qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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|---|---|---|---|---|---|
167,962 | [
"https://chemistry.stackexchange.com/questions/167962",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/127364/"
] | <strong>Here is my (limited) understanding of my question:</strong>
A pH probe consists of two half cells. One is a reference cell, constructed such that the EMF across the cell is stable and well defined. In the case of an Ag/AgCl reference cell the silver wire is connected electrically to the negative terminal of a ... | Consider the case where you wish to remember a friend's address with a reference to a famous restaurant, but the restaurant magically keeps shifting its position without warning day by day! This would certainly be a disappointment. Such an unpredictable and constantly shifting "reference" may be useless for a... | In other words, you propose replacing the reference electrode with its own solution with a logistically simpler "copper vs test solution" electrode.
<ol>
<li>Your copper electrode potential will depend on copper ions concentration in the solution. You know it, right?
</li>
<li>Should there be no much of coppe... | https://chemistry.stackexchange.com |
459,985 | [
"https://stats.stackexchange.com/questions/459985",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/280537/"
] | According to Wikipedia,
<strong><em>A result has statistical significance when it is very unlikely to have occurred given the null hypothesis</em></strong>
does that mean if our alternative hypothesis is true we will call our results "Statistically Significant"? which certainly shouldn't be the case.
| <blockquote>
does that mean if our alternative hypothesis is true we will call our results "Statistically Significant"?
</blockquote>
No. If the alternative really is the case, we can still fail to reject the null resulting in a type II error (or a false negative).
The mathematial definition of significance is st... | More or less, yes.
You call the descriptive quantity of interest *statistically significant" if the associated null hypothesis is rejected at the prespecified level.
Consider e.g. a randomized study comparing a new drug versus a placebo with null hypothesis
<span class="math-container">$$
H_o: \mu_\Delta = 0,
$$</spa... | https://stats.stackexchange.com |
352,541 | [
"https://electronics.stackexchange.com/questions/352541",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/176165/"
] | I have seen too many tutorials on how to increase HC-06 bluetooth module range. They all involve cutting the on-board antenna and adding an external one (a piece of wire or a 2.4GHz antenna). I was wondering how this affects the bleutooth module, for example, the power consumption, the frequency. And the relation betwe... | <blockquote>
I know that the circuits which employ negative feedback are stable
</blockquote>
Any feedback system is potentially unstable. What might seem like negative feedback at low frequencies can easily turn to positive feedback at higher frequencies.
<blockquote>
whereas those which employ positive feedback... | Your premise is wrong with real op-amps, as has been pointed out.
To analyze the situations, start with the balanced condition and introduce a small perturbation at the input. If the resulting output change is opposite to that created by the input error you have the possibility of stability, but if it increases the e... | https://electronics.stackexchange.com |
12,145 | [
"https://security.stackexchange.com/questions/12145",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6001/"
] | Does anyone know of a method to fingerprint machines in the LAN and find out what kind of AV software is installed?
| There are two ways to detect this, Passive or Active.
<h2>Passive</h2>
This is what Iszi was referring to. If you can get yourself in the data stream you can glean lots of information. Using flow analysis you can watch for machines making connections to known update servers. So look around at some AV products, get a ... | Do you have access to these machines from an admin standpoint, it might be difficult to tell AV software based only on a vulnerability scan.
If you have admin access on these machines, you might be able to pull WMI or some other service. Using something like a credentialed scan with Nessus will often tell you what AV... | https://security.stackexchange.com |
3,425 | [
"https://dba.stackexchange.com/questions/3425",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136/"
] | Just again looking at some log from an oracle script, where the developer intended to comment out some part not to add documentation.
I don't want that a script containing code like this
<pre><code>/*
select getWochentag(SYSDATE) from DUAL;
select
getWochentag (SYSDATE ) || isWeekend (SYSDATE ),
getWoc... | <code>SET DOC[UMENT] OFF</code>
At least in 9i. I can't make these comments display at all in 10g, so I think they've made this option even more obsolete - it still controls explicit <code>DOC</code> blocks, but apparently not comment blocks...
| I wanted to suppress comments from login.sql
While using "--" style comments are not displayed, rem and /* */ are displayed!
Environment: Using SQL*Plus: Release 9.0.1.3.0
| https://dba.stackexchange.com |
64,056 | [
"https://cs.stackexchange.com/questions/64056",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/59103/"
] | I am trying to show whether this language is regular or not:
<span class="math-container">$$L = \{0^m1^n \mid m \neq n\}$$</span>
Since I cannot create or think of an automaton that recognizes <span class="math-container">$L$</span>, I am suspecting that <span class="math-container">$L$</span> is not regular. From t... | You don't need to invoke the PL directly here. Instead, we'll do a proof by contradiction. Suppose $L$ was regular, then, since regular languages are closed under complement, $\overline{L}$ is regular (where the overbar represents complement), and since regular languages are closed under intersection, $\overline{L}\cap... | It's not so evident, but <em>you can also apply the PL directly</em>:
<ul>
<li>let $p$ be the pumping length </li>
<li>pick $w = 0^p 1^{p + p!}$</li>
</ul>
Clearly $w \in L$
The pumping lemma says that $w = xyz$ with $|xy| \leq p, |y| \geq 1$, so we have that $y$ must be "made of" $0$s; suppose that $y = 0^a\;, 0<... | https://cs.stackexchange.com |
179,108 | [
"https://security.stackexchange.com/questions/179108",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/71945/"
] | <strong>Background</strong>
When I run Metasploit, it hangs at the same place no matter what I do. It stops at this line,
<blockquote>
[*] Using code '404' as not found.
</blockquote>
<strong>Steps to reproduce,</strong>
<pre><code>msf > mfsconsole
msf > load wmap
msf > wmap_sites -l
msf > wmap_targe... | <blockquote>
Whenever I change the <code>"</code> to <code>'</code> in any other configuration within the query, it fails.
</blockquote>
That would be:
<pre>
SELECT * from users where
username = "1' or '1' = '1"
and
password = "1' or '1' = '1"
</pre>
This fails because you're literally querying for a user ... | In your query:
<pre><code>SELECT * from users where username="1" or '1' = '1" and password="1' or '1' = "1"
</code></pre>
<code>username="1"</code> evaluates to false
<code>'1' = '1" and password="1'</code> evaluates to false, as don't get confused by double quotes, these are treated as normal string because they ar... | https://security.stackexchange.com |
22,563 | [
"https://dba.stackexchange.com/questions/22563",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10768/"
] | We have a table that is clustered on identity/datetime2. It is partitioned on the same datetime2. Are there any reasons to cluster on datetime2/identity instead? I understand the reasoning behind clustering generally, but with partitioning included, do things change?
| Partitioning a table only divides it into "chunks" based on the partition function. The clustered index will give order to the data within each partition.
If you're planning to run queries that involve <em>parts</em> of a partition (i.e., show me sales between Jan 5th and Jan 12th), then it can be advantageous to thos... | From a partitioning perspective there's no need to change the clustering key to datetime2/identity. It would be totally dependent on your queries.
| https://dba.stackexchange.com |
326,067 | [
"https://softwareengineering.stackexchange.com/questions/326067",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8818/"
] | Here are some requirements for a queue:
<ul>
<li>Every few days add ~100k tasks with various priorities</li>
<li>Workers will pull tasks at typically less than 10 / second</li>
<li>Tasks need to be completed by ~2 unique workers (for error checking), and then depending on outcome potentially by an additional worker</l... | It's hard to say without a complete understanding of what you are trying to accomplish but based on what you are saying, I think a database makes more sense. You might want to use a database and a queuing system together.
The reason is that in this kind of situation you generally want to have some sort of audit-balan... | What impresses me most here isn't the slow throughput. It's ~100k tasks every few days. Sounds like batch processing to me. The sort of thing you'd want to be persistent so you could shut down to install an update every once in awhile. That doesn't necessarily mean DB but it's certainly not something you want to on... | https://softwareengineering.stackexchange.com |
13,567 | [
"https://astronomy.stackexchange.com/questions/13567",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/10690/"
] | Does the CMB contain any clues to what caused the Big Bang? Does a mathematical model theorize it?
| Galaxies are gradually being extinguished. Most star formation activity occurs near the start of a galaxy's life, or in response to merger activity with other galaxies.
The star formation rate of the universe peaked at redshifts of around 3, corresponding to a look-back time of around 9 billion years. Since then the s... | Far more stars die than stars are born, The number isn't exact but I would say 90 to 10.Then what occurs next is a large percentage of those dead stars form black holes from supernovas and the occasional neutron star collision will form black holes, Giving the new stars less of a chance to reach maturity.The Universe i... | https://astronomy.stackexchange.com |
199,711 | [
"https://security.stackexchange.com/questions/199711",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/190837/"
] | I have been learning about hiding and executing msfvenom created shellcode and came to a technique where we xor the shellcode and when executing we reverse it.Would it be the same if i just encrypt it via AES and then decrypt it before executing.Would the end result be same?Is encoding better than encryption for shellc... | Encoding and encrypting are not the same: encoding does not need a key, encrypting does. XOR is not encoding, is a <strong>very weak</strong> form of encryption. Base64 would be an example of encoding. Uuencode is another example.
The difference between XOR and AES is the difference between a wooden box with nails clo... | No, encoding is not the same thing as encryption.
"Would it be the same if i just encrypt it via AES and then decrypt it before executing." No, the ciphertext on the wire and at rest is less recoverable than encoded payloads.
"Would the end result be same?" Yes, as long as you end up with the same plaintext as you ... | https://security.stackexchange.com |
132,262 | [
"https://physics.stackexchange.com/questions/132262",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57813/"
] | I know I should have listened to my teacher in physics class but I didn't. I need help on a thing I am trying to do for a game.
I want to be able to calculate Gravity pushing down on a object over a certain amount of time. (I want the object to slow down to a stop and then go back down due to gravity).
I've been look... | Assuming you are using C code:
<pre><code>#include <stdio.h>
int main(void) {
float position = 0, velocity = 8, time, timeStep = 0.01;
float g = 9.8;
for(time = 0; velocity > -10; time+=timeStep) {
velocity = velocity - timeStep * g;
position = position + velocity * timeStep;
printf("time %f... | The standard approach in numerical simulations is to do a discrete time stepping. If the motion is limited to the vertical direction, you just need to keep track of vertical position $z$ and vertical velocity $v$ (with positive $v$ denoting upward speeds). Starting with given values for $z$ and $v$ (the initial positio... | https://physics.stackexchange.com |
233,639 | [
"https://stats.stackexchange.com/questions/233639",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/93111/"
] | I have a LSTM (Long-Short Term Memory) Neural Network that has this structure:
<pre><code>model = Sequential()
model.add(Masking(mask_value=0.0, input_shape=(271,2)))
adam = Adam(lr=.0000001, clipnorm = .001)
model.add(LSTM(271, activation = 'linear', input_shape=(271,2))) #return_sequences = True
#model.add(LSTM(3,... | I had this problem before and one solution that worked for me was to use weight and activation regularization, specifically l2 regularization. Even setting the alpha values very small (0.000001) helped a lot without compromising accuracy too much.
For your code, add the following import statement:
<pre><code>from ker... | I am having this issue since 2 days. In this time I have changed a lot in my network without much success.
The solution for me was to adjust my optimizer, you might want to reduce the learning rate even further, if you still have problems and the network becomes unstable.
Adam(lr=0.0001, clipnorm=1.0, clipvalue=0.5... | https://stats.stackexchange.com |
32,137 | [
"https://chemistry.stackexchange.com/questions/32137",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/13432/"
] | In IR spectroscopy, the $x$-axis is used to represent wavenumber, in $\mathrm{cm^{-1}}$. Why is wavenumber, equal to $1/\lambda$, used in place of wavelength, which is simply $\lambda$?
