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
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106,378 | [
"https://physics.stackexchange.com/questions/106378",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/43704/"
] | Assume that a coin is placed on circular disk and now a disk is rotated with constant angular velocity.
If there is no friction between the surfaces of a disk and coin, according to theory the coin will move away from centre of disk. But I have confusion here that the centripetal and centrifugal forces are of equal ma... | The coin will not move.
First, to differentiate between centrifugal and centripetal, I'll start by stating the definitions first.
<em>Centrifugal force is the apparent force that draws a rotating body away from the center of rotation. It is caused by the inertia of the body as the body's path is continually redirecte... | Here, because the coin is placed at the center, the centrifugal forces balance each other. Every point mass in the coin has it's conjugate point at the diameter passing through it and on the same distance from the center on the other side.
Hence the coin is under equilibrium and does not fly off.
| https://physics.stackexchange.com |
470,202 | [
"https://physics.stackexchange.com/questions/470202",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | The entropy <span class="math-container">$S$</span> of a system is defined as <span class="math-container">$$S = k\ln \Omega.$$</span> What precisely is <span class="math-container">$\Omega$</span>? It refers to "the number of microstates" of the system, but is this the number of <em>all</em> accessible microstates or ... | Entropy is a property of a macrostate, not a system. So <span class="math-container">$\Omega$</span> is the number of microstates that correspond to the macrostate in question.
Putting aside quantization, it might appear that there are an infinite number of microstates, and thus the entropy is infinite, but for any le... | Entropy logarithmically measure of the number of microscopic states corresponding to some specific macroscopically-observable state, not the system as a whole. Put another way: systems that have not yet found their equilibrium state, when left alone, increase their entropy. This would not be possible if the system had ... | https://physics.stackexchange.com |
647,899 | [
"https://physics.stackexchange.com/questions/647899",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/221747/"
] | <blockquote>
The Zeroth Law of Thermodynamics states that if two systems are in thermodynamic equilibrium with a third system, the two original systems are in thermal equilibrium with each other.
</blockquote>
It says that they reach the same temperature after an infinite amount of time. Why can't we quantify this time... | In the simplest model of heat transfer, the rate of heat transfer is proportional to the temperature difference between the two systems. This gives an exponential temperature curve, for which the temperature difference between the two systems approaches zero as closely as we like, but never reaches zero.
This is, howev... | The zeroth law of Thermodynamics is speaking about systems already at thermodynamic equilibrium. It does not say anything about the time required to get equilibrium. The equilibration time depends on the efficiency of the exchanges of energy (not only thermal exchanges but also volume variations and particle exchanges,... | https://physics.stackexchange.com |
41,883 | [
"https://mathoverflow.net/questions/41883",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5513/"
] | Let $G$ be an abelian group, $A$ a trivial $G$-module. We know that $\text{Ext}(G,A)$ classifies abelian extensions of $G$ by $A$, whereas $H^2(G,A)$ classifies central extensions of $G$ by $A$. So we have a canonical inclusion $\text{Ext}(G,A)\hookrightarrow H^2(G,A)$. Is there some naturally arising exact sequence/s... | You get a description from the universal coefficient theorem which gives a (split) exact sequence
$$
0\to \mathrm{Ext}(H_1(G),A) \to H^2(G,A) \to \mathrm{Hom}(H_2(G),A) \to 0
$$
and the fact that $H_1(G)=G$. We have that $H_2(G)=\Lambda^2G$ and the map $H^2(G,A) \to \mathrm{Hom}(H_2(G),A)$ associates to an extension it... | Let $G$ and $A$ be groups and assume that $R \rightarrowtail F \twoheadrightarrow G$ is a presentation of $G$.
Then, by a general theorem of MacLane, there is an exact sequence
$\textrm{Hom}(F_{ab}, A) \to \textrm{Hom}(R/[R,F], A) \to H^2(G, A) \to 0$.
Moreover, if $G$ and $A$ are Abelian there is an exact sequence ... | https://mathoverflow.net |
113,830 | [
"https://physics.stackexchange.com/questions/113830",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/47020/"
] | I have came across two separate explanations for why atoms have a positive atomic radius (as opposed to electrons "collapsing" into the nucleus).
<ol>
<li>The first is via Heisenberg Uncertainty Principle, where decreasing the atomic radius would raise momentum and hence kinetic energy (while potential energy decreas... | The first explanation is just a quick argument to avoid doing calculations proposed in the second explanation.
As you're looking for ground state of the system, you want to minimize energy $\langle \psi | \hat{H}| \psi\rangle$. Now, from commutation relations between position and momentum operators $[\hat{q},\hat{p}] ... | "Are these two explanations just two sides of a single coin/a matter of interpretation?"
- No, they aren't.
First of all solvin Schrödinger's equation gives correct energy for the ground state, but using Heisenberg's uncertainity principle can give only a rough estimate and it even fails if you assume that electron co... | https://physics.stackexchange.com |
337,288 | [
"https://physics.stackexchange.com/questions/337288",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/148682/"
] | The properties of the projection operators are defined as:
$$P_+ = \frac{1}{2}(1+\gamma^5)$$
$$P_- = \frac{1}{2}(1-\gamma^5)$$
where $\gamma^5 = -i\gamma^0\gamma^1\gamma^2\gamma^3$
and their key properties are that $P_+^2 = P_+, P_+P_- = 1, P_-^2 = P_-$.
But since $\gamma^0$ has the same property as $\gamma^5$ that... | Please note that the transition function $t_{NS}$ defined on the equator $U_N \cap U_S \approx S^1$ of the bundle $P(S^2, U(1))$ is given by the formula:
$$ t_{NS}(\phi) = \exp[i\varphi(\phi)] \qquad (\varphi:S^1\to \mathbb R) \tag{10.90}$$
and it is periodic in the azimuthal angle $\phi\ $: $\ t_{NS}(\phi +2\pi) \eq... | It is just a matter of convention. Nakahara uses the gauge covariant derivative <span class="math-container">$D_\mu \phi = ( \partial_\mu + \mathcal{A}_\mu ) \phi$</span> in the chapter. This is equivalent to the common definition <span class="math-container">$D_\mu \phi = ( \partial_\mu + i e/\hbar A_\mu ) \phi$</span... | https://physics.stackexchange.com |
7,672 | [
"https://engineering.stackexchange.com/questions/7672",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/5257/"
] | Is there a good way to estimate the power consumption of an oven/heating device given the volume of the oven? I'm trying to do really, really dirty/quick math - I know that the average oven uses probably between 2-4000 Watts, but I'd be looking for a similar estimate with a volume of about 1.3 cubic <em>inches,</em> so... | If you can make a guess at the interior and exterior surface temperatures, then you can use the following simplified steady-state equation for conduction through an arbitrary shape. It is from A.F. Mills, "Heat Transfer 2nd Edition", equation 3.32:
$$
\dot{Q} = k \Delta T \sum_i S_i
$$
where $\dot Q$ is the rate of ... | The volume, in itself, doesn't make much of a difference as this just determines the mass of air that you need to heat and air has quite a small specific heat capacity.
However the volume is directly related to the external surface area, which will have a significant effect. Assuming that the walls of your oven are r... | https://engineering.stackexchange.com |
608,372 | [
"https://physics.stackexchange.com/questions/608372",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/286076/"
] | If a jet engine is bolted to the equator near ground level and run with the exhaust pointing west, does the earth speed up, albeit imperceptibly? Or does the Earth's atmosphere absorb the energy of the exhaust, and transfer it back to the ground, canceling any effect?
| It's the latter. Look at the system earth + engine + atmosphere. Conservation of angular momentum must hold for the whole system (assume no gases leave the atmosphere due to the engine, which is a fair assumption).
| Briefly, the Earth's rotation rate will change; and the net rotation rate of the atmosphere will change in the opposite way. But very soon, friction between the air and the ground will ensure that the air and ground have no net rotation difference, which means that the Earth's rotation will return to the original rate... | https://physics.stackexchange.com |
297,476 | [
"https://softwareengineering.stackexchange.com/questions/297476",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/196878/"
] | I want to write a program in Python that illustrates the tree-like nature of recursion. Given a recursive function (for instance fibonacci(n)) there should be a way to print the tree-like call trace of the recursive function. With the following function:
<pre><code>def fibonacci(n):
if n == 1 or n == 2:
retu... | You can't just modify <code>fibo</code> to get what you want. For instance, the order in which the different calls to <code>fibo</code> happen is not the one in which you have to write their arguments to the console, and because you don't know the width of your tree to begin with, you don't know how far to the right t... | You can pass another argument to the recursive function that starts from 0 and increments by 1 in every call in order to determine the depth of recursion tree. Then you can use stacks to store "function(x)" strings and finally print them according to depth.
e.g. fibo(5,0) -> fibo(4,1),fibo(3,1) -> fibo(3,2),fibo(2,2),... | https://softwareengineering.stackexchange.com |
328,495 | [
"https://mathoverflow.net/questions/328495",
"https://mathoverflow.net",
"https://mathoverflow.net/users/101861/"
] | Tannakian formalism tells us that for any rigid, symmetric monoidal, semisimple category <span class="math-container">$\mathcal{C}$</span> equipped with a fiber functor <span class="math-container">$F: \mathcal{C} \to Vect_k$</span> for a field <span class="math-container">$k$</span> (of characteristic <span class="mat... | Another criterion is that there should be only finitely many objects of bounded dimension. This condition might be easy to check in practice from abstract finiteness theorems. The proof is that, if the group is not semi simple, you can take any 1-dimensional character of the identity component and induce up to the main... | In order for <span class="math-container">${\mathcal C}$</span> to come from an algebraic group rather than a pro-algebraic one, you want <span class="math-container">${\mathcal C}$</span> to be finitely generated. And for semisimplicity, you want the group to have finite center. The center can be read off from the cat... | https://mathoverflow.net |
21,866 | [
"https://physics.stackexchange.com/questions/21866",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4521/"
] | Undergraduate classical mechanics introduces both Lagrangians and Hamiltonians, while undergrad quantum mechanics seems to only use the Hamiltonian. But particle physics, and more generally quantum field theory seem to only use the Lagrangian, e.g. you hear about the Klein-Gordon Lagrangian, Dirac Lagrangian, Standard ... | In order to use Lagrangians in QM, one has to use the path integral formalism. This is usually not covered in a undergrad QM course and therefore only Hamiltonians are used. In current research, Lagrangians are used a lot in non-relativistic QM.
In relativistic QM, one uses both Hamiltonians and Lagrangians. The reaso... | I would say because of the way you efficiently solve problems as well as pedagogy. Both are used in both cases though.
The Hamiltonian operator approach emphasises the spectrum aspects of quantum mechanics, which the student is introduced to at this point $-$ but here is a Lagrangian
$$\mathcal{L}\left(\psi, \mathbf{... | https://physics.stackexchange.com |
127,009 | [
"https://chemistry.stackexchange.com/questions/127009",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/88240/"
] | The question is as follows:
<blockquote>
If <span class="math-container">$\pu{1.23 g}$</span> of <span class="math-container">$\ce{MnI2}$</span> reacts with <span class="math-container">$\pu{25.0 g}$</span> of <span class="math-container">$\ce{F2}$</span>, what mass of <span class="math-container">$\ce{MnF3}$</span>... | Here we have an already balanced equation given in the question-
<span class="math-container">$$\ce{2 MnI2 + 13 F2⟶ 2 MnF3 + 4 IF5}$$</span>
We find the given number of moles of each reactant by dividing their given masses by their respective molar masses
Given mass of <span class="math-container">$\ce{MnI2}=\pu{1.2... | <span class="math-container">$F_2$</span> is present in great excess. Do the calculation with the manganese compounds.
<span class="math-container">$1.23$</span> g <span class="math-container">$MnI_2$</span> contains <span class="math-container">$1.23 g /308.74$</span> = <span class="math-container">$0.004$</span> mol... | https://chemistry.stackexchange.com |
663,717 | [
"https://physics.stackexchange.com/questions/663717",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/304657/"
] | In an adiabatic process we know there is no change in enthalpy or basically enthalpy change is zero. which means any external work done the internal energy does equal opposite work so as to keep <span class="math-container">$dH=0$</span>. which means in adiabatic process the pressure and temperature have to change. but... | Let me try to clarify a few key points.
