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 |
|---|---|---|---|---|---|
5,001 | [
"https://mathoverflow.net/questions/5001",
"https://mathoverflow.net",
"https://mathoverflow.net/users/491/"
] | In algebraic topology, we define a degree for a map $f: S^n \to S^n$ as where the induced map $f_*$ on the $n$-th homology group of $S^n$ sends $1$.
In differential topology, we have a different (same?) notion of degree for $f$. You take a regular value $b \in S^n$, consider $f^{-1} (b)$ (which is finite by the inver... | I think what you need is the following lemma (usually called the "Stack of records" lemma):
Consider a smooth proper map of manifolds of the same dimension $f \colon M \to N$ and let $y \in N$ be a regular value of $f$.
Then there exists a neighbourhood $V \subset N$ of $y$ such that $f^{-1}(V) = \cup\_{i=1}^n U\_i$ ... | I think so: it looks like the local degree according to Hatcher's definition measures whether $f$ preserves orientation or reverses it on the neighborhood of $x$. On page 233 he begins discussion of orientation using excision classes: an orientation for an neighborhood in an $n$-manifold at a point $x$ is just a choic... | https://mathoverflow.net |
337,374 | [
"https://physics.stackexchange.com/questions/337374",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/151259/"
] | I have seen two contradictory descriptions of how electrons and other charged particles travel around magnetic fields; in one, they travel in circles around magnetic field lines, in the other, they travel in coil or spring-like paths around magnetic fields, with that said, which path do they actually travel when it's ... | <blockquote>
So finally, this should yield $\Delta v = \sqrt{\frac{2GM}{r_o}} - \sqrt{\frac{2GM}{r_f}}$ plus any extra speed we wanted to have at that height, maybe enough to sustain a stable orbit. Is my reasoning correct?
</blockquote>
No, it's not. You are calculating the difference between escape velocity at two... | That extra speed, enough to sustain a stable orbit, makes all the difference! We need to compute the speed on a circular orbit, to keep things simple. The radial acceleration is equal to the pull of gravity:
$$ m\frac{\Delta v}{r_f} = \frac{GMm}{r_f^2},$$
which results in the ultra-classic
$$ \Delta v = \sqrt{\frac{... | https://physics.stackexchange.com |
455,123 | [
"https://electronics.stackexchange.com/questions/455123",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88636/"
] | I just read about buck converters and boost converters and buck/boost converters. Great stuff.
But, why is a step-down converter called a buck converter?
I tried to research this myself. According to Google Book search, the phrase <code>buck-boost transformer</code> was in use at least as early at 1891 in a periodi... | It's the same sense as to "buck" a trend:
<ol>
<li>to oppose or resist (something that seems oppressive or inevitable).
"the shares bucked the market trend"
synonyms: resist, oppose, contradict, defy, fight (against), go against, kick against
"it takes guts to buck the system"</li>
</ol>
So you're "bucking" the inp... | I may be wrong(apparently there is no way to qualify any answer here as correct), but I had always assumed that "buck" referred to an action similar to a "bucking bronco or bull". A buck converter sends a voltage pulse only as often as it needs to in order to provide the rectified and filtered DC output required, just... | https://electronics.stackexchange.com |
25,414 | [
"https://physics.stackexchange.com/questions/25414",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3018/"
] | I've been doing some research on RR Lyrae stars and haven't been really able to find an answer to this question.
RR Lyrae are well known for their periodic magnitude, and also are usually found in certain color ranges ("RR Lyrae Color Box"). My question is: does the color of RR Lyrae Stars (G-R in particular) vary ove... | The short answer is that yes the color would have to change somewhat. All the stars in the instability strip (RR Lyrae, Cepheids, etc) are variable because they pulsate. Over the course of the pulsation, they vary in brightness, size and surface temperature.
It is the temperature change that is important here. As... | Although I'm a regular variable star observer, I don't observe RR Lyrae variables because they are not suitable targets for visual observers like myself. However, the long period Mira-type variable that I observe the most also change colour with brightness. At their dimmest, they look like glowing red coals, but they f... | https://physics.stackexchange.com |
12,218 | [
"https://cs.stackexchange.com/questions/12218",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/8123/"
] | I'm fairly new to the syntax of relational algebra, and I'm having a hard time understanding how I could set a "at least one" clause.
Example: I have:
<ul>
<li>a table with books (listing the title, year published and ID), </li>
<li>a table with authors (listing their name and ID),</li>
<li>a table which lists what ... | A first hint toward a solution is to think about "what's the result of a <em>natural</em> join between $Author$, $Publication$ and $AuthorPublication$?"
The answer is "the universal relation" $R(BookID,AuthorID,Title,Year,Name)$ describing who wrote a book and when. Note that a book without any author or an author wit... | <strong>This is an answer by the OP, which is removed from the question.</strong>
<em>A friend gave me a tip and a possible solution appeared:</em>
For Author(Name,AuthorID) | Publication(Title,Year,BookID) | AuthorPublication(BookID,AuthorID)
$ RenamedAP = \alpha_{(AuthorID:linkAuthorID, PublicationID:linkPubID)} (... | https://cs.stackexchange.com |
3,774,460 | [
"https://math.stackexchange.com/questions/3774460",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/794439/"
] | <blockquote>
If <span class="math-container">$$y = \frac{2}{5}+\frac{1\cdot3}{2!} \left(\frac{2}{5}\right)^2+\frac{1\cdot3\cdot5}{3!} \left(\frac{2}{5}\right)^3+\cdots$$</span> what is <span class="math-container">$y^2+2y$</span>?
</blockquote>
Attempt:
We know that for negative and fractional indices,
<span class="mat... | You can calculate <span class="math-container">$y$</span> using a "well known" binomial series expansion for
<span class="math-container">$$(1-4x)^{-\frac 12} = \sum_{n=0}^{\infty}\binom{2n}nx^n$$</span>
To see this rewrite the coefficients
<span class="math-container">$$\prod_{k=1}^n\frac{2k-1}{k} = \prod_{k... | Substitute <span class="math-container">$x=\frac{2}{5}$</span>:
<span class="math-container">$$y=\sum_{i=1}^\infty\frac{x^i}{i!}(\prod_{k=1}^{i}(2k-1))$$</span>
<span class="math-container">$$y=\sum_{i=1}^\infty\frac{x^i}{i!}((2i-1)!!)$$</span>
For <span class="math-container">$|x|<\frac{1}{2}$</span>, this is the T... | https://math.stackexchange.com |
1,765 | [
"https://mechanics.stackexchange.com/questions/1765",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/826/"
] | I have a Honda Civic 2008 whose exterior plastic on one of the taillights was broken sometime ago. I duck taped it to keep it in place. The taillight bulb itself is good and functioning properly.
What options do I have in terms of doing this DIY?
Is it possible to just replace the exterior plastic/glass?
| Usually the glass is bonded on to the reflector unit, so you probably won't be able to buy the glass on its own - You'll have to buy a complete unit.
Your best bet is to ask around any scrapyards/junkyards in your area, see if they have any Civics in stock, as that would be considerably cheaper than a new unit from Ho... | It is possible to replace just the exterior plastic/glass, but the problem is finding it for a decent price. Since your car is a 2008 (newer), it may be harder to find at a scrapyard. If you can, then buy the part. If not, you'll have to get the replacement from Honda and probably pay an arm and a leg, but once you... | https://mechanics.stackexchange.com |
39,773 | [
"https://datascience.stackexchange.com/questions/39773",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/49590/"
] | I have two data frames <code>df1</code> and <code>df2</code> which look something like this.
<pre><code> cat1 cat2 cat3
0 10 25 12
1 11 22 14
2 12 30 15
all_cats cat_codes
0 10 A
1 11 B
2 12 C
3 25 D
4 22 E
5 30 F
... | You can convert <code>df2</code> to a dictionary and use that to replace the values in <code>df1</code>
<pre><code>cat_1 = [10, 11, 12]
cat_2 = [25, 22, 30]
cat_3 = [12, 14, 15]
df1 = pd.DataFrame({'cat1':cat_1, 'cat2':cat_2, 'cat3':cat_3})
all_cats = [10, 11, 12, 25, 22, 30, 15]
cat_codes = ['A', 'B', 'C', 'D', 'E'... | <pre><code>df3 = pd.merge(df1,df2,left_on=['cat'+str(i)], right_on = ['cat_codes'], how = 'left')
</code></pre>
I would iterate this for cat1,cat2 and cat3. This does not replace the existing column values but appends new columns.
| https://datascience.stackexchange.com |
37,240 | [
"https://quant.stackexchange.com/questions/37240",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/30652/"
] | I am trying to prove the need of a convexity adjustment to a forward rate by calculating the next expectation:
\begin{align*}
P(t_0, T_s)E^{T_s}\big(L(T_s, T_s, T_e) \mid \mathcal{F}_{t_0}\big).
\end{align*}
Where $E^{T_s}$ denotes the expectation under a T-measure with $P(t,T_s)$ as numéraire and $t_0< T_s < T... | By definition <span class="math-container">$Q^{T_s}$</span> is risk neutral for the numeraire <span class="math-container">$P(t,T_s)$</span>, and <span class="math-container">$Q^{T_e}$</span> is risk neutral for the numeraire <span class="math-container">$P(t,T_e)$</span>, hence
<span class="math-container">$$
\left(\f... | I think that your question can be solved easier. You may ask me why. Here is my answer:
First of all the LIBOR forward rate <span class="math-container">$L(t, t, T)$</span> is <span class="math-container">$\mathbb{Q}^{T}$</span>-martingale, where <span class="math-container">$\mathbb{Q}^{T}$</span> is a <span class="ma... | https://quant.stackexchange.com |
88,562 | [
"https://physics.stackexchange.com/questions/88562",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35040/"
] | Given the equation
$$F_{\text{net}} = ma$$
Does this not imply that if the net force on a certain object is positive, its acceleration will also be positive, and theoretically this object would accelerate forever to an infinite velocity?
i.e
envision a block on a surface. If a person were to apply a force (push) on... | Yes. Your analysis is completely true on the basis of Newtonian Mechanics. But upon observation of the universe this turns out to be wrong, as once the objects in consideration approach the speed of light, we have to apply Relativistic Mechanics. So, as far as Newtonian Mechanics is concerned, objects <em>can</em> have... | ...and infinite acceleration still applies, just not an infinite coefficient of velocity. As one approaches the speed of light a smaller and smaller speed gain is realized for the same input of force. So even though the force remains constant, the increase in speed decreases so that the object under acceleration approa... | https://physics.stackexchange.com |
18,271 | [
"https://cstheory.stackexchange.com/questions/18271",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/674/"
] | What is known about the class of languages recognized by finite automata having the same initial and accepting state? This is a proper subset of the regular languages (since every such language contains the empty string), but how weak is it? Is there a simple algebraic characterization?
Ditto for languages recognize... | This question is solved for deterministic automata and for unambiguous automata in the book [1]
[1] J. Berstel, D. Perrin, C, Reutenauer, Codes and automata, Vol. 129 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, 2009.
In the case of deterministic automata, the characterization is g... | Finite automata in which the initial state is also the unique accepting state have the form $r^∗$, where $r$ is some regular expression. However, as J.-E. Pin points out below, the converse is not true: there are languages of the form $r^*$ which are not accepted by a DFA with a unique accepting state.
Intuitively, gi... | https://cstheory.stackexchange.com |
421,671 | [
"https://electronics.stackexchange.com/questions/421671",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/212513/"
] | Some would say carrying solar panels to charge a Tesla would be inefficient, and would take up all the space, however towing a trailer would. Solar panels plus inverter are also not that heavy.
Would carrying a folding device that stacks solar panels in a 3 meter by 2 meter 2 wheel trailer be efficient, especially in... | Using the sun as energy source is actually one of the few reasonable ways to overcome the issues we are globally facing. The problem is the efficiency of conversion from sunlight to electricity (the conversion efficiency of photovoltaic modules is about 20%), plus the energy storage (Expensive, heavy batteries with lim... | <blockquote>
Would carrying a [folding] device that stacks solar panels in a 3 meter by 2 meter 2 wheel trailer be [worthwhile] efficient?