Sources I’ve already found explain why it was chosen rather than energy of waves, but the conversion from wavelength to wavenumber i... | The choice to use wavenumbers for infrared spectroscopy (rather than wavelengths, frequencies, or energies) was probably done to provide a range that has both the appearance of width (so that the difference between two peaks is more meaningful) and spans a set of reasonable values that do not contain very large or very... | Not only in IR spectroscopy. Wavenumber is unit of energy and therefore you can directly deduce the difference of energy between states.
In addition, humans like to think in acceptably small numbers (0.01 - 10,000). Wavenumber allows this for IR and conveniently supplements the eV unit in small energy separations rang... | https://chemistry.stackexchange.com |
80,243 | [
"https://mathoverflow.net/questions/80243",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19063/"
] | I'm a physical chemist and I am involved in “colloidal dice”. These are small, cube-like particles with a really nice, regular shape. These particles are not really cubic, but more rounded, much like a dice. I've got a neat way to quantify their size and "roundness" and I'm interested in their volume and surface area. ... | You can't expect a closed formula for this surface area. The perimeter of an ellipse, much less the perimeter of a superellipse or the surface area of an ellipsoid or a superellipsoid, is already an integral that doesn't have a formula in the usual sense of an elementary formula. Instead, people did what they always ... | This is hardly what you asked, but you might consider a different description for colloidal dice, constants $A,B,C,D$ and
$$ A(x^6 + y^6 + z^6) + B ( y^4 z^2 + y^2 z^4 + z^4 x^2 + z^2 x^4 + x^4 y^2 + x^2 y^4) + Cx^2 y^2 z^2 = D.$$ If you take $A=2, B=-1, C=2, D=2$ the result is a slightly non-convex cuboid shape that ... | https://mathoverflow.net |
234,474 | [
"https://softwareengineering.stackexchange.com/questions/234474",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/124276/"
] | I see a lot of APIs that use custom collections instead of just using strongly-typed packaged generics.
For instance, the API will have a <code>Object1Collection</code> instead of just a <code>List<Object1></code> (or whatever the appropriate generic would be).
When do you know to use one or the other? I under... | In general, rarely if ever.
You'll occasionally make things that wrap collections and work on collections of things, but you will rarely make a class that is a generic, reusable collection. More often you'll have some class that represents some concept which uses a collection, rather than <em>is</em> a collection.
Wh... | Custom collections don't really make sense for general programming. Thats why <code>List<T></code> exists. But they sure make lots of sense in domain modelling. For example, you would like to have special behavior that happens when you add a new item into a collection. The best way to do it is to create custom co... | https://softwareengineering.stackexchange.com |
11,927 | [
"https://stats.stackexchange.com/questions/11927",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5023/"
] | Could someone tell me what the term 'persistence' mean in time series analysis? It's regarding econometrics and applied regression.
| Roughly speaking, the term <em>persistence</em> in time series context is often related to the notion of <em>memory</em> properties of time series. To put it another way, you have a persistent time series process if the effect of infinitesimally (very) small shock will be influencing the future predictions of your time... | A persistent series is one where the value of the variable at a certain date is closely related to the previous value. The two basic measures of persistence are the autocovariance and the autocorrelation coefficient.
| https://stats.stackexchange.com |
713,059 | [
"https://physics.stackexchange.com/questions/713059",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/335850/"
] | I read that in gauge theories the assumption that "all fields decay sufficiently rapidly at infinity" is not justified anymore and therefore, one needs to consider boundary terms that ultimately lead to asymptotic symmetries.
But why is the assumption not possible in gauge theories?
| Well for a theory to be considered as a candidate for the new potential unified theory, it should provide some new "perspective" that the current theories do not have. Weak interaction, strong interaction and electromagnetism have been somewhat unified under quantum mechanics, the current challenge to be able... | All of the requirements in the example can be simplified to a single requirement. Then there is one further requirement:
<ol>
<li>It must explain all the observations done by previous experiments with fewer initial assumptions.
</li>
<li>It must predict at least one novel outcome of experiments that have not yet been p... | https://physics.stackexchange.com |
3,355,567 | [
"https://math.stackexchange.com/questions/3355567",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/704453/"
] | If <span class="math-container">$A$</span> is matrix if order <span class="math-container">$4\times 8$</span> and <span class="math-container">$B$</span> is a matrix of order <span class="math-container">$8\times 4$</span> s.t. <span class="math-container">$AB=I$</span> then find the ranks of <span class="math-contain... | Since <span class="math-container">$A$</span> has only 4 rows its rank is at most 4.
The rank of <span class="math-container">$AB=I$</span> is precisely 4. We know that <span class="math-container">$$\text {Rank} (AB)\le \text {Rank}(A)$$</span>
and therefore the rank of <span class="math-container">$A$</span> is at... | Rank of A = rank of B = 4.
Because, we know that,
Rank of(AB) <= min{rank of A, rank of B}. And that ensure that rank of A and rank of B can not lass then 4.
Now, we also know that row rank and colome rank of a matrix are same. In matrix A row space is the subspace of R^8. And colome space is the subspace of R^4. T... | https://math.stackexchange.com |
131,711 | [
"https://softwareengineering.stackexchange.com/questions/131711",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8413/"
] | I've just begun using a popular, well-documented graphics engine, and was given a month to create some small programs and get familiar with it.
The library is huge, and there are sections I haven't explored.
Due to a time-crunch, my tech-lead has asked me to start designing my software (<em>sequence and class diagram... | Your own sequence and class diagrams probably do not depend that much on how the graphics engine behaves. During implementation, you will probably run into little quirks like 'I must call initFoo() before setupBar()' but those details most likely do not affect the design of your classes. Your tech-lead needs your desig... | There is a risk: just because the engine is popular and well documented, that might not reflect reality. I did use one game engine recently that used a wiki to documentation how the engine worked. What you found was a mixture of old pages that didn't reflect the most recent version, current pages, and ones that were ta... | https://softwareengineering.stackexchange.com |
26,821 | [
"https://chemistry.stackexchange.com/questions/26821",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/13177/"
] | I was just reading about how Nitrogen and Oxygen combine to form Nitric oxide.
<img src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcQ1yqvfJf_UlPknaS5h0frI6LP-MkMehrThZHiQRf-n1Y73v9Gi" alt="Image result for n2 + o2 = 2no"/>
<br>
My question is, why would this reaction even occur? Isn't the valency of Nitroge... | Think about it this way. If a molecule of nitrogen and a molecule of oxygen were to collide with enough kinetic energy to break the bonds that hold the molecules together, and they collide at such an angle that allows their orbitals to overlap and form new bonds, then $\ce{NO}$ can be made. The octet rule is a rule. ... | You're right: $\ce{NO}$ is a free radical and the reaction between $\ce{N2}$ and $\ce{O2}$ can be achieved - <strong>supposed that enough energy is provided</strong>.
This may happen through an <strong>electrical arc discharge</strong> in the lab or, in the mesosphere (50-85km above earth) through <strong>ionizing cos... | https://chemistry.stackexchange.com |
97,153 | [
"https://chemistry.stackexchange.com/questions/97153",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/62155/"
] | <ol>
<li>$\ce{Br2/FeBr3}$</li>
<li>$\ce{CH3Cl/AlCl3}$</li>
<li>$\ce{KMnO4}$</li>
<li>$\ce{HNO3/H2SO4}$</li>
<li>$\ce{NBS}$/hv</li>
<li>$\ce{NaOH}$</li>
<li>$\ce{Sn/HCl}$</li>
<li>$\ce{NH4SH}$</li>
<li>$\ce{NaBH4}$</li>
</ol>
I'm able to get the amino group onto the ring by using 4 and 7.
But I have no idea how to get ... | I am not happy with the idea of trying to convert a bromobenzene into a phenol using sodium hydroxide. Normally an aryl halide is very inert to nucelophiles, the nitro group will increase the rate but it will not make much difference.
What I would do is to do the following
<ol>
<li>Nitrate benzene with a mixture of n... | <strong>Steps:</strong>
<ol>
<li>Use $\ce{Br2/FeBr3}$ to make bromobenzene.</li>
<li>Nitrate with $\ce{HNO3/H2SO4}$ to make 4-bromo-nitrobenzene.</li>
<li>Treat with $\ce{NaOH}$ to displace the $\ce{Br}$ making 4-nitrophenol.</li>
<li>Reduce with $\ce{Sn/HCl}$ to make the required <em>p</em>-aminophenol.</li>
</ol>
| https://chemistry.stackexchange.com |
391,894 | [
"https://physics.stackexchange.com/questions/391894",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/187845/"
] | I see very often that electric and magnetic fields ($\mathbb{R}^3$) in free space are assumed to have the form:
$$\vec{E}=\vec{E}_0{(x,y)}\exp{[i(wt-kz)]}$$
$$\vec{H}=\vec{H}_0{(x,y)}\exp{[i(wt-kz)]}$$
that is, $\vec{E}$ and $\vec{H}$ are propagating along the z-axis and are harmonic in t and z coordinates (<strong>w... | The quantity $\frac{dV}{dn}$ is defined by Griffiths to be equal to $\frac{dV_{above}}{dn}-\frac{dV_{below}}{dn}$. This is equivalent to the following (valid) definition of the derivative of a function:
$$f'(x)=\lim_{h\to 0}\frac{f(x+h/2)-f(x-h/2)}{h}$$
Regarding your specific problem, the trick is that the potential... | Griffiths equation $$\sigma=-\epsilon_0 \frac{\partial V}{\partial n}$$hold for the case of a metal surface charge where the interior electric field is zero. It is equivalent to $$\frac{\partial V_{above}}{\partial n}-\frac{\partial V_{below}}{\partial n}=-\frac{\sigma}{\epsilon_0}$$ where $$\frac{\partial V_{below}}{... | https://physics.stackexchange.com |
276,645 | [
"https://physics.stackexchange.com/questions/276645",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/89669/"
] | In the case of DC motors why is the mechanical power output equal to back emf multiplied by armature current.
| You probably have no trouble with the concept of a simple rotating coil generator.<br>
A coil is rotated in a magnetic field and an emf $\mathcal E$ is generated.
If there is a resistance $R$ across the terminals of the generator then a current $I$ flows in the circuit.
To simplify matters assume that the frictiona... | Short version: with any motor/engine the total energy put in is equal to the total energy put out, averaged over a full cycle, always. In the case of an electric motor, the power put in will be the back emf times the current, because $P=IV$. If you assume that heat losses are small, then all of that power has to come o... | https://physics.stackexchange.com |
549 | [
"https://cogsci.stackexchange.com/questions/549",
"https://cogsci.stackexchange.com",
"https://cogsci.stackexchange.com/users/468/"
] | We've all heard that listening to classical music and such while studying can be beneficial, but I was wondering about actually playing an instrument? If I were to absentmindedly play my accordion while reading a textbook, would it have any benefit to either my absorption of the material or ability to play music withou... | Multitasking research suggests that people can't really multitask. I don't have any evidence to back this up, but I suspect that it's much better for your instrument skills than your studying. The accordion detracts from your focus and attention while you work, perhaps even if it doesn't feel like it. At the same time,... | There is a reason why (at least where I'm at) it it illegal to hold and talk on a cell phone while driving. Not that hands-free talking really makes any difference.
One loses efficiency or what-have-you when attention needs to be shared amongst different activities that require cognitive control. By shared I mean more... | https://cogsci.stackexchange.com |
324,746 | [
"https://softwareengineering.stackexchange.com/questions/324746",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/230628/"
] | This is a academic question, but I think only professional programmers are the people who can answer this.
<blockquote>
Is it true that whatever we can do with pointers, we can do without them as well?
</blockquote>
This is something one of my undergrad teachers mentioned and I never really cared to find out, now i... | I don't think you could use the heap (via malloc, or even stack allocation via alloca) without pointers in C as these functions return pointers; so, you'd give up memory allocation. Without memory allocation, you're crippled; might as well write in Fortran '66 -- which by the way is all about writing code using compi... | Professional programmer's answer: Anything you can do easily, you can do in a hard way. Sometimes in a very hard way that only masochists would consider. Anything you can do with an excavator you can do with a shovel. Anything you can do with a shovel you can do with a teaspoon.