<ol>
<li><span class="math-container">$c_p=c_v+R$</span> is an equality between two <em>state</em> functions (the specific heat depends on the process connected to the heat transfer, but the final quantity is a function f the state). The two specific heats actually correspond to ... | “In an adiabatic process we know there is no change in enthalpy or basically enthalpy change is zero.”
<strong>This is untrue</strong>. Adiabatic compression of a real or ideal gas will increase its enthalpy and temperature. (For an ideal gas, enthalpy is a function of temperature.)
People often think enthalpy is the s... | https://physics.stackexchange.com |
53,909 | [
"https://mathoverflow.net/questions/53909",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10299/"
] | I have some problems proving that a Differential Matrix Equation has a solution. I apologize if the question is too elementary, but I've found this theorem stated everywhere on the web without any reference or clue about how to prove it.
What I exactly mean with a Differential Matrix Equation is:
$X'=AX+B$. Where $A$ ... | This was a many years lasting problem to me, but now that I began to think of it anew, I found the solution: Since $E$ has the Heine−Borel property, taking $V$ to be $\mathcal T\ $−closed, we get $S\cap V$ also such, and hence $\mathcal T\ $−compact. Having a compact zero neighbourhood, so $S$ must be finite−dimensiona... | I guess that the answer is NO.
Since
<ul>
<li>$C^\infty(I)$ is nuclear, </li>
<li>any closed subspace of a nuclear space is nuclear, </li>
<li>any nuclear Banach space is finite-dimensional.</li>
</ul>
Edit : for another proof, replace "nuclear" by "Fréchet-Montel".
| https://mathoverflow.net |
82,288 | [
"https://mathoverflow.net/questions/82288",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8737/"
] | Let $(x_1 \ldots ,x_n) \in \mathbb{R}^n$ and $f_i = \Pi_{j=1, j \neq i }^n ( x_i - x_j )$
I'm trying to evaluate $(f_1, \ldots, f_n)$. A trivial algorithm runs in $\mathcal{O}(n^2)$ but given the very specific form of the problem, there's got to be something faster. Maybe I've overlooked something simple, maybe a four... | The following may be of some help, if you haven't thought of it already. Let $V$ be the Vandermonde matrix with $(i,j)$th entry $x^{i-1}_{j}$, $i,j=1,\ldots,n$. Its inverse $W$ has $(i,1)$th entry
$$
(-1)^{n} \frac{x_1 \ldots x_{i-1} x_{i+1} … x_n}{f_i}.
$$
Hence, to find $f_1,\ldots,f_n$ we need to solve $V \alpha =... | I heard there's a method called non-equispaced FFT (though I know very little about it), which should be able to compute the coefficients of the polynomial $p(x)=\prod(x-x_j)$ from the $x_j$ in quasi-linear time.
Using it, we can get a divide-and-conquer algorithm as follows:
<ol>
<li>Divide your points in two sets $... | https://mathoverflow.net |
27,722 | [
"https://electronics.stackexchange.com/questions/27722",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8534/"
] | I am hoping somebody could help me diagnose the cause of failing electrolytic capacitors in a circuit. The context is a charger circuit, more specifically its power supply unit:
Given a diode bridge rectifier that is connected on one set of terminals to the mains via a filter circuit and on the other side to two elect... | 230V AC swings between +230V and -230V RMS, but that means it reaches +/- 325 V peak-to-peak. With a rectifier, that's between 0 and 325V, which split on two 200V capacitors would be just about enough -- except the capacitors have to be perfectly matched for that to be true.
If there are differences in manufacture, th... | The two capacitors that were connected in series are probably rated for lower voltage than the one that the power supply actually produces. In this case, if one of the capacitors gets shorted or something, the other sees the full supply voltage and goes explodes.
Replace both capacitors with ones that are rated for mo... | https://electronics.stackexchange.com |
25,509 | [
"https://mathoverflow.net/questions/25509",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2000/"
] | I've recently been interested in the following type of functions. A total computable function <em>f</em>:<strong>N</strong>→<strong>N</strong> is <em>effectively closed</em> if there is a computable function <em>p</em> such that <em>f</em>[<strong>N</strong> \ W<sub>e</sub>] = <strong>N</strong> \ W<sub><em>p</em>... | I like your concept a lot, and have been able to find a characterization.
Suppose that $f:N\to N$ is effectively closed in your sense.
First, as you mentioned, it is easy to see that $\text{ran}(f)$ is
computable, since by taking $W_e$ to be empty your equation shows that
$\text{ran}(f)$ is both c.e. and co-c.e.
Sec... | I think that this is probably studied in Russian/Markov School of Constructivism. A good starting point might be the chapters on Russian Constructivism in Michael Beeson's book:
Michael Beeson, "Foundations of Constructive Mathematics: Metamathematical Studies", Springer, 1985
| https://mathoverflow.net |
25,415 | [
"https://stats.stackexchange.com/questions/25415",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/199/"
] | Two related questions from me. I have a data frame which contains numbers of patients in one column (range 10 - 17 patients) and 0s and 1s showing whether an incident happened that day. I'm using a binomial model to regress probability of incident on number of patients. However, I would like to adjust for the fact that... | If you are interested in the probability of an incident given N days of patients on ward then you want a model either like:
<pre><code>mod1 <- glm(incident ~ 1, offset=patients.on.ward, family=binomial)
</code></pre>
the offset represents trials, <code>incident</code> is either 0 or 1, and the probability of an in... | <h3>Offsets in Poisson regressions</h3>
Lets start by looking at why we use an offset in a Poisson regression. Often we want to due this to control for exposure. Let $\lambda$ be the baseline rate per unit of exposure and $t$ be the exposure time in the same units. The expected number of events will be $\lambda \ti... | https://stats.stackexchange.com |
105,269 | [
"https://mathoverflow.net/questions/105269",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25869/"
] | Can someone describe explicitly an abelian group $A$ such that the extension $$0 \to \mathbb{Z} \to A \to \mathbb{Q} \to 0$$ doesn't split ?
Background: The Stein-Serre theorem (Hilton, Stammbach: A course in homol. algebra, Theorem 6.1) states that if $A$ is abelian of countable rank (=maximal number of linear indep... | Nice question. For a prime $p$ let $\mathbb{Z}_{(p)} = \lbrace \frac{a}{b}\in \mathbb{Q}\mid p \nmid b\rbrace$ and $\mathbb{Z}[p^{-1}] = \lbrace \frac{a}{p^n}\in \mathbb{Q}\mid n \ge 0 \rbrace$. Then
$$A := \lbrace (x,y) \in \mathbb{Q} \times \mathbb{Z}[p^{-1}] \mid x-y \in \mathbb{Z}_{(p)} \rbrace$$
has the desired ... | Building on Ralph's answer a bit we can get uncountably many inequivalent examples as Mark Grant's comment on the original post suggested there should be.
Let $S,T$ be a partition of the primes into two nonempty sets (or if you prefer, the multiplicative sets generated by these). Localize at these sets and form the s... | https://mathoverflow.net |
243,306 | [
"https://dba.stackexchange.com/questions/243306",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/185838/"
] | We are migrating a few tables' data from one application to another application. These two applications are totally different tables and schema.
We have created general T-sql scripts and temporary tables to store the required data to transform the data in an acceptable format of destination application tables.
Checki... | For a one-off migration that's a good way. For continuing movement of data from a source to destination system e.g. OLTP system to a data warehouse, a proper ETL tool (SSIS/ BIML) would be better.
| Depending on what you need to accomplish the two main options I would suggest are using SSIS to transform and move the data or writing T-SQL scripts like you mentioned to convert data to the proper table structures. If this would be a ongoing migration using ETL tools may be a better option to creating scripts.
I had a... | https://dba.stackexchange.com |
204,576 | [
"https://softwareengineering.stackexchange.com/questions/204576",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/96319/"
] | I am working on a tool (Python, may or may not be important) that will allow a user to maintain a configuration file containing arbitrary shell and/or language code to be executed on particular events and intervals. The code will potentially involve multiple statements.
I understand there are potential behavioral and ... | How about storing the commands in an actual executable file? The end user creates a bash/python/ruby script, and all they supply to your configuration is the name of the script to execute.
This allows the script to be arbitrarily simple or complex, and also lets the end user use any scripting language supported by the... | Well, for your example script only the first two methods will actually work. It has a <code>cd</code> in it, and therefore the two commands must be part of the same shell script.
Therefore, if you want to use commands that have the form of a shell script, you have to store them in form of a string anyway. If the code ... | https://softwareengineering.stackexchange.com |
71,935 | [
"https://mathoverflow.net/questions/71935",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16758/"
] | Let $L$ be a regular language over alphabet $\Sigma$ and let $A:=(Q,\Sigma,\delta, q_0, F)$ be the minimal DFA recognizing $L$. For every $w\in \Sigma^*$ define the variation of $w$ w.r.t. $L$ by
$$\mathrm{Var}_L(w) := \#\{0\leq k < n \text{ s.t. } \delta(w_1\cdots w_k)\neq \delta(w_1\cdots w_{k+1})\},$$
if $w:=w... | It seems to me that FV should be the variety of languages associated to $\mathcal R$-trivial monoids. A monoid is $\mathcal R$-trivial if Green's relation $\mathcal R$ is trivial. This is the same as satisfying $(xy)^{\omega}x=(xy)^{\omega}$ for all $x,y$ where $z^{\omega}$ is the idempotent power of $z$.
Suppose ... | As for my question on literally idempotent closure of $\mathrm{FV}=\mathrm{R}$ I can now answer by myself, thanks to Benjamin Steinberg.
By literally idempotent closure $\overline{V}$ of a $*$-variety of languages $V$ we mean the class $\overline{V}:=\{\overline{L} | L \in \mathrm{V}\}$, provided $\overline{L}:=\{w\in... | https://mathoverflow.net |
11,438 | [
"https://stats.stackexchange.com/questions/11438",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3700/"
] | I have a model $$Y=\beta_0 + \beta_1 x_1 + \beta_2x_2 +\epsilon$$
I would like the minimum variance unbiased estimate of $\gamma=\beta_1 + \beta_2$. Assuming the Gauss Markov conditions hold, but $x_1$ and $x_2$ are correlated, is there a more efficient way to estimate $\gamma$ than running OLS and adding the estima... | The Gauss-Markov theorem states that the covariance matrix of any unbiased estimator $\tilde{\beta} \ne \hat{\beta}_{OLS}$ exceeds that of $\hat{\beta}_{OLS}$ by a positive semidefinite matrix. Let's label the OLS covariance matrix $\Omega$ and the positive semidefinite matrix $D$. The variance of the sum of the OLS ... | The short answer is no. By the Gauss-Markov theorem, if you want an unbiased estimator, then the OLS is the minimum variance estimator.
However, if you relax the unbiasedness condition, you can get better expected mean square error by using some kind of regularization (e.g. ridge regression).
| https://stats.stackexchange.com |
267,662 | [
"https://dba.stackexchange.com/questions/267662",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/84541/"
] | Below query never completes and runs for over 14 hours:
<pre><code>SELECT
U.Age, U.CreationDate, U.DisplayName,
P.AcceptedAnswerId, P.ClosedDate, p .Title, P.ViewCount,
C.CreationDate,C.Score ,C.UserId
FROM dbo.Users As U
LEFT JOIN dbo.Posts As P on U.id = P.id
LEFT JOIN dbo.Comments As C on U.id =C.id
WHERE
(
U.Loc... | The biggest problem I see is in your joins. You're joining the "id" of Users, to the "id" of Posts and Comments. This basically says, take every record in Users and join it to every record in Posts, then join it to every record in Comments.
