qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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33,104 | [
"https://stats.stackexchange.com/questions/33104",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12877/"
] | Given a set of extracted data from different sources with different accuracies, how can I combine the accuracy of those who give the same output?
Example :
<pre><code>Data from source A are 80% correct
Data from source B are 85% correct
Data from source C are 90% correct
</code></pre>
If two of the sources give the ... | So if I assume there is a single binary state (0 or 1) that is measured three times, where the three observations are independent, we can calculate the probability of each state. This is a likelihood-based analysis without any real equations.
So for your example, A says 1, B says 1, and C says 0. The two choices are... | The above answer corresponds to a special case of a more general answer. First of all, it makes certain assumptions regarding the prior distribution of the true state and conditional independence assumptions, as noted by matted.
I'll try to provide the answer for the general case, showing where these assumptions come... | https://stats.stackexchange.com |
111,370 | [
"https://stats.stackexchange.com/questions/111370",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/53811/"
] | I am using the <code>earth</code> package in <code>R</code> to estimate the number of breakpoints in a curve. There is only a single predictor.
I was hoping there was a sensible way to compare a slope for some segment against 0. Normally I would use the estimate and standard error, but it's not obvious (to me) what to... | The short answer: you can't quantify that precisely.
You can have confidence in the model AS A WHOLE (because of the GCV, see for example the FAQ in the earth package vignette "What is a GCV in simple terms?") but can't easily quantify the significance of each part of the model.
The problem is actually worse than qua... | To some extent, MARS has already "tested" the slopes in so far as predictive ability via the CV procedure used. Of course, this assumes the CV has been done in a way that matches the experimental design or dependencies in the data.
If you wanted to get better estimates of the standard errors, I would suggest a bootstr... | https://stats.stackexchange.com |
449,149 | [
"https://physics.stackexchange.com/questions/449149",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/209277/"
] | I know it may be a very silly question. But when we are calculating the total energy, shouldn't we also consider the potential energy due to the centrifugal force acting on the body?
Or as, we are working in the inertial reference frame, we wouldn't add the potential energy term of the fictitious force...
Please someon... | Basically, it depends on the reference frame. There are two obvious reference frames you can pick to work with here. The first is the "lab" observer who is watching you twirl the string from some inertial viewpoint. The other is of an observer who is riding on mass. This second one is noninertial frame, so things can b... | Only conservative forces contribute potential energy, so there is no potential corresponding to the centrifugal pseudoforce. For the case of a mass on rotating string, the total energy is the sum of the linear kinetic energy and rotational kinetic energy, assuming gravitational and other potential energies are negligib... | https://physics.stackexchange.com |
2,110,614 | [
"https://math.stackexchange.com/questions/2110614",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/233132/"
] | So I have this question here which says:
"An object of mass m is thrown vertically upward from the surface of the earth. It is subject to a constant gravitational field and air resistance proportional to the square of the object's velocity. If $g > 0$ is the constant acceleration due to gravity and $b > 0$ is th... | Your way is true and answer is right. For an object of mass $m>0$ which is thrown vertically upward from the surface of the earth, and air resist proportional to the square of the object's velocity, with $b>0$ is the coefficient of quadratic air resistance, you obtain
$$\int_{v_o}^v \frac{dv}{-g-\frac{b}{m}v^2}=\... | At the maximum height of the projectile, you have a velocity of $v = 0$. One thing you can do is:
$\hskip 6.5cm\int_{v_0}^0 \frac{dv}{-g-\frac{b}{m}v^2}dv = \int_0^tdt$
Here, $t$ will tell you the time at which the projectile reaches maximum height.
Then, I believe on the way down your differential equation should ... | https://math.stackexchange.com |
1,380 | [
"https://mathoverflow.net/questions/1380",
"https://mathoverflow.net",
"https://mathoverflow.net/users/792/"
] | Suppose $X$ and $Y$ are Banach spaces whose dual spaces are isometrically isomorphic. It is certainly true that $X$ and $Y$ need not be isometrically isomorphic, but must it be true that there is a continuous (not necessarily isometric) isomorphism of $X$ onto $Y$?
| Indeed, $\ell_1$ provides a strong counterexample. As noted by Matt, the spaces C(X), where X is countable and compact, provide nonisomorphic Banach spaces whose duals are isomorphic to $\ell_1$. If X is countable and compact (and Hausdorff, of course!) then X is homeomorphic to a closed ordinal interval [0, <em>a</em>... | If X is any countable, compact topological space, then consider the Banach space C(X). The dual space is the finite measures on X, but as any measure is countably additive, and X is countable, taking some ordering we get an isometric isomorphism between C(X)* and $\ell_1$. But not all such C(X) are isomorphic: you ca... | https://mathoverflow.net |
63,185 | [
"https://dba.stackexchange.com/questions/63185",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/37096/"
] | I am looking at a SQL Server database for an application I have inherited. I have not looked into SQL Server for approximately 10 years, so please bear with me.
The database table I am looking at has a <code>bigint NOT NULL</code> column called <code>id</code>, yet, when I check for constraints, I don't see any, and t... | These two queries may help you. The first will list all of the tables and indexes on those tables in your database. If the table does not appear in the list is does not have any indexes defined on it. These queries assume SQL Server version 2005 or newer.
<pre><code>SELECT
IndexName = QUOTENAME(I.name),
T... | No, something is incorrect.
The check on <code>sys.indexes</code> should return a row even if your table has no indexes. The heap still has a record in <code>sys.indexes</code> with a <code>type_desc</code> of 'HEAP' and <code>type</code> of 0.
