qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
3,207,885 | [
"https://math.stackexchange.com/questions/3207885",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/654749/"
] | <blockquote>
<span class="math-container">$a$</span>, <span class="math-container">$b$</span> and <span class="math-container">$c$</span> are three positives such that <span class="math-container">$\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 1$</span>. Prove that <span class="math-container">$$\dfrac{a}{b^2} + \frac... | Let <span class="math-container">$x=\frac{1}{a}$</span> , <span class="math-container">$y=\frac{1}{b}$</span> and <span class="math-container">$z=\frac{1}{c}$</span>, so <span class="math-container">$\sum_{cyc} x=1$</span>. Then we have
<span class="math-container">$(LHS-RHS)\cdot xyz=(\sum_{cyc}x)\cdot(\sum_{cyc}y... | Let <span class="math-container">$a=\min\{a,b,c\}$</span>, <span class="math-container">$b=a+u$</span> and <span class="math-container">$c=a+v$</span>.
Thus, <span class="math-container">$u\geq0$</span>, <span class="math-container">$v\geq0$</span> and we need to prove that
<span class="math-container">$$\sum_{cyc}\fr... | https://math.stackexchange.com |
15,859 | [
"https://dba.stackexchange.com/questions/15859",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6173/"
] | We have a payment table, and agents get commission on payments. Commission is based on a few different factors, such as how long it took to get the payment, so there is some calculations involved when figuring out the commission rate the agent gets, but nothing obscenely complex.
For example, it will probably never be... | If the query is run fairly infrequently (for example a report) then building the table on the fly is probably better<sup>1</sup>. If the query is run frequently and the temp table is required for performance then you potentially have a problem.
<ul>
<li>If the table is cheap to build, then do it as a temp table. As ... | One issue not covered in the accepted answer is "do you need this value over time" and "will the formula possibly change".
For instance consider the commision example. If the commission is paid, the amount should be stored as that is a historical figure of what was actually paid. The way to calulate commisions could ... | https://dba.stackexchange.com |
35,937 | [
"https://stats.stackexchange.com/questions/35937",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13888/"
] | Imagine a graph where the x-axis is time in minutes (continuous) from 0 to 360. And the y-axis represents 'z' values. Of this continuous time course graph, I have 8 time points w/ their corresponding real z-values. Here is the data frame 'real_df' with that real data.
real_df:
<pre><code>timepoints real_z
... | <strong>This is a great question</strong> because it explores the possibility of alternative procedures and asks us to think about why and how one procedure might be superior to another.
The short answer is that there are infinitely many ways we might devise a procedure to obtain a lower confidence limit for the mean,... | The first option does not take account of the reduced variance that you get from the sample The first option gives you five lower 95% confidence bounds for the mean based on a sample of size 1 in each case. Combining them by averaging does not create a bound that you can interpret as a lower 95% bound. No one would... | https://stats.stackexchange.com |
1,344,230 | [
"https://math.stackexchange.com/questions/1344230",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Let $a,b>0$ show that
$$\dfrac{1}{1+a}+\dfrac{2}{1+a+b}<\sqrt{\dfrac{1}{a}+\dfrac{1}{b}}$$
</blockquote>
It suffices to show that
$$\dfrac{(3a+b+3)^2}{((1+a)(1+a+b))^2}<\dfrac{a+b}{ab}$$
or
$$(a+b)[(1+a)(1+a+b)]^2>ab(3a+b+3)^2$$
this idea can't solve it to me,are we aware of an elementary... | Use Cauchy-Schwarz inequality we have
$$\left(\dfrac{1}{1+a}+\dfrac{2}{1+a+b}\right)^2\le\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\left(\dfrac{a}{(1+a)^2}+\dfrac{4b}{(1+a+b)^2}\right)$$
so suffices to show that
$$\dfrac{a}{(1+a)^2}+\dfrac{4b}{(1+a+b)^2}<1$$
since
$$\dfrac{4b}{(1+a+b)^2}<\dfrac{4b}{4(1+a)b}=\dfrac{1}... | if op go ahead , he will get from his last step :LHS-RHS$=(4a^4+4a^2+b^3-6a^2b)+(a^2b^2-3ab+b+a)+a^2b^3+ab^3+3a^3b^2+a^2b^2+ab^2+2b^2+3a^4b+a^3b+a^5+6a^3 >0 \iff$
$(4a^4+4a^2+b^3-6a^2b) \ge 0 \cap (a^2b^2-3ab+b+a)\ge 0$
| https://math.stackexchange.com |
34,503 | [
"https://astronomy.stackexchange.com/questions/34503",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/25088/"
] | Does the frequency of the number of visible meteors during a daily shower start off lower at the beginning only to increase as the night goes on or does the frequency remain the same for the entire night?
| The rate depends on the distribution of the dust and rocks in space as the earth passes through the cloud. Some may be very short lived, some may start slowly, some may tail off slowly, some may last all night - they are all different.
| The number you are able to detect increases as it gets darker.
The number occurring is apt to be greater when the zenith of the sky is closest to pointing in the direction the earth takes orbiting the sun
(like a windshield hitting more bugs than back window when a car is moving forward)
The last factor I can thin... | https://astronomy.stackexchange.com |
3,484,546 | [
"https://math.stackexchange.com/questions/3484546",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/682364/"
] | <blockquote>
Let <span class="math-container">$x,y,z > 0$</span> such that <span class="math-container">$3x(x+y+z)=yz$</span> . Find the minimum value of <span class="math-container">$$P=\frac{y+z}{x}$$</span>
</blockquote>
<hr>
<span class="math-container">$$3x(x+y+z)=yz\Leftrightarrow 3(x+y)(x+z)=4yz$$</span>
... | Let <span class="math-container">$y+z=2u$</span> and <span class="math-container">$yz=v^2$</span>, where <span class="math-container">$v>0$</span>.
Thus, since by AM-GM <span class="math-container">$$\frac{y+z}{2}\geq\sqrt{yz},$$</span> we obtain <span class="math-container">$u\geq v$</span>,
<span class="math-con... | Your solution is wrong because in your solution equality occurs when <span class="math-container">$a=b=1$</span> which is not possible because <span class="math-container">$x=y=z$</span> doesn't satisfy the constraints. Instead, you should use method of lagrange multipliers. Let <span class="math-container">$m = \frac{... | https://math.stackexchange.com |
197,918 | [
"https://mathoverflow.net/questions/197918",
"https://mathoverflow.net",
"https://mathoverflow.net/users/63939/"
] | David Cox's book Primes of The Form: $x^2+ny^2$ does a great job proving and motivating a lot of results for $n>0$. I was unable to find anything for negative numbers, let alone the case I am interested in, $n=-2$.
What is the reason for this? Maybe I am missing something. Any references to results involving prime... | Take any square free $1 \neq n \in \mathbb{N}$ and recall that $R_n = \mathbb{Z}[\sqrt{n}]$ has a multiplicative norm function $N \colon R \to \mathbb{Z}$ given by $N(x + y\sqrt{n}) = x^2 -ny^2$ so a prime $p$ is of the required form iff $p$ is a norm in $R_n$ (i.e $p$ is in the image of $N$).
Now take $n$ which is no... | As $2 = x^2 -2y^2$ for $x = 2$ and $y=1$ we fix an odd prime number $p$, and
<strong>Claim:</strong> There exist integers $x,y$ such that $p = x^2 -2y^2$ if and only if $p \equiv \pm1 \mod 8$.
First if $p = x^2 -2y^2$ for some $x,y \in \mathbb{Z}$ then observing that the squares mod $8$ are $0,1,4$, we conclude that... | https://mathoverflow.net |
478,271 | [
"https://physics.stackexchange.com/questions/478271",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228031/"
] | I've been reading Chapter 3.2 and 3.3 of Purcell's Electricity and Magnetism, 3rd ed, and found that I don't really understand a few ideas that Purcell makes about electric fields and conducting material.
An example is given with a point charge q placed arbitrarily inside a neutral conducting spherical shell. The exa... | For a reversible process with an ideal gas, the molar entropy change is determined in one of two ways.
<span class="math-container">$$ \Delta\bar{S}^\star = \int \bar{C}_V\ d\ln(T) + R \ln\left( \frac{V_f}{V_i}\right) $$</span>
<span class="math-container">$$ \Delta\bar{S}^\star = \int \bar{C}_p\ d\ln(T) - R \ln\left... | If it's an ideal gas, you can relate volume to temperature by the ideal gas law. That should be enough for you to proceed.
ADDENDUM:
With regard to your edit, if it is an ideal gas your assumption that <span class="math-container">$\Delta U=0$</span> would not be valid, since <span class="math-container">$\Delta U$</... | https://physics.stackexchange.com |
53,238 | [
"https://security.stackexchange.com/questions/53238",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/40694/"
] | I am wondering if there is a way to detect if a reverse shell is blocked by egress filtering or an obligatory proxy, or the exploit just failed.
I am asking this question in the context of a SE media dropping senario.
| There's no way to tell directly from that actual test, there's no enough information. However, you could tell whether the exploit works or not by telling the target system to do something that it is allowed to do, for instance browse to a web server under your control (presuming that any outbound web connectivity is al... | As an addition to GdD's answer, have the "payload" try several things, since you'd have no idea about finding out if your code / exploit was actually executed. A range of things could be one of the following:
<ul>
<li>fetch a webpage using the system's browser settings' proxy</li>
<li>send an email to an outside add... | https://security.stackexchange.com |
3,475,537 | [
"https://math.stackexchange.com/questions/3475537",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/649402/"
] | Given a natural number <span class="math-container">$n \ge 4 $</span>, what is the maximum number <span class="math-container">$\ell$</span> of subsets <span class="math-container">$A_1,A_2,\ldots, A_\ell$</span> of <span class="math-container">$\{1,2,\ldots,n\}$</span> satisfying:
<ol>
<li><span class="math-container... | For <span class="math-container">$n \geq 4$</span>, the maximum is <span class="math-container">$n-2$</span>.
Clearly, <span class="math-container">$\ell \geq n-1$</span> is impossible: wlog <span class="math-container">$A_1 = \{1\}$</span> and <span class="math-container">$A_2 = \{2, 3\}$</span>. Because <span class=... | Let the maximum <span class="math-container">$l$</span> for some <span class="math-container">$n$</span> be given by <span class="math-container">$l_n$</span>.
The first thing to note is that <span class="math-container">$l_n \leq n-2$</span> for all <span class="math-container">$n\geq 4$</span> as the element in <spa... | https://math.stackexchange.com |
24,944 | [
"https://quant.stackexchange.com/questions/24944",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/12126/"
] | I am not a quant geek.I always have doubt what should be the VaR output for portfolio contains long and short of the same maturity @ same traded price. e.g. CME corn future of sept expiry
<h1>Groundwork</h1>
I was using the full revaluation with PnL approach at 95 percentile. The output was coming as zero.
| Here, we assume that the bottom is zero and the top is $K_2-K_1$. Then, in mathematical form, the ${\color{blue} {blue}}$ option payoff is given by
\begin{align*}
& \ (K_2-K_1)\pmb{1}_{S_T \le K_1} + (K_2-S_T)\pmb{1}_{K_1 < S_T \le K_2} \\
=& \ (K_2-K_1)\pmb{1}_{S_T \le K_1} + (K_2-S_T)\left(\pmb{1}_{S_T \le... | Think like this:
<ol>
<li>Start with a long call option for K1. This would give you a payoff reflected at K1.</li>
<li>Short some cash to move the payoff vertically down.</li>
<li>Short a call option for K2. The payoff of this short option will offset the payoff of your long call option for <code>>K2</code>.</li>
<... | https://quant.stackexchange.com |
45,116 | [
"https://mathoverflow.net/questions/45116",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10626/"
] | It is well known that total space of the tautological line bundle $\mathcal{O}(-1)$ over projective space $\mathbb{P}^n$ is closed subvariety of $\mathbb{P}^n\times\mathbb{A}^{n+1}$. My question is how to realize total space of $\mathcal{O}(1)$ over $\mathbb{P}^n$ in such manner, i.e. I need an embedding of $Tot(\mathc... | It is the complement $\mathbb{P}^{n+1} - \{x\}$ of a point in a projective space.
| Dear Luther King, since you ask for equations, let me add them to Tony's beautifully geometric answer.
