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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13,714 | [
"https://engineering.stackexchange.com/questions/13714",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/9993/"
] | I am trying to create a simulation for car suspension and tyre physics and to do the tyre physics I need to know how much weight is over the friction point that is under the spring.
| The force associated with springs is well described by Hooke's law. The spring force is given by,
$$ F = k x $$
where $F$ is the spring force, $x$ is the displacement of the spring from its original resting position, and $k$ is the spring constant in units of force per length.
| The weight supported by each spring will depend on how the weight is distributed by the vehicle. Most vehicles are slightly heavier at the front so, a 60:40% or 55:45% distribution would be a good approximation for most cars. Sports cars get closer to an even split. Then, you would subtract the weight of the tyre an... | https://engineering.stackexchange.com |
128,815 | [
"https://stats.stackexchange.com/questions/128815",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/32346/"
] | I'm trying to estimate the value of a property depending on the property characteristics. I did some research and I found out, that it would be better to use the <strong>Hedonic Model/Regression</strong> instead of <strong>Linear Square Regression</strong>.
After reading a couple of papers about it, I still have some ... | 1) There is no such thing as a hedonic regression as estimation method, you will use least squares / maximum likelihood estimator.
2) I understood that your goal is to estimate effects of different characteristic, it might be that your understanding concerning different factors affecting pricing is not complete. Of c... | Some hints on your question 2 re environmental characteristics.
A. Care is needed in interpreting estimated coefficients as small, since their size will depend on the units in which both the independent and the dependent variables are measured. It may be helpful to consider what the percentage effect on the dependent... | https://stats.stackexchange.com |
5,282 | [
"https://physics.stackexchange.com/questions/5282",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1495/"
] | That is, are they identical to their anti-particles? (Any results of double beta decay experiments?)
| Great question. The experimental situation remains inconclusive. However, theoretically, there exists a damn good reason to think that the neutrinos have Majorana masses - and, consequently, the double beta decays should be possible. It's called the seesaw mechanism.
The mechanism is justified by an intriguing observa... | This is just a clarification regarding the see-saw. The see-saw is inside a particular model--- an SO(10) GUT. It is interesting, but Majorana neutrino masses of the right order of magnitude do not require an SO(10) GUT, or any other type of GUT, in order to work. All they require is that there is some new interactions... | https://physics.stackexchange.com |
556,242 | [
"https://stats.stackexchange.com/questions/556242",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/337106/"
] | This is a very simplistic question, but is the "grand mean of the data" another name for the null hypothesis of regression? This horizontal straight line (slope of zero) is what we are comparing our model to, to see if it's a better fit?
| <strong>YES</strong>
But it depends on what you mean by "the null hypothesis of regression".
Software packages like <code>R</code> give an overall test of the regression. This is testing if any of the non-intercept parameters are nonzero.
<span class="math-container">$$
y = \beta_0 + \beta_1x_1 +\cdots+\beta_... | The <em>Grand Mean</em> of the data is the pooled average of a parameter.
The basic null hypothesis of linear regression for the relationship: <span class="math-container">$y = \beta_0 + \beta_1 x+\epsilon$</span>,
is <span class="math-container">$H_0:\beta_1 = 0$</span>.
If you were to consider <span class="math-conta... | https://stats.stackexchange.com |
461,611 | [
"https://physics.stackexchange.com/questions/461611",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/174380/"
] | <blockquote>
I'm given the equation <span class="math-container">$ V = 120X_1 + 70X_2+X_1X_2*(15X_1+8X_2)$</span> and told to calculate <span class="math-container">$\bar V_1 $</span> & <span class="math-container">$ \bar V_2$</span> and then to show that <span class="math-container">$ V = \Sigma_i X_i*\bar V_i$<... | As mentioned in the comments, it all depends on what is constant in your system. For example, if the linear velocity <span class="math-container">$v$</span> is constant as you move outward from the center of rotation, then <span class="math-container">$\omega=v/R$</span> must be decreasing. So, if you wanted to see how... | An example might be helpful: consider a car going in circles.
<ul>
<li>Assume the car has constant speed <span class="math-container">$v$</span>. In sharp curves (small <span class="math-container">$R$</span>), the centripetal force that is required to keep the car on the road is large and for large <span class="math... | https://physics.stackexchange.com |
21,662 | [
"https://dsp.stackexchange.com/questions/21662",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/3666/"
] | Since a couple of months I started working on the extraction (estimation) of signal frequency and amplitude components by means of two different time-frequency approaches, namely the Hilbert transform and the Teager-Kaiser energy operator.
I tested both methods on standard signals, such as chirps, sine, cosine, etc. T... | This paper may be of interest:
David Vakman, "On the Analytic Signal, the Teager-Kaiser Energy Algorithm, and Other Methods for Defining Amplitude and Frequency." IEEE Trans. Signal Processing. (1996)
Summarising from the paper:
$$\Psi(u) = a^2w^2 = [u'(t)]^2 - u(t)u''(t)$$
$$\Psi'(u') = a^2w^4 = [u''(t)]^2 - u'(t)u... | You might try applying a median filter to avoid the extreme glitches?
In Matlab, <code>medfilt1</code>.
| https://dsp.stackexchange.com |
99,088 | [
"https://physics.stackexchange.com/questions/99088",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23290/"
] | I'm a philosophy undergraduate student who has an interest in, and respect for (as most people do) what physicists know about the world.
In philosophy, the traditional criterion of physical existence has been extension in some dimension of space (not necessarily the three most familiar dimensions). For example, we mi... | Giving a precise answer to this is I suspect impossible, as the very notion of physical existence is quite subjective. Please therefore treat this answer as subjective - I would not expect all physicists to agree with it. But here goes…
As a first stab, I’d be inclined to reason a bit like this: Your suggested philo... | What is gravitation's extension in space to an observer in vacuum free fall versus one not? Does time exist in space?
| https://physics.stackexchange.com |
420,050 | [
"https://mathoverflow.net/questions/420050",
"https://mathoverflow.net",
"https://mathoverflow.net/users/165301/"
] | Consider the set
<span class="math-container">$$\\\{ (A,B) \in \mathbb{P}^{n\times n-1} \times \mathbb{P}^{n\times n -1} : \text{im}(A) \subseteq \text{im}(B)\}.$$</span>
That is, this is the set of pairs of square matrices <span class="math-container">$(A,B)$</span> so that the image of <span class="math-container">$A... | I am making my comment an answer. The specified set is not Zariski closed. If it were, then its intersection with every Zariski closed subset <span class="math-container">$C$</span> would be relatively closed in <span class="math-container">$C$</span>. But now let <span class="math-container">$C$</span> be the curve... | Another way to see your set is not closed: it is evidently not the whole space of pairs, but yet it contains the open dense set <span class="math-container">$U\times U$</span> where <span class="math-container">$U \subset \mathbb{P}^{n^2-1}$</span> consists of (classes of) invertible matrices. So your set is different ... | https://mathoverflow.net |
1,539,918 | [
"https://math.stackexchange.com/questions/1539918",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/276586/"
] | Im trying to find the inverse laplace of : $ F(s)= \frac{s+8}{s^{2}+4s+5}$
I reached the following: $$ F(s)= \frac{s}{(s+2)^{2}+1} + 8 \times \frac{1}{(s+2)^{2}+1}$$
Now i have the 2nd term in the right form, but my first one is not so im confused on how to go about putting it :S.
So basically in the first part how ... | Let $\mathfrak{p}$ be a maximal element (maybe the symbol is a bit presumptuous). You should first tell me why $\mathfrak{p}$ isn't the whole ring. Now take two elements $a,b$ not contained in $\mathfrak{p}$. Then, for instance, the ideal $\mathfrak{p} + Ra$ properly contains $\mathfrak{p}$ and hence can't be one of th... | If you are familiar with localizations, they provide a very nice alternate way to frame this argument. By considering the ring $S=R/B$, it suffices to show the following: if $x\in S$ is in every prime ideal of $S$, then $x^n=0$ for some $n\in\mathbb{N}$. To prove this, consider the localization $S[x^{-1}]$ (i.e., the... | https://math.stackexchange.com |
136,618 | [
"https://mathoverflow.net/questions/136618",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31310/"
] | are there any invariants of matrices, that are not affected by row- and/or column permutations?
To me it seems that the sequence of singular values could be such an invariant; am I right, resp. are there other invariants?
My guess for the sequence of singular values comes from the observation that a row permutation $... | As said in the comment, the <em>permanent</em> of a square matrix is such an invariant.
It is interesting for many topics in combinatorics.
For $A=(a_{ij})$ it is defined as $\Sigma_{\sigma \in S_n}\prod_{i=1}^na_{i,\sigma(i)}$.
For $n=3$, as an example,
$Perm(A)=a_{11}a_{22}a_{33} + a_{11}a_{23}a_{32} + a_{12}a_{21}a... | Singular values are definitely an invariant (because permutation matrices are orthogonal) but not a complete invariant! If you modify only the rows and columns order you do not modify the list of entries of your matrix. And there are many (=uncountably many) matrices with the same singular values.
Some other invariant... | https://mathoverflow.net |
285,479 | [
"https://dba.stackexchange.com/questions/285479",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/224076/"
] | I have a large table with 1 billion+ records. These are the important columns:
<pre><code>CREATE TABLE BigTable
(
id BIGSERIAL PRIMARY KEY NOT NULL,
hexid VARCHAR(255), -- usually 24 or 48 characters
type VARCHAR(255),
<and other columns>
);
</code></pre>
I need to find some records matching on a sub... | The version with <code>IN</code> will be slightly faster, because <code>= ANY</code> is cheaper than <code>~</code>.
The estimate suggests otherwise, but only because it estimates a different number of result rows.
You can make these queries faster with an index on the more selective condition.
| You can get a pretty good estimate with:
<pre><code>CREATE TABLE foo AS SELECT * FROM bigtable LIMIT 1000000;
</code></pre>
And run your query on this subset, which should be a lot faster than on the huge table. Since postgres regexps are slow, IN() should win by a large margin. I'll try with a bunch of generated data:... | https://dba.stackexchange.com |
19,361 | [
"https://physics.stackexchange.com/questions/19361",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7047/"
] | I've been looking at a few papers in experimental physics (from the ATLAS collaboration, for example) and I've often run across phrases such as "high-$p_T$ electron." What exactly is $p_T$? Is it simply momentum, but with the component parallel to the main beam projected off?
Also, why is $p_T$, as opposed to $p$, an... | The component of momentum transverse (i.e. perpendicular) to the beam line.
It's importance arises because momentum along the beamline may just be left over from the beam particles, while the transverse momentum is always associated with whatever physics happened at the vertex.
That is, when two protons collide, they... | The collisions of protons are complicated, because the proton has a big mess inside. In order to see simple collisions, you want to find those cases where a single quark or gluon, a single parton scattered off another parton in a nearly direct collision. Such collisions are relatively rare, most proton proton collision... | https://physics.stackexchange.com |
106,060 | [
"https://dba.stackexchange.com/questions/106060",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/55677/"
] | I have a table in MySQL.
The table structure is as follows.
<pre><code>id | emp_id | call_start | call_end | call_type
--------------------------------------------------------
1 | 20043 | 20:20:10 | 20:21:19 | SALES
2 | 20043 | 20:25:34 | 20:27:12 | NON-SALES
3 | 20044 | 21:25:3... | Thanks for all your efforts,
I did this way.
