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 |
|---|---|---|---|---|---|
3,514,519 | [
"https://math.stackexchange.com/questions/3514519",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/33176/"
] | so I got the following solution for a problem:
<span class="math-container">$u(x,)=\begin{cases}
1 & x\leq y \\
\sqrt{\frac{x-1}{y-1}} & 1< x < y\\
0 & x\geq 1
\end{cases} \tag{1}$</span>
and the master solution is
<span class="math-container">$u(x,)=\begin{cases}
1 & x\leq y \\
\sqrt{\frac{1-x... | For every fixed positive integer <span class="math-container">$k$</span> we have: <span class="math-container">$$\left\{ S<M\right\} \subseteq\bigcap_{n=1}^{k}\left\{ X_{n}<M\right\} $$</span>
so that:<span class="math-container">$$P\left(S<M\right)\leq P\left(\bigcap_{n=1}^{k}\left\{ X_{n}<M\right\} \right... | Start by understanding the problem.
<span class="math-container">$$\forall_{M>0} \ \ \mathbb{P}(S\ge M)=1 \ \iff \ \mathbb{P}(S=\infty)=1. $$</span>
Note that if <span class="math-container">$X_{n}\sim \exp(\lambda_{n}) \ $</span> with <span class="math-container">$\lambda_{n} \in (0,1)\ $</span>, then
<span cla... | https://math.stackexchange.com |
3,484,065 | [
"https://math.stackexchange.com/questions/3484065",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/640691/"
] | A problem from the National Mathematical Olympiad in Bulgaria:
<blockquote>
Solve the system:
<span class="math-container">$$\begin{aligned} x^2+y^2 &= \dfrac{2xy}{z} \\ y^2+z^2 &= \dfrac{2yz}{x} \\ x^2+z^2 &= \dfrac{2xz}{y} \end{aligned}$$</span>
</blockquote>
As always: <span class="math-container">$$\beg... | Given,
<span class="math-container">$$ x^2+y^2 = \dfrac{2xy}{z} \tag 1$$</span>
<span class="math-container">$$y^2+z^2 = \dfrac{2yz}{x} \tag 2$$</span>
<span class="math-container">$$ x^2+z^2 = \dfrac{2xz}{y} \tag 3$$</span>
Take (1)-(2) and (3)-(2) to get
<span class="math-container">$$(x^2-z^2)(xz-2y) = 0$$</span>
... | Assume <span class="math-container">$x,y,z > 0$</span> . WLOG assume further that : <span class="math-container">$x \ge y \ge z$</span>. Then : <span class="math-container">$\dfrac{1}{z} = \dfrac{x^2+y^2}{2xy} \ge 1 \implies z \le 1$</span>. By the same argument, we have: <span class="math-container">$x \le 1, y \le... | https://math.stackexchange.com |
23,126 | [
"https://dsp.stackexchange.com/questions/23126",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/14872/"
] | I am a beginer. I have read that any given signal whether it is simple or complex one,can be represented as summation of orthogonal basis functions.
Here, what the terms <strong>Orthogonal</strong> and <strong>Basis function</strong>s denote in case of signals?
| If you think of a signal as a function of time $s(t)$ ($t$ could be a continuous variable or a discrete one $t_n$) that satisfies certain criteria, it can be thought of as a vector in some vector space of functions. It depends which vector space you want to use (e.g. $L^2$ or tempered distributions), but as most signal... | The X and Y axis can be used to describe any point in an XY plane. Thus any non-zero vector in the X direction and one in the Y direction can be used in a linear combination to describe any point in that space. That linear combination is separable if the two basis vectors are orthogonal. Or you can turn or translate... | https://dsp.stackexchange.com |
65,179 | [
"https://softwareengineering.stackexchange.com/questions/65179",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/935/"
] | In the last few months, the mantra "favor composition over inheritance" seems to have sprung up out of nowhere and become almost some sort of meme within the programming community. And every time I see it, I'm a little bit mystified. It's like someone said "favor drills over hammers." In my experience, composition a... | Though I think I've heard composition-vs-inheritance discussions long before GoF, I can't put my finger on a specific source. Might have been Booch anyway.
<rant>
Ah but like many mantras, this one has degenerated along typical lines:
<ol>
<li>it is introduced with a detailed explanation and argument by a well... | Experience.
Like you say they are tools for different jobs, but the phrase came about because people were not using it in that way.
Inheritance is primarily a polymorphic tool, but some people, much to their later peril, attempt to use it as a way of reusing/sharing code. The rationale being "well if I inherit then I... | https://softwareengineering.stackexchange.com |
357,358 | [
"https://math.stackexchange.com/questions/357358",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/67416/"
] | How can you show that
<blockquote>
$$\left(1-\frac{2}{n^2}\right)^{n^2/2} \le \frac{1}{e}\:\: \qquad\forall n \ge 2$$
</blockquote>
Any ideas? Infinite series have never really been my thing. Thanks
| Hints:
$$\left(1-\frac{2}{n^2}\right)^{n^2/2}=\left(1-\frac{1}{\frac{n^2}{2}}\right)^\frac{n^2}{2}$$
Now just use the fact that
$$\left(1-\frac{1}{f(n)}\right)^{f(n)}\xrightarrow[n\to\infty]{}e^{-1}$$
for any function $\,f\,$ s.t. $\,f(n)\xrightarrow[n\to\infty]{}\infty\,$ and, perhaps (depending on what you can as... | You know that $$\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n} = e$$
Hence, you know that $$\lim_{n\to\infty}\left[\left(1+\frac{1}{\frac{-n^2}{2}}\right)^{\frac{-n^2}{2}}\right]^{-1} = e^{-1} = \frac{1}{e}$$
You could calculate the derivate of this expression for example and show that it increases and then show that ... | https://math.stackexchange.com |
41,874 | [
"https://mathoverflow.net/questions/41874",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7576/"
] | A) Given a non-constant polynomial $q\in\mathbb{Z}[\alpha_1,\alpha_2,\ldots,\alpha_n],$ if we pick random $\omega_i\in\mathbb{F}$ (a finite field) uniformly and independently across $1\leq i\leq n,$ then, we know that $q(\omega_1,\omega_2,\ldots,\omega_n)\neq 0$ with high probability (i.e. the probability goes to 1 as ... | Following [Giusto and Simpson, <em>Located sets and reverse mathematics</em>, J. Symbolic Logic Volume 65, Issue 3 (2000), 1451-1480], the Mandelbrot set <span class="math-container">$M$</span> is <em>located</em> if the distance function <span class="math-container">$f:\mathbb C\rightarrow\mathbb R$</span>, <span clas... | I just want to add one small piece of information to Bjørn's answer. The distance function for the Mandelbrot set $M$ is not known to be computable as a map into the reals, but it is computable as a map into the <em>upper</em> reals. This means that we can calculate <em>upper</em> bounds for the distance: given $z \in ... | https://mathoverflow.net |
7,674 | [
"https://chemistry.stackexchange.com/questions/7674",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/4117/"
] | I want an high-school level answer. What I mean with "valence electrons" is the outermost electrons in that atoms' electronic arrangement? For example, 3 in an atom with an electronic arrangement of 2, 8, 3.)
Without actually writing the electron configuration, or orbitals, and knowing electron number, is there any wa... | You can get the valence electrons in an atom's electronic arrangement by consulting the periodic table:
<img src="https://i.stack.imgur.com/VrFqx.jpg" alt="enter image description here">
<ul>
<li>The Group 1 atoms have 1 valence electron.</li>
<li>The Group 2 atoms have 2 valence electrons.</li>
<li>The Group 3 atoms... | Yes there is! For all elements in the following groups;
Group 1A= +1
Group 2A= +2
Group 3A= +3
Group 4A= +4 or -4
Group 5A= -3
From group 5, the valency descends in this order;
-3, -2, -1, 0.
Group 8A elements have a valency of Zero.
I hate complicated stuff too lol.
| https://chemistry.stackexchange.com |
249,252 | [
"https://math.stackexchange.com/questions/249252",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/12500/"
] | In a proof to show that $D(L\circ f)_a = L \circ Df_a$, where $f: U \subset E \rightarrow F$ and $L \in L_c(F,G)$.
They take the following limit to show that the frechet derivative exists,
$$\lim_{h\rightarrow 0} \frac{(F\circ f)(a+h) - (L \circ f)(a) - (L\circ Df_a)(h)}{\lVert h \rVert}$$
My question: normally, in... | A ring $R$ is local if and only if the associated reduced ring $R_{red} = R/Rad(0)$ is local. In both of your cases this latter ring is the field $k$, hence both of your rings are local.
| <blockquote>
Let $R$ be a commutative ring and $I\subset R$ an ideal. If $\sqrt{I}\in\operatorname{Max}(R)$, then $R/I$ is a local ring of Krull dimension $0$.
</blockquote>
<em>Proof.</em> Let $P\in\operatorname{Spec}(R/I)$. Then there is $\mathfrak{p}\in\operatorname{Spec}(R)$, $\mathfrak{p}\supseteq I$, such that... | https://math.stackexchange.com |
1,901,545 | [
"https://math.stackexchange.com/questions/1901545",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/328577/"
] | $\lim_{n\to ∞}\sin(\pi(2+\sqrt3)^n)$
I tried to write it as $\sin (n\pi - \theta)$ to get the form $∞-∞$ form within $\sin$ function. But could not proceed after that. How should I do it?
Edit:I am sorry, I forgot to mention $n\in \mathbb{N}$
| Note $|2-\sqrt{3}|<1$ and hence $\lim_{n\to\infty}(2-\sqrt{3})^n=0$.
Since $(2+\sqrt{3})^n+(2-\sqrt{3})^n$ is an integer, one has
\begin{eqnarray}
&&\lim_{n\to\infty}\sin[\pi(2+\sqrt{3})^n]\\
&=&\lim_{n\to\infty}\sin\bigg[\pi\big[(2+\sqrt{3})^n+(2-\sqrt{3})^n\big]-\pi(2-\sqrt{3})^n\bigg]\\
&=&am... | <strong>Hint(s)</strong>: $(2+\sqrt{3})^n$ is closer and closer to an integer as $n$ increases, since
$$ (2+\sqrt{3})^n+(2-\sqrt{3})^n $$
is an integer and $|2-\sqrt{3}|<\frac{1}{3}$. The sine function is a Lipschitz-continuous function and $\sin(\pi m)=0$ for any integer $m$, hence your limit equals zero.
| https://math.stackexchange.com |
564,335 | [
"https://physics.stackexchange.com/questions/564335",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/269376/"
] | The Bernoulli equation as a statement on the conservation of energy as I understand it is the observation in an idealized flow that the bulk fluid velocity relates to the kinetic energy of the fluid and must therefore increase/decrease to agree with the conservation of energy in the system. The internal energy of stati... | The fluid assumptions you describe assume speeds that are sufficiently lower than the speed of sound that it is valid to speak of a fluid particle "knowing" that it must speed up.
At a more exacting level, the particles are colliding a great many times every second. If there is a substantial pressure differe... | Narrowing the tube by itself is not the cause for increasing the fluid velocity. But if there is a fluid tank above for example, gravity potential is the source of the flow.
Once there is a flow, if part of the tube has a narrow section, the fluid velocity must be greater there to keep the continuity.
The pressure decr... | https://physics.stackexchange.com |
2,857,887 | [
"https://math.stackexchange.com/questions/2857887",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/545073/"
] | Are there Hilbert space <span class="math-container">$H$</span> and adjoint operator <span class="math-container">$T$</span> s.t., <span class="math-container">$||T||=1$</span>, <span class="math-container">$(Tx,x) (\forall x \in H)$</span> and <span class="math-container">$T^n$</span> not convergent uniformly?
I ... | How about $\frac 13+4\cdot \frac 15+6\cdot \frac 17+\frac 1{105}=2$?