Presuming that the UserID exists as a foreign key in Posts and Comments, the c... | Here what you need to do:
1) use #Temp table<br>
2) break down query on parts, get data step by step<br>
3) make sure columns which you use in the WHERE or join ON clause, are indexed
Temp Table - column data types below are just an example, use data types that exactly match column data types on your tables
<pre>
c... | https://dba.stackexchange.com |
220,737 | [
"https://physics.stackexchange.com/questions/220737",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99738/"
] | A drop is falling in humid air with air resistance equal $F_r = - \alpha v^2$. In $t = 0$ the drop is ideally spherical, $h$ above the ground, has mass $m_0$ and velocity $v_0 = 0$.
What mass and velocity will the drop have when it reaches the ground? Which additional information do we need to know to solve this prob... | With the capacitor remaining connected to the battery, then the potential difference between the plates is unchanged. If the potential difference stays the same and the gap between the plates stays the same, then the electric field stays the same.
Your initial assumption that the field is reduced by a factor $K$ is on... | The first equation assumes the external electric field (caused by the charges on the plates of the capacitor) doesn't change. When a battery is connected, it can fill and discharge the plates as necessary to maintain the voltage. So, the E_0 value increases as you add the dielectric.
| https://physics.stackexchange.com |
244,808 | [
"https://mathoverflow.net/questions/244808",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1384/"
] | If $f\in\mathbf{C}[[q]]$ is non-constant, and algebraic over $\mathbf{C}[q]$ (in the sense that it is a root of a polynomial with coefficients in in $\mathbf{C}[q]$) then can $f$ be the $q$-expansion of a modular form (for some congruence subgroup of $SL(2,\mathbf{Z})$)?
I ask for the following reason. There are geome... | A non-constant modular form has a natural boundary on the real line. A power series that's algebraic in $q = e^{2\pi i \tau}$ can't.
| In characteristic $p>0$ the quotient field ($K$ say) of the ring generated by $E_4,E_6$ (i.e. modular forms of level one) is of transcendence degree $1$. But $q$ (in the sense of the Tate curve) is transcendental over $K$ (I proved this in J. Number Theory 58 (1996) 55-59). So any non constant modular form or modula... | https://mathoverflow.net |
1,066,257 | [
"https://math.stackexchange.com/questions/1066257",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/190098/"
] | Calculate the limit:
$$\lim_{x \to 1} \frac{x\cos(x-1)-1}{x-1}$$
I manipulated the expression to get:
$$\lim_{x \to 1} \frac{\sin^2(x-1) }{(x-1)^2} \frac{-x(x-1) }{\cos(x-1)+1}$$
But I can't use $\lim_{x \to 0 } \frac{\sin x}{x} = 1$ because obviously x is not approaching 0, what can I do in order to calculate this... | More directly, letting $y=x-1$ your original limit becomes$$\require\cancel \lim_{y\to0}\frac{(y+1)\cos y-1}{y}=\lim_{y\to0}\frac{\cancel{y}\cos y}{\cancel{y}}+\lim_{y\to0}\frac{\cos y-1}{y}=\cos0+0=1. $$
| You could do a change of variable. Let $y=x-1$, and then your expression changes to:
$$\lim_{y \to 0} \frac{\sin^2(y) }{(y)^2} \frac{-(y+1)(y) }{\cos(y)+1}$$
Does that help?
| https://math.stackexchange.com |
79,286 | [
"https://electronics.stackexchange.com/questions/79286",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/27595/"
] | I have a solar panel, a battery and a charge controller. I didn't pay for any of it so I thought I would just wire them up and see how it goes.
The battery won't charge. The charge controller has a battery level indicator and it has stayed at middle for over a week. The solar panel doesn't have a high wattage so I was... | You do need more than 12 volts to charge a 12 battery. Also how do you know that your solar panel is producing even 12 volts? Just because that is it's rating doesn't mean it always produces that value. Do you have enough sunlight? Have you measured the output of the panel? Can you provide more information on the c... | Buy a DC-DC step up converter then u can change output voltage from 12V solar panel to lets say 14,5V then it will charge your battery.
| https://electronics.stackexchange.com |
2,623 | [
"https://engineering.stackexchange.com/questions/2623",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/1434/"
] | I have a structure like such:
<img src="https://i.stack.imgur.com/CZvAm.png" alt="Structure">
Due to my lack of knowledge of ANSYS, I have made the singular distributed loading (GI) represented as two distributed loadings (GH and HI).
Would this be an accurate model?
<img src="https://i.stack.imgur.com/iFnkL.png" alt... | I would expect the modeling as a single load to be accurate. Force per linear area is the same expressed either way. You could look at a linear load on a single beam and just add more points of integration analytically and try it in ANSYS to see it.
The HE and BE segments will undergo buckling as its deformation mec... | Splitting a uniform load into separate pieces that are still continuous will have no effect. This is frequently done.
As far as your question about bending in HE and EB, there shouldn't be any bending because all of the forces are balanced. A sum of the moments at H or E will show that the moments from the beams on e... | https://engineering.stackexchange.com |
957,978 | [
"https://math.stackexchange.com/questions/957978",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/180392/"
] | Take a number $N = \overline{abcdef...}$ where $a, b, c, d,e,\dots$ are the digits of $N$.
Let $k$ be the sum of those digits :
$a+b+c+d+e+... = k$
If $k$ is any of ${1, 2, 4, 5, 7, 8 }$ then $N$ is <strong>prime</strong>. Otherwise it is not a prime.
Example: $N = 17$ and $k = 1+ 7 = 8,$ Therefore $N$ is prime.
... | Any number is congruent with the sum of its digits modulo 9.
Therefore, if the sum of the digits is 3,6 or 0 $\pmod{9}$ the number is divisible by $3$. And in this case, the number is either $3$ or composite.
If the sum of the digits is $1,2,4,5,7,8 \pmod{9}$ the number <strong>could</strong> be prime.
There are inf... | The digit sum operation you describe is invariant modulo 9.
The 5-digit number $abcde = a 10^4 + b 10^3 + c 10^2 + d 10 + e$. Since $10 = 9 + 1 \equiv 1 \mod 9$, you can see that $abcde \equiv a + b + c + d + e \mod 9$.
So if a number's digit sum is divisible by 3 that means the number itself is also divisible by 3.... | https://math.stackexchange.com |
99,263 | [
"https://chemistry.stackexchange.com/questions/99263",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/30886/"
] | Why does 2,4 DNP give orange crystals on reacting with solution of aldehydic or ketonic group? Why does this test give orange crystals? Is this related to the electron emissions?
This is just a question from a curious student after 2 hours of lab work.
| Hydrazines react with ketones and aldehydes to make hydrazones. For example, see Chapter 11 of <em>Organic Chemistry</em> by Clayden, Greaves, and Warren.
For the case of the product from 2,4-dinitrophenyl hydrazine, the resulting hydrazones have an extended network of conjugated π bonds. That makes them good chrom... | Generally, you will notice that compounds containing chromophore and auxochrome groups have a colour. Chromophore groups are groups that are responsible for colour of the molecule once they are “attached” to it: benzene is colourless, but nitrobenzene is pale yellow. Apart from a chromophore group there are groups call... | https://chemistry.stackexchange.com |
238,947 | [
"https://softwareengineering.stackexchange.com/questions/238947",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | Take the (unprecedented and groundbreaking) example of the calculator:
<pre><code>public class Calculator
{
public double Add(double augend, double addend)
{
return augend + addend;
}
}
</code></pre>
When I write <code>calculator.Add(val1, val2)</code> which of the following am I doing?
<ul>
<li... | <blockquote>
is it a method of the object or is it a method on the object?
</blockquote>
It is a method of the <em>class.</em>
You create instances of classes to encapsulate <em>state,</em> not <em>code.</em> All of the code in that method is the same code across all of the objects; only the state (private variabl... | In my opinion it's a matter of the context in the system, and sometimes depends on the conceptual role of the component in the system.
For example in a game, a character might have a method <code>attack()</code>. Is it meant to allow other characters to attack this character? Or is it a method used to tell the charact... | https://softwareengineering.stackexchange.com |
75,211 | [
"https://physics.stackexchange.com/questions/75211",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25244/"
] | please help me to solve this problem..
<img src="https://i.stack.imgur.com/2z1Gz.png" alt="enter image description here">
this is only the #3 on my homework and the only thing i didn't know here is how to calculate the tension T. please teach me how to solve the tension here because the future problems that will be ... | Since the system is in equilibrium, the torque at point A must be 0. There are three components of that torque: from the force of 200, the force of 100 and the force that comes from string at point C.
At this moment it is necessary to calculate the angle at point C.
$\tan \angle ACD={8 \over 4}=2 \implies \angle ACD ... | Consider the free body diagram with the tension split into components
<img src="https://i.stack.imgur.com/mcdAW.png" alt="FBD 1">
Now follow the equilibrium conditions that sum of forces is zero and sum of moments is zero. As @QuadntumDrzewo said taking moments about point <em>A</em> is advantageous because you do no... | https://physics.stackexchange.com |
131,078 | [
"https://mathoverflow.net/questions/131078",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4423/"
] | A real closed field can be ordered in one and only one way, and is therefore provided with a unique
order topology. Given any infinite cardinal number k, does there always exist a real closed field F
(whose cardinal number is greater than k), such that no non-empty subset of F having a cardinal number
not greater than ... | If $\delta$ is the cofinality of an ordered field $F$, that is, the size of the smallest unbounded subset of $F$, then every point of $F$ fills a cut of type $(\delta,\delta)$. In other words, every point in $F$ is the limit of an increasing $\delta$ sequence from below and a decreasing $\delta$ sequence from above. On... | <em>Notice: I thought you would require the field to be of cardinality $k^+$. In that case the proof uses the generalised continuum hypothesis. But without this restriction it is completely unnecessary. The construction is similar to the construction of “the” hyperreals (you might get “them” in the case $\kappa=\omega$... | https://mathoverflow.net |
23,166 | [
"https://physics.stackexchange.com/questions/23166",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8434/"
] | I am facing the following question. It is well known that power laws arise in many situations in nature. They arise even in thats physical systems that are completely deterministic (e.g. sand piles). But power law is a probability distribution function and can be thought as generated from a stochastic variable. What is... | I don't think that anyone has answered your question yet ( this one "How a probabilistic behavior arise from a deterministic system? Or how happens that we pass from trajectories to frequencies densities?" )
If you can answer this question you have demonstrated that statistical mechanics and so thermodynamics derive f... | Umm. After giving it some thought I came to this conclusions.
As you point out, is clear why you can obtain statistical mechanics from stochastic variables. See Monte Carlo for example. All is deterministic each step but the choice of the random number that gives your ensemble.
Another way to put it is adding noise ... | https://physics.stackexchange.com |
153,402 | [
"https://mathoverflow.net/questions/153402",
"https://mathoverflow.net",
"https://mathoverflow.net/users/44973/"
] | Let $\Sigma$ be a compact oriented surface with boundary. Assume that the genus of $\Sigma$ is positive. We say that an element $h \in H_1(\Sigma)$ can be <em>realized by a simple closed curve</em> if there exists an oriented simple closed curve $\gamma$ on $\Sigma$ such that $[\gamma] = h$.
If $\Sigma$ has $0$ or $... | First notice that we can separate the condition depending the relative position of $a,b$, and $x$ in (b): let $F_0$ be such that for any $a,b$ there are finitely many $x<\min(a,b)$ with
$F_0(x,a)=F_0(x,b)$, let $F_1$ be likewise for $a<x<b$ and let $F_2$ be for $a,b<x$. Then $F(a,b)=\langle F_0(a,b),F_1(a,... | While this is extremely late, I previously ran into something similar when looking for examples of objects on $\omega_2$ that can be forced with side conditions, and I think the following method has certain advantages. If you want to avoid the use of a Delta-function and force directly, using the poset that you'd imagi... | https://mathoverflow.net |
50,203 | [
"https://engineering.stackexchange.com/questions/50203",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/36483/"
] | In a race car rear wing with 2 airfoils, why does the second airfoil have a greater angle of attack compared to the leading airfoil? Also, what is the best offset distance between the 2 airfoils in a racing car rear wing?
| No. It might blind it but it would not attract it.