<pre><code>select a.emp_id, a.total, b.TOTAL_CALLS
from (SELECT a.emp_id,count(*) total FROM `Dash_Agent_Disp` a where a.call_type = 'sales' GROUP BY a.emp_id) a,
(select emp_id, count(*) total_calls from `Dash_Agent_Disp` group by emp_id) b
WHERE a.emp_id=b.emp_id
</code... | You need to filter you subquery with <code>call_type='SALES'</code>, then run:
I use your information:
<pre><code>INSERT INTO test.Dash_Agent_Disp
(id,emp_id,call_start,call_end,call_type)
VALUES
('1','20043','20:20:10','20:21:19','SALES'),
('2','20043','20:25:34','20:27:12','NON-SALES'),
('3','20044'... | https://dba.stackexchange.com |
281,321 | [
"https://electronics.stackexchange.com/questions/281321",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/136470/"
] | By using the open loop transfer function for a control system, how would you then sketch the Nyquist plot by hand?
I'm aware you'd substitute any <span class="math-container">\$s\$</span> term for <span class="math-container">\$j\omega\$</span> and then rationalise the denominator by moving the <span class="math-contai... | Most of the answers are correct.
Trying to condense them: the feedback doesn't count. Whatever the 6 resistors and Vo try to contribute to V-, all it ever sees is Vs. Similarly, the 25k load doesn't matter. So, all the op amp sees is Vs which has it banging its head against the op amp's rails, whatever they are, w... | Assuming Vs is a conventional 0\$\Omega\$ source impedance independent voltage source, the gain is -\$\infty\$.
All the resistors can be ignored since they are connected between 'stiff' (0\$\Omega\$ impedance) voltage sources.
Imagine the input Vs is a very tiny voltage (say +1uV or whatever you consider to be inco... | https://electronics.stackexchange.com |
55,325 | [
"https://datascience.stackexchange.com/questions/55325",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/71218/"
] | <pre><code>x_train, x_test = train_test_split(x, test_size = 0.3,random_state=250)
y_train, y_test = train_test_split(y, test_size = 0.3,random_state=250)
</code></pre>
Is this the way to coincide the same individuals in <code>x_test</code> and <code>y_test</code> as well as <code>x_train</code> and <code>y_train</cod... | <code>train_test_split</code> has this capability built-in. Just pass all of the data in the first go like:
<h3>Code:</h3>
<pre><code>x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.3, random_state=250)
</code></pre>
<h3>Test Code:</h3>
<pre><code>from sklearn.model_selection import train_tes... | I would recommend using indices to split the dataset into train and test for both features and targets.
| https://datascience.stackexchange.com |
8,594 | [
"https://scicomp.stackexchange.com/questions/8594",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/5089/"
] | I've been using LAPACK <code>dgeev</code> in FORTRAN in the last months spending hours to diagonalize ~4000*4000 matrices. It takes about 2'75 hours to find eigenvalues and eigenvectors this way. I thought FORTRAN should be faster than Mathematica as it usually is for this kind of tasks. After all this hard work and co... | The LAPACK/BLAS implementation surely matters, but even with the reference BLAS (via the Numpy python library) it took less than 15 minutes (on a Core i7 laptop) to compute the eigenvalues for a random 4000*4000 real matrix.
Was your matrix real or complex? Are you able to check the performance from eg. R or python, ... | The LAPACK routine dgeev in turn calls routines from the BLAS library to perform more basic linear algebra such as matrix-matrix multiplications. It's likely that the slow performance of dgeev on your problem is caused by using a BLAS library that isn't highly optimized.
Do you know which implementation of BLAS yo... | https://scicomp.stackexchange.com |
1,363,891 | [
"https://math.stackexchange.com/questions/1363891",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/255031/"
] | Let $$\theta(p) = \sum_{i=1}^n f_i(p) \, dx_i$$
be a $1$-form in local coordinates.
then we define $F^*(\omega(p))(X_1,\ldots,X_n) = \omega(F(p))(DF(p)(X_1),\ldots,DF(p)(X_n))$ as the pullback of a general n-form
My question is now, can we also express the pullback of the $1$-form $\theta$ in local coordinates?
I sus... | I do not think there is any geometric intuition behind the convergence you mentioned. As much as there is no geometric intuition which can help solving Zeno's paradox of the Tortoise and Achilles.
Indeed, the convergence is due to how the integral is defined - in terms of Riemann sums (here I assume you are talking a... | I made drawings of both functions.
With respect to 1/x^2 I was very strict: I calculated the area under the straight line connecting ( 1,1) and (2,1/4) and so on. This gives two series that are both convergent by comparison with the series 1, 1/2, 1/4 ....The area of this series is larger than the area we are interest... | https://math.stackexchange.com |
653,274 | [
"https://physics.stackexchange.com/questions/653274",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/292137/"
] | In Newton's <span class="math-container">$3$</span>rd law of motion, it states that
<blockquote>
All forces between two objects exist in equal magnitude and opposite direction
</blockquote>
How did Newton knew exactly that the "reaction" force will be equal in magnitude to the "action" force? What w... | <blockquote>
but because of the difference in mass, the rock is the one moving.
</blockquote>
Actually, <em>both</em> you and the rock are moving. The difference in mass just causes the rock to move faster - but you move as well (this is according to Newton's 2nd law).
<blockquote>
how do we know for sure that the rock... | To add to Steeven's answer:
The action-reaction principle of Newton's third law leads to the conservation of momentum. If the action-reaction principle were not true, then neither would the law of conservation of momentum be true.
And we know that the law of conservation of momentum always holds true.
| https://physics.stackexchange.com |
146,439 | [
"https://softwareengineering.stackexchange.com/questions/146439",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/42303/"
] | I have a reservation system that I have coded and my final task is to allow the user to enter a set of dates and then show them all available options.
The reservation table is set up with <code>unit_id</code>, <code>check_in</code> and <code>check_out</code>. There are twelve different unit numbers.
So I have to some... | I come across this kind of requirement all the time. Let's say you have a date range you want to check (ie, find free units for) which is defined with a start and an end date. In the database, for the sake of making it clear what we're talking about, lets say existing reservations have a first and a last date (of the r... | Lets assume that the customer wants the date range <code>date_from</code> to <code>date_to</code>, where <code>date_from <= date_to</code>. You told us that you have a reservation table, let's call it <code>reservation_table</code>.
Using the column names you provided, i.e. <code>reservation_table</code> = <code>un... | https://softwareengineering.stackexchange.com |
41,484 | [
"https://mathoverflow.net/questions/41484",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9891/"
] | Let G be a semisimple Lie group and let k be some number field. Let A be a finite index subgroup of some group B which is discrete and Zariski dense in G. Suppose A is in G(k). Then can we expect that B is in G(k') where k' is a finite Galois extension of k? When can we expect k'=k?
| I'll prove this when $G=SL(n,\mathbb{C})$. So assume $B\leq SL(n,\mathbb{C})$ is discrete, and $A\leq B$ is a finite-index subgroup. Let $A'\lhd A$ such that $A'\lhd B$ is the core, which is also finite index (by considering the kernel of the action on cosets of $A$ in $B$). Suppose that $A\subset SL(n,k)$ where $k$ is... | Agol's argument is really nice. For what it is worth, I would like to add a few comments. Suppose we assume that $G$ is absolutely simple (in particular, $G$ is centreless). Then Agol's argument shows that $k'=k$. Secondly, one can replace $G$ by a conjugate in its adjoint representation and assume that the smaller Za... | https://mathoverflow.net |
61,041 | [
"https://mechanics.stackexchange.com/questions/61041",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/43418/"
] | Experienced problems starting engine.
Removed battery, checked fluid level, hooked it up to trickle charge, and it readily accepted the charge.
Put it back in and reconnected both cables, and engine started.
Allowed to sit overnight, and checked battery voltage at 10.3VDC and engine would not crank.
Jumped off and ... | What I suspect is, your battery can only charge with what is considered a "surface charge". This usually means one or more of the cells are bad in the battery. When in this condition, the battery will somewhat accept a charge, then will sometimes work. Once the surface charge is gone from it, which can happen... | The zap you hear when you reconnect the battery and the immediate voltage drop suggest you have a short somewhere which is trying to consume a lot more current than your battery can supply. Have you recently done any work on the car? any bulbs blown? any fuses burnt out?
If you have any cable harnesses visible inspect ... | https://mechanics.stackexchange.com |
51,004 | [
"https://security.stackexchange.com/questions/51004",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/39551/"
] | If you don't want to read all of the details, skip to the bottom; I'll make a summary.
I created a computer program as a proof of concept (I threw it together in 12 hours, so I wrote it in Visual Basic to get it done quickly). Normally I'd be using Linux but my client wanted a Windows version, so I resorted to VB.
An... | The most important part of this post is "with antivirus".
Do you have automatic submissions turned on? If so, those computers might have sent in an 'automatic submission' to the AV mothership at some point. It might have been flagged for evaluation, and possibly run in a controlled environment to see what behavior i... | sounds like your software should have some sort of authentication with your 'online service'
If your online service gets pinged, would it report that as a connected user? It is possible its just a robot hitting your online service?
| https://security.stackexchange.com |
68,999 | [
"https://datascience.stackexchange.com/questions/68999",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/76653/"
] | When I have the data set to train a model with SVM, which procedure is performed first, cross validation or grid search? I have read this in a couple of books but I don't know in what order all this should be done. If cross-validation is first performed, what hyperparameters do I use there if I have not found the optim... | Well, grid search involves finding best hyperparameters. Best according to what data set? a held out validation set. If that's what you mean by cross validation, then they necessarily happen simultaneously.
It doesn't really make sense to do something called cross validation before testing hyperparams - indeed, what w... | <strong>Both are done together!</strong>
Grid search is how you determine the hyperparameters of a model whereas, Cross-Validation is the process of running your model on a data separate from training datase to gauge your models performance on a particular hyperparameter.
Grid search allows you to have some potentia... | https://datascience.stackexchange.com |
74,871 | [
"https://mechanics.stackexchange.com/questions/74871",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/54356/"
] | I’ve had this car for about a month, and never had a single problem starting up. This morning, after filling the gas tank, I turn the key and absolutely nothing. No electronics or anything. I tried to push start it among a few other checks, and after sitting for about 20 min, the electronics came back on. So, I tried t... | I think you are looking at the wrong area of the car. If the electronics didn't come on, this is an electrical power issue, not a fueling issue. I'd check to ensure all connections are good from the battery, to wires, etc. Make sure your ground connection is clean. Make sure the battery is up to snuff (you may need to ... | In addition to what @paulster2 suggests, following on from your comment -
<blockquote>
"I would turn the ignition on periodically after checking various
things, like oil and fuses, to see it came back on...and one time, it
did!"
</blockquote>
I would also be checking for a faulty ignition switch.
| https://mechanics.stackexchange.com |
1,088,936 | [
"https://math.stackexchange.com/questions/1088936",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/60353/"
] | Prove that if a set A of natural numbers contains $n_0$ and that whenever A contains k it also contains k+1.
<strong>Prove that A contains all natural numbers $ \geq n_0 $</strong>
This is rather similar to a question already on this site but its not quite the same and the only answer to that question is incomplete.... | Suppose that not every element larger than $n_0$ is in $A$, consider the set of numbers larger than $n_0$ that do not belong to $A$ and call this set $B$,this set is not empty, apply the well ordering principle to find the least element of this set, call it $m$.
Since $m>n_0$ we conclude $m-1\geq n_0$ since $m$ wa... | Your proof seems circular. You conclude in case 1 that $D=N$, however, that seems to require the statement you are trying to prove.