If we put them over a common denominator, it is $105$, so we need to find a subcollection of $1,21,21,21,21,15,15,15,15,15,15,35$ that sums to $105$. If we take all the ones ending in $1$ to get a multiple of $5$ we have $85$ and can't complete it... | This is an expansion of @Michael Lugo's comment.
The proposition is not true even if all denominators have to be unique. A counterexample: $(2,3,4,5,7,8,9,10,12,14,16,49,35280)$.
Here is a Python program which checks that these numbers are different, and the sum of the reciprocals of these numbers is 2, and that ther... | https://math.stackexchange.com |
371,011 | [
"https://physics.stackexchange.com/questions/371011",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/123260/"
] | I am confused about my teachers notation.
I have a set of problems about "gravitational potential $\Phi$."
But is $\Phi$ normally written as $U$ is a lot of caseses? Is there a difference?
<h2>Rant or My Understanding</h2>
I think that he wants an equation for the field rather than a given point but I am confused on... | I'm going to assume you (and your prof or teacher) are using standard notation.
In that case, $U$ denotes the gravitational potential energy of a configuration of two (or more) objects interacting gravitationally. $\Phi$ denotes the gravitational potential of one object. The difference between them, is that $U$ requi... | They mean the same thing. In order to find the potential of a field, you have to start from first principal of gravitation Potential
| https://physics.stackexchange.com |
24,679 | [
"https://chemistry.stackexchange.com/questions/24679",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/13221/"
] | I need to write the redox reaction from tin and a sulfuric acid solution. Here is the solution given:
<blockquote>
The first half-reaction: $\ce{Sn->Sn^2+\+2e^-}$<br>
The second half-reaction: $\ce{2H+\+2e^-->H2}$<br>
Adding both reactions will give you: $\ce{Sn\+2H+->Sn^2+\+H2}$
</blockquote>
Why is... | The sulfuric acid dissociates in water: $$\ce{H2SO4 -> H+ + HSO4-}$$$$\ce{HSO4- -> H+ + SO4^{2-}}$$
When writing redox equations the spectator ions are left out because they do not participate in the redox reaction.
In this case it is the hydrogen ions which are oxidising the tin and the sulfate and hydrogensu... | I doubt the answer because I'm sure you'll get $\ce{Sn_{(s)} + 2H2SO4_{(aq)} → SnSO4_{(aq)} + 2H2O_{(l)} + SO2_{(g)}}$ as your Products
anyways , The Arrhenius concept of acids and bases is as follows: an acid is a substance that when dissolved in water increases the concentration of the hydrogen ion, $$\ce{H+}$$
Whe... | https://chemistry.stackexchange.com |
111,642 | [
"https://security.stackexchange.com/questions/111642",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/93860/"
] | Would it be a good idea if you had one account which would require two different passwords ?
For example your login details were:
<pre><code>email: example@gmail.com
password 1: P4$$w0rd1
password 2: HereIsMySecondPassword
</code></pre>
Now when the user logs in to my site he is required to enter both passwords.
Wou... | Not really. It's essentially one password, with a press of the return key as one character.
It adds complexity to the log in process, which isn't generally a good thing (users would probably choose one good password, and one quick to type password). Don't forget @AviD's rule: "Security at the expense of usability, com... | I've seen banking sites where a user is required to answer 2 security questions(randomly chosen out of a set of 5 pre-decided questions, at the time of account creation).
The point is, if one password can be compromised(either on user's front or because of website loopholes), how much likely is that the second passwo... | https://security.stackexchange.com |
141,546 | [
"https://physics.stackexchange.com/questions/141546",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62211/"
] | $q_eV_s = hf - \phi$
My question is... suppose we are testing the photoelectric effect. One plate is illuminated. We have applied the stopping potential. Suppose an electron leaves one plate with $KE = hf - \phi$ Now by the time it reaches the other plate, it should have 0 kinetic energy right?
My question is about ... | You are right - the electron might make it all the way to the other plate. But then it will have zero velocity, and it still feels the electric field. So it will "fall back" to the plate it came from - and the net current is zero.
In reality the velocity distribution of the electrons is continuous (they don't all trav... | Some notes:
<ul>
<li>this <strong>Kinetic Energy</strong> that you use is the <strong>Maximum</strong> amount of kinetic energy among the electrons. it means maybe just a few of them has this amount of energy, other photo electrons with lower kinetic energies (therefor lower Velocity) just accelerate back to the plate... | https://physics.stackexchange.com |
19,638 | [
"https://security.stackexchange.com/questions/19638",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6205/"
] | Using ettercap and ARP poisoning, I was able to eavesdrop on other connections, but suddenly I was unable to make any connection to the Internet. To restore Internet connectivity, I had to restart my router. (I have tested this on 3 different routers: sagem, linksys and huawei.)
Am I doing something wrong or is there... | ARP spoofing usually works by fooling all the clients into thinking that you're the router, by faking the ARP responses that translate IP addresses to MAC addresses. When clients receive the ARP response, they remember the MAC that was associated with the IP.
Once you stop the application that's handling the man-in-th... | If you only have one network interface card, you may be blackholing everything. You would need one nic (or virtual nic) to connect to the clients and act as the spoofed router/switch and one to forward traffic on to the switch. I know that ettercap can handle this for MiTM'd traffic, but don't recall if it also provide... | https://security.stackexchange.com |
136,287 | [
"https://cs.stackexchange.com/questions/136287",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/110780/"
] | Could you please help me understand the following Language
<span class="math-container">$L = \{ a | a ∈ \{0, 1\}^∗, |a| = k ≥ 4, a = a_1a_2...a_{k−1}a_k, ∃i ∈ N, 1 ≤ i < k : a_i = a_{i+1} \}$</span>
what does <span class="math-container">$a_i = a_{i+1}$</span> mean? Could you please give me an example of word in <sp... | Reading the quote literally without the interpolated interpretation, I think what Backus is saying is that a powerful language is one which makes no distinction between expressions and statements.
That is, where all statements are also expressions, like a functional language.
I don't think Backus was claiming that an &... | Backus says in that quote that splitting statements from expressions makes the “combining forms” (such as <strong>if</strong>-<strong>then</strong>-<strong>else</strong>) less powerful, because they can only be applied to statements, but not to expressions.
He wants to see a language all of whose elements may be combin... | https://cs.stackexchange.com |
3,238,068 | [
"https://math.stackexchange.com/questions/3238068",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/14096/"
] | <blockquote>
If <span class="math-container">$(9-x^2)>|x-a|$</span> has at least one negative real solution for <span class="math-container">$a\in\mathbb{R}.$</span> Then complete set of values of <span class="math-container">$a$</span> is
</blockquote>
Plan
If <span class="math-container">$x>a$</span> Then... | <span class="math-container">$G = \{a^mb^n:0\le m\le 8,0\le n\le 5\}$</span>. For an element <span class="math-container">$a^mb^n\in G$</span>, <span class="math-container">$b^{-1}a^mb^nb = a^{2m}b^n$</span> and thus for a fixed <span class="math-container">$n$</span>, <span class="math-container">$a^mb^n$</span> (with... | From the defining relations try to get a description of all the elements.
Any element is a "word" involving <span class="math-container">$a$</span> and <span class="math-container">$b$</span>.
Last condition <span class="math-container">$b^{-1}ab = a^2$</span> can be rewritten as <span class="math-container">$ab= ba... | https://math.stackexchange.com |
53,655 | [
"https://mathoverflow.net/questions/53655",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4721/"
] | I think in priciple it's possible to consider a theory of "conformal-symplectic manifolds", in an analogous fashion as the usual conformal geometry.
To spell out the spontaneous definitions: say that two symplectic forms $\omega_1$, $\omega_2$ on a smooth manifold $M$ are <em>conformal</em> to each other if there is ... | If the manifold has dimension bigger than 2, I think the conformal class of $\omega$ is just $k\omega$ for constants $k$. Locally, by Darboux we can write $\omega = \sum_i dq^i \wedge dp_i$. If the dimension is greater than 2, the only way for $0 = d(f\omega) = df \wedge \omega$ is if $df = 0$.
| There is a notion of conformal symplectic structure related to what you are asking. I refer to <em>locally conformally symplectic manifolds</em>. These are manifolds $M$ equipped with a non-degenerate two-form $\omega$ and a good open cover $\left\{ U_{a}\right\}_{a\in I}$ such that for every $U_{a}$ there exists a fun... | https://mathoverflow.net |
964,363 | [
"https://math.stackexchange.com/questions/964363",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1650/"
] | It seems to be well-known that a principal $\mathrm{SL}_n$-bundle on a scheme or manifold $X$ is the same as a vector bundle of rank $n$ whose determinant is a trivial line bundle. One direction is clear to me: A principal $\mathrm{SL}_n$-bundle corresponds to a principal $\mathrm{GL}_n$-bundle whose cocycles can be ch... | If $$GL_n\rightarrow E\stackrel{\pi}{\rightarrow} B$$ is a principal $GL_n$-bundle with a trivializing open cover ${U_i}$, trivializations $$\psi_i\colon U_i\times GL_n\rightarrow \pi^{-1}(U_i)$$ and induced cocylces $$\psi_{ij}\colon U_i\cap U_j\rightarrow GL_n,$$ the determinant of this bundle is the principal $GL_1$... | Disclaimer: this answer does not address the question of cocycles specifically, and is only about topological vector bundles (i.e., it might not be useful at all).
You can think of the equivalence this way: the short exact sequence $1 \to SL_n \to GL_n \xrightarrow{\mathrm{det}} GL_1 \to 1$ gives rise to a fibration s... | https://math.stackexchange.com |
14,807 | [
"https://quantumcomputing.stackexchange.com/questions/14807",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/7598/"
] | Is it possible for me to construct a gate that inverse everything (<span class="math-container">$|0\rangle \rightarrow -|0\rangle, |1\rangle \rightarrow -|1\rangle$</span>, etc. basically like a <span class="math-container">$-I$</span> gate) from the basic <span class="math-container">$X, Y, Z, CX,...$</span> gates, fo... | As a general rule, you wouldn't bother constructing this: it is just a global phase that has no observable consequence.
If you really insist on doing this, introduce an ancilla qubit in the <span class="math-container">$|1\rangle$</span> state and apply a <span class="math-container">$Z$</span> gate to it.
PS "inv... | You might be interested in controlled version of <span class="math-container">$-I$</span>. Despite the fact that you can neglect global phase in case of non-controlled gates, you cannot do so in case of controlled version.
The controled gate <span class="math-container">$-I$</span> is described by matrix
<span class="m... | https://quantumcomputing.stackexchange.com |
26,838 | [
"https://mathoverflow.net/questions/26838",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1464/"
] | Let $p$ be an odd prime. An old theorem of Jacobi asserts that $p$ has exactly $8(p+1)$ representations as a sum of four squares of integers (solutions counted with order and sign). What is the most effective way to enumerate these solutions computationally? Can it be done in time $p^{1+\varepsilon}$, or even in tim... | Form the set $S$ of all squares less than $p$. This has $O(\sqrt{p})$ elements, and writing them down takes $O(\sqrt{p} \log p)$ time. (You don't have to implement fast multiplication to do this; just compute the list of squares by successively adding odd numbers.)
Let $T$ be the set of all integers expressible as the... | Subtract a square you've not seen before and check for form 4^k(8m + 7)? If not, you have a sum of three squares. If yes, this square occurs in no decomposition as sum of four squares. After a number of trials only as large as the square root of p, you seem to have a list of possible summands and a simpler such questio... | https://mathoverflow.net |
61,481 | [
"https://mechanics.stackexchange.com/questions/61481",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/43750/"
] | My car has 225/50r17 tires. I have a set of four winter tires from my last car that are still good. They're 215/50r17. Given that they're fairly close in side, with the same radius, just 10mm thinner - can I save $700 on new tires and get these installed on the new car?
| Those tires should fit fine, when you get them fitted do ask the fitter to check they are still in good condition.
Winter tires degrade over time - especially in sunlight, so their performance is severely reduced after 2 years or so...