Yes, everything you can do with pointe... | https://softwareengineering.stackexchange.com |
255,653 | [
"https://security.stackexchange.com/questions/255653",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/267857/"
] | As of today, web security gateways add a layer of complexity to corporate web traffic while - in my opinion - only adding a small layer of protection, as most web traffic is encrypted nowadays.
Of course, it's - as of now - possible to MITM the encrypted traffic, but that has additional drawbacks in fact - again in my ... | <blockquote>
.. possible to MITM the encrypted traffic, but that has additional drawbacks in fact - again in my opinion - does not add a layer of security but removes one.
</blockquote>
True, MITM taken only by its own does not add a layer of security and instead weakens it. But security solutions do not simply add MI... | There are two level of web security gateways. The outer level prevents any network access to the inner network that contains the web servers and other application servers like the database except for the HTTP/HTTPS traffic. That part is specifically encapsulated there, which allows to easily and quickly ban some domain... | https://security.stackexchange.com |
318,282 | [
"https://softwareengineering.stackexchange.com/questions/318282",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/219569/"
] | <strong>Background</strong>
I am working on a project with C# .NET, and I've just added a new unit test project to my solution in Visual Studio. The way that I always have been doing this is:
<ol>
<li>Create a new unit test project.</li>
<li>Have that project <em>include a reference</em> to the <em>project under test... | Your unit tests are in a separate project and serve a separate function from your main code, so putting them into a separate namespace makes the most sense to me.
If you're considering putting them into the same namespace just to save the <code>using</code> line, then don't. Less code is good, clearer code is better.
| I've used unit tests project with the same namespace as the real project (by manually removing the <code>Tests</code> suffix on the test project namespace) for a few years with zero issues.
I think it leads to more straightforward code so I usually suggest going that approach. Some of the drawbacks, like potential nam... | https://softwareengineering.stackexchange.com |
144,392 | [
"https://mathoverflow.net/questions/144392",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41081/"
] | Suppose that I have two matrices $A$ and $B$, and I want them to share a common eigenvector $x$. For simplicity let's just assume that the eigenvalue associated with $x$ is $1$ for both matrices, so $Ax=x$ and $Bx=x$. Is there a simple condition on $A$ and $B$ which is both necessary and sufficient for this to occur?... | Let $A,B$ be two $n\times n$ matrices with entries in a field $K$.
Then $A,B$ have a common eigenvector iff
$\cap_{k,l=1}^{n-1}\ker([A^k,B^l])\not=\{0\}$.
This result is due to
D. Shemesh. Common eigenvectors of $2$ matrices. Linear algebra and appl., 62, 11-18, 1984.
| This may be a partial solution to your problem:
I claim that if there exists a shared eigenvector, $x$ of $A$ and $B$ with common eigenvalue of $1$ then $\det(AB - BA) = \det[A,B] = 0$.
Proof:
Suppose that there exists a shared eigenvector $x$ such that $Ax=x$ and $Bx=x$.
Then, as Muro suggested, $ABx=x=BAx$. Hence... | https://mathoverflow.net |
66,060 | [
"https://dsp.stackexchange.com/questions/66060",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/49492/"
] | I stuck this question. Frequency response is written as magnitude and phase and I don't find inverse fourier given signal which as magnitude and phase.How can I solve it ? Can you explain the solution way in order? magnitude of signal is : y=−ω while −1≤ω<0,
y=ω while 0≤ω<1 phase of signal is: y=−3ω
What is the ... | Your decision to normalize or not does not change the accuracy of your answer, as it is simply a scaling factor. If you use the common scaling of <span class="math-container">$1/N$</span>, then the output for each DFT bin will represent the average of the portion of the input signal that is at the frequency defined by ... | Whether you want to normalize or not depends on whether you want to know the level or the energy of the DFT input.
IIRC, the SciPy FFT returns energy (complies with Parseval’s relation). A signal N times as long at the same level has N times more energy. So you could divide by N to get an estimation of a level inste... | https://dsp.stackexchange.com |
19,750 | [
"https://physics.stackexchange.com/questions/19750",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7050/"
] | Assume a photon enters the event horizon of a black hole. The gravity of the black hole will draw the photon into the singularity eventually. Doesn't the photon come to rest and therefore lose it's mass?
| We don't know what will happen when a photon or any other particle hits a singularity of a black hole. The singularity is a phenomenon of classical general relativity and the singularity is really is an indication that classical general relativity breaks down there. To really understand what happens near a singularity ... | Meh, no string theory or singularity or unitology etc. Black Holes are accelerators. Every particle is broken down to the lowest level, accelerated to the highest speed and shot out. The path is non-vectorial, because the exitement of such magnitude makes the low-level particles act as "quantum binded particles". Which... | https://physics.stackexchange.com |
2,727,320 | [
"https://math.stackexchange.com/questions/2727320",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/25805/"
] | I've seen a proof of the uniqueness of <span class="math-container">$q,r$</span> in <span class="math-container">$a=bq+r$</span> when <span class="math-container">$a,b$</span> are given. The proof is as follows:
<blockquote>
Suppose <span class="math-container">$a=bq+r=bq'+r'$</span> with the obvious assumptions on <sp... | A higher slope should correspond to a steeper line. Thus, if $\Delta Y$ increases while $\Delta X$ stays the same, the line gets steeper (visualizing this on the $XY$-plane), so we should expect the slope to increase as well. If the slope was $\Delta X/\Delta Y$, the slope would decrease, and thus a word like "flatness... | When you're graphing a function like $y=f(x)$, the slope of the function $f$ means "when you change the input $x$ by an amount, how much does the output $y=f(x)$ change?"
To measure that, you take the ratio of the change in output $\Delta y$ and divide it by the change in the input $\Delta x$.
For example, $f(x)$ mig... | https://math.stackexchange.com |
63,292 | [
"https://security.stackexchange.com/questions/63292",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/52133/"
] | My GF just hit me up and told me she just sent some of her personal info over an email. She was trying to send her folks some documents.I guess the documents had some sensitive info on them Like her full name, SSN#, etc. The email was not encrypted. How at risk is she and what should she do from here? She is freaking o... | Most of the people who are in power to eavesdrop on the email, like the internet service providers and email providers of her and her recipient and the three letter agencies, are likely not very interested in that information. Providers are in a position to collect lots of sensitive information, but they can not risk t... | <strong>First tell her</strong> that unencrypted email is sent via various servers that all can read all information. Then tell her that this happens all the time, and still it seems like all this information is seldom stolen.
<strong>Then teach her</strong> about password protected zips and Word documents. Or even b... | https://security.stackexchange.com |
53,419 | [
"https://mathoverflow.net/questions/53419",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6646/"
] | The following fairly specific question comes up in a bordism computation I'm trying to do:
Are there compact $\mathbb Z$-oriented $4k+2$ dimensional manifolds with boundary $M$ such that $im(H_{2k+1}(M; \mathbb Z/2)\to H_{2k+1}(M, \partial M; \mathbb Z/2))$ has odd dimension as a $\mathbb Z/2$ vector space?
Clearly t... | I claim it is not possible. The image is the rank of $H_{2k+1}(M;\mathbb Z_2)/rad$, where
$rad$ is the radical of the intersection form on $H_{2k+1}(M;\mathbb Z_2)$.
The intersection form on $H_{2k+1}(M;\mathbb Z_2)/rad$ is hyperbolic, i.e. has a "symplectic" basis, therefore this vector space has even dimension.
Le... | Martin O's answer is very nice. So in an oriented $2n$-manifold with $n$ odd the mod $2$ self-intersection of any $n$-dimensional mod $2$ homology class is $0$.
Looking for a more geometric explanation of that, or anyway an explanation with no Steenrod operations in sight, I came up with the following (which is also ... | https://mathoverflow.net |
198,233 | [
"https://dba.stackexchange.com/questions/198233",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/107602/"
] | I would like some advice on how I could <strong>optimize the performance</strong> of a query that is stored in a procedure.
Previously, it took <strong>20 minutes</strong> and now we can get it in <strong>13 minutes</strong>. But it's still a long time.
I've checked the indexes several times, updated the statistics t... | Good work updating statistics as well as checking indexes.
With that monster, you need to simplify and reduce the load and complexity as early as possible.
<ul>
<li>Anything in your <code>WHERE</code> clause that can be put into a <code>JOIN</code> safely should be, unless you measure a performance degradation.
<u... | I'd do all the already-mentioned tricks in the other answers, but also clean up that inner query to the following. (there was some crazy filter logic overcomplications)
<pre><code> ...
FROM [telecom].[CallDetailRecord] AS [t]
JOIN [telecom].[TelecomBill] AS [a] ON [a].[Id] = [t].[TelecomBillId]
AND ... | https://dba.stackexchange.com |
373,713 | [
"https://softwareengineering.stackexchange.com/questions/373713",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/309772/"
] | I am currently working on a project that generates videos from templates (a template being a collection of JSON files and assets).
It seems natural to have a <code>Template</code> class that contains all the info of how this specific template is structured (e.g. which parts are personaliseable, what assets are require... | Alright, here's my thoughts after hearing your suggestions:
First of all, a Template really should only be a data class that reads a config file and then exists in that state without doing much.
There are two ways a Template can be interacted with:
1) its configuration can be changed (i.e. TemplateFields added/remov... | The question is, what do you want to achieve by using this design. If what you're intending to do makes sense may also depend on it being the common way of achieving this in the language of your choice.
To me your explanation sounds to me like your Job inherits from your Template.
Your code looks like your Template i... | https://softwareengineering.stackexchange.com |
44,943 | [
"https://electronics.stackexchange.com/questions/44943",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15376/"
] | I've got a simple project on host device that should drive 2 pins with high logic level (voltage 3.3V, 5V or 12V - doesn't matter) and wait for 2 others pins become driven high level by the peripheral device.
Can I implement such host device with a standard PC and what hardware (built-in or extra) should I use?
| It's not clear what you want the PC to do and what the device is supposed to do ("host device" makes no sense), but it seems you want basic digital I/O from a PC.
PC's are not really designed for direct digital I/O to external devices. But, you can buy digital I/O modules that connect to the PC via USB, which then al... | If you can still find one, it's worth mentioning that a true parallel port is about as close to a GPIO as you'll find in an off-the-shelf PC. Classic implementations lack some flexibility in that many of the pins have fixed direction, and some are inverted, but people have been working around that for years.
The grea... | https://electronics.stackexchange.com |
176,251 | [
"https://stats.stackexchange.com/questions/176251",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/91668/"
] | I have two hypotheses in which there is 1 independent variable (2 separate samples). I want to find out if the outcome of each of the 2 dependent variables is affected by the independent variable. Would it be appropriate to conduct a two-sample t-test, once for each dependent variable? Or, would it be appropriate to co... | So you weighted the weights by themselves?
Then the same concept applies; imagine the numbers from the "Weighted" column as the ones in the "To_Weight" column. You said yourself that you expected the weighted average of To_Weight to be different from the unweighted average of To_Weight. The same can apply for any set ... | Let me try and explain this difference with a simple example. Suppose I wanted to take the weight average of 2 and 4, with weight 2 and 4, respectively. As you know from your computations that would be equal to:
$$
\frac{2\cdot2 + 4\cdot4}{2 + 4} = \frac{2+2+4+4+4+4}{6}.
$$
A weighted average of $\mathbf{x} = (x_1,... | https://stats.stackexchange.com |
243,031 | [
"https://dba.stackexchange.com/questions/243031",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/184883/"
] | I have a table that contains User information from different countries. Information like - <code>Name</code>, <code>Country</code>, <code>LastLoginDate</code>, <code>IsUpdated</code>, <code>Certification</code>.
