n=0}^\infty a_n\cdot z^n.$$</span>
has a closed-form expression in terms of the function <span class="math-container">$f(x)$</... | https://math.stackexchange.com |
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