I, personally, change my winter tires so they only ever do 2 winter seasons ie Nov... | you can install those tires, when this tires are fitted then ask the tire fitter to check the tires properly; that the tires are in good condition or not....
The winter tires degrade the of usage, the sunlight effect the tires which reduce the usage of the tires using it for 2 years........
so I advice you that insta... | https://mechanics.stackexchange.com |
600,933 | [
"https://physics.stackexchange.com/questions/600933",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/282764/"
] | For Changing magnetic field we have the simple Faraday's Experiment. Similarly for Changing electric field is there a simple experiment where we could see what is happenening.
I searched the internet it showed electric motors. But is there any a simple physical example?
| Consider a charging capacitor. The magnetic field produced inside the capacitor can be found through the displacement current term on Ampere's Law, since the electric field through the capacitor is changing.
In fact, consider an infinitely long wire with a small gap cut in the middle of width much less than the radius ... | I'm not sure there is a correspondingly <em>simple</em> convincing demonstration. <br><br>
However, at RF frequencies the magnetization in a ferrite ring will respond to the changing electric flux threading the ring. This changing magnetization should be readily picked up with a coil wound on the ring. In principle, i... | https://physics.stackexchange.com |
39,621 | [
"https://biology.stackexchange.com/questions/39621",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/19393/"
] | NZT is a fictional compound in a movie called limitless, basically it's a brain booster, it gives access to more simultaneous neuron activity.
are there any real cognitive enhancers out there?
| As others have said, this compound is fictional. Leaving illegal compounds aside, I would vote for nootropics. And from them I find pramiracetam to be the best fit. I have found its action to be rather similar to the one described in the movie, although with no side effects. One of the most notable mechanisms of it is ... | Yes there are a few out there, though the mechanism is quite different to the film. Things that increase the activity of dopamine and norepinephrine particularly in the prefrontal cortex where a lot of your higher functions like decision making seem to be. Things that do this can include amphetamines (ritalin and other... | https://biology.stackexchange.com |
160,241 | [
"https://dba.stackexchange.com/questions/160241",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/114451/"
] | Consider Relations R and S where are R is having m tuples and S is having n tuples . m<=n . What would be the minimum and maximum number of tuples in each of the following cases (Assume that nothing is mentioned about key constraints)
<ol>
<li>R union S</li>
<li>R intersection S</li>
<li>R-S</li>
<li>S-R</li>
<li>R... | Yes, your answers are mostly right, except a few mistakes:
<strong>1. <code>R UNION S</code></strong>
<ul>
<li>max : n+m ( union we add all the tuples from both relations)<br>
<strong>Correct</strong>, when R and S have no common tuple.</li>
<li>min: 0 ( taking m=n=null )<br>
<strong>Wrong,</strong> the minimum is <c... | I have recompiled the above answer more lucidly and added some more relational algebra operations. Hope, it's useful :)
Consider Relations R and S where R is having m tuples and S is having n tuples. m<=n . What would be the minimum and maximum number of tuples in each of the following cases (Assume that nothing is ... | https://dba.stackexchange.com |
165,546 | [
"https://security.stackexchange.com/questions/165546",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/153738/"
] | I have a system where clients securely communicate with a remote server over internet using TLS. In this scenario, how CA signed server certificates are better than pre-sharing the server public key? When the server private key is compromised, new keys pairs will replace the old then it is tiresome to do the pre-sharin... | Let's compare the workflows of the two processes, specifically how the handle key compromise.
<h2>Pre-shared Secret</h2>
The server generates a keypair, you copy this to every client machine (manually, through a script, etc). When connecting to the server, the client will check that the public key presented matches the... | With pre-shared keys, you need to secure ALL endpoints: server and clients. If a single one of the participant is compromised, you have to re-distribute a new set of keys.
Also, the only time you need an external secure channel with a PKI is when you initially setup your trust chain. After that, you do not have to use... | https://security.stackexchange.com |
102,100 | [
"https://mathoverflow.net/questions/102100",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25092/"
] | Let $G$ be a finite group and let $G$ act on a vector space $V$. Let $S(V)$ be the representation sphere. In the monoidal category of $RO(G)$-graded spectra $S(V)$ is invertible, so it's dualizable too.
Is $S(V)$ dualizable in the monoidal category of naive $G$-spectra?
| Let $G$ be of order $2$, and let $V$ be the nontrivial one-dimensional representation. I'll write $S(V)$ for the unit sphere in $V$ (which is just $G$); the one-point compactification of $V$ is then the unreduced suspension of $G$, which I'll call $S^V$. We can only form spectra from $G$-spaces with fixed basepoint, ... | There is a strongly related result of Gaunce Lewis that I would like to advertise. We have different kinds of $G$-spectra for different ``universes'' $U$, which are countable sums of representations that include $\mathbf{R}$ and countably many copies of each representation they contain. Naive $G$-spectra are indexed... | https://mathoverflow.net |
339,782 | [
"https://math.stackexchange.com/questions/339782",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/63095/"
] | A bag contains $4$ balls .Two balls are drawn at random and are found to be white.
What is the probability that all the four balls in the bag are white?.
The options are
$\large\frac{1}{5}\space ;\frac{2}{5} ;\frac{3}{5} ;\frac{4}{5}$
My work:
It's given that two balls are white.So the rest of the balls could be
<... | Your list of $3$ possibilities is correct. But there is no reason to assert that these possibilities are <strong>equally likely</strong>.
The problem is poorly posed, since we are not given any information about how the balls were put into the urn. (This is technically called the <strong>prior</strong> distribution.) ... | This question cannot be answered as it is stated. You need to make some assumptions about the probabilities of the balls in the bag. How were the 4 balls chosen? Randomly between white and non-white? Randomly between white and 10 other colors?
| https://math.stackexchange.com |
101,628 | [
"https://security.stackexchange.com/questions/101628",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/69594/"
] | I am able to directly input with next to no constraints a value into a nest of functions, but I am unsure how I could exploit this. I got this by injecting PHP code into the URL to display the source code, I have to hack this function to capture the flag hidden in a file in the root directory (the same directory as the... | The URL they requested explains everything. Your Node.js server is open to the public Internet, listens on a port commonly used by HTTP proxies, and a service that scans the internet for proxies stumbled upon it and decided to test it by requesting an URL and seeing whether your Node.js would return the contents of tha... | Most chances are that your new server received an IP that once belonged to that host, which has another system (watchdog, or some client) that remembers the old IP that once matched this DNS record.
My guess is that <code>testp2.czar.bielawa.pl</code> is not the host name of your server, since it is accessible and sh... | https://security.stackexchange.com |
20,396 | [
"https://physics.stackexchange.com/questions/20396",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5114/"
] | I was curious if there was a forumla to find the energy required to reach 1 wavelength in a given substance. (or a vacumn if that's too hard).
I am also wondering if this number can tell us anything about the way the wave acts?
My knowledge of electromagnetic radiation is pretty small... Maybe these things don't real... | The energy of a photon depends only on its frequency, or equivalently its wavelength:
$$E=h\nu=\frac{hc}{\lambda} $$
So the energy of a $144MHz$ photon is ~$6\times10^{-7}eV$; and the energy of a $800Hz$ photon is ~$3.3\times10^{-12}eV$. (I assume you mean MHz megahertz, and not mHz millihertz)
It doesn't matter ho... | It doesn't take any energy for a photon of a given wavelength to travel any distance.
Assuming you are in empty space a photon will travel essentially forever - the cosmic microwave background is photons that have been travelling to us for nearly 15Bn years.
Travelling in a medium light will lose some energy to the st... | https://physics.stackexchange.com |
2,669,096 | [
"https://math.stackexchange.com/questions/2669096",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/515578/"
] | Given $a>0$ that satisfies $4a^2+\sqrt 2 a-\sqrt 2=0$.
Calculate $S=\frac{a+1}{\sqrt{a^4+a+1}-a^2}$.
<strong>Attempt:</strong>
There is only one number $a>0$ that satisfies $4a^2+\sqrt 2 a-\sqrt 2=0$, that is
$a=\frac{-\sqrt{2}+\sqrt{\Delta }}{2\times 4}=\frac{-\sqrt{2}+\sqrt{2+16\sqrt{2}}}{8}$
However obvio... | Rewrite using the value of $a^2 = \frac{1-a}{2\sqrt2}$
$$\frac{a+1}{\sqrt{\tfrac{(a-1)^2}{8}+a+1}+\tfrac{(a-1)}{2\sqrt{2}}} = \frac{(a+1)2\sqrt2}{\sqrt{a^2+6a+9} + a-1} = \frac{(a+1)2 \sqrt 2}{(a+3) + a-1} \\= \sqrt{2}$$
| First, we have
$$\begin{align}S&=\frac{a+1}{\sqrt{a^4+a+1}-a^2}\\\\&=\frac{a+1}{\sqrt{a^4+a+1}-a^2}\cdot\frac{\sqrt{a^4+a+1}+a^2}{\sqrt{a^4+a+1}+a^2}\\\\&=\frac{(a+1)(\sqrt{a^4+a+1}+a^2)}{a+1}\\\\&=\sqrt{a^4+a+1}+a^2\tag1\end{align}$$
We have
$$4a^2+\sqrt 2 a-\sqrt 2=0\implies (4a^2)^2=(\sqrt 2-\sqrt 2... | https://math.stackexchange.com |
75,362 | [
"https://softwareengineering.stackexchange.com/questions/75362",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23901/"
] | Not sure if the title <em>really</em> fits with the question, but figured it was the closest to give an overview of my question..
I'm working on a web application that (fairly heavily) employs the use of browser-specific CSS functions such as -moz-transform) and I'm curious as to what approach those with more experien... | As long as it isn't completely broken in other browsers, it is best to focus on a single browser during development.
The non-standard hacks you need to add for IE tend to conflict with each other or affect other parts of the page, so making small adjustments before the page is complete just leads to having to repeat ... | It depends a lot on what your userbase is. Are they mainly using a single browser or can you actively push them into the direction to use a specific browser? Then I'd completely agree to the statement made before me: "As long as it isn't completely broken in other browsers, it is best to focus on a single browser durin... | https://softwareengineering.stackexchange.com |
681,824 | [
"https://physics.stackexchange.com/questions/681824",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/321387/"
] | Using the <span class="math-container">$U = -GMm/r$</span> where <span class="math-container">$r$</span> is a distance which would be positive how could potential energy ever be positive?
How could it be positive according to the equation <span class="math-container">$mgh$</span>?
| It does not need to be positive. In physics we only care about potential energy <strong>differences</strong>. The first formula the OP quotes already has a chosen reference at infinity. With such a reference point gravitational potential energy will always be negative.
The <span class="math-container">$mgh$</span> form... | It could become zero as r tends to infinity , positive potential energy indicated system is not bounded which is not possible unless r tends to infinity
| https://physics.stackexchange.com |
2,883,123 | [
"https://math.stackexchange.com/questions/2883123",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/342519/"
] | <blockquote>
Find the maximum value of $3(\sin{\theta \over 2}) (1+\cos{\theta} )$.
</blockquote>
I tried A.M-GM. but the equality doesn't hold for any value . Please help me!
| Building upon OP's idea of AM-GM, let $\,t = \sin \dfrac{\theta}{2}\,$, then $\,3\sin{\dfrac{\theta}{2}} (1+\cos{\theta} ) = 6t(1-t^2)\,$, and the square of the expression is:
$$\require{cancel}
36 t^2(1-t^2)^2 = 18 \cdot (2t^2)(1-t^2)(1-t^2) \le 18 \cdot \left(\frac{\cancel{(2t^2)}+(1-\cancel{t^2})+(1-\cancel{t^2})}{... | <em>This is very similar to dxiv's solution but does not use $AM-GM$.</em>
Using the double angle formula
$$f=3 \sin \left(\frac{\theta }{2}\right) (1+\cos (\theta ))=3 \sin \left(\frac{\theta }{2}\right)\left(1+1-2\sin^2 \left(\frac{\theta }{2}\right)\right)=6 \sin \left(\frac{\theta }{2}\right) \left(1-\sin ^2\left(... | https://math.stackexchange.com |
74,756 | [
"https://mathoverflow.net/questions/74756",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16750/"
] | Let $E$ be the total space of the sphere bundle $S^k\to E\to M$, is it true that there exists a disk bundle $D^{k+1}\to N\to M$ such that $E=\partial N$? (where $D^{k+1}$ is the unit disk in $\mathbb R^n$)
| If you don't specify what structure group you want the disc bundle $D^{k+1} \to N \to M$ to have, then it is always true: you just take the fibrewise cone on the original family.