Consider $\mathbb P^{n+1}$ with homogeneous coordinates $(z_0:z_1:\ldots:z_{n+1})$ and $\mathbb P^{n}$ enbedded as the hyperplane $z_0=0$. If $x\in\mathbb P^{n+1}$ is the point $x=(1:0:\ldots:0)$, the required total... | https://mathoverflow.net |
309,087 | [
"https://physics.stackexchange.com/questions/309087",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/144033/"
] | I have a simple and a dumb question.
If I have, say, a hydro-electric generator which is generating electricity, and I am not using this power for anything, is this hydro-electric power converted to something at this point? Where does this energy go?
| It goes into friction of your "Water wheel". And since you don't have a closed circuit, that energy is if we're looking at a steady state not being used. If you put some load in the circuit and closed the circuit, that would generate current inside the wire which would then do work. but the ammount of work it did would... | This is not a simple nor dumb question at all.
The answer is complex, and really depends on the exact details of the control system for the power station in question. Essentially, there will be control systems in place, either active or passive, that are designed to try and make sure energy is not wasted in the way y... | https://physics.stackexchange.com |
338,189 | [
"https://physics.stackexchange.com/questions/338189",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/148271/"
] | I have a uniformly charged disk, radius $R$, with surface charge density $\sigma$. I want to find the electric field along the axis through the centre of the disk (which I've called the $x$ axis).
I am aware that one method is to consider small rings and integrate from $0$ to $R$, but that is not how I approached the... | If a small piece of your disk is located at
$$
x=r\cos\theta\, ,\qquad y=r\sin\theta,\qquad z=0
$$
then the density would be $dq=\sigma dA=\sigma r dr d\theta$ where $\theta$ is the polar angle on the disk since $dA=r dr d\theta$ is the area of a small piece of your disk, with radius $r$ and arclength $rd\theta$.
For... | $$dq=\sigma dA$$
Thus, your question reduces to writing the surface element on a horizontal disk in polar coordinates.
If I move an infinitesimal distance $dr$ along $\mathbf{\hat r}$, I have traced an infinitesimal line segment.
I want to make an infinitesimal rectangle, so what should I choose for the other side? ... | https://physics.stackexchange.com |
1,364,668 | [
"https://math.stackexchange.com/questions/1364668",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/161104/"
] | <strong>Question:</strong>
<blockquote>
Solve the following integral: $$\int \frac{\sin x}{\sin4x}dx$$
</blockquote>
<strong>Attempt:</strong>
Using trigonometric identities to expand $\sin4x$, I obtained the integral:
$$\int \frac{1}{4\cos x \cos2x}dx$$
Now I'm not sure how to proceed. I tried writing $\cos2x$ in... | Substitute $\cos 2x=1-2\sin^2(x)$ and multiply by $\cos(x)$ on top and bottom, and then let $u=\sin(x)$ and $du=\cos(x)dx$:
$$\frac{1}{4}\int \frac{1}{\cos x \cos 2x} dx\\
=\frac{1}{4}\int \frac{\cos x}{\cos^2 x (1-2\sin^2(x))} dx\\
=\frac{1}{4}\int \frac{\cos x}{(1-\sin^2 x) (1-2\sin^2(x))} dx\\
=\frac{1}{4}\int \frac... | $$\begin{eqnarray*}\int\frac{\sin(x)\,dx}{\sin(4x)}&=&\frac{1}{4}\int\frac{dx}{2\cos^3 x-\cos x}=\frac{1}{4}\int\frac{\cos x\,dx}{2\cos^4 x-\cos^2 x}\\&=&\frac{1}{4}\int\frac{\cos(x)\,dx}{(1-\sin(x))(1+\sin(x))(1-2\sin^2 x)}\end{eqnarray*}$$
so it is enough to integrate:
$$\begin{eqnarray*}\int\frac{dt}... | https://math.stackexchange.com |
377,052 | [
"https://physics.stackexchange.com/questions/377052",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/124129/"
] | Suppose a person is standing in a bus moving with constant velocity. Assume that static friction between his feet and bus surface is very low (you could assume he is on roller skates) and we are observing this situation from the frame of reference of the bus. Then the driver applies the brakes and thus we feel accelera... | The simple answer is the the person on the roller skates is not accelerating and no force is acting on them.
Suppose I am standing on the pavement outside the bus when the bus starts to move. Clearly I am not accelerating because I am just standing there. If I watch the roller skater through the bus windows then when ... | <blockquote>
What's the actual reason for him accelerating
</blockquote>
The reason is that when the bus slows down, he is <strong>not slowed down along with it</strong>.
The bus and him have the same speed to start with. When the bus slows down, it looks like it moves backwards from his perspective. He still con... | https://physics.stackexchange.com |
3,824 | [
"https://physics.stackexchange.com/questions/3824",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41/"
] | Given that the electrical force is so much stronger than gravitational force at atomic levels, why is it that it's the gravitational force between you and the earth that keeps you on the ground rather than the electrical force between you and the earth?
| Gravitational force is what keeps us on the ground rather than electrical force because there's no negative gravitational mass. Electric charge can be neutralized, while gravitational attraction not.
| Actually, if you were at rest on the ground, the van der Waals repulsion between the atoms of the soles of your feet and the atoms of the ground — which is electrical in origin — exactly cancels the gravitational force between your <em>entire</em> body and the <em>entire</em> mass of the Earth.
Imagine tha... | https://physics.stackexchange.com |
144,214 | [
"https://dba.stackexchange.com/questions/144214",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/100389/"
] | Having the table with 3 columns:
<pre><code>ID category flag
1 A 1
2 A 0
3 A 0
4 B 0
5 C 0
</code></pre>
I want to select all rows that have <code>flag = 1</code> at least once per category.
Expected results:
<pre><code>ID category flag
1 A ... | <code>GROUP BY</code> cannot be used alone because it only returns 1 row per group (<code>category</code>).
<hr>
<ul>
<li>You can use a sub query with <code>flag = 1</code> and <code>INNER JOIN</code>:
<pre><code>SELECT d1.ID, d1.category, d1.flag
FROM data d1
INNER JOIN (
SELECT DISTINCT category FROM data WHER... | Assuming that <code>Flag</code> is a <code>BIT</code> column or an <code>INT</code> that takes only <code>0</code> and <code>1</code> as values, this could be achieved using windowed functions as well. For instance:
<pre><code>DECLARE @Test TABLE
(
ID INT
, Category VARCHAR(1)
, Flag BIT
);
INSERT INTO @Test (I... | https://dba.stackexchange.com |
617,223 | [
"https://electronics.stackexchange.com/questions/617223",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/312160/"
] | I've been reading (some Q&As on here and other bits on the web) about the behaviour of bipolar capacitors in AC circuits.
I understand that a polarised capacitor cannot work and will likely explode in an AC circuit due to the voltage going negative for half of the AC cycle. Only a bipolar cap can be used with AC.
... | A capacitor does not magically work differently in AC. It tries to maintain a steady voltage, causing a current flow to do so. This has some interesting <em>effects</em> when the source is AC (such as leading current, and reactive power) but the mechanism is not different.
So yes, if the AC source is disconnected, the ... | Yes, there can be some energy stored. If the supply is disconnected at the peak supply voltage, this could be as much as 1.41 times the RMS supply voltage. That's about 325V for a 230V AC supply.
For devices that can be unplugged, this can be a safety hazard for users, who aren't expecting a high DC voltage across the ... | https://electronics.stackexchange.com |
40,230 | [
"https://softwareengineering.stackexchange.com/questions/40230",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7428/"
] | One of our senior developers has stated that we should be using a naming convention for stored procedures with an "objectVerb" style of naming such as ("MemberGetById") instead of a "verbObject" type of naming ("GetMemberByID"). The reasoning for this standard is that all related stored procedures would be grouped toge... | Look at it like this. How are your methods organized in code? By object, with the methods hanging off.
<pre><code>MyObject.GetById(int)
MyObject.Save()
</code></pre>
By having your stored procs mimic that naming, it will be much easier to see how they relate to your source code.
<pre><code>MyObjectGetById
MyObject... | I too can see the logic; it groups actions together by entity. However, if your actions are always GET, PUT, and DELETE the change in naming might not matter that much. I see the best benefit from the new naming standard occurring when you have unique action names e.g. "AccountTransferMoney," that kind of thing.
The... | https://softwareengineering.stackexchange.com |
27,879 | [
"https://mathoverflow.net/questions/27879",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6757/"
] | I have an immersion of a 2-simplicial complex S in $\mathbb{R}^3$, and then a piecewise linear motion of that immersion over an interval of time [0,1].
<blockquote>
Is there an existing name for the map $f:S\times[0,1]\to\mathbb{R}^3\times[0,1]$?
</blockquote>
Update: here is a more detailed definition of f. Let $... | The map $f$ is usually called a <em>level-preserving homotopy</em> (or <em>level-preserving regular homotopy</em> if each $i_t$ is an immersion). At least this seems to be the accepted terminology in Geometric Topology.
| Looking at the comments on the question, it doesn't seem like this object $f$ is sufficiently interesting to have a standard name.
For the project I'm working on, using a name that's intuitive for computer scientists (who work on computer graphics) has taken precedence over using a mathematically appropriate term. So... | https://mathoverflow.net |
1,949,133 | [
"https://math.stackexchange.com/questions/1949133",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/367976/"
] | $\newcommand{\Reals}{\mathbb{R}}\newcommand{\Vec}{\mathcal{T}}\newcommand{\Brak}[1]{\left\langle #1\right\rangle}$
Just a question about the following exercise.
<strong>Exercise</strong>
Let $C=\{(x,y,z)\in\mathbb{R}^3|x^2+y^2=1\}\subset\mathbb{R}^3$. The cylinder $C$ can be identified with $M=\mathbb{R}^2\diagdown\{... | Secretly, the induced metric on the cylinder $C$ is the Euclidean (!) metric
$$
g_{C} = d\theta^{2} + d(\log \rho)^{2}
= d\theta^{2} + dz^{2}
$$
in the $(\theta, z)$-plane. Consequently, the geodesics are "straight lines parametrized at constant speed". (On the cylinder, these paths trace meridians, helices, or latit... | As a set, $C$ is same to flat cylinder we already know In further in problem $C$ has induced metric from canonical metric on $\mathbb{R}^3$ So it is in fact flat cylinder
And since we give a new coordination which is usually not used we obtain nontrivial geodesic equation
| https://math.stackexchange.com |
20,119 | [
"https://stats.stackexchange.com/questions/20119",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/996/"
] | In a traditional filtering context, you'd analyse polls coming in with something like
<pre><code>mu[i] <- alpha[date[i]]
prec[i]<- SampleSize[i]/(alpha[date[i]]*(1-alpha[date[i]])
y[i] ~ dnorm(mu[i],prec[i])
</code></pre>
If the surveys are observed with rounding, this <em>usually</em> won't make a difference. ... | I think something like:
<pre><code>mu[i] <- alpha[date[i]]
prec[i]<- SampleSize[i]/(alpha[date[i]]*(1-alpha[date[i]])
e[i] ~ dunif(-0.5,0.5)
mu.round[i] <- mu[i] + e[i]
y[i] ~ dnorm(mu.round[i],prec[i])
</code></pre>
would do the job. The <code>e[i]</code> represent the difference between the observed (roun... | No promises about the computational efficiency of this solution, but the best way to take into account rounding to the nearest integer in JAGS is to use the dinterval "distribution". The JAGS manual includes this passage:
<blockquote>
The dinterval distribution represents interval-censored data. It has
two parame... | https://stats.stackexchange.com |
602,261 | [
"https://math.stackexchange.com/questions/602261",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/79934/"
] | I feel a bit silly asking this question as it is no doubt relatively simple, but it has been bugging me.
Given the polar curve described by $r^2 = cos(2\theta)$, find the area inside the curve.
