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674,331 | [
"https://physics.stackexchange.com/questions/674331",
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] | It is well known that the electroweak interaction can be studied as a <span class="math-container">$SU(2)_L \otimes U(1)_Y$</span> gauge theory. It is also known that the electromagnetic interaction is a <span class="math-container">$U(1)$</span> gauge theory, and it works perfectly on its own (by "it works" ... | There is no gauge theory describing the weak interaction after electroweak breaking. The meaning of symmetry breaking, after all, is that the resulting effective theory no longer has all the symmetries of the theory prior to breaking.
There is no problem at all in writing down a standalone <span class="math-container">... | No; it's tricky. Recall, QED runs on the <em>single</em> generator of the four in the SM (<span class="math-container">$\tau_3+{\mathbb I}/2$</span>) that escapes SSBreaking by leaving the Higgs doublet v.e.v. invariant upon exponentiation, even though it does <em>not</em> commute with all three of them.
So, singling o... | https://physics.stackexchange.com |
433,768 | [
"https://physics.stackexchange.com/questions/433768",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/209241/"
] | The answer key says fluid level goes down. So, I understand the the ice would sink since density of alcohol is less than ice. However, I remember that when ice is in water and it melts, the water level would stay the same, that's why I thought it would be the same for this question. What is different about this that th... | In a simple harmonic oscillator, energy is <em>conserved</em>; in other words, the sum of the kinetic and potential energy is always the same. But the potential energy is at a minimum when the object is at its equilibrium position; specifically, the potential energy is zero. This means that all of the object's ener... | Conservation of energy. In harmonic motion the energy is:
<span class="math-container">$$E=K+U$$</span>
K is the kinetic energy: <span class="math-container">$K=\frac 1 2 m v^2$</span>
U is the potential energy: <span class="math-container">$U=\frac 1 2 kx^2$</span>
Since <span class="math-container">$E$</span> is con... | https://physics.stackexchange.com |
49,873 | [
"https://quant.stackexchange.com/questions/49873",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/43429/"
] | I am trying to better understand multi-curve bootstrapping, but I am clearly misunderstanding what is meant by:
a) projection curve
b) discount curve
I've tried googling the definitions but it's not making it any clearer.
Could someone please help give a definition and an example?
I'd thought that (for example) a ... | Let us examine what happens when we price our bread and butter, the vanilla interest rate swap in two worlds - the single curve world and the multi curve world.
Let the first reset date be <span class="math-container">$T_\alpha$</span> and the last payment date be <span class="math-container">$T_\beta$</span>.
In the... | If I promise to pay you 1000 USD year from now, we can use a Discounting Curve to find out how much this is worth in today's dollars. If I promise to pay you "3m LIBOR on a million dollars" a year from now, we need to do 2 steps: (1) Find out the market's current estimate of what 3m LIBOR will be, and convert it to dol... | https://quant.stackexchange.com |
716,071 | [
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"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/336781/"
] | In the quantum textbook I'm currently working from, the completeness relation is written as:
<span class="math-container">$$
\sum_i |\psi_i \rangle \langle \psi_i| = \mathbb{1}.
$$</span>
But this seems to specifically require knowledge of individual bra and ket vectors. I know wavefunctions are supposed to satisfy bot... | One way you can show the completeness relation without bra-ket notation is just
<span class="math-container">$$\sum_{i} \langle \psi_i , v \rangle \psi_i = v \qquad \forall v\in\mathcal{H},$$</span>
where <span class="math-container">$\mathcal{H}$</span> is the Hilbert space in question, and <span class="math-containe... | The completeness relation reads:
<span class="math-container">$$\sum_{I=1}^{\infty} \psi^{*}_{I}(x') \psi_{I}(x)=\delta(x'-x
).$$</span>
Proof:
Suppose any wave function <span class="math-container">$\Psi$</span> can be expanded using the <span class="math-container">$\psi_i$</span>:
<span class="math-container">$$ \Ps... | https://physics.stackexchange.com |
264,123 | [
"https://physics.stackexchange.com/questions/264123",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95978/"
] | So, I was thinking about the Bohr model of atom and I started to wonder how we could find the magnetic field due to a revolving electron (produced at the location of proton) of hydrogen atom in first orbit.
Example:- How to find the magnetic field due to a revolving electron of hydrogen atom in first orbit? Given h ~... | If you naively use a Bohr-like model for the hydrogen atom, then the electron in its ground state is imagined as moving in a circular orbit of radius $r$ and moving with a speed $v$. In this case you could argue the electron is moving, moving charge is current, current creates a magnetic field. Following this model you... | If taking the equation from the Hartree atomic units for magnetic flux density (ℏ/e*bohr radius squared) the answer is 235,051 T.
| https://physics.stackexchange.com |
1,780 | [
"https://quant.stackexchange.com/questions/1780",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/1269/"
] | Can one use options on Treasury bond futures to hedge a typical fixed income portfolio? If so, how can one estimate the duration for an option on a Treasury futures contract, and taking this a step further, how would one then use the duration to determine the option's contribution to the overall portfolio duration?
| Yes, it is definitely possible to do so.
With a long fixed-income portfolio, you'd typically be buying puts on treasury futures or writing calls on them (writing calls may not be feasible if you're an institutional investor due to regulatory reasons). In general, duration for long puts/short calls would be negative. H... | Black-model deltas may be calculated on standard call and put options on Treasury bond futures. A naive estimate of the duration of the option would be the duration of the future times the Black delta.
| https://quant.stackexchange.com |
10,991 | [
"https://physics.stackexchange.com/questions/10991",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3976/"
] | If I have a car (with a particular engine) optimized (shape & weight distribution-wise) for attaining the top speeds possible, and I put that engine into a car which is heavier (but otherwise the same shape & design), will the heavier car have the same top speed in the real world?
I'm guessing that the heavier ... | The problem you've formulated is that these two cars are identical aside from the mass difference, so let's just limit this to two identical cars where one has an added weight in it. The heavier car will accelerate slower, based on simple <span class="math-container">$F=ma$</span>, where <span class="math-container">$... | The way I see it, the heavier car will have a higher top speed. Here's why:
Top speed occurs when the forces pushing the car forward (engine power) are equal to the forces holding the car back (aerodynamic drag, rolling resistance).
If you take two identical cars, but increase the mass of one car, they will have the ... | https://physics.stackexchange.com |
141,063 | [
"https://stats.stackexchange.com/questions/141063",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/46705/"
] | Let's say that I have one categorical variable with six levels, and I then create five indicator variables in order to represent the six levels. If two of the five variables are insignificant, then do I drop these two? I assume not, but I was not sure. I was thinking that it might be better to test the full (all five v... | You should leave all five indicator variables in. Dropping predictors because they are non-significant leads to biased estimates for regression coefficients and inflated <em>p</em>-values.
A good reference that discusses this at length is Frank Harrell's <em>Regression Modeling Strategies</em>. You can find a summary ... | The latter approach (comparing two models with and without the five variables and decide if you should keep them as a set) is better.
The problem with dropping the indicator is that you'll change the p-values of the remaining levels as well, as you're shifting the intercept (aka the reference group.) Given a model:
$... | https://stats.stackexchange.com |
67,554 | [
"https://mechanics.stackexchange.com/questions/67554",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/48595/"
] | Wouldn't post a new question if the internet wasn't full of <em>"Yep, perfectly fine"</em> one one side and <em>"Nope, you're going to hit the closest tree"</em> on the other side.
Driving a FWD Volvo S40 2.4i. Wearing a set of 205/55/R16 Hankook Ventus Prime 2. One of my rear tires got a side bubble and no stores aro... | If they are matched brand across the axle you'll be fine for the sort of driving you describe - assuming the new rears are of comparable quality to the fronts. If you put ditchfinders on the rear you might find it a bit unpleasant in the wet!
Regarding sizes - the OP mused in the comments about putting 225/50/R16 on t... | If it is winter and you have summer on the back and winter on the front <strong>then</strong> you will definitely notice. Summer all round and not four wheel drive will be ok.
If it was 4 wheel drive then keeping the tires matched is important depending on the 4wd drive system - and Volvo is one known for that.
| https://mechanics.stackexchange.com |
39,396 | [
"https://security.stackexchange.com/questions/39396",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/28611/"
] | We're trying to determine if pushing data through a firewall is more safe than pulling it. The data will be from SSIS to SSIS through the firewall. An advisor here has suggested that pushing the data through the firewall is safer than allowing an external connection in to pull the data out.
Is this so ?
| Allowing an inbound connection means opening up a port on your firewall and having a network service listening on that port 24/7 and that creates risk. If you are the client, you reach out to a remote network listener and pull the data back. You don't have that 24/7 risk.
There are some things you can do to lower th... | <strong>Theoretically</strong> an inbound connection can be considered just as safe as an outbound one -- you can limit the conditions in which inbound connections can be made; trusted source, trusted conditions, etc.
But <strong>typically</strong> inbound connections are significantly less restricted than outbound o... | https://security.stackexchange.com |
512,858 | [
"https://physics.stackexchange.com/questions/512858",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231957/"
] | In dynamical systems with linear differential equations, we almost always break up the function of independent variable in sines and cosines.
But suppose that my function is smooth and periodic. Then what advantage do I get by using Fourier series instead Taylor?
Inside the radius of convergence, the Taylor series co... | Many of the other answers are addressing the practicalities of expanding in Fourier series versus Taylor series. But there is at least one <em>physical</em> reason for choosing one over the other, and that is that the expansion coefficients of a vector written in an orthonormal basis reveal particular types of <em>phys... | <ol>
<li>The complex exponentials are eigenfunctions of the derivative and integral operators. So if you're analyzing linear differential equations, and using Fourier series, then you can consider each term on its own. If you use Taylor series you have to consider interactions between one term and other terms in the se... | https://physics.stackexchange.com |
117,945 | [
"https://softwareengineering.stackexchange.com/questions/117945",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/38762/"
] | I work for a company where we build enterprise applications, and we maintain three environments: <em>development</em> (or <em>dev</em>), staging (or <em>stage</em>) and production (or <em>prod</em>).
The meaning of <em>dev</em> is intuitive: it's the environment used during development of the application.
What's the ... | For smaller companies (it's not clear how big yours is), three environments (dev, stage, production) are common. Larger companies will often have a QA environment between dev and stage.
These normally break down as follows:
<strong>dev</strong>: Working code copy. Changes made by developers are deployed here so integ... | I am a bit surprised that a test environment is not present as well, as a location for code to go to before being promoted to staging.
To answer the question:
A stage environment should mirror the production environment as closely as possible.
It is used for verification of deployment procedures - making sure that w... | https://softwareengineering.stackexchange.com |
242,485 | [
"https://security.stackexchange.com/questions/242485",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/247842/"
] | I'm a beginner in Information Security and am learning about salting. Unfortunately, most of the time I have to learn by myself since the lecturer doesn't provide deep explanation on these. I now have to solve some problems related to this and having trouble understand how salting slow down the attack
<blockquote>
An a... | <blockquote>
but remain the security level of the system as if we are using a
password of length 7
</blockquote>
Each character can have 96 different possibilities, and the it should be as if we are using a password 7 characters long. So, this is 96^7 different possibilities, which is 7.5144748e+13 possibilities. To ... | (This isn't the literal answer to your question, but provides context for you and others to understand why the question itself is somewhat incomplete for the problem space.)