Laser guided weapons aren't just laser versions of heat-seeking weapons. You would modulate the targeting laser so that it could be differentiated even in the presence of another light of the same wavelength.
And if the missile has optical filters (which it will) they ... | <h2>Probably not.</h2>
Look, anything is possible. You could throw some rocks at a keyboard, and have it open SE, log in, and post an proof of trisection.
It ain't real likely.
Laser guided weapons usually have some specific frequency they're looking for. Then, on top of that, the laser is pulsed as an identifier (thin... | https://engineering.stackexchange.com |
149,959 | [
"https://mathoverflow.net/questions/149959",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $\kappa$ be a (finite or infinite) cardinal. Assuming consistency of $\text{ZFC}$ (and probabely some additional assumptions) is the following consistent with $\text{ZFC}$?
There is a countable transitive model of $\text{ZFC}$ like $M$ and a partial order $\mathbb{P}$ in $M$ and $\mathbb{P}$-generic filter $G$ ove... | Write the Riemann zeta function as a product of its Euler factors
$\zeta (s)=\prod_i E_{i}(s)$. Repeated application of the Leibniz rule shows
$$\frac{\zeta^{(k)}(s)}{\zeta (s)}=\sum_{i_1+\cdots+i_k=k}\sum_{t_1,\dots,t_k}\frac{E_{t_1}^{(i_1)}(s)}{E_{t_1}(s)}\cdots \frac{E_{t_k}^{(i_k)}(s)}{E_{t_k}(s)}.$$
The left hand ... | Everything I know about these generalized von Mangoldt functions goes through the identity
$$
\Lambda_{k+1}(n) = (\Lambda_k \ast \Lambda)(n) + \Lambda_k(n) \log n
$$
(where $\ast$ denotes Dirichlet convolution); this identity isn't obvious, but can be proved by identifying the Dirichlet series corresponding to both sid... | https://mathoverflow.net |
2,236,402 | [
"https://math.stackexchange.com/questions/2236402",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/433205/"
] | I can not figure out how to solve the following problem :
$ |x^2 +x| + |3x-9| = x+13 $
should I solve it through factorization ?
| Four cases:
1)$x^2+x\ge 0$ and $3x-9\ge 0$ this means $x\ge 3$
If $x \ge 3$ then
$|x^2+x|+|3x-9|=x+13$
$x^2+x+3x-9=x+13$
$x^2+3x-22=0$
$x=\frac {-3\pm \sqrt {9+88}}2$ but as $x \ge 3$
$x=\frac {\sqrt {97}-3} 2$
2) $x^2+x \ge 0 $ and $3x-9 <0$. That means $0\le x <3$ or $x \le -1$.
If $0\le x <3$ or... | hint: write the equation in the form
$$|x||x+1|+3|x-3|=x+13$$ and do case work.
the solution is given by $$x=-1$$ or $$x=\frac{1}{2}\left(\sqrt{97}-3\right)$$
| https://math.stackexchange.com |
102,076 | [
"https://mathoverflow.net/questions/102076",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17294/"
] | I need to answer (affirmatively, I hope) the following question:
<blockquote>
In a Lie group $G$ whose Lie algebra $\mathfrak{g}$ is equipped with an $\mathrm{Ad}$-invariant scalar product, is the open subset
$$\{g \in G \mid \operatorname{ker} (1 + \operatorname{Ad}_{g}) = \{0\}\}$$
dense in $G$?
</blockquote>... | [This is an embellished version of the answer I gave in the comment section]
The key to the solution lies in recalling that when one is playing with Lie groups, the functions that one encounters are not mere $C^\infty$ functions but are actually real-analytic. There is some discussion of this in the second edition of ... | If $\pi_0(G)$ is odd, it's dense. For each nonzero connected component, for some $n$, $g \to g^{2^n}$ maps the connected component to itself. Take an element $g$ of the connected component. For some $m$, $g^{2^{nm}}$ has no $-1$ eigenvalues. (we can ignore the non-root of unity eigenvalues, and the roots of unity event... | https://mathoverflow.net |
41,321 | [
"https://physics.stackexchange.com/questions/41321",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12035/"
] | I understand that
$$\begin{align}
J = \sum F \Delta t &= \Delta p \\
\sum F &= \frac{\Delta p}{\Delta t} \\
&= \frac{mv_2 - mv_1}{\Delta t} \\
&= m \cdot \frac{\Delta v}{\Delta t} \\
&= ma
\end{align}$$
<blockquote>
$J$ is impulse, $p$ is momentum
</blockquote>
However, by just looking at the ... | <blockquote>
"I seem to think that impluse is high if for same force, time is higher."
</blockquote>
This is correct, to develop an intuitive understanding, we must just realize that impulse simply refers to a change in momentum. So lets say you apply a force of 1N to an object. Is the object going to have a larger ... | I think it is better to think that if you apply a force for a longer time, you will accelerate the object and achieve a higher speed. This consequently will lead to a higher momentum change.
| https://physics.stackexchange.com |
25,602 | [
"https://scicomp.stackexchange.com/questions/25602",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/20148/"
] | I have a legacy DG finite element code for which I would like to write some unit tests. As it is written, for 2D problems, each degree of freedom has associated with it a Jacobian matrix (for later transformation to the master element). All elements are straight-sided.
Is there a good way of sanity checking that these... | Like with any other thing you want to test, you need to come up with a list of situations where you know that something is true, and then check this. In many cases, knowing that something is true does not require being able to actually compute the numerically correct answer, which simplifies things.
For example:
<ul>... | Well, the first obvious test is to check if the determinant of the Jacobian matrix is positive. If it not, it means that your element has inverted and your answer is going to be invalid.
Otherwise, I am not sure of any other test that would be good... For a unit test you could rotate a triangle 360 degrees by incremen... | https://scicomp.stackexchange.com |
339,714 | [
"https://softwareengineering.stackexchange.com/questions/339714",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/258744/"
] | I was hoping you could give some feedback on an idea I had for designing functions.
I am trying to think of a unifying principle for choosing what functions should return. The specific project is mostly data access classes.
So the principle is this: "When deciding what value to return as a status code, either True or... | It's a matter of taste and style, however a function, in my opinion, should only return <code>true</code> or <code>false</code> if it is performing a test. It should not use a boolean value as a poor man's status code.
Now, some code bases do use status codes, in which case a <code>byte</code> or an <code>int</code> w... | Yes it is common to have such design principles, but they are usually depending on the language used.
For example in C it is convention to return 0 if a function succeeds and a non-zero number, indicating an error code, if for some reason it fails.
In languages with exceptions, the convention is to throw an exceptio... | https://softwareengineering.stackexchange.com |
199,982 | [
"https://dba.stackexchange.com/questions/199982",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/71655/"
] | I see in lots of output from <code>SHOW FULL PROCESSLIST</code> only <code>COMMIT</code> or <code>commit</code> (lowercase and upercase mix).
What are those transactions? Why no SQL statement? We are running MariaDB 10.1.x and Galera replication (3 nodes).
How to intepret those transactions?
<pre><code>> select C... | If data has been written/updated during an explicit transaction, it may not get written to the data files at all until the final <code>COMMIT TRANSACTION</code> statement when it is copied from the log file. This makes rolling back after an error, an explicit <code>ROLLBACK TRANSACTION</code> statement, on restart afte... | Some transactions need to finish up things during the <code>COMMIT</code>. I think that is what you are seeing.
However, 494 seconds is a loooong time! Even 121s is long. Look at your code and find the SQL statements for a likely transaction. Present the SQL here; maybe we can explain things further.
| https://dba.stackexchange.com |
302,291 | [
"https://physics.stackexchange.com/questions/302291",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/139035/"
] | In Ampere's law:
$$
\nabla\times\mathbf{B}=\mu_0\mathbf{J}
+\mu_0\epsilon_0\frac{\partial\mathbf{E}}{\partial t}
$$
the current density is listed explicitly as a separate term from the change in electric field. My understanding of the history (perhaps completely wrong), is that the $J$ term was determined first, and... | Nothing in Maxwell's equations depends on the fact that the charges that we encounter in the real world are all tied to individual particles.
So we can imagine that we have an infinite rod of charge in space and it's moving with uniform velocity along its axis, and Maxwell's equations will still apply to this situatio... | Just by looking at the two equation that you wrote down, you get immediately that for them to be consistent you need to have $\mathbf{J}=0$. In other words the two systems of equation are not equivalent (unless you are in the trivial case $\mathbf{J}=0$).
Looking at the whole structure of Maxwell's equation + Lorentz ... | https://physics.stackexchange.com |
1,700,852 | [
"https://math.stackexchange.com/questions/1700852",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/283662/"
] | I am having some difficulties doing some line integrals exercises, could someone please check my working and solution?
The question is as follows :
<blockquote>
A particle moves from point <span class="math-container">$A = (0,0,0)$</span> to point <span class="math-container">$B=(2\pi,0,2\pi)$</span>, under the action ... | Ok Lets start with part 1:
We want to calculate the work done by a force field on the particle along a path
$$ \int \vec{F}(\vec{r}) \cdot \mathrm{d}\vec{r} = \int \vec{F}(\vec{r}(t))\cdot \vec{r}'(t) \mathrm{d}t $$
We are given that the path is a conical helix given by
$$\vec{r}(t) = t \cos{t} \;\hat{i} + t \sin{t} ... | i'm also struggling with a question like this, the question actually says that F=xi+yj-zk, your answer has taken F to be equal to xi+yj+zk, I worked out part 1 to overall equal 0?
Edit: My rep couldnt comment on the above answer, please make sure he finds this!
| https://math.stackexchange.com |
747,048 | [
"https://physics.stackexchange.com/questions/747048",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/356427/"
] | I'm pretty confused with the concepts of bound and free charges as well as current.
1.Bound charge density (pb) arises due to polarization of a dielectric material. Free charge density (pf) have no relationship with the polarisation of material, it solely depends on the current flowing through the material.
The net su... | LIDAR has usually greater flux than Radar because it is using a laser so the magnitude of the light is still high when received by the cars because the magnitude decreases as distance because of the inverse square law
Also transparency increases by frequency, so LiDar usually works in IR so it can go past the fog more ... | <em>Our TV news today said the cops have switched from radar to lidar because it is more accurate in fog.</em>
All other things being equal in good visibility conditions lidar has a greater spacial accuracy than radar. Lidar also a better angular resolution which means that the lidar can differentiate between differen... | https://physics.stackexchange.com |
234,625 | [
"https://electronics.stackexchange.com/questions/234625",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/110296/"
] | I am looking to drive an electrical motor to power a cart with some substantial weight.
I want to power this with as simple a method as possible but want to maximise the force for it.
I have several 18650 cells I can use for the main power source and the intended motor runs on 12v dc from a scooter.
I would like to try... | We are assuming you are talking about the flash circuit in a disposable camera. The principle there is that the very low voltage from the battery is used to charge up the large photo-flash capacitor to provide a very large voltage/current to the Xenon flash tube. Note, however that this provides power for only a very ... | <blockquote>
would a capacitor from a microwave which is apx 9000uf at 2000v be
able to work for this?
</blockquote>
No, it would be completely useless. Despite its size, a microwave oven capacitor can only store a small amount of charge at 12V (certainly not enough to run a scooter motor). But even if you could s... | https://electronics.stackexchange.com |
56,481 | [
"https://physics.stackexchange.com/questions/56481",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11657/"
] | $$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$
Essentially, why is $\Phi$ independent of the <em>distribution</em> of mass inside the surface $\partial V$, and the shape of surface $\partial V$? That is, I'm looking for a mathematical justification for the characterization of flux as a kind of "fl... | Maxwell's equations say that the divergence of E is the charge density. By Stokes' theorem, the flux through a surface is equal to the volume integral of the divergence over the volume enclosed. This completes the proof of Gauss' Law.