Different way:
Let $B=\{ n \in N \mid n\geq n_0 and n\notin A \}$. Now suppose that the statement is not true. Then, since $B$ is a subset of $N$, $B$ must contain a smallest element, $x... | https://math.stackexchange.com |
108,332 | [
"https://security.stackexchange.com/questions/108332",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/94733/"
] | I use my personal lap top for work. The other day I took it in an opened it, logged in and there was a NSFW page open from when I last used it at home. I immediately closed the (incognito) page, no clicks or further browsing. Will that have been captured as I was logged into the wifi?
| It depends on several factors.
If you restored the PC from sleep/slumber/hibernation, then what you saw was the PC state before sleep, not something that had just been downloaded. No traffic was generated, nothing could possibly have been logged.
<strong>But</strong> the page might have had some active content that w... | Typically, a network admin can only see traffic that goes over the network. Unless they have installed special monitoring tools on your computer, they can not see what programs you have running. If you load a new web page, they'll definitely see it because it has to pull the data from the internet over the network, but... | https://security.stackexchange.com |
128,334 | [
"https://security.stackexchange.com/questions/128334",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/115613/"
] | I am no security expert, but do know some concepts.
We have a web application which currently uses Java Applets to do some operations on files in Client's File system (Browse, create, upload and download). Since Java applet support is being removed. We are planning to go for client side websocket server. Which will be... | You're trying to do the impossible here. You're having the localhost server authenticate the client application running in the browser. This is <strong>impossible</strong> to do securely.
What you would want is to write a browser plugin/add-on. The browser plugin/add-on should only activate itself when visiting author... | @AEonAX : you can use the double handshake token method to use authorize and take care of security. Encryption of token can also be done.
Sheldon
| https://security.stackexchange.com |
66,067 | [
"https://datascience.stackexchange.com/questions/66067",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/87993/"
] | <strong>Problem statement :</strong>
We have documents with list of words in them.
Overall these documents are classified into 2 group (say, good quality vs bad)
docs -
<pre><code>doc1 = [w1,w2,w3,w4]
doc2 = [w4,w3,w3,w4]
doc3 = [w2,w4,w8,w1]
doc4 = [w5,w4,w0,w9]
</code></pre>
doc group -
<pre><code>good_grp = [do... | I think here you must maintain the actual tf-idf and create corpus over it.. Assuming you already have lables for documents available. You can rum classification over it.
Best classification I am anticipating for this problem would be naive bayes..
| A direct way to find the words which are the most representative of a class is to calculate the probability of the class given a word:
<span class="math-container">$$p(c|w)=\frac{\#\{\ d\ |\ label(d)=c\ \land w\in d\}}{\#\{\ d\ |\ w\in d\ \}}$$</span>
Ranking the words according to their probability <span class="mat... | https://datascience.stackexchange.com |
635,438 | [
"https://physics.stackexchange.com/questions/635438",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I'm in Junior High and I still have some confusion towards speed and velocity. They sound like the same thing, where some object moves in a given direction, but there is a difference from both topics.
So where does speed and velocity differ from their characteristics?
| Speed is the magnitude of the velocity. It's a scalar quantity, which basically means that it's a "normal" number. Velocity is a vector, which basically means that it has a direction. So if one car is going north at 30 m/s and another is going south at 30 m/s, they have the same speed, but they have different... | Velocity is a vector. It has both an magnitude and a direction. Speed is a scalar. It does not refer to a direction. Speed is the magnitude of velocity.
For example, a car travelling 60 mph in the Northbound lane of a highway has the same speed as a car travelling 60 mph in the Southbound lane. However, if the velocity... | https://physics.stackexchange.com |
25,925 | [
"https://cstheory.stackexchange.com/questions/25925",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/25556/"
] | Given a finite language $L$ with $|L|$ number of elements, what is $|L^i|$ (the language $L$ concatenated with itself $i$ times)? If there is no exact result, is there an upper/lower bound?
Define concatenation of $L$ with itself to be as the classical definition: $LL = \{wx \space | \space w,x \in L\}$. Similarly, $L... | You can show $ |L|^i $ is a tight upper bound by using the following language:
<blockquote>
$ L = \{ ab,aab,aaab,\ldots,a^kb \mid k \geq 1 \}. $
</blockquote>
Any concatenation gives a new string. For a lower bound, I can suggest the following unary language:
<blockquote>
$ U = \{a,aa,aaa,\ldots,a^k \mid k \geq ... | If $L$ is any finite code (that is, if $L^*$ is a free monoid of basis $L$), then $|L^i| = |L|^i$. This is the case in particular if $L$ is a prefix code: no word of $L$ is a proper prefix of another word of $L$.
The lower bound is $i|L| - i$ (a slight improvement over the suggested $i|L| - i + 1$). It is obtained fo... | https://cstheory.stackexchange.com |
136,557 | [
"https://electronics.stackexchange.com/questions/136557",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54402/"
] | I'm trying to understand the behavior of batteries a bit more. I've noticed that chargers for given batteries have different current capabilities. Do batteries need to be charged with a voltage that is near their nominal output? E.g., a 12V battery should be charged with 12V? If one charger for a battery has a 1A ou... | Batteries are usually charged with a bit more voltage than their "full" voltage, but the details vary widely. Often batteries that are deeply discharged need to be brought up slowly until they are reasonably full. Most batteries can be charged with simple logic that applies some fixed voltage or some fixed current, w... | A battery charger must produce a voltage a little higher than the battery voltage - how much higher depends on the battery chemistry, temperature, and other things.
1 Amp and 2 Amp chargers for a given battery type will produce the same final voltage, but the 2 Amp charger can deliver a higher currrent into a discharg... | https://electronics.stackexchange.com |
61,068 | [
"https://electronics.stackexchange.com/questions/61068",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20103/"
] | Pic18fxxx family has a lot advantages and improvements from the pic16fxxx family of microcontrollers. What is the particular feature that make them better for C programming than the pic16fxxx devices?
| I don't know about "ideal for". That's a marketing term that has no place in a learned discussion.
However, one big advantage of the PIC 18 architecture versus the original PIC 16 architecture, especially related to compilers, is that it is possible to implement a software data stack on a PIC 18 with single instructi... | Some C compilers store local variables on a hardware or software stack. When code enters a subroutine, the size of its local variables is added to or subtracted from a register which is used as a stack/frame pointer. When the "enhanced instruction set" is enabled, PIC18Fxx instructions can access the first ~96 bytes ... | https://electronics.stackexchange.com |
36,058 | [
"https://physics.stackexchange.com/questions/36058",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9960/"
] | In Zee's quantum field theory in a nutshell, 2nd edition, pg 551 he has the charge of a Dirac field written as
<blockquote>
$Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s \{b^\dagger(p,s)b(p,s)-d^\dagger(p,s)d(p,s)\}$
</blockquote>
He then goes onto write
<blockquote>
We find $[Q,\psi(0)]=-\psi(0)$, thus showing t... | $$[Q,\psi(0)]=-\psi(0)\implies [Q,d^\dagger]=-d^\dagger $$
If the charge of a general state is $q$:
$$Q|\Psi\rangle=q|\Psi\rangle $$
Then the charge of a state with one more $d$-quantum is:
$$Qd^\dagger|\Psi\rangle=(q-1)|\Psi\rangle$$
Then the $d$-quantum has negative charge.
Analogously for $b$.
| From the basic anticommutators such as $[b,b^\dagger]\sim \delta$ – according to your normalizations etc. – and similarly for the $d$'s, it follows that the commutator of the first, $b^\dagger b$ term, with any $b$ is $-b$ (the same one). The second term doesn't contribute. This $[Q,b]=-b$ is interpreted as "$b$ carrie... | https://physics.stackexchange.com |
371,728 | [
"https://softwareengineering.stackexchange.com/questions/371728",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/306950/"
] | I am beginning with unit testing in c#.
Here is my converter:
<pre><code>public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
{
int c = 0;
if (value != null)
{
var path = value.ToString();
for (int x = 0; x < path.Length; x++)
{
... | First, I would like to separate the design approach from the concept of frameworks. Dependency injection at its simplest and most fundamental level is simply:
<blockquote>
A parent object provides all the dependencies required to the child object.
</blockquote>
That's it. Note, that nothing in that requires interfa... | Dependency injection is, like most patterns, a <strong>solution to problems</strong>. So start by asking if you even have the problem in the first place. If not, then using the pattern most likely will make the code <em>worse</em>.
Consider first if you can reduce or eliminate dependencies. All other things being equa... | https://softwareengineering.stackexchange.com |
3,159 | [
"https://scicomp.stackexchange.com/questions/3159",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/1965/"
] | Is it a good idea to use <code>vector<vector<double>></code> (using std) to form a matrix class for high performance scientific computing code?
If the answer is no. Why? Thanks
| It's a bad idea because vector needs to allocate as many objects in space as there are rows in your matrix. Allocation is expensive, but primarily it is a bad idea because the data of your matrix now exists in a number of arrays scattered around memory, rather than all in one place where the processor cache can easily ... | In addition to the reasons Wolfgang mentioned, if you use a <code>vector<vector<double> ></code>, you'll have to dereference it twice every time you want to retrieve an element, which is more computationally costly than a single dereferencing operation. One typical approach is to allocate a single array (a ... | https://scicomp.stackexchange.com |
382,335 | [
"https://physics.stackexchange.com/questions/382335",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28359/"
] | A point charge $q$ is located at a distance $l$ from the infinite conducting plane. What amount of work has to be performed in order to slowly remove this charge very far from the plane? (<em>Irodov 3.55</em>)
I understand there is a method of images for solving such problems. I did use it, but I have three reasonable... | For the first two methods you have missed out an important idea.
The electric potential energy is "stored" in the electric field.
With your first two methods you have found the energy stored by the system of two charges in the electric field which occupies the "whole of space".
The infinite conducting plates cut... | Method of images is being used only to solve the problem, there is not any real point charge behind the plane. So in order to find the work done in dismantling the system if we follow the usual process by which we dismantle the two point charges placed at a distance, if we move one charge with respect to origin while k... | https://physics.stackexchange.com |
438,890 | [
"https://stats.stackexchange.com/questions/438890",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/181073/"
] | I am dealing with a linear system of equations that I am solving by OLS:
<span class="math-container">$$
\mathbf{y} = \mathbf{X} \mathbf{p} + \mathbf{e}
$$</span>
Where I have <span class="math-container">$n$</span> samples and <span class="math-container">$k$</span> parameters (<span class="math-container">$\mathbf{... | If you have a linear model such as:
<span class="math-container">$$
\mathbf{y} = \mathbf{X} \mathbf{p} + \mathbf{e},
$$</span>
where <span class="math-container">$\mathbf{X}$</span> is known and <span class="math-container">$\mathbf{e}$</span> is zero mean with covariance <span class="math-container">$\mathbf{C_e}$</sp... | Start off simple. Start with <span class="math-container">$y_i = \beta_0 + \beta_1x_i + \epsilon_i$</span>. The regression line is given by <span class="math-container">$E(y_i) = \beta_0 + \beta_1x_{i}$</span>. Suppose you have <span class="math-container">$n$</span> observations (i.e. a sample size of <span class="mat... | https://stats.stackexchange.com |
134,939 | [
"https://security.stackexchange.com/questions/134939",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/122460/"
] | Example URL <code>www.[somewebsite].com/[10_digit_number]</code>
Getting the correct number loads a page.
I know there would be 10 billion possible digits to choose from, but how long would it take? What are the resources one would need?
| <strong>About a day</strong>
If we're lucky: there's no throttling, we can perform each test with a HEAD request, can perform many tests on a single HTTP connection with Keepalive, and can have many concurrent connections.