A truly complete answer to this question should answer the local mathematical question first, and then expand to explain why that simple answer is... | https://security.stackexchange.com |
29,614 | [
"https://stats.stackexchange.com/questions/29614",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11032/"
] | The other day I had a consultation with an epidemiologist. She is an MD with a public health degree in epidemiology and has a lot of statistical savvy. She mentors her research fellows and residents and helps them with statistical issues. She understands hypothesis testing pretty well. She had a typical problem of c... | Well, from what you've already said, I think you've got most of it covered but just need to put it in her language: One is a difference of risks, one is a ratio. So one hypothesis test asks if $p_2 - p_1 = 0$ while the other asks if $\frac{p_2}{p_1} = 1$. Sometimes these are "close" sometimes not. (Close in quotes beca... | Mind that in both tests, you test a completely different hypothesis with different assumptions. The results are not comparable, and that is a far too common mistake.
In absolute risk you test whether the (average) difference in proportion differs significantly from zero. The underlying hypothesis in the standard test f... | https://stats.stackexchange.com |
316,371 | [
"https://stats.stackexchange.com/questions/316371",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/186737/"
] | I have to solve the following problem:
Let X be distributed over N (natural numbers) with probability mass function $P(X=i) = \frac{\alpha}{2^i}$ for some fixed alpha (which is an element of R, the real numbers). Find alpha.
I know that $\sum_{i=1}^{\infty} P(x=i) = 1$. Therefore $\sum_{i=1}^{\infty} \frac{\alpha}{2^... | Say that you are predicting sells of some products given their price and some other variables. Your data is noisy, since you have many different products and there are many factors that you are not able to account. You may assume that there is some kind of effect that may be <em>approximated</em> with linear function (... | If the underlying process is linear, linear regression will be superior. What comes to mind is estimating calories on food; the amount of calories will be strictly linear (i.e., they won't interact with each other). A neural network (etc) could be trained to do this but it would be more computationally demanding and pr... | https://stats.stackexchange.com |
18,316 | [
"https://mechanics.stackexchange.com/questions/18316",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10623/"
] | During a recent oil change Istripped the oil pan bolt. It took a bit of trial and error for me to realize the stripped hole was a 14mm 1.25 thread so I got a tap and rethread it to 14mm 1.5 thread with a new bolt to match.
However, what I completely failed to think of at the time was all the metal I was cutting when ... | Judging by your other questions on the site your motorcycle is a '12 Yamaha R6. If so, you have an oil filter, which should pick up the metal flakes and any other debris.
A new oil filter and fresh oil should be sufficient to clean out the unwanted debris.
It is unlikely that the metal flakes are responsible for a pe... | You could use oil flushing agent which is available from most motor factors or, if you cant get any, add a small amount of diesel to the old oil and allow the vehicle to idle for a short period prior to removing the old oil.
Also, a large magnet on the sump pan which you then draw to the drain hole should drag out any... | https://mechanics.stackexchange.com |
650,605 | [
"https://electronics.stackexchange.com/questions/650605",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/246213/"
] | Suppose there is a really long track (not infinite) running over a 2-layer PCB with the bottom plane being the ground plane (just to complete the reverse path of the current). Now, on one end, 5V is supplied. But since the track is really long and the only one existing track on the PCB, there will be voltage loss with ... | <ol>
<li>Capacitors are useless. You have the PCB trace resistance, and you have a load which can be modeled as resistance. That's a resistive divider and thus under load the capacitor would not even charge up to the voltage fed on the PCB trace input. A capacitor would help only with pulsed loads, assuming the capacit... | 98% of the time, you just make the track bigger until the voltage drop is as low as you need it to be.
If you don't have space to make the track bigger, you may solder a wire in parallel, or even a busbar, or just deal with the fact your PCB is too small and make it bigger anyway.
This is almost always how excessive vo... | https://electronics.stackexchange.com |
536,129 | [
"https://physics.stackexchange.com/questions/536129",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/213859/"
] | Suppose two charged particles <span class="math-container">$a$</span>(+) and <span class="math-container">$b$</span>(-) exert force on each other.
The work by <span class="math-container">$F_{ab}$</span> plus the work by <span class="math-container">$F_{ba}$</span> is equal to the increase in total kinetic energy of t... | The work energy theorem is indeed a tricky beast and it is easy to misuse it. Unfortunately, most derivations are rather lax about identifying the assumptions in the derivation. Most derivations assume that the system being analyzed is a point particle with no internal degrees of freedom. Your system here has internal ... | <span class="math-container">$F_{ab}+F_{ba}=0$</span> tells us that there is no net force on the <em>system</em> consisting of the two particles. That is, there is no <em>external</em> force on the system, and no work done on the system. The total mechanical energy of the system is constant.
But there are <em>intern... | https://physics.stackexchange.com |
28,118 | [
"https://mechanics.stackexchange.com/questions/28118",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1631/"
] | After a bit of intensive study I've learned the ins and outs of how a car works, the majority of it. Not well enough to stop needing a mechanic, but well enough to understand what every component does, the basics of how it works, and how it relates to the other components. Which is a great start!
But I'd like to be ab... | Recommend going to your nearest auto parts store and picking up a Chilton manual for your make/model. There are a few other publishers you may like better. From what I can tell they're all about the same.
These manuals aren't perfect, and don't always have as much detail as you'd want, but they do have a lot of diagra... | A Troy says, you want a workshop manual - as well as the Chilton ones he mentions, there are also Haynes (the dominant publisher in the UK) and other publishers - plus the 'official' ones for your particular car - the latter can often be found on well-known online auction sites, particularly for older cars.
| https://mechanics.stackexchange.com |
2,803,747 | [
"https://math.stackexchange.com/questions/2803747",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/549145/"
] | <strong>Problem:</strong> The vertices of the base of an isosceles triangle are $(-1,-2)$ and $(1,4)$. If the third vertex lies on the line $4x + 3y = 12$, find the area of the triangle.
<strong>Attempt 1 :</strong> Convert $4x + 3y = 12$ to point slope form which is $(y-0) = \frac{-4}{3}(x-3)$ then use (0,3) and the ... | <strong>hint</strong>
$$A=(-1,-2) $$
$$B=(1,4) $$
$$C=(a,b) $$
$$AC^2=BC^2\implies$$
$$(a+1)^2+(b+2)^2=(a-1)^2+(b-4)^2$$
$$\implies 4a+12b=12$$
on the other hand
$$4a+3b=12$$
thus $$a=3,b=0$$
the middle of $[A,B] $ is
$$J=(0,1) $$
the area is $$S=\frac {AB.CJ}{2} $$
| How would I approach such problem?
We know that the third vertex, call it $C$ lies on the perpendicular bisector of $AB$. The midpoint of $AB$ is $((-1+1)/2, (-2+4)/2)=(0, 1)$. The slope of $AB$ is $3$, thus the perpendicular bisector is determined by line $y = -x/3 + 1$. Compute the intersection with $4x+3y=12$ to ge... | https://math.stackexchange.com |
65,527 | [
"https://physics.stackexchange.com/questions/65527",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24813/"
] | I'm just expressing my guess.
Let two particles A and B experiences forces $F_1$ and -$F_2$ between them and let guess also there are two observer, one is stationary and other is moving with constant speed. Now my measurement time for the collision will not same for the moving observer.
So If I am stationary, the... | <blockquote>
<b>So If I am stationary, the moving observer may say that my measurement is wrong that means Newtons third law is violated? Is it right?</b>
</blockquote>
No that isn't right.
Each observer is in an inertial reference frame and each observer will independently see that Newton's third law applies.
| Actually, third law won't apply <em>solely to particles</em> in Special Relativity because you need to include the field into conservation of total momentum.
| https://physics.stackexchange.com |
313,105 | [
"https://softwareengineering.stackexchange.com/questions/313105",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/67307/"
] | When I add logging (e.g. log4j2 in Java) to existing code, is it ok (good practice), to alter the code?
Consider the following example:
<pre><code> //if process returned 0 return true
return (returnCode == process.waitFor());
</code></pre>
This construction is rather neat, but when I want to add logging to it, and ... | Broadly speaking, yes, of course you can alter the code to add logging. If logging had been part of the project from the beginning, how would the code have been written?
There's exceptions to every rule, but these are so situation dependent it's out-of-scope to discuss here. (Consider a critical production problem whe... | Best practice for handling logging kind of cross cutting concerns through AspectJ/AOP and handle the input parameter and results logging from single place. This shall enhance the code maintainability.
| https://softwareengineering.stackexchange.com |
111,558 | [
"https://mathoverflow.net/questions/111558",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22684/"
] | Dear All,
I am absolutely lost in the following problem:
Let $P_s, \: s \in [0,1],$ be a uniformly bounded family of projections (idempotents) in a Banach space $X$ such that $P_s P_t = P_{{\rm min}(s,t)}$. Let $Q$ be a bounded linear operator on $X$ such that $QP_s = P_sQ$ for every $s \in [0,1]$ and the function $... | I guess that the answer is no in general. More precisely what I consider as the discrete version of your question has a negative answer. I guess that one should be able to find a couterexample to your question by an ultraproduct argument, but I did not check the details.
By discrete version of your question I mean: if... | I'm not sure if I like the ultrafilters, so I decided to find some elementary construction. I do not have much imagination for chains of commuting projections either, so let us consider the space of all functions $f:[0,1]\to X$ where $X$ is the space of all sequences and let $P_s$ just keep the values to the left of $s... | https://mathoverflow.net |
23,551 | [
"https://chemistry.stackexchange.com/questions/23551",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/-1/"
] | I am really confused between them. I know that an enantiomer is an isomer having optical activity, non super-imposability of image on original configuration, same molecular formula(Correct me if I am wrong). The thing that is causing me trouble is what diffrentiates this from diasteriomerism. It would be appreciated if... | Your definition of enantiomer is correct.
This simple further classification might be helpful. Let's take 2 molecules with the same molecular formula. These molecules are either constitutional (or structural) isomers or stereoisomers. If they have different structures (or connectivity patterns) and are separated... | One additional thing to add to @ron's answer is that <em>diastereomers</em> have different chemical properties .. they can be distinguished using conventional spectroscopic techniques, or even by measuring thermodynamic parameters (at least in principle .. sometimes the differences are very small and hard to resolve). ... | https://chemistry.stackexchange.com |
79,884 | [
"https://physics.stackexchange.com/questions/79884",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29157/"
] | Conservation of momentum applies when net force is zero. Suppose that there is a system of a canon and a canonball. Total momentum of the system is zero before canonball is fired. Now canonball is fired from the canon, and in frictionless cases, horizontal-axis momentum of the whole system would be preserved.
Now fri... | The momentum of the whole system is still conserved -- it's just that when you add friction between the cannon and the ground, you have to include the ground (and in fact the whole planet that it's attached to) as part of "the system". When the cannon ball flies off in one direction, the cannon is pushed in the other. ... | Yes. If you consider a simplistic case where at one instant everything is at rest and at the second instant the cannonball shoots in one direction and the cannon recoils in the opposite direction, then as far the cannonball is concerned, it is no longer in contact with the cannon or Earth. So momentum is preserved. Lat... | https://physics.stackexchange.com |
172,422 | [
"https://mathoverflow.net/questions/172422",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50068/"
] | <blockquote>
Are there arbitrarily long arithmetic progressions in which all the
prime factors of all the terms are at most $N$, for some $N$? Assume
all the terms are positive and the sequence of terms is increasing.