I think you probably need to make sure you are in the right database con... | https://dba.stackexchange.com |
210,460 | [
"https://mathoverflow.net/questions/210460",
"https://mathoverflow.net",
"https://mathoverflow.net/users/75536/"
] | Let $R$ be a complete dvr and $k$ its residue field of positive characteristic.
Let $H$ be a finite subgroup of $PGL_2(k)$ such that the order of $H$ is prime with $char(k)$.
Is there some elementary way to show that $H$ is a subgroup of $PGL_2(R)$?
| I don't know if the following qualifies as "elementary", but here is how I would prove this (for $2$ replaced by some $d\in \mathbb{N}$):
$\DeclareMathOperator{\gl}{GL}$
First, choose some finitely generated subgroup
$U \leq \gl(d, k)$ with $U/(U\cap k^*) = H$.
Then $U\cap k^*$ is finitely generated abelian and thu... | I think that an alternate strategy (which also works, as in Frieder Ladisch's answer, for general $d$, at least when $k$ and $R$ are large enough) is to "lift" finite $H \leq {\rm PGL}(d,k)$ to a central extension which is a finite $p^{\prime}$-subgroup ${\tilde H}$ of ${\rm GL}(d,k)$. Then ${\tilde H}$ is completely r... | https://mathoverflow.net |
1,592,416 | [
"https://math.stackexchange.com/questions/1592416",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/275806/"
] | Do the rules of algebra apply when you’re working with proportionalities? For example, I know that $P \propto \rho$, where $P$ is pressure and $\rho$ is density, and $\rho \propto m$, where $m$ is mass. It would be logical to conclude that $m \propto P$ and
$$P \propto \rho \propto m$$
However, if I wanted to isolate $... | <strong>(A)</strong>
You are right: semi-direct product of $H$ by $K$ depends on choice of homomorphism $\varphi\colon K\rightarrow Aut(H)$.
<strong>(B)</strong> When we start with group $G$, and subgroups $H,K$ with
(1) $H\trianglelefteq G$,
(2) $HK=G$,
(3) $H\cap K=1$,
then (the known group) $G$ <em>is called... | I find it helpful to distinguish between the <em>inner</em> semidirect product and the <em>outer</em> semidirect product. (Similiar to the distinction between the inner direct sum and the outer direct sum of vector (sub)spaces.)
Given a group <span class="math-container">$G$</span> and two subgroups <span class="math-... | https://math.stackexchange.com |
119,114 | [
"https://cs.stackexchange.com/questions/119114",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/113937/"
] | I need to find the minimum number out of <span class="math-container">$N$</span> vertices on a tree with <span class="math-container">$N-1$</span> edges, so that at least <span class="math-container">$K$</span> edges of that tree are connected to these vertices.
For example, if <span class="math-container">$N=9$</span... | There is a <span class="math-container">$\mathcal{O}(nk)$</span> DP approach.
Call an edge covered if we select a vertex next to it. Root the tree at an arbitrary vertex <span class="math-container">$r$</span>. Define <span class="math-container">$DP[i][b][t]$</span> as the maximum number of edges in the subtree of no... | A simple solution is to use the state <span class="math-container">$dp(n,2,n)$</span>. Let <span class="math-container">$dp(i,0,j)$</span> be the maximum number of edges we can get by using <span class="math-container">$\leq j$</span> nodes in the subtree rooted at node <span class="math-container">$i$</span>, with nod... | https://cs.stackexchange.com |
1,888,514 | [
"https://math.stackexchange.com/questions/1888514",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/143976/"
] | <strong>Question:</strong>
If y=y(x) and $\frac{2+sin(x)}{y+1}\frac{dy}{dx}=-cosx,y(0)=1$, then find $y(\frac{\pi}{2})$.
<hr>
<strong>My attempt:-</strong>
$$\frac{2+sin(x)}{y+1}\frac{dy}{dx}=-cosx$$
$$\frac{dy}{1+y}=-\frac{cos(x)}{2+sin(x)}dx$$
Integrating both sides
$$\int\frac{dy}{1+y}=-\int\frac{cos(x)}{2+sin(x)... | You made a mistake by antiloging. The line $ 1+y=\frac{1}{2+\sin(x)}+C $ is wrong.
It would be easier if you would write $\log C$ instead $C$ in the line before. So in the next step you would get:
$$1+y=\frac{1}{2+\sin(x)} \cdot C$$
| $$
\frac{2+\sin(x)}{y+1}\frac{\mathrm{d}y}{\mathrm{d}x}=-\cos(x)
$$
Separating variables gives
$$
\int\frac1{y+1}\mathrm{d}y=-\int\frac{\cos(x)}{2+\sin(x)}\,\mathrm{d}x
$$
Integrating yields
$$
\log(y+1)=C_1-\log(2+\sin(x))
$$
or
$$
y=\frac{C}{2+\sin(x)}-1
$$
Since $y(0)=1$, we get $C=4$. Thus, $y\,\left(\frac\pi2\righ... | https://math.stackexchange.com |
1,680,889 | [
"https://math.stackexchange.com/questions/1680889",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/209695/"
] | I need to prove that $\lim\limits_{n\to\infty} x^{1/(2n-1)}= \begin{cases}
1, & \text{if}\ x>0 \\
0, & \text{if}\ x=0\\
-1, & \text{if}\ x<0
\end{cases}$.
But I have no idea where to start. I don't know how a definition of the limit could be applied here, if at all. Could the... | For $x=0$ the terms are identically $0$, so there is nothing to prove.