In that case we're mostly limited by bandwidth. Say we craft a tight request that is 100 bytes... | Rolling a 10 digit number doesn't lake long on most systems, regardless of the script/language used. The bigger problem here is the number of connections you open simultaneously and the delay between requests. A good configured system will block too many requests that originate from the same address (either by the fire... | https://security.stackexchange.com |
84,349 | [
"https://security.stackexchange.com/questions/84349",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/70868/"
] | I'm developing a school, I just applied all the SQL injection protections that exist and database security, administrative roles, parametrized queries, sanitize input from the client.
But FOOL ME! I never hash user passwords, I just store them. But I don't think any hacker will reach the dabatase.
So should I hash th... | Yes, you should.
Nobody hashes (passwords are hashed, not encrypted) passwords because they KNOW that they have an SQL injection vulnerability. It's a second layer of defense.
And it's needed because you just can't be sure that you don't have an SQL injection. Or that a library you use doesn't have any. Or that the... | YES!! You absolutely MUST both hash and salt the passwords. How do you know that "no hacker will reach the database"? There are probably hundreds of ways a database could be compromised; SQL injection is just one of them. And even if both your server and web application have zero security vulnerabilities (unlikely), yo... | https://security.stackexchange.com |
101,950 | [
"https://math.stackexchange.com/questions/101950",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/18887/"
] | Here's a question we got as a homework assignment:
<blockquote>
Calculate the number of trees for a graph of n labeled vertices in which the degree of $v_1$ is $k$.
Hint: Use the formulas for the multinomial coefficients.
</blockquote>
I have no idea where to start here, so any (more) hints would be great. Thanks... | A tree with two leaves is a path, no? So the 1st question asks for the number of paths on $n$ labeled vertices. A path that uses all $n$ vertices is the same as a permutation of the $n$ vertices, and I think you know how many of those there are, and it's a lot more than $n$-choose-2. It's not clear to me from the wordi... | Maybe I am misunderstanding your question, you mean you want to count the number of labeled trees on $n$ vertices for which node 1 has degree $k$, right?
Remember that if $f(d_1,d_2,..,d_n)$ is the number of trees in which node $1$ has degree $d_1$ , ..., node $n$ has degree $d_n$ (*) then we have $f(d_1,..,d_n) = \fr... | https://math.stackexchange.com |
43,024 | [
"https://engineering.stackexchange.com/questions/43024",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/33054/"
] | A Deep Sea Vehicle (DSV) like Trieste or Limiting Factor or now Fundouzhe have control thrusters, ballast that has to be dumped, and other equipment to operate the DSVs.
But the pressure hull is a solid sphere minus the porthole windows and a hatch?
How does the pilot control these systems? Is there some conduits cut t... | Obviously putting it in series is better than the other two options. Putting in series, means that If you put two (perfectly calibrated) flow meters in series, then you will be able to make inferences on the actual value based on the calibration uncertainty, the reading uncertainty, and the sampling statistics.
<h2>Pro... | In series would usually be best, with two caveats:
<ul>
<li>the setup has to be such that the upstream meter does not affect the downstream meter, either systematically or by adding noise.</li>
<li>if the total flow is near the full scale of the sensor, and the sensor type is such that there is a "sweet spot"... | https://engineering.stackexchange.com |
603,623 | [
"https://physics.stackexchange.com/questions/603623",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/283964/"
] | Can someone please help me with this problem I am unable to find a suitable generating function?
The question says:
<blockquote>
To find a canonical transformation such that Hamiltonian of a freely falling body with one degree of freedom becomes, <span class="math-container">$H'(P,Q)=P$</span>.
</blockquote>
The hint g... | The Hamiltonian of the vertically free-falling mass-point has one degree of freedom and it looks like this:
<span class="math-container">$$H(q, p) \, = \, \frac{1}{2m}\, p^2 \, + \, mg\, q$$</span>
Since it is a conservative, time-independent Hamiltonian, one should look for a generating function of a canonical transfo... | I haven't thought about canonical transformations in a while so I thought it would be fun to give some hopefully constructive comments on this question. Note that we can use simple physical reasoning to determine the relationship between the new and old coordinates <span class="math-container">$(p,q)\leftrightarrow(P,Q... | https://physics.stackexchange.com |
214,555 | [
"https://security.stackexchange.com/questions/214555",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/120516/"
] | Why not just create a network named: <code>Starbucks_passIsHelloWorld</code>, wouldn't that prevent the network from having some security issues?
After that every user would be able to login using the password and have better security.
| <blockquote>
Why not just create a network named: Starbucks_passIsHelloWorld,
wouldn't that prevent the network from having some security issues?
</blockquote>
There is a few reasons to use captive portals instead of just a password.
<ol>
<li>In a shop/college its hard to authenticate with just a
password.Basical... | The answer to this question is yes, and no. You see it would make it secure if no one was able to sniff the wireless traffic. But when using a shared key, if I can sniff packets, and watch your device authenticate and associate to the network, and I capture your devices 4 way handshake, I now have all the information I... | https://security.stackexchange.com |
105,592 | [
"https://physics.stackexchange.com/questions/105592",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42843/"
] | My physics textbook says "Electrostatic field lines do not form closed loops. This is a consequence of the conservative nature of electric field." But I can't quite understand this. Can anyone elaborate?
| A force is said to be conservative if its work along a trajectory to go from a point $A$ to a point $B$ is equal to the difference $U(A)-U(B)$ where $U$ is a function called potential energy. This implies that if $A=B$ then there is no change in potential energy. This fact is independent of the increase or not of the k... | If there was a closed field line a particle following that line would eventually return to the same place but having a different energy so the field would not be conservative.
| https://physics.stackexchange.com |
1,164 | [
"https://stats.stackexchange.com/questions/1164",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/438/"
] | When solving business problems using data, it's common that at least one key assumption that under-pins classical statistics is invalid. Most of the time, no one bothers to check those assumptions so you never actually know.
For instance, that so many of the common web metrics are "long-tailed" (relative to t... | Researchers want small p-values, and you can get smaller p-values if you use methods that make stronger distributional assumptions. In other words, non-robust methods let you publish more papers. Of course more of these papers may be false positives, but a publication is a publication. That's a cynical explanation, bu... | I would suggest that it's a lag in teaching. Most people either learn statistics at college or University. If statistics is not your first degree and instead did a mathematics or computer science degree then you probably only cover the fundamental statistics modules:
<ol>
<li>Probability</li>
<li>Hypothesis testing</... | https://stats.stackexchange.com |
111,838 | [
"https://softwareengineering.stackexchange.com/questions/111838",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12110/"
] | Sometimes it comes to me that the biggest challenge for an engineer when he find his application getting worse in performance is lack of enough information.
Imagine that you go through the weekly performance report from your application's access log, and find you get much lower response times from July. All you can d... | Without more details on the type and nature of your application, it is hard to give more than general hints:
<ul>
<li>Measure, measure, measure. Profile your app to detect the performance bottlenecks. Then measure again after any changes, to verify the effects of the changes.</li>
<li>Identify what changed from June t... | If you do not have sufficient information, you need to collect the information you need. If you do not have a hard goal for what is satisfactory performance, you need to get one (otherwise you cannot tell if you reached the goal or not):
Information is typically collected in several ways:
<ul>
<li>Profiler attached.... | https://softwareengineering.stackexchange.com |
65,470 | [
"https://electronics.stackexchange.com/questions/65470",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20788/"
] | <img src="https://i.stack.imgur.com/I8O0o.jpg" alt="schematic">
I'm having trouble with this particular inverting Op Amp question.
I know that there are 2 nodes and I must apply KCL on the nodes.
What I tried was \$\frac{0-V_i}{49k\Omega}+\frac{0-V_o}{79k\Omega}=0\$
and I'm not sure about the second KCL equation.
and ... | KCL at V-:
<span class="math-container">\$\frac{V1 - V_{in}}{R1} + \frac{V1 - V2}{R2} = 0\$</span>
KCL at V2: (just above R4)
<span class="math-container">\$\frac{V2-V1}{R2} + \frac{V2-0}{R4} + \frac{V2-V_{out}}{R3} = 0\$</span>
Vout should equal:
<span class="math-container">\$V_{out}=-V_{in} \frac{R2}{R1} (1 + \... | There is an easier way to think about this problem, assuming ideal components. First, since the noninverting pin is grounded, the inverting pin is at virtual ground. This means:
\$V_{R1}=V_{in}\$.
\$\therefore I_{R1}=I_{R2\parallel R4}=I_{R3}\$
Calculate the voltage drop across \$R_{2\parallel 4}\$ in series with \$... | https://electronics.stackexchange.com |
317,331 | [
"https://softwareengineering.stackexchange.com/questions/317331",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/225136/"
] | We are implementing a <strong>CAD program (in C++, Qt)</strong> where we have interdependant classes :
The smallest brick is the <strong>Pattern</strong>, it is just a distribution of points. Then we have <strong>Layouts</strong> which contain Patterns at a given height (z = constant). And finally <strong>Stacks</stron... | First thing I would check is if using an <strong>existing CAD format</strong> would not be sufficient. That would not only prevent you from reinventing the wheel, but also improve the interoperability with other CAD programs. Moreover, adapting the terms of such a format like "Layers" and "Entities", instead of using t... | JSON is simple and portable. External tools won't have any problems reading or writing it. You won't have any problems yourself reading and writing the data on any architecture, which is very nice. It is also very easy to be compatible with older and newer version, often just by ignoring items that you don't understand... | https://softwareengineering.stackexchange.com |
224,755 | [
"https://electronics.stackexchange.com/questions/224755",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/104793/"
] | I just want to learn how to get all the necessary components like intel cpu, amd or allwinner and wire them together.
How do I even start?
What knowledge I have.
<ol>
<li>CompSci Degree (Maths are covered here)</li>
</ol>
1a. Yes, still far away from EE degree but I think not so far.
<ol start="2">
<li>Basic Ard... | Your question is worded very innocently, but it asks for a <em>lot</em>:
<ul>
<li>which components you should use</li>
<li>how to connect them</li>
<li>how to realize those connections on a PCB</li>
</ul>
You didn't specifically ask, but I asumme you also need to
<ul>
<li>construct (solder) your product</li>
<li>por... | <blockquote>
How do I <strong>begin to learn</strong> how to build a device like beaglebone or
raspberry pi [emphasis mine]
</blockquote>
As suggested in comments and other answers, building a fully complete turn-key device like this is a very tall order. This is why many people buy turn-key solutions: the heavy l... | https://electronics.stackexchange.com |
94,033 | [
"https://stats.stackexchange.com/questions/94033",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/43914/"
] | I don't think I understand how you can have a standard deviation of a mean <em>σ<sub>x̅</sub></em>.
<em>x̅</em> is all the sum of all values divided by the sample size <em>n</em>. It's a single value.
How can there be a standard deviation <em>σ</em> for a single value? Does it mean <em>σ</em> of the sample it came fr... | Imagine you sample the population many times. Each time you have a new sample of n observations and you compute its mean. That mean would be somewhat different for each sample. The standard deviation of this distribution is $\sigma_\bar{x}$.
$\sigma_\bar{x}$ would be zero only if n is so large that it covers the enti... | You can encounter a standard deviation when bootstrapping the mean.
For example let's say you want to have an estimation of the robustness of your mean (which is a statistic) calculated on N observations.
One way to do that is to randomly pick with replacement N individuals and then calculate the mean.
Now if you... | https://stats.stackexchange.com |
130,607 | [
"https://mathoverflow.net/questions/130607",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13625/"
] | Are there other integers $n$ than even perfect numbers such that $\sigma(n)=\omega(n)n$ and $\omega(n)\vert n$?<br>
Thanks in advance.
| For $n=120$ we have $\omega(120)=3$ and $\sigma(120)=360=3\cdot 120=\omega(120)\cdot 120$
with $\omega(120)\mid 120$. This is not an even perfect number.
| Humbled by Dietrich Burde's example, here is my motivation for saying that there won't be many such.