</blockquote>
I have proved that no such infinite sequence exists. Note the $N$ may vary from A... | A simple proof is available as well. Pick p coprime to d and let t be such that td=1 mod p. Then, mod p, t times the arithmetic progression looks like a sequence of consecutive integers. Thus its length has to be less than p to avoid one of the terms being a multiple of p, which means the original progression also h... | If $x,y,z$ are in arithmetic progression, then $x+z-2y=0$. By the S-unit theorem of Evertse, Schmidt and Schlikewei, this equation has only finitely many solutions in $x,y,z$ having all its prime factors in a fixed finite set (e.g. all primes at most $N$). So you can't have arbitrarily long arithmetic progressions of n... | https://mathoverflow.net |
179,457 | [
"https://physics.stackexchange.com/questions/179457",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/67724/"
] | When we lift an object upwards with a constant velocity for a distance of $ h $ the work that we've done is $mgh$ and the work done by the force of gravity is $-mgh$. So the net work on the object is zero and it doesn't gain any energy. how its potential energy will be converted to kinetic energy when we drop that obje... | The <em>total</em> work done on the object is the change in <strong>kinetic energy</strong>:
$W_{total} = \Delta E_K$*
While the <strong>gravitational potential</strong> energy of the object is:
$U_G = mgh$
So, although it costs energy to lift the object up, the total work done on it is $0$ because both at the begi... | <blockquote>
So the net work on the object is zero and it doesn't gain any energy.
</blockquote>
The object obviously did gain energy. The object's potential energy increased by $mgh$, and its kinetic energy didn't change. So what's going on? Is the work-energy principle wrong?
The answer is no, the work-energy pri... | https://physics.stackexchange.com |
72,354 | [
"https://physics.stackexchange.com/questions/72354",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/27271/"
] | I have laser beam path that fires two pulses of light in a gaussian distribution, so the intensity graph over time is two identical gaussians separated by a distance $t_0$. In other words, a gaussian convolved with two $\delta$ functions equidistant from the origin. When I take the Fourier transform of this, I get a gr... | This is a great question because you have to think carefully about what you experiment is actually doing to answer it.
As in Andreas H's answer, you may in principle (and in some practice) see the intensity comb (the "beats" as you call them) at the output of grating spectrometer. But in practice it won't always be li... | The spectrometer measures the absolute value squared of the Fourier transform of the input signal, so you see "beating".
It is just a fact that also far "separated" pulses in time domain affect the spectrum and you see beating. But this is nothing mysterious, because if you have two pulses the frequency component cor... | https://physics.stackexchange.com |
99,790 | [
"https://cs.stackexchange.com/questions/99790",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/96158/"
] | How could you design an efficient algorithm that uses the least amount of memory space and outputs, in ascending order, the list of integers in the range 0..255 that are not in a randomly generated list of 100 integers?
The aim is to output the number of such integers, and determine if the randomly generated list of 1... | The error is in the definition of <span class="math-container">$\overline{L}$</span>. It should be
<span class="math-container">$$
\overline{L} = \{ \langle M \rangle \mid \exists w \, w \in L(M) \land w[0] = 1 \}.
$$</span>
In other words, <span class="math-container">$\overline{L}$</span> consists of all Turing machi... | Your language is indeed co-c.e.; the mistake is in the argument claiming recognizability of <span class="math-container">$L$</span>. You have the existential and universal quantifier mixed up.
| https://cs.stackexchange.com |
606,878 | [
"https://physics.stackexchange.com/questions/606878",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/285235/"
] | Is it possible for an electromagnet of around 50mm diameter to produce a force of 1000N at 10mm distance far away ferromagnetic object (air between them) ? If yes, how much power (approx) will it need to do so?
| Yes it is possible, theoretically with zero power. In practice power needed will be greater than zero, it depends on size of the ferromagnetic object (the bigger the object the less current and less power needed), the magnetic properties of the object and the electromagnet core, ohmic resistance of the wires (the great... | The atomic dipoles within a ferromagnetic material tend to align themselves with a strong external magnetic field. Then the force on each depends on the divergence of the field at their location. Outside of the end of an electromagnetic, both the field and its divergence vary from point to point in a complex fashion... | https://physics.stackexchange.com |
336,055 | [
"https://stats.stackexchange.com/questions/336055",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/201007/"
] | I'm getting a 100% accuracy for my decision tree. What am I doing wrong?
This is my code:
<pre><code>import pandas as pd
import json
import numpy as np
import sklearn
import matplotlib.pyplot as plt
data = np.loadtxt("/Users/Nadjla/Downloads/allInteractionsnum.csv", delimiter=',')
x = data[0:14]
y = data[-1]
fr... | Your test sample is a <em>subset</em> of your training sample:
<pre><code>x_train = x[0:2635]
x_test = x[0:658]
y_train = y[0:2635]
y_test = y[0:658]
</code></pre>
This means that you evaluate your model on a part of your training data, i.e., you are doing in-sample evaluation. In-sample accuracy is a notoriously poo... | You are getting 100% accuracy because you are using a part of training data for testing. At the time of training, decision tree gained the knowledge about that data, and now if you give same data to predict it will give exactly same value. That's why decision tree producing correct results every time.
For any machine ... | https://stats.stackexchange.com |
100,469 | [
"https://mathoverflow.net/questions/100469",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24644/"
] | A few questions, hopefully to spark some discussion.
How can one define a product of measures?
<ol>
<li>We could use Colombeau products by embedding the measures into the distributions? I'm not sure why this approach is frowned on?</li>
<li>Since measures are map from sets into numbers, can we not define the product ... | Counterexample for suggestion 2: Take a measure on a 2-point set, assigning to each singleton measure 1 and therefore assigning to the whole set measure 2. The pointwise product of this measure with itself still gives the singletons measure 1 but gives the whole space measure 4, so it's not a measure.
For suggestion ... | Not a definitive answer, just some thoughts that I hope you might find useful. Firstly, there is a celebrated example of Schwartz that shows that you can't do this globally in the sense of getting a ring structure on the space of measures which extends that on the space of continuous functions. It can, however, ofte... | https://mathoverflow.net |
720,940 | [
"https://physics.stackexchange.com/questions/720940",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/334905/"
] | I have recently heard the claim that sun can not be composed of plasma because plasma can not be a black body.
I am an uneducated layman, I've seen a lot of people (laymen) deviate from accepted scientific consensus. I am skeptical and I don't have enough knowledge about physics to argue it.
| Plasma in many concrete cases often is not a black body, e.g. plasma in Earth's ionosphere, or in a discharge lamp, or in tokamak. This is because plasma in these cases is very thin (rarified gas), and not a good absorber of radiation, as there is not enough layers to make it absorb close to 100% of incoming radiation ... | The argument is silly if the claim is that plasmas cannot appear anything like blackbodies, since there are observable examples like the Sun.
To be a blackbody, a volume of plasma needs to come into equilibrium at a reasonably uniform temperature and to be thick enough that it will absorb all radiation incident upon it... | https://physics.stackexchange.com |
202,941 | [
"https://softwareengineering.stackexchange.com/questions/202941",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/91765/"
] | I find that whenever I want to go run a past project, it will take a long time before I can find it and before I have everything set-up again for it to be able to run.
For example, I have python projects I created in Linux, and it depends on software packages that are easily installed in Linux, yet I no longer have ... | What I have done in the past is either convert the physical development machine to a VM, or if it is already a VM, retain it for future use. It's not as efficient as I'd like for disk space usage, but space is cheap. Also, this process is so much less expensive time-wise than trying to re-configure an environment in th... | My current favorite methodology is to maintain a script that installs ALL needed dependencies for a project, downloads the source, and hooks everything up. Some scripts have two modes - one for production, which usually is pretty much a subset of the other mode: development.
Some environments only take about 5 minutes... | https://softwareengineering.stackexchange.com |
83,544 | [
"https://dba.stackexchange.com/questions/83544",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/52826/"
] | I'm getting a very weird MySQL replication error No. 1146 for a <code>REPLACE INTO</code> query on a slave host replicating all tables in all databases from a master, and I'm having a bit of a hard time understanding why.
Here's my scenario:
<ol>
<li>New data is generated solely on the master server, MySQL 5.5.40.</l... | Not too sure why still, but this problem disappeared after some of the troubleshooting steps I took to hunt down the culprit. Maybe it was the open files limit that caused the errors while opening the MyISAM tables, perhaps because of the high activity of other services running on the slave2 server, like Rackspace's cl... | I am not sure what was causing the issue for the original poster, but in my case it was a case sensitivity issue. A Master server in my replication topology was using PascalCase for its table names when specifying them in queries, where the actual table name files on disk were lowercase. For example, see my error messa... | https://dba.stackexchange.com |
48,126 | [
"https://dba.stackexchange.com/questions/48126",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/21283/"
] | <em>Let me start out by clarifying that <strong>this is not a duplicate question</strong>, nor a potential duplicate for that matter. I have tried implementing every answer to every single variant that already exists of this problem on StackOverflow and DBA Stack Exchange, without any luck.</em>
I've been struggling w... | I have run into this a few times and the issue has been a mismatch of data types in the export/import parameters. First thing to do is check those parameters by right click on source or destination, selecting Advanced Editor. Go to Input and Output Properties and check the data type for that column for all items - bo... | <em>Ignoring the error</em>
First of all, you should be able to ignore string truncation by going to your Flat File Source, Error Output and then changing "Fail Component" under "Truncation" to "Ignore Error".
<em>Better solution</em>
The real issue could be that the string length inside the SSIS pipeline is still w... | https://dba.stackexchange.com |
29,782 | [
"https://softwareengineering.stackexchange.com/questions/29782",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I am novice developer.
While development is going on, we come across different error issues. However for the novice of programming, it is always hard to directly understand them & solve them.
I believe, errors are generally related to typing error OR data structure error OR run-time memory error - which is relate... | My thoughts:
I don't think many errors are related to typing errors. Typos will generally not produce stuff that will compile so rarely produces anything that gets even as far as unit testing, let alone beyond that. Those few that do are generally very easy to spot.
In 16 years in development the only issues that I... | A lot, rather <strong><em>most</em></strong> of what you do as a programmer is debugging. You are either debugging your code or someone else's. As a novice, you don't want to focus on faster. You need to focus on detail, organization, and correctness:
<ul>
<li>Study the details. Don't just debug, seek to know <em>why<... | https://softwareengineering.stackexchange.com |
127,003 | [
"https://electronics.stackexchange.com/questions/127003",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52228/"
] | I am trying to figure out if I can melt Aluminum cans using a heater coil from a toaster oven.
I've already used q=mc∆T and q=m*(Latent heat of fusion) to figure out how much energy is required to melt a mass m of aluminum, considering no heat loss to surroundings.
What I'm having a hard time with is that I know the ... | The heater will never stop drawing current, the current will be quite constant because it is made of material with low thermal coefficients of resistance.
The heating element loses heat by three principles: conduction (contact with cold air), convection (wind) and radiation (far-IR)
Conservation of energy works also ... | The coil will keep drawing power an dissipating energy as heat.<br>
By itself, a coil (resistive heater) doesn't have a negative feedback mechanism.
As the material around the coil is heating up, the coil will keep drawing electric energy and dissipating it, so it will keep heating the target material. The gradient b... | https://electronics.stackexchange.com |
5,937 | [
"https://astronomy.stackexchange.com/questions/5937",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/1030/"
] | Many asteroids are today known to be binary, to have "moons".