For $x>0$, we have
\begin{align}
\lim_{n\to\infty} x^{\frac1{2n-1}} &= e^{\lim_{n\to\infty} \log\left(x^{\frac1{2n-1}}\right)}\\
&= e^{\log x\lim_{n\to\infty}\frac1{2n+1} }\\
&= e^0\\
&=1.
\end{align}
For $x<0$, let $y=-x$, th... | I think it is wrong problem. Because the function $x^\alpha$ ($\alpha \in \mathbb R\backslash \mathbb Z$) is not well-defined if $x<0$.
| https://math.stackexchange.com |
676,149 | [
"https://physics.stackexchange.com/questions/676149",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/318785/"
] | While deriving <span class="math-container">$E = mc^2$</span> I found following in book by Arthur Beiser :
<blockquote>
In non relativistic physics, the kinetic energy of an object of mass <em>m</em> and speed <em>v</em> is <span class="math-container">$\mathrm{KE} = \frac {1}{2} \ mv^2$</span> . To find the correct re... | We start with the starting point
<span class="math-container">$$K=\int_0^s\frac{d(\gamma mv)}{dt}ds=\int_?^? vd(\gamma mv)$$</span>
which is simply the work-energy theorem. The limits here are of distance traveled by the particle.
Now, the limit depends on the variable about which the integration is. To make things sim... | We know that :
<blockquote>
<span class="math-container">$dP=(dE/c,d\vec{p})$</span>
<span class="math-container">$dX=(cdt,d\vec{x})$</span>
<span class="math-container">$V=(\gamma c,\gamma\vec{ v})$</span>
</blockquote>
And :
<span class="math-container">$ dP.dX= dEdt-d\vec{p}.\vec{x}=0$</span>
<span class="math-conta... | https://physics.stackexchange.com |
305,377 | [
"https://stats.stackexchange.com/questions/305377",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/178790/"
] | I have data that falls under three categories. Using a Chi-squared goodness of fit test, I have a P-Value of <.001, so my proportions do not fit within the expected numbers.
<pre><code>Observed Observed proportion Expected Proportion
70751 .678107 .454545
30036 .287878 ... | You could do an exact multinomial test, using as $H_0$ that the true proportions vector equals your expected one $\mathbf{p}_0 = (0.45,0.45,0.09)$. The P-value is then the probability of your observed proportion or more extreme under this null hypothesis. This is an omnibus test that tests all proportions, taking into ... | Since the sample size is so huge, you can actually do a very intuitive test based on Chebyshev's inequality.
Standard deviation for the first category is $\sqrt{np(1-p)}$=160.8. So the observation is 145 standard deviations away from the expected value of $np = 47425.4$.
Chebyshev's inequality says that the probabil... | https://stats.stackexchange.com |
117,466 | [
"https://softwareengineering.stackexchange.com/questions/117466",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/39810/"
] | We have developed a WCF service which acts as an API to our system.
some of the methods expose functionality which eventually writes and updates data to DB.
Lets say that the client sent one of those requests, the service performed the needed operations while the client disconnects for some reason and did not get the... | <strong>Send a transaction Id.</strong>
The server stores the transaction ID (And the client ID).
When a new transaction is sent the server checks if it has already been processes.. If it has is sends an error code the the client.
| If it's vital that the client receive the response, then you'll have to do a two-phase-commit type of interaction (client invokes service; service returns token of some sort; client ACKs with token). It's not clear from your question though whether this is really required or simply "nice to have". Would it be accepta... | https://softwareengineering.stackexchange.com |
144,474 | [
"https://electronics.stackexchange.com/questions/144474",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54699/"
] | Schottky diode have a low forward voltage drop (typically \$0.15-0.45V\$) and very fast switching action, as compared to traditional diode, which typically have a \$0.7V\$ voltage drop (Silicon diodes). What is then the advantage of traditional diode as compared to Schottky diodes?
| Full semiconductor junction diodes have much lower reverse leakage. Take a look at a Schottky diode datasheet, and note the reverse leakage, particularly at maximum working temperature.
Semiconductor junction diodes are also available at much higher reverse voltages.
| Schottky diodes typically have much higher reverse leakage currents than traditional diodes.
| https://electronics.stackexchange.com |
2,953,254 | [
"https://math.stackexchange.com/questions/2953254",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/457183/"
] | Given <span class="math-container">$\vec{a} \times \vec{b} = \vec{n}$</span> where <span class="math-container">$\times$</span> is the cross product, is it possible to solve for <span class="math-container">$\vec{b}$</span> given <span class="math-container">$\vec{a}$</span> and <span class="math-container">$\vec{n}$</... | No, it's not possible. If you manage to find some <span class="math-container">$\vec b$</span> which works, then so will <span class="math-container">$\vec b+t\vec a$</span> for any real number <span class="math-container">$t$</span>. And none of those solutions stick out in any way as better or more natural than any o... | Nope. You can figure out that <span class="math-container">$\vec{n}$</span> is normal to <span class="math-container">$\vec{a}$</span> and <span class="math-container">$\vec{b}$</span>. This means given only <span class="math-container">$\vec{a}$</span> and <span class="math-container">$\vec{n}$</span> any vector norma... | https://math.stackexchange.com |
4,279,493 | [
"https://math.stackexchange.com/questions/4279493",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I have the following complex equation:
<span class="math-container">$2z + \overline{z} + 4 = \frac{z}{1-i}$</span>
I have tried doing it by assuming <span class="math-container">$z = x + yi$</span>
but at a point I get, <span class="math-container">$2x-3xi+y-4i+4 = 0$</span> which is just unsolvable
Any other method or... | A different way to solve this linear equation with conjugate, without using real and imaginary parts:
First collect the terms in <span class="math-container">$z$</span> getting
<span class="math-container">$\frac{3-i}2z+\overline z=-4$</span>
Apply the conjugate equation:
<span class="math-container">$z+\frac{3+i}2\ove... | When you get equation like
<span class="math-container">$$ 2x-3xi + y- 4i +4 = 0$$</span>
an you know that <span class="math-container">$x,y\in\mathbb{R}$</span>, it means that the real and imaginary parts are equal to <span class="math-container">$0$</span> separately:
<span class="math-container">$$ 2x+y+4 = 0 $$</sp... | https://math.stackexchange.com |
36,946 | [
"https://mechanics.stackexchange.com/questions/36946",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/22795/"
] | When I press the brake pedal, my car is shakes. However, it is fine when I drive it. Does anyone know what's going on with my car and how should I fix it? If I ask someone to fix it, how much would it cost and how long would it take approximately?