</blockquote>
It's a great question, but I think that stopping driving and then fast charging is the wrong methodology and makes the solution impractical as shown in the other an... | https://electronics.stackexchange.com |
314,635 | [
"https://softwareengineering.stackexchange.com/questions/314635",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/223080/"
] | <strong>Note: There are many questions answers related to the licensing. But I think my requirement is specific, so asking a separate question.</strong>
We are considering to fork a GPL 2 project and use it for commercial purposes. This project has not been updated in past 2 years, but it's a great solution for our re... | Yes, GPLv2 code can be used in the manner you describe. That in fact is one of the motivations for the AGPL and GPLv3. The modified code must, of course, never be given to anyone outside the organization or the obligation to make the source code available <em>will</em> be incurred.
There will probably be a negative re... | Read the GPL 2 license carefully, and be prepared to share the code along with all your changes with others.
If you hand over the software to anybody outside your company without giving them the source code, then you have the obligation to provide the source code to anybody in the world who asks you for it.
| https://softwareengineering.stackexchange.com |
203,568 | [
"https://security.stackexchange.com/questions/203568",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/143610/"
] | As in the title - I received an email reply to a months old thread containing a password protected zip file. I had previously asked them for a particular CAD file, but this was months ago and we had resolved the issue without me ever needing the file.
My internal alarms are going off. The thing is, it was sent as a re... | When setting up TOTP with a site, they give you a shared secret.
<ol>
<li>Yubico Authenticator uses your Yubikey to store that info. As long as your key is present, all instances of Yubico Authenticator are interchangeable.</li>
<li>Most sites will only share a single secret with you, but you can freely update that... | While anyone using a OTP token should allow you to configure more than one token source (at least two so you can have a secured backup), not all do. If all of your places will let you enroll two authenticator apps, then just enroll one on each YubiKey (I'd recommend sticking with a 5 for the backup as well, so you can... | https://security.stackexchange.com |
329,445 | [
"https://physics.stackexchange.com/questions/329445",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/121705/"
] | One of the question in my book says that if $E$ denote the rest mass energy of a nucleus and $n$ a neutron then,
a.) $E(U^{236}_{92})>E(I^{137}_{53})+E(Y^{97}_{39})+2E(n)$
b.)$E(U^{236}_{92})<E(I^{137}_{53})+E(Y^{97}_{39})+2E(n)$
c.) $E(U^{236}_{92})<E(Ba^{137}_{53})+E(Kr^{97}_{39})+2E(n)$
d.) $E(U^{236}_{... | <blockquote>
the rest mass energy of a nucleus is smaller than the rest mass energy of its constituent nucleons in free state
</blockquote>
This sentence speaks about $protons$ and $neutrons$ as the constituents. In your equation you have three nuclei and the sentence is valid for each of the three nuclei separately... | The BE per nucleon is higher in the region of mass number where you have the two fission fragments as compared to the region of mass number 236. Therefore you get the answer. Higher BE lower rest mass.
| https://physics.stackexchange.com |
241,927 | [
"https://dba.stackexchange.com/questions/241927",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/184290/"
] | I have a table that has the following format:
<pre><code>id | price | category
---------------------
1 22 hardware
2 11 software
3 null hardware
4 null hardware
5 55 software
6 null hardware
</code></pre>
I want to fetch any row whatsoever that has price = null and category = hardware. I only ... | <blockquote>
I only want to know if a row with a null price exists.
</blockquote>
MySQL:
<pre><code>SELECT
EXISTS ( SELECT 1 FROM tbl
WHERE price IS NULL
AND category = 'hardware' );
</code></pre>
will return true or false (1 or 0).
Beneficial:
<pre><code>INDEX(price, ca... | <em>Answering for SQL Server. I don’t know that there will be a single answer that will work on all three platforms you’ve tagged. If that was unintentional, please only tag the engine you’re using. If you want an answer per platform, might be better to ask separate questions.</em>
You can leave <em>which</em> id is r... | https://dba.stackexchange.com |
711,907 | [
"https://physics.stackexchange.com/questions/711907",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/14275/"
] | The <em>third law of thermodynamics</em> states, in one rather intuitive formulation, that:
<blockquote>
It is impossible to refrigerate a system to a temperature of exactly <span class="math-container">$0$</span> <span class="math-container">$K$</span> using a finite process (finite energy or finite lapse of time).
</... | The thermodynamic definition of temperature is based on the way that the entropy of a system changes as we increase the energy. We expect that as we increase the energy of a system it will become more disordered and its entropy will increase, and this corresponds to the usual positive temperatures that we measure with ... | Negative temperatures are possible only in systems that can saturate in entropy. An atom or a nucleus has a theoretically infinite number of high energy states and hence should never be able to achieve negative temperature.
My knowledge on this topic is limited and I would love to see what others have to say about this... | https://physics.stackexchange.com |
161,437 | [
"https://electronics.stackexchange.com/questions/161437",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4700/"
] | How many lithium iron phosphate (LiFePO4) can safely be connected in parallel, in order to achieve higher power output (and capacity)? Wired directly together, without components such as resistors or power transistors limiting current flowing between parallel cells.
Precautions taken would include ensuring they're br... | There really isn't a maximum!
You have already hit the major concerns including using the same state of charge, using batteries that are in the same condition, from the same manufacturer (and preferably the same lot number to get an even closer match). You also want to make sure that you never short circuit that ba... | Suggest you use protected cells if you're going to put them in parallel- protected against overcurrent (in or out) and overcharging and overdischarging (they have a small PCB inside- at the end actually- with a bunch of parts on it).
Many cells are not protected, some are only partially protected (short-circuit only)... | https://electronics.stackexchange.com |
582,116 | [
"https://physics.stackexchange.com/questions/582116",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1002/"
] | Title basically says it all.
I'm not a physicist by any stretch. I'm an IT professional with slightly more than a passing interest in mechanics.
I got to thinking the other day how much power is generated when a manned rocket is launched to go to the moon (or ISS, etc etc).
Wouldn't it be possible to set up the hydroge... | As mentioned by other posters, oxygen is not a fuel, it is an oxidizer, and as such, it will not be part of my reply.
Regarding coal, if you believe the geologists, coal is the product of a large amount of dead plant and animal material that was heated and compressed over vast time frames to squeeze it into carbon. Th... | This is being done in remote locations. They have hydrogen electrolysis systems connected to wind turbines. When the wind is blowing they have normal wind power. When the wind stops they have stored hydrogen to provide the power. Not very efficient but certainly worthwhile in remote locations. I am in the hydrogen ele... | https://physics.stackexchange.com |
54,162 | [
"https://physics.stackexchange.com/questions/54162",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7993/"
] | To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere.
Is this right?
Space also gets distorted parallel to the direction of motion, but not perpendicular to it.
Does this m... | There is a more precise sense in which the question is ill-posed (at least mathematically); namely, it is a fundamental assertion of relativity (special and general) that the time 'measured' (counted, experienced, observed...) by an observer between two events occurring on her worldline is the length of her worldline-s... | There is no such thing as an observer traveling with a photon. Photons don't have experiences. So there's really no valid answer to this question.
| https://physics.stackexchange.com |
41,719 | [
"https://cs.stackexchange.com/questions/41719",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/30946/"
] | The most appropriate way to implement a heap is with an array rather than a linked list, why is this?
I don't completely comprehend why this is? is it because it is easier to traverse?
| It doesn't make any sense at all to implement a heap as a linked list. (The most common kinds of) heaps are inherently binary trees. You can store a heap in an array because it's easy to compute the array index of a node's children: the children of the node at index K live at indices 2K+1 and 2K+2 if indices start at 0... | array based implementations are much easier to work with, as they can be iterated through internally making element updates and destruction much simpler. However they only work on heaps with a defined number of children on each node (like binary heaps). If you are doing something like a pairing heap you will need point... | https://cs.stackexchange.com |
366,413 | [
"https://physics.stackexchange.com/questions/366413",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/174081/"
] | I am not a physicist nor a student of physics. I am just an old man that wonders. As such, I probably do not belong in this society.
I've had a long interest in neutron stars. This interest began when a PBS scientist (physicist?) commented on a program (probably NOVA) that "a neutron star would be cool to the touch (a... | So 5.5 Pg of neutrons is $3.3 \times 10^{39}$ neutrons. Their diameter is 1.75 fm--so end-to-end:
5.75 Ym.
| By basic calculation (forgetting neutron-neutron interactions) in one teaspoon there should be about 10^39 neutrons and if you take the classical proton radius as size, it would make a line of about 1000 000 light years in distance (more than 10 times the size of the galaxy).
| https://physics.stackexchange.com |
318,354 | [
"https://softwareengineering.stackexchange.com/questions/318354",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/150257/"
] | I'm having trouble understanding a small passage in The Structure and Interpretation of Computer Programs, and I'm hoping someone can help me interpret it.
In the book's introduction to Orders of Growth (Big O Stuff--Page 48 in volume 2) the book states:
<blockquote>
We say that R(n) (resources required to compute ... | The short answer is that this is just the definition of an asymptotic limit. We can try a more intuitive construction though:
Let's say we think our algorithm <strong>A</strong> is linear, so the order of growth is just <code>θ(n)</code>. We don't know the coefficient: maybe it actually requires 2.7 "resources" per ad... | The three Big-notations are all related to each other:
<ul>
<li>Big-O is an upper bound. so n ∈ O(n), but also n ∈ O(n*n) and any other larger upper bound.</li>
<li>Big-Ω is a lower bound. similarly, n ∈ Ω(n), and also n ∈ Ω(1).</li>
</ul>
Upper and lower bound are corresponding to each other in the obvious way: f ∈ ... | https://softwareengineering.stackexchange.com |
192,404 | [
"https://physics.stackexchange.com/questions/192404",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/36066/"
] | We have two airconditioning systems in the office. For the sake of this question, let us assume the following current conditions:
<ul>
<li>AC1 (old) outputs air of 26°C</li>
<li>AC2 (new) outputs air of 18°C</li>
<li>Office temperature is currently 23°C</li>
<li>outside temperature is 35°C</li>
</ul>
Now as far as I ... | Without knowing a <em>lot</em> more about the details of the entire system, we can't say exactly what the difference will be between the AC1+AC2 case and the AC2-only case. However, there are a few things we can work out from simple energy balance.
In the following, I'm considering the air as an ideal gas with a fixed... | If you're objective is to cool down the office, and you have a machine blowing air into the office which is warmer than the current (indoor) ambient temp. then I would by all means turn the damned thing off!
air conditioners are heat pumps, just like a fridge. They take in the ambient air, pass it over a cool surface... | https://physics.stackexchange.com |
8,156 | [
"https://physics.stackexchange.com/questions/8156",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2958/"
] | When finding the discrete energy states of a operator I have been taught to use the time-independent Schrodinger equation which restates the definition of eigenvalues and eigenvectors. What I don’t understand is why the eigenvalues are the energy states, is there firstly a mathematical reason and secondly a physical re... | As has been remarked by others and explained clearly, and mathematically, the eigenvalues are important because a) they allow you to solve the time-dependent equation, i.e., solve for the evolution of the system and b) a state which belongs to the eigenvalue $E$, i.e., as we say, a state which is an eigenstate with eig... | Both eigenvalues and eigenstates belong to some <strong>operator</strong>. In your case, this is the Hamiltonian operator $\hat H$. It's fundamental because of many reasons. First is that it is indeed an operator that represents energy in a sense that possible energy levels are encoded in its spectrum (i.e. a set of ei... | https://physics.stackexchange.com |
557,525 | [
"https://physics.stackexchange.com/questions/557525",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/250506/"
] | How can I formally show (or at least argue) that, given the crystal Hamiltonian expansion around a Weyl node in a three-dimensional Brillouin Zone located at <span class="math-container">$\vec{k}_{0}$</span>,
<span class="math-container">$\hat{H}=f_{0}(\vec{k}_{0})\mathbb{I}+\vec{v}_{0}\cdot\vec{q}\mathbb{I}+\sum_{a=x,... | At Weyl points (<span class="math-container">$K$</span>, <span class="math-container">$q = 0$</span>), we can approximate a tight-binding Hamiltonian as
<span class="math-container">\begin{equation}
H(\vec{K}+\vec{q})= v \vec{q} \cdot \vec{\sigma}.