To show that Coulomb's Law follows, take a point charge and calculate the flux throu... | Its because the divergence is undefined at the origin and 0 everywhere else. Thus as long as the volume you integrate over contains the origin, it doesn't matter what region you integrate over.
| https://physics.stackexchange.com |
125,912 | [
"https://physics.stackexchange.com/questions/125912",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45557/"
] | A vehicle moving with some velocity on a rough horizontal road finally comes to rest after its engine has been turned off. Intuitively, it seems a vehicle with greater mass would stop first because it would experience a greater friction force, but if we go by the work-energy theorem as follows, it's clear that the dist... | This is admittedly a late answer. Hopefully it will clear up some of the confusion.
If you ignore aerodynamic drag, ignore that the coefficient of rolling friction varies with load, and ignore a number of other factors such as friction between the axle and the bearings that support it, then yes, stopping time / stoppi... | Your intituition is totally different because ennumerous forces change the situation from the ideal situation predicted by work enrgy theorem, some of them are: Air Drag/Friction, Rotational Friction due to differences in size of tyres, different aerodynamic effects due to different body design.. etc.
| https://physics.stackexchange.com |
450,922 | [
"https://physics.stackexchange.com/questions/450922",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/47212/"
] | A hyperelastic solid is defined as one for which the stress tensor <span class="math-container">$\sigma$</span> can be written as the derivative of some stored energy function <span class="math-container">$W$</span> w.r.t. the strain <span class="math-container">$\varepsilon$</span>:
<span class="math-container">$\sig... | I've done some more reading and found that this idea is discussed in several sources, but many of them use different names for the same thing, and many of the names have really bad SEO. For example, [1] was one of the first papers to discuss what they refer to as a "flow potential" <span class="math-container">$\Omega(... | I might be misunderstanding your question, but it seems to me that the two cases are quite different. The first relation, what you call a "hyperelastic solid" is essentially the definition of the second Piola Kirchoff stress tensor (PK-II). In that case, <span class="math-container">$\epsilon$</span> is the full nonlin... | https://physics.stackexchange.com |
275,922 | [
"https://physics.stackexchange.com/questions/275922",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101699/"
] | I'm a Non-physics major student. Recently, I am puzzling by the dispersion relation.
For a wave, we have $v=f\lambda$, where $v$, $f$ and $\lambda$ is the velocity, frequency and wave length of the wave, respectively. According to this relation, velocity should depends on the frequency. Then why should we have the d... | For media where the speed does not depend on frequency, the equation $v = f \lambda$ does not mean $v$ depends on the frequency. It is a relationship between $f$ and $\lambda$ such that when you multiply them together they give the speed $v$.
For a non-dispersive medium if you know the frequency of the wave and its wa... | This question has an interesting connection to a post a few days ago. I can't find that question at the moment. The questioner there asked if it made any difference if one writes $F=ma$ or $a=F/m$. Of course, the math is the same, but the way the expression is written suggests "cause" and "effect".
Here's an example... | https://physics.stackexchange.com |
415,251 | [
"https://electronics.stackexchange.com/questions/415251",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/142915/"
] | When calculating the input impedance of a voltage divider biased BJT common emitter amplifier, we calculate the parallel resistance of the bias resistors and the emitter resistance. But why do we consider both bias resistors? Looking from the amplifier input (the transistor base), the other resistor leads to the voltag... | I'm not sure how to give you a hint without giving you the complete answer.
But consider the difference between these two situations:
<ul>
<li>If <strong>any</strong> of the inputs to the upper encoder are asserted, then its outputs become the overall outputs, and Y2 needs to be asserted.</li>
<li>If <strong>none</st... | Connect Y0, Y1 to both 4:2 in parallel.
Use Y0 as the 3rd "address" line and a NOT gate to enable one or the other.
| https://electronics.stackexchange.com |
266,181 | [
"https://dba.stackexchange.com/questions/266181",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/117588/"
] | I understand that innoDB will store select statement result in the buffer pool, does InnoDB store newly inserted data (insert into statement) into buffer pool even after data has committed and wrote to disk?
| Yes and no. Yes, buffer pool will contain the recently inserted data. No, the buffer pool doesn't contain <code>SELECT</code> statement output, that is what the query cache does, but it is generally harmful, deprecated and removes in MySQL 8.0. The buffer pool contains InnoDB pages (both index and data).
| <ul>
<li>All data and index activity for all InnoDB read and write queries must have the data in the buffer_pool</li>
<li>The buffer_pool is structured around 16KB blocks, just as the BTrees in tables for data and secondary indexes.</li>
<li>Blocks are pulled into the buffer_pool when needed by queries.</li>
<li>Blocks... | https://dba.stackexchange.com |
2,830,221 | [
"https://math.stackexchange.com/questions/2830221",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/349034/"
] | I am trying to prove the following statemt:
<blockquote>
Let $(\Omega, \mathcal A, P)$ be a probability space. Let $(Z_n)_{n\in \mathbb N}$ be i.i.d. random variables with $Z_1 \in \mathcal L^1$. Let $\theta \in \mathcal L^1$ be independent from $(Z_n)_{n\in \mathbb N}$ and define $\forall n\in \mathbb N: Y_n := Z_n... | A first remark is that without loss of generality, we can assume that $Y_i$ is centered.
It seems that we do not need $\theta$ to be independent of $\left(Y_i\right)_{i\geqslant 1}$. Moreover, we only need that $N^{-1}\mathbb E\left\lvert \sum_{i=1}^NY_i\right\rvert\to 0$ which would for example hold if $\left(Y_i\rig... | I am actually not sure if I need the independence of $\theta$, but I still have a different solution.
By the strong law of large numbers,
$$ \frac{1}{n}S_n = \frac{1}{n}\sum_{k=1}^n Y_n = \frac{1}{n}\sum_{k=1}^n Z_n + \theta\longrightarrow \mathbb E[Z_1] + \theta$$ or $$\frac{1}{n}S_n - \mathbb E[Z_1] \longrightarrow \... | https://math.stackexchange.com |
317,640 | [
"https://softwareengineering.stackexchange.com/questions/317640",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44110/"
] | I am writing a poker application and trying to figure out how to deal with split pots and side pots
There are four rounds of betting and each round of betting can have multiple orbits
Can only bet the chips in front of you<br>
So if a player is all in a side pot is created
Hands can tie - in which case the p... | Here is a working code to create and distribute winnings from side-pots.
<pre><code>class Player:
def __init__(self, l, i, hs):
self.live = l #False
self.invested = i #0
self.hand_strength = hs #100
self.result = 0
def distribute(pot, players):
for p in players:
p.resul... | In my code, after every player has spoken, for every stake in the <strong>set</strong> of stakes of the players who are still in play, i create a pot. Then i order the pots from the smallest (that will be the main pot) to the highest (side pots).
The side pots are represented as a list, in this format:
[ needed stake, ... | https://softwareengineering.stackexchange.com |
19,836 | [
"https://mechanics.stackexchange.com/questions/19836",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4906/"
] | Does driving with your foot always resting on the clutch (not pushing) generally wear it down?
| It absolutely does. It's called <em>riding the clutch</em>. Even though you "believe" you just have your foot there, it forces the pedal down and takes up the slack which is there. This causes the throw out bearing to ride against the clutch fingers, which presses so ever slightly and causes the clutch to not have as m... | I do not see how you can rest your foot on the pedal without exerting any force at all on that pedal. What is the point? You might as well use the pedal properly and ONLY apply force to it when required. Resting your foot on the clutch pedal WILL adversely affect the operation of the clutch release bearing (throw-out b... | https://mechanics.stackexchange.com |
113,937 | [
"https://mathoverflow.net/questions/113937",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2039/"
] | Given a scheme $X$ with structure sheaf $\mathcal{O}_X$, we can associate to each $\mathcal{O}_X$-module $\mathcal{F}$ its global sections $\Gamma(\mathcal{F})$, which gets the structure of a $\Gamma(\mathcal{O}_X)$-module.
<blockquote>
Suppose $\mathcal{F}$ is a vector bundle on $X$. Is then $\Gamma(\mathcal{F})$ ... | This is not always a projective module. Here is the simplest counterexample I can think of, but there are plenty of others. Let $Y$ be $\text{Spec} k[x,y,z]$, where $k$ is a field. Let $X$ be the complement of the closed point $\langle x,y,z \rangle$. Then $\Gamma(X,\mathcal{O}_X)$ equals $k[x,y,z]$ since $k[x,y,z]... | Here is another example that wont work (another variant of Jason Starr's example): consider a local ring $(R,\mathfrak{m})$ and let $U=\mathrm{Spec}\:R-\{\mathfrak{m}\}$ be its punctured spectrum. Assume that $\mathrm{depth}\:R\geq2$ and $\mathrm{Pic}(U)\neq0$. Now $U\hookrightarrow\mathrm{Spec}\:\Gamma(\mathcal{O}_U)$... | https://mathoverflow.net |
211,793 | [
"https://stats.stackexchange.com/questions/211793",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/49771/"
] | I am fitting the linear probability model,
$$
Y_i=\beta_0 + \sum_{j=1}^J \beta_j G_{ji} +\varepsilon_i
$$
where $Y_i \in \{0,1\}$ and $G_{ji} \in \{0,1\}$, for $j=1,\ldots,J$ and $\sum_{j=1}^J G_{ji}=1$, i.e., the $G_{ij}$ are groups and each individual is placed into one of these groups.
I use OLS to get estimates f... | Recall that the standard errors are the diagonal elements of the matrix
$$
\hat\sigma^2(X'X)^{-1}
$$
As pointed out by @repmat, this result requires that each group is of equal size, i.e., that
$$\sum_iG_{ji}=c$$
for $j=1,\ldots,J$.
In that case, you can easily check that
$$
X'X=n
\begin{pmatrix}
1&1/J&\cdot... | This will happen if, and only if, the two (or more variables) have the same variance, or in other words that all groups are equally large (in terms of 1's). The nature of $y$ does not matter.
Here is an example from R:
<pre><code>set.seed(42)
year1 <- data.frame(rep(1, 333))
year2 <- data.frame(rep(2, 333))
ye... | https://stats.stackexchange.com |
423,108 | [
"https://electronics.stackexchange.com/questions/423108",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/208358/"
] | I wonder if its possible to run a common 16x2 LCD with 3.3v power supply. Its datasheet shows supply voltage = 5V. Are there any 3.3V variants of 16x2 LCD modules?
| It might be possible to use it at 3.3v. Usually the chip itself will work at 3.3v but the liquid crystals in the LCD glass may needs higher voltages. It might be possible to give negative contrast voltages to drive the glass better, but the glass supply voltage biasing may not be optimal. There is no module type code o... | There are a few character mode displays that are available for operation at 3.3V. The ones that I have encountered are OLED modules so you may want to investigate that type including the NewHaven brand.
Almost all other displays that I have found that operate at 3.3V are going to be graphic type displays. These take a... | https://electronics.stackexchange.com |
2,129,942 | [
"https://math.stackexchange.com/questions/2129942",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/178248/"
] | <blockquote>
Let $P = \text{span } \{ v_1, v_2\}$ be a plane in $\mathbb{R}^3$ with normal vector $n$, show that $\{v_1, v_2, n\}$ is a basis for $\mathbb{R}^3$
</blockquote>
It must be that $\{v_1, v_2\}$ is linearly independent (LI) by def of a plane, thus $c_1v_1 + c_2v_2 = \overrightarrow{0}$ for $c_1 = c_2 = 0$... | The equation of a tangent in $(x_0, y_0)$ to the circle is $xx_0+yy_0=9$.
Now suppose there is such $k$. Then:
$$\frac {k}{x_0} =\frac {-1}{y_0}=\frac {2-k}{-9}$$ and from here:
$$\frac {k^2}{(x_0)^2} =\frac {1}{(y_0)^2}=\frac {(2-k)^2}{81}=\frac {k^2 + 1}{(x_0)^2 + (y_0)^2}=\frac {k^2 + 1}{9}$$
therefore $$\frac {(2... | "First line is tangent to the second" equals to "this lines have only one intersection point"
Result of subtitution of $y=kx + 2 -k$ to $x^2 +y^2 = 9$ is
$(k^2+1)x^2 + 2k(2-k)x + (k-2)^2-9 = 0$
This equation (over x) has one root =>
$(k(2-k))^2-(k^2+1)((k-2)^2-9) = 0$
Try to solve this equation over k and chec... | https://math.stackexchange.com |
717,564 | [
"https://physics.stackexchange.com/questions/717564",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/303868/"
] | I get the idea that thermodynamic potentials are introduced because it is not always easy to describe a system's energy as a function of variables like <span class="math-container">$S,V,N$</span> as we normally do with internal energy <span class="math-container">$U=U(S,V,N)$</span>. For example, temperature is much ea... | We do not use Legendre transformation in Thermodynamics. Due to the presence of first-order phase transitions, we must use the Legendre-Fenchel transform (LFT).