But what <strong>comets</strong> are known to be binary? Or what fraction of them are theoretically thought to be binary? And if possible, then separate Oort cloud comets from comets with more local asteroid like orbits in this respect.
| <strong>None</strong>. and that doesn't surprise me much.
Comets are thought to be Oort-cloud objects which by interaction either with other Oort-cloud objects or with objects passing the Solar system have been perturbed to venture into the gravitational reach of the outer planets, whence they are
flung into the inner... | Contact binaries, in which two objects are touching may be fairly common. This is one interpretation of the "rubber duck" shape of the "Rosetta comet" 67P/Churyumov–Gerasimenko, and radar observation of 8P/Tuttle suggest it is also formed of two objects in contact with each other.
The low mass and so weak gravity of c... | https://astronomy.stackexchange.com |
122,468 | [
"https://mathoverflow.net/questions/122468",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31622/"
] | Gowers' dichotomy theorem asserts that every Banach space either contains an HI subspace or a subspace having an unconditional basis. There are examples of HI spaces without quotients having unconditional bases (was Argyros the first who proved that?). This strange phenomenon tempts me to ask
whether every reflexive ... | Every quotient of the original Gowers-Maurey space is HI; Ferenczi proved this. Argyros-Felouzis produced examples of reflexive spaces that are not HI (e.g. contain some $\ell_p$) and have HI duals. Any of these spaces give an example of a space such that no quotient has an unconditional basis. I think it's safe to say... | The space of Gowers and Maurey is reflexive and H.I. , and as proved by Ferenczi every of its quotients and its dual is also H.I. (as mentioned in the answers of Bill Johnson (giving the reference) and Kevin Beanland). The results of Argyros and Felouzis are answering to the question.
Moreover the remark of Bill Jo... | https://mathoverflow.net |
487,516 | [
"https://electronics.stackexchange.com/questions/487516",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/240441/"
] | I am learning to program microcontrollers (with PIC18FXXXX) and what I have seen so far is that everything that is programmed within the main function is what is executed.
My question is, if you can make a call to a function that is outside the <code>main</code> and is running a scheduled task.
For example.
Press a s... | <h1>Multitasking?</h1>
Yes or no, depending on how you define it.
<h2>In the truest spirit of multiprocessing:</h2>
<strong>No</strong>.
A small single-core MCU only executes a single instruction at any given instant.
<h2>In the spirit of the 90's multitasking:</h2>
(when almost all PCs had only a single CPU, but... | Why do you think it is not possible? Functions can be called and not using functions leads to undecipherable spaghetti code. There are both professional quality designs but also beginner hobbyist code so you can find both. Some extremely tiny microcontrollers can have a limited hardware stack so subroutines are not use... | https://electronics.stackexchange.com |
377,291 | [
"https://softwareengineering.stackexchange.com/questions/377291",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/313504/"
] | In an environment where you can't merge code that fails tests you obviously can't merge new, failing tests.
But how to deal with a newly found bug exploit, meaning you wrote a new test exposing an already existing bug? Test-driven-development would say: Hooray, you have the test, now fix the bug and then commit both.
... | Never break the build. But tests that should pass in the future are completely valid. Many test runners understand an “xfail”, “pending”, or “todo” category for this kind of case. If one of those tests (unexpectedly) starts passing you can remove this category. By merging these todo tests, you can make sure that they c... | Option one. Just because you can't <em>merge</em> code doesn't mean you can't <em>check it in</em>. You simply need to create a branch for your failing test, and then it's ready when someone starts to work on it.
That being said, this isn't for us to decide. This is something your team needs to decide for itself. Ther... | https://softwareengineering.stackexchange.com |
129,449 | [
"https://physics.stackexchange.com/questions/129449",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/50322/"
] | The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position.
If wave function gives the probabilities of positions, why do we calculate "expectation value of position"?
I don't understand the conceptual difference, we already have a wave function of a position. Ex... | In position-space (that is, when your functions are functions of x), the function $\int|\Psi|^2$ gives the probability of finding the particle in a given range. The expectation value of x is where you'd expect to find the particle. It is often essentially the weighted average of all the positions where the probability ... | Expectation value is a different concept from probability. In fact, you can have an expectation value of energy, angular momentum, etc., not just for position.
An expectation value of an observable for a given state $\Psi$ is the average value of a large number of measurements of that observable, assuming each measure... | https://physics.stackexchange.com |
112,593 | [
"https://mathoverflow.net/questions/112593",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3544/"
] | Let $X$ be a smooth, projective, geometrically connected curve over a field $k$ and $G$ an an affine algebraic group group over $k$ (we can put more hypotheses on $G$ if necessary). If $K$ denotes the function field of $X$ and $\mathbb{A}$ the corresponding ring of adeles with integral adeles $\mathcal{O}$, I expect th... | The one-sentence answer to this question is: use fpqc descent theory (and an "answer" which doesn't address the role of fpqc descent -- sometimes presented in the form of a reference to a paper of Beauville and Laszlo -- is missing the key technical issue in the rigorous proof when working with general $G$, as far as I... | First let's remove the condition that $X$ is projective. Then we will replace the adeles with a product over the points actually in $X$, and do the same for the integral ideles.
Then let's make this set into a category. A map from $x \in G(\mathbb A_X)$ to $y \in G(\mathbb A_X)$ is a pair $a \in G(\mathcal O_{\mathbb ... | https://mathoverflow.net |
2,968,842 | [
"https://math.stackexchange.com/questions/2968842",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/230668/"
] | <blockquote>
Evaluate <span class="math-container">$$\lim_{x \to 0} \left(\frac{1}{x^2}-\cot^2x\right).$$</span>
</blockquote>
<strong>Attempt</strong>
<span class="math-container">\begin{align*}
&\lim_{x \to 0} \left(\frac{1}{x^2}-\cot^2x\right)\\
= &\lim_{x \to 0} \left(\frac{1}{x}-\cot{x}\right)\left(\fra... | As @user21820 encouraged, I am going to explain the errors in this post.
The problem is the <span class="math-container">$=$</span> at the last 2nd line. Before this everything could be accepted, since they are the process to find the limits. But at this step you generally claim that
<span class="math-container">$$
... | <span class="math-container">\begin{align}\lim_{x\to0}\frac1x+\cot x&=\lim_{x\to0}\frac{\sin x+x\cos x}{x\sin x}\\&=\lim_{x\to0}\frac{2\cos x-x\sin x}{\sin x+x\cos x}\\&=\infty.\end{align}</span>Besides,<span class="math-container">$$\lim_{x\to0}\frac1x-\cot x=0.$$</span>
The error you made lies in the use... | https://math.stackexchange.com |
13,994 | [
"https://security.stackexchange.com/questions/13994",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/5400/"
] | I'd like to encrypt IP addresses in my MySQL database, with the following constraints:
<ul>
<li>Does not need to be resistant to attackers that can execute queries.</li>
<li>Must be resistant to attackers that have access to files on disk.</li>
<li>Must be able to validate an IP against the encrypted form, to check if... | Public / private key encryption is slow. It's ideal for write it & forget it, but it's not a fast process.
For the sake of speed, consider this: use a randomly generated symmetric key that is chosen when the daemon starts and possibly is rotated out every hourly, daily, weekly, or monthly (depending on your traffi... | Your scheme is a good solution. Nicely done!
<strong>A possible performance optimization.</strong> If you need a way to make it more efficient, there are ways to improve the efficiency. For instance, here is one. The application can pick a random symmetric key <em>K</em>, encrypt <em>K</em> under the public key, th... | https://security.stackexchange.com |
23,806 | [
"https://mechanics.stackexchange.com/questions/23806",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/13825/"
] | There is an excellent Q&A about why diesel engines have lower redline RPMs (about 4500 RPM) than gasoline engines (about 6500 RPM). The reason is related to the combustion of diesel fuel.
However, what would happen if you manage to over-rev a diesel engine to, say, 5500 RPM by downshifting a manual transmission on... | The rev limit of a petrol (gasoline) engine is generally set to protect the internals of the engine. Less sporty engines are designed to a cost and their components may not have the strength or manufacturing tolerances to cope with the higher forces experienced at higher engine speeds.
Diesel engines, as you say, are ... | Piston speed is the limiting factor. Diesels have a longer stroke. Even though they aren't reving fast the piston speed still gets as high as a gasoline engine.
| https://mechanics.stackexchange.com |
1,556 | [
"https://stats.stackexchange.com/questions/1556",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/559/"
] | What is the difference between having something statistically significant (such as a difference between two samples) and stating if a group of numbers are independent or dependent.
| Based on your additional explanation in the comments, it appears that you have 8 groups (each corresponding to a column) and a continuous outcome variable that you grouped into 10 bins (each bin corresponding to a row). Note that it also implies that the rows are ordered with later rows implying larger values.
First o... | Was going to leave this as a comment, but it was getting too long...
While the chi-square statistic may not be significant, its numerical value is large. You can interpret $\frac{1}{2}\chi^{2}$ as an approximate log-likelihood ratio against the best alternative in the Bernoulli class. So the data supports the best a... | https://stats.stackexchange.com |
24,220 | [
"https://math.stackexchange.com/questions/24220",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/4736/"
] | Thank you~
<blockquote>
Show that if $G$ is a finite nilpotent group, then every Sylow subgroup is normal in $G$.
</blockquote>
I know that the normalizer of any proper subgroup of a nilpotent group contains this subgroup properly. So I think maybe I can prove the normality of the Sylow subgroup of $G$, say $P$, by... | Let $G$ be any finite group, and let $P$ be a Sylow $p$-subgroup of $G$, and $N(P)$ the normalizer in $G$ of $P$.
Note that $P$ is a Sylow $p$-subgroup of $N(P)$, and in fact is normal in $N(P)$; that means that $P$ is the <em>only</em> Sylow $p$-subgroup of $G$ that is contained in $N(P)$.
Now, suppose $g\in G$ nor... | A fairly simple way to do this is to note that a normal Sylow-subgroup is always characteristic. Thus, since you can make a subnormal chain from the Sylow-subgroup to the group itself, this Sylow-subgroup must in fact be normal in each subgroup in the chain and thus in the entire group.
| https://math.stackexchange.com |
289,372 | [
"https://dba.stackexchange.com/questions/289372",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25572/"
] | I'm in a situation where I'm being submitted a (potentially quite long) list of "match entities", each of which contains user data to match, along with a unique ID for that match information. Actual user data from matched users, along with the unique ID for that match, needs to be returned from my SQL query.... | What I ended up doing in the end was passing in JSON representing the different set of queries, and breaking them into a table using <code>OPENJSON</code>. This actually makes the query simple enough that it doesn't even need to be in a stored procedure or create a temp. table, as <code>OPENJSON</code> can be used dir... | Schematically:
<pre class="lang-sql prettyprint-override"><code>CREATE TABLE tmp ([parameters group] INT, [client_handle] CHAR(11), [mobile_no] CHAR(15));
INSERT INTO tmp VALUES
(1,'axtwe-wasst','+44 7747 122123'),
(1,'axtwe-wasst','+44 7904 223323'),
(2,'zjfft-albwq','+44 7758 444111'),
(2,'zjfft-albwq','+44 7758 444... | https://dba.stackexchange.com |
23,426 | [
"https://mechanics.stackexchange.com/questions/23426",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/13651/"
] | At 60mph my engine revs at 2800RPM and at 70 it's 3200RPM. My qustion is which condition would give the most miles from my engine.
| 60 MPH assuming you are in the same gear at both speeds.