\end{equation}</span>
As this is a general <span class="math-containe... | To simplify the maths, let us set the zero of energy at the crossing point and make the velocity isotropic (essentially re-scale your definition of <span class="math-container">$\mathbf{q}$</span>), so that the Hamiltonian around the Weyl point becomes:
<span class="math-container">$$
\hat{H}(\mathbf{q})=v_{\mathrm{F}}... | https://physics.stackexchange.com |
1,679,655 | [
"https://math.stackexchange.com/questions/1679655",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/319245/"
] | Does this question have a solution? I think it's impossible to know if line segments P1Q1 and P2Q2 intersect at all with just the information about their end points Q1 and Q2.
Thanks.
| There are many ways to associate a group to a graph, some interesting, some artificial. I'm not sure what the motivation is behind the question.
Given a graph $G$, the automorphisms of $G$ form a group called $\mbox{Aut}(G)$.
Given a connected graph $G$, think of it as a topological space, pick a base point, and co... | Other ways to associate a group (but typically infinite ones) are the following:
<strong>Graph of Groups</strong>: See e.g. <em>Serre, "Trees"</em> or the corresponding wiki-article. These are groups arising from actions on graphs (trees). See also its generalization, called <em>Complexes of groups</em> (see e.g. <em>... | https://math.stackexchange.com |
11,295 | [
"https://robotics.stackexchange.com/questions/11295",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/14767/"
] | For a sorting machine where the objects to be sorted have various sizes, color, shapes, and patterns, is it more optimal (in terms of minimal time of the overall process and maximal precision and accuracy) to use a sorting algorithm or to use different dimensions in the physical design to do the sorting?
| It really depends on the objects you are sorting, and the flexibility you're looking for as the system is maintained over the years.
Using physical methods to sort is very reliable. Many times you can align the parts, such as by using curves, chutes, vibration, and parts feeding mechanisms. Look up vibratory bowl... | You would have to do both. It's very very challenging to move an object without using hardware, and it's incredibly hard to see the colour of a brick with hardware.
You'd have to break it down into a few pieces:
<strong>Hardware</strong>
<ul>
<li>Shape and size (you can't detect the size and shape with a robot easi... | https://robotics.stackexchange.com |
166,645 | [
"https://electronics.stackexchange.com/questions/166645",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/73181/"
] | This is the quetion :
Find the capacitive reactance that when connected in parallel with the load will make the
load look purely resistive.
<img src="https://i.stack.imgur.com/kru0g.png" alt="enter image description here">
And this is the answer
<img src="https://i.stack.imgur.com/3p9zc.png" alt="enter image descripti... | the answers provided along with the question (in image) seems wrong(99%, as i haven't done the calculations)
<blockquote>
<blockquote>
for your question you need to know the concept of Leading and lagging VAR. <strong>the pure resistive load never consumes VARs, but capacitance consumes lagging and inductor cons... | Purely resistive loads have a real reactance, while inductive and capacitive loads are imaginary reactances. You simply need to provide a capacitive reactance that has the same but opposite value as the inductive reactance the circuit already has.
| https://electronics.stackexchange.com |
6,380 | [
"https://datascience.stackexchange.com/questions/6380",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/9793/"
] | <ol>
<li>I want to avoid overfitting in random forest. In this regard, I intend to use mtry, nodesize, and maxnodes etc. Could you please help me choose values for these parameters? I am using R.</li>
<li>Also, if possible, please tell me how I can use k-fold cross validation for random forest (in R).</li>
</ol>
| Relative to other models, Random Forests are less likely to overfit but it is still something that you want to make an explicit effort to avoid. Tuning model parameters is definitely one element of avoiding overfitting but it isn't the only one. In fact I would say that your training features are more likely to lead to... | @xof6 is correct in the sense that the more depth the model has the more it tends to overfit, but I wanted to add some more parameters that might be useful to you. I do not know which package you are using with R and I am not familiar with R at all, but I think there must be counterparts of these parameters implemented... | https://datascience.stackexchange.com |
422,990 | [
"https://electronics.stackexchange.com/questions/422990",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/131591/"
] | I generated gerber files to the pcb manufacturer, but I noticed that the top pad master (.GPT) was not generated, the top solder mask (.gts) was.
<ul>
<li>The pcb manufacturer did not complain, but I'm wondering, what can happen if top pad master (.GPT) was not generated ?</li>
<li>Why it did not appear as option to... | In ancient times when PC boards were layed out using sticky tape and Bishop Graphics pad patterns on mylar film, you would make a pad master showing all pads, and that mylar would apply to both sides of the board. The single pad master ensured that the pads on both sides of the board would line up. You would make sep... | Normally when you generate Geber files with altium you have :
<ul>
<li>.GTL : Top copper</li>
<li>.GTO : Top overlay (silks)</li>
<li>.GTP : Top paste (for stencil)</li>
<li>.GTS : Top soldermask</li>
</ul>
And Other layers, drill file and at least 1 mechanical layer for cutout.
If you plan to solder components you... | https://electronics.stackexchange.com |
99,765 | [
"https://electronics.stackexchange.com/questions/99765",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9983/"
] | this may be more of a geometry question than an EE one, but i'll ask it here anyway. I'm trying to build a weather vane, and am looking at using several linear hall effect sensors (such as the allegro 1324) laid out around a shaft with a free-spinning magnet on it.
how many sensors would i need? this is what i'm look... | Your magnet has a south pole and a north pole. A noth pole will produce the opposite signal in a Hall sensor compared to a south pole and so, if you have two Hall sensors at 90 degrees, you can infer any angle from the two readings you acquire.
You have to watch out for increased noise though but this should not be a ... | Check out the MagAlpha devices. Only one sensor will do the whole job and the precision will be much higher. You just need a ring magnet that is magnetized diametrically.
| https://electronics.stackexchange.com |
370,595 | [
"https://mathoverflow.net/questions/370595",
"https://mathoverflow.net",
"https://mathoverflow.net/users/164620/"
] | Let <span class="math-container">$f\colon X\to Y$</span> be a surjective morphism of smooth projective varieties. If the decomposition theorem for <span class="math-container">$f$</span> is given by <span class="math-container">$$Rf_*\mathbb{C} \simeq \bigoplus_i R^if_*\mathbb{C}[-i],$$</span> what are the necessary co... | Here is an example where <span class="math-container">$f$</span> is not smooth but <span class="math-container">$Rf_* \mathbb{C}$</span> behaves as if it were:
Let <span class="math-container">$X$</span> be a hyperelliptic surface and <span class="math-container">$f$</span> the natural morphism to <span class="math-con... | I don't know how to characterize such morphisms, which I think is your first question. However, this can certainly happen, even if <span class="math-container">$f$</span> is not smooth. (By the way, your comment about absence of local monodromy, and purity of limit MHS isn't correct.)
<blockquote>
Prop (Zucker). If ... | https://mathoverflow.net |
2,084,593 | [
"https://math.stackexchange.com/questions/2084593",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/277855/"
] | I'm interested in the following inequality : let $x\in [0,1]$ and $k\geq 1$, $$ (1+x)^k \leq 1+(2^k -1)x.$$
How to tackle this inequality ? Is it "obvious" ?
Thanks a lot.
| Since $x\in [0, 1]$,
\begin{align*}
(1 + x)^k
&= \sum_{n=0}^k \binom{k}{n} x^n
= 1 + \sum_{n=1}^k \binom{k}{n} x^n
\leq 1 + x\sum_{n=1}^k \binom{k}{n}
= 1 + (2^k - 1)x.
\end{align*}
| Induction does the trick. For $k = 0$ both sides equal $1$. No suppose, the equation holds for $k$, we then have
\begin{align*} (1+x)^{k+1} &= (1+x)(1+x)^k \\ &\le (1+x)\bigl(1+(2^k-1)x\bigr)\\
&\le 1 + 2^kx + (2^k -1)x^2\\
&\le 1 + 2^kx + (2^k - 1)x\\
&= 1 + (2^{k+1} - 1)x
\end{al... | https://math.stackexchange.com |
742,995 | [
"https://physics.stackexchange.com/questions/742995",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/354313/"
] | I'm asking this question to better understand how "abrupt" a frame of reference change is when a spaceship accelerates. Apologies if this is not the right forum, and for the unrealistic scenario.
Let's say Alice leaves Earth on a spaceship with an excellent camera (>50,000 fps), and starts going around it ... | I'll consider a similar problem in the setup of the twin's paradox, since it is easier to analyze and allows me to write the expressions explicitly.
Consider the traveling twin departs from Earth at a constant velocity <span class="math-container">$v$</span> (as measured in the Earth frame) and travels away from Earth ... | She could record all of it, in principle, with a slightly faster camera.
The relevant quantity here is the Doppler shift factor, not the time dilation factor.
The relativistic blueshift factor for a stationary emitter at the origin is <span class="math-container">$γ(1+β\cos θ)$</span>, where <span class="math-container... | https://physics.stackexchange.com |
560,279 | [
"https://physics.stackexchange.com/questions/560279",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Will the coin spin forever or will it be de-accelerated by the gravitational force?
| Assume there is no other force (such as friction), and say the coin is near the Earth and experiences the Earth's gravitational field, then with classical mechanics, the gravitational force only acts on the center of mass of the coin, and produce no torque, so the coin, if it is spinning initially, will remain spinning... | If would like to elaborate on the answer give by Leo L.
Tidal forces have to be considered, too. Those will eventually lead to a rotation of the coin locked to its orbit, like moon. In this specific set up, however, I reckon that tidal forces are so small that they can be ignored for all practical purposes. The term „p... | https://physics.stackexchange.com |
559,109 | [
"https://physics.stackexchange.com/questions/559109",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/235334/"
] | <blockquote>
I want to show that by applying the ladder operators one can obtain:
<span class="math-container">$$
\Psi^{'}(x) = \frac{1}{\sqrt{2}x_0}(\sqrt{n}\Psi_{n-1}(x) - \sqrt{n+1}\Psi_{n+1}(x))
$$</span>
with:<br>
<span class="math-container">$\Psi_n(x) = C e^{-\frac{\xi^2}{2}} H_n(\xi)$</span>, <span class="mat... | I am not sure what the question is here. The last and first equations you wrote are virtually the same, maybe you're confused because the notation is not the best. In the last equation you should write <span class="math-container">$\vert \Psi' \rangle$</span> for the right-hand side of the equation is a combination of ... | If you express the ladder operators in the position basis you’ll get what to do. Use the following fact:
<span class="math-container">$$\mathscr{O}|\psi\rangle=\int \mathscr{O}|x\rangle\langle x|\psi\rangle dx$$</span>
Remember that the ladder operators are linear combinations of position and momentum operators.
| https://physics.stackexchange.com |
256,395 | [
"https://security.stackexchange.com/questions/256395",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/269016/"
] | DocuSign requires that your password "must not contain the characters <, > or spaces."
Is this not an odd requirement? Despite being a leader in online document signing, my gut tells me there's something odd under-the-hood.
| Generously? Because that restriction was created by somebody with no understanding of web security. (Less-generous possible explanations are up to the reader.)
The typical danger in such characters is if they're ever output into the response, in which case they could lead to XSS. However, that shouldn't ever be a probl... | Only DocuSign can give you the definitive answer, but one plausible explanation for the angle brackets is that they have generated a false positive in a security tool.
For example, many applications run behind a Web Application Firewall (WAF). These examine the traffic between the user and website for any suspicious ac... | https://security.stackexchange.com |
8,384 | [
"https://mechanics.stackexchange.com/questions/8384",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4280/"
] | As much of the United States struggles through the end of the nasty cold spell, a thought came to mind: Is it generally energy efficient to run the heat in my car?