| Sounds like your rotors are warped pretty bad on the front honestly. Sounds like you need brakes and rotors, might as well do the whole car. Rotors are easily warped nowdays due to quality, usage, and even by hitting a puddle of water after or during braking because it shifts the rotors temperature so quickly from hot ... | If the car shakes when you apply the brakes while it is moving, then the problem is likely with the rotors. However since it happens when the car is <strong>not</strong> moving, then I'd suspect a vacuum leak.
Listen carefully around the brake booster (the large round object more or less in front of the driver in the ... | https://mechanics.stackexchange.com |
312,122 | [
"https://electronics.stackexchange.com/questions/312122",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/89774/"
] | We always say that a low current can kill. However my knowledge of current is the amount of Coulomb. When that is explained, there is no mention of voltage level...
However, shouldn't voltage be important too? Do we consider a voltage of 120V because this is the voltage in common wire?
Let's make an extreme suppositi... | It is the level of current that determines how dangerous electricity is when it flows into the human body. The level of current is determined by the voltage and the resistance of the path that the electricity is using to enter the body. Thus both voltage and current are important. Assuming the body's resistance is fix... | Remember Ohm's Law - the current that can flow through your body depends on the resistance that the current is flowing through (your body's resistance, and any other resistances in series with your body) and on the applied voltage.
If you can somehow manage to get 1 Amp flowing through your heart with only 1 picoVolt ... | https://electronics.stackexchange.com |
127,253 | [
"https://mathoverflow.net/questions/127253",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30081/"
] | Dear mathematicians,
I want to know how much advance there has been in complex dynamics of several variables. I am at present reading Carleson's book on Complex Dynamics on one variables.Curious to know about several variables case.t
Specifically,what are the best papers in this area.
| A more advanced/comprehensive course can be based on Atkinson's book Discrete and continuous boundary
problems. No functional analysis is required, neither for Hilbert-Courant nor for Atkinson.
(When Courant wrote the first volume of HC, functional analysis did not exist yet:-)
Another book which studies some of thes... | The classic "Methods of Mathematical Physics" by Courant and Hilbert has a wealth of material on the Sturm-Liouville problem and its connections to various themes of mathematical physics. In fact, one could almost say that the treatise is constructed around this topic. Little or no knowledge of Functional Analysis is ... | https://mathoverflow.net |
161,346 | [
"https://electronics.stackexchange.com/questions/161346",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5542/"
] | According to all textbooks and articles, a thermocouple must have a cold junction somewhere on the middle of it.
<img src="https://i.stack.imgur.com/ImAXz.png" alt="enter image description here">
But none of the commercial products have a middle point or a marked spot for indicating the position of the cold junction.... | Your cold junctions (at least two!) are where you connect the two (different!) thermocouple metals to your circuit. Note that this can be in multiple steps, like: thermocoupe - connector - wires - PCB. These are all cold junctions. Keep them all at the same temperature and measure that temperature. If no heating or chi... | These days, there are often (if not usually), virtual cold junctions in amplifiers meant to deal with thermocouples. It is often referred to something like "electronic ice point
reference". The temperature of the virtual cold junction is measured by some other means, and the temperature is internally compensated for.... | https://electronics.stackexchange.com |
32,609 | [
"https://mechanics.stackexchange.com/questions/32609",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2095/"
] | My battery died and I suspect the alternator. To test I need to get the car running again and so borrowed a wall socket charger.
I have no idea how long I need to let the battery charge for.
Would anyone know how long I need to wait?
| How long does it take to charge a battery? Ideally assuming 100% percent efficiency a 10 A battery charger would charge a 50 A/h (Ampere/hour) battery in about 5 hours.
Hours of charge = Ampere-Hour rating/charge rate ....ideally
In reality due the fact that when a battery is charging the charge rate is not cons... | If the battery is okay, you might need an hour to make it turn the starter and start a car. The rest should be done by alternator IF IT WORKS.
| https://mechanics.stackexchange.com |
103,873 | [
"https://physics.stackexchange.com/questions/103873",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42673/"
] | So that the problem:
<blockquote>
<em>There are 2 trains at speed of 30km/h in the same trail and opposite directions and moving for a collision at 60km of distance of each other. One bird in front of one of the trains fly at 60km/h toward of other train. When he reaches he flies back to the other train until the t... | This is a classic question. The trains travel one hour till the collision. So the bird flies a distance of 60 km. Which is in contradiction with the other answer.
| Can you rephrase the question? I don't understand what you're asking.