My intuition is to integrate from $0$ to $2 \pi$, but this clearly just yields 0. I have found that the area is 1, but this... | The problem is the curve is not orientable. So when you integrate to a singularity point, wrong orientation makes the area negative. Hence the total area zero by symmetry. A similar example is integration of $f(x)=x$ on $[-\pi,\pi]$ leads to zero.
| It's the same reason why integrating $f(x)=sin(x)$ from $T: 0 \rightarrow 2\pi$ yields a value of $0$; you're integrating over the negative portion of the $x$ and $y$ axes and because your function displays radial symmetry, when you take the integral over half your period it is equal in magnitude to the other half, but... | https://math.stackexchange.com |
9,625 | [
"https://physics.stackexchange.com/questions/9625",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3350/"
] | Quite new to all this - simple question.
"A ball starting from rest rolls down a hill and reaches 10m/s at the bottom. If the same ball starts rolling down the hill from an initial velocity of 5m/s, will it's velocity at the bottom be:
(A) Less than 15m/s;
(B) Equal to 15m/s;
(C) Greater than 15m/s."
The answer I ha... | Dear nulliusinverba, this server usually tries to avoid solving homework problems but let me give you a hint where your reasoning goes awry. You have assumed that the kinetic energy is proportional to $v$, haven't you? That's why you could think that by adding a fixed amount of kinetic energy, you always increase the v... | You reasoned correctly that in both cases the ball converts the same amount of potential energy into kinetic energy (at least it appears that you came to this conclusion).
The problem you are having is that you need to realize that kinetic energy is proportional to v^2. So, it takes NINE times as much energy to get f... | https://physics.stackexchange.com |
110,288 | [
"https://stats.stackexchange.com/questions/110288",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/53239/"
] | I have come across something that has got me kind of confused, I hope someone can help me out.
I did a mixed ANOVA with one within subjects factor with two levels 'time' and one between subjects factor 'group'. It was a comparison between a positive group and a negative group on scores pretraining and posttraining.
... | One possibility you might try is simulating Gaussian Processes with different kernels. In that way, you can get a feel for what the different kernels will produce. This can most easily be done by selecting a grid of values and simulating from the multivariate normal implied by that grid. To make things easier, just use... | Set aside a second set of training data, and "train" your model architecture using that.
i.e.
1) select an arbitrary kernel
2) train it using training set 1
3) evaluate it on training set 2 (using accuracy, precision, recall, whatever)
4) if !tired: goto 1)
5) else: return kernel with highest evaluation scor... | https://stats.stackexchange.com |
233,820 | [
"https://math.stackexchange.com/questions/233820",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/35001/"
] | If $Ax\geq b$, under what conditions on $K$ can I premultiply it and preserve the sign?
i.e
What is a sufficient condition on $K$ for:
$$KAx\geq Kb$$
| Suppose you have two vectors which satisfies the component-wise inequality (denoted $\ge_c$)
$$\mathbb{x} \ge_c \mathbb{y}$$
If you want a matrix such that
$$A\mathbb{x} \ge_c A\mathbb{y}$$
then that is equivalent to requiring
$$\mathbb{a_i}\cdot \mathbb{x} \ge \mathbb{a_i}\cdot \mathbb{y}$$
for each row vector $\mathb... | Let $y = Ax-b$
Assume $A$ is full rank. Then your question is the condition for matrix $K$, so that $Ky ≥_c 0,\ \forall y \geq_c 0 $
Necessary and sufficient condition for this, is non negativitity of $A$.
| https://math.stackexchange.com |
132,193 | [
"https://softwareengineering.stackexchange.com/questions/132193",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/20379/"
] | I am using a class through a dll to which I do not have direct control. So in effect, I am only a client of this class.
The class represents a form that can be printed, sent to clients and tracked in the system. I need to calculate two types of dates after which, if the form is received it is considered late.
Rather... | I'd use approach A and hide it behind an interface, since it'll make the algorithm easily exchangeable where you use it.
I'd only use B when I have to store/cache multiple values that are created by a single algorithm. If the costs of a calculation are cheap and I only have to calculate two dates then I'd stick with ... | All options are valid, I don't see anything particularly bad about any of them (well, maybe <code>A</code> unless it's a static class... but that logically resolves to <code>C</code> eventually anyway) but I see <code>C</code> as being the one I would choose. Here's why:
<ol>
<li>In code, you'll already have a form, a... | https://softwareengineering.stackexchange.com |
171,400 | [
"https://electronics.stackexchange.com/questions/171400",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/66847/"
] | Background:
My goal is to use an Arduino with two proximity probe sensors to achieve some output.
It is worth mentioning that the output of the proximity probe has two components:
<ol>
<li>DC output that determines the position or the GAP</li>
<li>AC component on the top of that DC voltage to determine the vibration<... | Your output looks fine to me.<br>
There is always a period at start up of a filter where its output is off, and it converges to the correct output in a time period related to the cutoff frequency - a lower cutoff for a low pass filter means it will take longer to converge to the true value. This explains the "changing... | If I understand the problem you have to
<ol>
<li>invert the signal</li>
<li>Scale the signal </li>
<li>Remove the AC component</li>
</ol>
At the very least an OPAMP is required to forfill #1 and #2 so this active component might as well be used to remove "some" of the AC component.
To remove the AC component however... | https://electronics.stackexchange.com |
61,069 | [
"https://mechanics.stackexchange.com/questions/61069",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/43442/"
] | In a car with a manual transmission, you can start it by taking the car out of gear and pressing the clutch, then turning the ignition. You can also start it by pressing the clutch <strong>without actually taking the car out of gear</strong>.
Bikes, with kickstart mechanism, on the other hand (at least in my experien... | Actually you could BUT... Motorcycles have WET multiple disc clutches in contrast with cars that usually have a single dry plate clutch engagement.
The friction and mainly the drag produced by these multiple discs is often very hard to overcome by kick starter, especially when the engine is cold.
You can simulate thi... | The same can be done with a bike, whether electric or kick start. Except with a kick start bike even with the clutch in, you get a lot of clutch drag transferred through the kickstarter as the clutches are often wet, so they're sat in gear oil making it a lot harder to kick over.
| https://mechanics.stackexchange.com |
552,158 | [
"https://physics.stackexchange.com/questions/552158",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/245449/"
] | Suppose we are given a sphere with total charge <span class="math-container">$Q$</span> and radius <span class="math-container">$R$</span>. To find the total charge <span class="math-container">$Q$</span>, we can use the relationship <span class="math-container">$$\rho = \frac{dQ}{dV}\implies Q=\int_0^R\rho \cdot dVdr$... | The charge density <span class="math-container">$\rho(x,y,z)$</span> is the charge per unit volume. So when you want to get the total charge of a given density in a Volume <span class="math-container">$V$</span> you have to integrate the density over the volume.
<span class="math-container">\begin{equation}
Q = \int_... | First of all, from the formula you have written for Q, it's dimensions are not of charge, but it's dimensions is charge*length
You have written extra dr in the integration formula.
<span class="math-container">$\rho$</span> is volume charge density and to make it charge, you just have multiply it by volume. (Note- if... | https://physics.stackexchange.com |
128,989 | [
"https://softwareengineering.stackexchange.com/questions/128989",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32803/"
] | From a security perspective, the special characters like '&' or <code><b></code> are a big no no in URLs and query strings. I could find the articles that explained the ways to bypass this restriction, but could find something that explained with example how can this be a security risk.
Please explain the ri... | In ASP.NET, those characters are blocked by default to prevent a beginner developer introducing a security hole in the application.
Consider the following scenario:
<ul>
<li>On a home-made blog, users can post comments.</li>
<li>Those comments are stored in the database.</li>
<li>The comments are loaded later and dis... | The ampersand (<code>&</code>) character isn't really forbidden, but because it is the separator for query string parameters, using it unescaped in a parameter name or value will cause undesired behavior - for example, if you have a parameter <code>foo=bar&baz</code> and another <code>quux=1</code>, a naive att... | https://softwareengineering.stackexchange.com |
2,095,460 | [
"https://math.stackexchange.com/questions/2095460",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/405852/"
] | How do I solve the differential equation $$7x(x-y)dy = 2(x^2+6xy-5y^2)dx$$
Is it homogeneous? I have tried taking the variables from the LHS and applying them to the RHS, making $\frac{dy}{dx}$ subject and ending up with:
$$\frac{dy}{dx} = \frac{2(x^2+6xy-5y^2)}{7x(x-y)}$$
After simplifying the numerator:
$$\frac{... | First notice that $$1^5 + \dots + n^5 = \sum_{i=1}^n i^5 = \frac{2n^6 + 6n^5 + 5n^4 -n^2}{12}.$$ Now recall the definition of $g(n) \in \Omega(f(n)).$
<blockquote>
<strong>Definition.</strong> A function $g(n) \in \Omega(f(n))$ if $\exists n_0 \in \mathbb{N},c\in\mathbb{R}$ such that if $n \geq n_0$ then $$g(n) \geq... | I'd simply say that $i^5 \leq n^5$ for all $1 \leq i \leq n$, and so $$\sum_{i=1}^n i^5 \leq \sum_{i=1}^n n^5 = n^6$$
Therefore the ratio $$\frac{\sum_{i=1}^n i^5}{n^6}$$ is always at most $1$ as $n \to \infty$.
| https://math.stackexchange.com |
96,711 | [
"https://mathoverflow.net/questions/96711",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12586/"
] | Suppose $f_1,f_2,\ldots $ is a sequence of convex functions that converges to a continuous convex $f$. Let $x_1^*,x_2^*$ be their respective (not necessarily unique) minima, and let y be a minima of $f$ (once again need not be unique). Can we prove that there exists a version of $x_1^*,x_2^*,\ldots$ such that $x_n^*\ri... | No; here's a counterexample: let $f = 0$ and consider the minimizer $y = 0.$ Then you can construct convex functions which converge to $0$ pointwise but whose minima are always moving away from $y =0,$ e.g. $f_n(x) = (x - n)^2/n^n.$
| No. Let $f_n=x^2/n$ for $n$ odd and $(x-1)^2/n$ for $n$ even. Then $x_n^*$ is an alternating sequence of $1$s and $0$s, which does not converge to anything. But $f_n$ converges pointwise to $f=0$.
We can modify this to make the convergence uniform, by using an absolute value instead of a square, or to make $f$ noncons... | https://mathoverflow.net |
6,381 | [
"https://mechanics.stackexchange.com/questions/6381",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2667/"
] | Currently I own a Mk5 Astra SRi, however I am looking to sell this and buy a Ford Focus Mk2.
The other day I looked at a Ford Focus Zetec Mk2. My understanding is that Zetec is sort of the ford equivalent of an Astra SRi (given that ST is the equivalent of a VXR).
The only thing that really threw a spanner in the wor... | Drum brakes are cheaper to manufacture than disc brakes, because there are fewer moving parts and because in the rear the parking brake (which often works by a drum-and-shoe mechanism even on four-wheel-disc-equipped cars) can share a drum with the "regular" brakes.
All other things being equal, discs work better than... | The rear brakes hardly contribute to stopping your car. They do between 20% and 30% of the work, so they can be cheap without compromising your safety or stopping distance. Mind you, drum brakes last much MUCH longer than discs. I have a Vauxhall Corsa B that has done 100k miles (160k kilometers) and the drums and shoe... | https://mechanics.stackexchange.com |
179,507 | [
"https://mathoverflow.net/questions/179507",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13767/"
] | Pictures in introductory texts to Morse theory are often drawn as to interpret a Morse function as a height function. Typically, an embedding of a torus into $\mathbb{R}^3$ is drawn, and the Morse function is then the height function by projecting onto one component (call the projection $\pi$).
This is a great picture... | Simply take the ordinals $\omega+1,...,\omega+n$ and one obtains $n!$ distinct products (This solution was taken from Chapter 8 Problem 39 and Chapter 9 Problem 66 in the book Problems and Theorems is Classical Set Theory).
This follows from the easily provable fact that for natural numbers $r_{1},...,r_{n}$ we have $... | For a lower-bound partial answer, note that there are at least as many ways to form a product as a sum, and so $F(n)\leq G(n)$. This is because we may replace an ordinal $\alpha$ with $\omega^\alpha$ and thereby turn multiplication into addition via $\omega^\alpha\cdot\omega^\beta=\omega^{\alpha+\beta}$. Since $\omega^... | https://mathoverflow.net |
2,759 | [
"https://physics.stackexchange.com/questions/2759",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1213/"
] | How would I figure out the Cartesian graph that describes a bar clamped flat for a length on one end with downward force being applied to the other?