If you want to know whether smooth $S^k$-bundles always bound smooth disc bundles, this is true iff
$$O(k+1) \to \mathrm{Diff}(S^k)$$
is a h... | The question of whether or not a smooth sphere bundle fibrewise extends to a smooth disc bundle over a space $X$ boils down to whether or not the classifying map
$$ X \to BDiff(S^n) $$
lifts up
$$ BDiff(D^{n+1}) \to BDiff(S^n)$$
Where $Diff(D^{n+1})$ is the group of diffeomorphisms of the disc.
The map $Diff(D^{n... | https://mathoverflow.net |
20,441 | [
"https://stats.stackexchange.com/questions/20441",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7064/"
] | Both the likelihood ratio test and the AIC are tools for choosing between two models and both are based on the log-likelihood.
But, why the likelihood ratio test can't be used to choose between two non-nested models while AIC can?
| The LR (likelihood ratio) test actually is testing the hypothesis that a specified subset of the parameters equal some pre-specified values. In the case of model selection, generally (but not always) that means some of the parameters equal zero. If the models are nested, the parameters in the larger model that are no... | The derivation of AIC as an estimator of Kullback-Leibler information loss makes no assumptions of models being nested.
| https://stats.stackexchange.com |
13,676 | [
"https://stats.stackexchange.com/questions/13676",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/862/"
] | I have a question on reading t-test p-value. If I understand correctly, the t-statistic is computed as:
$t = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}$
where $\bar{X}$ is sample mean, $\mu$ is population mean, $\sigma$ is sample standard deviation and $n$ is size of sample. Degrees of freedom is $n-1$.
Now, we can see... | A little change in notation might help in answering your question: What you call $\mu$ is often called $\mu_{0}$ because it is the population mean under the null hypothesis, whereas $\mu$ is the actual population mean - which is unknown because we don't know whether the null hypothesis is true. Also, what you call $\si... | Someone else can probably give a more rigorous answer, but:
For any given (fixed) difference between $\bar{X}$ and $\mu$, the difference is more meaningful if n is high.
Increasing n <em>will</em> result in a sample mean closer to the population mean, but <strong>only</strong> in the case that your sample is not diff... | https://stats.stackexchange.com |
35,368 | [
"https://math.stackexchange.com/questions/35368",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/9046/"
] | I just need my solution checked since I'm not sure if it's valid, especially the final statement
<strong>Question:</strong>
Show $p \Rightarrow (\neg(q \land \neg p))$ is a tautology by assuming:
$u \Rightarrow v$ is logically equivalent to $\neg u \lor v$
<strong>My solution:</strong>
$\neg(q \land \neg p))$ is l... | You can prove $F$ is countable without appealing to its characterization as the set of all programs by the following argument. $F$ is constructed as follows: Let $F_0$ be the collection of base functions which is easily seen to be countable. Let $F_{n+1}$ be $F_n$ together with every composition of finitely many ele... | The closure under composition and primitive recursion of the set of base functions <em>and</em> the Ackermann function is countable.
| https://math.stackexchange.com |
144,265 | [
"https://cs.stackexchange.com/questions/144265",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/143691/"
] | We say <span class="math-container">$x$</span> is a majority substring of <span class="math-container">$y$</span> if <span class="math-container">$y \in \Sigma^* x \Sigma^*$</span> and <span class="math-container">$|x| \geq \frac 12|y|$</span>. If <span class="math-container">$B$</span> is a regular language, is the se... | Since <span class="math-container">$|\cos n| \leq 1$</span>, we have <span class="math-container">$1 \leq 2-\cos n \leq 3$</span>, and so <span class="math-container">$$ T(n) = T(n/2) + \Theta(n). $$</span> This is something that the master theorem can handle.
| <span class="math-container">$n(2-\cos n)$</span> always lies between <span class="math-container">$n$</span> and <span class="math-container">$3n$</span>.
On expansion, we get:
<span class="math-container">$T(n) \leq 3 (n+n/2+n/4+\dotsc+1) \leq 6n$</span>
and
<span class="math-container">$T(n) \geq (n+n/2+n/4+\dotsc+... | https://cs.stackexchange.com |
46,467 | [
"https://mechanics.stackexchange.com/questions/46467",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/5109/"
] | For some reason, by the time I reach 50 miles/hour (80 km/hour) the noise has already gone down. It could be failing wheel bearings. It could be sawtooth tires.
Can a wheel fly off? I'm avoiding highways (65+ miles/hour - 100+ km/hour) until this is fixed, but are country roads, and country road speeds, also to be avo... | A noisy wheel bearing isn't generally that dangerous a condition, usually they will just get noisier for awhile. However, if a bearing suddenly fails and takes the rest of the bearings out your wheel could suddenly seize up, or more likely it will get a serious shimmy, which is dangerous no matter what road you are dri... | The faster you travel wind noise will often shroud noises that the vehicle is making so don't think that the fault has gone away at that point.
It depends really on how bad the bearing is with regards to what driving it's ok to continue with, really a failed bearing should be replaced ASAP. Some bearings will just hu... | https://mechanics.stackexchange.com |
237,556 | [
"https://mathoverflow.net/questions/237556",
"https://mathoverflow.net",
"https://mathoverflow.net/users/90978/"
] | Let $G$ be a semi-simple algebraic group over a field $K$, I am considering a question about whether there exists a finite set of semi-simple $K$-subgroups, say $H_1,...,H_r$, such that for any semi-simple $K$-subgroup $H\subset G$, $H$ is conjugate to one of the $H_i$ by an element in $G(K)$?
I know the answer is "n... | For fields of characteristic zero one can argue as follows: Assume first that $K$ is algebraically closed. Since semisimple subgroups of $G$ correspond bijectively to semisimple subalgebras of $\mathfrak g={\rm Lie}\,G$ it suffices to consider the same problem in $\mathfrak g$. The advantage is that the subalgebras of ... | In case it is useful to the OP, here is a reference:
Richardson, R. <em>A rigidity theorem for subalgebras of Lie and associative algebras.</em> Illinois J. Math. 11 1967 92–110.
Proposition 12.1 seems to be the relevant result.
| https://mathoverflow.net |
2,164 | [
"https://softwareengineering.stackexchange.com/questions/2164",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/895/"
] | So I'm sure everyone has run into this person at one point or another, someone catches wind of your project or idea and initially shows some interest. You get to talking about some of your methods and usually around this time they interject stating how you should use method X instead, or just use library Y. But not as ... | Don't just let them talk. Get them in front of a keyboard. The phrase "ok, show me" should do it. My experience is most blow hards aren't that great, and when they actually try to do what they say it doesn't work and things get real quiet.
| I've been programming for thirty years. I know lots of people who consider me a "programming master." Want to know my dirty little secret? I'm just barely competent in a few areas, but that's it. Mostly I <em>suck</em>.
I've worked with some incredible geniuses in those years, not the actress-on-a-podium-bubbling-... | https://softwareengineering.stackexchange.com |
314 | [
"https://cstheory.stackexchange.com/questions/314",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/25/"
] | There is often-quoted philosophical justification for believing that P != NP even without proof. Other complexity classes have evidence that they are distinct, because if not, there would be "surprising" consequences (like the collapse of the polynomial hierarchy).
My question is, what is the basis for belief that th... | PPAD is pretty "low" above P and not much would change in our understanding of complexity if it was shown equal to P (except that the few problems in PPAD would now be in P). The main "evidence" that PPAD!=P is an oracle separation, which is essentially equivalent to the combinatorial fact that no "black-box simulati... | Buhrman et al. showed there is an oracle relative to which all TFNP functions are poly-time computable, yet the Polynomial Hierarchy is infinite. TFNP is a class which contains PPAD and its cousins. This is another result strengthening our sense that PPAD being easy would not generate unlikely consequences in complex... | https://cstheory.stackexchange.com |
570,878 | [
"https://electronics.stackexchange.com/questions/570878",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/171611/"
] | I've never worked with or studied electro-mechanical components, but my understanding is that relays and motors are basically just inductors. If they're inductors, wouldn't they act as a short under DC and need the current controlled by an external resistor or transistor?
| No component is ideal, and inductors tend to be the least ideal of the passive components--and relays and solenoids are even <em>less</em> ideal than your average inductor, because they aren't designed to be close to ideal.
All materials (other than superconductors in their superconducting phase) have some positive res... | All inductors have series resistance. Well, unless they are made with super-conducting wire, I guess. But coils designed for DC operation have sufficient DC resistance to limit the DC current to a reasonable level for continuous operation. This is convenient so that the user of the coil does not have to figure out a wa... | https://electronics.stackexchange.com |
722,093 | [
"https://physics.stackexchange.com/questions/722093",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/335039/"
] | I was informed by @hft that by combining the total time derivation:
<span class="math-container">$$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} +
\frac{\partial L}{\partial \dot{x}}\ddot{x} +
\frac{\partial L}{\partial t}$$</span>
and:
<span class="math-container">$$\frac{\partial L}{\partial t}=0$$</span>
We c... | The first formula is the total momentum of the system which does not change, On the left-hand side is the expression for the <em>before</em> impact momentum, and on the right-hand side the <em>after</em> impact momentum. The two are equal, regardless of the reference frame, as long as the observer is in an inertial fra... | You are clearly learning physics (good!). A very important lesson is that the physics is in the derivation of the formula, not in the result! So quoting the formula without knowing where it came from is a bad plan.
The formulae you quote express different physics. The first formula (from your 'introductory' text book) ... | https://physics.stackexchange.com |
134,840 | [
"https://electronics.stackexchange.com/questions/134840",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/56207/"
] | The circuit below is the Hartley oscillator circuit. I simulated it in Multisim to understand exactly how oscillations occur.
While doing so I just separated the tank circuit (from transistor base and collector) then applied 12V DC voltage across it (across tank as shown below). Now also the tank circuit is producing... | <blockquote>
I thought oscillations will not occur
</blockquote>
Think of an LC tuned circuit as a pendulum. At rest it produces no oscillations but if you push it a bit it will swing back and forth at its resonant frequency no matter how small or big in amplitude the swing is. Pushing the pendulum is the same as ap... | Your circuit model contains no lossy elements, so the response to the initial turn on transient never dies out. There's a transient because the capacitor will be assumed to have 0 voltage, and the inductors 0 current, before time 0.
If you add realistic series resistance values to your inductor and capacitor models, ... | https://electronics.stackexchange.com |
48,129 | [
"https://stats.stackexchange.com/questions/48129",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14836/"
] | <blockquote>
Two containers $A$ and $B$ are placed adjacently to each other and gas passes through a small aperture joining them.
A total of $N(>1)$ molecules is distributed among the containers.
Assume that at each epoch of time one molecule, picked uniformly at random from the $N$ available, passes th... | When you're solving this kind of problem, it helps to draw a diagram with the state transitions and the respective probabilities, like this:
<img src="https://i.stack.imgur.com/NKF1k.png" alt="enter image description here">
In words: your state space is $S=\{0,1,\dots,N\}$ and $X_n$ is the number of molecules in the ... | Assuming the molecules are indistinguishable (a fairly standard assumption from any quantum treatment) then the set of states is simply the set of integers $\left\lbrace 0,1,\dots,N \right\rbrace$, representing the number of molecules in container A. Because at each epoch a single molecule must make a transition throug... | https://stats.stackexchange.com |
946 | [
"https://stats.stackexchange.com/questions/946",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/569/"
] | New to the site. I am just getting started with R, and want to replicate a feature that is available in SPSS.