[Would comment, but insufficient reputation]
So maybe a good way to start is to describe the distance remaining between the trains as a function of time, which seems to me like it should be
$$ d(t) = 60 - 60t, 0<t<1$$
since in the rest fra... | https://physics.stackexchange.com |
369,307 | [
"https://softwareengineering.stackexchange.com/questions/369307",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/302963/"
] | Our application creates audit trails in response to system actions and user actions. Our business logic depends on these audit trails to find out which user performed what action.
Is it good practice to have business logic use audit trail data?
| No.
The problem is the audit trail should never change once written. So lets say I have some business logic
"Show the buy button if the customer has not bought previously"
And when the customer buys we add an Audit record.
We implement the business logic by checking that customers audit record and display the butto... | It depends (but I guess for most real-world situations the answer is <strong>no</strong>, you risk to run into trouble).
A general-purpose audit trail may collect data which, depending on the details, might be affected by laws of data security and privacy of the jurisdiction where your application will be used. If thos... | https://softwareengineering.stackexchange.com |
118,451 | [
"https://physics.stackexchange.com/questions/118451",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | In an arbitrary number of dimensions, one can naturally define two tensors, Kronecker delta and Levi-Civita epsilon tensor. However, why isn't it advantageous to define some totally symmetric tensor as well? Is there an intuitive reason for that or is it basically related to differential forms?
| The Kronecker delta and the Levi-Civita tensors are very different <em>kinds</em> of tensors.
The Kronecker delta is, abstractly, a linear map: the identity map. That's all it is and all it can be.
The Levi-Civita, however, can be interpreted <em>geometrically</em>: as an oriented volumetric subspace (or four-volum... | Isn't the Kronecker delta symmetric? Let's see:
$$\delta_{ij}=1 \, \, \, \text{if} \, \, \, i=j, \quad \delta_{ij}=0$$
otherwise. I'm pretty sure that is symmetric. The Levi-Cevita symbol is indeed anti-symmetric though.
| https://physics.stackexchange.com |
433,622 | [
"https://stats.stackexchange.com/questions/433622",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/153364/"
] | When running a regression with a categorical independent variable, we get results for each level of the variable except for the base, which we can choose.
Now I've always had a hard time on how to interpret these results.
Say we have a study of aneurysm locations. They can be located in, say, 10 different areas.
We ... | Given the development of aneurysm in one area mutually excludes developments of aneurysm in another it is possible to let the dependent variable be <span class="math-container">$Y_{ij}=1$</span> if individual <span class="math-container">$i$</span> has developed aneurysm in the area <span class="math-container">$j$</sp... | A way I use to help me interpret is to create a table with the two variables I'm looking at - the dependent and the independent I'm focusing at that moment. In a regression, the other independent variables may change this relation a bit, but usually I can get a good idea regarding what's going on.
Following your examp... | https://stats.stackexchange.com |
30,705 | [
"https://quant.stackexchange.com/questions/30705",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/19502/"
] | I'm reviewing stuff from the past and I'm very confused all of a sudden. Some verification would help about the following.
<span class="math-container">$$
\mathbb{E}[e^{\sigma W(t)}|{\cal F}_s] =
\mathbb{E}[e^{\sigma (W(t) - W(s) + W(s))}|{\cal F}_s] =
\mathbb{E}[e^{\sigma (W(t) - W(s))}|{\cal F}_s]e^{W(s)}
$$</span... | We have
\begin{equation}
\sigma \left( W_t - W_s \right) \sim \mathcal{N} \left( 0, \sigma^2 (t - s) \right).
\end{equation}
Let $X \sim \mathcal{N} \left( 0, \xi^2 \right)$, then
\begin{eqnarray}
\mathbb{E} \left[ e^{X} \right] & = & \frac{1}{\sqrt{2 \pi} \xi} \int_\mathbb{R} \exp \left\{ x -\frac{x^2}{2 \x... | Depending on how well you are familiar with stochastic calculus, another way of getting to this result is to recognise that:
$$ e^{\sigma W_t} = \mathcal{E}[\sigma W_t] e^{\frac{1}{2}\sigma^2 t} $$
where
$$ \mathcal{E}(X_t) = \exp\left(X_t - \frac{1}{2}\langle X \rangle_t\right) $$
denotes the Doléans-Dade exponential... | https://quant.stackexchange.com |
361,778 | [
"https://physics.stackexchange.com/questions/361778",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167699/"
] | I have read that since the magnetic force acting on moving charge is always perpendicular to the velocity of moving charge, the field is not doing any work on the charge.
However, if a ball rolling on the X axis collides with a heavier ball rolling on the Y axis, the first ball will get some of the kinetic energy of t... | First, there certainly could be collisions where no energy is transferred, only direction changes. But you're right, we could construct a case where the initial contact is perpendicular, but energy is transferred.
<blockquote>
Is energy transferred in the second case because the collision is not
instant, and we ... | In your second example, the collision is not instantaneous, and the velocity of the lighter ball changes throughout the collision.
It's easiest to think of this velocity at the instants just before the balls part, at which the velocity of the lighter ball is already close or equal to its final velocity, with a nonzer... | https://physics.stackexchange.com |
152,918 | [
"https://physics.stackexchange.com/questions/152918",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60433/"
] | What are the factors on which coefficient of restitution depend? What is the reason for more coefficient of restitution of two glass balls (0.95) than for two lead balls (0.20)?
| The only factor is the capacity to return to the original shape when it is deformed by an external force.