I have an idea that the bar will try to average out the stress over the free length. Does it in fact evenly distribute stress over the whole free length? If so, can I u... | I know this question is a little old, but so far there is no correct answer posted. It happens that I used to argue this question with Civil Engineering students years ago. They had trouble with it because they learned about "bending moment", which is basically the same thing as curvature only no one told them that. Th... | I think if the boundary conditions were perfectly symmetric, you'd get a simple circular shape. In your case you have somewhat different conditions on both ends. The inside of the curve will be in compression, and the outside in tension. But I think your clamped end restricts some of the material degrees of freedom, so... | https://physics.stackexchange.com |
112,854 | [
"https://physics.stackexchange.com/questions/112854",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/785/"
] | Oil underground is much denser than greenhouse gas in the atmosphere.
Does the conversion in anyway effect the gravitational force from earth.
| As Hoytman points out, fossil fuel combustion does not change the mass of the earth, and so its gravitation with celestial bodies is unchanged. But moving mass from the subsurface to the atmosphere would slightly decrease surface gravity.
Let's see whether that decrease would be <em>measurable</em>. Let's suppose th... | Because gravity is a property of mass and mass is neither created or destroyed when fuel is burned, the only measurable difference would be caused by the change in the location of the mass. When fuel is burned, mass is taken from the surface of the planet and added to the atmosphere. this would cause a (slight) reduc... | https://physics.stackexchange.com |
1,984,499 | [
"https://math.stackexchange.com/questions/1984499",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/382525/"
] | My dad just sent me a math problem on email and asked if I could solve it, but frankly, I have no idea where to start. I've got 3 equations with 4 unknowns and some information about the unknowns.
First, the equations:
$$2(z-1)-x=55$$
$$4xy-8z=12$$
$$a(y+z)=11$$
I am supposed to determine the 2 greatest real number va... | You have from the two first equations :
$ 2z-x = 57$ and $xy-2z = 3$
thus $$x(y-1) = 60 = 2^2\times3\times5$$
Therefore since $x$ divides 60, $$x\in\{1,2,3,4,5,6,10,15,18,20,30,60\}$$ and thus $$xy=60+x \in \{61,62, 63, 64, 65, 66, 70, 75, 78, 80, 90, 120\}$$
However from $xy - 2z = 3$ we see that $xy$ is odd, th... | You can solve the first equation for $x$ and plug into the second.
$$2(z-1)-x=55\\
x=2(z-1)-55\\
8zy-8y-8z-220y=12\\
2z(y-1)-57y=3\\
z=\frac {3+57y}{2(y-1)}=\frac{30}{y-1}+\frac {57}2$$
To make $z$ integral, we must have $y-1$ a multiple of $4$ but not $8$ and divisible into $60$, so $y$ can equal $5,13,21,61$ giving t... | https://math.stackexchange.com |
694,894 | [
"https://physics.stackexchange.com/questions/694894",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/326858/"
] | i wanted to know why does a moving charge and bar magnet not experience force similar to how two bar magnets experience since they both have magnetic fields. In bar magnets they attract or repel but in a moving charge there is just force?
Can you tell what actually happens here?
| Indeed, you cannot solve it that way because <span class="math-container">$v$</span> is a function of time. Instead you treat it as a differential equation: <span class="math-container">$$a = \frac{d v(t)}{dt}=-k v^2(t)$$</span>
This has the solution <span class="math-container">$$v(t)=\frac{1}{kt+C}$$</span> and we ca... | The initial equation should be:
ma = -2
Then apply answer 1.
Air resistance is a force, not an acceleration. It is not dependent on the mass of the object - just coefficient of drag, density of the air, and cross sectional area of the object. This equation above maintains a mass term in the solution, which makes sense... | https://physics.stackexchange.com |
311,738 | [
"https://electronics.stackexchange.com/questions/311738",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/152454/"
] | I want to design water level controller with PIC micro controller.
Simple working is: two inputs 1) tank_high and 2) tank_low which pulled up initially, and one wire will be connected to lowest point in tank which is dc ground.
The problem is PIC microcontroller is working on 5V DC and if accidentally in water tank ... | It's pretty common to activate the internal pullup at least, and perhaps provide a stronger external one. Floating inputs don't just cause false signals; an input near the logic level crossover voltage can cause a chip to consume excessive current, since both the upper and lower FET's can be partially turned on, causi... | I faced same problem when I custom designed my ATmega64 PCB.
It was working fine when TX/RX connected to computer through FTDI USB Cable and if I disconnect FTDI from computer or from ATmega64 Board then Controller Output Pins were toggling without any input.
<ol>
<li>Solution: I had LM317 on board set at 3.7 V... | https://electronics.stackexchange.com |
518,779 | [
"https://physics.stackexchange.com/questions/518779",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246807/"
] | Okay, so power is work/time. Most cases, when power is provided to something, energy is gained as kinetic energy or lost to friction.
But in a car, the engine puts power ( torque x rpm/5252) to wheels, but very little ends up in the wheels, assuming friction keeps them from spinning.
So where does the power go? Do th... | When the engine applies a torque on the wheels via the gear mechanism, the wheels want to spin around, but the mass of the car and the friction between the road and the tires constrains it. So the only way is to move the vehicle forward. The friction between the tires and the road provides the necessary traction to do ... | The engine applies torque to the wheels. The wheels turns and apply friction force to the road. By Newton's third law the road applies force to the wheels which make the car moving. Engine power goes to kinetic energy of the car, dissipated heat to friction, air resistance force, battery charging and air conditioning
| https://physics.stackexchange.com |
481,093 | [
"https://stats.stackexchange.com/questions/481093",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/292938/"
] | I'm composing a survey where I compare two mobile apps and am not sure how to formulate the questions.
Should I compare the apps directly like this:
"Which app was more intuitive to use?"
1 (App A) ... 5 (App B)
Or pose one question per app like this:
"How do you rate the intuitiveness of App A/B?"
... | There are a few things we can say about this situation
<ul>
<li>the condition of normality of residuals only needs to hold <em>approximately</em>. If the sample size is small then it can be difficult to distiguish a uniform from a normal distribution, and it is reasonable in such circumstances to assess the residuals a... | A classic linear regression model works under the assumption that the data can be modeled as
<pre><code>y = Ax + b + eta
</code></pre>
where <code>eta ~ N(0,sigma)</code> .
if your residuals are uniformly distributed, it means that the above assumptions doesn't hold.
However, this linear regression can still work for y... | https://stats.stackexchange.com |
3,017,615 | [
"https://math.stackexchange.com/questions/3017615",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/607124/"
] | <blockquote>
Consider numbers <span class="math-container">$n \geq r \geq 1$</span> where <span class="math-container">$n,r \in \mathbb{Z} $</span>, prove the following:
<span class="math-container">$$\binom {r}{r} + \binom {r+1}{r}...+ \binom n r = \binom {n+1}{r+1}$$</span>
</blockquote>
Only thing I know is tha... | Note that
<span class="math-container">$$
\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1}
$$</span>
Therefore repeatedly applying this in reverse,
<span class="math-container">$$
\begin{split}
\binom{n+1}{r+1}
&= \binom{n}{r} + \binom{n}{r+1} \\
&= \binom{n}{r} + \binom{n-1}{r} + \binom{n-1}{r+1} \\
&= ... | Base case <span class="math-container">$n=r$</span>. Thus <span class="math-container">$$\sum_{k=r}^{n=r}\binom{k}{r}=1=\binom{r+1}{r+1}$$</span>
For the inductive case suppose, for some <span class="math-container">$i\in\mathbb{N}\; :\; i>r$</span>, <span class="math-container">$$\sum_r^{i}\binom{k}{r}=\binom{i+1}{... | https://math.stackexchange.com |
379,482 | [
"https://softwareengineering.stackexchange.com/questions/379482",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/297718/"
] | I'm developing backend for a dating app, in which each user has
<ol>
<li>a profile of his/her characteristics </li>
<li>a profile of ideal match's characteristics </li>
</ol>
There are dozens of characteristics like gender, height, looks and so on.
Some characteristics are strings, others are numbers or arrays.
Each... | <h3>Identify the different kind of characteristics</h3>
Your sample data illustrates very well that different kind of characteristics need to be handled in a different way:
<ul>
<li>Heigh is a <strong>scalar</strong> attribute: a profile has one numeric value, but the ideal always looks for a range.</li>
<li>Ethnicity ... | Unfortunately it isn't enough just to know the type to be able to perform fuzzy matching. For instance if you wanted to select persons with varied height, what is the difference between a search with height 5'10" and importance 4 vs an importance 1? Even if you try to apply some formula such as height can be in the r... | https://softwareengineering.stackexchange.com |
15,248 | [
"https://dsp.stackexchange.com/questions/15248",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/8373/"
] | I am planning to implement a pattern matching algorithm using something like correlation as a matching metric.
I know that the template I am going to use will, if present, have different sizes in the target images. The interval of sizes might be something like :
x 0.5 , x 0.75 , x 1.0 , x 1.25 , x 1.5 , x 2.0 of the o... | Many image display devices only have an 8-bit DAC. So if one wants to analyze only what will be displayed on such a device (without added dithering or noise filtering, etc.), one can convert to that 8-bit format and potentially save storage memory. Many standard image file formats also only support 8 bits of luminanc... | Other than the data being smaller and thus requiring less memory there is usually no benefit to converting to 8 bit unsigned.
There is never a benefit in terms of image quality, and there is usually not a benefit in terms of processing speed. Most processors handle 16 bit values as fast as they do 8 bit values (thoug... | https://dsp.stackexchange.com |
585,295 | [
"https://stats.stackexchange.com/questions/585295",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/202930/"
] | This seems like a trivial question but I am currently stuck and cannot see what I am doing wrong.
So let us consider a function <span class="math-container">$f(x) : \mathbb{R}^d \rightarrow \mathbb{R}^d$</span>.
I want to compute the derivative w.r.t. <span class="math-container">$x \in \mathbb{R}^d$</span> of an expre... | Let <span class="math-container">$(\nabla f)_{ik}=\frac{\partial f_i}{\partial x_k}$</span>. Then derivative is
<span class="math-container">$$
\frac{\partial I}{\partial x} = (\nabla f)^T C f + (\nabla f)^T C^T f.
$$</span>
I think you perhaps implicitly assumed that <span class="math-container">$C$</span> is symmetri... | Given a differentiable vector field <span class="math-container">$\mathrm f : \mathbb R^d \to \mathbb R^d$</span> and a matrix <span class="math-container">$\mathrm C \in \mathbb R^{d \times d}$</span>, let function <span class="math-container">$F : \mathbb R^d \to \mathbb R$</span> be defined by
<span class="math-cont... | https://stats.stackexchange.com |
475,630 | [
"https://electronics.stackexchange.com/questions/475630",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/239944/"
] | Today I as a Computer Scientist stumbled about some strange facts.
Recently, I bought a new Macbook Model 16" inch. Today I tried to stress test it because I wondered if the 96 Watt charging cable could even keep up with this processor and GPU power consumption.
Running Cinebench showed, that running the program witho... | <h2>A short story</h2>
Long before solid-state electronics and vacuum tube electronics, lead acid batteries were and are the longest living battery technology. Being a multiple of 2V +/- 0.1 per cell or 2.36V on float charge or 14.2V, the <strong>12V battery was not the 1st common voltage for cars</strong>. Initially... | There is no guaranteed correct answer, but the "nominally 12V" available from 6 x lead acid cells and its adoption as the standard for most domestic motor vehicles is a powerful force in setting a standard in other areas. Some early cars used 6V, which proved far from ideal, and larger non-domestic vehicles use 24V (as... | https://electronics.stackexchange.com |
275,493 | [
"https://math.stackexchange.com/questions/275493",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/44344/"
] | If $g \circ f$ is monic, then $f$ is monic. Or, if $g \circ f \circ h = g \circ f \circ k \implies h = k$, then $ f \circ h = f \circ k \implies h=k$.