Let me be a little more specific. I own a Chevrolet HHR, and as far as my understanding goes, heat is provided to the cabin by means of circulating part of... | You are correct that the only extra energy consumed is the electricity used by the blower fan to move the warmed air. In the grand scheme of things the extra fuel required to generate that electricity is miniscule. The coolant is circulated regardless of the heater setting. Moving the selector to cool or warm merely di... | Here's a nice tip: if you turn up the heat in your car, it helps lower the operating temperature of your engine. Sometimes by as much as 10%. Not a problem when you're driving around in icy cold weather, but if your car is overheating, turning on the heat, opening the windows and putting the blower on full could save y... | https://mechanics.stackexchange.com |
70,866 | [
"https://security.stackexchange.com/questions/70866",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/44774/"
] | Using <kbd>Ctrl</kbd> + <kbd>←</kbd> / <kbd>→</kbd>, it's a common behavior across different operating systems to jump from word to word (or from blank to blank) in text input fields.
Now I've discovered that this also applies on password fields in Internet Explorer 8 and 11 (I haven't tried it on other versions yet):... | No that is not a security risk.
Having stored passwords in a browser is a security risk. Letting an attacker access your computer between when you've typed in the password and before it is submitted is a security risk (and even after you've submitted it, you need to worry about theft of valid session cookies). Being... | Yes, is a security risk, but exploiting it is very unlikely.
It can be exploited this way:
<ol>
<li>Someone uses your computer without you around</li>
<li>Have enough time to open IE</li>
<li>Connects to a website with a saved password</li>
<li>Gets the profile of your password and goes away</li>
</ol>
If the intrud... | https://security.stackexchange.com |
509,112 | [
"https://electronics.stackexchange.com/questions/509112",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/249500/"
] | I always assumed that when an unhandled ARM exception occurs (i.e segfault), the microcontroller just stops executing code. This assumption comes from debugging observation: most MCU I worked with stopped in an assembly routine when segfaulting.
As I'm building more safety-critical applications, I want to better unders... | You should handle all exceptions/fault interrupts, so there should not be any "unhandled" ones. Unhandled means that the exception and/or interrupt table has an instance which sends the program counter nowhere/to the wrong address.
Please note that in circuit debuggers might be designed to halt upon encounter... | It is all up to the software developer. Has nothing to do with the hardware. The hardware has known locations for where handler code should go (be it an exception table or vector table depending on which ARM core you are talking about, or in general for any core).
The software developer chooses how to handle each. W... | https://electronics.stackexchange.com |
287,685 | [
"https://electronics.stackexchange.com/questions/287685",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/139418/"
] | I am trying to detect a switch input so that, if the switch is pressed, a number is incremented on the seven segment display. For example if the seven segment display shows <code>0</code>, and the switch is pressed, the SSD will now show <code>1</code>. If pressed again, it will show <code>2</code> and so on.
<ul>
<li... | Two issues I can see. Firstly when setting the display to show a 2 you don't first clear the display so all of the segments that were lit remain lit.
Secondly my guess is that you are seeing switch contact bouncing issues. When a switch or button closes the contacts touch, bounce apart, touch again, bounce apart etc..... | <blockquote>
How can I detect each time the switch is pressed?
</blockquote>
polling frequently or interrupt will do.
<blockquote>
However this part is not working properly.
</blockquote>
because the code is wrong. it can handle just 1 and 2. anything else, the display is unchanged. your code runs so fast you a... | https://electronics.stackexchange.com |
172,901 | [
"https://softwareengineering.stackexchange.com/questions/172901",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/10072/"
] | <pre><code>> shutdown /?
> Usage: shutdown [/i | /l | /s | /r | /g | /a | /p | /h | /e | /o] [/hybrid] [/f]
</code></pre>
The windows <code>cmd.exe</code> command <code>shutdown</code> only documents forward slash <code>/</code> switches, but it accepts dash <code>-</code> switches as well. For instance, both wo... | I would venture that multiple escape characters are supported for switches so that users that are used to a particular escape character can still use the application from the command-line.
| Slashes are Windows's original option syntax and not all windows commands accept the dash-options.
With <code>Dir /?</code> you the list of the options for <code>dir</code>.
But with
<pre><code>Dir -?
</code></pre>
you get a <em>file not found</em>-message (tested with Windows XP) (Same with <code>dir -w</code>...... | https://softwareengineering.stackexchange.com |
220,746 | [
"https://mathoverflow.net/questions/220746",
"https://mathoverflow.net",
"https://mathoverflow.net/users/81421/"
] | Any submersion $f: M → N$ defines a foliation of M whose
leaves are the connected components of the fibres of $f$. Foliations
associated to the submersions are called simple foliations. The foliations
associated to submersions with connected fibres are called <em>strictly
simple</em>. A simple foliation is strictly sim... | $\newcommand{\QQ}{\mathbb{Q}}$
$\newcommand{\ZZ}{\mathbb{Z}}$
Okay, so the solution appears to be this (Thanks to Ari Shnidman, Joseph Silverman, nfdc23, and eric for their comments)
Fix an $N\ge 3$. Let $y\in Y(1)$ be a $\QQ$-point, then the fiber $Y(N)_y$ of $Y(N)$ above $y$ is a $\QQ$-algebra $A$ of degree $d_N :=... | I think there are two issues. One, as Ari noted, your triple $(E^d/K,P(d),Q(d))$ is not really defined over $K$, since the action of Galois is twisted by the character of $K(\sqrt d)/K$. But more importantly, you're not really getting different points on $Y(3)$, because the points of $Y(3)$ classify up to $\overline K$... | https://mathoverflow.net |
426,122 | [
"https://softwareengineering.stackexchange.com/questions/426122",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/391708/"
] | I am currently working on an application that models a complex business process that consists of many steps, each having a 1:n relationship with subsequent steps. The software is written Java using Hibernate and PostgreSQL.
Users request quotes (each containing multiple items). Requests are then matched with suppliers.... | So essentially you've run into performance issues, and decided to go lower down in abstraction levels. This is a sensible approach although sometimes it's not the most long term approach; but it certainly tackles the problem.
I'd like to respond to something about your concerns and beliefs this is bad:
<blockquote>
The... | <strong>What to do? Organise it well.</strong>
In my experience, databases have been terrible due to:
<ul>
<li>Database Procedural Languages (TSQL, plsql)</li>
<li>Internalising (Triggers)</li>
</ul>
Basically, database procedural languages are terrible programming languages to work with. Conditional logic isn't great,... | https://softwareengineering.stackexchange.com |
186,620 | [
"https://physics.stackexchange.com/questions/186620",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/82370/"
] | I'm just curious about why many physical identities build relationship with the same units as angular momentum like the action, Lagrangian$\cdot$time, Hamiltonian$\cdot$time, phase space area etc?
| The Lagrangian and Hamiltonian both have units of <em>energy</em>. You can get a long way in classical mechanics by only thinking about energy. In field theories the relevant unit becomes energy density.
The action must have units of energy times time, as it is the time integral of the Lagrangian.
I don't think the... | Well, OK, this is a resolutely vague question, but there <em>is</em> something special, actually, about angular momentum dimensions.
In quantum mechanics, the fundamental constant, $\hbar$ has dimensions of angular momentum (and is very <em>small</em> in terms of angular momenta, actions, or phase-space areas of our ... | https://physics.stackexchange.com |
42,696 | [
"https://dba.stackexchange.com/questions/42696",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | Sorry is this seems a stupid question, but I have a table of server addresses and a second table with a list of hardware devices which use the addresses, it is possible for multiple devices to use the same server address and a device to use multiple server addresses, so there is a many to many mapping between them.
I a... | You are doing the right way,
In many-to-many relation your must have a third table mapped by the ID of the two other tables. The two Id must be foreign key, and the association of the two is the primary key of your association's table
You can also store in this table the information that are related on the relation.
| You can create another table between these two and put many to this table from both sides. This table will have it's ID and foreign IDs' from another two tables.
| https://dba.stackexchange.com |
350,776 | [
"https://electronics.stackexchange.com/questions/350776",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88310/"
] | I am the recipient of an incomplete set of data for several 120 volt, single phase, AC drive systems driving induction motors under various loads. The measurements were taken at the AC voltage source. I do not have a way to take more or better measurements so am forced to work with data I have. The only data I have ava... | There isn't enough information to figure out exact AC voltage or current. You will have to assume a value for V or I. You could graph I for a range of V=100-120. That will give you a reasonable range of possible values for I taking possible voltage sag into account.
| If I told you that a machine was turning a shaft and producing 1000 watts of mechanical power into a mechanical load, would you be able to tell me the torque or the speed?
The answer is no because, all you can say is that power = \$n T\$ where n is radians per second and T is torque. You don't know anything about the ... | https://electronics.stackexchange.com |
95,976 | [
"https://electronics.stackexchange.com/questions/95976",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/32554/"
] | Here's an image from another question:
<img src="https://i.stack.imgur.com/CuiIZ.png" alt="pull down">
I get what the pull down resistor is there to do, but I don't really understand exactly how it works.
When there is no voltage applied through the base wire, why does any induced current then go through R2, but whe... | I've seen some comments here stating that the pulldown is needed to keep the transistor turned off, instead of floating, or for noise reasons. The base pulldown does in fact help keep the transistor off, but no one has answered why. This is why I chose to answer, rather than extend the comments. User alexan_e is think... | When the left side of R1 gets disconnected then there is no current flow through R1 or R2 and that means that there will be no voltage drop across it.<br>
If there is no voltage drop across R2 the base level becomes 0v and the transistor is held in an off state.
On the other hand when there is a voltage applied to the... | https://electronics.stackexchange.com |
16,636 | [
"https://electronics.stackexchange.com/questions/16636",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3757/"
] | It seems that reading a ceramic capacitor value out of its written values is harder than decoding enigma machine.
I wonder if experienced users here does have a trick to quickly figure out these values. Some examples:
I know that 103M is 0.01µF but how does one figure this out?
Another example 104Z/LK ...this one I c... | The numbers work like a resistor.
The first two numbers are just numbers.
The third number is the number of 0's after. It's in picofarads.
So:
<ul>
<li><strong>103</strong> is 1 0 000 or 10,000pf or 10nF</li>
<li><strong>104</strong> is 1 0 0000 or 100,000pf or 100nF</li>
</ul>
The letter next is the tolerance:
... | The "Z" tolerance is most often omitted. If there is no letter after the value then assume it to be "Z". IE: The actual value could be double the shown value or 80% of the shown value - or anything in between. These are suitable as noise decoupling and/or differential coupling applications. Note that they should NOT be... | https://electronics.stackexchange.com |
257,036 | [
"https://physics.stackexchange.com/questions/257036",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/112190/"
] | The essential property that two waves must own in order to interfere with each other is to be coherent.
<blockquote>
Two waves are <strong>coherent</strong> if their phase difference $\phi_2-\phi_1$ does not change in time
</blockquote>
The phase of a one dimensional wave is $\phi=kx-\omega t+\delta$
Does saying... | This is actually much more subtle, the question is very deep and whole books are written about theory of coherence in optics, quantum mechanics etc. What is important is that you might have an ensemble of sources (say in a lightbulb) which all emit light of the same frequencies but in random moments, making the relativ... | Yes. Omega is the time derivative of phi. Phi1 dot = phi2 dot means omegas are the same.
See my other answer a couple days ago on the subtleties of coherency. There is phase noise on any transmitter and freq as a result has drift and random noise. It depends on the time proof, it could be coherent to 1 part in 10^6 f... | https://physics.stackexchange.com |
111,310 | [
"https://electronics.stackexchange.com/questions/111310",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43195/"
] | My question is simple: Shouldn't a MOSFET keep the gate charged as long as a negative or at least zero voltage isn't applied to discharge, i.e. turn the MOSFET off?