At a constant gear, your engine turns at a fixed ratio to the distance you travel. So if you travel from A to B your engine will always turn X revolutions, regardless of speed. In other words, the piston experiences the exact same number of cycles regardless o... | While @Robert-Ryan is technically correct, I'd be surprised if there was a measurable difference in engine lifetime. Engine wear is dominated by cold starts. Once the engine is thoroughly warm, engine wear is minimal. If you want to maximize engine life, minimize the number of short trips where the engine doesn't get w... | https://mechanics.stackexchange.com |
1,144 | [
"https://dsp.stackexchange.com/questions/1144",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/6/"
] | I was explaining to someone how Fourier series work in context of constructing signals that are not everywhere differentiable, e.g. square waves, sawtooth waves, etc. When I mentioned the Gibbs phenomenon however, I realized that I never really learned of why it happens. In fact, as the story goes, not everyone even re... | The book "Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills", by P. Nahin, Princeton University Press, leads up to and contains an explanation of the Gibbs phenomena which might be suitable for someone with a good undergraduate university level math background.
| You can always say that <code>sin</code> and <code>cos</code> has curved shape, and you need infinite amount of frequencies to form a sharp edge from a many curved shapes.
| https://dsp.stackexchange.com |
23,228 | [
"https://dsp.stackexchange.com/questions/23228",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/15032/"
] | <ul>
<li>What is the difference between <span class="math-container">$X(j\omega)$</span> and <span class="math-container">$X(\omega)$</span> notation?
</li>
<li>What is the meaning of <span class="math-container">$j\omega$</span>?
</li>
</ul>
Does it represent frequency, and if yes, what is the meaning of an imaginary... | Both notations are common and correct. As pointed out by Yuri Nenakhov, the advantage of the argument $j\omega$ is that it coincides with the complex (Laplace transform) variable $s$ when its real-part is zero. Note that in the complex $s$-plane the frequency axis is the imaginary axis. So $j\omega$ has nothing to do w... | $X(j \omega)$ (frequency response) is a Fourier transform of system's impulse response. It's actually a function of frequency ($\omega$) but usually is written as $X(j \omega)$ because replacing $j \omega$ in the formula with $s$ will give you system's Laplace transform $X(s)$ without any additional conversions. (This ... | https://dsp.stackexchange.com |
61,397 | [
"https://datascience.stackexchange.com/questions/61397",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/83378/"
] | I'm new to machine learning and am trying to use it to solve a specific problem related to seating students in a classroom. I want to take a list of students and allocate them each to a seat, such that a certain output value is maximised.
An example:
Students (each one containing all the data from which a compatibili... | Since SHAP gives you an estimation of an individual sample (they are local explainers), your explanations are local(for a certain instance)
You are just comparing two different instances and getting different results. This is normal and can happen in train and test set. This doesn't mean also that your train and test s... | You have to make sure that the problem doesn't come from your data or your model :
<ul>
<li>Make sure that your data don't change significantly (same % of classes) but also general distribution / correlation of features, correlation between features and output.</li>
<li>Make sure that your model is not overfit on your... | https://datascience.stackexchange.com |
385,334 | [
"https://softwareengineering.stackexchange.com/questions/385334",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/37685/"
] | Still trying to wrap my head around microservice architecture since I'm used to a monolithic approach
Suppose we try to build a <em>extremely simplified</em> Uber booking system. To simplify things we let's say we have 3 services and a gateway api for the client: <code>Booking</code>, <code>Drivers</code>, <code>Noti... | People often hear "micro-service" and think "nano-service", and this can cause some confusion. These are <strong>micro</strong>-services, so you don't need a separate service for every single entity. Everything you are trying to do should be in the <code>booking</code> and <code>notification</code> services. You don't ... | It all depends of your exact requirement.
Let's say you have two applications doing the booking :
<ol>
<li>First case : One application may allow one users to book multiple times, the other allow only ones. This means that the restriction of the booking is on the application level, as such either you have two entry ... | https://softwareengineering.stackexchange.com |
461,521 | [
"https://physics.stackexchange.com/questions/461521",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/223071/"
] | I have worked with the Navier Stokes equations before but I'm a physicist. I was talking to a mathematician and they use a complete different notation and I am very lost.
First of all, I use the Control Volume method for discretization and they use Finite Element.
Second, they talk about variational forms and H and ... | First of all, an expression like
<span class="math-container">$$dE_{x} = d\vec{E}\,\cos\theta$$</span>
can never be correct. If you have a vector on the right, you will also have a vector on the left. The correct expression would be
<span class="math-container">$$dE_{x} = d\vec{E} \cdot \hat{u}_x = \frac{dq}{4\pi\epsil... | You cannot have a scalar equal to a vector.
Starting from <span class="math-container">$d\vec{E} = \dfrac{dq}{4\pi\epsilon_{0}r^{2}}\hat{u}$</span> to get to the componet in the <span class="math-container">$\hat x$</span> direction
<span class="math-container">$d\vec{E} \cdot \hat x = dE_{\rm x} = \dfrac{dq}{4\p... | https://physics.stackexchange.com |
677,407 | [
"https://physics.stackexchange.com/questions/677407",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/319414/"
] | A car is travelling straight in one direction. If the car is accelerating (a positive one, so it becomes faster) on a nonfrictionless road, then the ground exerts two forces to the car, each in opposite direction, to the car, right? The first one is required to accelerate the car, and the second one is the static frict... | <blockquote>
then the ground exerts two forces to the car, each in opposite
direction, to the car, right?
</blockquote>
No. The ground only exerts one force, and that's the static friction force acting forward on the wheel. The other force is exerted by the wheel on the ground acting backward. The two are equal and opp... | The car accelerates because of the friction alone. The only reason the road can exert a force on the car to accelerate it is because the car is exerting a force on the road to accelerate it in the opposite direction.
If there was no friction between the tires and the road, the car would stand still.
| https://physics.stackexchange.com |
33,167 | [
"https://physics.stackexchange.com/questions/33167",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1224/"
] | Magnesium powder burns extremely well and reaches temperatures of 2500°C. However, attempts to extinguish such a magnesium fire with conventional water (e.g. from a garden hose) only make it worse: the flame grows astronomically and the whole thing gets even hotter. Why is this?
| Magnesium reacts with water to produce hydrogen and a lot of heat. Metallic magnesium reacts only slowly, but magnesium vapour, produced when Mg burns, reacts extremely quickly due to the high temperature and efficient mixing, and produces heat very rapidly. Hence the explosion when water is added to burning magnesium.... | The total energy released <strong><em>per gram of magnesium</em></strong> stays the same:
<span class="math-container">$$\rm Mg+O_2 \to MgO_2$$</span> is identical in overall effect to the pair of reactions <span class="math-container">$$\rm Mg+2H_2O\to MgO_2+2H_2$$</span> <span class="math-container">$$\rm2H_2+O_2\... | https://physics.stackexchange.com |
372,891 | [
"https://mathoverflow.net/questions/372891",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16183/"
] | Let <span class="math-container">$B\subset \mathbb{R}^n$</span> be a open ball. Let <span class="math-container">$\{f_i\}$</span> be a sequence of functions bounded in the Hölder norm <span class="math-container">$C^{k,\alpha}(B)$</span> for a given integer <span class="math-container">$k\geq 0$</span> and <span class=... | At first, if partial derivatives of order at most <span class="math-container">$k$</span> of <span class="math-container">$f_{n_i}$</span> converge to those of <span class="math-container">$f$</span>, than automatically <span class="math-container">$f\in C^{k,\alpha}(B)$</span>, since <span class="math-container">$$|(D... | For completeness, let's mention a simpler and more general statement: For <span class="math-container">$\Omega\subset\mathbb{R}^n$</span> a bounded open set, <span class="math-container">$k\in\mathbb{N}$</span> and <span class="math-container">$0<\beta<\alpha\le1$</span> there is a compact embedding
<span class=... | https://mathoverflow.net |
160,665 | [
"https://mathoverflow.net/questions/160665",
"https://mathoverflow.net",
"https://mathoverflow.net/users/45729/"
] | I would like to know the proof of the following theorem:
<blockquote>
Consider two Banach spaces $X\hookrightarrow Y$ and $1<p,q\leq\infty$. Let $(f_n)_{n\geq 0}$ be a bounded sequence in $L^q(I,Y)$ and let $f:I\mapsto Y$ be such that $f_{n}(t)\rightharpoonup f(t)$ in $Y$ for a.a. $t\in I$. If $f_n$ is bounded in... | Here is an answer when $p<\infty$ and $I$ bounded. The argument might be adapted to $p=\infty$ by replacing some weak $L^p$ convergences below by the weak-* $L^{\infty}$ one, and I really believe $I$ bounded is not an issue (otherwise argue locally on any $J\subset I$)
Just a few obvious remarks first: if $X$ is re... | I also had troubles with this theorem when I read the Cazenave's book. Recently I found this answer for proving the theorem. However, I think there is still a little flaw in the proof, namely in step 1, we can not directly use that <span class="math-container">$L^p(I,Y)$</span> has dual <span class="math-container">$L^... | https://mathoverflow.net |
693,431 | [
"https://physics.stackexchange.com/questions/693431",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/315871/"
] | I was reading about Avogadro's law which states that
<blockquote>
Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.
</blockquote>
My question is, <strong>how can one verify this practically</strong>?
The way that I think we can test this is by filling di... | (Edit to address an ambiguity pointed out by Chet: Since I know what relation you're trying to achieve, I know that you mean that <span class="math-container">$T_1$</span> is the boiling temperature at the given conditions, i.e., that vaporization is reversible at <span class="math-container">$T_1$</span> but not at <s... | None of these answers is correct. The correct answer for <span class="math-container">$\Delta S_{vap}(T_2)$</span> is <span class="math-container">$$\Delta S_{vap}(T_2)=\frac{\Delta H_{vap}(T_2)}{T_2}$$</span>From Hess' Law, <span class="math-container">$$\Delta H_{vap}(T_2)=-\int_{T_1}^{T_2}{C_{p, liquid}dT}+\Delta H... | https://physics.stackexchange.com |
7,212 | [
"https://quantumcomputing.stackexchange.com/questions/7212",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/8330/"
] | <pre><code>result = execute(circuit, backend=simulator)
plot_histogram(result.get_counts(circuit))
</code></pre>
I used the above code to plot a histogram for a simple entanglement circuit. I got the error mentioned below. I am running the code in Google Colab.
<pre><code>AttributeError: 'AerJob' object has no attribu... | This should fix your problem:
<pre><code>result = execute(circuit, backend=simulator).result()
plot_histogram(result.get_counts(circuit))
</code></pre>
| Execute returns a job instance. The job has a result, job.result(), and you get counts from the results, ie job.result().get_counts()
| https://quantumcomputing.stackexchange.com |
67,595 | [
"https://mathoverflow.net/questions/67595",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5756/"
] | To say I am a novice in $K$-theory is to overstate my experience with the field. I've been reading the various wiki articles so as to have some preparation before jumping in, and I couldn't answer the following question to myself:
I understand that $K$-theory had started with the Grothendieck-Riemann-Roch in mind, and... | The idea of considering higher K-groups comes from topology, and is due to Atiyah, Bott, and Hirzebruch. Atiyah and Hirzebruch defined topological K theory and observed that Bott periodicity says that $K(X)$ is more or less the same as $K(S^2X)$. This suggested to them defining a generalized cohomology theory of peri... | After having defined <i>K</i><sub>0</sub>, a natural things to do is to study its functoriality properties.