I am not exactly sure how to prove this. I don't know what my possible actions or manipulations are to get from one statement to the other. I drew a (messy) commuting d... | You don't need to draw any commutative diagrams for this problem (but if you ever do you can learn quite quickly how to draw very complicated diagrams using XYpic (works with Latex and/or Lyx)).
Given that $g\circ f$ is monic we show that $f$ is monic. Assume that $f\circ h = f\circ k$ holds. The claim will follow by... | There's no need for a commutative diagram to prove this:
Using the fact that $g\circ f$ is monic, we show that $f$ is monic.
Assume $$f\circ h = f\circ k\tag{1}$$
Compose $g$ on the left with each of $f\circ h, f\circ k$ in equation $(1)$:
$$g\circ (f\circ h)= g\circ (f\circ k).\tag{2}$$
By associativity of comp... | https://math.stackexchange.com |
237,123 | [
"https://security.stackexchange.com/questions/237123",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/241225/"
] | Let's say that I have an unencrypted file and I'm trying to encrypt it and make sure the original file can not be recovered from my disk. If I, for example, create an archive, put the file into it and encrypt the archive it seems pretty obvious that even if I delete the original file it is still on the disk and can be ... | The best option is to use <em>full-disk encryption</em> that encrypts everything whether it's explicitly encrypted with <em>file encryption</em> or not.
In your situation, you could try and write a file so big that it fills the whole drive, making it more likely you overwrite the original file. However, there could be ... | There are clever ways of doing that. I would create the file on a RAM drive (if you have enough of RAM to create the partition to store your file in RAM initially) encrypt it and then save it to the SSD this way the unencrypted copy of the file does not exist on the drive at any point of time (except for when you decry... | https://security.stackexchange.com |
31,201 | [
"https://stats.stackexchange.com/questions/31201",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12236/"
] | If I have daily data set and it's a non-stationary series, then what is the lag I have to consider for the first difference 1 or 7?
| This depends on the form of nonstationarity. If it is a because of a linear trend then you take a first difference. If it is a season of period 7 then it would be seven. However the method of detrending does depend on the type of trend. Knowing only that the series is nonstationary is not sufficient to answer the qu... | If a series is non-stationary in the mean then there are two distinctly different ways to approach this problem. The actual data will tell you which is the best remedy. Let us for the moment assume that we have detected the presence of non-stationarity. In effect, we have a symptom and need to apply the appropriate rem... | https://stats.stackexchange.com |
152,729 | [
"https://physics.stackexchange.com/questions/152729",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2481/"
] | What will happen to permanent magnet's magnetic field or magnetic ability if we keep same magnetic poles of two permanent magnet for long time?
<img src="https://i.stack.imgur.com/uPciF.jpg" alt="enter image description here">
Will any magnetic loss happen over the long period of exposure or does the magnetic strengt... | If we keep two magnets with same poles together, then they'll become weaker overtime. I once deliberately did it to find out what would happen.
This could be explained with Magnetic Domain Theory. In magnets, the magnetic domains are aligned in the same direction, giving them a strong magnetic field. If two magnets a... | In my experience (with ferroxcube materials) nothing happens. In fact, to change the magnetic properties the magnetic domains inside must be reoriented. But the force excerted by the second magnet is not strong enough to do so. But one can magnetize a non-magnetic piece of iron (for instance the tip of a screwdriver) b... | https://physics.stackexchange.com |
47,025 | [
"https://electronics.stackexchange.com/questions/47025",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9901/"
] | <img src="https://i.stack.imgur.com/4XzsN.png" alt="enter image description here">
I made a schematic for an h-bridge motor driver that will be connected to a MCU.
Is this schematic correct? I'm not sure if the flyback diodes are working correctly since I added that NPN transistor.
A and B are used to control the mo... | There are several problems:<ol>
<li>I didn't look up to see what kind of FET exactly a IRF540 is, but in any case you can't just flip it upside down and expect it to work in a complementary way.
<li>Even with the right FETs oriented correctly, it doesn't make sense to tie the gates of opposite corners together. The ... | Search for "high side gate drive" ICs/hybrids. That is what you likely want to ensure you saturate Q1 and Q3 if you want to stick with N-channel parts on the high side. A high side gate driver will handle the DC/DC conversion and level shifting for you so that you can apply logic-level inputs while still pulling the ... | https://electronics.stackexchange.com |
461,203 | [
"https://electronics.stackexchange.com/questions/461203",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/198421/"
] | I have a signal y[n], represented by the vector y in this form
<ul>
<li>y[n] =x[n] + ax[n−N]</li>
</ul>
About this signal:
<ol>
<li>x[n] is the uncorrupted speech signal which has been delayed by N samples and added back in with its amplitude decreased by a<1</li>
<li>N= 1000, and the echo amplitude,a= 0.5.</li>
... | <blockquote>
Determining and plotting the impulse response of the signal.
</blockquote>
You are confusing signals and systems. Systems have impulse responses, signals don't. You can calculate the output signal of a linear time invariant system for any given input vy convolving the input signal with the impulse resp... | You need to create a unit impulse signal to drive your filter in order to see its impulse response. Create an array <code>x[1000]</code> with a 1 in the first location, and 0 everywhere else.
If you pass this signal through your filter, your <code>y</code> array will be the impulse response. But it should be obvious b... | https://electronics.stackexchange.com |
13,270 | [
"https://mathoverflow.net/questions/13270",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3610/"
] | Hello,
I've been working deriving the orthogonality relation for quadratic Dirichlet characters $\chi_d(n)$ (or real primitive characters). The statement I'm trying to prove is
$$\lim_{X \rightarrow \infty} \frac{1}{D} \sum_{0 < |d| \leq X} \chi_d(n)= \begin{cases}
\prod_{p|n} \left(1 + \frac{1}{p}\right)^{-1} ... | So I think I solved half of the problem. Suppose that $n$ is a perfect square. Then $\chi_d(n) = 1$ unless $\gcd(d,n) > 1$, in which case its $0$. So, for $\gcd{d,n} = 1$, we are simply pulling out the subset of fundamental discriminants having no common divisor with $n$. To quantify the size of this subset, we must... | I'm not 100% sure I know what you mean by an "analytic proof" but I'll try to give an argument similar in style to what you already worked out. In particular I won't go into any detail on the correspondence between average values of arithmetical functions, and the analytic behavior of the relevant generating Dirichlet... | https://mathoverflow.net |
321,585 | [
"https://math.stackexchange.com/questions/321585",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/49811/"
] | I am working on the chapter one practice problems in Hardy and cannot seem to figure it out.
My attempt has actually left me with a result contrary to what the question is looking for.
<strong>The Question</strong>
In what circumstances can $\dfrac{aA+b}{cA+d}$ be rational, where $a,b,c,d$ are rational and $A$ is irr... | Your steps are fine. But since $A=\dfrac{qz}{pt} \dfrac{wt-sx}{uz-yv}$ is an irrational then, denominator must be $0$ and then $A$ to be defined, numerator must be $0$ too which gives $wt=sx$ and $uz=yv$ which implies $a:c::b:d$
| assuming your calculations are correct, that means that you have a contradiction (and therefore $p$ and $q$ do not exist) unless $p(uz−yv)=0$ (as $t$ already can not be $0$)
Dividing by $0$ is very bad :)
My answer using this logic :
$$\frac{p}{q} = \frac{aA+b}{cA+d} \Longrightarrow p(cA+d)=q(aA+b) \Longrightarrow ... | https://math.stackexchange.com |
50,179 | [
"https://softwareengineering.stackexchange.com/questions/50179",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/963/"
] | In many other languages like C++ and Javascript, OOP is optional. Procedural code is ok. But in languages like Java and C#, OOP is somewhat enforced. Everything is to be a part of a class or an object. What are the benefits?
| Both C# and Java are marked as languages known not for what they enable, but what they <em>disable</em>, in terms of the feature set they use. (C# less so these days with LINQ but that's a whole different can of worms) Both of these languages are designed such that it's more difficult to create bad designs, at the expe... | It isn't so much that OOP is enforced, as that an OOP framework is enforced. It's possible to write procedural programs in Java, although it's easier if they're only one file.
The advantage is uniformity. There are several different types of functions and data in C++, and this does cause some problems and confusion ... | https://softwareengineering.stackexchange.com |
745,618 | [
"https://physics.stackexchange.com/questions/745618",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/337240/"
] | The deeper I carve into physics, the more clear it becomes to me that there might be a better way to analyze the universe than our mathematical frameworks. Not like defining new algebras or thinking outside the box - I feel there must be something bigger than math itself that we can use to make predictions. What this i... | This is an excellent question, but, of course, some who don't want to face the issue hate it.
Mathematics is an essential tool of physics. We've been using it for millennia, and we've never found an adequate substitute. Physics is not founded on mathematics: the phenomena of the real world are in charge. However, to pr... | I think this is misunderstanding of what science is: unlike philosophy, its goal is not understanding the Universe for the sake of understanding, but <em>understanding in order to make quantitative predictions</em>, thus permitting improving human condition (e.g., with the aid of new machines.) <em>Quantitative</em> by... | https://physics.stackexchange.com |
184,655 | [
"https://dba.stackexchange.com/questions/184655",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/133608/"
] | This may be a bad structure. Let me know if it is, it's been a long time since I did any database design.
I have a <code>tblGame</code> in a mySQL database, which has two fields:
<pre><code>ID_Table
ID_Player
</code></pre>
In the actual game, multiple players will sit on the one table. So I have both fields set as ... | You could implement the following solution.
<h3>Game "Table"</h3>
This table stores the auto-generated values of the (playing) Tables for the game:
<pre><code>CREATE TABLE tblTable (
ID int NOT NULL AUTO_INCREMENT);
</code></pre>
<h3>Game "Players"</h3>
This table contains all the relevant Player data:
<pre><... | If you are using Mysql Database this query can help you
<pre><code>CREATE TABLE Your_table_name (
ID int NOT NULL AUTO_INCREMENT,
LastName varchar(255) NOT NULL,
FirstName varchar(255),
Age int,
PRIMARY KEY (ID)
);
</code></pre>
MySQL uses the AUTO_INCREMENT keyword to perform an auto-increment f... | https://dba.stackexchange.com |
69,809 | [
"https://chemistry.stackexchange.com/questions/69809",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/-1/"
] | I read in a textbook that in the case when we have a gas in a cylinder fitted with a massless frictionless piston being held with an external pressure <span class="math-container">$p_1$</span>, and when the pressure is reduced to become the value <span class="math-container">$p_2$</span>, the gas pushes up against the ... | If the piston is frictonless and massless, then, if you do a force balance on the piston, you must have that the force per unit area that the gas exerts on the inside face of the piston will always be equal to the external force per unit area that one imposes on the outside face of the piston. The sudden drop in press... | Consider a thought experiment; imagine playing your favourite sport competitively against someone. Imagine losing the game as time runs out (bleak scenario sorry). The work is what you actually put in to catch up. If they are good it becomes even harder to catch up. Winning is just how much better you were with your w... | https://chemistry.stackexchange.com |
567,623 | [
"https://physics.stackexchange.com/questions/567623",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/270597/"
] | Consider a simple resistance circuit with a cell and a resistor. It is stated that energy stored in cell appears as heat in resistance as current flows in ideal circuit (neglecting EM radiation) as whole.
<strong>POWER/RATE OF HEAT GENERATION = POWER/RATE OF ENERGY CONSUMPTION in CELL = VI</strong>
However we also know... | <blockquote>
1.Is energy needed to create magnetic field in general?
</blockquote>
Yes. When you are using circuit theory the mechanism for dealing with magnetism is called inductance and is usually represented by the variable <span class="math-container">$L$</span>. The inductance gives the total magnetic field so tha... | I agree with the answer @Dale provided.
To put things into perspective, the energy stored in the magnetic field of a straight conductor is minuscule compared to the energy dissipated in the resistance of the conductor.
The inductance of a straight copper wire 1 mm in dia and 10 cm long is about 105 nH. The energy store... | https://physics.stackexchange.com |
38,738 | [
"https://mathoverflow.net/questions/38738",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9232/"
] | For each positive integer n we may define the convergent sum $$ s(n)=\sum_{p}\frac{(n,p-1)}{p^2} $$
where the summation is over primes p and $(a,b)$ denotes the greatest common divisor of a,b.