An elastic object recovers its shape after it has been compressed and deformed, if you crush a plastic bottle and remove the cap it will partially return to his original length, a lead ball is almost completely ir... | Most of us will have discovered that a glass rings if you tap it, and the sound of the ring will persist for several seconds after hitting the glass. This shows that elastic energy stored in the glass is not dissipated fast.
I would guess that fewer people have tried the experiment with a lead beaker, but I have and I... | https://physics.stackexchange.com |
228,778 | [
"https://physics.stackexchange.com/questions/228778",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/103520/"
] | How do we justify taking the chemical potential, $\mu$ as $0$ when calculating the critical temperature of Bose-Einstein Condensates (BECs)?
I apologise as I do not how to use LaTeX, for if I did the elegance of mathematics would’ve allowed me to construct my question with ease...
I understand to calculate the total ... | To determine the upper limit on chemical potential for a gas of $\mathcal N$ bosons, look at the form of the Bose distribution in the grand canonical ensemble with $\langle N \rangle = \mathcal N$. When using the GCE, it's easiest to work at chemical potential $\mu$ and to then choose $\mu(\mathcal N)$ so that $\langle... | You can think of the chemical potential as the amount of free energy needed to add one additional particle to the system. Because the ground state of a BEC is degenerate and can hold an infinite number of particles, there's no energy cost to add another particle to that state. So, $\mu = 0$.
| https://physics.stackexchange.com |
126,413 | [
"https://physics.stackexchange.com/questions/126413",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52187/"
] | <em>(I didn't even have a basic formal education in physics. I'm learning through the internet out of my own interest, so if there are any silly mistakes, kindly bear with and guide me through.)</em>
Everywhere, everyone is saying that pressure will same be for a given height. How is it possible? When volume changes, ... | If you replace the fluid scenarios with solids with matching have the same shapes, then indeed the pressure at bottom would be the weight of each solid divided by base area, i.e., they would be different! Then what's different about the fluid case?
I presume in scenario 1 you have a prism, in scenario 2 you have a bo... | Consider this diagram showing the three columns you describe all connected to the same body of water:
<img src="https://i.stack.imgur.com/tLLgJ.gif" alt="Pressure">
Your question asks whether the three pressures $P_1$, $P_2$ and $P_3$ will be the same. The answer is obviously yes, because the columns are all connecte... | https://physics.stackexchange.com |
315,886 | [
"https://softwareengineering.stackexchange.com/questions/315886",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/106917/"
] | A cursory glance at C#, Java, and other languages indicates this is not a feature that's required. I tried searching for justification for this maybe from a language design team or blog, but I haven't found anything that explains why such a type is ignored.
My current best guess is applications that use big integers w... | If you have a use case where you never have to deal with negative numbers inside of any big integer calculation, then you could use the signed big integers implementation as well, and your performance guess is what I would expect, too, the performance differences would most probably be negligible.
If you have a use ca... | The original reason to have unsigned integers in a language in the first place is to extend the numeric range of a fixed-size type upwards at the cost of limiting it downwards. Beneficial effects such as sane semantics of bitwise operations (in C) or implicit enforcement of a non-negative constraint are not the primary... | https://softwareengineering.stackexchange.com |
77,107 | [
"https://electronics.stackexchange.com/questions/77107",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/19282/"
] | <img src="https://i.stack.imgur.com/S1jym.png" alt="Schematic">
So I'm in the process of trying to reverse-engineer a hobby brushless ESC. Above is the schematic for a single half-bridge drive circuit.
VIN is 11.1V
D1 is an unidentified diode; all that I've been able to glean so far from it its orientation and that ... | The LOW signal can be a logic level signal from the 5V MCU because the lower N-Channel FET in the bridge has its Gate-Source voltage referenced to the GND. Due to this the FET can be turned on with a signal that rises above GND.
The HIGH signal needs to be buffered through the 2N3094 because the upper N-Channel FET in... | D1 is probably a Schottky of some sort - high speed and low drop.
To expand on Michael Karas' answer above:
When LOW is high and HIGH is low, the lower FET turns on and C6 charges to (Vin-Vd1). When it changes state, the bottom end of C6 is referenced to the source of the upper FET, and its Vgs is (roughly) equal to... | https://electronics.stackexchange.com |
122,650 | [
"https://mathoverflow.net/questions/122650",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13441/"
] | I would like to know if there can be some kind of classification of normal rational surfaces with Gorenstein singularities, such that their canonical divisor is effective.
<strong>Additional question.</strong> Are there such surfaces at all?
I could imagine constructing such a surface by blowing up several points on... | Here is an example (I hope!).
Take $X$ a double cover of $\mathbb P^2$ branched over a normal sextic $B$. It is a normal Gorenstein surface and the standard formulae for double covers give $K_X=0$.
Now assume that $B$ has an ordinary quadruple point $P$ and is smooth elsewhere, so that $X$ has an elliptic Gorenstein... | EDIT: The proof below is wrong, because it is false that $h^0(X',-mK_X')=h^0(\mathbb{P}^2,-mK_{\mathbb{P}^2})$ (see comments)
Consider a normal rational surface $X$ with Gorenstein (or $\mathbb{Q}$-Gorenstein) singularities. Let $\mu:X'\to X$ be a resolution.