Consider $\sigma(n)/n$. This is bounded above by a number I will call
$P(n)$ and define as $P(n) = \prod_{0 \lt i \leq \omega(n)} \frac{p_i}{p_i - 1}$,
which involves the smallest primes $p_i$.
Note that when $\omeg... | https://mathoverflow.net |
493,766 | [
"https://electronics.stackexchange.com/questions/493766",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/249617/"
] | I can't understand the following statement:
<ul>
<li>"A contactor coil with a small control voltage, e.g. 24V AC, consumes
a higher coil current than a similar contactor coil for 230V AC."</li>
</ul>
Does this phenomenon have something to do with the fact that the self-induced voltage creates a current and that curr... | A 230 V AC coil will have many more turns and therefore much more inductance than a 24 volt AC coil. Given that it is ampere_turns that generates the magnetic field inside a contactor, for the same pulling force on both, the current in the 230 V coil will be proportionately smaller due to it having many more turns.
<b... | Generally the power taken by the coil of any given contactor is constant, regardless of whether it's wound for a low or high voltage.
Consider the coil has two windings, that can be connected in series or parallel. In series, they take twice the voltage of the parallel connection. In parallel, they take twice the cur... | https://electronics.stackexchange.com |
433,115 | [
"https://softwareengineering.stackexchange.com/questions/433115",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/404306/"
] | When coding resharper recommends that if you're to discard or ignore the return of a method, that you use this syntax:
<pre><code>_ = TheMethodICouldCareLessAboutTheReturnValue();
</code></pre>
I know you could just call it without assignment to <code>_</code> just the same, so why does the <code>_</code> as an assignm... | It matters for two reasons. One is conventional, the other technical.
The conventional reason is that <code>_</code> conveys active disinterest in the returned value. Sure, you could write <code>var dontcare</code> instead, but that's just a different arbitrary value.
But as you pointed out, you could also omit the ass... | By using the discard <code>_</code>, you are making it explicit that you, as the developer, understand that the method is returning a value but that you do not care about the value. This gives some insight into the code for reviews or future developers.
If you don't explicitly capture the return value, it is ambiguous ... | https://softwareengineering.stackexchange.com |
100,476 | [
"https://physics.stackexchange.com/questions/100476",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/40895/"
] | I was working out a relatively simple problem, where one has three inertial systems $S_1$, $S_2$ and $S_3$. $S_2$ moves with a velocity $v$ relative to $S_1$ along it's $x$-axis, while $S_3$ moves with a velocity $v'$ along $S_2$s $y$-axis.
So I constructed the Lorentz transformation by multiplying the transformation ... | You may know already that "symmetry" is not always important when it comes to non-Euclidean spaces. For instance, in quantum mechanics, a symmetric operator is seldom important, but one that is equal to its Hermitian conjugate--one that is Hermitian or "self-adjoint"--is incredibly important, for those operators have ... | Indeed NowIGetToLearnWhatAHeadIs's comment answers your question:
<blockquote>
"Simply because I hadn't encountered one that was not." A rotation is a lorentz transformation which is not symmetric.
</blockquote>
Indeed the transpose of a rotation matrix is its inverse, and only trivial rotations or rotations throug... | https://physics.stackexchange.com |
113,962 | [
"https://mathoverflow.net/questions/113962",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25947/"
] | I know that for some L-series there is still a rapidly-converging series. My question is about the existence of a such a series for the Dirichlet series of the Hasse–Weil L-function associated with an elliptic curve over rationals. A google search do not gives important answers.
| No, such an $a$ does not always exist. The lowest dimension in which an example without an $a$ could possibly exist is dimension $5$, and, low and behold, there is such an example. I will give one now, but I will also leave the $8$-dimensional example as part of my answer, since I think it is nice and since it illust... | For what is worth, here is a simple coordinate example in dimension 6. Take
$$
\omega_0 = dx_1\wedge dx_2 + dx_3\wedge dx_4 + dx_5\wedge dx_6 ,
$$
$$
\omega_1 = dx_1\wedge dx_3 + dx_2\wedge dx_4 ,
$$
$$
\omega_2 = dx_3\wedge dx_5 + dx_4\wedge dx_6 ,
$$
$$
\omega_3 = dx_5\wedge dx_1 + dx_6\wedge dx_2 .
$$
The sum of ... | https://mathoverflow.net |
2,779 | [
"https://scicomp.stackexchange.com/questions/2779",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/1748/"
] | Many algorithms used in scientific computing have a different inherent structure than algorithms commonly considered in less math-intensive forms of software engineering. In particular, individual mathematical algorithms tend to be highly complex, often involving hundreds or thousands of lines of code, yet nonetheless ... | Having done numerical software for 15 years, I can unambiguously state the following:
<ul>
<li>Encapsulation is important. You do not want to pass around pointers to data (as you suggest) since it exposes the data storage scheme. If you expose the storage scheme, you can never change it again because you will access t... | Encapsulation and data hiding are extremely important for <em>extensible</em> libraries in scientific computing. Consider matrices and linear solvers as two examples. A user just needs to know that an operator is linear, but it may have internal structure such as sparsity, a kernel, a hierarchical representation, a ten... | https://scicomp.stackexchange.com |
514,164 | [
"https://physics.stackexchange.com/questions/514164",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95576/"
] | Let us consider scalar field theory. Why usually we do not have a linear term in the potential, like
<span class="math-container">$$V(\phi)=a\phi+\frac{1}{2}m^2\phi^2+\frac{1}{4!}\lambda\phi^4,$$</span> or equivalently, after a field redefinition,
<span class="math-container">$$V(\phi)=\frac{1}{2}m^2\phi^2+\frac{1}{4!... | In perturbation theory of QFT, we often (possibly implicitly) Taylor expand the action
<span class="math-container">$$ S[\phi]~=~S[\phi_0] ~+~\underbrace{\left. \frac{\delta S[\phi]}{\delta \phi^{\alpha}}\right|_{\phi_0}}_{=0}\eta^{\alpha}~+~\frac{1}{2}\left. \frac{\delta^2 S[\phi]}{\delta \phi^{\alpha}\delta \phi^{\be... | If you write a general potential as a function of the field and you expand in Taylor series you have a linear term but if you want to have some global minimum of the potential at the field value zero then you have to ensure that there is no linear term. This is the best I can do.
| https://physics.stackexchange.com |
105,589 | [
"https://physics.stackexchange.com/questions/105589",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/43448/"
] | What is the difference between rotational velocity & rotational frequency? Their units seem to be the same, and I've read that one is a 'scalar' and the other is a 'vector,' but how do they differ?
| There exists indeed a subtle difference, and are often referred to as angular frequency and angular velocity. Both are $\omega$ and have units $\text{s}^{-1}$.
The difference lies in the fact that angular frequency is the magnitude of angular velocity, and is hence a scalar-, instead of vector quantity. The direction ... | A vector quantity has a direction and a magnitude. The direction of the rotational velocity vector is along the axis around which a body is rotating. Its magnitude is the rotational frequency which tells you how fast the body is rotating.
| https://physics.stackexchange.com |
103,294 | [
"https://mathoverflow.net/questions/103294",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16941/"
] | When solving non-linear equations via Newton's method, load increments are often used to improve convergence. In mechanics for example, if the final load in 90N, one could choose 3 load steps of 30N each. At each load step several Newton iteration are used until convergence, and the final converged result is used as t... | To answer completely, one should know what is the application that you have in mind and if there is any specific convergence result for the Newton method.
But, in general, I think that you are right: solving an inexact model to full precision is not needed. If you are solving an inexact problem $P'$ whose solution $x'... | Could I ask one question, what's the meaning of load increment? I have used Wiki to search <em>load increment</em>, but there's no answer. Can you offer some derivations and explanations of this terminology?
| https://mathoverflow.net |
57,568 | [
"https://datascience.stackexchange.com/questions/57568",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/76801/"
] | I need to estimate the GDP % of a country three years into the future, based on historic data.
I have 30+ years of the following monthly data that includes features such as inflation and unemployment rate:
<pre><code>Year Month Inflation Unemployment % Other Features GDP %
1990 1 1.1 6.2 ... | I ended up using Recurrent Neural Networks, it's a good fit with time series.
| I think you should consider time series modeling instead of observation based classification models. In the letter, you are propagating error in each prediction year.
I would use ARIMA, LSTMs, maybe semi-supervised models and motif discovery techniques.
| https://datascience.stackexchange.com |
17,582 | [
"https://mechanics.stackexchange.com/questions/17582",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10829/"
] | I brought my car into a new mechanic today for brake issues, and they discovered that my rear brake calipers had completely seized up. They gave me an itemized quote for parts (~$700) and labor (~$300).
With my previous mechanic, I shopped around for parts on my own and brought them to him to install. He would charg... | This is not normal behavior of a typical mechanic. Most mechanics/shops will still continue to charge their normal hourly rate no matter if you bring in the parts or if they get you the parts. The only difference is, they <em>will not warrant the parts you bring in</em>.
You may want to look at the fine print of <em>w... | Mechanics make money off of the parts they buy for you.
Look for a small shop with 1-4 mechanics. They like business even if it's not the most profitable. They are about building a relationship with their customer. If you're cool and your mechanic is cool, they'll install just about anything that's legal for their ... | https://mechanics.stackexchange.com |
1,016,922 | [
"https://math.stackexchange.com/questions/1016922",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/191660/"
] | Please tell me an efficient equation to calculate the nth sum of the series
$$(-1) + 2 + (-3) + ... + (-1)^{n}\cdot n$$
| The answer is false. I believe my logic is correct.
<strong>1)</strong> Consider an equilateral triangle with side length of $100\ \text{cm}$
<strong>2)</strong> Since we're looking for two seeds that are with a distance of $25\ \text{cm}$ we can break the big triangle up into little equilateral triangles with side l... | Here is a picture to accompany Fmonkey2001's answer. Each dot represents a seed. I have 15 of them. From each dot we draw a circle with radius 25.
<img src="https://i.stack.imgur.com/T9XhT.png" alt="enter image description here">
| https://math.stackexchange.com |
46,142 | [
"https://security.stackexchange.com/questions/46142",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/34752/"
] | I run a small e-commerce website hosted on a dedicated server with Debian 6 Squeeze.
I need to become PCI compliant (the card industry standard for security).
Therefore I have registered with TrustWave TrustKeeper which scans my site for potential security vulnerabilities.
The scan reported plenty of vulnerabilities... | Normally the version of Apache within Debian squeeze should be up-to-date with all security patches. This means that the version itself might run behind but that all security updates have been applied in form of backported fixes (this is often done by Debian).
You should follow a hardening guide as well, most of these... | Distributions like Gentoo and Arch (no specific releases, just continuous updates of all packages) usually have most recent versions but there can still be these same kinds of issues.
I had OpenSSH 6.1 installed on one of my Gentoo servers, and the banner clearly stated 6.1, but the security scanner insisted we needed... | https://security.stackexchange.com |
72,406 | [
"https://electronics.stackexchange.com/questions/72406",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7523/"
] | Suppose I print an eight-layer PCB, with a spiral starting on the top layer and continuing through all the inner layers to the bottom. Assuming I keep the spiral turning in the same direction on all layers, this PCB should act as an inductor. (I could leave a hole in the middle of the spiral for a core, or if not, I co... | An inductor fabricated by etching a spiral in a PCB works fine. This has occasionally been used in tight budget high current applications, where EMI radiating from the "coil" is not a major concern, and nor is the precise value of the inductance.