This table has 1.5 million rows. Now to filter this, I have a stored procedure that takes input as -
<code... | You can split the search parameters and use a join instead. Example
<pre><code>-- Some data to test with
CREATE TABLE testdata ( x varchar(100) not null primary key );
INSERT INTO testdata (x) VALUES ('a'),('c'),('e');
-- This can be a temporary table, add all numbers up to
-- the maximum number of tokens in paramete... | For a million rows, don't use
<pre><code>WHERE find_in_set(Name, 'Leslie,Dana,Ricky') <> 0
</code></pre>
because <code>INDEX(Name)</code> will not help.
Instead, use
<pre><code>WHERE Name IN ('Leslie', 'Dana', 'Ricky')
</code></pre>
and have that index.
As for constructing that string, I recommend doing it ... | https://dba.stackexchange.com |
296,726 | [
"https://softwareengineering.stackexchange.com/questions/296726",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/148612/"
] | I have a complex object which routinely needs to compute a sub-object representing various aspects of the parent's state as a bundle. For example, imagine the object represents information about an aircraft and the sub-object is a summary of various key parameters of the aircraft at some particular time such as its hea... | It's not a problem to <strong>define</strong> a variable within a loop. In fact, it's good practice, since identifiers should be confined to the smallest possible scope.
What's bad is to <strong>assign</strong> a variable within a loop if you could just as well assign it once <em>before</em> the loop runs. Depending o... | Complex types have non-trivial constructors and destructors.
Those will get called at the start and end of the loop body (as it's initialized and goes out of scope). If the initialization is expensive like it needs to allocate some memory then that should be avoided.
However for trivial types that is no problem. The ... | https://softwareengineering.stackexchange.com |
2,417,965 | [
"https://math.stackexchange.com/questions/2417965",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/272127/"
] | Let $A_{(2n+1)\times(2n+1)}$ be a symmetric matrix of Rank $2n$. Then does $\operatorname{tr}A=0$ imply $\operatorname{tr}A^3=0$? If not, Under what condition?
| The answer is NO. For a counterexample, let
$$A=\operatorname{diag}(1,3,-2,-2,0)$$
We have $\operatorname{Tr}(A)=0$ and $\operatorname{Tr}(A^3)=12\ne0$.
| <strong>Hint</strong>
$1)$ If $A$ is symmetric then we can write:
$$A=P^TDP$$
where $D$ is a diagonal matrix and $P$ is orthogonal. So,
$$A^3=P^TD^3P$$
$2)$ Use that $Trace(XY)=Trace(YX)$
So,
$$Trace(A)=Trace(D)=0$$
and,
$$Trace(A^3)=Trace(D^3)$$
Now compare $Trace(D)$ and $Trace (D^3)$.
| https://math.stackexchange.com |
133,732 | [
"https://mathoverflow.net/questions/133732",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34960/"
] | What is the tightest upper bound we can establish on the central binomial coefficients $ 2n \choose n$ ?
I just tried to proceed a bit, like this:
$ n! > n^{\frac{n}{2}} $
for all $ n>2 $. Thus,
$ \binom{2n}{n} = \frac{ (n+1) \ldots (2n) }{n!} < \frac{\left(\frac{\sum_{k=1}^n (n+k) }{n}\right)^n }{n^{n/2}}... | Here's a way to motivate and refine the argument that
Péter Komjáth attributes to Erdős.
Start by computing the ratio between the <span class="math-container">$n$</span>-th and <span class="math-container">$(n-1)$</span>-st
central binomial coefficients:
<span class="math-container">$$
{2n \choose n} \left/ {2(n-1) \ch... | Even the asymptotically sharp inequality
${2n \choose n} < 4^n \left/ \sqrt{\pi n} \right.$
has a short proof:
$$
{2n \choose n} =
\frac{4^n}{\pi} \int_{-\pi/2}^{\pi/2} \cos^{2n} x \phantom. dx <
\frac{4^n}{\pi} \int_{-\pi/2}^{\pi/2} e^{-nx^2} dx <
\frac{4^n}{\pi} \int_{-\infty}^{\infty} e^{-nx^2} dx =
... | https://mathoverflow.net |
101,503 | [
"https://mathoverflow.net/questions/101503",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12218/"
] | Let $G$ be a reductive affine algebraic $\mathbb{C}$-group (not necessarily connected). Suppose $X$ is an irreducible affine algebraic set over $\mathbb{C}$ where $G$ acts rationally. Suppose that $H$ is a reductive subgroup of $G$ (again not necessarily connected). Let $x\in X$.
If the orbit $G\cdot x$ is closed... | <span class="math-container">$\def\smat#1{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)}$</span>
The answer to your question is "no". Let <span class="math-container">$G=GL(2,\mathbb C) \times GL(2,\mathbb C)$</span> act on <span class="math-container">$X=GL(2, \mathbb C)$</span> by <span class="math-co... | No, $H\cdot x$ need not be closed. Consider the standard action of $G=\mathbf{PGL}_2$ on the projective line $X=\mathbb{P}^1$. Consider the point $x=[1,1]$. Then $G\cdot x$ is all of $X$. Yet for a maximal torus $H$, the subgroup of diagonal matrices, the orbit $H\cdot x$ is $\mathbb{P}^1 \setminus \{ [1,0],[0,1] \... | https://mathoverflow.net |
741,309 | [
"https://physics.stackexchange.com/questions/741309",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/329037/"
] | So far, I know that a trajectory in general relativity is a 4-vector, and a force-free particle follows a geodesic which is in 4D as well. My question is: how do we make an observation of such a trajectory if we, observers, have only access to a 3D world? Excuse my question if it turned out to be too naive!
| We don’t only have access to a 3D world. We can measure time with clocks and three dimensions of space with rulers. To measure a 4D worldline we just measure the location at many times, typically with respect to some physically implemented coordinate system.
| Your basic assumption is not correct. Did Arthur Eddington have access to only a 3D world? Of course not - his experiment photographed a 4D geodesic that curved past the sun. He could not only measure 4D, he could see it with his eyes during an eclipse.
| https://physics.stackexchange.com |
212,050 | [
"https://physics.stackexchange.com/questions/212050",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95310/"
] | Centripetal acceleration has a direction towards the center of the rotating object and if the magnitude of the speed of rotation remains same, then why do we call it an centripetal acceleration? Doesn't both the direction and magnitude remain same?
| Firstly in rotational motion there is a continuous change of velocity vector. Since the direction of linear velocity of the rotating particle change constantly.And we know the rate of change of velocity is acceleration. Here centripetal acceleration is arise due to change of this linear velocity vector.
In another poin... | No, the direction of the velocity is constantly changing so that it is always tangent to the circle.
There is another quantity, called angular acceleration, which captures the fact that the rotation around the center is unchanging. You see angular velocity quoted when people talk about the revolutions per minute of... | https://physics.stackexchange.com |
31,932 | [
"https://mathoverflow.net/questions/31932",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1355/"
] | The Hessian matrix $\{\partial_i \partial_j f \}$ of a function $f:\mathbb{R}^n \to \mathbb{R}$ depends on the coordinate system you choose. If $x_1,\cdots,x_n$ and $y_1,\cdots,y_n$ are two sets of coordinates (say, in some open neighborhood of a manifold), then $\frac{\partial f(y(x))}{\partial x_i} = \sum_{k} \frac{\... | No, no, no! You left out a term involving $\frac{df(y(x))}{dy}\frac{d^2y}{dx^2}$. This term vanishes at critical points -- points where $df=0$ -- so that indeed at such a point the Hessian define a tensor -- a symmetric bilinear form on the tangent space at that point -- independent of coordinates. Paying attention to ... | Sorry for reviving this question. Everything Tom said is correct, but there is more to say about "coordinate-free Taylor series".
It is true that arbitrary jet bundles $J^k(M,N)$ are subtle. The fibers are vector spaces but the transition maps are not linear. The special case $J^k(M,\mathbb{R})$ <b>is</b> a vector bu... | https://mathoverflow.net |
630,481 | [
"https://math.stackexchange.com/questions/630481",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/118782/"
] | I've managed to prove the statement for $x \geq 0 $ and $x \leq -1$ but I can't manage to construct a proof for $ -1 < x < 0 $
My lecture done it by proving $ \exp(x) - (1+x) = \displaystyle \sum_{n=2}^\infty \dfrac{x^n}{n!} $ and showing that is greater than or equal to 0. For $ -1 < x < 0 $ he set $a=-x$... | To proceed from the series, write the summation in the following way: $$\exp (x)-(1+x)=\sum_{k=1}^{\infty} \left(\frac{x^{2k}}{2k!} + \frac{x^{2k+1}}{(2k+1)!} \right)$$ notice the summand is positive for $-1<x<0$, since $|x|^{2k} >|x|^{2k+1},\ x^{2k}>0>x^{2k+1},\ 1/(2k)!>1/(2k+1)!$
| The function $f\colon x\mapsto e^x$ is <strong>convex</strong> hence its <strong>curve</strong> is <strong>above the tangent line</strong> at the point $x=0$ with equation
$$y=f'(0)x+f(0)=x+1$$
so we have the desired inequality.
| https://math.stackexchange.com |
1,140,236 | [
"https://math.stackexchange.com/questions/1140236",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/166237/"
] | <blockquote>
Consider a linear transformation $T:\mathbb{R}^3\to\mathbb{R}^3$ satisfying $$T \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}
\ \text{and} \ T \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix} = \begin{pmatrix} 5 \\ 6 \\ 7 \end{pmatrix}.
$$
</blockquote>
The question t... | Suppose I introduce you to one of my friends, and tell you the following:
<blockquote>
My friend here is French, but he speaks fluent Japanese.
</blockquote>
If you later find out my friend is Dutch, you know I was lying.
Likewise if you ask my friend an easy question in fluent Japanese and he isn't able to
answer,... | "Her judgement is firm, but fair" is both firm and fair with the connotation that judgement is not often both. The qualities are held in contrast.
"This ice-cream is soft and creamy" is both soft and creamy, with the connotation that this is better than ice-cream being either alone. The qualities reinfor... | https://math.stackexchange.com |
55,978 | [
"https://mechanics.stackexchange.com/questions/55978",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/38982/"
] | I have a problem with my TVS Jupiter Million R.
When i pull the choke and kick start ...the scooter doesn't start and when I pull down the choke the scooter start very easily in one or two kick. But it goes off automatically due to cold engine.
So now i start every morning without pulling choke and giving a revs for ... | An automatic transmission will have a torque converter on the output of the engine, typically combined with the flywheel. On more sophisticated or exotic vehicles, you'll find computer controlled clutch systems. A torque converter is a fluid coupling, which can be compared to pointing one desk fan at another, but putti... | There are other methods that could be considered to lock the engine :
1) use a "sparkplug lock" available to purchase but you could make one : old plug with internals removed tapped to receive a bolt...
2) bar and socket on the crank pulley - does need some precise mark s to make sure it does not slip...
3) sometime... | https://mechanics.stackexchange.com |
197,141 | [
"https://electronics.stackexchange.com/questions/197141",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29996/"
] | We need to get some kind of a simple sensor, that can sense someone is standing close to a product . But, it has to be behind plastic, and not seen at all .
We only need to detect someone 1 meter away from the product .
<ol>
<li>Using PIR sensors is a problem because its covered.(is it possible somehow?)</li>
<li>us... | You might consider a <em>capacitive proximity sensor</em>. Commercial models are mainly aimed at detecting smaller objects much closer than a meter, but the same principle can be used over larger distances too.
Place a large metal plate just inside the plastic cover of the product, or metallise the inside of the cover... | put an infrared thermometer behind an infrared transmitting, visually opaque acrylic window.
| https://electronics.stackexchange.com |
315,888 | [
"https://dba.stackexchange.com/questions/315888",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/251923/"
] | When we need to store boolean fields in the database, which is better? true and null or true and false combination.
I have seen many article which says to use true and false. Some reports say true and null combinations provide better performance.
I am designing a website with Ruby on Rails and mariadb. I need to add a ... | In MySQL / MariaDB / InnoDB, <code>NULL</code> is indexed as if it were just another possible value.
What does matter...