You do that, and you notice some exact sequences... that you happen to be able to extend a
bit by using the functors <i>K</i><sub>1</sub>, and then later <i>K</i><sub>2</sub>.
It is then natural (specially if y... | https://mathoverflow.net |
511,063 | [
"https://electronics.stackexchange.com/questions/511063",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/194559/"
] | Assuming that one just want to control a single power transistor or MOSFET with a microcontroller and that one is using an intermediary transistor(s) between the microcontroller and the power MOSFET to get the full range of allowed voltages to the gate. What are the issues of just using the analog output of a microcont... | It has a designator of C38 which means it is a high voltage capacitor with a spark gap.
Typically the coaxial cable interface is isolated from the PC chassis ground, with the exception that the cable shield is connected to PC chassis via a 1 Mohm resistor in parallel with a 10nF high voltagre capacitor. The capacitor v... | it's a spark gap. I'm sure this has been answered before.
| https://electronics.stackexchange.com |
57,171 | [
"https://electronics.stackexchange.com/questions/57171",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18249/"
] | I have an Atmel board, precisely an Atmega1280. I uploaded my code on the board and I want debug it to take a look at the stack memory.
I just have the mini usb cable for the communication.
I read that JTAG is also a debugger but I don't understand what exactly it is and if works with my cable.
Hence, my question is... | During the firmware build process, the Map stage maps the top level signals of your firmware to physical FPGA pins. This assignment is almost always done manually by including pin assignments in a file called the constraints file (by the xilinx tool set, at least). If no constraints are found the pins will be allocated... | I assume that in your previous FPGA projects, the modules you were writing interfaced with other modules inside the same FPGA. As such, you had to pay attention to the timing relationships among the various inteface signals.
Interfacing an FPGA to one or more external chips, from a functional point of view, is no diff... | https://electronics.stackexchange.com |
51,308 | [
"https://engineering.stackexchange.com/questions/51308",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/28906/"
] | I have an old laptop which I revived with the addition of a SSD. The problem now with this laptop is that it gets very hot causing thermal shutdowns in the middle of work. I thought of a lot of solutions and finally repasted the heat sink, bought a cooling pad and removed the bottom cover. It is now running fine. Now t... | If the existing heatsink is made of copper, then yes you can <em>solder</em> more copper onto it and it will probably dissipate more heat.
You can probably weld copper, but it's not commonly done.
If the existing heatsink is made of aluminum, your best bet would be to use thermal epoxy to attach your heatsink extension... | I think, it is necessary to find a cause of overheat. This may be due to bad thermal contact somewhere:
<ul>
<li>between integrated circuit and metal pad through thermal paste or pad</li>
<li>between metal pad and heat pipe</li>
<li>between heat pipe and heat exchange plates</li>
</ul>
Heat exchange plates could be blo... | https://engineering.stackexchange.com |
252,262 | [
"https://softwareengineering.stackexchange.com/questions/252262",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/145150/"
] | I am somewhat new to C# and just found out that: in C# all of the fields and methods in a class are default private. Meaning that this:
<pre><code>class MyClass
{
string myString
}
</code></pre>
is the same as:
<pre><code>class MyClass
{
private string myString
}
</code></pre>
So because they are the same shoul... | Just because you can omit linefeeds and indentations and your C# compiler will still understand what you want to tell it, it's not automatically a good idea to do that.
<pre><code>using System; namespace HelloWorld{class
Hello{static void Main(){Console.WriteLine
("Hello World!");}}}
</code></pre>
is much less reada... | C# is not the only programming language for .NET; other languages can and do have different default accessibility in various contexts. Specifying <code>private</code> will make it clear to anyone reading the code that such accessibility is intended, whereas omitting the spec leaves open the question of whether the mem... | https://softwareengineering.stackexchange.com |
587,434 | [
"https://physics.stackexchange.com/questions/587434",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/273611/"
] | My question is related to a statement:
<blockquote>
If a pendulum is experiencing free fall, then it will not oscillate.
</blockquote>
The statement is true in the sense that its acceleration is (approaching to) zero, then according to the period equation <span class="math-container">$T$</span> would be infinity.
I thi... | <blockquote>
why we should consider general relativity for this pendulum, rather than a pure Newtonian senario
</blockquote>
There is no need to consider general relativity at all for this scenario. Newtonian gravity clearly replicates this behavior.
In a Newtonian context we would consider a free falling frame to be n... | Indeed you don't need GR here as was clarified by the previous answer.
But if we look at the situation from the GR point of view, then according to the equivalence principle, a small enough non-rotating freely falling frame, which is falling for a short enough amount of time, is the closest thing we have to an inertial... | https://physics.stackexchange.com |
134,776 | [
"https://mathoverflow.net/questions/134776",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $A\in \mathbb{R}^{n\times n}$ and $u$ and $v$ be independent random $\{-1,1\}^n$-vectors. (i.e., each coordinate of $u$ is $1$ with prob. $1/2$ and $-1$ with prob. 1/2 and the coordinates of $u$ are independent with each other)
<strong>Question.</strong> Is there a tail bound for $\Pr\{u^T A v > t\}$?
I am ho... | You can write the bilinear form as a quadratic form, by letting x = (u,v) and rewrite the matrix A.
| The Hanson-Wright inequality says
$$
\mathop{\mathbb{P}}_{u,v}(|u^T A v| > t) \le C\cdot \max\left\{e^{-c t^2/\|A\|_F^2}, e^{-c t/\|A\|}\right\}
$$
where $\|\cdot\|$ is the largest singular value and $C,c>0$ are universal constants (independent of $A,n$).
| https://mathoverflow.net |
11,440 | [
"https://dba.stackexchange.com/questions/11440",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5794/"
] | I have problem in updating table.
I need to update table by comparing date and name with another table.
I have two tables:
<pre><code> table 1 : dim_sesid
name(varchar) role
20111012133513aaa123
20110908072611aaa121
20111002210235bbb853
2012011311... | If you want to ignore the time part and match where the days are the same then:
<pre><code>UPDATE dim_sesid ds
SET role =
(SELECT min (er.role)
FROM EMPLOYEEROLE er
WHERE substr(DS.NAME, 1, 8) || 'xxxxxx'
|| substr(DS.NAME, 15, length(USERNAME))
... | <pre><code>UPDATE dim_sesid d
SET role = e.roles
FROM (
SELECT replace(left(thedate, 10), '-') AS day
, username
, string_agg(role, ', ') AS roles
FROM employeerole
GROUP BY 1, 2
) e
WHERE e.day = left(d.name, 8)
AND e.username = substring(d.name, 15) ~~ (d.name || '%')
</cod... | https://dba.stackexchange.com |
670,560 | [
"https://physics.stackexchange.com/questions/670560",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/315970/"
] | The bubbles in champagne are familiar to most people. They form almost exclusively at the specific points in the champagne glass, and from these they rise faster and faster. Why <em>do</em> the bubbles in champagne accelerate?
| As the other answers point out, the force that accelerates the bubble is buoyancy counteracted by drag and the weight of the bubble. The process that leads to perceptible acceleration of the bubble all the way while it rises, however, is that the bubble grows as gas diffuses into it, which increases the terminal veloci... | Basic forces which compete are buoyancy force and body weight. From here we can write net force equation :
<span class="math-container">$$ ma = mg - \rho_{_f} gV $$</span>
where <span class="math-container">$\rho_{_f}$</span> is fluid density, <span class="math-container">$V$</span> - body volume, or body's expelled li... | https://physics.stackexchange.com |
4,044,708 | [
"https://math.stackexchange.com/questions/4044708",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/886848/"
] | [3,4] is closed in R <-- R-[3,4] is open
[5,6] is closed in R <-- R-[5,6] is open
Show that [3,4] x [5,6] is closed in R x R by writing it as the complement of the intersection of two open sets in R x R.
(R - [3,4]) x (R - [5,6]) not equal R x R - [3,4] x [5,6]
| Using that <span class="math-container">$u$</span> is midpoint-convex works in higher dimensions as well.
<span class="math-container">$y \mapsto x - (y-x) = 2x-y$</span> maps the sphere <span class="math-container">$\partial B_r(x)$</span> bijectively onto itself (each point is mapped to the “opposite” point on the sp... | Martin gives a very reasonable answer extending the question's second argument; here's how to extend the first one.
If <span class="math-container">$u: \mathbb{R}^{d} \to \mathbb{R}$</span> is continuous and convex, then mollification of <span class="math-container">$u$</span> gives a family of smooth functions <span c... | https://math.stackexchange.com |
131,148 | [
"https://security.stackexchange.com/questions/131148",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/108786/"
] | Should the Session ID generated after logging in be marked invalid when the user closes the browser without logging out?
Could this be a security flaw? If yes,is it possible to exploit this?
| Browsers do not normally listen to any port so there are no port to send the SYN-ACK to. The browser is also often behind a NAT so you cannot even reach any port on the computer the browser is running on except when answering requests. Having an open AJAX request or using web-sockets is of course possible but will be c... | Yes, keeping the session valid after the user closes their browser is a minor risk. You want to keep the time that a session token is valid to the minimum. After the user closes the browser he certainly is not going to use it anymore, so there is no sense in keeping it valid.
The problem is you don't get notified when... | https://security.stackexchange.com |
319,453 | [
"https://softwareengineering.stackexchange.com/questions/319453",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/210271/"
] | I am working on a project and we have regular (usually weekly), informal meetings, where we discuss the status of the project and the GUI of it.
I'm the only developer there, the other 4-5 people have a non-IT background.
This meeting took much longer than usual, but at one point, one of my colleagues asked about so... | "As long as they need to be, and no longer."
The thing to realize here is that meeting time to saved development time is in no way linear. For your team, for your company, for <em>this</em> topic, then 1 hour of meetings might save 2 hours of dev work. If you have 10 hours of meetings, another hour of meetings might s... | <strong>Not exactly.</strong>
Understanding the customer/stakeholder can save development time. And conversations need to be long enough to facilitate understanding. But, discussing a feature you already presume to understand will not necessarily improve your understanding.
If no one in the room has any suspicions of... | https://softwareengineering.stackexchange.com |
54,867 | [
"https://mathoverflow.net/questions/54867",
"https://mathoverflow.net",
"https://mathoverflow.net/users/450/"
] | Consider a compact connected complex manifold $X$ of dimension $n$. Siegel proved in 1955 that its field of meromorphic functions $\mathcal M (X)$ has transcendence degree over $\mathbb C$ at most $n$. Moishezon studied those complex manifolds for which the degree is $n$, and consequently these manifolds are now called... | maybe the following argument works. (It's quite possible a sign went wrong somewhere, though.)
Let <span class="math-container">$\pi: Y \rightarrow X$</span> be the blowup. By assumption <span class="math-container">$Y$</span> is projective, so it carries an ample line bundle <span class="math-container">$A$</span> sa... | There is a sledgehammer available for this particular nut: Mori's results on extremal rays, in his paper (Annals 1979?) on smooth projective varieties $Y$ where $K_Y$ is not nef: if $Y=Bl_PX$, with exceptional divisor $E$, then any line in $E$ will span an extremal ray and then can be contracted in the category of proj... | https://mathoverflow.net |
1,966,428 | [
"https://math.stackexchange.com/questions/1966428",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/372987/"
] | How to prove that $\int_0^{\infty}e^{x^2}dx$ is divergent.