Then $\mu^*(K_X)=K_{X'}+E$, where $E$ is a $\mu$-exceptioa... | https://mathoverflow.net |
258,699 | [
"https://softwareengineering.stackexchange.com/questions/258699",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/145516/"
] | I created a table in a Postgres database. I would like to create a form in a Java application to insert rows into that table. Certain fields have default values. What is the best way for the database and UI to agree on what the default values are? Also, what is the best way for the form to communicate the user's intent... | Referential integrity and other constraints should be managed by the database and not the application that uses it.
In the case of default constraints, I would have the UI pass in <code>NULL</code> for those fields or simply do not specify them at all in the <code>INSERT</code> query. The database will then supply the... | Preferably, you should construct your workflow so that new records are initialized in the GUI only and not from the database. That will ensure that front-end and back-end don't <em>need</em> to agree about the default values, because the DB defaults never become visible to the user.
If you <em>must</em> process addin... | https://softwareengineering.stackexchange.com |
211,614 | [
"https://softwareengineering.stackexchange.com/questions/211614",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54268/"
] | Recently I came across a moderately large python codebase with lots of <code>MyClassAbstractFactory</code>, <code>MyClassManager</code>, <code>MyClassProxy</code>, <code>MyClassAdapter</code> etc. classes.
While on the one hand those names pointed me to research and learn the corresponding patterns, they were not very... | <ul>
<li><code>AbstractFactory</code> is indeed a poor choice for a name. <strong>There is no way to know <em>what</em> is created by this factory</strong>, and when you'll look for an entity which creates <code>Animal</code>s, you'll never find the corresponding factory by name.</li>
<li><code>AnimalAbstractFactory</c... | Depends on the specific example. The Builder pattern is almost always best served by naming your class *Builder, while a Singleton doesn't usually need to be named as such.
If you don't put the pattern name in your class name, and maybe even if you do, you should generally put a comment in the class which explains tha... | https://softwareengineering.stackexchange.com |
290,745 | [
"https://stats.stackexchange.com/questions/290745",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/168332/"
] | I have a time series sampled in days and when I plot the amplitude vs time it looks like the signal is oscialating at an annual frequency. The series is 15 years long.
Is there a test I can use to test the significance of this frequency in the data? Meaning, test what is the probablity the oscilation is random.
I ha... | I think the correct way to phrase this is whether the priors are independent or not. The priors can always be described as (for example in your Normal example) $p(\mu, \sigma^2)$, but the question is does that joint prior factorize as $p(\mu, \sigma^2) = p(\mu)p(\sigma^2)$ or not.
Once we have that phrasing in place ... | All the priors you mention are "joint" priors in that they define a joint distribution on the parameter vector $\mathbf{\theta}=(\theta_1,\ldots,\theta_p)$. When the prior writes down as
$$\prod_{i=1}^p \pi_i(\theta_i)$$
each component $\pi_i(\theta_i)$ can also be interpreted as a (marginal) prior on the component $\t... | https://stats.stackexchange.com |
371,491 | [
"https://stats.stackexchange.com/questions/371491",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14803/"
] | I'm trying to learn bayesian statistics from "Statistical rethinking" by Richard McElreath. In chapter 4, a model with Gaussian distribution of heights is introduced:
<span class="math-container">$h_i \sim N(\mu, \sigma)$</span>
<span class="math-container">$\mu \sim N(178, 20)$</span>
<span class="math-container">$... | I think I have the answer having played around with it for a while. Firstly, it is important to remember that the denominator is just a scaling constant and really all it does is re-scale the area under the posterior to 1.
McElreath doesn't bother calculating this marginal likelihood and instead re-scales. However, h... | The denominator in the expression for the posterior is called the marginal likelihood or the evidence. One way to think about it is as a normalizing constant that ensures the posterior integrates to 1. This means the numerator is proportional to the posterior. In some applications (e.g. inference using MAP estimation o... | https://stats.stackexchange.com |
164,476 | [
"https://mathoverflow.net/questions/164476",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50064/"
] | Good night, anyone know of any reference where I can find the proof of the <strong>Stable/Unstable Manifold Theorem for a Morse-Bott function</strong>. I'm interested in the dimensions of the stable and unstable manifolds, these dimensions are intuitive but wanted to know of some reference.
Thank you very much, all r... | The paper <em>Morse-Bott theory and equivariant cohomology</em> by D. M. Austin and P. J. Braam (in The Floer memorial volume, Progr. Math., 133, 1995) is a good reference for Morse-Bott theory. In particular Proposition 3.2 and Theorem A.9 seem to contain what you want.
| The most general sort of theorem along those lines can be found in the book Invariant Manifolds by Hirsch, Pugh, and Shub, Springer Lecture Notes in Mathematics Volume 583.
| https://mathoverflow.net |
24,280 | [
"https://mathoverflow.net/questions/24280",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5292/"
] | $(A, \mathfrak{m})$ a Noetherian local ring, $a\in\mathfrak{m}$ a <em>zero divisor</em>. Then is it true that $\mbox{dim}\ A/(a) = \mbox{dim}\ A$ ?
| No. Let A be the ring k[x,y,z]/(xz,yz) localized at (x,y,z). Then the dimension of A is 2, but the dimension of A/(x) is one. Note that xz = 0 in A.