The calculator mentioned by OP in comments is optimistic compared to res... | Making small-valued inductors like this definitely works. The problem is that the number of turns is very limited for the size, even if multiple layers are used. Another problem is that since the turns expand radially outward, the magnetic field is not well concentrated in the center as it would be with wire wound ar... | https://electronics.stackexchange.com |
23,329 | [
"https://security.stackexchange.com/questions/23329",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/11012/"
] | I have a static site which has forms. The forms submit to a Rails endpoint which captures the submitted data. The static site and the Rails endpoint are on the same domain, on different subdomains and all traffic is completely on HTTPS.
I understand how Rails CSRF works for server generated forms. But in my case, thes... | I can make any request to your server, with any headers and values that I want. So an attacker can very easily send you a packet with a referrer that's picked by him. But how'd you go about this in a CSRF attack?
CSRF works by me sending you to a webpage that I control, and then that webpage redirects your browser to ... | Personally, I do not recommend using the Referer header to stop CSRF attacks. It has two issues:
<ul>
<li>First, it is fragile. There is a long past history of attacks on the Referer header, involving (variously) exploits on plugins (e.g., Flash), bugs in browser APIs (e.g., XHR), and redirection. To be clear, I'm ... | https://security.stackexchange.com |
207,232 | [
"https://electronics.stackexchange.com/questions/207232",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/95070/"
] | I need to add the state of all zeros to the states of an linear feedback shift register.
How can I do this?
| The standard LSFR with XOR feedback has two stable 'orbits', stuck at zeroes, and the 'm-sequence' consisting of all remaining 2<sup>n</sup>-1 states, where the shift register has n binary flip-flops.
A modified LSFR with XNOR feedback, also has two stable orbits, stuck at ones, and a sequence of the 2<sup>n</sup>-1 re... | What state occurs before you would like the all 0s state? What state would occur after the all 0s?
For instance, in a 5 bit, 00001 becomes 10000, it might be handy to have 00000 between those.
Normally, the XOR next state logic of a LSFR turns one into the other.
You have to detect 00001 and override the logic to f... | https://electronics.stackexchange.com |
296,500 | [
"https://physics.stackexchange.com/questions/296500",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99217/"
] | For example, if we consider the case where two balls on a frictionless surface are colliding with each other.It is a elastic collision but there is nevertheless the normal force and the weight of the object which acts on the system, so why are we saying that there is no external force acting on the system ?
| For the example that you suggest, collision of two rolling balls on a (horizontal) surface, you would be considering the conservation of momentum in the horizontal plane as there are no horizontal external forces.<br>
Even if there were forces acting at right angles to the horizontal plane they would not affect the hor... | You are right. It is incorrect to say that no external forces are acting on two rolling balls when they collide on a surface, and in many other situations when that statement is carelessly made. The correct statement is that no external <em>net</em> force is acting. Too often in the literature "ne... | https://physics.stackexchange.com |
83,362 | [
"https://security.stackexchange.com/questions/83362",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/64130/"
] | I just discovered that someone is pointing their domain name to the server I use for a website, which results in traffic to their domain displaying the content of <em>my</em> website.
How can I stop this illegitimate use of content?
| The answer depends on the web-server you are using. For example, apache allows for the creation of multiple virtual hosts, of which the first described is considered the default one.
What I suggest to do, is to create this default "catch-all" virtual-host with a global deny rule on it. Then configure your own web-sit... | Typically, if you add SSL and enforce it then he's got two choices - act as a HTTP proxy that strips the encryption (potentially mirror the site instead; waste of resources on his side either way) or let the user see a big fat warning message about a certificate error.
This should be sufficient for most circumstances... | https://security.stackexchange.com |
18,613 | [
"https://astronomy.stackexchange.com/questions/18613",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/14479/"
] | When talking about the expansion of the universe, it is said that it can be proven by the red-shifting of light.(As we would need higher than lightspeed to get this redshift by the Doppler effect)
I am an amateur, so I am not sure I am correct, but here is what I think.
Redshifting increases the wavelength of the lig... | The problem is that conservation of energy is a slippery concept in General Relativity. There are arguments back and forth but most people accept that conservation of energy is only a local law - it applies only to a local inertial frame and cannot be applied to the universe as a whole. However in an expanding universe... | One way to answer this is to say that conservation of energy is a law intended to be applied in a single reference frame-- it is not intended to work if you change reference frames. It is true that general relativity makes this an even more difficult point, because it's not just changing reference frames there, but a ... | https://astronomy.stackexchange.com |
58,345 | [
"https://security.stackexchange.com/questions/58345",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/46938/"
] | PCI DSS 2.0 Requirement 5.1 states:
<blockquote>
5.1 Deploy anti-virus software on all systems commonly affected by malicious software (particularly personal computers and servers).
</blockquote>
This requirement (although I'm not 100% positive it is the only one) caused IT security team in our company to request a... | <blockquote>
Can you pass PCI DSS without installing antivirus on all linux
workstations and servers?
</blockquote>
Yes, absolutely.
<blockquote>
Can you pass PCI DSS without installing additional firewalls or
configuring iptables on all linux workstations?
</blockquote>
Yes, absolutely.
In both cases the P... | With regards to Anti Virus malware that effects Linux servers is more commonly rootkits. Therefore CHKRootkit and RKHunter should be deployed to fill this Anti Virus requirement I believe. This was accepted by our auditors.
Not having protection to detect changes for Netstat or Top and similar applications is ill advi... | https://security.stackexchange.com |
212,575 | [
"https://softwareengineering.stackexchange.com/questions/212575",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/80843/"
] | It seems like a lot of university-level computer science programs and programmer job interviews focus heavily on algorithms and data structures. I'm curious as to why universities and employers put so much emphasis on the theoretical aspects of computer science rather than on specific languages and technologies, which ... | You can play a musical instrument, say a guitar, to a reasonable standard without studying technique, be self taught, find a few chords on the internet, play a few songs.
If you want to play fast though, or play jazz, or play sufficiently difficult things with relative ease technique becomes important. It becomes imp... | <strong>Learning about algorithms allows you to make smarter decisions about what code to write.</strong>
Imagine that you want to display a list of names in alphabetical order. How will you sort the list? The answer is an algorithm. Now, you could just use the sort associated with a data structure library you are usi... | https://softwareengineering.stackexchange.com |
27,694 | [
"https://dba.stackexchange.com/questions/27694",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/14795/"
] | I have a table of 2 columns <code>(Date, Text)</code>. I am getting data from the <code>Text</code> column according to the <code>Date</code> using a query like this:
<pre><code>SELECT Text
FROM MyTable
WHERE Date>= @userDate;
</code></pre>
This works, except when <code>@userDate</code> is bigger than the most rec... | <pre><code>DECLARE @tablename varchar(100)='site'
DECLARE @table1 table(date1 date)
INSERT INTO @table1
EXEC ('SELECT MAX(insdt) AS date FROM '+@tablename+'')
DECLARE @yourvariable date
SELECT @yourvariable=date1 FROM @table1
DECLARE @userDate date
IF @userDate>@yourvariable
BEGIN
SELECT top 1 text FROM MyTab... | <pre><code>SELECT
CASE
WHEN T.Date IS NULL THEN M.TEXT
ELSE T.TEXT
END AS TEXT
FROM (
SELECT TOP(1) *
FROM MyTable
ORDER BY Date DESC
) AS M
LEFT JOIN MyTable T ON T.Date>= @userDate11
</code></pre>
This is one of several ways to solve the problem. The <code>TOP(1)</c... | https://dba.stackexchange.com |
134,771 | [
"https://physics.stackexchange.com/questions/134771",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57666/"
] | I know the equation for displacement as a function of time is $$\vec{s} = \vec{v_i} \Delta{t}+\frac{1}{2}\vec{a}\,(\Delta t)^2$$
I need to solve for $\Delta t$ I'm having problems rearranging to do this. As of now, I created a Python program to run through the displacement formula, adding a set amount of time in each ... | If you truly have a vector equation, then you really have three quadratic equations - one each for the X, Y and Z component.
Let's write them:
$$s_x = v_x \Delta t + \frac12 a_x (\Delta t)^2\\
s_y = v_y \Delta t + \frac12 a_y (\Delta t)^2\\
s_z = v_z \Delta t + \frac12 a_z (\Delta t)^2$$
If there is only one value o... | You've written a vector equation, but any solution involving numbers has to involve one coordinate at a time, or what amounts to the same thing, three simultaneous equations.
For simplicity, let's assume a one-dimensional version. All of the displacements, velocities, and the acceleration point in the same direction:... | https://physics.stackexchange.com |
72,616 | [
"https://mathoverflow.net/questions/72616",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8646/"
] | I have a system to solve, set up as :
$$Ax = b$$
with a square rank deficient matrix $A$. The paper suggests to use a Moore Penrose pseudo inverse, which in my case can be computed using the traditional inverse :
$$ A^+ = (A+\frac{ee^T}{n})^{-1} - \frac{ee^T}{n} $$
where $e$ is a vector containing only ones, and $n$ i... | For black-box linear algebra (GMRES and the like) you don't need "sparse", you only need "can compute products quickly". If you check the docs for your sparse solver, I'm sure there'll be a version where you can provide directly the function $v\mapsto Av$ (and sometimes $w\mapsto A^Tw$ is needed, too). In your case, yo... | Are you looking for a fast practical method, or a fast theoretical method? If the former, there are very fast solvers based on sparse Cholesky or sparse LDL decomposition (both of which can be reused for many $b$). You should check out Tim Davis' beautiful book called something like "Sparse direct solvers".
There are ... | https://mathoverflow.net |
353,853 | [
"https://physics.stackexchange.com/questions/353853",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167466/"
] | Internal energy at a specific state can't be calculated, but using kinetic theory of gases and the law of equipartition of energy, average kinetic energy is directly proportional to temperature. For an ideal gas, internal energy is due to kinetic energy, as we neglect potential energy. This means internal energy is a... | <blockquote>
But what should I do when I want to obtain some of these quantities?
</blockquote>
In general, the wavefunction encodes the probability amplitudes for a particular value of an observable to be measured. Only in the special case that the wavefunction corresponds to an eigenstate of the observable can on... | $\hat{O}$ will have a set of eigenvectors $\phi_i$ and eigenvalues $o_i$.
You can expand your wave-function $\psi$ in terms of the basis set $\phi_i$, i.e. $\psi=\sum_i c_i\phi_i$.
If you make a single measurement then your wave-function $\psi$ will collapse to one of the eigenvectors $\phi_i$ with probability $|c_i|... | https://physics.stackexchange.com |
529,626 | [
"https://physics.stackexchange.com/questions/529626",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101989/"
] | I would like to understand both in an intuive and in a mathematical way the meaning of the sentence "The Hubbard Hamiltonian has an SU(2) symmetry". What are the symmetry transformations that leave the Hubbard Hamiltonian unchanged?
Moreover, I would like to understand how is it possible to generalize the Hubbard mode... | The Hubbard model is described by nearest-neighbor hopping <span class="math-container">$H_t = -t\sum [c^{\dagger}_{\sigma,i}c_{\sigma,j}+\rm{h.c.} ]$</span>, which preserves the spin-orientation, plus an on-site Coulomb replusions <span class="math-container">$H_U = U \sum n_{i,\uparrow}n_{i,\downarrow}$</span>. Both ... | Let me give a completely mathematical description, since I think the accepted answer is more physically motivated.