Simply, I build a "Custom Table" in SPSS with a single categorical variable in the column and many continuous/scale variables in the rows (no interactions, just stacked on top of each other).
The table r... | As I read in help for the <code>t.test</code>, it is only applicable for the 2-sample tests. If you want to perform it to every combination of the columns of a matrix A, taken 2 at a time, you could do something like this (for the moment, I can't recall a better way)
<pre><code>apply(combn(1:dim(A)[2],2),2,function(x)... | <pre><code>summary(df)
</code></pre>
Will give you 5 number summaries and counts of <code>NA</code> for continuous variables, and counts for categorical variables.
As for the significance tests, you'll have to do that by hand with <code>t.test()</code> or <code>wilcox.test()</code>.
| https://stats.stackexchange.com |
133,718 | [
"https://chemistry.stackexchange.com/questions/133718",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/92934/"
] | <blockquote>
Which has stronger hydrogen bonding, <span class="math-container">$\ce{CH3OH}$</span> or <span class="math-container">$\ce{CH3NH2}$</span>
</blockquote>
I think it comes down to which has more dominance; number of hydrogens, number of lone pairs, or electronegativity.
| I'll assume that you know that charges of opposite sign attract each other and charges of like sign repel each other. Every atom consists of a tiny, positively charged nucleus and one or more negatively charged electrons (such that the overall charge is balanced to neutral).
Let us talk through what happens when two ... | You may also consider an image I read once in a book that makes science accessible to the general public. It starts from the idea that electrons have a property called spin that corresponds to male or female behavior : electrons try to make pairs if they are alone. If half of the electrons are male and half female, the... | https://chemistry.stackexchange.com |
497,307 | [
"https://electronics.stackexchange.com/questions/497307",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/248718/"
] | <strong>What is the difference between maximum power transfer and maximum efficiency in a circuit ?****strong text</strong>
| Heating elements shouldn't care, but the motors will run slower and have less torque, but still run hotter than they otherwise would for with this decreased power output.
Particularly vulnerable are things that have a high starting load like your paper shredder. Fans have decreased torque when running slower so that h... | <blockquote>
I am curious though if there are potential problems with some of the
devices that I am consider bringing as well, e.g. due to 50Hz instead
of 60Hz, especially some the ones that contain motors:
</blockquote>
Devices which have mains frequency transformers or induction motors may have problems, also ... | https://electronics.stackexchange.com |
490,432 | [
"https://math.stackexchange.com/questions/490432",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93026/"
] | The question relates to orthogonality and inner product spaces. If $ W,W_{1}, W_{2} $ are subspaces of finite dimensional vector space V. We have to prove the following
(a) $ W_{1} \subset W_{2} \implies W_{2}^\bot \subset W_{1}^\bot $
(b) $ (W_{1} + W_{2})^\bot = W_{1}^\bot \cap W_{2}^\bot $
(c) $ (W_{1} \cap W_{... | The language makes things a little cumbersome, so let's try to avoid it as possible:
$$x\in\left(W_1+W_2\right)^\perp\iff \langle x,t\rangle=0\;,\;\forall\,t\in W_1+W_2\implies \forall\,w_i\in W_i\,,\,i=1,2\;:$$
$$0=\langle x,w_1+w_2\rangle\implies \;\text{choosing}\;\;w_2=0\;,\;\text{we get}\;\;\langle x,w_1\rangle=... | <strong>(1)</strong> Assume $W_1 \subset W_2$. Now, let
$$ w \in W_2^\bot \implies w \notin W_{2} \implies w \notin W_1 \implies w \in W_1^{\bot} \implies W_2^{\bot} \subset W_1^{\bot}.$$
<strong>Note:</strong>
<blockquote>
If $A\subset B$ and $x\in A$, then $x\in B$.
</blockquote>
| https://math.stackexchange.com |
15,783 | [
"https://electronics.stackexchange.com/questions/15783",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3552/"
] | Dictionaries say there's "battery attendant" specialty. The name implies that's a specially trained person who somehow services batteries while they are in operation.
AFAIK the only kind of batteries that require maintenance is flooded lead-acid and the actual maintenance is adding distilled water. I don't see how thi... | Also on aircraft most batteries are composed of Ni Cad cells. The must periodically be tore down, cleaned, tested, reassembled and recharged before being placed back in service. Poorly maintained batteries generate hydrogen gas which can build up and with the right (or wrong depending on how you look at it) mix of oxyg... | Depending on the technology, when not handled properly, batteries may catch fire or even explode. They also almost always contain hazardous chemicals.<br>
I think the battery attendant would be a person to take care of large battery installations. A hospital for instance has backup power from diesel generators, but nee... | https://electronics.stackexchange.com |
102,254 | [
"https://dba.stackexchange.com/questions/102254",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/37971/"
] | Upon reviewing some of our code a colleague posited that he was annoyed at always having to write <code>TRUNCATE TABLE</code> when there is no real other usage for <code>TRUNCATE</code>.
Googling this, I indeed can not find a specific reason why the <code>TABLE</code> part is needed.<br>
What am I missing? Is there so... | The syntax choice is likely for consistency, albeit redundant. <code>TRUNCATE TABLE</code> follows the same pattern as other DDL statements (CREATE, ALTER, DROP), where the object type immediately follows the action keyword.
I should add <code>TRUNCATE TABLE</code> is part of the ANSI SQL Standard as of the 2008 vers... | Seems to me its redundancy for future extensibility. There may not be any other use for <code>TRUNCATE</code> currently, but one could be added in the future. Or at least that would have been the mindset of the developers.
| https://dba.stackexchange.com |
125,333 | [
"https://mathoverflow.net/questions/125333",
"https://mathoverflow.net",
"https://mathoverflow.net/users/32416/"
] | If a graph embeds in the torus or the projective plane is there an upper bound on the number of edge crossings it has in the plane?
| No, there is no upper bound. For any $n$, if you take a sufficiently fine mesh on a torus or projective plane, deleting $n$ edges will still result in a graph with a $K_7$ or $K_5$ minor, respectively.
| There are two ways to read this question. (I'll just ignore the projective plane part.)
Zare's reading: Suppose that a graph $G$ embeds in the torus. Is there an upper bound on the number of edge crossings of $G$ when drawn in the plane?
The answer is "no". You can draw $K_7$ in the torus and then take many parall... | https://mathoverflow.net |
202,357 | [
"https://mathoverflow.net/questions/202357",
"https://mathoverflow.net",
"https://mathoverflow.net/users/69992/"
] | I am struggling to see how the symplectic action 1-form $\alpha_H$ on the loop space of a symplectic manifold $(M,\omega)$ is closed. It is defined by
$\alpha_H(Y) = \int_0^1 \omega(\dot{x}(t)-X_H,Y)dt$
with $Y \in T_{x(t)}M$ and $X_H$ a Hamiltonian vector field on $M$. Going the other way and obtaining it as the dif... | My answer is more a plan than a real answer. It aims to not close too early by a brutal "no-go" algebraic statement. Of course, if you ask for finite (i.e. algebraic) tensor product this is not true.
If you are thinking of completed tensor products, then, I think yes.
Of course, in order to have the <em>completed te... | This won't work. You can't approximate the restriction $\rho$ of one-dimensional Hausdorff measure to $\{(x,x): 0\le x\le 1\}$, say, in total variation norm by a finite linear combination $\sum c_j \mu_j\otimes\nu_j$. No matter what you do ($\mu_j,\nu_j$ continuous, or with a point part), $\mu\otimes\nu$ and $\rho$ wil... | https://mathoverflow.net |
140,509 | [
"https://electronics.stackexchange.com/questions/140509",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/58827/"
] | I have a op amplifier for which I want to calculate Vout depending on Vin.
The circuit looks like this:
<img src="https://i.stack.imgur.com/KaQQ4.jpg" alt="">
I know that with a circuit that just has ground connected to + of the amp, i can just calculate KVL: V1 = R1*I1+Rf*If+Vout but with this amp, there is also r... | The answer to your question is very simple if you know the fundamental gain expressions for the inverting resp. non-inverting opam amplifier: <strong>G(inv)=-Rf/R1</strong> and <strong>G(non)=1+Rf/R1</strong>. Note that the non-inverting gain G(non) is referenced to the non-inv. input terminal directly. Hence, we must ... | This circuit is a classic diff-amp. The output is V2-V1.
One way to analyze this circuit is to think of the affect from each input to the output separately. Start by grounding V2 and thinking about the response from V1 to the output. With V2 grounded, the + input is just held at 0. Now you have a simple inverting ... | https://electronics.stackexchange.com |
3,255 | [
"https://dba.stackexchange.com/questions/3255",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2109/"
] | I am trying to get an idea of the size of the "hot data" part of a rather large table, and I was wondering if this could be done directly in mysql. I know that with the percona version of mysql, I can have access to figures like "number of rows accessed per table", but I would actually need those data on a per row basi... | This is just intended to demonstrate redo usage of various <code>insert</code> operations rather than answer the whole question. Results on my 10g instance are not 100% deterministic, but the broad picture remained the same each time I ran through.
For the heap tables, I do not know why the <code>insert /*+ append */<... | Good question. I "solved" this problem for my situation a while back by making the MV's and any indexes on them NOLOGGING. There was no point to it my situation - I was doing a full refresh of the view anyway, why would I need redo?
| https://dba.stackexchange.com |
289,810 | [
"https://electronics.stackexchange.com/questions/289810",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/122006/"
] | Is the equivalent resistance across a set of n resistors connected in series greater than the equivalent resistance across them when they are connected in parallel? I want to find the relation between \$R_s\$ and \$R_p\$.
My attempt:
Let the resistance of the resistors be denoted by \$R_1, R_2, R_3,..., R_n\$ and the... | Let's try a very simple approach.
The collection of resistors will have a maximum value resistor \$R_{max}\$, and a minimum value resistor \$R_{min}\$. By definition $$R_{min} <= R_{max}$$ the equality is true if all resistors are equal, otherwise the inequality is true
The series connection will contain \$R_{max}... | Let's see if this works.
Start with \$n=2\$:
$$
R_s = R_1+R_2\\
R_p = \frac{R_1R_2}{R_1+R_2}\\
\text{Then: }\\
\frac{R_1R_2}{R_1+R_2} \stackrel{?}{<}R_1+R_2\\
R_1R_2 \stackrel{?}{<} (R_1+R_2)^2
$$
The last row can be derived from the one before if \$R_1+R_2>0\$ and it is true if both resistance are positive ... | https://electronics.stackexchange.com |
24,565 | [
"https://softwareengineering.stackexchange.com/questions/24565",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/9318/"
] | Ours is a software concern and we have a team structured like so: manager->team leads->team members. We are following the agile programming model and trying to develop a product in a collaborative fashion. We have daily morning meetings with team members and their team leads to discuss progress and issues.
When it co... | As often as is needed. Some projects - those where requirements might be fluid or political reasons mean that regular updates are critical - require more on-going communication than others.
As a minimum I'd suggest that it would be a very odd week in which some meeting / discussion (possibly informal or in passing)... | The best way to provide feedback would be to use the agile practices that already exists:
<ul>
<li><strong>Iteration demo.</strong> This is where the team demonstrates actual working software and explains how the iteration went. Everyone is invited and are free to ask questions.</li>
<li><strong>Big Visible Charts.</s... | https://softwareengineering.stackexchange.com |
220,487 | [
"https://dba.stackexchange.com/questions/220487",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/163170/"
] | We are running <em>MySQL Ver 5.7.18</em> on an <em>Amazon Lightsail Linux</em> instance (2GHz Single Core CPU, 2GB RAM, 40GB SSD).
Besides MySQL, we also run some <em>Java</em> services on this machine, which access the database.
MySQL runs on the default configurations.