It is immediate to deduce that s(n) is bounded on average:
Using $\sum \limits_{d|a, d|b}\phi(d)=(a,b)$ and inverting the or... | Your guess that $s(n)$ gets large if $\omega(n)$ is large is not correct.<br>
It is possible for $n$ to have many primes, and for $s(n)$ still to be small.
This can be seen from some of the work in your question. As you note $s(n) =\sum_{d|n} \phi(d) a_d$ where $a_d =\sum_{p\equiv 1\pmod d} p^{-2} \ll 1/d^2$. There... | Are you just trying to show $s(n)$ is unbounded? and do you insist on a non-trivial technique? Let $n=m!$; then $s(n)>\sum_{p\lt m}{p-1\over p^2}=\sum_{p\lt m}{1\over p}+O(1)$ and of course the sum diverges.
| https://mathoverflow.net |
223,806 | [
"https://electronics.stackexchange.com/questions/223806",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/98056/"
] | There are 2 systems,A and B. Communication between them is via Uart.
As part of periodic health check for CAN Bus, its possible to do a loopback and check the status of the CAN transceiver and the bus(in addition to those taken care of the CAN spec itself like error counters).
Similarly, if my choice is UART for comm... | If "functioning properly" means proving that Tx and Rx lines are not open circuit then "no". To check this requires "something" at the far end however, even with something at the far end you cannot simply know that a line open fault is due to Tx, Rx or both.
You could develop a form of TDR (time domain reflectometry) ... | Usually the transmit line is held high by the driver. You could add a weak pull-down on your receive line and measure the voltage there. If it's high, you know the transmitter on the other side is connected.
| https://electronics.stackexchange.com |
594,003 | [
"https://physics.stackexchange.com/questions/594003",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/150174/"
] | So I've become rusty in Quantum Mechanics. What is <span class="math-container">$\langle x_1 |V(\hat x)| x_2 \rangle$</span>? Where <span class="math-container">$V$</span> is the potential and <span class="math-container">$|x \rangle$</span> is the postion eigenket?
<span class="math-container">$$ \langle x_1 |\hat ... | You can think of it in the sense of distributions, and then Philip's answer applies, in the sense that, as distributions
<span class="math-container">$$ f(x)\delta(x-y)=f(y)\delta(x-y)$$</span>
but more intuitively, you can also think of <span class="math-container">$\delta(x-y)$</span> as having support only on <span ... | I'm not very good at the rigorous math, but the way I think about it is that "functions" like the Dirac Delta are actually <em>distributions</em>, meaning that they only make sense inside of an integral of the form:
<span class="math-container">$$\int_{a}^b \text{d}x\,\,f(x)\delta(x),$$</span>
where <span cla... | https://physics.stackexchange.com |
352,030 | [
"https://physics.stackexchange.com/questions/352030",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/166459/"
] | How to calculate speed in min/km given distance in meters and time seconds? I used formula <code>v = d/t</code>but having problems converting units.
I've tried <code>((distance_m/1000) / (time_sec/60))</code> and got something <code>~ 0.2</code> and I'm expecting something around <code>4:08 min/km</code>
| Unit conversions are an important part of any science. Usually, to convert from one unit to another, you can just multiply by one or more conversion factors.
For example, to get ${min\over km}$ from ${m\over s}$ you convert $s$ to $min$ by the factor of $60 s\over 1 min$ and $m$ to $km$ by the factor of $1000 m \over ... | How many seconds are in a minute? Every second is equal to...?
How many metres are in a kilometre? Every metre is equal to...?
The part where you're most likely to go wrong is whether to multiply or divide to go from second to minute or metre to kilometre. Just remember that if the unit at the end denotes something b... | https://physics.stackexchange.com |
14,598 | [
"https://engineering.stackexchange.com/questions/14598",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/10736/"
] | So today when I was taking a taxi and looked at the vehicles, I observed that the majority of the light vehicles (i.e. 16-person minibus/ 4-6 person cars) use 5 (or less frequently, 6) wheels studs for each wheel.
Intuitively, 6 evenly distributed components are more stable as it has 3 axes of symmetry, as compared t... | On reason is that die cast (alloy wheels) generally have an odd number of spokes. This is because having directly opposed spokes causes problems with residual stress distribution as the casting cools and shrinks (this is also why cast iron hand wheels often have S shaped spokes). So 5 studs tends to be a more convenie... | Most probably cost optimization. 6 might be stronger, but 5 is strong enough and when you make thousands of vehicles a year those 4 nuts, bolts and assembly time add up to a significant enough value. 4 lug wheel mounting systems are more common in Europe where the cars are smaller and 10 inch rims are common in 'mini' ... | https://engineering.stackexchange.com |
423,073 | [
"https://stats.stackexchange.com/questions/423073",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/255768/"
] | When a model fitted in a dataset with multiple time series from different sites, does the temporal correlation should check for each site? And if some sites show auto-correlation but some don't, what's that mean and how to deal with? Thanks.
Here is details. I fitted a model like:
<pre><code>m1 <- gam(Abundance ... | You state:
"<em>I'd like to isolate the effect of this separate policy from the main policy, by comparing the affected individuals in the treatment group to the unaffected individuals from the treatment group (so basically, a DiD analysis within the original treatment group). The second policy did not affect the origin... | In theory, your <span class="math-container">$\beta_6$</span> should compare only those affected by policy 2 in the second time period to (1) all those never affected and (2) those in S2 in the previous time periods. So that basically seems like what you want to measure. You might want to include an S2 dummy to take ca... | https://stats.stackexchange.com |
76,124 | [
"https://softwareengineering.stackexchange.com/questions/76124",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/21184/"
] | I work in healthcare IT, reviewing data management processes of various observational studies. One problem I have repeatedly faced is the poorly encoded data, especially when some values are missing.
<hr>
<strong>Background, skip if you like</strong>
I am currently reviewing a study which collects data on patients s... | There are two common ways of going about this sort of thing:
<ol>
<li>Non-normalized, with a status field and a result field. The status field can be a <code>bit</code>, <code>char(1)</code>, <code>char(3)</code>, whatever, it doesn't matter. You allow <code>NULL</code> values in this field but more importantly you <... | Profound insight here: NULL has no useful semantics.
<blockquote>
Use an additional field in the same table, e.g. a boolean field "bloodtest_perf" where "perf" stands for "actually performed".
</blockquote>
Correct.
That is precisely what you must do.
A single field may not be sufficient. If you have multiple... | https://softwareengineering.stackexchange.com |
326,898 | [
"https://electronics.stackexchange.com/questions/326898",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/161578/"
] | My phone charger consists of two parts (like every smartphone charger nowadays); the adapter and the Micro USB cable. Some time ago, it had an accident and the cable has interruption now. So I bought a new cable.
On the adapter, it writes "DC OUTPUT: 5V 2.1A". Does the cable I use affect V and A values? (There is no su... | In short, yes, I've found important differences between charging cables.
The original USB spec was 500mA, so old cables will have thinner wires than the ones which came out after most smartphones were able to draw 2 amps. These thinner wires were alright for 500mA, but for 2A the voltage drop can be a nuisance.
Also,... | In short, no, the cable does not meaningfully affect the voltage and current.
A micro-USB cable is just wires, so the voltage and amperage will be almost entirely dictated by the charger. I say "almost" because there is some small resistance in the wires, and so there will be a small (negligible for most of us) voltag... | https://electronics.stackexchange.com |
244,531 | [
"https://physics.stackexchange.com/questions/244531",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/111863/"
] | When we have e.g. metallic cube of dimensions 1x1x1m and we put it on the space
without gravitational force the cube has equal 1x1x1m and we can use Euclidean geometry.
<ol>
<li>But when this cube move on the Earth's surface where the space-time is curvature and twisted this cube has not-Euclidean geometry? So now it... | Yes, in principle you can observe difference of size and form in view of the geodesic deviation. If you have a pair of particles of matter very close to each other, at rest in a reference frame, in a generic region of spacetime where curvature is present, they experience relative acceleration in view of the so-called g... | First of all, the curvature of space is expected to change (in proportion) everything you use to measure the cube. Including scales, lasers etc. everything. And so, you would not observe any difference.
However, the curving of space is not necessarily a geometrical one. Even if it is geometrical, It may not necessari... | https://physics.stackexchange.com |
138,117 | [
"https://security.stackexchange.com/questions/138117",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/125780/"
] | My (human) client has asked if a client service we are developing for them can somehow support TLS 1.3 for when TLS 1.3 officially rolls out. The issue is, the client service will be installed once, and probably never updated (I know this seems odd). It will be using the .NET implementation of TLS, so they want the ser... | This is probably a more appropriate question for stackoverflow.
That said:
<ul>
<li>It's impossible to know what MS will do. At one end of the spectrum, they could limit TLS 1.3 support to a specific release of .NET (in which case you'll be unable to support it without retargetting your application to that new versio... | Since TLS 1.3 is not released yet and since it is not supported by .NET yet it will be impossible for the client for magically speak TLS 1.3 if the client never receives any software updates. But, it should be able to deal with a TLS 1.3 enabled server as long as the server also support the lower TLS version supported ... | https://security.stackexchange.com |
64,006 | [
"https://physics.stackexchange.com/questions/64006",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23873/"
] | My problem is the following: I'm trying to model a dust (pressure-less relativistic gas) in the presence of electromagnetic field using colisioness vlasov-equation (relativistic version of boltzmann equation). Please note that I'm in flat minkowski spacetime with signature $(+,-,-,-)$.
So, I have the following:
Colis... | As for you distribution, I think it should be correct, because you can note $p^0=\frac{m}{\sqrt{1-v^2}}$, so your distribution is actually
$$
f_k=\frac{1}{m}n'_k\delta(p-p_k),
$$
where $n'_k$ is the particle density in your lab frame, which is (up to your normalization $m$ which is unclear to me) really the phase-space... | Relativistic kinetic theory is not that easy because you can't define what "t" stands for. One knows how to write the interaction between two particles in terms of retarded times and proper time, but beyond two interacting particles the question arises of what time do we have to use ? Poulain if I correctly remember ha... | https://physics.stackexchange.com |
50,241 | [
"https://electronics.stackexchange.com/questions/50241",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15763/"
] | Physical address is hardware address of physical memory and virtual address is the one the processor will be seeing, it has it has a tag and offset. I understand this. Can any one describe it with an example, like how the MMU does this operation (what it adds to the physical address) and what's memory mapping? And what... | Address translation is handled through a translation lookaside buffer (TLB), which is just a cache of translation information (and some metadata like permissions, cacheability, etc.). The TLB works by substituting the physical page number (the address bits above those used to index within a page) for the provided virt... | It is difficult to tell what you are asking, and this isn't the place for a book on virtual memory. It seems you are asking how the address translation from virtual to physical addresses works. I'll try to explain it briefly.
There are many ways this can be done, with some tradeoffs between what is handled automatic... | https://electronics.stackexchange.com |
13,984 | [
"https://chemistry.stackexchange.com/questions/13984",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/6912/"
] | What would be the product formed when 1-bromo-3-chlorocyclobutane with two equivalents of metallic sodium in ether?
I know that there would be a free radical formation and then it will form a compound whose bond line structure would look like a square with a diagonal.
But why is such an unstable compound being form... | In the Wurtz coupling reaction, an alkyl halide first reacts with a metal in a one-electron transfer step to produce an alkyl radical which quickly reacts in a second electron transfer with the metal to form a carbanion. In the final step of the reaction, the carbanion displaces a halogen from a carbon-halogen bond by... | Considering the torsional strain; the maximum relief will be in the bottom most molecule[<strong>Note that there may be other possible products from various combinations</strong>]; but from top to bottom as you can see, you require more and more molecules and thus there will be a huge loss of entropy; but as$$\Delta G=... | https://chemistry.stackexchange.com |
54,570 | [
"https://dba.stackexchange.com/questions/54570",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/31354/"
] | I have a table which has a column <code>Name</code>, which is of type <code>VARCHAR2(20)</code>, unique, cannot be null, and cannot be changed.