I am trying some experiments with power MOSFETs like IRF540 and IRFP450 applying 12V between gate and source for a moment, disconnect the voltage source (... | If your gate-source capacitance is (say) 1nF and your multimeter input impedance is 1M ohm then you better be quick because the input impedance will discharge the 1nF in about 5*CR = 5 milli seconds.
Even if the input capacitance were 10nF and your multimeter 10Mohm, it'll discharge in about half a second.
| The gate has a fixed capacitance, and your meter has a load resistance. Your meter will discharge that capacitor like an RC circuit, which means that even though the capacitor starts out charged, by the time your meter has a chance to read it will probably just show 0V. An oscilloscope would probably show the discharge... | https://electronics.stackexchange.com |
212,299 | [
"https://mathoverflow.net/questions/212299",
"https://mathoverflow.net",
"https://mathoverflow.net/users/38867/"
] | I was trying to find a proof, or a counterexample to the claim that if $X/\mathbb{C}$ is connected smooth projective, then $X$ is a $K(\pi^{\mathrm{\acute{e}t}},1)$ if and only if $X^\mathrm{an}$ is a $K(\pi,1)$.
For me, $X/\mathbb{C}$ should be a $K(\pi^{\mathrm{\acute{e}t}},1)$ if for all LCC $\mathcal{F}$ the natur... | Let $G$ be a group, $\iota: G\to \hat G$ its pro-finite completion. We call a $G$ a <em>good group</em> (cf. J.-P. Serre <em>Cohomologie galoisienne</em>, 2.6) if for every finite $\hat G$-module $M$, the maps
$$ \iota^* : H^q(\hat G, M) \to H^q(G, M) $$
are isomorphisms for all $q\geq 0$.
Some examples of good group... | Let me expand my comment. I found the reference I had in mind: Ihara and Nakamura, <em>Some examples for Anabelian geometry in high dimensions</em>. The moduli space of $g$ dimensional principally polarized abelian varieties with level $n\ge 3$ structures is a $K(\pi, 1)$ because the universal cover, which is the Siege... | https://mathoverflow.net |
8,065 | [
"https://quant.stackexchange.com/questions/8065",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/5407/"
] | I'll be starting a MFE grad program in Fall, and some of the classes have a lab that use the IB TWS & API. I'd like to play around with it for fun this summer. Unfortunately, I don't have an IB account, and they require a funded account to even use their paper trading services.
Do you know if I could still effecti... | The IB website have a demo version of TWS for download which you can use with their C++, Java etc API. The price feed is stale and orders are not cleared but it shouldn't matter for your purposes. The demo version doesn't require a account/username.
There are also active groups which can be very helpful for details on... | You can fund the account with the minimum account requirement for setup, then withdraw your funds immediately. You will then only need enough in your account to cover monthly data usage fees. (You don't have to maintain an account minimum to keep the account open.)
It's not an ideal solution but you may be able to bor... | https://quant.stackexchange.com |
2,111,747 | [
"https://math.stackexchange.com/questions/2111747",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/409322/"
] | <blockquote>
Suppose you are playing a game where you flip a coin to determine who plays first. You know that when you play first, you win the game 60% of the time and when you play the game second, you lose 52% of the time. <strong>A</strong> Find the probability that you win the game?
</blockquote>
Let $A = \{ \t... | Hint:
$$P(A)=\text{chance you get heads at the coin flip}$$
| You flip a coin to decide who plays first and the probability of getting a favourable outcome in the coin toss is $0.5$. Hope it helps.
| https://math.stackexchange.com |
212,552 | [
"https://physics.stackexchange.com/questions/212552",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95555/"
] | In a double slit experiment done with particles having mass (say electrons), the results are inferred as being caused by probability waves. The wavelength of these waves is dependent upon the velocity (momentum) of the particles( de broglie wavelength = h/p). Now if the observer is in another frame in a way that the ve... | It is valid in all frames, but I don't know why you used the special relativity tag. The Schrödinger equation is a Newtonian equation, so it uses Galilean Relativity.
Now let's get to how it works. To make the mathematics simple people assume a single monochromatic plane wave matter wave with a constant phase at each ... | <blockquote>
In a double slit experiment done with particles having mass (say electrons), the results are inferred as being caused by probability waves. The wavelength of these waves is dependent upon the velocity (momentum) of the particles( de broglie wavelength = h/p).
</blockquote>
The de Broglie wave of the el... | https://physics.stackexchange.com |
81,041 | [
"https://mathoverflow.net/questions/81041",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17812/"
] | Smooth (closed, connected, orientable) 3-dimensional manifolds are very special, in that for any 3-manifold $M$ there are two handlebodies, $V$ and $W$, of genus $g$ and an orientation reversing homeomorphism $f$ of their boundaries so that $M=V\ \cup_f W$. Such a decomposition is called a Heegaard splitting.
I want ... | Every odd-dimensional manifold has an open book decomposition (T. Lawson, Topology 17, 189-192 (1978)) and is thus a twisted double. In the even dimensions there is an asymmetric
Witt group obstruction to the existence of an open book decomposition (F. Quinn, Topology 18,
55-73 (1979)), which is also the obstruction to... | Any closed connected n-manifold admits a Morse function f with one critical point of index zero and one critical point of index n (see <i>e.g.</i> Matsumoto's "Introduction to Morse Theory", Theorem 3.35). If n is odd, you can slide all handles of index $< \frac{n}{2}$ to below $f^{-1}(\frac{1}{2})$ and all handles ... | https://mathoverflow.net |
642,970 | [
"https://electronics.stackexchange.com/questions/642970",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/277364/"
] | I'm choosing between two USB DACs for a pair 32 Ω headphones and need to choose the one with the greater output, i.e. with the greater loudness. One DAC has a maximum power rating of 18 mW at 16 Ω and the other has a rating of 45 mW at 32 Ω.
I guess it is the second, but which is louder?
How many watts would the first ... | <blockquote>
<em>How many watts would the first produce if run into 32ohms?</em>
</blockquote>
There are options worth considering: -
<ul>
<li>The device that produces 18 mW into 16 Ω might provide twice the drive voltage into 32 Ω. This means that twice the power is delivered to the 32 Ω speaker i.e. 36 mW</li>
<li>Th... | Typical USB headphone amplifier will have a fixed output voltage delivered through a few ohms series resistance. Assuming the series resistance is negligible compared to 16 ohms (typically the case for quality devices):
18 mW into 16 Ω is 0.53 Vpp.
45 mW into 32 Ω is 1.2 Vpp.
So the second device has a larger output.
| https://electronics.stackexchange.com |
1,230,040 | [
"https://math.stackexchange.com/questions/1230040",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/230530/"
] | Let $G$ be a group which satisfies $Z(G)=\{1\}$ and ${\rm Inn(G)} \space \mathbb{char} \space {\rm Aut(G)}$; then every automorphism of $A={\rm Aut(G)}$ is an inner automorphism. ($H \space \mathbb{char} \space G$ means that $H$ is a characteristic subgroup of $G$. Note that we can assume $G \subseteq A$, since $Z(G)=\... | Let $I = {\rm Inn}\, G$ and $C = C_{{\rm Aut}(A)}(I)$. Then $C \unlhd {\rm Aut}(A)$ and $A \unlhd {\rm Aut}(A)$. Since $A$ is by definition the group of automorphisms of $G \cong I$, no nontrivial element of $A$ can centralize $I$; i.e. $C \cap A = 1$. Hence $[C,A] \le C \cap A = 1$; i.e. $C \le C(A)$.
| Let $\sigma\in C(Inn(G))$,
Then we have $\sigma i_g\sigma^{-1}=i_g$ where $i_g:G\to G$ by $i_g(x)=gxg^{-1}$ for $x\in G$.
We have,
$$i_g(x)=\sigma i_g \sigma^{-1}(x)$$
$$i_g(x)=\sigma(g\sigma^{-1}(x)g^{-1})$$
$$i_g(x)=\sigma(g)\sigma(\sigma^{-1}(x))\sigma(g^{-1})$$
$$i_g(x)=\sigma(g)x\sigma (g)^{-1}=i_{\sigma(g)}$$
... | https://math.stackexchange.com |
71,368 | [
"https://electronics.stackexchange.com/questions/71368",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24611/"
] | <ol>
<li><img src="https://i.stack.imgur.com/VNFAx.png" alt="circuit 1"></li>
<li><img src="https://i.stack.imgur.com/vzCwB.png" alt="circuit 2"></li>
</ol>
I know that \$τ = \frac{L}{R}\$, but what is \$R\$ in this formula? It seems to be the total resistance, but how to find it in the schematics?
| The arrows on the switches seem to indicate they are opening. I assume (but your problem statement should be more clear about this) that this means the switches are closed for t < 0 and open for t > 0, and you want to solve for the indicated voltages as a function of time for t > 0.
For the 1st one, once you open t... | As far as i think
<ul>
<li>In the First case:</li>
</ul>
Solve Short the inductor and solve both resistances in parallel
<ul>
<li>In the second case:</li>
</ul>
Short the inductor again, Solve two 1k resistances in series and then solve again in series this equivalent resistance with 4k.
you will get your overall... | https://electronics.stackexchange.com |
314,948 | [
"https://stats.stackexchange.com/questions/314948",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/180168/"
] | I'm facing this new concept: the quasi likelihood. I'm looking for some clear explanation of what it is. I have a very basic knowledge about this, so I need to go step by step very slowly. I discovered this concept in dealing with overdispersed count data.
Quasipoisson models will estimate relative rates with no distr... | What happens is that the likelihood equations depend on the distribution of Y only through the mean ($\mu$) and the variance ($V(\mu)$). Other moments of the distribution do not affect the coefficients $\hat \beta$, neither the asymptotic covariance.
The quasi-likelihood approach is based on this fact, requiring that... | In general, quasi-likelihood has score function $\frac{y-\mu}{\phi V(\mu)}$. Under mild conditions, the estimator has the same asymptotic distribution as the MLE. In your GLM notation, the score function is $D^{T}V^{-1}\frac{y-\mu}{\phi }$, where $D= \partial \mu/ \partial \beta$ is the $n \times p$ derivative matrix.... | https://stats.stackexchange.com |
487,783 | [
"https://physics.stackexchange.com/questions/487783",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/212474/"
] | Consider the simple dynamical equation
<span class="math-container">$$ \dot{x}(t) = u H(t-\tau),$$</span>
where the timescale <span class="math-container">$\tau$</span> is an exponentially distributed random variable <span class="math-container">$\tau \sim \omega \exp\{\omega \tau\}$</span> and <span class="math-cont... | Almost there. The two <span class="math-container">$\text{Prob}$</span>'s are correlated:
<span class="math-container">$$u^2 \int_0^t dt_1 \int_0^t dt_2 \langle H(t_1-\tau) H(t_2-\tau) \rangle = u^2 \int_0^t dt_1 \int_0^t dt_2 \text{Prob}(\tau>\max(t_1, t_2)) = \dots = \frac{2u^2}{\omega^2}\left(1-(1+\omega t)\exp\{... | I revisted this problem to solve for the probability distribution of position. I'm posting this as an answer in case anyone is ever interested.
The equation of motion for the particle's displacement is
<span class="math-container">$$ \dot{x} = u \Theta(\tau-t).$$</span>
For a particular travel time, this integrates for... | https://physics.stackexchange.com |
238,558 | [
"https://softwareengineering.stackexchange.com/questions/238558",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/79484/"
] | So, pretty straight forward question. Somebody told me that all shopping carts should be secure. I can see in some instances where this would be beneficial... but all instances?
I realize that typically carts are stored on the server via a session, but in the end the details of the cart have to be sent to the user so ... | The simple answer is yes. You already need encryption when communicating passwords or payment details, so it's easy to extend the encryption to the whole site. This might even simplify some things. Yes, serving encrypted pages is more computationally intensive than serving plain files, but we've come to generally expec... | It depends on which stage you're talking about.
The paying for the contents of a shopping cart? This <strong><em>must</em></strong> be secure; you've probably got financial data involved (or something very similar). Failure to secure this will get you into trouble in virtually all jurisdictions.