After rebooting the machine or restarting the... | <ul>
<li>Leave the Query cache off -- You don't have enough RAM to waste it on the QC.</li>
<li>With only 2GB of RAM, 256M may be as big as is safe for <code>innodb_buffer_pool_size</code>. Raising it would lead to swapping, which is <em>worse</em> for performance.</li>
<li>The best solution is speeding up queries. W... | Please deal with these two problems first:
<pre><code>[!!] name resolution is active : a reverse name resolution is made for each new connection and can reduce performance
[OK] Query cache is disabled by default due to mutex contention on multiprocessor machines.
</code></pre>
You said it's a single CPU, so ...
| https://dba.stackexchange.com |
42,254 | [
"https://quant.stackexchange.com/questions/42254",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/31825/"
] | The VIX index is based on the S&P, I am wondering the feasibility of creating a VIX index for each of the S&P 500 Industries?
Would this even be possible?
| The VIX Index is computed from option prices on S&P Index.
A VIX-like Index for other industries would first require to have a liquid option market.
| In theory that would be possible. However, liquidity in industries could in some instances be substantially less than liquidity in the SPX thus making the hedging of volatility derivatives such as vol futures more difficult. Also, there may not be sufficient interest from investors to make the launching of industry/sec... | https://quant.stackexchange.com |
434,707 | [
"https://physics.stackexchange.com/questions/434707",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/176157/"
] | <img src="https://i.stack.imgur.com/wgbg3.jpg" alt="the picture">
I have to find a substitute for this circuit. (The substitution is on the right)
The arrows in one circle are perfect voltage sources.
The arrows in two circles are perfect current sources.
It seems easy but the concept of ideal current sources baff... | We are talking about cycles here. After a complete cycle the system must be right back where it started. Since entropy is a state variable, it must then be that after one complete cycle the entropy is at its "initial" value. By the second law this must mean that the entropy has to "go somewhere else". If you "gathered ... | <blockquote>
In my understanding, we could gather more and more extra entropy, while converting all the heat into work
</blockquote>
You can't store entropy while still converting all the heat into work. Storing an amount of entropy <span class="math-container">$dS$</span> requires that you also store an amount of ... | https://physics.stackexchange.com |
47,134 | [
"https://datascience.stackexchange.com/questions/47134",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/69358/"
] | I am pretty new to deep learning and really hope that you can help me.
I want to write a python program that lets me choose an area in a reference image. This subimage of variable size should then be used to search in a database of images. Then the parts of the images with the highest similarity to the reference sub i... | There's nothing about a recommendation system that absolutely necessitates some kind of machine learning. Indeed, I've seen decision systems in use that were essentially just someone's idea about what the customer's preferences ought to be.
A recommender can be based on anything from a few ad-hoc 'common sense' rules,... | The recommendation system is a broad term to describe everything from a poster "in case of fire.. " to ML-based systems that continuously evolve over time.
A simple recommendation system consists of:
<ul>
<li>Knowledge database representing some wisdom that will be used to make new recommendations. This database can ... | https://datascience.stackexchange.com |
76,131 | [
"https://security.stackexchange.com/questions/76131",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/61676/"
] | I can't understand why IP spoofing (even basic) is very limited.
Suppose Bob and Alice are about to communicate and Eve can see network communication, why eve can't use IP spoofing for making "Man In The Middle" ? I know there is a TCP issue with predictable stats (ACK, sequence), but if these informations are not en... | If you are directly on the path of the information, then there is absolutely nothing preventing you from pretending you are that IP address. If you were the first device along the network that Alice talked with, you could absolutely convince her that you are Bob's IP.
This is a big part of why browsers require sign... | Imagine the scenario using physical letters, as it's easier to picture.
Say I send a letter with a return address that doesn't correspond with my actual house (or somewhere I can collect mail). What will happen to the letter?
As long as the send address is correct, the mail service will deliver this letter to the c... | https://security.stackexchange.com |
49,990 | [
"https://chemistry.stackexchange.com/questions/49990",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/24308/"
] | Why are there different values for enthalpy of combustion, depending on the calculation method?
Take for example the combustion of ethanol:
$$\ce{C2H5OH(l) + 3O2(g) -> 2CO2(g) + 3H2O (l)}$$
If I calculate this using enthalpy of formation:
\begin{array}{c|c}
\text{Substance} & \Delta H^\circ /\pu{(kJ/mol)} \\
... | <strong>Average</strong> bond enthalpies (note the word "average") are calculated in a different way from formation enthalpies. Formation enthalpies are well-defined and precise, meaning that two different people could measure them the same way and get the same answer. Average bond enthalpies are averages over many dif... | Because calculation with bond energies are notoriously imprecise.
Those bond energies that you use do not reflect the exact C-C bond energy in ethanol, for example. It is merely an "average" C-C bond energy taken from a wide variety of organic compounds. Obviously if you use it to calculate the enthalpy change of a re... | https://chemistry.stackexchange.com |
32,617 | [
"https://chemistry.stackexchange.com/questions/32617",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/16551/"
] | <blockquote>
<img src="https://i.stack.imgur.com/hmnE6.jpg" alt="enter image description here">
</blockquote>
I tried finding the slope between two points but I keep getting wrong values, how does one find the initial rate by using such graphs?
So I started by trying to find a slope of two points, <span class="math... | It seems like you have the right idea to me,
For the "Initial Rate," you're taking a curve and doing a straight approximation of the curve over a small portion, as you appear to be doing.
Your logic also appears correct to me, a decrease in concentration should correspond to a negative rate.
My guess is that the qu... | This is a <strong>standard exam question</strong> pertaining to the kinetics material that is typically presented in a first year general chemistry course. Usually the coverage is restricted to discussion of zero, first and second order kinetics and this is what gets tested on exams. From the photo of the exam question... | https://chemistry.stackexchange.com |
180,296 | [
"https://softwareengineering.stackexchange.com/questions/180296",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/75667/"
] | Our Architecture team is proposing a framework that would see our SQL queries moved from coded strings within our applications, into a file based system where we would invoke them with function calls. Our application makes heavy use of SQL queries ranging from the mundane, to very complex. This is a .NET solution.
The... | If your problem is "impossible to understand" SQL, focus on that problem. Can not imagine that SQL with attributes does anything to make it easier to understand.
Instead it will create a maintenance burden on parsing attributes etc on an already complex language like sql. Sooner or later your extensions will prevent ... | I ran into this same dilemma at my job a while back. I got the same advice you did, and here's what I thought about it:
Pros:
<ul>
<li>SQL queries can be tested on their own, separate from the mainline code.</li>
<li>Your queries can be modified without having to recompile.</li>
</ul>
Cons:
<ul>
<li>SQL <strong>is... | https://softwareengineering.stackexchange.com |
54,038 | [
"https://cs.stackexchange.com/questions/54038",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/21124/"
] | Is there any situation that bidirectional search on a graph is not applicable? for example is there any classes of graph that we can only use ordinary Dijkstra's algorithm, and can not use its bidirectional variant.
The graph may be a dynamic graph.
| Yes, a simple one is coming to my mind, a dynamic graph where the <strong>search operators are not reversible</strong>, i.e. both predecessors and successors of a node in the graph can not be calculated.
| There are no such graphs.<br>
If you have directed tree-like graph - it would make no sense to go from leaves, but... from the root it will work as intended, and from the leaves - it will stop there and wait to meet the previous.<br>
It will be wasteful, but working. In given example, the same applies - it will produce... | https://cs.stackexchange.com |
322,195 | [
"https://electronics.stackexchange.com/questions/322195",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/158946/"
] | I've become fairly familiar with the clearance and creepage requirements of UL/IEC/etc 60950, 60730 and derived/related standards. I've just realised, though, that they only refer to distances through air (clearance) or along a surface(creepage). In fact, solid insulation is specifically used as a barrier to increase t... | PCBs are treated by the IEC 60950-1 "separately" as for solid insulation, that is when the path of discharge passes through a solid object (i.e. the substrate / prepreg).
<ol>
<li>The main requirement is that the thickness must be >= 0.4 mm: that barely fits the 4-layer pcb with standard thickness of 1.6 m... | <blockquote>
Can I safely have 240VAC on one side of the PCB and user accessible low-voltage circuits on the other, provided there aren't any vias in the vicinity?
</blockquote>
It's best to separate high voltage with other secondary voltage components. If you need them on the same board, ensure the trace is at leas... | https://electronics.stackexchange.com |
55,274 | [
"https://mechanics.stackexchange.com/questions/55274",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/38434/"
] | Can I use 15w40 synthetic oil in my 2015 vw jetta tdi and how long can go between oil changes?
| Replace the battery and those issues will stop.
Reason? The bad battery is so discharged after starting the engine the alternator takes a few seconds to bring the system voltage high enough for some electronics to work properly.
| The same belt is possibly driving the power steering pump and the alternator. If the belt is slipping when you first start the engine, then the power steering will not work correctly and the alternator will not be providing power.
Friction on the slipping belt may then make it heat up and start to grip. The power st... | https://mechanics.stackexchange.com |
238,060 | [
"https://softwareengineering.stackexchange.com/questions/238060",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25416/"
] | This is more of a theoretical question. If jvm is implemented in go which itself is a garbage collected language, then does that jvm need a separate garbage collector to be implemented for its own operation?
| No, it can rely on the host language's garbage collector. Of course it has to be careful not to reference memory that is logically unreachable (unreachable from the guest program and not needed for the VM). But that is not fundamentally different from avoiding "logical memory leaks" (holding onto memory you don't need ... | Yes, it does. The reason is that garbage collection can only reclaim inaccessible resources, but what is accessible depends on the level on which you view the system.
The host VM implements garbage collection to reclaim memory that the guest program used but has now released. In your case, the guest program is another... | https://softwareengineering.stackexchange.com |
12,347 | [
"https://mathoverflow.net/questions/12347",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3396/"
] | Let $X$ be a smooth projective algebraic variety over $\mathbb{C}$. Then I think that someone (Serre?) showed that the Cohomological Etale Brauer Group agrees with the torsion part of the Analytic Brauer Group $H^{2}(X,\mathcal{O}^{\times})$. This latter group is calculated in the classical (metric) topology on the a... | Although the other answers correctly explain the basic logical equivalence of the two proof methods, I believe an important point has been missed:
<ul>
<li><em>With good reason</em>, we mathematicians prefer a direct proof of an implication over a proof by contradiction, when such a proof is available. (all else being ... | Strictly speaking, the contrapositive of a statement which is not an implication doesn't make sense. However you can always fake the implication, the contrapositive of $\top \to A$ (or just $A$) is $\lnot A \to \bot$, i.e., a "proof by contradiction" is the contrapositive of a "proof (from tautology)."
<hr>
I guess I... | https://mathoverflow.net |
64,226 | [
"https://physics.stackexchange.com/questions/64226",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10352/"
] | Dark energy may be described as a fluid with <em>negative</em> pressure.
We say that this negative pressure counteracts gravity and accelerates the expansion of the Universe.
Now consider, for example, a star. Gravity contracts the star, but <em>positive</em> (thermal) pressure counteracts the collapse.
This makes ... | Imagine you have a star sized ball of gas that is in equilibrium i.e. the pressure of the gas exactly balances the inwards gravitational force. Now imagine compressing the gas. This has two effects:
The first effect is the obvious one that compressing the gas increases the pressure, so the result is an outward force a... | You should distinguish two things: the pressure itself, and the gravitation that it creates. First of all, why does it create some gravitation? Because energy does. It is not the mass of the Earth that pulls us down - it is the energy of that mass, $E=mc^2$, that makes us heavy and not flying but walking.
And the ener... | https://physics.stackexchange.com |
140,050 | [
"https://security.stackexchange.com/questions/140050",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/28790/"
] | A reverse TCP is a connection that starts <strong>from the victim</strong> back to the attacker, which in fact opens the 'door' for the attacker to hack the target system.