At first I used it as a Primary Key for this table but I was wondering if it was better to create another column <code>Id</code> (with a more appropriate naming of course) an... | As name is unique and will never change, it is certainly a good candidate key from a relational theory point of view.
You might find using a integer surrogate key preferable for space and performance reasons though as it will take less space than the text in every table that has a foreign key to this table (and every ... | In this case you don't <em>need</em> to create an <code>Id</code> column, and your tables would be more readable if you use <code>Name</code> as the primary key.
On the other hand, you are probably using this column a lot for foreign keys and it will make a difference whether your database will have to store a VARCHAR... | https://dba.stackexchange.com |
17,176 | [
"https://dsp.stackexchange.com/questions/17176",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/-1/"
] | Let us consider following code:
<pre><code>fs=100;
N=1000;
t=0:1/fs:N-1;
y=10*sin(2*pi*100*t)+0.5*randn(size(t));
plot(y)
plot(t,y)
</code></pre>
<img src="https://i.stack.imgur.com/qzlpG.png" alt="enter image description here">
I have applied following threshold methods:
<pre><code>thr = 0.4;
% Perform hard thre... | You're on the right track. Let's call the impulse response of the second system (equalizing the first one) $h_2(n)$. The trick is to assume causality of the second system, i.e. $h_2(n)=0$ for $n<0$. By doing so, the solution for $h_2(n)$ becomes unique.
The total impulse response of the cascaded system is
$$h(n)=h... | But this is first difference system . If you consider constant input, output is always 0. So it should be non-invertible right? I dont think you can always solve like this mathematically by taking input as discrete delta function.
| https://dsp.stackexchange.com |
969,367 | [
"https://math.stackexchange.com/questions/969367",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/182541/"
] | So I need to prove the inequality :
$$n < 2^n$$
by Induction.
What I have done so far is :
<blockquote>
Step $1$: Prove that the statement is true for $n=1$
$$1<2^1$$ (true)
Step $2$:
Prove that, if $p(n)$ is true, then $p(n+1)$ is also true.
Assume that $p(n): n < 2^n$ is true. then :
... | Assume that it holds for $n=k$, i.e.
$$k\lt 2^k.$$
Then, we have
$$\begin{align}k+1\lt 2^k+1\lt 2^k+2^k=2\cdot 2^k=2^{k+1}.\end{align}$$
Here, note that for $k\ge 1$, we have
$$1\lt 2^k.$$
| The inductive step
$$2^{n+1}=2\times 2^n>2n\ge n+1$$
| https://math.stackexchange.com |
474,021 | [
"https://electronics.stackexchange.com/questions/474021",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/239029/"
] | Sorry I'm new to electrical engineering, trying to clear up some confusion on how static electricty works and why both people feel a shock when touched by static electricity.
When creating a circuit, Electrons flow from the source through the load back to the source. However, lightning an electricity seem more like ... | A static discharge is a “one way” circuit phenomenon and, is due to an unequal amount of surface charge on one body compared to the other. At the point of contact, the charge flow (aka current) concentrates for both parties and this means that the current density is higher and therefore the power dissipated in that sma... | Try this:
Charge yourself up. Then hold a coin in your fingers. Have your "victim" do the same. Now zap the two coins together.
No shock!
Next, charge yourself up again, but use your coin to zap your victim (avoiding surface of eyeball, inside of nostril, use your imagination.)
You feel nothing. But they go "Y... | https://electronics.stackexchange.com |
398,875 | [
"https://softwareengineering.stackexchange.com/questions/398875",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/309190/"
] | I recently started trying to use the Lazy class to implement lazy loading.
However, I'm finding that doing so does not seem to have any advantages over simply implementing it myself via a null-coalescing operator.
For example, if I want to have Task lazy-load a Contact, I can do it like so:
<pre><code> public clas... | Those two versions do different things.
Consider what happens if the <code>DataException</code> is thrown and caught. The first will search <code>_contactRepo</code> at most once. The second will search <code>_contactRepo</code> each time the property is accessed.
| Thanks to Caleth and VisualMelon for pointing out how Lazy has certain advantages (thread safety, not repeatedly querying if the result is null or exception) over a naive null-coalescing approach.
For convenience, I've also created a slightly improved version that uses a null-coalesced Lazy:
<pre><code>public class T... | https://softwareengineering.stackexchange.com |
562,035 | [
"https://physics.stackexchange.com/questions/562035",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/230783/"
] | Consider the situation when a ball hits a plane surface at an angle of incidence <span class="math-container">$\theta$</span> with speed <span class="math-container">$u$</span> and rebounds with the same angle. One can notice that there is a change in momentum in this scenario but I can't seem to find out what is the e... | Basically you are right: there is a lot of redundancy in the expression and what happens is that it leads to many copies of the homogeneous Maxwell equations. But the index notation can help you. If you keep the indices general as much as possible, then you don't need to obtain all the repeated versions one by one. You... | The fastest way is perhaps by using exterior algebra: start by writing Faraday's tensor as
<span class="math-container">$$F = E_x\ \text dt\wedge\text dx + E_y\ \text dt\wedge\text dy + E_z\ \text dt\wedge\text dz + B_x\ \text dy\wedge\text dz + B_y\ \text dz\wedge\text dx + B_z\ \text dx\wedge\text dy$$</span>
and the... | https://physics.stackexchange.com |
2,441,115 | [
"https://math.stackexchange.com/questions/2441115",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I would like to know how to approach this in the first place. I would think just subbing the function equations in for <span class="math-container">$f(x)$</span> and <span class="math-container">$g(x)$</span> would work, but all the answers are integers with no x in them. Any help would be greatly appreciated
<blockquo... | I guess the difficulty that you face is how to evaluate $(-10f+5g)$
Note that $$(-10f+5g)(x)=-10f(x)+5g(x)$$
Evaluate it by letting $x= - 4$.
| $$(-10f+5g)(-4)=-10\cdot\frac{7(-4)+6}{5}+5\cdot(10(-4)+10)=-106$$
| https://math.stackexchange.com |
17,285 | [
"https://cstheory.stackexchange.com/questions/17285",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/3337/"
] | Ford-Fulkerson can find sparse s-t flows in time linear in the size of the flow and number of nodes if the edges have unit capacity.
How could I use a sparse s-t flow to find an s-t min-cut in time proportional to the size of the flow and the number of my nodes, for the sparse/low-volume max-flow case?
| If you don't use the flow per se, but use the Ford-Fulkerson algorithm (or some version, like Edmonds-Karp), you can get both the max-flow <em>and</em> the min-cut directly as a result. When looking for augmenting paths, you do a traversal, in which you use some form of queue of as-yet-unvisited nodes (in the Edmonds-K... | Is there a quick reference for the definition of a sparse s-t flow?
In the general case, having the max-flow it is quite easy to determine the min-cut, via the max-flow , min-cut theorem. The edges that are fully saturated form a cut set, so by selecting one vertex for each such edge, one can form a min-cut. Triviall... | https://cstheory.stackexchange.com |
518,139 | [
"https://physics.stackexchange.com/questions/518139",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249030/"
] | Say I put a satellite in orbit with several LEDs on the outside: red, yellow, blue, white and green. Could I see them from the ground with consumer-grade binoculars or telescopes?
If I can see them, could I differentiate between the colors? (e.g. would the color affect how well I could see them?)
Say I have 20/20 vi... | <blockquote>
<strong>My question</strong> How could an infinitesimally thin bridge be fully responsible for the expansion of the (possibly enormous) gulf between left and right sides? ...let’s ask what happens if the metal is on top of a frictionless surface and the metal is not fixed to anything.
</blockquote>
When yo... | As the bridge is getting thinner, if the centers of mass of the two rectangles are held in place, the bridge will want to expand in length, but it will be constrained by the rectangles. So compressive stress will develop in the bridge. (If the bridge were free to expand, the rectangles would move apart.) For a very ... | https://physics.stackexchange.com |
69,016 | [
"https://dsp.stackexchange.com/questions/69016",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/51399/"
] | What's the notion of negative amplitude? I hope the title and the question don't mean different things.
| Sound is a pressure wave in a fluid medium. That medium has a "static"or average pressure and sound is simply a small change of that pressure (as a function of time). Negative sound pressure just means that the current pressure is a little lower than the average pressure.
For example, static air pressure is a... | In a sound wave, troughs are regions of low (with respect to an average value) pressure, and, accordingly, low density. So, the answer to the title question, troughs are rarefactions.
The answer to the body of your question: the amplitude is always positive. But acoustic pressure level, a logarithmic measure of the eff... | https://dsp.stackexchange.com |
15,162 | [
"https://mathoverflow.net/questions/15162",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3248/"
] | Please consider a random walk on a finite N-dimensional lattice with vectors $(x_1, ..., x_N)$. We define the origin to be $(0, ..., 0)$ and the target to be at the point in the lattice furthest away from the origin - i.e. $(||x_1||, ..., ||x_N||)$ where $||x_k||$ is the integer length of the lattice in the $x_{k}$ di... | Assuming you mean Leonid Kovalev's interpretation, the distribution of the hitting time in the $N = 1$ case is the same as the distribution of the number of cycles of a random permutation of $[n]$.
To be more specific, I'll change coordinates. Let $X_0 = (x_0^1, \ldots, x_0^N) = (S, S, \ldots, S)$. Let $X_1 = (x_1^1... | While I like Michael Lugo's answer better, I thought I might as well put up the solution I sketched out for myself for the one-dimensional case:
The probability that the walker visits a particular point on the one-dimensional lattice can be expressed as $\frac{1}{||x_k||-p}$ where $p$ is the distance between the latti... | https://mathoverflow.net |
418,846 | [
"https://softwareengineering.stackexchange.com/questions/418846",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/379184/"
] | I am looking to understand the difference between the words index and offset.
I have never seen "offset" in reference to lists/arrays/etc in programming. I have only seen index.
To me, these mean the same thing. But how one is used heavily and one never implies they have different meanings. They might also ju... | An index stands alone, though some data structure (e.g. array) is implied in using the index. Still the index can be used (e.g. as an id) without an array.
An offset has to be an offset from something, so the difference is in the degree with which another entity is implied. <code>s[105]</code> is offset by <code>5</c... | An offset is a displacement you add to a position. If you are talking about the position in a list or an array, and the offset is from the beginning. Then yes, in that context, the offset is the index in refers to.
Instead, you could be talking about an offset from a given position on the array (from the end, for examp... | https://softwareengineering.stackexchange.com |
366,511 | [
"https://stats.stackexchange.com/questions/366511",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/220300/"
] | <blockquote>
Let X be a positive r.v. with density $f$ with $f(x) > 0~ \forall~ x>0$. Let Y be a r.v. that is equal to X if $X \leq 5$ and $X^3$ if $X > 5$.
</blockquote>
I am self-studying probability, and I'm quite stuck on this question. I want to find the joint CDF of (X, Y). The way I'm thinking is:
... | Let $x,y>0$,
\begin{align}F_{(X, Y)} &= P(X \leq x, Y \leq \color{red}y)\\
&= P(X \leq x, Y \leq y| X \leq 5)P(X\leq 5) + P(X \leq x, Y \leq y| X > 5)P(X> 5)\\
&= P(X \leq x, X \leq y| X \leq 5)P(X\leq 5) + P(X \leq x, X^3 \leq y| X > 5)P(X> 5) \\
&= P(X \leq \min(x, y)| X \leq 5)P(X\leq... | Continuing your way:
\begin{align}F_{X, Y}(x,y) &= P(X \leq x, Y \leq y)\\
&= P(X \leq x, X \leq y| X \leq 5)P(X\leq 5) + P(X \leq x,X^3 \leq y| X > 5)P(X> 5)\\
&= P(X \leq min(x,y) | X \leq 5)P(X\leq 5) + P(X \leq min(x,\sqrt[3]{y})|X>5)P(X \gt 5)\\
&= P(X\leq min(x,y,5)) + P(5 < X\leq min... | https://stats.stackexchange.com |
6,684 | [
"https://stats.stackexchange.com/questions/6684",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/196/"
] | <strong>Note: I've updated the example case code, there were some errors in the previous version</strong>
Cross posted to R-help, because I half suspect this is 'unexpected behaviour'.