The integrand goes to infinity as x goes to infinity. But I have no idea how to prove it rigorously
| let $X>0$
we have
$\forall x\in [X,+\infty) e^{x^2}\geq1$
and
$\int_0^Xe^{x^2}dx\geq\int_0^Xdx=X$
when $X$ goes to $+\infty$ the integral
goes also to $+\infty$ and it's divergent.
| Hint: compare it with $\int_0^\infty e^x$
| https://math.stackexchange.com |
411,940 | [
"https://softwareengineering.stackexchange.com/questions/411940",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/368855/"
] | A customer has reported a bug that neither them nor us have been able to reproduce. This is the only report of this bug happening so far.
We've spent a lot of time trying to replicate the issue (followed the customers' exact path, with their same browser, and even set the server and local machine clock to replicate the... | Customers generally at least begrudgingly understand if you can't reproduce a bug, especially if you have worked with them and made very visible attempts. What it usually takes to close such bugs is some sort of mitigation.
If it happens again, have you put something in place that will prevent data loss, give you more ... | Respond politely and honestly.
Document your attempts to reproduce the bug. Add logging capabilities if possible. Clean up the code around the bug to the best of your ability.
If this bug ever comes up again, you want to build up a backlog of evidence on how to fix it.
Sometimes you'll fix the bug while working on othe... | https://softwareengineering.stackexchange.com |
55,233 | [
"https://chemistry.stackexchange.com/questions/55233",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/31622/"
] | As we all know, if we put $\ce{H^+}$ ions in water then water reacts with them and produces $\ce{H_3O^+}$:
$$\ce{H_2O + H^+ <=> H_3O^+}$$
My question is, why does water react with $\ce{H^+}$ in the first place? It doesn't have an electron, then how can the reaction occur?
And again, it's already stable and add... | Water has two lone pairs. H$^+$ is a naked nucleus with a positive charge. It is extremely reactive and would bind to any neutral molecule. Water has two lone pairs of electrons and H$^+$ binds one of them to form H$_3$O$^+$.
In absence of water it would bind other things. For example, it would bind methane to form un... | The simple answer is that H$_3$O$^+$ is more stable that H$^+$+ H$_2$O. The reason for this is that the H$_3$O$^+$ ion is isoelectronic with ammonia and has the same type of geometry, a triangular based pyramid (trigonal pyramid). It is possible to crystallise some salts with H$_3$O$^+$ as a counter ion, but of course... | https://chemistry.stackexchange.com |
17,256 | [
"https://stats.stackexchange.com/questions/17256",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6096/"
] | I asked 312 people how many times they visited their preferred local supermarket in a month
The results are as follows:
<ul>
<li>5% did not visit at all</li>
<li>7% visited once a month</li>
<li>33% visited twice a month</li>
<li>22% visited three times a month</li>
<li>15% visited four times a month</li>
<li>18% vis... | You need to be creative, because these data are consistent with <em>any</em> mean exceeding $0\times .05 + 1\times .07 + \cdots + 5\times .18$ = $2.89$ and <em>any</em> standard deviation exceeding $1.38$ (which are attained by assuming nobody visited any more than five times per month).
For reporting purposes, simply... | You definitely have to associate a numerical value to the class "visited five and more times a month".
By the way, I would calculate the mean and the standard deviation in the usual way. In fact, $x_i$ are your values and $p_i$ are their empirical frequency estimated on the sample. In your case
$$x_0=0 \ x_1=1 \ x_2=2... | https://stats.stackexchange.com |
363,421 | [
"https://physics.stackexchange.com/questions/363421",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/172515/"
] | Suppose a man of mass 50 kg climbs a stair of height 10 m.Clearly it gains 5000 J of potential energy.But since work done by normal reaction on the man is zero does'nt it violates the principle of conservation of mechanical energy because no non-conservative force is acting on the man and thus mechanical energy should... | By "work done by normal", you probably mean that since the foot does not move relative to the stairs, whatever the normal force on man exerted by the stairs, there cannot be work done by this force as displacement is zero. In the case of discrete stairs with horizontal top surface, that is correct.
However, when your... | When the man applies force to the stairs, the stairs apply an equal force back.
The mans force down is acting <em>on the stairs</em>. If the stairs started moving downwards, you could say the man is doing work on the stairs. Instead, the stairs do not move; the force is static, and there is no work done on the stair... | https://physics.stackexchange.com |
113,395 | [
"https://electronics.stackexchange.com/questions/113395",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/44159/"
] | Suppose I have a component, called Top_Level, that has a bunch of registers that it uses. There are some subcomponents that perform some combinational logic using the registers. There is also a clocked process, Process_1, that does sequential operations on the registers. So, every clock cycle, Process_1 does some seq... | Yes, and it is actually a good practice. It seems like you have already answered most of your own question: turn the registered values into outputs of the lower-level component. This should get you on the right path; if you need more details on how to do that, please show us your source code.
Some other hints that mig... | If your concern is about reading outputs from inside the entity, you just have use a regular signal for the desired internal feedback, and also assign it to the output port. This way, you are not directly reading the output label, which is the language's limitation. The following code should make this clearer:
<pre>... | https://electronics.stackexchange.com |
371,114 | [
"https://physics.stackexchange.com/questions/371114",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/174161/"
] | There are two expressions regarding relativistic mass of photon; namely relativistic approach:
$$m = \frac {m_0} {({1 - \frac {v^2 } {c^2 }) } ^\frac {1 } {2} }. $$
And, energy-mass equivalence formula:
$$ E = m {c}^2. $$
<blockquote>
There common uses in physics books:
</blockquote>
First formula is used to pr... | In general, there's nothing we "expect" about how often transitions between separable and entangled states happen, except that if the Hamiltonian is non-interacting, i.e. of the form $H = H_1\otimes\mathbf{1}_2 + \mathbf{1}_1\otimes H_2$, then separable states will never become entangled. However, the set of separable ... | Following up on ACuriousMind's answer: it's certainly possible for entangled states to evolve into product states, but it's unlikely for a generic process to do this very often, because "almost all" states in the Hilbert space are entangled, and only a vanishingly tiny fraction are product states.
You can see this jus... | https://physics.stackexchange.com |
200,267 | [
"https://security.stackexchange.com/questions/200267",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/195187/"
] | I'm doing some hacking courses, and in one of the lessons, I have a possible SQLi, but in the Python source code there's an if clause just before the SQL statement, which filters the quote symbol:
<pre><code>user="user"
pass="pass"
if "'" in user+pass:
print "error"
else:
db.execute("select * from users where us... | Use a backslash as the last character in user. For example, for the inputs <code>user\</code> and <code>or 1=1 --</code> the following query is run:
<pre><code>select * from users where username = 'user\' and password = ' or 1=1 -- '
</code></pre>
Where the string input is interpreted like this:
select * from users ... | You control two inputs. That means you can end the first one with an escape character, effectively extending it to the start of the second input, and then put arbitrary SQL in the second one. To avoid an unmatched quote at the end of the second input, you'll need to comment out the rest of the query.
| https://security.stackexchange.com |
76,013 | [
"https://security.stackexchange.com/questions/76013",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/12335/"
] | Little background: I forgot one of my CCTV accounts password, so used the admin account to create a new one. However I can't access the old one as it's not possible to change a user account password, even with the admin account (Via the interface at least) (And I'd like to either delete the account, or get access to it... | Based on a google search of your hash it's a Dahua hash.Luckily for you it looks like it has some vulnerabilities
www.exploit-db.com/download/29673/ I don't know if they fixed vulnerability and I don't really know much about CCTV systems.If that fails you could try bruteforcing the hash.
| This might help others looking for a similar vulnerability in the Dahua cameras. In their IP camera line (specifically, in my case, the IPC-HFW4300), they have two default users: 666666 (the regular user) and 888888 (the admin user), with matching passwords. The web UI does no effort hiding this information, and thes... | https://security.stackexchange.com |
29,170 | [
"https://stats.stackexchange.com/questions/29170",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11551/"
] | I am running an experiment where I collect two data sets and I wish to measure the difference between the two. The two data sets are independent, with unknown probability distribution, and may not always have the same length.
Calculating the mean difference is easy as pie, but i also want a measure of the standard dev... | If $X$ and $Y$ are independent, the variance of $X-Y$ is $Var(X) + Var(Y)$. So the variance of the difference of means is the sum of the variances of each mean. This variance is unknown, but you can estimate it easily by the sum of the estimated variances: $S_1^2/n_1 + S_2^2/n_2$.
| There are better ways to estimate the standard deviation of the difference of two independent emperical datasets, when the probability distributions are unknown. You can use convolution, but a more simple nonparametric method is to use all possible differences between the two variables.
For a detailed explanation see:... | https://stats.stackexchange.com |
105,414 | [
"https://cs.stackexchange.com/questions/105414",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/75308/"
] | I was looking at some problems about graphs, and I got stuck on this one. Namely, we have given matrix of size <span class="math-container">$N \cdot N$</span> representing the length of the shortest path in undirected graph between some pairs of nodes in the graph <span class="math-container">$(i,j)$</span>.
We don't ... | The short and simple answer is: it doesn't. No modern mainstream CPU ISA works the way you think it does.
For the CPU, it's just a bit pattern. It's up to you, the programmer, to keep track of what that bit pattern means.
In general, ISAs do not distinguish between different data types, when it comes to storage. (Ign... | Short version: it doesn't know. There's no way to tell.
If <code>1111</code> represents -7, then you have a <em>sign-magnitude representation</em>, where the first bit is the sign and the rest of the bits are the magnitude. In this case, arithmetic is somewhat complicated, since an unsigned add and a signed add use di... | https://cs.stackexchange.com |
603,499 | [
"https://physics.stackexchange.com/questions/603499",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231818/"
] | Suppose an initial quantum state <span class="math-container">$\psi = a_1\phi_1 + a_2\phi_2 + ... + a_n\phi_n$</span>, where <span class="math-container">$\phi_i$</span> is the eigenfunction with eigenvalue <span class="math-container">$\lambda_i$</span> of some measurement operator. Post-measurement, we will find the ... | In quantum mechanics, states are represented by <em>rays</em> in Hilbert space, or more accurately, the space of states is <em>projective Hilbert space</em> - for example, for a finite dimensional system, the space is <span class="math-container">$H_n / \sim \ \cong \mathbb{C}P^{n-1}$</span>, where for <span class="mat... | Wavefunction collapse is just a fiction that we employ because it would be a hassle to describe measurements realistically as entanglement of the observer with the thing being observed, with decoherence.
Phase in quantum mechanics isn't an observable. You can only determine the phase of something relative to something ... | https://physics.stackexchange.com |
178,762 | [
"https://physics.stackexchange.com/questions/178762",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57936/"
] | If the buoyant force on an object is equal to the weight of the water displaced by the object, why do people have an easier time floating on their back than vertically with their head sticking out of the water?
| The chest region provides the least dense region in the body since it traps a large airspace. And for either scenario (back floating or vertical) the chest is submerged.