Legendre transforms are a special case of LFT. It is not a minor point, because, in the presence of a first-order phase transition, there is an interval of val... | If we didn't use Legendre transform, we would waste precious information. Consider the case of a function of one variable for simplicity: <span class="math-container">$y=g(x)$</span>. Now what you propose to do is to define <span class="math-container">$t=\frac{dg}{dx}(x)$</span> and obtain <span class="math-container"... | https://physics.stackexchange.com |
87,602 | [
"https://mathoverflow.net/questions/87602",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20756/"
] | After reviewing the (locally convex)
topological vector spaces that I know,
the only examples I could find where there is an isomorphism from the
space to its (anti)dual, are Hilbert spaces.
So my question is :
Are there topological vector spaces $V$ such that the topology does not come from a Hilbert structure, an... | An interesting family of examples comes from number theory (or algebraic geometry, depending on who you ask): If you have a field $k$, the Laurent power series field $k((t))$ has an ultrametric topology where $\{ t^n k[[t]] \}_{n \in \mathbb{Z}}$ form a neighborhood basis of zero. This space is isomorphic to its topol... | Take a reflexive TVS $V$, and consider $V \times V^\ast$.
| https://mathoverflow.net |
59,001 | [
"https://datascience.stackexchange.com/questions/59001",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/80981/"
] | I'm new to machine learning and I try to create a simple model myself. The idea is to train a model that predicts if a value is more or less than some threshold.
I generate some random values before and after threshold and create the model
<pre class="lang-py prettyprint-override"><code>import os
import random
impo... | You have two separate problems going on.
<h1>Use <code>sigmoid</code></h1>
First, when performing a binary classification problem, you should set the activation of your final layer to <code>sigmoid</code> (or <code>softmax</code>, which is equivalent in the binary classification case).
<h1>Scale your data</h1>
Seco... | The problem i am seeing here is that you are using the same <code>train_data</code> for both <code>training</code> and <code>evaluation</code> of model.I would recommend you to use a <code>shuffled subset</code> of <code>train_data</code> as <code>test_data</code> or <code>validation_data</code> and try to <code>evalua... | https://datascience.stackexchange.com |
2,068 | [
"https://security.stackexchange.com/questions/2068",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/1351/"
] | I'm a student and fairly new to the IT security field. Most articles and books say you should only patch a vulnerability if the costs of a breach are higher than the costs of patching the vulnerability. However, I can't find any explanation that can give me at least some basic knowledge and skills about this issue.
<u... | As a security professional, it is often best to 'outsource' this calculation to the business. For example, if you identify a vulnerability which you can demonstrate is easy for an unskilled attacker to exploit to destroy the customer database, and the operations team estimate bringing it back from backups will take 4 h... | In short, it's not easy.
Pretty much all IT security decisions should be made in context of what the "business" is trying to do (when I say "business", I mean "people paying for the system and making money from it" - usually a business).
To estimate the cost of an incident, you have to weigh in all related costs rela... | https://security.stackexchange.com |
3,251,746 | [
"https://math.stackexchange.com/questions/3251746",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/679826/"
] | Can somebody give an example of process in which we have at least three events <strong>A, B, C</strong> and:
<strong>P(A ∩ B ∩ C) = P(A) * P(B) * P(C)</strong>
But A, B, C are not pairwise independent
| Your are correct, and the proof is rather simple (not requiring the wall of text you wrote :)
<span class="math-container">$$\begin{align}P(\neg B|C)&=\frac{P(\neg B \land C)}{P(C)} &\text{by definition}
\\&= \frac{P(C) - P(B\land C)}{P(C)} & \text{Because $B\land C$ and $\neg B\land C$ form a partitio... | Let <span class="math-container">$(\Omega,\mathcal A,P)$</span> denote a probability space and let <span class="math-container">$C\in\mathcal A$</span> with <span class="math-container">$P(C)>0$</span>
Then the function <span class="math-container">$P(-\mid C):\mathcal A\to\mathbb R$</span> is a <em>probability me... | https://math.stackexchange.com |
23,361 | [
"https://mathoverflow.net/questions/23361",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5800/"
] | I am delving a bit into category theory and something has me curious about opposite categories. I have checked several books and I can't seem to find an answer.
Given a category C, the opposite category is just the abstract category with the objects of C and with the arrows of C reversed. However, the opposite categor... | One way of formalizing the desired categories is given by concrete categories. A category is called concrete (more precise: "concretizable") if it has a faithful functor to the category of sets $Set$. Thus the question is: Is the dual of a concrete category concrete again? The answer is yes: Since a composition of fait... | I am going to spell out Martin's construction with minimal use of category-theoretic terminology (such as "faithful" and "representable") because it's exactly what, uhm, CrazyHorse, asked for. (I can't believe I am talking to a crazy horse.)
Take a concrete category $\mathbf{C}$. Its objects are of the form $(X,S_X)$ ... | https://mathoverflow.net |
346,122 | [
"https://electronics.stackexchange.com/questions/346122",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/172538/"
] | I want to power one 3V LED with a 3V source. Let's say I'm using a 10 Ohm limiting resistor, and the LED eats 20mA of current. Using a CR1225 with 50mAh capacity that will last for about 2.5h.
What if I connected another 10 Ohm in parallel with the diode + limiting resistor? The voltage across would still be 3V - enou... | If you add the resistor across the battery, so it's in parallel with your existing circuit it will draw an additional 300 mA (I = V / R), assuming the battery is able to supply it. This is not what you want.
You could reduce the current draw by adding the additional resistor in series with your current circuit.
| If you add another resistor in parallel with the LED and its limiting resistor it will not change the current going through the LED, just draw more current from the battery. That MIGHT drop the battery voltage a little bit which would reduce the LED current, but that really is a secondary effect.
You effectively have ... | https://electronics.stackexchange.com |
14,653 | [
"https://quant.stackexchange.com/questions/14653",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/9336/"
] | Basically all Quant Finance theory is build on No-Arbitrage presumption and Efficient Markets Hypothesis.
The known <strong>Grossman-Stiglitz Paradox</strong> says: if one can't make money from trading, one wouldn't trade any asset in the first place.
I did some private trading and watched markets over time, to see t... | this is just theory, don't take it as serious, theory it's just take on approximation of reality and in this case not good one, people trade to check that strategy is profitable or trade because they think it will profitable, besides that you have many other spaces on what people compete with each other in this game
| Making money is not the only reasonable objective to trading. Another common reason is to manage/reallocate risk. For example, this is exactly the objective of liability-driven-investors, such as pension funds. They're specifically trying to match durations of their liabilities. It doesn't matter if pension fund manage... | https://quant.stackexchange.com |
105,732 | [
"https://physics.stackexchange.com/questions/105732",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/43514/"
] | I recently have been studying Electro-statics and I couldn't understand properly how the potential energy of two particle system is found.
<blockquote>
Suppose you have two particles with charges $Q_1$ and $Q_2$ respectively. The distance between them is $r$. What is the total electrical potential energy of the sys... | As far as I remember, that $\frac{1}{2}$ comes because $Q_1$ isn't just in a potential $\varphi_2(\mathbf{r})$ that just happens to be there, but is being created by another charge, $Q_2$. Taking potential with respect to the other means: let $\varphi_1(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \frac{Q_1}{|\mathbf{r} -... | The electric potential energy of a system of charges is defined as the energy stored in the electric field between the charges that make up the system.
<img src="https://i.stack.imgur.com/j6vkI.png" alt="enter image description here">
Consider a positive charge $Q$ $C$ $fixed$ at a point. The electric field lines po... | https://physics.stackexchange.com |
666,819 | [
"https://physics.stackexchange.com/questions/666819",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/195949/"
] | According to the principle of relativity, the laws of nature should be independent of the relative movement of different frames. My doubt is the meaning of "laws of nature".
So, suppose a spaceship starting from earth with zero velocity, and (except for a few minutes after lauching) keeping acceleration <span... | You can think of the laws of nature as being rules about the relationships between different physical quantities. The principle of relativity is that the rules should appear to hold regardless of the reference frame you chose to label positions in time and space.
Clearly that doesn't mean that the values of physical pr... | A pendulum on the ship will have the same <em>proper</em> period as it would on Earth, but the ship's pendulum will have a shorter period in the Earth's reference frame. As a consequence, the number of oscillations the pendulum undergoes is frame invariant, since it is given by the ratio of the proper time of the traje... | https://physics.stackexchange.com |
15,978 | [
"https://stats.stackexchange.com/questions/15978",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6453/"
] | What is the formula for variance of product of dependent variables?
In the case of independent variables the formula is simple:
$$ {\rm var}(XY) = E(X^{2}Y^{2}) - E(XY)^{2} = {\rm var}(X){\rm var}(Y) + {\rm var}(X)E(Y)^2 + {\rm var}(Y)E(X)^2 $$
But what is the formula for correlated variables?
By the way, how can I... | Well, using the familiar identity you pointed out,
$$ {\rm var}(XY) = E(X^{2}Y^{2}) - E(XY)^{2} $$
Using the analogous formula for covariance,
$$ E(X^{2}Y^{2}) = {\rm cov}(X^{2}, Y^{2}) + E(X^2)E(Y^2) $$
and
$$ E(XY)^{2} = [ {\rm cov}(X,Y) + E(X)E(Y) ]^{2} $$
which implies that, in general, ${\rm var}(XY)$ ... | This is an <em>addendum</em> to @Macro's very nice answer which lays out
exactly what needs to known in order to determine the variance of
the product of two correlated random variables. Since
\begin{align}
\operatorname{var}(XY) &= E\left[(XY)^2\right] - \left(E[XY]\right)^2
\tag{1}\\
&= E[(XY)^2] - \left(\o... | https://stats.stackexchange.com |
417,946 | [
"https://physics.stackexchange.com/questions/417946",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/123084/"
] | Can all of an electromagnetic wave's momentum be changed to orbital angular momentum? I'd imagine this would be easier to test with radio waves.
| If we have functional defined as
$$S({\boldsymbol {q}})=\int _{t_0}^{t_1}L(t,{\boldsymbol {q}}(t),{\boldsymbol {\dot {q}}}(t))\,\mathrm {d} t$$
Then we have a theorem that says that a function $\mathbf{q}$ for which this functional is stationary must satisfy the Euler-Lagrange equations.
Now the principle of least act... | The Euler-Lagrange equations solve a particular variational problem where you want to extremize a functional is of the form
$$
F = \int_a^b f(x(t), \dot{x}(t), t) dt
$$
One such example for $f$ is the Lagrangian $L$, in which case $F$ would be the action $S$. From my point of view, this is the principle of least acti... | https://physics.stackexchange.com |
3,282,005 | [
"https://math.stackexchange.com/questions/3282005",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/65223/"
] | I am reading an example that gives a sequence and show how two topologies on the vector space containing the sequence will give different limits of the sequence. They conclude without proof: "the two norms cannot be equivalent" (equivalent in the sense <span class="math-container">$C_1 \|\cdot\|_1 \leq \|\cdot\|_2 \leq... | Suppose <span class="math-container">$C_1 \| \cdot \|_1 \le \| \cdot \|_2 \le C_2 \| \cdot \|_1$</span>, where <span class="math-container">$C_1, C_2 > 0$</span>. If <span class="math-container">$x_n \to x$</span> with respect to <span class="math-container">$\| \cdot \|_1$</span>, then
<span class="math-container">... | A basic fact: <strong>if</strong> two norms are equivalent (in the <span class="math-container">$C_1-C_2$</span> sense you mentioned) <strong>then</strong> they have the same convergent sequences. (the proof is easy.) So the logical reformulation (contrapositive) is: <strong>if</strong> we have two sequences with diffe... | https://math.stackexchange.com |
231,711 | [
"https://softwareengineering.stackexchange.com/questions/231711",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/80146/"
] | I am developing an application containing a class which loads application settings from a configuration file.