I want to predict values from an existing lm (linear model, e.g.
lm.obj) result in R using a new set of predictor variables (e.g.
new... | When you use the <code>predict</code> with <code>newdata</code> argument you must supply the the data.frame with the same column names. In your code you have
<pre><code>newdata <- expand.grid(X1=c(-1,0,1),X2=c(-1,0,1))
names(newdata) <- c("scale(xxA)","scale(xxB)")
</code></pre>
But the formula supplied to lm o... | See if this console scrape shows what you might have wanted. Changed the names of the new data columns:
<pre><code>> dat <- data.frame(xxA = rnorm(20,10), xxB = rnorm(10,20))
> dat$out <- with(dat,xxA+xxB+xxA*xxB+rnorm(20,20))
> xVar <- "scale(xxA)"
> traceVar <- "scale(xxB)"
> D... | https://stats.stackexchange.com |
576,689 | [
"https://physics.stackexchange.com/questions/576689",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/273566/"
] | I'm studying physics in the fifths semester and I'm still confused by some aspects of circular motion. So, I understand that the centripetal force changes the direction of the velocity, whereas the speed stays the same. But when the direction of the velocity changes, what causes the change of the tangential velocity at... | First some clarification. In circular motion, velocity is actually the same as tangential velocity, or in other words, there is no radial component of the velocity (otherwise it wouldn't describe a circle).
Now, a force produces an acceleration since <span class="math-container">$\vec{F}=m ~\vec{a}$</span>, and an acce... | If you are talking about a mass moving in a vertical circle on the end of a string, there are two forces acting: the tension in the string and gravity. At the top of the circle, both are acting down and the tangential speed is not changing. (The sum of the two produces the centripetal acceleration.) At any other poin... | https://physics.stackexchange.com |
288,559 | [
"https://math.stackexchange.com/questions/288559",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/10993/"
] | Let $f(n)=o(g(n))$. By definition there exists $n_0$ so that for all $n>n_0$ it holds that $\varepsilon \cdot g(n) \geq f(n)$ for $\varepsilon>0$ however small.
So, in plain language, starting from a certain point, $g(n)$ grows significantly faster than $f(n)$. However, how about the part before asymptotic behav... | Yes for example, $f(x) = \frac{1}{x}$ defined on $[\frac{1}{2},\infty)$ is $o(1)$ and $\forall x \in [\frac{1}{2},1): \frac{1}{x} > 1$, and $f(x)$ reaches maximal value: $2$.<br>
| I think you are confused. The little $o$ notation just means $|\frac{f(n)}{g(n)}|<\epsilon$ for any $\epsilon>0$ if $n$ is large enough. So it is totally possible that for some $n$ value $f(n)\ge g(n)$. For example $\sin[1/x]=o(x^{2})$.
| https://math.stackexchange.com |
345,238 | [
"https://softwareengineering.stackexchange.com/questions/345238",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/154753/"
] | I have designed what I think is a useful, reusable functionality that I'd like to:
<ol>
<li>Implement in C/C++ as an open source library; and then</li>
<li>Write different "<em>native binding libraries</em>" for it in various higher-level languages, such that end users writing applications in these languages (Java, Ru... | If you are careful about writing platform-neutral code, you might be able to write one C++ version and just compile it several times. I would not take any bets that this would be 100% successful.
What is more common is that 90% of the code is platform neutral and the rest ends up in sections that are controlled by co... | The answer is: <strong>Maybe</strong>.
There are really two aspects to your question.
<blockquote>
<em>C++ Language</em>
As long as you target a particular version of the C++ specification
(say, C++ 11) and find a compiler on each platform that supports it,
everything should just work (in theory).
... | https://softwareengineering.stackexchange.com |
300,568 | [
"https://physics.stackexchange.com/questions/300568",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140114/"
] | Assume that the linear charge density is the same for the charged infinite cylinder and the infinite line. By Gauss' Law, I know the charge enclosed is the same given a Gaussian cylinder of a certain length and so the E fields must be the same at any given distance from the axis of symmetry for both objects, given that... | Maybe it helps to compare your cylinder with a cylinder with a tiny radius, but with the same linear charge density. To have the same linear charge density, the smaller cylinder has to have a large surface density, because its surface per unit length is smaller.
| Contours of equal field strength are concentric rings around a single charge (in 2D, spheres in 3D).
So if you instead create a ring of equal charges it's as if you created one of those contours, from outside the ring and in the plane of the ring anyway.
Inside the ring it is v. interesting because there is an integr... | https://physics.stackexchange.com |
34,343 | [
"https://scicomp.stackexchange.com/questions/34343",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/32679/"
] | For the Krylov subspace method to solve the large sparse linear system, we first need to generate a subspace <code>Km = span{v,Av,...A^{m-1}v}</code>, which indeed a process that we convert a linearly independent basis to an orthonormal basis:
<span class="math-container">$$
V_mAV_m = H_m,
$$</span>
where <span class="... | Your view is correct, Matlab does store the zeros. As pointed out by @rchilton1980, this particular non-optimization that you are pointing out here is not too harmful, since the bulk of the storage in Krylov methods is the matrix V, not H. But that is just an instance of a general phenomenon. That is just Matlab's choi... | In practice I don't think that particular factor of <span class="math-container">$2$</span> is worth pursuing. Thinking of gmres applied to a large problem (<span class="math-container">$n >> m$</span>), the <span class="math-container">$m^2$</span> storage of that small Hessenberg projection is dwarfed by the <s... | https://scicomp.stackexchange.com |
254,856 | [
"https://security.stackexchange.com/questions/254856",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/215852/"
] | I have found myself with the need to block online conversion tools for pdf files and such, but I can't think of a nice catch-all (or even catch most) solution (without blocking all file uploads in browsers). Does anybody have any ideas on how to block such sites company-wide without disabling all file uploads?
At first... | It sounds like what you're looking for is a Data Loss Prevention (DLP) system, which can identify sensitive internal data or documented (based on various factors), and then prevent people from sending them outside of the organisation unless they're doing so via an approved channel.
| <h3>You're looking for a technical solution for a human problem.</h3>
And that won't work.
The problem you're facing is that using online tools for sensitive files is prohibited, yet people use them. Ask yourself: Why?
Two main reasons:
<ol>
<li><strong>They don't know it's wrong.</strong> People have no inhibitions of... | https://security.stackexchange.com |
41,193 | [
"https://datascience.stackexchange.com/questions/41193",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/62568/"
] | I'm having trouble understanding the use of Vector in machine learning to represent a group of features.
If one looks up the definition of a Vector, then, according to wikipedia, a Vector is an entity with a magnitude and direction.
This can be understood when applying Vectors to for example physics to represent forc... | <blockquote>
I'm having trouble understanding the use of Vector in machine learning
to represent a group of features.
</blockquote>
<strong>In short</strong>, I would say that "Features Vector" is just a convenient way to speak about a set of features.
<br />
<strong>Indeed,</strong> for each label 'y' (to be pr... | First lets talk about how to organize your data.Lets assume you organize your in a spreadsheet, where columns represent your features and rows your different samples. Imagine you asked 3 people about their sex and age, then you get a spreadsheet with 3 rows (3 people) and 2 columns (sex, age).
Now you can interpret e... | https://datascience.stackexchange.com |
1,733,518 | [
"https://math.stackexchange.com/questions/1733518",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/251171/"
] | I have this
$$a_{n+1} = a_n + 4n - 1\qquad a_1 = 2$$
And I need to find general formula for $a_n$.
This is one of the last exercises for the question related to it so I'll give a summary of what I did before because maybe it could be needed for this.
$$b_n = 2n^2 + 2n - a_n$$
I found that $b_n$ is an arithmetic prog... | For the non-homogeneous part try $b_n=cn^2+dn+e$ so
$$
b_{n+1}=b_n+4n-1\quad\Longrightarrow\quad c(n+1)^2+d(n+1)+e=cn^2+dn+ e+4n-1\\
cn^2+2cn+c+dn+d+e=cn^2+dn+ e+4n-1\\
2cn+c+d=4n-1
$$
and then $c=2$ and $d=-3$.
For the homogeneous part $a_{n+1}=a_n$ so that $a_n=k$.
So the general solution is
$$
a_n=k+2n^2-3n
$$
Fro... | $$\begin{align}
a_{n+1}&=a_n+4n-1\\
a_{n+1}-a_n&=4n-1\\
a_n-a_{n-1}&=4(n-1)-1\\
&\vdots\\
a_2-\underbrace{a_1}_{=2}&=4(1)-1\\
\end{align}$$
Summing the last $(n-1)$ lines by telescoping gives
$$\begin{align}
a_{n}-2&=4\cdot \frac {n(n-1)}2-(n-1)\\
a_n&=2n^2-3n+3\qquad\blacksquare\end{align}... | https://math.stackexchange.com |
8,984 | [
"https://cardano.stackexchange.com/questions/8984",
"https://cardano.stackexchange.com",
"https://cardano.stackexchange.com/users/7200/"
] | I've got a very simple question, is it possible to transfer funds from Shelly to Byron or Byron to Shelley Wallets? If it's possible, do I need to consider anything else different than sending as usual between two Shelley Wallets?
| <blockquote>
No, transactions where the destination address is a Byron era address are no longer valid. I <em>think</em> you can send funds in Byron era addresses to Shelley addresses.
If you still have a Byron era wallet I highly recommend that you upgrade it to Shelley sooner rather than later. At least in the Daedal... | Yes, you can send funds to Byron address from Shelley address and vice-versa. You can spend ADA and native assets like that. Nothing special is required.
| https://cardano.stackexchange.com |
173,993 | [
"https://electronics.stackexchange.com/questions/173993",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54453/"
] | I have a power supply that outputs constant 5v DC power. It's not adjustable or anything fancy. Using a multimeter, I found that there is continuity between the 2 output leads. Is this a bad thing? If not, then why does it happen?
| How do you measure this continuity ? In the diode/beep test of your multimeter ?
Now switch off the supply (very important !) wait a couple of minutes for verything to discharge and now measure again but use the Ohms range.
Is it 0 ohms ? I expect that it is not !
On my Fluke multimeter the continuity test already bee... | There nothing bad about it, maybe the two leads are shorted internally to provide more current. What is the current rating?
| https://electronics.stackexchange.com |
226,890 | [
"https://physics.stackexchange.com/questions/226890",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/40021/"
] | I understand atomic emission and absorption spectra well - photons of a specific energy can be emitted or absorbed by atoms, if that energy corresponds perfectly to the energy difference between two states of the electron of the atom - but I don't quite understand <strong>how</strong> the photons are absorbed and emitt... | Neither the photon nor the electron are classical particles and there is no Newtonian picture of the process. Instead you have to imagine relativistic fields that describe the probabilities to detect photons and electrons in different spacetime points. Before the absorption there is a non-zero probability to detect the... | The mechanism of interaction is very much the same as a radio wave interacting with an antenna. The "photon" is manifested as oscillations of the electric field, which drive the electron like a mass on a spring. The oscillation frequency is given by the difference between the initial state and the excited state, and yo... | https://physics.stackexchange.com |
259,222 | [
"https://dba.stackexchange.com/questions/259222",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/200657/"
] | I do try to create a dump of a table, that is stored inside of my database.
The table is called
<pre><code>webapp_product
</code></pre>
In order to create the dump, I do use following commands:
<pre><code>docker-compose exec db1 pg_dump -F tar -d db -U user -t webapp_product > /home/backup.tar
</code></pre>
Th... | You really have two questions here. First you have a corrupted tar file. I'd blame that on your usage of docker. If you run <code>tar -tf ...</code> on the docker side before moving the file, was it corrupted there?
Second, you don't want to restore data, you want to merge it. pg_dump/pg_restore doesn't do that. ... | @jjanes was right.
Docker was making the causing the errors
Docker was causing the error. File, that I have created using Docker was corrupted. Once I have exported it straight from Docker, using shell & run command:
<pre><code>tar -tf backup.tar
</code></pre>
the file has been defined as a valid one.
Moreover... | https://dba.stackexchange.com |
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