So the only difference you need to consider is that in the vertical position, the head (at least above the nostrils) needs to be above the water line... | To answer the title: because there are two forces, weight and buoyant uplift, acting on the body and these act on the body at <em>different points</em>: the center of weight (and the center of bouyancy, respectively. Therefore, the pair will exert a <em>torque</em> on the body unless line joining them is aligned with t... | https://physics.stackexchange.com |
308,415 | [
"https://math.stackexchange.com/questions/308415",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/21523/"
] | Durring our lectures our professor calculated an integral like this:
$$
\Psi = \Psi_0 \int\limits^{k+\delta k}_{k-\delta k} \! e^{ikx}\, \textrm{d}k = \Psi_0 \int\limits^{k+\delta k}_{k-\delta k} \! \frac{ix \, e^{ikx}}{ix}\, \textrm{d}k = \frac{\Psi_0}{ix} e^{ikx} \Big|^{k+\delta k}_{k-\delta k}
$$
I dont understand... | $$
\Psi_0 \int\limits^{k+\delta k}_{k-\delta k} \! \frac{ix \, e^{ikx}}{ix}\, \textrm{d}k = \frac{\Psi_0}{ix} \int\limits^{k+\delta k}_{k-\delta k} \! ix \, e^{ikx}\, \textrm{d}k =\frac{\Psi_0}{ix} e^{ikx} \Big|^{k+\delta k}_{k-\delta k}
$$
Because $$\frac{\textrm{d}e^{ikx}}{\textrm{d}k} = ix e^{ikx}$$
What I don't r... | We have
$$\frac{ixe^{ikx}}{ix} = e^{ikx}$$
and $i$ and $x$ should be considered as constants because you are integrating with respect to $k$. So you just use the rule for integration of an exponential:
$$\int e^{ak}\mathrm{d}k = \frac{1}{a}e^{ak} + C$$
| https://math.stackexchange.com |
123,141 | [
"https://softwareengineering.stackexchange.com/questions/123141",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/42120/"
] | I have the following problem:
<blockquote>
Given <code>n</code> chips [note: these are VLSI chips] out of which majority of chips are good, we need to find one good chip. The only test that we can apply is on a pair of chips that answers if both chips are good or both are bad.
The second part is to find a good ch... | I think this is a clustering problem: you have two clusters - the good chips and the bad chips. Your test tells you if two chips belong in the same cluster or not - at least under my interpetation of the question you have asked. The reference provided in the answer by Woot4Moo suggests a different question to this.
Fo... | To find the wrong results, I would compare each chip to multiple other chips. If chips 1 and 2 give a wrong result, the likelihood that comparing 1 to 3, 4, 5, and 6 all also giving wrong results in those four comparisons is greatly diminished. Since you know the percentage of wrong results, it's probably possible to d... | https://softwareengineering.stackexchange.com |
75,873 | [
"https://softwareengineering.stackexchange.com/questions/75873",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22390/"
] | Off the clock I'm going to try and come up with a strategy for version control for my company; we currently use SVN but there's no structure to it - we basically only have a trunk and only commit to that. Recently the development manager started a second repository that acts as our "tag", but it has to be manually mer... | If you want a unified build process, then be sure to put branches/tags/trunk at the root, like this:
<pre><code>branches/
tags/
trunk/
dev/
...
</code></pre>
If you don't need a unified build process, then you can put branches/tags/trunks within each project if you want. However, it might be difficult to migrat... | <ol>
<li>As far as code structure within svn goes this is really personal choice.</li>
</ol>
I would suggest that if the projects are related or share code then they want a common trunk. If they are independent then they want separate trunks or even separate repositories. If you ever need to provide a third party wi... | https://softwareengineering.stackexchange.com |
257,735 | [
"https://softwareengineering.stackexchange.com/questions/257735",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8689/"
] | I need to ask a question that have been bugging me for some time now:
If I have a single core and one OS thread, this thread will get 100% of the CPU time and all is good.
If I have a single core and two or more OS threads, they will share the CPU time using time slices.
So, is the time slices always the same amout ... | If your quantum (the time each thread gets to run) is the same, then you'll have the same number of context switches regardless of the number of threads (assuming no threads are blocked). The amount of time each thread <em>gets</em> will be affected, but the context switching overhead will be constant. This is in an i... | Context switching itself imposes an overhead on the system, because the OS has to perform book-keeping on which threads exist, which are running, which are ready, which have already received their fair share, etc. In a well-designed OS this overhead is not great, and usually it is not dependent on the number of threads... | https://softwareengineering.stackexchange.com |
177,103 | [
"https://electronics.stackexchange.com/questions/177103",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/79545/"
] | We know that a Fourier series formula for any signal $s(t)$ is given as
<span class="math-container">$$\frac {a_0} 2 + \sum \limits _{m=1} ^\infty (a_m \cos \frac {2 \pi m t} T + b_m \sin \frac {2 \pi m t} T)$$</span>
Here,as we see from the formula ,except the DC component and fundamental frequency components there a... | In general, Fourier coefficients are given by the formulas:
$$a_n = \frac{2}{T}\int_{x_0}^{x_0+T}g(x)\cos\left(\frac{2\pi nx}{T}\right)dx\\
b_n = \frac{2}{T}\int_{x_0}^{x_0+T}g(x)\sin\left(\frac{2\pi nx}{T}\right)dx$$
For any integrable \$g(x)\$ on the interval \$[x_0, x_0+T]\$. For periodic functions this interval c... | To answer your recent comment: yes, in the formula for Fourier series, ANY of the \$a_m\$ or \$b_m\$ terms can be zero. The fundamental frequency has no special privileges.
Perhaps, to convince you, consider a composite signal:
\$g(\theta)=sin(2\theta)+sin(5\theta)\$, where \$\theta=2\pi ft=2\pi t/T\$
This does n... | https://electronics.stackexchange.com |
185,290 | [
"https://electronics.stackexchange.com/questions/185290",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/80802/"
] | I am starting with UART communication in <code>PIC32MX795F512l</code>. This UART will communicate with PC. I was just wondering that it is important to connect <code>RTS</code> & <code>CTS</code> or just connecting Rx Tx GND will make the communication? Some websites say RTS & CTS are also important but some sa... | RTS & CTS are not always important. You can directly make cross connections like
Rx -> Tx
Tx -> Rx
GND -> GND
| Rx, Tx, GND pins are enough for communication. However in UART bootloader applications RTS pin is important and used for resetting MCU
| https://electronics.stackexchange.com |
557,278 | [
"https://physics.stackexchange.com/questions/557278",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16713/"
] | In textbook electromagnetism we are used to seeing neat, coordinate-free, expressions for the scalar potential from an electric dipole (using Gaussian units)
<span class="math-container">$$\phi(\mathbf{r}) = \frac{\mathbf{p} \cdot \mathbf{r}}{r^3}$$</span>
and vector potential from a magnetic dipole
<span class="math-c... | The dipole potential is given by
<span class="math-container">$$
\phi_\text{dip} (\mathbf{r}) = -(\mathbf{p} \cdot \mathbf{\nabla}) \phi_\text{mono}(\mathbf{r})
$$</span>
where <span class="math-container">$\phi_\text{mono}$</span> is the familiar monopole potential <span class="math-container">$\phi_\text{mono}(\mathb... | Remember that polynomials become differential operators and viceversa when switching between spatial and Fourier coordinates, while products become convolutions and viceversa. Hence it is expected that the Fourier of that potential are <em>sort of</em> convolutions of third-order Green operators.
On the case of inverse... | https://physics.stackexchange.com |
251,092 | [
"https://dba.stackexchange.com/questions/251092",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/44404/"
] | I've got a table of Product records from an old db that I must change to import on a new php system. They have the form:
<pre><code>name, property1_IT, property1_EN, property1_FR
</code></pre>
I need to transform them by duplicating each row and change it like:
<pre><code>name, language, property1
</code></pre>
whe... | You can do it like this:
<pre><code>create new_table as
select name, 'italian' as language, property1_IT as property1 from old_table
union all
select name, 'english' as language, property1_EN as property1 from old_table
union all
select name, 'french' as language, property1_FR as property1 from old_table;
</code></pre... | A a compendium to @tombom's answer, I'd like to add the fact that if the table has a lot of fields (as in my case) and field order is not a problem, another approach can be to simply add translations after all the other fields, and then delete the old translation ones. So, first:
<pre><code>CREATE TABLE `V36_test` AS
... | https://dba.stackexchange.com |
65,189 | [
"https://dba.stackexchange.com/questions/65189",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/31969/"
] | I'm currently building an education data warehouse.
I have three factless fact tables for distinct set of grades due to the fact I have no measures (I'm not aggregating anything), the grades are completely unrelated to each other hence why they're in different tables. I'm only slicing student dimension by grade fact t... | I think i've found the problem. SSAS doesn't seem to relate data between tables if there are no measures defined. I added a simple measure like grade count and voila i have my data relationship.
| From the Looks of the image I asked you to post, you have a many to many relationship between students and grades
<pre><code>many students can have many grades
</code></pre>
I can not tell from either Image, if each entity Contains a Grade. Consider breaking each relationship into a one to many.
<pre><code>one st... | https://dba.stackexchange.com |
4,673 | [
"https://quantumcomputing.stackexchange.com/questions/4673",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/1867/"
] | In superdense coding, you can use one qubit to control the Hilbert space of two qubits and steer it into 4 mutually orthogonal states, so that measurement of both qubits together will not have a probabilistic outcome.
I think the idea is cool. I want to understand a more general question that arises from this result.
... | <blockquote>
There are a total of 5 qubits. I have 2, and my friend has 3. Clearly
the upper bound of classical bits I can send to my friend is 5. But is
it possible to find 5 unitary operations I can perform on my two
qubits to steer the state into 5 orthogonal states.
</blockquote>
You can simply set up two ... | Let me call you A and your friend B.
You initially share a state <span class="math-container">$|\psi\rangle$</span>. W.l.o.g., we can write this in its Schmidt decomposition:
<span class="math-container">$$
|\psi\rangle = \sum_{i=1}^d \lambda_i |i\rangle_A|i\rangle_B.
$$</span>
You are now asking how many (orthogonal)... | https://quantumcomputing.stackexchange.com |
73,526 | [
"https://mathoverflow.net/questions/73526",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36814/"
] | This is a soft question. How do people usually use arxiv to put their papers? At which stage does one usually put his/her paper/report there? Someone suggests me to submit a paper while putting it on arxiv. Is that the convention that people follow?
Thank you!
Anand
| My comments above formulated as an answer:
People typically post a preprint on the arxiv at the same time that they post it on their own homepage, with the goal of disseminating their work to their colleagues. (These days, posting on the web is more important than journal publication for sharing your work, and the arx... | What I personally do is as described by Emerton in his post, and so the following is what other people have told me, and not perhaps totally my own thoughts.
I have also heard that people do the following: post to the arxiv after acceptance by the journal but before giving the final proofs. Advantages:
<ul>
<li>You ... | https://mathoverflow.net |
3,372,635 | [
"https://math.stackexchange.com/questions/3372635",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/30229/"
] | On the plane <span class="math-container">$\mathbb{R}^{2}$</span> consider the unit circle <span class="math-container">$S^{1}$</span> and let <span class="math-container">$N$</span> denote the North Pole <span class="math-container">$(0,1)$</span>. The stereographic projection is a homeomorphism of <span class="math-c... | It is impossible. For any map <span class="math-container">$h : \mathbb R^2 \to \mathbb R^2$</span> the set <span class="math-container">$h(S^1 \setminus \{ N\})$</span> is contained in <span class="math-container">$h(S^1)$</span> which is compact and thus cannot contain the <span class="math-container">$x$</span>-ax... | There is no ambient homeomorphism of <span class="math-container">$\mathbb{R}^{2}$</span> onto itself which carries <span class="math-container">$S^{1}−N$</span> onto the <span class="math-container">$x$</span>-axis. If such an ambient homeomorphism existed then the complements of <span class="math-container">$S^{1}-N$... | https://math.stackexchange.com |
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