<ul>
<li>Use <code>NULL</code> for business logic, not performance. For example: 'not yet answered', 'decline to state', 'N/A', 'not yet known' (eg <code>end_time</code>), 'do not care'.
</li>
<li>I... | Which is better?
<blockquote>
True and False<br />
True and <strong>Don't Know</strong>.
</blockquote>
<pre><code>NULL != True
NULL != False
</code></pre>
Also ...<br />
NULL values are frequently <em>not included</em> in Indexes, so any kind of searching based on <code>WHERE .. IS NULL</code> is likely to run poorly.... | https://dba.stackexchange.com |
172,414 | [
"https://physics.stackexchange.com/questions/172414",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/64080/"
] | Assume it's an circular orbit. Object A orbits around object B. Take object B as frame of reference.
.$E=KE_a + GPE$
.$E=\frac 12m_av_a^2 +(-\frac {GM_bm_A}r)$
.$E=\frac 12m_a(GM_br)+(-\frac {GM_bm_a}r)$
.$E=-\frac {GMm}{2r} < 0$
What does negative total energy at any instant of time mean?
| Negative energies are totally fine, because you had to pick a zero-point for energy. In your calculation you picked it to be at infinity. You could have chosen the zero-point for potential energy in such a way that your system had zero energy, or whatever. Only changes in energy are meaningful, in general.
Consider th... | As another answer points out, a constant can be added to the <em>potential</em> energy without affecting the equations of motion. Often, we impose the boundary condition that the potential energy is zero 'at infinity'.
For the case of a central gravitational (attractive) force, imposing the "zero at infinity" boundar... | https://physics.stackexchange.com |
698,062 | [
"https://physics.stackexchange.com/questions/698062",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/324713/"
] | Why do force vectors behave like displacement vectors?
| I think the other answers don't talk about why it is <strong>counterintuitive</strong>, so this one will.
First, we must see what we found <strong>intuitive</strong>, before we were taught about Newton's laws and vectors in school.
An common situation is to push a ball forward. After it has traveled a bit, we may kick ... | Imagine I apply a force horizontally to an object and then stop, the object will be moving in that direction.
Then after that, I apply a separate force vertically this will cause an acceleration in the vertical meaning the object will be the superposition of the velocities.
Aka a diagonal trajectory
Now imagine I just... | https://physics.stackexchange.com |
140,864 | [
"https://cs.stackexchange.com/questions/140864",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/98050/"
] | I've been stuck on this problem for some time now..
Given an array A of size N that ranges between [1..N], a "move" is to increase or decrease an element (by 1). After each move the array must remain within [1..N]
I need to find the minimum number of move operations to make the array pairwise distinct.
| First Observation:<br />
Consider the result array, which contains <span class="math-container">$N$</span> distinct numbers between 1 and <span class="math-container">$N$</span>.<br />
Since there are only <span class="math-container">$N$</span> numbers between 1 and <span class="math-container">$N$</span>, all those n... | Consider an array of all <span class="math-container">$1$</span>'s. Then, the number of increments required (no decrements are required) is exactly
<span class="math-container">\begin{equation}\sum_{i=1}^{N-1} i\end{equation}</span>
This value is known to be equal to <span class="math-container">$\frac{N(N-1)}{2}=\Thet... | https://cs.stackexchange.com |
302,352 | [
"https://electronics.stackexchange.com/questions/302352",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/147437/"
] | I'm fairly new to this and I was wondering if it makes a difference if I put the current limiting resistor of a LED on the cathode or on the anode. Any "best practice" and why?
Thanks!
| Several reasons to put it on the high side. Though there is little practical reason to do it.
<ul>
<li>Its fairly common practice to put the resistor on the high side. You will make other engineers happy because they recognize what they see and understand its behavior. Most schematics are like that and its good pract... | Either is fine, though if the LED is remote it should go on the high side (Vcc or whatever you are powering the LED from.)
| https://electronics.stackexchange.com |
150,899 | [
"https://physics.stackexchange.com/questions/150899",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/66174/"
] | This was recently brought up, and I haven't been able to conclude a solid answer.
Let's say we have two identical boxes (<code>A</code> and <code>B</code>) on Earth, both capable of holding a vacuum and withstanding 1 atm outside acting upon them.
<code>A</code> is holding a vacuum, while <code>B</code> is filled wit... | The buoyant force on a body immersed in a fluid is equal to the weight of the fluid it displaces. In other words,
<span class="math-container">$$
F_B = -\rho_{\text{fluid}} V_{\text{body}} ~g
$$</span>
The force of gravity on the body is equal to
<span class="math-container">$$
F_g = m_{\rm body} ~g
$$</span>
The appar... | Just my two cents to complement the other answers. The mistake in your reasoning is that:
<blockquote>
the state above (where the top touches the bottom) is equivalent to having a box like A (just a box holding a vacuum).
</blockquote>
is incorrect, it rather equivalent to a box full of air (there is air in between... | https://physics.stackexchange.com |
130,703 | [
"https://physics.stackexchange.com/questions/130703",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57160/"
] | This question is to end an old argument.
Given a (space) vehicle with an acceleration of X, and projectile with an acceleration of 2X (rocket, not bullet), what would the relative acceleration of the projectile be if fired from the vehicle along its axis of motion?
My assertion is that, relative to the vehicle, the r... | Your friend is correct.
The acceleration of the projectile is determined by the thrust its rocket motor can produce. If the acceleration of the projectile is $2g$ then the thrust of its motor would be $2mg$.
But launching the projectile from your space vehicle can't increase it's thrust. You can increase its initial ... | To make this easy, I will assume that all speeds are small compared to the speed of light $c$.
The motion is in one dimension, so the trajectory of the space vehicle will be the following:
$$x(t) = x_0 + v_0 t + \frac12 a t^2$$
We can easily set $x_0 = 0$ if the put the origin of the coordinate system at the start poi... | https://physics.stackexchange.com |
151,312 | [
"https://physics.stackexchange.com/questions/151312",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/66301/"
] | Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first go(the same height as the fir... | The spherical pendulum conserves angular momentum about a vertical axis running through the fixed point of the pendulum. Consider when the pendulum reaches its lowest elevation, so that its velocity is completely horizontal. Its angular momentum at this point is $L = mvr$, where $m$ is the mass of the pendulum bob, $v$... | No, you cannot, athe pendulum, given any initial speed and initial height will reach a given balance point. By conservation of energy (and in absense of any loses from friction) it will always return to the same height (or balance point), there no way to it could go higher next time, it would need to acquire energy fro... | https://physics.stackexchange.com |
410,444 | [
"https://mathoverflow.net/questions/410444",
"https://mathoverflow.net",
"https://mathoverflow.net/users/173490/"
] | We denote by <span class="math-container">$C[0, 1]$</span> the space of continuous functions on <span class="math-container">$[0, 1]$</span> under the supremum norm, equipped with the Borel sigma algebra.
A <em>covering</em> of <span class="math-container">$C[0, 1]$</span> is a (possibly countably infinite) collection ... | To give a positive answer to the question it is enough to, for a fixed <span class="math-container">$\varepsilon$</span>, give a collection of disjoint balls in <span class="math-container">$C[0,1]$</span> of radius <span class="math-container">$\varepsilon$</span> which is dense in <span class="math-container">$C[0,1]... | We may take <span class="math-container">$\epsilon=1$</span> as if <span class="math-container">$\bigcup E_i$</span> has eccentricity constants <span class="math-container">$1-\delta$</span> and <span class="math-container">$1+\delta$</span>, then <span class="math-container">$\bigcup rE_i$</span> has eccentricity cons... | https://mathoverflow.net |
21,985 | [
"https://cs.stackexchange.com/questions/21985",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/14724/"
] | My lecturer for Algorithms said that most of the data structures I will encounter in the algorithms course I am taking have a basic action which is of O(1).
Ex: Binary heap.
Basic action is:
<blockquote>
<ol>
<li>Compare 2 childen.</li>
<li>Compare the "winner" with his parent.</li>
<li>Replace when needed.<... | What was meant is that every data structure is designed to do something <em>really well</em>, e.g:
<ul>
<li>For an array, lookup by index is O(1)</li>
<li>For a linked list, insertion at the head is O(1)</li>
<li>For a heap, finding the smallest element is O(1)</li>
</ul>
... and so on. This doesn't mean that the ope... | <strong>After EDIT in Question:</strong>
The operations in step 1, 2 and 3, you mentioned, are actually <code>O(1)</code>.
By <code>O(1)</code> it is not meant that it is going to take 1 step only but it means that whatever time it is taking is CONSTANT. That constant can be small or large, but as you increase numbe... | https://cs.stackexchange.com |
192 | [
"https://softwareengineering.stackexchange.com/questions/192",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/55/"
] | If I have some code that has 80% test coverage (all tests pass), is it fair to say that it's of higher quality than code with no test coverage?
Or is it fair to say it's more maintainable?
| In a strict sense, it is not fair to make any claims until the quality of the test suite is established. Passing 100% of the tests isn't meaningful if most of the tests are trivial or repetitive with each other.
The question is: <strong>In the history of the project, did any of those tests uncover bugs?</strong> The g... | By one definition it's more maintainable, as any breaking change is more likely to be caught by the tests.
However, the fact that code passes the unit tests doesn't mean it's intrinsically of higher quality. The code might still be badly formatted with irrelevant comments and inappropriate data structures, but it can ... | https://softwareengineering.stackexchange.com |
43,036 | [
"https://stats.stackexchange.com/questions/43036",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/54260/"
] | I was fiddling with my independent variables in a linear model and I note how the y-intercept becomes 0 when all the variables become standardized. Intuitively I understand that I'm shifting the line by changing with the mean of the normal distributed variables, but I was wondering if there is some more rigorous/theore... | Your model is:
<span class="math-container">$$y_j = \text{X}_{j} b + \epsilon_j = \sum_{i=0}^px_{ij}b_i + \epsilon_j$$</span>
Let <span class="math-container">$b_0$</span> be the intercept, so every <span class="math-container">$x_{0j} = 1$</span>
<span class="math-container">$$y_j = b_0 + \sum_{i=1}^px_{ij}b_i + \e... | As implied in the link given by @miura in the comments, the least squares regression line/surface/etc. always goes through the point ($\bar x$, $\bar y$). Intutively this makes sense since if you are predicting $y$ when all the $x$'s are at their mean value then should not the prediction for $y$ be at its mean value.
... | https://stats.stackexchange.com |
196,876 | [
"https://electronics.stackexchange.com/questions/196876",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/89794/"
] | I have been working on a project controlling a coil to attract a metal ball at high speed.
I measure the speed of the ball in front of the coil and then decide how fast I want the ball to accelerate because the speed it needs to have when it leaves the coil is about 10 m/s.
I found out I have about 9 miliseconds to u... | If you don't use diodes, then the whole matrix will get shorted together and it will be impossible to read anything.
Think about the following case:
<pre><code> B0 B1
| |
W0 ---X--X--
| |
W1 ---X--+--
</code></pre>
In this case, X represents either a diode or a wire connection and + represents a... | Diode matrix is effectively an AND-OR gate array with programmed connections on the inputs of the AND gates. If you use wires you just shorted a bunch of address and data lines together - bad idea.
| https://electronics.stackexchange.com |
316,865 | [
"https://math.stackexchange.com/questions/316865",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/45767/"
] | How do you find this limit?
$$\lim_{x \rightarrow \infty} \sqrt[5]{x^5-x^4} -x$$
I was given a clue to use L'Hospital's rule.