This connection is being triggered normally by a malware that contains the <strong>attacker address</strong> or some other address, and when the vi... | "Spoof" may be a poor term that will lead you down unhelpful paths.
You want to <em>obfuscate</em> your location. Dynamic DNS or pivoting off of another server that you have cracked are ways to put layers in between yourself and the target and not expose yourself directly.
So, the victim connects to a static address... | I think a hacker would buy a stolen credit card in the dark net, rent a linux server in China or Russia with that credit card and then maybe establish a Tor SOCKS tunnel to her own box. Not 100% sure about the Tor thingy but since you can send nmap traffic through Tor FROM the attacker TO the client I don't see why the... | https://security.stackexchange.com |
31,927 | [
"https://electronics.stackexchange.com/questions/31927",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9781/"
] | I have learnt in school about opcodes and how it works with the ALU to add numbers and such, now is my question how the computer is able to understand this, because it is codes and the computer needs something to translate that to actually doing that, in't it? (correct me if I'm wrong plz)
I also want to, when I unders... | At the very lowest level, consider something like <i>microcode</i>. That's what Wouter was talking about when he mentioned Very Long Instruction Word architectures.
A CPU is a collection of busses, registers, memory, and arithmetic logic unit (ALU). Each of these do simple and finite things. Any one higher level in... | Any translation from one set of codes to another set of codes can be done by a (conceptually) simple piece of logic. A ROM for instance will do. A simple (not pipelined or microprogrammed) processor translates (parts of) the instruction to bits that control the various hardware parts inside the CPU, like the ALU functi... | https://electronics.stackexchange.com |
711,721 | [
"https://physics.stackexchange.com/questions/711721",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/312234/"
] | The Balmer series only shows electrons dropping to the energy level n=2 and the Lyman series only shows those that drop to n=1. How did they restrict the electron's energy transition so that the electrons only return to a specific energy level?
| For a glass of water, the buoyant force is a small correction to the gravitational force arising because the pressure is different at different altitudes. The timescales in this problem are short enough that we can neglect the center-of-mass motion due to gravity, so we can absolutely neglect the center-of-mass motion... | It's not just buoyancy because the slug of liquid can move. Your "force field" at the top of the glass modifies the premise of the XKCD scenario. If you look closely at the illustrations, his slug of liquid moves downward as the glass moves upward. The atmosphere pushes down on the slug of liquid and up on... | https://physics.stackexchange.com |
437,235 | [
"https://electronics.stackexchange.com/questions/437235",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/45692/"
] | I'm designing a schematic and board in Eagle 9.4.0. I have couple different power nets: signal 5V, power 5V (for servos) and power 8V (from battery). I'd like the power nets to be wider than others, so I designed specific net class for them. Matching GND nets will also be wider than others.
The problem is that I want ... | You rename them into one single name. That's all.
If you want to keep the different names and properties and simply connect them, use a zero-ohms resistor. You can design such an element consisting of two pads and a track yourself.
| Janka's suggestion of zero-ohm resistor (or jumper) is a good one.
If, for some reason, you don't want to do that, I've seen people draw a copper rectangle on the PCB which overlaps both nets. This works, but it has a few drawbacks:
<ol>
<li>It doesn't show up on the schematic, so you should make note of it manually.... | https://electronics.stackexchange.com |
64,826 | [
"https://cs.stackexchange.com/questions/64826",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/60088/"
] | Given a fully connected graph $G(V,E)$ with associated edge weights and a set of constraints specifying distance $D(V_i, V_j) < M_{ij}$, where $\left\{V_{i..j}\right\} ⊂ V$, how can I go about finding the smallest subset graph $G'(V', E')$ such that none of the constraints are violated?
In other words, find the sma... | This is NP-hard by reduction from Set Cover. The problem remains NP-hard even if edge weights are restricted to $\{1, 3\}$.
In the Set Cover problem, we are given a ground set $U$ containing $m$ elements $x_1, \dots, x_m$, a collection $\mathbf S$ of $n$ subsets $S_1, \dots, S_n$ of $U$, and an integer $k$, and our t... | This problem is NP-hard problem, you should go with heuristics or meta-heuristics, to find acceptable solution in acceptable time.
try first Genetic algorithms, they are very powerful and they will give you great ideas.
| https://cs.stackexchange.com |
258,903 | [
"https://dba.stackexchange.com/questions/258903",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/194321/"
] | I'm using the MD5 hash function of MySQL to hash some data I import into the database from a CSV file.<br>
The issue is that some lines have an incorrect hash (but not all of them).<br>
When I use a query:
<pre><code>UPDATE mytable SET email_md5 = (SELECT MD5(email))
</code></pre>
MySQL inserts some wrong hashes in... | There is a Carriage Return (hex 0D) at the end of
<pre><code>627269636540696775616E6573747564696F2E636F6D0D
^^
</code></pre>
Recommend you trim emails of all "whitespace" before feeding them into your database in any way.
To confirm with your original email:
<pre><code>S... | Maybe:
<pre><code>UPDATE mytable SET email_md5 = MD5(email) WHERE email_md5 != MD5(email)
</code></pre>
| https://dba.stackexchange.com |
102,045 | [
"https://dba.stackexchange.com/questions/102045",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39636/"
] | I would like to mirror/replicate my databases to the cloud. The cloud is setup using VPN to my actual machine.
I am a bit confused by the options I have and would like to get some light into it.
My setup is a SQL Server 2012 (standard edition) Instance which should be mirrored/replicated to a SQL server 2014 instance.... | <ol>
<li>Create dummy, empty tables on the local server so that the procedure creation can happen.</li>
<li>Change the procedure code to use two-part synonyms. On the server that needs to use the linked server:
<pre><code>CREATE SYNONYM dbo.whatever FOR linkedserver.dbo.whatever;
</code></pre>
On the local server tha... | you can create a linked server that goes nowhere
<pre><code>EXEC master.dbo.sp_addlinkedserver @server = N'THISSERVERNAME', @srvproduct=N'', @provider=N'SQLNCLI'
</code></pre>
Then any queries notice that the linked server is there, but has no access to anything within it. you'll find quite often that the queries for... | https://dba.stackexchange.com |
146,653 | [
"https://mathoverflow.net/questions/146653",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31308/"
] | It's conjectured that, asymptotically, half of elliptic curves have rank 0, half have rank 1, and elliptic curves of rank $\geq 2$ have density 0. But what if we disregard elliptic curves of rank 0 or 1: Are there any conjectures about the average rank of elliptic curves of rank $\geq 2$?
More generally, for any integ... | A very simple random matrix heuristic says, based on the function field model, that the rank of a random elliptic curve is the dimension of the invariant subspace of a random element of $O(n)$ for large $n$.
We can easily compute the dimension of the space of matrices that preserve exactly $k$-dimensional subspace. We... | These types of questions are pretty speculative. One should be aware firstly that there is no reason for there to be roughly equal numbers of rank 2 curves and rank 3 curves.
Mark Watkins has a paper where he comes up with a conjecture, using random matrix theory, that the number of rank 2 elliptic curves with conduc... | https://mathoverflow.net |
450,850 | [
"https://physics.stackexchange.com/questions/450850",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/168400/"
] | In the book Classical Mechanics by David Morin,while discussing Work Energy theorem he gives an example of importance of choosing System. As he considers lifting the book upward then by WE theorem:
<em><span class="math-container">$W_{external}$</span>= ∆K+ ∆U +∆Internal Energy</em>
Now,if we consider lifting the boo... | You sure this is the exact statement. Because <span class="math-container">$\Delta U = -W_{Earth}$</span> is the definition of gravitational potential energy. You should never include both of them in the same expression.
Either this or the fact that since you are only considering the book as your system the potential ... | The book & Earth as a system has gravitational potential energy whereas the book by itself as a system cannot have gravitational potential energy.
<hr>
When you have only the book as the system and an external force (you?) lifting the book then the book has two external forces acting on it; the contact force th... | https://physics.stackexchange.com |
159,615 | [
"https://mathoverflow.net/questions/159615",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24478/"
] | Take a prime other than 2,3 or 5 and look at the part of it that repeats in base 10. Is it true that the sum of the digits in the end divided by the period(number of repeated digits id always $\frac{9}{2}$ Can we extend this result to other bases? Why does this happen?
Regards.
This is a crosspost from math.se
| Note first that the counterexamples to user4140's observation involve decimal expansions with odd period length. In the case of even period length, what user4140 has observed is a consequence of Midy's theorem, which says the following: let p be a prime not dividing 10, and suppose that the repeating part of the decima... | The reason why this seems to be true for lots of cases is that it is true when the period of the fraction is even (hence different from 3) and $p$ is coprime with $10$ (hence different from $2$ or $5$). This is a known result which follows from Fermat's little theorem and actually the fraction can have any numerator $r... | https://mathoverflow.net |
23,170 | [
"https://dba.stackexchange.com/questions/23170",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11128/"
] | Which is the best way to create a <strong>connection string</strong> for SQL Server?
Should I be using a trusted connection string (<strong>windows authentication</strong>) or an untrusted connection string (<strong>sql server authentication</strong>) and why?
My concern is to make my connection string more secure, s... | Windows Authentication is going to be the most secure means, as opposed to SQL Server Authentication. The reason behind this is because with Windows Authentication, the OS handles the auth as opposed to SQL Server handling it with its respective method.
When you use Windows Auth, SQL Server just uses the authenticati... | In my opinion, when it comes how secure the connection is, Windows authentication might works better, however you will be constraint and dependent on that along the way. For example if for some reasons there was a problem in windows users, the issue will flow to SQL accessibility as well. Usually the network and infras... | https://dba.stackexchange.com |
281,025 | [
"https://physics.stackexchange.com/questions/281025",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/78665/"
] | Are living organisms physically deterministic at any given time? Since it's all physics and chemistry, it leads me to believe they are.
| In the sense that <em>most</em> people mean, I'd say <strong>no</strong> because quantum mechanics isn't deterministic (at least the way most people think of "determinism").
<hr>
Ultimately, to be more specific, I think this depends on your interpretation of quantum mechanics, and how reductionist you are.
The best... | Note that systems are not deterministic, dynamical theories are. So you can look at a dynamical theory, and see if "deterministic" is an attribute of that theory or not, but all you can do with a system is ask "do I have a theory that predicts to satisfactory accuracy what that system does?" Here's the key point: if ... | https://physics.stackexchange.com |
298,281 | [
"https://mathoverflow.net/questions/298281",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27832/"
] | I intend to learn KAM Theory. Could you please suggest me a good book on KAM Theory to begin with, where main results are discussed with complete proofs.
Thank you.
| There are many good books. I can recommend two:
<ol>
<li>S. Sternberg, Celestial mechanics, Part 2, W. A. Benjamin Inc., NY 1969</li>
<li>V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, there are two English translations. The original Russian title
is "Additional chapters of the the... | <ul>
<li>MR1997070
Kappeler, Thomas(CH-ZRCH); Pöschel, Jürgen(D-STGTMP)
KdV & KAM.
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 45. Springer-Verlag, Berlin, 2... | https://mathoverflow.net |
30,221 | [
"https://stats.stackexchange.com/questions/30221",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7556/"
] | I have some questions regarding generalization and recall:
<ol>
<li>It usually hear that a good classifier should "generalize" from the training data. Is that true? </li>
<li>I feel(?) that a "general" classifier should improve recall, however a "specific" classifier should have more precision, is this true? </li>
<li... | "Generalization" refers to the ability of a classifier to correctly classify instances that it has not yet seen as part of its training and is always a desirable feature. The opposite of generalization would be over-fitting, which you always want to avoid (Although a classifier might also not generalize well if the tra... | Answering your 3rd question. Your training data should be as representative of the domain you are trying to learn as possible. The learned classifier should then be used in this same domain.
If you want to make use of the things you have learned in one domain and you think that this might be applied in another but som... | https://stats.stackexchange.com |
93,138 | [
"https://softwareengineering.stackexchange.com/questions/93138",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/64/"
] | I am thinking of doing a short presentation at work about using Stack Overflow as a resource for your day job.