Settings class:
<pre class="lang-cs prettyprint-override"><code>public sealed class MyAppSettings : IMyAppSettings
{
private IMyAppSettings DefaultSettingsInstance;
public MyAppSettings()
{
... | In your Version 2, the requirement of a default language is explicit, which I think is a good thing.
In Version 1, if you don't look at the source code it will be not obvious where it takes the default language from, and appear like "magic", which is not a good thing.
There's definitely no one-size-fits-all solution ... | In version 1 it looks like you're using a static reference to look up the setting, which is generally more cumbersome to control in unit-testing (you're writing tests, right?) than a constructor-injected value, as in version 2.
Also with version 2, as Janos says in his answer, the explicit requirement of a default lan... | https://softwareengineering.stackexchange.com |
158,852 | [
"https://softwareengineering.stackexchange.com/questions/158852",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/60525/"
] | I'm working on a project which uses GIT as the main version control system for trunk, the official branches and most sub-projects/unofficial branches. As such, I want to make my own branch use GIT to allow the rest of the community to access my branch using the system they know.
However, I'm working on a part of the p... | You shouldn't do this for the same reason you shouldn't have a variable which tries to track the state of another - you might lose track of which version is authoritative.
| I currently do this using git and svn. While there are reasons <em>not</em> to do it, there is no general rule. Git can do things svn cannot, I am used to those features so my workflow hence productivity increases when I can use git. Looking at the pros and cons in my situation, I would be stupid not to use both. You s... | https://softwareengineering.stackexchange.com |
97,294 | [
"https://electronics.stackexchange.com/questions/97294",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/33599/"
] | Can I get 500 kW from solar panels using series and parallel operation?
If I connect 18 panels each of 250 watts 24 volts in series to get 415 volt direct current and 116 panels in parallel to get 1205 amperes, then combine it into series and parallel. Can i get 500000 watts from it ?
Since,
Power= Voltage*Current
(ex... | As Dave said, you don't have to actually run the tube in a real circuit to get the visual effect. All you have to do is power up the heaters.
Your particular tube actually is two tubes in one package and has two heaters. Each heater is 6.3 V. You can put 12.6 V accross pins 4 and 5, or 6.3 V accross both pins 9-4 a... | If all you're after is the visual effect, the only thing you need to do is apply power to the heaters. Ignore everything else. Get a hefty 6.3VAC transformer and wire all of the heaters in parallel, making sure the total current doesn't exceed the transformer's rating.
All of the other terminals of the tube don't need... | https://electronics.stackexchange.com |
146,748 | [
"https://softwareengineering.stackexchange.com/questions/146748",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31950/"
] | What should be the attitude towards getting stories done that are assigned to a sprint? Obviously you want to prioritize getting them done in the sprint, but to me the whole point of agile is to be dynamic: You don't want to deliberately procrastinate or make it "ok" to miss finishing user stories in a sprint, but at t... | You should <strong>absolutely</strong> aim to get items done within a sprint.
One of the main benefits of SCRUM is that it gives the project a 'heartbeat'.
You prioritise, pick items off a list, you deliver them, you demo them, you reflect how they went, then you do it again in preditable cycles.
All of the plan... | The key is that there needs to be <em>accountability</em> around not getting the stories complete.
That means there should be a solid reason why a story was not complete, and that this reason is accounted for in the project plan going forward so it is not repeated.
This reason needs to be more than a vague "stuff cam... | https://softwareengineering.stackexchange.com |
2,959,913 | [
"https://math.stackexchange.com/questions/2959913",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/587009/"
] | Let <span class="math-container">$V$</span> be a finite-dimensional vector space over <span class="math-container">$F, T∈L(V)$</span>.
Suppose 0 <span class="math-container">$\neq v∈V$</span> and m is a positive integer for which <span class="math-container">$T^{m-1} v \neq $</span> 0 but <span class="math-contain... | When you are asked to prove that a set in linearly independent you should usually start from writing a combination <span class="math-container">$\lambda_0v+\lambda_1T(v)+...+\lambda_{m-1}T^{m-1}(v)=0$</span>. You have to prove all coefficients <span class="math-container">$\lambda_0,\lambda_1,...\lambda_{m-1}$</span> m... | If <span class="math-container">$m=1$</span> then there is nothing to prove, otherwise let us assume they are linearly dependent, then we have:
<span class="math-container">$$\alpha_0 v + \dots + \alpha_{m-1} T^{m−1}v =0$$</span>
Applying <span class="math-container">$T^{m-1}$</span> on both sides we obtain:
<span cl... | https://math.stackexchange.com |
90,860 | [
"https://stats.stackexchange.com/questions/90860",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/18276/"
] | I have been occupied with a fairly simple question regarding ordinary inference procedures where my own, and many others, practice feels slightly uncomfortable. We know that the purpose of ordinary inferential methods is to deal with the situation wehre we don't have full knowledge of the population. The populaton para... | The difference between your two examples is that you want to understand/predict a variable that is income in your second example.
So in the first example you said 'I know something' and in the second you wanted to infer a variable (with a regression for example) => you end up there because you asked a very different ... | <blockquote>
I have encountered reasoning like 'this census can be regarded as a sample in time' or similar, but that usually seems farfetched and hypothetical.
</blockquote>
Actually, I'd say the whole issue hinges on this point. If you consider the current council body to be your population of interest, the usual ... | https://stats.stackexchange.com |
722,896 | [
"https://physics.stackexchange.com/questions/722896",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/337062/"
] | In space for example if we apply two forces 10,6 respectively at the end of an elastic string (<strong>10 at the right end and 6 at the other</strong>) then obviously that body will expand and accelerate. But how would you find young's modulus <span class="math-container">$ {Y}= \frac {FL}{Al}$</span> ? What would be t... | It's because complex time does not exist. There are many occasions in physics where a root is taken and a negative or complex solution is discarded because the quantity can only be positive (e.g. mass), or can only be real (time, or virtually any observable quantity in physics).
There is a use for the idea of imaginar... | I believe a problem like this is dealt with in Paul Nahin's book <em>The Story of (sqrt (-1)), An Imaginary Tale</em>. If I understand this correctly, an accelerating pickpocket is trying to escape a jeep traveling at constant speed. The "physical" solution occurs in the unique case where the jeep is travelin... | https://physics.stackexchange.com |
636,030 | [
"https://physics.stackexchange.com/questions/636030",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/253144/"
] | Say a beam, 3m long from end to end, has a pivot placed at its centre of mass, at half its length i.e. 1.5m. Objects with weight 200N each are placed on both ends of the beam. The system is in equilibrium and thus no turning effect.
Now a force of 30N is applied on one of the ends until the beam turns 15deg to the hori... | The other answers are correct in saying that if the pivot is at the centre of mass of the beam, the beam will not return to the horizontal position when released.
You might have assumed it would return because that is the way in which weighing balances operate. However, those balances have a pivot which is placed sligh... | it won't return to zero angle. It will remain in balance at 15deg. In fact, if it has any rotational speed when the force is lifted it will continue to lean.
If you work out the math, you will see that the two weights cancel out the torque on the pivot regardless of the tilt angle.
| https://physics.stackexchange.com |
55,554 | [
"https://dba.stackexchange.com/questions/55554",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/31202/"
] | i am new to JDBC and trying following code. Could not find the error in it
<pre><code>try{
Connection con = ConnectionProvider.getCon();
stmt=con.prepareStatement("insert into create_request values((select count(reqno) from create_request)+1,?,?,?,?,?");
stmt.setString(1,obj_Leaverequest.... | Specify the columns and use SELECT:
<pre><code>"insert into create_request (col1,col2,etc..col6)
select ?,?,?,?,?, count(reqno) +1 from create_request"
</code></pre>
Just make sure the values and columns match.
| I guess you have forgotten a ')'.
try this:
<pre><code>stmt=con.prepareStatement("insert into create_request values((select count(reqno) from create_request)+1),?,?,?,?,?");
</code></pre>
| https://dba.stackexchange.com |
830,741 | [
"https://math.stackexchange.com/questions/830741",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/116377/"
] | <strong>Question</strong> : Show in the one-dimensional case, how for potential forces
$F(x) = \dfrac{−dV (x)}{dx}$, energy conservation follows from Newton’s 2nd law
From Newton's second law we know $$F=ma=m\ddot{x}$$
How do we derive the conservation of energy equation from this?
So far I have:
$F=ma$
$\implies ... | Writing
$m \ddot x = -\dfrac{dV(x)}{dx}, \tag{1}$
we have
$m \ddot x + \dfrac{dV(x)}{dx} = 0; \tag{2}$
multiplying by $\dot x$ yields
$m \ddot x \dot x + \dfrac{dV(x)}{dx} \dot x = 0, \tag{3}$
which, using the chain rule may be re-written as
$\dfrac{1}{2} \dfrac{d(m\dot x^2)}{dt} + \dfrac{dV(x)}{dt} = 0, \tag{4}... | $$
-\frac{dV}{dx} = m\frac{d}{dt}\frac{dx}{dt}
\\
-\frac{dV}{dx}\frac{dx}{dt}
= m\frac{dx}{dt}\times
\frac{d}{dt}\frac{dx}{dt}
$$
Now LHS is $$
-\frac{d}{dt} V(x(t))
$$and RHS is
$$
m\frac{d}{dt}\left(\frac 12
\left(\frac {dx}{dt}
\right)^2 \right)$$
It means that, if $m$ does not depend on $t$ (already assumed when ... | https://math.stackexchange.com |
31,419 | [
"https://security.stackexchange.com/questions/31419",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10714/"
] | In an office if a person approaches an employee and claims to be a new IT staff and to give them access to their computer, what can prevent this kind of attack? I've worked a couple tech support jobs and people are all to happy to hand over their password and laptop when I tell them I'm here to fix it.
| as @TerryChia said the correct defence against this kind of attack is strong policies. In this case users should be trained not to provide passwords to people in person or on the phone regardless of what the circumstances are.
If IT need to log in to a users account they should either use something like sudo (for *ni... | Train the employees properly.
Teach them the need and importance of verifying a person's identity through some sort of identification method before handing over important information.
No amount of technical measures in place can protect against clueless users. So make sure your users aren't clueless.
| https://security.stackexchange.com |
232,168 | [
"https://physics.stackexchange.com/questions/232168",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99495/"
] | Would it be possible to make something like two metal balls, one positively charged and one negatively charged, in space, where the negatively charged ball would orbit the positively charged one like a moon orbiting a planet or like a macroscopic Rutherford model atom?
Would it be possible to make on earth by making t... | As safkan & Brionius have said, as a first guess the resulting orbit is just as stable as a normal Newtonian one. There is a catch however.
The problem with this planetary system is exactly the same as with the Rutherford atom. As the electron travels around the nucleus it is being accelerated towards the centre. ... | The overall problem with magnetic or electrically charged objects "orbiting" each other is that those forces decay by the square of distance. So if you can get an object into a perfectly circular orbit at exactly the right speed, it works; but if the orbiting "moon" every strays out of that, the unstable orbit collapse... | https://physics.stackexchange.com |
3,642,571 | [
"https://math.stackexchange.com/questions/3642571",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/556399/"
] | For a given space <span class="math-container">$X$</span>, define <span class="math-container">$S_1(X)$</span> to be the free <em>Abelian group</em> with basis all paths <span class="math-container">$\sigma : I \to X$</span>, and let <span class="math-container">$S_0(X)$</span> be the free Abelian group with basis X.
... | Suppose <span class="math-container">$x_0$</span> and <span class="math-container">$x_1$</span> lie in different path components <span class="math-container">$X_0$</span> and <span class="math-container">$X_1$</span> respectively.