I did it this way:
<strong>UPDATE 1:</strong>
$$
\begin{align*}
\lim_{x \rightarrow \infty} \sqrt[5]{x^5-x^4} -x
&= \lim_{x \rightarrow \infty} x\begin{pmatrix}\sqrt[5]{1-\frac 1 x} -1... | You got the answer, but I'd like to note something different. I see you are doing derivations, so I am writing an answer based on it. We say the function $\alpha(x)$ is very small at $x\to a$ when $$\lim\alpha(x)\to 0$$ We can prove that by using Taylor expansion that $\sqrt[n]{1+\alpha(x)}-1\sim\frac{\alpha(x)}{n}$. S... | Your working out is fine and you've shown all the steps now. $$\sqrt[5]{x^5 - x^4} < x$$ and so a negative limit is more likely than a positive limit :)
| https://math.stackexchange.com |
306,997 | [
"https://physics.stackexchange.com/questions/306997",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/142976/"
] | I'm on the very beginning of learning quantum mechanics. When we solve the time independent Schrödinger Equation as far as I understand we will get the general solution:
$$\Psi(r,t)=\sum c_n\cdot \psi(r)\cdot \exp(-iE_nt/\hbar)$$
But I have learnt that $\Psi$ has no physical meaning, and that we have to use $\mid \Ps... | You are mistakenly assuming that $|\sum_k a_k|^2 = \sum_k |a_k|^2$.
Make sure you understand why this relation does not hold (find a counterexample), and you should be able to apply it to your problem.
| It's not quite correct that the wavefunction lacks physical meaning. If you left out the imaginary rotation term, you couldn't get interference effects. It'd be kinda okay if your system was in an energy eigenstate, as those do have time symmetry when you look at the probability density with respect to time, but the sa... | https://physics.stackexchange.com |
406,194 | [
"https://softwareengineering.stackexchange.com/questions/406194",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/359185/"
] | I'm wondering what's the best approach, and its advantages, when specifying parameters for the Web Service methods. Best to explain it through examples.
In my (SOAP) WebService, used by a Xamarin mobile app, I have a WebMethod <code>SubmitForm(int, TransactionData, List<Answer>)</code>, where:
<code>int</code> ... | There is a few things to unpack here:
<h2>Having multiple parameters in a method</h2>
It creates a dependency on the caller of the method because it now needs knowledge about <strong>order</strong> of parameters. Having a single parameter that semantically represents what the parameter is will help decouple things a ... | To be honest, <em>three is a lot of leeway with API design that is open to personal preference</em>. That said, that preference should be informed by the trade-offs of design decisions. SOAP is a bit deceptive in a sense because it allows you to behave as if you have separate arguments to your function, but when you ... | https://softwareengineering.stackexchange.com |
67,287 | [
"https://physics.stackexchange.com/questions/67287",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25483/"
] | I am trying to figure out the amount of work done when I walk X miles or for X minutes. So I got Work=Force x Distance and Force=Mass x Acceleration and Acceleration=(change in velocity)/time. I am stuck at the acceleration part. As far as I am concerned my velocity is constant, so Acceleration=0 therefore Force and Wo... | When it comes to modeling the human body and its movements it becomes a lot more complex, because you actually have to model the different components of your body and how they attribute to the system. Plus you are not traveling at a perfectly constant velocity when walking at a steady pace.
If you were to model the w... | When we walk 3 forces act on us normal, gravitational and friction. For normal and gravitation force perpendicular to total displacement so by dot product rule work done is 0.and for static friction 0 displacement, when we displace we don't contact with ground so friction don't do any work.so over all work done in walk... | https://physics.stackexchange.com |
35,033 | [
"https://electronics.stackexchange.com/questions/35033",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7976/"
] | Today I had an interview, there they asked me, if given a microcontroller and Battery then how do you measure the voltage level. Write the steps from scratch with pseudo code.
How can this be done?
| If they were after the pseudo code then that was a bad question; it all depends on the microcontroller. I probably would have given the candidate the microcontroller's datasheet and observe how he works his way through that 300 pages document.
Anyway, you connect the battery to an ADC input (assumptions: microcontro... | I think the catch here is that Microcontrollers need an extrenal reference for their A/D. The default reference is the power supply. You can use an external reference, and divide the battery voltage to something below that reference, but that puts a constant drain on the battery which might not be a good idea.
My ans... | https://electronics.stackexchange.com |
708,958 | [
"https://physics.stackexchange.com/questions/708958",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/319695/"
] | Corpuscular theory of light States that:
<blockquote>
Light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity.
</blockquote>
According to Einstein,
<blockquote>
Light is composed of small particle are known as photons. And ener... | The corpuscular theory was opposed to the wave theory, and was rejected when diffraction experiments confirmed the wave theory. The blackbody spectrum also confirmed the wave theory at low frequencies, but at high frequencies it didn't work. Thus, the photon theory emerged with its counterintuitive mix of particle and ... | As an example, when using the corpuscular theory refraction of light and Snell’s Law is predicted using Newtonian Mechanics but a requirement of the theory is that the speed of light in glass is greater than that in air which is found by experiment not to be true. Theory related to photons have the speeds in different... | https://physics.stackexchange.com |
617,656 | [
"https://electronics.stackexchange.com/questions/617656",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/270326/"
] | We know computer and another device like microcontroller is not accurate in ticking clock comparing to wall clock that using cesium atom.
I heard RTC module is purpose to making accurate the ticking.
But microcontroller that I used is Espressif family which they have built-in Wi-Fi module.
I mean, I can just syncron th... | Only talking about the ESP32:
The internal RTC is quite useful because it keeps running even when the ESP32 reboots (via any kind of software reset, watchdog reset, crashes,...).
It makes totally sense to combine RTC with NTP because the RTC is not that precise and should be adjusted once in a while (e.g. once a day).
... | As long as the ESP has a network connection, you can update the time periodically with it. Then the ESP will calculate the time based on the processor cycles. Since this is not 100% accurate, there may be larger deviations over a longer period of time.
But if you update the clock every hour via NTP, this is negligible.... | https://electronics.stackexchange.com |
664,712 | [
"https://physics.stackexchange.com/questions/664712",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/254513/"
] | I was reading a textbook and found the statement that said that there is no such term as instantaneous work, however the textbook does not give a reason as to why it cannot be defined. To me it sounds perfectly fine to define instantaneous work for particles where force applied remains constant as
<span class="math-con... | To do nonzero work you must apply nonzero force across nonzero distance. To speak of something instantaneous you must do it in time <span class="math-container">$\Delta t \to 0$</span>. To cross nonzero distance in time <span class="math-container">$\Delta t \to 0$</span> one needs <span class="math-container">$v \to \... | One may consider an instant work <span class="math-container">$E(t)$</span> as a work done up to the current instant <span class="math-container">$t$</span> from <span class="math-container">$t=0$</span>.
| https://physics.stackexchange.com |
408,196 | [
"https://physics.stackexchange.com/questions/408196",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101134/"
] | I was reading photoelectric effect , which was completely explained by Einstein. And a bit difficult question , atleast seems to me is whether photoelectric effect is inelastic collision or elastic collision . Every where it is written that photoelectric effect is example of inelastic collision . But as far as I know ... | When a photon interacts with an atom, three things can happen:
<ol>
<li>elastic scattering, when the photon keeps its energy, and changes angle</li>
<li>inelastic scattering, when the photon gives part of its energy to the atomic system and changes angle</li>
<li>absorption, when the photon gives all its energy to th... | Photoelectric effect is an example of inelastic collision as we know that photon transfer it's all energy to electron but electron emit with kinetic energy smaller than the energy of photon as some energy is absorbed as work function Hence it is the example of inelastic collision
| https://physics.stackexchange.com |
5,332 | [
"https://dba.stackexchange.com/questions/5332",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2467/"
] | While testing some migration scripts with a copy of production data (scripts run fine with development data) I found a curious situation. A CONSTRAINT has changed so I'm issuing DROP + ADD commands:
<pre><code>ALTER TABLE A_DUP_CALLE
DROP CONSTRAINT A_DUP_CALLE_UK1;
ALTER TABLE A_DUP_CALLE
ADD CONSTRAINT A_DUP_CALLE_... | At a guess I'd say Marian is right and this is caused by a unique index and constraint having the same name, eg:
<pre><code>create table t( k1 integer, k2 integer,
constraint u1 unique(k1,k2) using index(create unique index u1 on t(k1,k2)),
constraint u2 unique(k2,k1) using index u1);
... | Seems very strange.
You can run:
<pre><code> SELECT *
FROM user_objects
WHERE object_name = 'A_DUP_CALLE_UK1'
</code></pre>
to check if what kind of object that is Oracle complains about. Then you can run the approriate DROP statement for that.
The only other thing I can think of is to drop the table entirely usi... | https://dba.stackexchange.com |
2,823,051 | [
"https://math.stackexchange.com/questions/2823051",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/411542/"
] | Let $X$ be a Banach space. Then $\int_a^b x'(t)dt=x(b)-x(a)$ if $x:[a,b]\rightarrow X $ is continuously differentiable.
I have a few problems understanding what I have to show.
First of all, what is $x'(t)$? From the deffinition of differentiability of functions $f:\mathbb{R}^n\rightarrow \mathbb{R}^m$, it should be ... | In fact, the case of a function $x: [a,b] \to X$ is in some ways somewhat simpler than that of a function $f: \mathbb{R}^n \to \mathbb{R}^m$.
Since the domain of your function is a subset of $\mathbb{R}$, $x$ is differentiable at $t \in [a,b]$ if and only if
$$x'(t) := \lim_{h \to 0} \frac{x(t + h) - x(t)}{h}$$ exists... | One typical approach is to reduce the problem to real valued functions first and
then 'stitch' the result together.
One convenient way of defining the integral $\int f$ is the unique $I \in X$ such that
$\int \phi (f) = \phi(I)$ for all $\phi \in X^*$.
It is straightforward to show that the Frechet derivative of $x$ ... | https://math.stackexchange.com |
124,307 | [
"https://stats.stackexchange.com/questions/124307",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31003/"
] | This started as a simple discussion where everyone thought they new the answer, and ended up with arguments and dozens of paper quotations. Thoughts appreciated.
We have 10 samples: Control, A, B, C, ..., I, with good enough sample size, and the groups have similar variances.
The following comparisons were made using... | Yes, it is necessary to adjust for repeated testing to control for increasing probability of false positives. In terms of reporting, I think it is best to report both raw and adjusted p-values, specifying which correction was used (<em>eg</em> Bonferroni). But why did you do a series of t-tests instead of <em>eg</em> A... | You have multiple treatment groups that are each compared to the control group, but not compared to each other. There's a method called the Dunnett procedure designed specifically for controlling the familywise error rate in this situation.
| https://stats.stackexchange.com |
71,062 | [
"https://chemistry.stackexchange.com/questions/71062",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/42851/"
] | <ol>
<li>One carbonyl group</li>
<li>5 hydroxyl groups </li>
<li>One primary alcholic group</li>
</ol>
| <strong><em>1. Reaction with $\ce{HCN}$, or with hydroxlyamine ($\ce{NH2OH}$)</em></strong>
Glucose reacts with $\ce{HCN}$ to give a cyanohydrin, or with a schiffs base to give an oxime. This shows the presence of a carbonyl group.