What is your experience doing this?
Would you deem it a valid resource to tell your colleagues about it or is it similar to telling them about Google as a resource?
Is there a better way of doing it?
... | Key points:
<ol>
<li>Registration is easy.</li>
<li>It's free</li>
<li>Quality answers.</li>
</ol>
I would suggest your group create a question during the presentation (do a search first.). If you don't get a response before the presentation/meeting is over, keep everyone posted via email and follow-up if necessary. ... | You should track down each time you find a solution on SO of a problem you had. Do that for a month or so.
For each problem:
<ol>
<li>estimate how much time (in hours) you would have spent solving the error yourself.</li>
<li>estimate the time (in hours) you spent looking for a solution.</li>
</ol>
Substract the sum... | https://softwareengineering.stackexchange.com |
244,000 | [
"https://physics.stackexchange.com/questions/244000",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56263/"
] | Why is the time of ascent less than the time of descent in a projectile motion.
I understand that while going up the air resistance and gravity act downwards and while coming down gravity is downwards and air resistance upwards but I still dont get it.
Is there another explanation or perhaps a mathematical proof to t... | For simplicity assume the resistance to be be constant F.
During ascent mg and F both oppose motion of the body.
During descent F opposes motion while gravity supports it.
Thus the rate of decrease in velocity during ascent is greater than the rate of increase in the velocity during descent.
| The neatest answer I know to this uses energy rather than force....
The projectile passes any height <span class="math-container">$h$</span> twice, on the way up and on the way down, and in both cases it has potential energy <span class="math-container">$mgh$</span>.
Between these two occurrences it loses some energy -... | https://physics.stackexchange.com |
23,983 | [
"https://dba.stackexchange.com/questions/23983",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11178/"
] | I have created a table <code>testtable</code> inside the database <code>testbase</code> that have the following structure:
<pre><code>product_no (int, not null)
product_name (varchar(30), not null)
price (money, null)
expire_date (date, null)
expire_time (time(7), null)
</code></pre>
which I used the Microsoft SQL Se... | At last I know why the message appear in the MS SQL Server Management Studio.
The MS SQL Server Management Studio require one to restart it after creating a stored procedure in it.
After restarting the MS SQL Server Management Studio, there is no such error anymore.
(Strange, does that mean that every time I create... | <img src="https://i.stack.imgur.com/TT8gv.jpg" alt="">
IntelliSense Refresh local Cache should fix it
| https://dba.stackexchange.com |
87,562 | [
"https://stats.stackexchange.com/questions/87562",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/40739/"
] | Suppose $X$ and $Y$ are independent. To be concrete, suppose $X$ is $N(0,a)$ and $Y$ is $N(0,b)$. For any scalar c,d with c < d, is there a way to bound the following probability from above in terms of a,b,c,d?
$P(cX<Y<dX)$
| In the full model there are $n-1$ coefficients for the main effect of $X$, $p-1$ for the main effect of $M$, & $np -n - p +1$ for the interaction; giving a total, as you say of $np-1$. In the model with interaction only, there are just $np -n - p +1$ coefficients; so some combinations of levels of $X$ & $M$ sha... | @scortchi gave you a good answer, but I thought a specific example might be useful, if not for you then for others who will see this.
Suppose your dependent variable is log(income) and your two categorical independent variables are sex (male, female, other) and race (White, Black, Asian, Native American, Hawaiian/Paci... | https://stats.stackexchange.com |
71,665 | [
"https://security.stackexchange.com/questions/71665",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | Just about now a friend of mine got compromised, actually she was compromised by various adware since long ago but she installed something (her browser was hijacked to deliver even more malware) and the machine crashed.
I told her to reinstall from the recovery partition since she's not tech-savvy and doesn't know how... | Worse! I can't find it but the other day I read about a UEFI hack that installs a rootkit in your UEFI - the bootloader. If that is possible, you can reinstall your system and still get infected.
But this is not common - yet. And I believe these rootkits are not easily made, probably need to be modified for many diff... | This would purely depend on the type of malware that infected the machine.
If the malware goes on to randomly create multiple points inside every partition of the machine, then it might affect the recovery partition as well.
Possible solution would be to try and do a recovery through partition and if the problem still ... | https://security.stackexchange.com |
62,010 | [
"https://quant.stackexchange.com/questions/62010",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/44729/"
] | I have two questions regarding the terminology used on the practitioner side regarding asset swap spreads. Asset swaps are mainly used to retain the credit exposure of a bond while minimizing the interest rate risk on it. Thus, the asset swap spread depends crucially on the bond involved and its credit risk.
<em>Questi... | <em>Question 1 I often read by research desk that ASW-spread have widened or tighten without concrete reference to the bond. As said above, the asset swap spread depends on the credit quality of the swapped bond. So is there a market standard for this? If people talk about USD, do they mean swapped Treasuries, in EUR s... | Let me add a couple of points.
<em>Question 1</em>: in my experience, ASW spread <em>always</em> refers to the spread between a particular Bond and the IRS of the same currency. Most commonly, this would be a spread between government bond and the corresponding IRS.
In a par-par ASW, you trade a fixed notional (say 500... | https://quant.stackexchange.com |
2,587,549 | [
"https://math.stackexchange.com/questions/2587549",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/116154/"
] | It is well-known that the group of (orientation-preserving) symmetries of the tetrahedron is isomorphic to $A_4$. Since $\mathbb{Z}/3$ is a quotient of $A_4$, $\mathbb{Z}/3$ also acts on the tetrahedron.
Is there a way to see this actions geometrically? i.e., are there $3$ natural parts of the tetrahedron that $\math... | Long divide to find,
$$
x_n=\frac{n}{n+1}=1-\frac{1}{n+1}
$$
From which it is clear that
$$
x_n=1+O(1/n)
$$
since
$$
x_n-1=\frac{1}{n+1}\leq \frac{1}{n}
$$
for any $n$.
For the second part, you need some $b$ with
$$
\lim_{n\to \infty}\frac{n^b}{n+1}=0
$$
but by inspection, you just need the order of $n$ in the nu... | Note that
$$\frac{n}{n+1}=\frac{1}{1+\frac1n}=\left(1+\frac1n\right)^{-1}=1-\frac1n+\frac1{n^2}...$$
Or without Taylor's expansion
$$\frac{n}{n+1}=\frac{n+1-1}{n+1}=1-\frac{1}{n+1}$$
Thus
$$x_n=1+O(n^{-1})=1+o(1)=1+o(n^{-b}) \quad b\in[0,1)$$
| https://math.stackexchange.com |
173,284 | [
"https://mathoverflow.net/questions/173284",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1162/"
] | I am interested in a proof of the following fact :
Suppose that $X$ is a Riemann surface homeomorphic to the Riemann sphere. Then $X$ is <em>conformally equivalent</em> to the Riemann sphere.
Of course, this follows from the uniformization theorem which states that every simply connected Riemann surface is conformall... | An alternative is to simply use Riemann-Roch, which does not depend on the Uniformization Theorem.
R-R says that $\ell(D)-\ell(K-D) = \mathrm{deg}(D)-g+1$, where $\ell(D)$ is the dimension of the space of meromorphic functions $f$ on your surface $C$ such that $(f)+D\ge0$.
If $C$ is homeomorphic to the sphere, th... | There are such proofs. See, for example Goluzin, Geometric theory of functions (Appendix).
He uses the following fact. Let $h$ be an analytic diffeomorphism of the circle onto
itself. Then there is a Jordan analytic curve $\gamma$ such that a conformal map
$f_1$ of the unit disc onto the inside of $\gamma$ and a confor... | https://mathoverflow.net |
123,290 | [
"https://dba.stackexchange.com/questions/123290",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/51198/"
] | I try to save a very large select (more than 70 milion rows into csv file) on Win 2012 R2 server
I execute query as root , but I think there is still some problem with privileges
<pre><code>select *
INTO OUTFILE 'D:\my_folder\my_file.csv'
FIELDS TERMINATED BY ','
ENCLOSED BY '"'
LINES TERMINATED BY '\n'
from my... | On Win2012 I found file my.ini.
In the file there is a definition of secure_file_priv - a folder when I can download to or uplload from ,
So I change my query as following:
<pre><code> SELECT *
INTO OUTFILE 'D:\<folder_defined_as_secure_file_priv>\my_file.csv'
FIELDS TERMINATED BY ','
ENCLOSED BY '"'
LIN... | I am using MySQL Server 8.0 on Windows 10. I tried to load data from csv file using the following commands:
<pre><code>LOAD DATA INFILE 'C:\ProgramData\MySQL\MySQL Server 8.0\Uploads\World_cup_dataset.csv'
INTO TABLE trial
FIELDS TERMINATED BY ',';
</code></pre>
When I run above commands, I got
<blockquote>
"ERRO... | https://dba.stackexchange.com |
32,896 | [
"https://quant.stackexchange.com/questions/32896",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/26911/"
] | I am having troubles with deriving the upper bounds on option prices. For example, I am trying to determine the upper bound on a European put option.
If I define the put price as $P$, the terminal stock price as $S_T$, the strike as $X$, the risk free rates as $r$, and the time to expiry as $T$, I am able to create th... | First, I think you got discounting and compounding wrong. The upper bound for the put price is $P_0 < X e^{-r T}$. This has to hold as long as $S_0 > 0$.
Your approach is generally correct though. Assume that $P_0 = X e^{-r T}$. Then you invest $P_0$ at time $t = 0$ and have $P_0 e^{r T} = X$ at time $t = T$. No... | Have you considered implied volatility ? It might be really high for some volatile stocks, so put price might goes to extremely high values due to iv ...
| https://quant.stackexchange.com |
115,505 | [
"https://dba.stackexchange.com/questions/115505",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/60985/"
] | I have a table with 2 columns, the date and the value for the date, e.g.
<pre><code>date value
2015-09-01 15
2015-09-02 17
2015-09-03 21
</code></pre>
and I want to create a column with the difference between the value and the value of the last day, like
<pre><code>date difference
2015-09-01 ... | <h1>PROPOSED QUERY #1</h1>
<pre><code>SET @diff = NULL;
SET @prevval = -1;
SELECT date,
(@diff:=IF(@prevval=-1,NULL,value - @prevval)) difference,
(@prevval:=value) prevval
FROM mytable;
</code></pre>
<h1>SAMPLE DATA</h1>
<pre><code>mysql> DROP DATABASE IF EXISTS tover;
Query OK, 1 row affected (0.03 sec)... | Hope this helps. It's SQL Server code, but you should be able to perform the same join on your table with the <code>date_add</code> function.
<pre><code>DECLARE @TABLE TABLE ([Date] Datetime, [Value] int);
INSERT INTO @TABLE VALUES ('2015-Sep-01',11);
INSERT INTO @TABLE VALUES ('2015-Sep-02',13);
INSERT INTO @TABLE V... | https://dba.stackexchange.com |
3,001,543 | [
"https://math.stackexchange.com/questions/3001543",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/614667/"
] | I am watching Lecture 1 of the differential equation course on MIT OpenCourseWare.
The teacher said, for <span class="math-container">$y'= f(x,y)$</span>, if <span class="math-container">$f(x,y)$</span> is continuous around a point <span class="math-container">$(x0,y0)$</span>, it would guarantee at least one solution,... | The teacher cites the Picard-Lindelöf theorem.
It says that in a neighbourhood of the considered point, the ODE has a solution if <span class="math-container">$f$</span> is continuous and that the solution is unique if <span class="math-container">$f(x,y)$</span> is Lipschitz continuous in <span class="math-container">... | For the differential equation <span class="math-container">$$y'=3|y|^{2/3}$$</span> you have (at least) <span class="math-container">$4$</span> solutions through the initial point <span class="math-container">$(x_0,y_0):=(0,0)$</span>, namely <span class="math-container">$y_1(x)\equiv0$</span>, <span class="math-contai... | https://math.stackexchange.com |
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