The configuring of wh... | https://softwareengineering.stackexchange.com |
522,394 | [
"https://electronics.stackexchange.com/questions/522394",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/142915/"
] | Loudspeakers, for example, should be impedance matched to deliver the highest <em>power</em> from the source to the speakers. But why do we care about <em>power</em> so much? A speaker is at its simplest, a coil around a magnet connected to a flexible fabric. As the coil current changes, the coil vibrates around the ma... | Different speakers run at different voltages and comparing current means you cannot directly compare speakers based on current unless you know they run at the same voltage.
<blockquote>
But isn't the amplitude of the coil vibration proportional to the current in the coil
</blockquote>
Sure, but number of turns also mat... | Actually speaker outputs are not impedance matched, speaker outputs have extremely low output impedance, to drive the element with voltage signal for best results, so that the voltage signal stays virtually undistorted regardless of load impedance and current.
Just as an example how to get most power into a speaker: if... | https://electronics.stackexchange.com |
146,972 | [
"https://softwareengineering.stackexchange.com/questions/146972",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | Here is the question I'm having trouble with:
<blockquote>
Give the resource graph and determine whether a deadlock state results. Assume that when a thread requests an available or unallocated resource, the OS immediately allocates that resource to the thread.
</blockquote>
<ul>
<li>There are three threads: T1, ... | I'll summarize our conversation in the comments.
<blockquote>
Have I drawn the graph appropriately? Based off of this graph, I assume there is no deadlock because there are no cycles.
</blockquote>
You are correct, your question does not show any deadlock conditions.
For me deadlock is not about "cycles" but about... | You have two processes accessing the same resource but a deadlock will not occur.
T2 is requesting R3. Since T1 is already
using R3 T2 can wait or try again at a later time.
T3 requests R1 but can wait or try again later once T1 has finished. A deadlock would ONLY take place when t3 requests R1 and T1 has not releas... | https://softwareengineering.stackexchange.com |
393,416 | [
"https://mathoverflow.net/questions/393416",
"https://mathoverflow.net",
"https://mathoverflow.net/users/157356/"
] | Let <span class="math-container">$J_\nu$</span> be a Bessel function of the first kind and let <span class="math-container">$\{\lambda_{n, \nu}\}_{n\ge 1}$</span> be a sequence of its zeroes. I claim that
<span class="math-container">$$
\inf_{n\ge 1}\bigg|\sqrt{\lambda_{n,\nu}} J_{\nu+1}(\lambda_{n,\nu})\bigg|>0.
$$... | You have, using the asymptotics for <span class="math-container">$\lambda_{n,\nu}$</span>,
<span class="math-container">\begin{align*}
& \cos\left(\lambda_{n,\nu} - \frac{2\nu+3}{4}\pi \right) \\
&= \cos\left(\lambda_{n,\nu} - \frac{2\nu-1}{4}\pi+\pi \right) \\
&= \cos\left(\lambda_{n,\nu} - \frac{2\nu-1}{4... | To see that the given infimum is positive one needs to combine the asymptotics
<span class="math-container">$$
J_{\nu}(x) = \sqrt{\frac{2}{\pi x}} \bigg( \cos\Big( x - \frac{2\nu+1}4 \pi \Big) + \mathcal{O}\big( x^{-1} \big) \bigg),
\qquad x \to \infty.
$$</span>
with the asymptotic formula for zeros, which I stated in... | https://mathoverflow.net |
2,239,379 | [
"https://math.stackexchange.com/questions/2239379",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/272910/"
] | <blockquote>
Prove for any $0<\lambda<1$, there exists $0<\alpha<1$ and $0<x<1$ such that $x^{\alpha}-x\geq 1-\lambda$.
</blockquote>
My solution: The maximum of the function $x^{\alpha}-x- 1$, over $x>0$ tends to zero as $\alpha \to 0$. Thus, there exist such $\alpha$.
Even if my solution is c... | You can always look at the classical $f_n(x) = nx^n$ on $(0,1).$
| Let the underlying space be $(0,1)$ with Lebesgue measure. Let $f_n=n\cdot 1_{(0,1/n)}$. Then $f_n\to 0$ pointwise, but $\int_0^1 f_n=1$.
| https://math.stackexchange.com |
24,372 | [
"https://robotics.stackexchange.com/questions/24372",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/33370/"
] | I have a general question about the benefit of Hand-Eye calibration.
I know that the Hand-Eye calibration can be done with many softawres by solving the AX=XB or AX=ZB equation. But my question is, how can I use this calibration information afterwards.
Say, I have an eye-to-hand calibration configuration where a 2D cam... | You answered yourself.
Your underlying model of point moving through space usually assumes the center of gravity to match the camera frame.
If your inertial sensor have a translational offset from the camera attached to a rotating rigid body, you would measure extra tangential and radiant acceleration components that ... | It's important to know the offset between the camera and the IMU because the IMU's information is only useful when it can be correleated with the camera data.
In a lot of the trivial cases this difference could be negligible. However depending on your requirements for accuracy you will need to compensate.
Lets use a th... | https://robotics.stackexchange.com |
135,368 | [
"https://electronics.stackexchange.com/questions/135368",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8464/"
] | I am trying to construct a circuit to control an LED in a bike light kind of circuit. This circuit must be designed so that a button press can change the current setting of the light.
So for instance first click turns on the light on slow blinking, one more click goes to fast blinking, a third click to continuous ligh... | Here's a circuit which should accomplish what you want. It uses a dual 555, namely a 556 with two different rates. A CD4022 is used to count the button pushes. A pair of NAND gates debounces of the push button input, so the counter doesn't advance erratically.
The first two outputs select one of the two rates using... | The easiest way to do this in small quantity is to use a microcontroller, such as a Microchip PIC10F or 12F series. There will be only a few parts in the circuit and a page or two of code. The micro should be under a dollar in single quantities.
The best way to do it in production quantity is a COB CMOS die designed ... | https://electronics.stackexchange.com |
282,974 | [
"https://physics.stackexchange.com/questions/282974",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/117616/"
] | Suppose we have the usual commutators ($J$=Angular Momentum, $P$=Momentum, $K$=Boosts, $H$=Hamiltonian.)
$$
[J_i,J_j]=i\epsilon_{ijk}J_k\quad[J_i,K_j]=i\epsilon_{ijk}K_k\quad[J_i,P_j]=i\epsilon_{ijk}P_k.
$$
and that
$$
[K_i,H]=iP_i.
$$
A professor has said that the first three relations state that $\vec J,\vec K,\vec ... | Under a linear transformation $T$ of the vector space, operators $O$ on it transform as $O\mapsto TOT^\dagger$. Since by definition the $J_i$ are the infinitesimal generators of rotation as $R(\phi) = \mathrm{e}^{\mathrm{i}J_i\phi}$, the finite rotation $\mathrm{e}^{\mathrm{i}J_i \phi}O\mathrm{e}^{-\mathrm{i}J_i\phi}$ ... | For the sake of being explicit, I will demonstrate what @ACuriousMind and @Valter Moretti said to do. I won't include all the $i$'s though.
Supposing we induce a rotation of our coordinate system by an angle $\phi$ about some axis. Seeing as the operators $L_i$ are the generators of such rotations, any operator existi... | https://physics.stackexchange.com |
79,243 | [
"https://electronics.stackexchange.com/questions/79243",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22582/"
] | <strong>EDIT 3 The correct solution is shown below, in TurboJ's answer in fact, this exact issue was mentioned in the LPC4300 errata ES_LPC43x0:</strong>
<img src="https://i.stack.imgur.com/kE1GB.png" alt="enter image description here">
EDIT: Nope, sorry false alarm. The new board started doing the same thing:(
EDIT... | One possible source of latch-up is <code>USB_VBUS</code>. The datasheet of the LPC43xx allow VBUS to be 5 V only when VCC is present - but in your case this takes a small amount of time until the regulators are fired up. Consider adding a resistor in this path.
Another issue is the ON-Switch of the FPGAs 3V3 LDO. It w... | NXP 4330 in accordance with IEC 60134 absolute max current should not exceed 100mA. The device is rated at 80mA at 200MHz at 3.3V. It sounds like it is dissipating much more than this, so I would suspect
if have a slow startup ramp on the supply, internal instability may cause max frequency oscillations so a power o... | https://electronics.stackexchange.com |
344,505 | [
"https://math.stackexchange.com/questions/344505",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/66342/"
] | Show that
$$\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$$
| Hint::
$$\frac{\sin x}{\cos 3x}=$$
$$= \frac{1}{2} \cdot \frac{2 \cdot \sin x \cdot \cos x}{\cos x \cdot \cos 3x}$$
$$= \frac{1}{2} \cdot \frac{\sin 2x}{\cos x \cdot \cos 3x}$$
$$= \frac{1}{2} \cdot \frac{ \sin(3x - x) }{ \cos x \cdot \cos3x }$$
$$= \frac{1}{2} \cdot \frac{ \sin 3x \cdot \cos x - \cos 3x \cdot \sin x}... | A more general result is in fact true.
$$\sum_{k=0}^{n} \dfrac{\sin\left(3^k x\right)}{\cos\left(3^{k+1} x\right)} = \dfrac{\tan\left(3^{n+1} x\right) - \tan(x)}2 \,\,\,\, (\spadesuit)$$
Take $n=2$ in $(\spadesuit)$, to get what you want.
<hr>
To prove $(\spadesuit)$, first note that
$$\dfrac{\sin \left(3^k \cdot x \... | https://math.stackexchange.com |
6,056 | [
"https://mechanics.stackexchange.com/questions/6056",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2274/"
] | I replaced the oil on my mom's Prius today, which is 3200 miles or so since I replaced it last. The car only takes 3 quarts of oil, but only drained a little over 2 quarts.
My jeep, on the other hand, takes 4.5quarts of oil, and drains 4.5quarts when I replace it.
I use the proper oil in the prius so I don't see why... | 1 quart every 3000 miles seems to be well within the spec for just about every Prius, so it seems almost certainly acceptable for yours ( though we still haven't heard what year yours is ).
| Try the owner's manual. If that doesn't say, contact your Toyota service department and have them check the maintenance manuals. Different cars have different acceptable burn off/losses. For example, my Toyota MR2 is within specification as long as it doesn't burn more than 1 quart every 1000 miles.
| https://mechanics.stackexchange.com |
118,479 | [
"https://mathoverflow.net/questions/118479",
"https://mathoverflow.net",
"https://mathoverflow.net/users/477/"
] | I am trying to understand what the obstructions are to orienting moduli spaces of pseudoholomorphic curves with totally real boundary condition.
I believe that Fukaya-Oh-Ohta-Ono have shown that if a Lagrangian is relatively spin, the moduli spaces of disks with boundary in it can be oriented.
My question has 3 rel... | 1) The problem of orienting moduli spaces of pseudo-holomorphic discs with totally real boundary conditions is really a problem in index theory. It was solved Vin de Silva in his (unpublished) D. Phil. thesis, using Atiyah's Real K-theory, and independently by FOOO. There's an excellent account in Seidel's book (sectio... | (0) I do not know what is contained in a thesis which is not published and is not even available online (12 years after the defense).
(1) By Proposition 8.1.4 in the 1000-page FOOO book, a relatively spin structure on a (necessarily orientable) Lagrangian submanifold $L$ of a symplectic manifold $M$ determines an orie... | https://mathoverflow.net |
234,807 | [
"https://electronics.stackexchange.com/questions/234807",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/79813/"
] | I am designing some PCBs, which I intend to prototype, and then get small volumes produced for personal use at a cheap PCB house such as Itead, DirtyPCBs, or Seeedstudio Fusion PCB. These board houses all charge about $12 for 10 copies of a PCB up to 5x5cm. My design will stick into a USB port like a little dongle, and... | The term is "panelizing", and PCB houses can certainly routinely accommodate this. In fact, when you get multiple boards of small size, this has probably happened behind the scenes and the boards have already been depanelized for you.