<strong><em>2. Reaction with acetic anhydride $\ce{(CH3CO)2O}$</em></strong>
Glucose... | <strong>To prove the presence of <span class="math-container">$\ce{-CHO}$</span> group:</strong>
When glucose reacts with <strong>hydroxylamine</strong>, <strong>oxime</strong> is formed and <strong><em>cyanohydrins are formed</em></strong> on the addition of hydrogen cyanide to it. This reaction can confirm the prese... | https://chemistry.stackexchange.com |
723,477 | [
"https://physics.stackexchange.com/questions/723477",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/250454/"
] | A Brownian particle of mass <span class="math-container">$m$</span> in a heat bath at temperature <span class="math-container">$T_{1}$</span> can be described by:
<span class="math-container">$$\frac{\mathrm dv}{\mathrm dt} = -\frac{\gamma}{m}v + \frac{1}{m}\xi .$$</span>
However, if I assume that a Brownian particle ... | The Langevin Equation for this system can be written as follows (assuming <span class="math-container">$m = 1$</span>):
<span class="math-container">\begin{align}
\dot{v} &= - \left(\gamma_{1}v + \gamma_{2}v\right)+ \xi_{1}(t) + \xi_{2}(t) \\
&= - \gamma v + \xi(t) \tag{$\star$}
\end{align}</span>
where the int... | For the two heat baths, you can write,
<span class="math-container">$$m\frac{\mathrm{d}v}{\mathrm{d}t}=-\gamma_{12}v+\xi_{12}\tag{1}$$</span>
where <span class="math-container">$\gamma_{12}=\gamma_1+\gamma_2$</span> and <span class="math-container">$\xi_{12}=\xi_1(t)+\xi_2(t)$</span>. Note that the autocorrelation of t... | https://physics.stackexchange.com |
280,368 | [
"https://mathoverflow.net/questions/280368",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18050/"
] | Consider the "$m$-th power" map $f:K(\mathbb Z,n)\to K(\mathbb Z,n)$ given by $m\in \mathbb Z\cong H^n(K(\mathbb Z,n),\mathbb Z)\cong [K(\mathbb Z,n), K(\mathbb Z,n)]$. Is it true that in any degree the map $f^*$ on integral cohomology sends any element to a multiple of $m$? It's obviously true in degree $n$ where $f^*... | As you say, we can reduce to the case where $m=p$ is prime. By the universal coefficient theorem we know that $H^*(K(\mathbb{Z},n);\mathbb{Z})/p$ injects in the ring $A^*=H^*(K(\mathbb{Z},n);\mathbb{Z}/p)$, so we just need to show that $f^*$ acts as zero on $A^*$ in positive degrees. The kernel of $f^*$ is an ideal a... | When $n=2$, $K(\mathbb Z,2) = \mathbb CP^{\infty}$, and one can see exactly what is going on: if $x \in H^2(K(\mathbb Z,2);\mathbb Z)$ is the fundamental class, then $m^*(x^k) = m^k x^k$.
For higher $n$, things are complicated I think, in part because $H^*(K(\mathbb Z,n);\mathbb Z)$ is too messy to easily describe. ... | https://mathoverflow.net |
1,571,523 | [
"https://math.stackexchange.com/questions/1571523",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/218189/"
] | Given a nominal rate of 6% per annum. Change it to an effective rate per month.
What I do is:
$$(1+\frac {0.06}{12})^{12}=(1+i)^{12}$$ where $i$ is the effective interest rate per month.
Now what if the question had said that it was the effective annual rate that was 6%, what would I do then?
Is it simply
$$1+{0.... | The answer is no, an easy way to see this
Suppose
$$\frac{|A \cap B|}{|A \cup B|} > \frac{1}{2} \Rightarrow |A \cap B| > \frac{1}{2} |A \cup B| \ge \frac{1}{2}|A| $$
hence $|A \cap B| > \frac{1}{2}|A|$, same argument shows that $|A \cap C| > \frac{1}{2}|A|$
since $B$ and $C$ are disjoint then $$|A| \ge... | Disclaimer: I assume $A,B,C$ are finite, otherwise the division makes little sense.
No, this is not possible.
First of all, you can see that if $B$ and $C$ are <em>not</em> subsets of $A$, you can repace them with $B'=B\cap A$ and $C'=C\cap A$, and the quantities you want to be bigger than $\frac12$ will merely incre... | https://math.stackexchange.com |
153,558 | [
"https://mathoverflow.net/questions/153558",
"https://mathoverflow.net",
"https://mathoverflow.net/users/32389/"
] | <img src="https://i.stack.imgur.com/tsxjs.jpg" alt="Counting in their heads - a painting of Bogdanov-Belsky">
This 1895 painting of Nikolai Bogdanov-Belsky shows mental calculations in the public school of Sergei Rachinsky. Boys in a Russian village school try to calculate $(10^2+11^2+12^2+13^2+14^2)/365$ in their he... | The equation $a^2+b^2+c^2=d^2+e^2$ defines a quadric $Q\subset\mathbb{P}^4$, with a rational point $p=(1,0,0,0,1)$. Therefore it is rational : projecting from $p$, say on the hyperplane $e=0$, defines a birational map $Q --> \mathbb{P}^3$. The inverse of that map, namely
$$ (x,y,z,t)\mapsto (x-\lambda ,y,z,t,\lambd... | <blockquote>
The following recipe (algorithm) generates all solutions. It may be viewed as a parametrization in a general(ized) sense.
</blockquote>
W.l.o.g. we may assume that $c$ is odd. Then
$$ \left(\frac{x-y}2\right)^2 + \left(\frac{u-v}2\right)^2 + c^2
\ =\ \left(\frac{x+y}2\right)^2 + \left(\frac{u+v... | https://mathoverflow.net |
100,401 | [
"https://cs.stackexchange.com/questions/100401",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/96716/"
] | <pre><code>Average memory access time = Hit time + Miss rate * miss penalty
</code></pre>
Assume a computer with only one cache level. What is the exact meaning of hit time? Is it the number of clock cycles to access data from cache? OR Clock cycles to execute an instruction? How does the number of clock cycle per ins... | First of all your equation is for the hierarchical cache where you have to search entire cache in any case irrespective of hit or miss.<br>
For simultaneous cache the first term in right hand side will be multiplied by hit time as well. Hit time is nothing but the time taken to sense the presence of data in cache if th... | It's back to the mechanism of cache. When the cpu wants a data in cache, try to read data from cache. If there is the data in cache, It will fetch data from cache. This time of reading data from cache (the different between the speed of cache memory and register!) will be denoted by <code>Hit time</code>.
If the want... | https://cs.stackexchange.com |
209,844 | [
"https://security.stackexchange.com/questions/209844",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/164535/"
] | Our company has online app that requires to create a business account. Yesterday some suspicious accounts were made and our system automatically blocked the account creators and ip addresses.
And today we have received an email saying "Hello my name is [name], I am white hat hacker and want to perform penetration test... | The person who contacted you was most certainly not a "white-hat hacker". This is not how they operate. The person is most likely trying to scam you in the simplest possible way.
<h1>What is a White-Hat Hacker?</h1>
In the simplest terms, a White-Hat Hacker (henceforth called "White-Hat") is a security professional h... | As MechMK1 mentions, this is just a scam. They are not a White-Hat hacker because that is not how they operate.
I did want to mention something I have heard referred to as "grey-hat hackers." These are hackers who attack a company illegally, then go to the company to work with them to fix the vulnerabilities as a pr... | https://security.stackexchange.com |
407,805 | [
"https://electronics.stackexchange.com/questions/407805",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/115992/"
] | I am trying to design a set of switches in a cmos design.
The switches are supposed to control a number of capacitors and I want to implement them as single NMOS or PMOS transistors.
Based on my understanding I have done the following: Choosing PMOS for switches where the voltage signals switched are closest to VDD an... | Yes, this diode is probably for reverse polarity protection. It does its job but has the disadvantage that about 0.6 V is dropped across it. It needs to be rated for the current, both continuous and surge, as well as the reverse voltage it might encounter. 1N4148 is fine for lower current applications. A shunt diode wi... | any diode that can handle the current and voltage.
zeners have a low breakdown voltage and are thus unsuitable as you surmise. IN4148 can only handle a few hundered milliamperes continuous and so could be used in low current applications.
IN4001 can handle 1A, enough for many small devices.
| https://electronics.stackexchange.com |
15,275 | [
"https://mechanics.stackexchange.com/questions/15275",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/9314/"
] | So... I stripped the bottom half of the threads due to trying to use a washer on a non-washer using drain plug. My aluminum oil pan (and plug) turns out to not be the standard oil pan for the vehicle so I have had difficulty finding the right plug size & thread.
I currently drive it still with the same drain plug.... | So...<br>
I pretty much took in all the advice you guys gave me (and from elsewhere too) and went ahead with the procedure with the oil pan still on the car.<br>
<strong>One big difference</strong> though: Instead of using a tap, I used my oversize plug... I was stubborn and did not want to buy the tap nor take the pan... | This is a pretty common problem. Buy an oversized drain plug tap kit and retap your drain plug threads with the tap. The kit will also usually come with a replacement drain plug that fits the new larger tapped threads.
| https://mechanics.stackexchange.com |
507,642 | [
"https://physics.stackexchange.com/questions/507642",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/227820/"
] | If a ball is kept on a table then there is gravity acting on it as well as a normal reaction force by the table on the ball. But as both the forces are being exerted on the same object i.e. the ball, then it cannot be called a- action reaction pair under Newton's third law of motion because it requires the forces actin... | <blockquote>
If a ball is kept on a table then there is gravity acting on it as well as a normal reaction force by the table on the ball.
</blockquote>
This is correct.
<blockquote>
But as both the forces are being exerted on the same object i.e. the ball, then it cannot be called a- action reaction pair under Ne... | <blockquote>
So, if it is not an action reaction pair, then how is any force being
exerted by the table on the ball? Also, is the ball applying any force
on the table?
</blockquote>
This is the crux of the issue.
There are two completely separate things happening here. One is gravity on the ball, the other is t... | https://physics.stackexchange.com |
1,430,565 | [
"https://math.stackexchange.com/questions/1430565",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/241025/"
] | Let $R$ be a ring with unity such that for each $a$ in $R$ there exists $x$ in $R$ such that $a^2x=a$. Prove the following:
a) $R$ has no nonzero nilpotent elements.
From now on, fix $a \in R$, and let $x \in R$ be such that $a^2x = a$. (As we know, such $x$ exists.)
b) $axa-a$ is nilpotent so $axa=a$.
c) $ax=xa$.
... | a). Suppose $a\ne 0$ and is nilpotent, i.e. there is a $n>1$ such that $a^n=0,\:a^{n-1}\ne 0$. There exists $x\in R$ such that $a^2x=a$. But $0=a^nx=a^{n-2}a^2x=a^{n-1}\ne0$, which is contradiction. So $R$ has no nonzero nilpotent elements.
b). If $axa−a\ne0$, then
$$
(axa−a)^2=\underbrace{axaaxa}_{aax=a}-a^2xa-axa... | Let us finish the proof. It has to be shown that $u$ is invertible. By e) we have $ua=ya=ay=au$ and $uay=y=ayu$. Now let $v=(1+a-ay)$, then
$$uv=u+ua-uay=u+ya-y=1 \quad\text{ and }\quad vu=u+au-ayu=u+ya-y=1.$$
So $u^{-1}=v\in R$ and $u$ is invertible.
| https://math.stackexchange.com |
742,962 | [
"https://physics.stackexchange.com/questions/742962",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/350462/"
] | If I have several wave packets, such that they consist of 1, 2, 3, etc. wavelengths of a single wave with a set frequency/amplitude what do the wave packets vary by?
Ie. what is the generic term for the number of wavelengths in a wave or wave packet?
| The first definition pertains to a real scalar field. The second definition to a complex scalar field. Moreover, the second one can be made much more alike the first as follows. Start from the second definition and distribute the exponential
<span class="math-container">$$\phi(x) = \int\frac{d^3p}{(2\pi)^3}\frac{1}{\sq... | Tong is considering 1 <em>real</em> scalar field, while OP's lecture notes are considering 1 <em>complex</em> scalar field <span class="math-container">$$\phi~=~\frac{\phi_1+i\phi_2}{\sqrt{2}},$$</span> which is equivalent to 2 <em>real</em> scalar fields. It is straightforward to check via canonical quantization that ... | https://physics.stackexchange.com |
2,089,153 | [
"https://math.stackexchange.com/questions/2089153",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/210391/"
] | I am taking a course in functional analysis and while reviewing the definition of a metric and various examples, my professor mentioned that one of the reason we care about swapping (possibly equivalent?) metrics is in pde, since a solution to a pde may be very difficult to find in one metric space, but easier in anoth... | Here's one perspective, involving the notion of distance on function spaces.