Let <span class="math-container">$U\in SU(2)$</span>. Then its second-quantization <span class="math-container">$W_U$</span> on the <span class="math-container">$n$</span>-particle Fock space would be just... | https://physics.stackexchange.com |
274,697 | [
"https://softwareengineering.stackexchange.com/questions/274697",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/98876/"
] | I have the following class, this class like many rely one parameters coming in as a pair.
Originally for convenience, I set them as <code>params Object[] values</code> and check if there is an even number of them <code>if (values % 2 == 0)</code>.
<strong>Example Code:</strong>
<pre><code>using RVD = System.Web.Routi... | I had to tackle this recently in Java. My solution was to make the Pair class fairly painless to instantiate: <code>Pair.of(..., ...)</code>. That's only 7 extra characters before the parentheses, and naming the factory method <code>of</code> seems to be a convention that value-based classes follow in Java 8.
But in m... | I read in "Effective C++" that APIs should always be easy to use correctly and hard to use incorrectly. Since you've stated that it can be used incorrectly, I would ditch it for a solution that can be safer.
| https://softwareengineering.stackexchange.com |
234,121 | [
"https://mathoverflow.net/questions/234121",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $C$ be a curve in a projective homogeneous variety $X$.
Fixed a general point $x$ in $X$, does there exist a curve $V$ in $X$ passing
through $x$ and such that $C$ and $V$ have the same homology class?
For instance when $X$ is a Grassmannian this is true.
Thanks.
| I think that this problem might not be appropriate for MathOverflow, since this follows immediately from homogeneity. On the other hand, perhaps the OP is indirectly asking why every projective homogeneous variety is homogeneous under the action of a <b>connected</b> group. This is a standard fact in the theory of a... | Any path connected topological group acting on a space has a trivial action on the homology, since the action of any group element is homotopic to the identity via a path in the group. Thus, if you have a homogeneous space under a path connected group, every translate of a submanifold represents the same homology clas... | https://mathoverflow.net |
558,612 | [
"https://electronics.stackexchange.com/questions/558612",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/123140/"
] | When creating a PCB design with multiple power rails at different voltages, all drive by switching power supplies, is it better to generate all of the voltages from a single input voltage, or two derive small voltages from other power rails? For instance, in my current project I have a 24V input, a 10V rail and a 3.3V ... | It all depends.
Let's just start by assuming that the ideal (or at least, most straightforward) way is to have a single converter for each output voltage straight from the raw voltage source. In that case, we run into beat frequencies if the converters do not have synchronized clocks and we have to deal with by using f... | This won't surprise you: it depends.
Sometimes it's easier to go directly, sometimes it's easier to work off an intermediate voltage. (This is often a function on how much voltage headroom you need for fast regulation, and whether the least voltage rail has low or high current draw compared to what's already on the int... | https://electronics.stackexchange.com |
131,326 | [
"https://security.stackexchange.com/questions/131326",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/78075/"
] | Most tutorials for setting up SSH recommend generating the keypair on a client machine. Why exactly is this?
Assuming your communication lines are not compromised, and you delete the private key from the server after acquiring it, is it safe to generate the keys on a remote host?
| Because most guides are written for people who are not experienced and it is assumed to be safer (by reducing possibilities for mistake) to prevent the private keys from being transmitted/stored outside of the client on which they were generated. <code>ssh-keygen</code> command also automatically sets the limited permi... | Just guessing here, but keys depend on randomness and most servers don't have great sources of entropy. Entropy often comes from mouse movements and typing on the keyboard, things found on clients.
| https://security.stackexchange.com |
186,358 | [
"https://physics.stackexchange.com/questions/186358",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/82259/"
] | Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example:
In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with current $I$. The usual approach is Biot-Savart law or Ampere law. I know you can derive Biot-Savart law from Maxwell equati... | Atoms themselves didn't form until well after the Big Bang. The Big Bang Nucleosynthesis (BBN) is when most nuclei formed and that happened somewhere between 10 seconds and 20 minutes after the Big Bang (that's a long time relative to how quickly everything was happening back then). That would be when ions formed, neut... | First, the early universe was incredibly hot. Second, Gravity is the weakest force. Third, when we talk about the early universe, we analyse things up to the point that gravity is not important. Why? Because we don't have a quantum theory of gravity. Forth, you need to think of the early universe as an <em>infinite</em... | https://physics.stackexchange.com |
81,705 | [
"https://softwareengineering.stackexchange.com/questions/81705",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27048/"
] | I have found a GPL library (no dual license), which does exactly what I need. Unfortunately, the GPL license on the library is incompatible with the license of a different library I use. I have therefore decided to rewrite the GPL library, so the license can be changed.
My question is: How extensive do the changes ne... | I'm not a lawyer, but AFAIK if you have seen the GPLed library code any emulation library you write would be tainted and may be declared a derived work by a judge if it is too similar in his appreciation.
So the process would be to write a functional spec and have someone which hasn't seen the GPLed code write the lib... | The usual way round this problem is to first contact the library's owner and ask if they will release it to you under a different licence.
If you're working on an open source project where the GPL is not compatible, then there's a good chance they'll do this, some projects end up with a GPL licence just because it see... | https://softwareengineering.stackexchange.com |
201,829 | [
"https://softwareengineering.stackexchange.com/questions/201829",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/46070/"
] | I'm building a contest where you can win prizes by opening boxes. Whatever the box is open, i just send a request to the server to test if the user won something. Since this contest is not a "Register and we'll draw a winner after some time" type of contest, i'm a bit puzzled at what algorithm i should be taking to cal... | You're thinking about it kind of backwards. Rather than calculating an individual player's odds, it's much simpler to randomly distribute the <em>time</em> between winners. For example, say you have 10 prizes, and the contest lasts an hour. Randomly generate 10 numbers between 1 and 3600. That gives a timestamp in ... | I created an algorithm for something similar recently which might be of help -- I'll try to tailor it to your scenario:
You have 100 prizes to give away in 5 days, so divide the total time (5 days) into 100 time-slots.
At some point in time during each time-slot, a prize should become available to be won. So, pick ra... | https://softwareengineering.stackexchange.com |
1,175,002 | [
"https://math.stackexchange.com/questions/1175002",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Is it possible to find a function $f(x,t)$ so that
$$\int_{-1}^1 f(x,t) \, dx=\log \left(\frac{t+1}{1-t}\right)\text{?}$$
I tried the Laplace transform, but it did not work.
| Try $f(x,t)= \frac{t}{tx+1}$. Then $\int_{-1}^1 f(x,t)=[ln(x+\frac{1}{t})]_{x=-1}^{x=1}$.
| It's easy to see that
$$f(x,t) = \frac{t}{1+x\cdot t}$$
is a solution because of the RHS being
$$\log(1+t) - \log(1-t) \ ,$$
so the desired antiderivative is
$$F(x,t) = \log(1+x \cdot t)$$
I guess you could derive that conclusively (without the need of any intuition) with a single differentiation w.r.t. $x$.
| https://math.stackexchange.com |
22,056 | [
"https://chemistry.stackexchange.com/questions/22056",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/8218/"
] | <blockquote>
Which of the following is the strongest base?
<ol>
<li>$\ce{LiOH}$</li>
<li>$\ce{CH3Li}$</li>
<li>$\ce{LiNH2}$</li>
<li>$\ce{LiF}$</li>
</ol>
</blockquote>
According to me the answer should be $\ce{LiF}$ as it has max number of lone pairs but the answer says its 2). I am confused.
| In order of decreasing basicity they are ranked $\ce{LiCH3}$ > $\ce{LiNH2}$ > $\ce{LiOH}$ > $\ce{LiF}$. We are dealing with the ions $\ce{F-}$, $\ce{OH-}$, $\ce{NH2-}$ and $\ce{CH3-}$ and so the factor which influences their basicity is the stability of the ion compared to its conjugate acid.
The stability of the ion... | Look at the conjugate acid of each of the anions (the base). If the conjugate acid is a strong acid (low pKa), then the anion is a weak base. If the conjugate acid is a weak acid (high pKa), then the anion is a strong base.
Let's list the anion or base, the conjugate acid and the pKa
\begin{array}{|c|c|c|} \hline
\te... | https://chemistry.stackexchange.com |
1,210,589 | [
"https://math.stackexchange.com/questions/1210589",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/125092/"
] | I'm supposed to implicitly differentiate the following and give the answer in terms of $y\prime$. $$\tan(x-y)={y \over 1+x^2}$$
$${ (1+x^2)y\prime - 2xy \over (1+x^2)^2 }$$
How do I solve for $y \prime$?
<strong>Edit:</strong>
After a ludicrous amount of algebra, i finally ended up at
$$ { sec^2(x-y)(1+x^2)^2+2xy \o... | <strong>hint</strong>: You differentiate both sides of the equation. What you did was differentiate the right side. For the left side, it is by the Chain Rule that $\tan(x-y)' = (1-y')\sec^2 (x-y)$, and set it equal to the expression you got. Can you continue toward the solution?
| Differentiating both sides from
$$\tan (x - y(x)) = \frac{{y(x)}}{{{x^2} + 1}}$$
gives:
$$\frac{1}{{{{\cos }^2}(x - y(x))}} - \frac{{y'(x)}}{{{{\cos }^2}(x - y(x))}} = \frac{{y'(x)}}{{{x^2} + 1}} - \frac{{2xy(x)}}{{{{\left( {{x^2} + 1} \right)}^2}}}$$
which can be solved and simplified for ${y'(x)}$ like so:
$$y'(x) = ... | https://math.stackexchange.com |
113,808 | [
"https://physics.stackexchange.com/questions/113808",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5788/"
] | Trying to solve a QM harmonic oscillator problem I found out I need to calculate $\hat{p}|x\rangle$, where $\hat{p}$ is the momentum operator and $|x\rangle$ is an eigenstate of the position operator, with $\hat{x}|x\rangle = x|x\rangle$. It turns out that $\hat{p}|x\rangle$ should be equal to $-i\hbar\frac{ \partial |... | The formula you quote is sort of correct, but I would encourage you to flip it around. More specifically, the old identification of momentum as a derivative means that
$$\langle x |\hat p|\psi\rangle=-i\hbar\frac{\partial}{\partial x}\langle x |\psi\rangle,$$
and from this you can 'cancel out' the $\psi$ to get
$$\lang... | Your state $\left|x\right>$ will have some expansion in the definite-energy basis of stationary states for the harmonic oscillator,
$$
\left|x\right> = \sum \alpha_n \left|n\right>.
$$
You can find all of these $\alpha_n$ by switching between $\hat x$ and the ladder operators,
\begin{align*}
\hat x &= ... | https://physics.stackexchange.com |
413,191 | [
"https://electronics.stackexchange.com/questions/413191",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/204718/"
] | I was wondering if anybody could suggest some common items around the house or at the hardware store that would make a passable core for an inductor. Or items that I could salvage material from. For example, maybe bundling together a bunch of nails could work? Maybe old radios or something are a good source?
I’m tryin... | Any AM (or AM/FM) radio built in the 1970's or later will have a loopstick antenna in it. Earlier radios will either have a loopstick antenna, or they'll have a loop antenna about as big as your hand built into the fiberboard back of the cabinet.
| <blockquote>
I’m trying to make a loopstick antenna, so I need a rod shaped core
for that and I’d rather not just order one on the internet.
</blockquote>
Use a proper ferrite rod because it won't kill the signal like a piece of conducting iron/steel will. Consider the effects of induced eddy currents and consider... | https://electronics.stackexchange.com |
131,985 | [
"https://physics.stackexchange.com/questions/131985",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9435/"
] | In David Chandler's 'intro to statistical mechanics' he states that for an ideal gas at high-temperature
$$
\langle n_j\rangle=\langle N\rangle\frac{e^{-\beta \epsilon_j}}{\sum e^{-\beta \epsilon_j}}
$$
Which I can believe from intuition, but he losses me on the derivation.