As you can tell from that example, some houses prefer that you provide the Gerbers f... | Usually these board houses are really charging you by the FR4 substrate sheet. What I usually do is wait to have a few designs ready to go, and then "panelize" them. If you order a whole sheet it's usually cheaper, because you save them the trouble of having to panelize your design with others. You can do it yourself, ... | https://electronics.stackexchange.com |
145,680 | [
"https://physics.stackexchange.com/questions/145680",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60080/"
] | An idea struck me as I was walking to class today. According to Wikipedia, entropy is defined as the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder. I believe this is because the more ways you have of arranging an object, the more chance there is of... | The aging of the body has nothing to do with entropy. As has been pointed out, the body is not a closed system. It takes in energy all during its life and the overall thermodynamic state of 2 bodies of different ages but identical everything else (such as fat content, state of hydration, and so on) are equivalent. Agin... | Interestingly, I have found an answer to your question in Geoffery West's book, <em>Scale</em>, that seems to contradict Abraxas' statement that the "aging of the body has nothing to do with entropy.
In his discussion on aging and death, G.W. states the following:
<blockquote>
All the evidence points to the origins... | https://physics.stackexchange.com |
129,579 | [
"https://security.stackexchange.com/questions/129579",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/117011/"
] | If a hacker got a hold of your wordpress wp-config.php file and a dump of your database containing your hashed password? How hard would it take for them to easily cracked your password even if you are using a hard to guess password like "Th1siSmyP@$$"
| That depends on their processing power. Cracking a password locally is much more efficient than remotely and doesn't require to avoid any detection.
Note that there is no point in asking such a question as your system is already compromised and the hacker already has access to your hosting space if they get access to... | The above answer is very good, but just to add to it:
Once that database is run against offline dictionary attacks with special rule files, I would not be surprised that over 40-50% of the passwords in it would be cracked. Those rule files is what would perform substitutions in order to go from a word like "this" to ... | https://security.stackexchange.com |
21,532 | [
"https://ai.stackexchange.com/questions/21532",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/35585/"
] | I know how pooling works, and what effect it has on the input dimensions - but I'm not sure why it's done in the first place. It'd be great if someone could provide some intuition behind it - while explaining the following excerpt from a blog:
<blockquote>
A problem with the output feature maps is that they are sensiti... | Pooling has multiple benefits
<ul>
<li>Robust feature detection.</li>
<li>Makes it computationally feasible to have deeper CNNs</li>
</ul>
<h2>Robust Feature Detection</h2>
Think of max-pooling (most popular) for understanding this.
Consider a 2*2 box/unit in one layer which is mapped to only 1 box/unit in the next... | In addition in general it somewhat aides in detection as only the strongest feature feature filter is activated so in a sense it removes additional information.
But it obviously has draw backs resulting in combinations of features being detected which aren't actual.objects.
| https://ai.stackexchange.com |
17,976 | [
"https://mechanics.stackexchange.com/questions/17976",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4935/"
] | <strong>About my bike</strong>
<ul>
<li>Model: Honda CBR 250R </li>
<li>Total Run: 35000kms </li>
<li>Total Time: 2 years 3 months </li>
<li>Clutch Plate changed at 30k kms after an accident </li>
<li>Engine oil, engine oil filter and air filter changed in last service</li>
</ul>
<strong>Problem Statement</strong>
A... | Issue got resolved in next service. The problem was the with the rotor. Front wheel rotor was touching the caliber causing too much resistance. On close observation it seemed that rotor its shape after a bike fall lately. Replaced it with a flat new rotor and was able to drive 420 kms in full tank.
| <h1>Background</h1>
This is a common issue with shim and bucket valve trains. As the valves are getting worn into the head a small groove is beat into the valve face after opening and closing so many times. As the valve pushes up into the head it takes up clearance between the cam lobe and the bucket which the cam lo... | https://mechanics.stackexchange.com |
51,616 | [
"https://dsp.stackexchange.com/questions/51616",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/34906/"
] | I have some problems rearranging exp terms to receive a cos or sin. I guess the solution is silly but I‘m not able to spot my mistake.
I know the solution (since i looked it up with wolfram alpha) has to be a $cos(\pi /4n)$ and therefore $\frac{e^{-j\pi/4n}+ e^{j\pi/4n}}{2}$.
My goal is to rearrange the two terms $e... | If I understand correctly, you're trying to show the following equality:
$$e^{jn\pi/4}+e^{j7n\pi/4}=2\cos(n\pi/4)\tag{1}$$
Note that $e^{\pm jn2\pi}=1$, $n\in\mathbb{Z}$, so you have
$$e^{j7n\pi/4}=e^{j7n\pi/4}e^{-jn2\pi}=e^{-jn\pi/4}\tag{2}$$
and plugging this into Eq. $(1)$ gives you the desired result.
EDIT (an... | <strong>Hint:</strong>
<ol>
<li>So you have proved that
<span class="math-container">$$\exp\left({j\frac \pi4 n}\right)+ \exp\left({j\frac{7\pi} 4 n}\right) =\exp\left({-j\frac \pi4 n}\right)+ \exp\left({j\frac \pi4 n}\right)$$</span>
</li>
<li>The second derivation does results in the same answer as well. It is not pr... | https://dsp.stackexchange.com |
4,318,839 | [
"https://math.stackexchange.com/questions/4318839",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/668360/"
] | I would like to see a rigorous proof that:
<span class="math-container">$$\lim_{R\rightarrow \infty}\int_1^R \left(\frac{1}{\sqrt{x^2-1}}-\frac{1}{x}\right)\frac{dx}{\sqrt{1-x^2/R^2}}=\int_1^\infty \left(\frac{1}{\sqrt{x^2-1}}-\frac{1}{x}\right)dx.$$</span>
Note that the second integral does converge (to <span class="m... | I don't think any of the standard theorems directly apply here. We can, however, still make use of the dominated convergence theorem after splitting the integral at an appropriate point (similar to your own answer).
Define <span class="math-container">$f,g,h \colon (2,\infty) \times \mathbb{R} \to \mathbb{R}$</span> by... | I finally was able to prove it, so I am posting the answer to my question. It was a case when doing it from scratch (the definition of limit) was easier (for me) than trying to find the right limit theorem that would apply. It is still possible it would follow right away from some limit theorem I don't know...
In my pr... | https://math.stackexchange.com |
817,210 | [
"https://math.stackexchange.com/questions/817210",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/131139/"
] | Why if $(\mathbb{Z}/N\mathbb{Z})^{\times}$ is cyclic, the group of his elements of order dividing $2$ is of order 2?
| You have an error in the second sentence: $n$ is not “the eigenvalue of $H$”, $n$ is “the largest eigenvalue of $H$.” The other eigenvalues of $H$ on $\operatorname{Sym}^n(V)$ are $n-2, n-3, \ldots, -n$ as you said. The eigenvalues of a direct sum are the union (with multiplicity) of the eigenvalues of the summands. I ... | A mechanical way is to use characters: the character of a representation $W$ of $\mathfrak{sl}_2$ is $\chi_W(x)=\sum_i m_i\,x^{n_i}$, where $n_i$ runs over all the eigenvalues of $H$ in $W$ and $m_i$'s are their multiplicities. Characters satisfy $\chi_{W_1\oplus W_2}=\chi_{W_1}+\chi_{W_2}$ and $\chi_{W_1\otimes W_2}=\... | https://math.stackexchange.com |
91,499 | [
"https://electronics.stackexchange.com/questions/91499",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/33102/"
] | I read in a book three opamp instrumentation amplifiers are better and they are more common, but why is it better than the single opamp instrumentation amplifier? It must be more expensive as they have two extra opamps.
| First, many InAmps are integrated into one IC, also the three-opamp versions. Then the cost of the extra opamps isn't that high. Consider the extra cost of less than a mm^2 real estate against the total cost to create an IC.
Next, I've never seen a single-opamp inamp. There are two-opamp and three-opamp versions, and ... | There are a number of different issues in play here. Assuming you're talking about a three-op-amp instrumentation amplifier and a one-op-amp differential amplifier.
First, lets talk about hand-made instrumentation-amps and differential amplifiers vs. purpose-built integrated circuits. Hand-made amplifiers of both cl... | https://electronics.stackexchange.com |
73,095 | [
"https://security.stackexchange.com/questions/73095",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/60975/"
] | I want to cover the possible cases of attacking. My application already has captcha and two-factor authentication, but how can I avoid a tiny attack without annoying my users? The possible cases that I'm thinking to cover are:
<ol>
<li>Show captcha after 3 failed login attempts based on Session, but the problem is ... | A relatively user-friendly way of mitigating brute-force attacks is delaying the minimum time between attempts. The first time your user enters wrong credentials, you let him wait 1 second before he can try again. The second time, you let him wait 2 seconds. The 3rd time, you make him wait 4 seconds. 4th time, 8 second... | A good compromise between user experience and security would be to have IP-based captchas that trigger after a few failed logins from a particular IP, regardless of username.
<ul>
<li>This approach isn't vulnerable to DoS attacks against a single user by bruteforcing his account until the backoff time reaches several ... | https://security.stackexchange.com |
407,062 | [
"https://mathoverflow.net/questions/407062",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36886/"
] | Let <span class="math-container">$X$</span> be a Polish space and let <span class="math-container">$(\mu_i)_{i=1}^{\infty}$</span> be a sequence of probability measures in the Wasserstein space <span class="math-container">$\mathcal{P}(X)$</span> on <span class="math-container">$X$</span>. Let <span class="math-contai... | It is true and clear if the metric space <span class="math-container">$X$</span> has a finite diameter, but false in general: Take <span class="math-container">$\beta_i=2^{-i}$</span> and <span class="math-container">$\mu_i$</span> the point mass at <span class="math-container">$3^i$</span>.
Details: In the case <span ... | Yet another answer, but just a comment first: which Wasserstein distance are you talking about? There is a whole family <span class="math-container">$\mathcal W_p$</span> of p-th Wasserstein distances, built upon the family of costs <span class="math-container">$c_p(x,y)=d(x,y)^p$</span> for any <span class="math-conta... | https://mathoverflow.net |
57,549 | [
"https://dba.stackexchange.com/questions/57549",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1259/"
] | Load on my 11g RAC looks like this:
<img src="https://i.stack.imgur.com/EFr9K.png" alt="enter image description here">
and I don't understand how to get insight into what this "scheduler" wait class is. It seems like "scheduler" that it refers to is the process that runs scheduled maintenance jobs? But can I see wh... | "no space left on the device" could also mean that the partition is out of inodes. Use <code>df -i</code> to check inode usage.
Edit: Each file, directory, and symbolic link requires one inode. So the idea is to remove some files from the / partition. It doesn't matter how large the files are. You can of course just p... | Selections on columns without indexes use up a large amount of temporary disk space. So you have the choice:
1) Check your temporary filesystem for sufficient space.
2) Check your SQL statement that it uses only columns that are in indexes.
3) Add the needed indexes.
| https://dba.stackexchange.com |
688,332 | [
"https://physics.stackexchange.com/questions/688332",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/323323/"
] | If we follow the formula <span class="math-container">$E=F/q$</span> it says that when the force is bigger the electric field is bigger as well but if the charge on which the force is being exerted to bigger the electric field is somehow smaller? How does this make sense?
| This is a great example of how causal understanding of physics is not manifestly obvious if you naively look at the mathematical expression.
What you say <em>is</em> true but is correctly formulated in the following way: for a <strong>given</strong> force <span class="math-container">$F$</span> on a charge <span class=... | I'd say that you are looking at it backwards; it is better to imagine that eletric fields generate forces on charges. For a given eletric field, the bigger the charge, the greater the force; to produce an increase on the force exerted on a charge, the eletric field needs to be increased as well; so, for a given force, ... | https://physics.stackexchange.com |
21,544 | [
"https://electronics.stackexchange.com/questions/21544",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6211/"
] | I have designed a program to count the frequency and time period of the pulse generated by a 555 timer IC using PC Parallel port. I’ve connected a base of BC547 (NPN) transistor to the output pin (no. 3) with a resistor of multiple values to the IC and its emitter to the common ground. Parallel port Input pin is connec... | Use 10kΩ for R3.