Think of different norms on function spaces as giving us different ways of measuring approximations. The basis for this intuition is that norms measure distance between functions and so they let us know in some sense how good approximations ... | This is really embedded into one of the central questions in PDE, namely well-posedness. The well-posedness of a PDE requires three things: existence of a solution, uniqueness of solutions, and continuous dependence of the solution on the data in the problem. In each of these statements there is actually a crucial mi... | https://math.stackexchange.com |
476,132 | [
"https://physics.stackexchange.com/questions/476132",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/93868/"
] | We know for an infinite plane sheet, electric field from the sheet is given by:
<span class="math-container">$$ E = \frac{\sigma}{2\epsilon_0} \hat n$$</span>
Therefore potential is given by
<span class="math-container">$$ - \frac{ \partial V}{\partial n} = \frac{\sigma}{2 \epsilon_0} $$</span>
However, in Griffiths,... | On page 125 of the 4th edition (I'm reading the international edition) of Griffiths that equation is not attributed to an infinite plane sheet but rather to the surface of a conductor, and has to do with the discontinuity in the field. He explains in more detail on page 88 and page 103.
| It could be that he might have been talking about two infinite sheets (metal plates) of charge densities <span class="math-container">$+\sigma$</span> and <span class="math-container">$-\sigma$</span> (capacitor plates or something) - with <span class="math-container">$E=\sigma/\epsilon_0$</span>.
| https://physics.stackexchange.com |
658,874 | [
"https://physics.stackexchange.com/questions/658874",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/310647/"
] | Recently came across Planck's theory, <span class="math-container">$E = h\nu$</span>.
It means that at any frequency, there is given energy. But I also saw that, <span class="math-container">$E$</span> can be <span class="math-container">$0, h\nu, 2h\nu, 3h\nu,...$</span>.
How is it possible that energy can be varied a... | So we have <span class="math-container">$E_1 = h \nu$</span>, i.e. a photon with frequency <span class="math-container">$\nu$</span> has a certain energy <span class="math-container">$E_1$</span>.
From here, <span class="math-container">$E_2 = 2 h \nu$</span> would mean either two photons with frequency <span class="ma... | This is the concept of photon, a quantized energy of radiation. In the wave theory, the energy density <span class="math-container">$u$</span> of a radiation is proportional to amplitude <span class="math-container">$\vec E$</span>:
<span class="math-container">$$ u = \frac{1}{2} \epsilon_0 E^2 $$</span>
which is a fu... | https://physics.stackexchange.com |
26,498 | [
"https://mathoverflow.net/questions/26498",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5309/"
] | While reading a paper, I came across the following peculiar condition:
Let $1 \rightarrow H \rightarrow G \rightarrow G/H \rightarrow 1$ be a short exact sequence, and let $H$ be abelian. We require that any automorphism, $\sigma$, of $G$ that preserves $H$ pointwise and such that $\sigma(g)H=gH$ (preserves cosets poi... | <blockquote>
Short answer: a typical example is G=SL(2,5), H = Z(G) = Z/2Z. If G/H and H are coprime and satisfy the condition, the G = G/H × H is quite dull.
</blockquote>
I'll assume you find this interesting, and want to read about it:
Let G be a group (finite is good), H be an abelian normal subgroup of G, and... | The condition implies that every stabilizing automorphism of $G$ is trivial.
Now the first cohomology group $\text{H}^1(G/H, H)$ is a quotient of the group of stabilizing automorphisms (denoted by $\text{Stab}(G/H,H)$) by the inner automorphisms stabilizing the extensions.
$$\text{H}^1(G/H, H)\cong \text{Stab}(G/H,H)/... | https://mathoverflow.net |
252,521 | [
"https://mathoverflow.net/questions/252521",
"https://mathoverflow.net",
"https://mathoverflow.net/users/99951/"
] | Let $x_1,...,x_m$ be fixed numbers from $[0,1]$ and let $k_1,..., k_m$ be fixed natural numbers ($\geq 1$).
Is the set
$$\{f\in C^\infty[0,1]: f^{(k_1)}(x_1)=0,...,f^{(k_m)}(x_m)=0 \}$$a dense subset of the Banach space $C[0,1])$, with the supremum norm?
| Here is a solution. We prove by induction on $m$. Denote by $P$ the subspace of $C([0,1])$ consisting of the restrictions to $[0,1]$ of the smooth functions $\mathbb{R}\to\mathbb{R}$. Assume first that $x_1,\dotsc, x_m$ are pairwise distinct. Set
$$ P_{x_1,\dotsc, x_k}:=\big\{ p\in P;\;\;p^{(k_i)}(x_i)=0,\;i=1,\d... | Yes, it is dense.
Given $f \in C([0,1])$ and $\epsilon > 0$, it is easy to find a continuous function $g$ which is constant on some $\delta$-neighborhood of each $x_i$ and has $\|f-g\| < \epsilon$. (For instance, Now extend $g$ continuously to all of $\mathbb{R}$, say by making it constant on $(-\infty, 0]$ and... | https://mathoverflow.net |
3,279,354 | [
"https://math.stackexchange.com/questions/3279354",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/455734/"
] | I need to prove that <span class="math-container">$\lim \limits_{x \to 1} x^3-4=-3$</span> with epsilon-delta.
<strong>My work</strong>
<span class="math-container">$\forall \varepsilon > 0 ,\exists \space \delta > 0: 0<|x-1|< \delta \implies |x^3-4+3| < \varepsilon$</span>
Working with the consequent... | Hint:
<span class="math-container">$c\ge d \iff c-d\ge 0 \iff 0\le c-d$</span>.
Add that last inequality to <span class="math-container">$a\le b-c$</span>.
| I think a weighing balance is a good analogy for this sort of thing.
Imagine keeping two weights on two pans of the balance. Let one of them be <span class="math-container">$a$</span> and the other be <span class="math-container">$b-c$</span>. Now this balance is either equal or tilted more towards <span class="math-... | https://math.stackexchange.com |
107,785 | [
"https://dba.stackexchange.com/questions/107785",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/71167/"
] | I would like to return the words beginning with ':' from <code>'select :barns, :fowl, :cows from farm'</code> using regexp_matches.
So far I have:
<pre><code>select regexp_matches('select :barns, :fowl, :cows from farm', '([:])\w+', 'g')
</code></pre>
But this only returns the set <code>{:}, {:}, {:}</code>. I would... | That was an issue with the regex syntax. To get the desired word, you will have to group it under ()
<pre><code> SELECT
regexp_matches(
'select :barns, :fowl, :cows from farm',
'(:\w+)',
'g'
)
</code></pre>
| Perhaps this will fit your needs?
<pre><code>SELECT regexp_matches('select :barns, :fowl, :cows from farm', '(:[a-zA-Z]*)', 'g');
</code></pre>
Cheers!
| https://dba.stackexchange.com |
152,513 | [
"https://mathoverflow.net/questions/152513",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36688/"
] | According to Jairo comment on the first version of this question I revise the question as follows;
Let $g$ be a real analytic Riemannan metric on $S^{2}$. Is it true to say that:
There are at most a finite number of disjoint simple closed geodesics on $S^{2}$.
If the answer is yes put $m$= the sup of the number of su... | As it was shown by Igor, there is no univeral bound on number of such geodesics.
Let me show that the number can not be infinite.
Assume it is possible to get infinite number of such geodesics,
say $\gamma_n$, $n\in\mathbb N$.
Note that the geodesics $\gamma_i$ for $i\le n$ cut $\mathbb S^2$ into surfaces with geodes... | The flat torus has infinitely many disjoint simple closed geodesics.
| https://mathoverflow.net |
10,011 | [
"https://scicomp.stackexchange.com/questions/10011",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/5553/"
] | This was so much easier in Python (so much so that I'm considering going back to matplotlib for data analysis). But really, trying to figure out ROOT and Boost graph library and mathgl makes me want to die.
What I'm thinking for the short term is to somehow export my 2d array to a text file and then import that file ... | There are a couple subtleties to your question that I think are important:
<ul>
<li>You're comparing an interpreted language (Python) to a compiled language (C++).</li>
<li>Most scientific and engineering software is developed with a heavy Linux (and UNIX) bias, and is not usually known for cross-platform compatibility... | Well, for one, you can call gnuplot as a library. Pretty much every command you'd use at the prompt has a similarly-named API function.
| https://scicomp.stackexchange.com |
4,404 | [
"https://quant.stackexchange.com/questions/4404",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/1112/"
] | I'm curious about how to construct the five basic greeks for an equity option portfolio when there are shares of the underlying in the portfolio.
For example, a portfolio of 100 call options and 100 put options has a portfolio delta of <code>100 * call_delta + 100 * put_delta</code> (assuming the 100 calls are the sam... | Ok so for completeness, assuming Black-Scholes and an example portfolio of 100 long <span class="math-container">$C_1$</span>, 100 long <span class="math-container">$C_2$</span> (both on the same underlying), and 10 long shares of the same underlying, <span class="math-container">$S$</span>.
<strong>Portfolio delta:</... | Delta is a derivative of the price with respect of the price of underlying, so for the unit stock position delta is 1 and gamma is obviously 0. As for theta, rho and vega of the stock position, they do not make sense, at least not in the Black-Scholes setting they don't. You would not be able to hedge say vega or theta... | https://quant.stackexchange.com |
258,684 | [
"https://mathoverflow.net/questions/258684",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33064/"
] | Let $S_g$ denote the closed oriented surface of genus $g\geq 2$. Let $x,y$ be two different (upto fixed base point homotopy) but freely homotopic curves, i.e. $y$ is a non-trivial element from a fixed conjugacy class of $x$. If there exist a simple closed loop $z$ (non-trivial) with $i(x,z)\neq 0$ , where $i(\ , \ )$ ... | This statement is most certainly nonsense; I guess what she meant to write was that in order to prove the existence of infinitely many number fields with class number $1$ it is sufficient to prove $h(F_n) = 1$ for infinitely many (and therefore for all) $n$.
| Let $K$ be any subextension of $F_n$. Then the natural map of class groups $\text{Cl}(K) \rightarrow \text{Cl}(F_n)$ is an injection. Indeed, you can see it in terms of unramified abelian extension via global class field theory. If $L$ is an unramified abelian extension of $K$, since $F_n$ is totally ramified at primes... | https://mathoverflow.net |
4,829 | [
"https://robotics.stackexchange.com/questions/4829",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/763/"
] | I have just sized the DC motors I want to use (corresponding to my robot and its intended applications - my figures include a 50% uncertainty factor to account for friction in reducers and other losses). Now I need to actually choose the exact motors I want to buy from the manufacturer (I am targeting maxon motors as I... | The other answer is not quite right. Nominal (rated) torque is the torque at which the motor can run continuously without overheating. This is not the same as the torque at maximum efficiency. A well designed motor will have its rated torque slightly higher than the torque at max. efficiency. Maximum torque of a DC... | No. The nominal (or rated) torque is a torque that motor delivers at nominal speed. The motor is the most efficient at that point. When you take a look at any DC motor characteristics, you will see that the more torque you get, the smaller is the speed (and bigger is the current). Maximum torque is when the motor is st... | https://robotics.stackexchange.com |
55,809 | [
"https://chemistry.stackexchange.com/questions/55809",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/31622/"
] | Let's take an acid, $\ce{HCl}$;
Now what do you mean by the $p\ce{H}$ of $\ce{HCl}$? Does $\ce{HCl}$
have free floating ions in it like water does?
Also, why can't the $p\ce{H}$ value of a substance be less than $0$? Like can't a substance have $10^1~\rm M$ of $\ce{H+}$ ions? In that case won't the $p\ce{H}$ be $-1$... | <strong>Dissociation of ions</strong>
Water, as you probably know, is highly polar and has a very high dielectric constant. When ionic compounds are added to the water, the electrostatic force of attraction between the ions get very weak and hence will result in dissociation of the compound.
The percentage of dissoci... | Water is a weak electrolyte, which means that it can act either as an acid or base. The ionisation reaction is 2H$_2$O = OH$^-$ + H$_3$O$^+$ and is highly endothermic, and the equilibrium constant <br/>$K_w$ = [OH$^-$][ H$_3$O$^+$] increases rapidly with temperature. This equilibrium exists in solution no matter what ... | https://chemistry.stackexchange.com |
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