Starting with the general form for the oc... | There are indeed other assumptions in the derivation you quote. Namely, Chandler considers the classical limit of an ideal quantum mechanical gas with average particle number
$ <N> = \sum_j <n_j> = \sum [ e^{\beta (e_j - \mu)} ± 1 ]^{-1} $
(plus for Fermi-Dirac, minus for Bose-Einstein statistics). In th... | Actually, it does make sense that $\mu \rightarrow - \infty$
Given the ideal chemical potential for in ideal gas:
$$
\mu = -k_B T\ln \left( \frac{V}{N} \left(\frac{mk_B T}{2 \pi \hbar}\right)^{3/2} \right )
$$
so
$$
\mu \beta \sim - \ln(T) \\
\:\\
\therefore \lim_{T \rightarrow \infty} -\mu \beta >> 1
$$
| https://physics.stackexchange.com |
34,349 | [
"https://dsp.stackexchange.com/questions/34349",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/23835/"
] | <blockquote>
The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as
$$y(t) = (x(t))^2$$
Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation
$$R_x(\tau) = e^{-a\lvert \tau \rvert} , \quad a>0$$
Find the output PSD?
</blockquote>
I tried using th... | Since the question has been raised as to whether the hint that I had given to the OP in a comment on the original question was appropriate for a newcomer to signal processing, here goes.
Stripped of extraneous baggage and notation, the question is whether it is possible to determine the value of $E[X^2Y^2]$ straightfo... | For this problem you can't use the formula involving $|H(f)|^2$ because it only applies to linear time-invariant (LTI) systems, and a squarer is obviously a non-linear system.
The only way to solve this problem that I can think of is to use the formula
$$E\{x^2y^2\}=E\{x^2\}E\{y^2\}+2E^2\{xy\}\tag{1}$$
which is vali... | https://dsp.stackexchange.com |
37,386 | [
"https://stats.stackexchange.com/questions/37386",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8686/"
] | I suspect that a series of observed sequences are a Markov chain...
$$X=\left(\begin{array}{c c c c c c c}
A& C& D&D & B & A &C\\
B& A& A&C & A&D &A\\
\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\
B& C& A&D & A & B & ... | I wonder if the following would give a valid Pearson $\chi^2$ test for proportions as follows.
<ol>
<li>Estimate the one-step transition probabilities -- you've done that.</li>
<li>Obtain the two-step model probabilities:
$$
\hat p_{U,V} = {\rm Prob}[X_{i+2}=U|X_i=V] = \sum_{W\in\{A,B,C,D\}} {\rm Prob}[X_{i+2}=U|X_{i+... | Markov property might be hard to test directly. But it might be enough to fit a model which assumes Markov property and then test whether the model holds. It may turn out that the fitted model is a good approximation which is useful for you in practice, and you need not to be concerned whether Markov property really ho... | https://stats.stackexchange.com |
1,592 | [
"https://cs.stackexchange.com/questions/1592",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/1183/"
] | How can I prove that the language that the operator $A$ defines for regular language $L$ is a context free language.
$A(L)= \{ w_1w_2: |w_1|=|w_2|$ and $w_1, w_2^R \in L \}$, where $x^R$ is the reversed form of $x$.
I understand that since $L$ is regular so does $L^R$.also on my way for a CFG I can reach $w_1$ by th... | You can show that it is decided by a PDA.
Check if the input string up to $i$th symbol is in $L$ while pushing them to the stack. Then check if the rest of the string is also in $L^R$ while poping one symbol from the stack for each symbol you read. (Note that if $L$ is a regular language so is $L^R$ and memberships in... | You can prove it's context-free by providing a PDA that accepts it (and proving the PDA works, typically by construction).
A PDA could work as follows. Read symbols and count them using the stack. Nondeterministically determine when you've read half the symbols. If what you've seen so far isn't in the regular language... | https://cs.stackexchange.com |
554,147 | [
"https://math.stackexchange.com/questions/554147",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/102164/"
] | if $A_n \longrightarrow \infty $ and $B_n \longrightarrow \infty $
then $(A_n+B_n) \longrightarrow \infty$.
How do you prove it?
| Assume not. Than there is a $\text{M}$ such that $\forall n \in \mathbb{N},\, a_n+b_n \leq \text{M} $.
As $A_n \rightarrow \infty$ then $ \exists m, \forall k>m, a_k>\text{M}$.
And the same thing for $b$ too, like:
$B_n \rightarrow \infty$ then $ \exists s, \forall t>s, a_t>\text{M}$.
Then for $\text... | Take $$(a_n)=n,~~(b_n)=1-n$$ to see that what will happen.
| https://math.stackexchange.com |
192,713 | [
"https://physics.stackexchange.com/questions/192713",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/71894/"
] | Why not four or five or even more?
Intuitively, the more leaves the more power.
So, what is the reason?
| I worked at the Wind Energy Project Group at the TU Delft in the Netherlands for a summer. One of the most interesting ideas was a wind turbine which only had one blade, with a massive ugly blob on the other side as a counterweight. The idea was, "if we spend three times as much money manufacturing just one really good... | It's the same reason that most airplane propellers have only two or three blades. As the blade moves through the air (or the air moves over the blade), it leaves a wake. If the next blade encounters the wake, it will be moving through disturbed air and will be less efficient. The more blades you have, the more likely e... | https://physics.stackexchange.com |
58,031 | [
"https://electronics.stackexchange.com/questions/58031",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16096/"
] | Given LED1: Vf = 3VDC for 700mA ---- and ---- LED2: Vf = 4VDC for 700mA
If I put LED1 + LED1 + LED2 (in series) and apply 10VDC across them, will I have 700mA flowing through them?
| It would be more precise to say that with a LED1+LED1+LED2 stack @ 700 mA that you would have approximately 10V Vf.
The Voltage vs. Current curves for diodes are very abrupt (exponential) it is never a good idea to drive them as if they are voltage mode devices.
If you apply 10V across that stack it is unlikely that... | Vf1 = 3 V, Vf2 = 4V.
Vf1 + Vf1 + Vf2 = 10V.
HOWEVER!!!!
LEDs, like almost all generic diodes, provide essentially NO current-limiting. You put voltage across them, they will generally draw as much current as the supply is willing to put out, until the inevitable occurs.
You MUST use some mechanism to limit the cur... | https://electronics.stackexchange.com |
253,005 | [
"https://electronics.stackexchange.com/questions/253005",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/87101/"
] | I have a few dry contacts on a device where the ratings are MAX 30V, 300mA.
I want to connect LED indicators (24V, 20mA) to these dry contacts and was thinking to setup an external 24V power supply to feed the LED indicators when dry contacts close.
However, there seem to be a reason for me to use 230V power supply, s... | When you switch a circuit involving 230 VDC the contact voltage when open circuit will be 230 VDC, which is greatly in excess of 30 VDC.
<strong>Contact voltage rating must be >= the voltage that will appear across the contacts when open circuit.</strong>
If you are using 230 VAC mains as the source of HV DC and r... | Your circuit does not down convert enough.
The reverse voltage needs to be blocked with a diode or bridged with 4 diodes for less flicker.
The peak voltage exceeds 230Vac by 40% and the switched voltage far exceeds 24V.
A small opto-Thyristor would work with a 5W resistor.
EDIT
A doorbell or old furnace thermost... | https://electronics.stackexchange.com |
342,040 | [
"https://softwareengineering.stackexchange.com/questions/342040",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/241134/"
] | I'm struggling with Object Oriented Programming.<br>
From a conceptual point view, are instance methods contained in objects (like instance variables are)?
I am picturing objects like this:
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/CPT-OOP-interfaces.svg/300px-CPT-OOP-interfaces.svg.png" alt... | Conceptually, methods are as much part of an object as the instance variables are. In that way, your view on objects is correct.
However, you should realize that if you have multiple objects of the same type, then physically there will be multiple copies of the instance variables in memory, but only a single copy of t... | It is important to grasp the differences inherent in objects, instances & inheritance.
<ul>
<li>An <strong>object</strong> or class <em>defines</em> a collection of what to store and how to process it complete with interface methods, some of each of these may be private others public.</li>
<li>An <strong>instance<... | https://softwareengineering.stackexchange.com |
163,384 | [
"https://mathoverflow.net/questions/163384",
"https://mathoverflow.net",
"https://mathoverflow.net/users/49605/"
] | Let $R$ be a commutative ring and let $A_1$ and $A_2$ be (not necessarily commutative) $R$-algebras. Under which conditions on $A_1$ and $A_2$ is the following true:
For every projective $A_1$-module $P_1$ and every projective $A_2$-module $P_2$ we have that $P_1\otimes_R P_2$ is projective as a $A_1\otimes_R A_2$-modu... | Since $P_1$ is projective there exists $Q_1$ $A_1$-module and an isomorphism
$$ P_1\oplus Q_1 = A_1^{\oplus I_1}$$
for some index set $I_2$. Analogously there exists $Q_2$ $A_2$-module and an index set $I_2$ such that
$$ P_2\oplus Q_2 = A_2^{\oplus I_2} $$
Tensoring the two previous relations
$$P_1 \otimes P_2 \oplus (... | Recall that $P$ is projective iff $\text{Hom}(P, -)$ is exact. We have
$$\text{Hom}_{A_1 \otimes A_2}(P_1 \otimes P_2, -) \cong \text{Hom}_{A_1}(P_1, \text{Hom}_{A_2}(P_2, -))$$
and a composition of exact functors is exact.
| https://mathoverflow.net |
562,800 | [
"https://physics.stackexchange.com/questions/562800",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/268781/"
] | How would I find the time evolution of the standard deviation of an operator? For example, how might I find the time evolution <span class="math-container">$\sigma_x (t)$</span> of the standard deviation
<span class="math-container">$\sigma_x = \sqrt{ \langle \hat{x}^2 \rangle - \langle \hat{x} \rangle^2}$</span>
of th... | It looks like the Schrodinger equation because it is the interacting Dirac equation. Dirac discovered the Dirac equation as a relativistic Schrodinger equation.
<span class="math-container">$$ (i\gamma^\mu\partial_\mu - m)\psi = 0. $$</span>
He added the electric field <span class="math-container">$A_\mu$</span>, findi... | It's the Dirac equation (RQM) for a fast charged particle in an EM field
| https://physics.stackexchange.com |
1,694,734 | [
"https://math.stackexchange.com/questions/1694734",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/287954/"
] | I just encountered a new type of question in my textbook that I'm not sure how to do. It says:
The one-one function $f$ is defined on the domain $x>0$ by $f(x)=\frac{2x-1}{x+2}$
I've been asked to find the range, $A$, of $f$ and obtain an expression for the inverse $f^-1(x)$, for $x∈A$
Would someone please explai... | Since the given function is continuous and bijective, you know that its range will be from $\inf_{(0,+\infty)} f$ to $\sup_{(0,+\infty)} f$, possibly including or excluding these two particular values.
In this case, the derivative of $f$ is always positive, so it attains its inferior bound for $x\to 0^+$, that is $-\fr... | Note that the inverse map $f^{-1}$ satisfies $f^{-1}(f(x)) = x$. For some $x >0$ say $y = f(x)$. Then $$y= f(x) = \frac{2x - 1}{x+2} = \frac{2f^{-1}(f(x)) - 1}{f^{-1}(f(x)) + 2} = \frac{2f^{-1}(y) - 1}{f^{-1}(y) + 2}.$$ Now you can solve for $f^{-1}(y)$ which will tell you what the inverse map looks like.
As for fi... | https://math.stackexchange.com |
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