I didn't look up a BC547, but if that's a typical small signal transistor as it should be, figure a gain of at least 50. 6V supply minus 700mV B-E drip leave 5.3V accross the resistor. 5.3V / 10kΩ = 530µA. Times the gain of 50, and that can support over 25mA of collector current. ... | Your problem is probably that you also need a so-called <em>pull-up</em> resistor between the collector of the transistor and the positive voltage (+5V).
As for the basis resistor, there are two constraints:
<ol>
<li>The resistor value should be small enough to switch the transistor completely on when the output of t... | https://electronics.stackexchange.com |
264,924 | [
"https://physics.stackexchange.com/questions/264924",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70392/"
] | In quantum mechanics if two quantities $A$ and $B$ are said to be <em>coupled</em> what does this actually mean?
I would guess that it means we have a term like $A\cdot B$ in the Hamiltonian but this is only a guess.
| Let me preface by saying that "coupling" is a favorite physicist word that is perhaps best described linguistically than rigorously; it's deployed in a few different situations.
In general, we say that a coupling exists in quantum mechanics if the evolution of one part of the system depends on another quantity, which ... | I think Entanglement may answer your question. Two systems are said to be entangled(coupled) if we cannot assign an independent and separate wavefunctions for each system, instead we define a composite system which is simply the tensor product of the original constitutes. To be precise, in the general case the wavefunc... | https://physics.stackexchange.com |
92,463 | [
"https://physics.stackexchange.com/questions/92463",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/36803/"
] | What is the name of this principle?
<blockquote>
If the speed of the centre of mass $\vec{v}_{CM}$ of a solid is constant ($cte$), then the sum of the exterior forces that exerts into this solid $\vec{F}_{ext}$ is zero, and the opposite is true, namely that:
$$\vec{v}_{CM}=cte\Leftrightarrow\sum\vec{F}_{ext}=\... | It is very similar to the first Newton's law: he says that in a body at rest or moving with a linear uniform motion there is no force acting on it or the vector sum of all forces acting on it is zero.
However, this law ignores Galilean relativity, because if one object and an observer are falling at the same accelerat... | As far as I know, it has no name but it is the simplest corollary of the <strong>first fundamental equation of dynamics of systems</strong>, reading
$$\sum \vec{F}_{ext} = M_{tot} \frac{d\vec{V}_{CM}}{dt}\:.$$
The formula says that the centre of mass of the system evolves as a single material point with all the mass o... | https://physics.stackexchange.com |
551,843 | [
"https://physics.stackexchange.com/questions/551843",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/261235/"
] | Is the gravitational acceleration we consider only the attraction due to the Earth's gravity or is it that of gravity plus the attraction due to Earth spinning?
We know that earth produces an acceleration towards the centre on any body near it
due to gravitational attraction.
We denote this acceleration as <span cl... | <span class="math-container">$g$</span> is measured by observing the freefall acceleration of objects in a vacuum. Since this is taking place in the non-inertial, rotating reference frame of the Earth's surface, it does include the centrifugal effects on acceleration. However, it is also worth noting that this effect i... | g is caused only by earth gravitational pull. While centripetal acceleration is an acceleration caused by centripetal force. Centripetal force is a net force of a body that undergoes circular motion.
| https://physics.stackexchange.com |
703,316 | [
"https://physics.stackexchange.com/questions/703316",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/314853/"
] | Say I push a box with a constant force <span class="math-container">$F$</span> causing a displacement <span class="math-container">$d$</span>. So magnitude of work done by me on the box is <span class="math-container">$W=Fd$</span>, and the kinetic energy gained by the box is <span class="math-container">$W$</span>. Bu... | Only forces on a body determine the work done on the body. In your case, work done on the box depends on the force applied to the box by you. For your case, the reaction force is not on the box, it is on you and has nothing to do with the work done on the box. The work done on you depends on all the forces acting on ... | You do work W on the box and the box does work -W on you. That much is true. It is also true that the total work done on the system consisting of you plus box is <span class="math-container">$W_{total}=W+(-W)=0$</span>.
In some respects work and energy resemble money. Say you borrow \$10 from me. If your reasoning h... | https://physics.stackexchange.com |
155,257 | [
"https://physics.stackexchange.com/questions/155257",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6068/"
] | Consider a system with $n$ identical particles. Let the wavefunction of the system be $\psi(r_1,\ldots, r_2)$. Let $P_{a,b}$ represent the exchange operator which exchanges particle $a$ with particle $b$. Similarly, $P_{c,d}$ represent the exchange operator which exchanges particle $c$ with particle $d$. Now, suppose ... | It is not possible to have a state with four indistinguishable particles such that $P_{12} \psi = -\psi$ and $P_{34} \psi =\psi$, for an algebraic reason. Namely, the exchange operators have to form a representation of the permutation group $S_4$. It is rather well known that there are exactly two representations of $S... | A wavefunction is a normalised vector (or a ray) in the Hilbert space of vector states (I will assume finite degrees of freedom, so the C*-algebra of the system can be taken to be $B(H)$, with $H$ an $L^2(\mathbb R^n)$ space). Spin gives a superselection rule, and therefore there must be superselection sectors. It foll... | https://physics.stackexchange.com |
456,485 | [
"https://physics.stackexchange.com/questions/456485",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98414/"
] | I'm looking at viscous dissipation of an incompressible fluid in fully developed pipe flow.
I'd like to generally derive the bulk temperature variation as a function of pipe length due to viscosity, and understand how viscous dissipation requires more work to make a fluid flow.
<hr>
The general bulk flow energy equ... | Your analysis is correct, but a much easier approach is to apply the open system version of the first law directly: <span class="math-container">$$\dot{Q}-\dot{m}(h_{out}-h_{in})=0$$</span>with <span class="math-container">$$h_{out}-h_{in}=C_p\Delta T+\frac{\Delta P}{\rho}$$</span>assuming constant density. Plus, <sp... | Heat equation in viscous incompressible flow
<span class="math-container">$\rho c_p(\frac {\partial T}{\partial t}+\vec {v}.\nabla T)=\lambda \nabla ^2 T+\frac {\mu}{2}(\frac {\partial v_i}{\partial x_k}+\frac {\partial v_k}{\partial x_i})^2$</span>
In the case of a Poiseuille flow, the terms can be calculated and av... | https://physics.stackexchange.com |
2,561,375 | [
"https://math.stackexchange.com/questions/2561375",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/269497/"
] | <blockquote>
Suppose a patient has to undergo, on the advice and prescription of an expert physician, three
medical tests A, B and C (say a urine test, a blood test, and an X-ray, to be specific). The physician has
imposed certain conditions on these tests:<br>
(i) Tests B and C must be done only after test A i... | Let us just straightway jump into the general case, starting from the fact that we should <strong><em>first</strong> get test $A$ done</em>.
For this we note that the test $A$ cannot be done on the $(n+1)^{\text{th}}$ day (why?). Let thus then safely assume that the test $A$ is done on the $k^{\text{th}}$ day.
Then, ... | Let us assume that B and C must be done 1 day before each other. Then, $x=2\cdot(3+2+1)=12$. Then find the value for 2 days after each other, which is $x=2\cdot(2+1)=6$. For 1, this would be $1\cdot2=2$. If you noticed, this is the sum of triangle numbers multiplied by $2$, or tetrahedral numbers. The formula, adapted ... | https://math.stackexchange.com |
238,060 | [
"https://mathoverflow.net/questions/238060",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41619/"
] | It is known that there are characterizations of weak compactness in most of classical non-reflexive spaces (e.g. $L_{1}$-spaces and $C(K)$-spaces). I wonder whether there are characterizations of weak compactness in James space $J$ or its dual $J^{*}$. Can we establish a criterion for it if there is no? Thank you!
| James space is a commutative Banach algebra with pointwise operations. <span class="math-container">$J^{\ast\ast} = J\oplus\mathbb{C}$</span> is just <span class="math-container">$J$</span> with a unit attached [https://doi.org/10.4153/CJM-1980-083-7].
Second, since <span class="math-container">$J$</span> contains no c... | One of the things which you can do is: to combine the following theorem of James [James, Robert C. Weakly compact sets. Trans. Amer. Math. Soc. 113 1964 129–140]: <em>A weakly closed subset $C$ of a Banach space $B$ is weakly compact if and only if each member of $B^*$ attains a maximum on $C$</em> with the description... | https://mathoverflow.net |
6,958 | [
"https://dba.stackexchange.com/questions/6958",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/3196/"
] | I actually want to get rid of the existing constraints in the database which I know sounds crazy but we are upgrading our application to a new framework which relies on the foreign key constraint names plus we're doing a bunch of cleanup and renaming of fields, tables etc.
I suppose a better way to frame the question ... | There comes a point when a step-by-step clean-up becomes more work than a clean slate and migrate approach. System availability and time to migrate may factor in to the decision when dealing with larger volumes but at this size, not an issue.
Key factors for me here are:
<ul>
<li>Renaming foreign key constraints to f... | I don't know about optimal, but it might be worth a shot for a quick conversion to write a bash script that follows a simple logic:
<ul>
<li>mysqldump database into a file </li>
<li>parse out the <code>CONSTRAINT</code> lines in the file</li>
<li>check if the <code>CONSTRAINT</code> name exists as a KEY, if it does re... | https://dba.stackexchange.com |
595 | [
"https://datascience.stackexchange.com/questions/595",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/1207/"
] | I'm new to machine learning, but I have an interesting problem. I have a large sample of people and visited sites. Some people have indicated gender, age, and other parameters. Now I want to restore these parameters to each user.
Which way do I look for? Which algorithm is suitable to solve this problem? I'm familiar ... | I had almost the same problem: 'restoring' age, gender, location for social network users. But I used users' ego-networks, not visited sites statistics. And I faced with two almost independent tasks:
<ol>
<li>'Restoring' or 'predicting' data. You can use a bunch of different technics to complete this task, but my vote... | There exist many possibilities for populating empty gaps on data.
<ul>
<li><strong>Most repeated value</strong>: Fill the gaps with the most common value.</li>
<li><strong>Create a distribution</strong>: Make the histogram and drop values according to that distribution.</li>
<li><strong>Create a new label</strong>: Si... | https://datascience.stackexchange.com |
136,504 | [
"https://stats.stackexchange.com/questions/136504",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | I'm wording a report on the averages of a discrete variable, and am trying to get the most appropriate sounding wording.
Consider the able below:
<pre><code>Average pets per household by income
Income ($) | Cats | Dogs
-----------+------+------
< 20k | 0.9 | 1.1
20k - 50k | 1.5 | 2.0
> 50k | 2.0 |... | The number of dogs in a household is a count. It is true that you cannot have $1.1$ dogs, but it is also true that the average of the number of dogs in low income households can well be $1.1$. There is nothing necessarily incorrect about this claim, and your top phrasing is the right one to use.
What people someti... | If you really thought your readers/listeners would struggle to make sense of a non-integer number of dogs you could perhaps say
<blockquote>
On average, ten low-income households will own eleven dogs between them.
</blockquote>
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82,196 | [
"https://stats.stackexchange.com/questions/82196",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/37288/"
] | For an IV to be valid, it must be:
<ol>
<li>Randomly assigned</li>
<li>Correlated with the endogenous variable in the model</li>
<li>Uncorrelated with the dependent variable in the model</li>
</ol>
<strong>What does the random assignment of an IV mean?</strong>
<strong>How does one assess whether an IV is actually r... | To add to @jmbejara's answer, there is no formal statistical test for the validity of an instrument (beyond, obviously, that there shouldn't be any apparent correlation with the outcome except through the endogenous variable). Selection of a valid instrument depends on subject matter knowledge.
To your example, I c... | To restate the requirements you've listed (for linear models), an instrument must be
<ol>
<li>exogenous in the sense that it is independent of the error term $u_i$,</li>
<li>correlated with the endogenous explanatory variable $STR$ after conditioning on the other covariates,</li>
<li>and uncorrelated with the dependen... | https://stats.stackexchange.com |
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