There is a group homomorphism <span class="math-container">$\phi:S_0(X)\to\Bbb Z$</span> ... | <span class="math-container">$x_1-x_0=\delta_1(\sigma)=\sigma(1)-\sigma(0)$</span> implies <span class="math-container">$\sigma(1)=x_1,\sigma(0)=x_0$</span> which proves the other hand, since <span class="math-container">$S_0(X)$</span> is the free Abelian group with basis X.
| https://math.stackexchange.com |
134,754 | [
"https://softwareengineering.stackexchange.com/questions/134754",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3530/"
] | We have a product that has a few different editions. The differences are minor: different strings here and there, very little additional logic in one, very little difference in logic in the other. When the software is being developed, most changes need to be added to each edition; however, there are a few that don't an... | This depends on the magnitude of the change, but I wouldn't consider it good practice for the differences you described.
Generally, you want a Git branch to be something that will be merged in the future or stored read-only for reference. Git branches that co-exist indefinitely mean work for everyone: Changes need to ... | That's not really what branches are for. Branches are supposed to be short to mid-term side paths to your line of development, not long-term parallel versions of the same code.
I'd put all the different versions into the same branch, with a subdirectories for the parts that are different between editions, and set up y... | https://softwareengineering.stackexchange.com |
38,470 | [
"https://mechanics.stackexchange.com/questions/38470",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1202/"
] | I bought a second hand car 18+ months ago and there was no information on how recently the wiper blades had been replaced. This wasn't an problem as the blades weren't obviously worn and they did their job perfectly adequately. The back wiper did squeak, but as I don't use it that often it wasn't a problem.
However, t... | Really depends on several factors. First is weather extremes. Blades exposed to bright hot sun (tropical latitudes) or freezing conditions will deteriorate quicker. Blades exposed to heavy dust or other contaminants will also experience shorter life. Do you clean the blades? Wiping the blade edge with alcohol peri... | I've always replaced mine as soon as they don't clean the window. Sometimes the problem is streaking, other times its chattering because the wipers don't want to flex right on the back stroke.
Another important thing to remember is that over time, your wiper arms can get bent (if they are not cast, or formed in some... | https://mechanics.stackexchange.com |
267,798 | [
"https://electronics.stackexchange.com/questions/267798",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/126160/"
] | I am trying to select different combinations of LED's using a 74HC238.
I am testing with an ESP8266, and supplying 3.3v from a regulator LM1117-3.3v.
My question is when I make the digital channels lets say put Y1 to high, will it be using the 3.3v that is being supplied from VCC, or will it go high and use current f... | 74HC238 will get current internally from its power rail, GPIO (should be in output mode to be proper input for 238) will have minimal current draw.
You need to look at nominal current for LED (in LED datasheet), and ensure that 238's output can provide such current under normal operation (in 238's datasheet), and use ... | The outputs are directly sourced by Vdd and sinked to GND. That's a basic function of logic gates. But be careful, some chips have open-collector/open-drain outputs which means they can only sink the output, not source it. Usually, this comes with more sink current capability and/or with a >>Vdd voltage compatibility a... | https://electronics.stackexchange.com |
85,980 | [
"https://electronics.stackexchange.com/questions/85980",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30624/"
] | I am trying to create a binary adder. I have this truth table:
<img src="https://i.stack.imgur.com/M57oL.png" alt="enter image description here">
This is the Karnaugh map that I made for this function (see that there is a mistake: instead of c, it had to be "c-in"):
<img src="https://i.stack.imgur.com/r8yvT.png" alt... | If we look at the top left corner, where a=0 and c=0, we see that s follows b. This gives us a partial result of <em>s=b</em>. Moving down to the bottom left corner, we see that s is inverted when a=1. This is the XOR operation, and gives us <em>s=a^b</em>. Moving over to the right side, we see that the output is inver... | Karnaugh maps are usually drawn in Grey Code (with one bit changing at a time, so 000, 001, 011, 010 rather than with decimal sequence*) and if you do that, you get:
<img src="https://i.stack.imgur.com/WxbJZ.png" alt="enter image description here">.
This corresponds to minterms
<blockquote>
C'A'B + C'AB' + CA'B' +... | https://electronics.stackexchange.com |
253,968 | [
"https://softwareengineering.stackexchange.com/questions/253968",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53301/"
] | Recently, I was in a situation where I wanted to release a simple piece of JavaScript software under an open source license.
However, I withdrew from it because the software contained several open source components that were released under different licenses.
Under what license should the bundled software be released... | If parts of the bundle are under licenses that don't allow sublicensing (which is true for the majority of licenses), then you can't distribute that bundle under a single license.
The best option in that case is to explicitly state that different parts of the software are distributed under different licenses and to cl... | It depends on the license.
There are licenses like MIT or BSD, which allow you to include them in software licensed under different terms as long as you just include their copyright message somewhere where the user can read it.
On the other hand, there are licenses like the GPL which make it impossible to use a libra... | https://softwareengineering.stackexchange.com |
3,184,312 | [
"https://math.stackexchange.com/questions/3184312",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/531680/"
] | <blockquote>
Let <span class="math-container">$${\bf F}(x,y)=y{\bf i}-6x{\bf j}.$$</span> Find a nonzero function <span class="math-container">$h(x)$</span>, where <span class="math-container">$h(1)=5$</span>, such that <span class="math-container">$h(x) {\bf F}(x,y)$</span> is a conservative vector field.
</blockquo... | Given the interval <span class="math-container">$\left(a-\frac{1}{n},a\right),$</span> there are uncountably many points, and only countably many points where <span class="math-container">$f$</span> is discontinuous, so we can find an <span class="math-container">$a_n\in\left(a-\frac{1}{n},a\right)$</span> such that <s... | If the function has only finitely many discontinuities in total, then the only such sequences are those that eventually (i.e., starting with some index) constantly equal <span class="math-container">$a$</span>.
| https://math.stackexchange.com |
163,861 | [
"https://softwareengineering.stackexchange.com/questions/163861",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/24829/"
] | I am planning to standardize our way of creating project for our new projects.
Currently we are using 3tier architecture where we have our ClassLibrary Project where it includes our Data Access Layer and Business Layer
Something like:
<pre><code> Solution ClassLibrary
>ClassLibrary Project :
>... | That's a pretty good approach. You've separated the concerns into projects and referenced the projects where they are used. That's good.
<hr>
Since you've tagged this Visual Studio, I'm going to share how I structure my .NET software projects.
Typically I'll have these three projects, each contained within a single ... | My main critique of your approach would be, don't make your BL directly depend on your DAL, put a layer of indirection in their where the BL receives the DAL via IOC or IPC (which is basically a form of IOC) Then the consumers of your BL get to choose what DAL it gets; If the consumer's a unit test it gives a mock DAL,... | https://softwareengineering.stackexchange.com |
388,693 | [
"https://physics.stackexchange.com/questions/388693",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/185558/"
] | Does gauge invariance imply charge neutrality? I understand that all physical observables must be gauge invariant. Does this mean that physical observables must be neutral?
If a quark is in red, a gauge transformation can transform it into blue. But gauge transformation cannot change any observable. Thus, colour of t... | You are right of course! Physical observables must be gauge invariant. But this does not mean that they must be neutral. They could be charged under the global symmetry and be neutral under the local gauge symmetry.
In particular, a local gauge symmetry is generated by a function $\alpha(x)$ where $\alpha(x) \to 0$ a... | A rough answer is that yes, all physical states must be charge neutral on <em>net</em>, but there can be local charge imbalances that are compensated somewhere else in space. A quick and dirty way to see this is to consider periodic spatial boundary conditions, and notice that the integral form of Gauss's law gives tha... | https://physics.stackexchange.com |
23,885 | [
"https://softwareengineering.stackexchange.com/questions/23885",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I didn't ask how the quality of the software is important to the product itself, the customers/users, the manager or the company. I want to know how it is important to the <strong>programmer</strong> that build it.
I'll be interested in any <strong>books</strong> (please specify the chapter), <strong>articles</strong>... | If your question mean that "Should quality be important to programmer as a professional", the answer is, "Unequivocally yes".
However if your question is "do programmers care about quality personally", answer is, "It depends".
On the one hand there are programmers who are not satisfied until they have perfected the ... | The quality of what <em>I</em> worked on is of the utmost importance to me - sometimes to my detriment (failed deadlines mostly). As long as I can take pride in what I've done on the project, then that's what really matters to me.
Quality of the product as a whole, is mostly a bonus.
Consider that I'm coming from a ... | https://softwareengineering.stackexchange.com |
634,722 | [
"https://physics.stackexchange.com/questions/634722",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/239012/"
] | Does the Oort cloud act as a kind of shield for the Solar System? When an interstellar object impacts the cloud, does its momentum get absorbed substantially?
| This collimation of light in the forwards direction is in fact also what you would expect if non-relativistically.
From the electron's perspective, light is radiated uniformly in all directions. However, the electron is itself moving with respect to an observer in the laboratory.
If we didn't know anything about specia... | If the charge radiated backwards, it would be gaining an additional momentum-energy.
| https://physics.stackexchange.com |
274,180 | [
"https://physics.stackexchange.com/questions/274180",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/124219/"
] | Basically, resistance is something that obstructs the flow of charge because of collision of electrons flowing in the conducting wires on either side of the resistor with the ions in the resistor right? So say I have a 9V battery connected to a 100 ohm resistor, the potential drop across it would be the full 9V i.e. 9J... | For the case of the $100 \Omega$ resistor connected to the $9 V$ battery means a current of $\frac{9 V}{100 \Omega} = 90 mA$ through the circuit. This means that every second $90 mC$ of charge flows through the resistor and the amount of energy used per second is $9 V \times 90 mC = 0.81 J$. When you have two resistors... | The potential difference between the terminals (eg 9V) determines how much energy will be released by each Coulomb going round the circuit (here 9J/C). Whether you place 1 resistor or 2 or 100 in the circuit, the total amount of energy released per Coulomb flowing through the circuit is the same.
If there are 2 ident... | https://physics.stackexchange.com |
160,424 | [
"https://math.stackexchange.com/questions/160424",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Define the function $f:[0,1] \to \mathbb{R}$ by
$$
f(x)=\int_E x^tg(t)d\mu(t)
$$
where $E \subset \mathbb{R^+}$,
$\mu$ is a nonnegative measure on $\mathbb{R}$
and $g:\mathbb{R} \to \mathbb{R}$ is a $\mu$-integrable function, that is $\int |g|d\mu < \infty$.<br>
Is $f$ a continuous function of $x$?
I would be tem... | Use the dominated convergence theorem noting that $|x^t g(t)| \leq |g(t)|$, when $x\in [0,1]$. Then if $x_n\to \hat{x}$, you will have $x_n^t \to \hat{x}^t$, hence $f(x_n) \to f(\hat{x})$. Since this is true for all such sequences, $f$ is continuous.
| It's a consequence of the dominated convergence theorem. We just need to show sequential continuity. Let $x\in [0,1]$ and $\{x_n\}\subset [0,1]$ a sequence which converges to $x$. Let $g_n(t):=x_n^tg(t)$. Then $g_n$ is integrable, $g_n(t)\to x^tg(t)$ for all $t\in E$ and $|g_n(t)|\leq |g(t)|$, which is supposed to be i... | https://math.stackexchange.com |
118,490 | [
"https://dba.stackexchange.com/questions/118490",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/78576/"
] | I have recently install Toad Data Modeler 5.3.4 and it only has Oracle data model templates. Where can I find and import the MySQL data templates so that I can create MySQL database models. I have Googled and looked on the Toad World website.
| The problem you have is that the where clause is executed before the Select clause of a query, so when it hits the where section it has no concept of what the muni_score is
There are two simple workarounds (not taking any performance into account here) and I'll note down a slightly more complex one.
The easiest is to... | To refer to an alias you need a Derived Table:
<pre><code>SELECT *
FROM
(
SELECT voter_id, first, middle, last, title, party, phone, ward,
households.hh_id, households.hh_long,
voters.1311 + voters.1111 + voters.0911 + voters.0909 + voters.1109 AS muni_score
FROM voters
JOIN households
on ... | https://dba.stackexchange.com |
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