The geometric picture is this: In 3-space, take the union of the horizontal z=0 plane with the vertical line x = y = 0, and look at the local ring at the origin. Then ... | Necessary and sufficient conditions for your question to have a positive answer are that $A$ be $\textit{unmixed}$, that is, every associated prime is a minimal prime, and $\textit{equidimensional}$, that is, $\mathrm{dim} (A/\mathfrak{p}) = \mathrm{dim}(A)$ for every minimal prime $\mathfrak p$. Charles Staats' examp... | https://mathoverflow.net |
217,142 | [
"https://physics.stackexchange.com/questions/217142",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/97835/"
] | I understand that, in the context of the Schwarzschild spacetime (General Relativity), a radially inward falling observer follows a time-like geodesic with zero four-acceleration. There are no forces acting on this observer and he is thus in free fall. In addition, the (Schwarzschild) coordinate acceleration is nonzero... | Feynman diagrams are most definitely <em>not</em> a representation of what's going on between the particles. Feynman diagrams are simply a tool to help you remember formulas: if you want to calculate the probability that two electrons will scatter off each other in so-and-so angle, you draw all possible diagrams with t... | The angle of the particle lines is irrelevant and it's just a convention. You could as well draw them as straight vertical lines. It doesn't affect the calculation of its contribution to the probability amplitude of scattering. For the same reason, Feynman diagrams do not intent to show attraction nor repulsion. They a... | https://physics.stackexchange.com |
704,452 | [
"https://physics.stackexchange.com/questions/704452",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/333328/"
] | Scientists say that it is impossible to reach a temperature of zero kelvin, because the atoms will stop moving, and the volume of the substance will become zero, But we have reached the pico kelvin temperature, which is almost zero, and there is no difference between it and zero, so why do they say it is impossible? an... | The difference is that <span class="math-container">$0$</span> is not the same as <span class="math-container">$10^{-9}$</span>. The latter is nearly zero, but it's not zero.
Why does it matter? Consider for example Charles's Law, which says that for gases, <span class="math-container">$V/T$</span> is a constant if the... | In some thermodynamic contexts, the inverse temperature <span class="math-container">$\beta=1/T$</span> is a more meaningful quantity. This makes it more clear that 0 Kelvin, or <span class="math-container">$\beta = \infty$</span> is approachable but unattainable. And so in asking about pico-Kelvin being "close... | https://physics.stackexchange.com |
38,475 | [
"https://cs.stackexchange.com/questions/38475",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/27819/"
] | I have trouble understanding Turing's halting problem.
His proof assumes that there exists a magical machine $H$ which could determine whether a computer would halt or loop forever for a given input. Then we attach another machine that reverses the output and we have a contradiction and therefore $H$ cannot exist.
My... | <strong>Short version:</strong> The outputs of the machines are not correct or incorrect, they are just contradictory, which proves that the initial machine that <em>decides</em> whether the input machine halts on the given string or not can't exist.
<strong>Long version</strong>: First we'll sketch the proof (or at l... | You’re discussing two different meanings of “contradict”.
In your analogy, the machine <em>A</em> and its flipped modification contradict each other just in the sense that their outputs are always different. (For instance, they might implement two test functions on integers, “<em>x</em> ≤ 5?” and “<em>x</em> > 5?”) T... | https://cs.stackexchange.com |
4,165 | [
"https://stats.stackexchange.com/questions/4165",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/253/"
] | I wish to decide if I should take a course called "INTRODUCTION TO STOCHASTIC PROCESSES" which will be held next semester in my University.
I asked the lecturer how studying such a course would help me as a statistician, he said that since he comes from probability, he knows very little of statistics and doesn't know ... | Stochastic processes underlie many ideas in statistics such as time series, markov chains, markov processes, bayesian estimation algorithms (e.g., Metropolis-Hastings) etc. Thus, a study of stochastic processes will be useful in two ways:
<ol>
<li>Enable you to develop models for situations of interest to you.
An expos... | You need to be careful how you ask this question. Since you could substitute almost anything in place of <em>stochastic processes</em> and it would still be potentially useful. For example, a course in biology could help with biological statistical consultancy since you know more biology!
I presume that you have a cho... | https://stats.stackexchange.com |
11,553 | [
"https://stats.stackexchange.com/questions/11553",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/795/"
] | The classical F-test for subsets of variables in multilinear regression has the form
$$
F = \frac{(\mbox{SSE}(R) - \mbox{SSE}(B))/(df_R - df_B)}{\mbox{SSE}(B)/df_B},
$$
where $\mbox{SSE}(R)$ is the sum of squared errors under the 'reduced' model, which nests inside the 'big' model $B$, and $df$ are the degrees of fre... | The noncentrality parameter is $\delta^{2}$, the projection for the restricted model is $P_{r}$, $\beta$ is the vector of true parameters, $X$ is the design matrix for the unrestricted (true) model, $|| x ||$ is the norm:
$$
\delta^{2} = \frac{|| X \beta - P_{r} X \beta ||^{2}}{\sigma^{2}}
$$
You can read the formu... | I confirmed @caracal's answer with a Monte Carlo experiment. I generated random instances from a linear model (with the size random), computed the F-statistic and computed the p-value using the non-centrality parameter
$$
\delta^2 = \frac{||X\beta_1 - X\beta_2||^2}{\sigma^2},
$$
Then I plotted the empirical cdf of the... | https://stats.stackexchange.com |
504,617 | [
"https://stats.stackexchange.com/questions/504617",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/301799/"
] | This is a pretty basic question.
So...backprop is an efficient algorithm for computing the gradients used by the optimizer to improve model parameters, no matter if SDG or something else. I get that.
The actual difference between classic gradient descent and stochastic gradient descent is the
batchsize used for computi... | The core concept is that the gradient is a <em>statistic</em>, a piece of information <strong>estimated</strong> from a limited sample.
The difference between GD and SGD is that if you repeated SGD twice for the same initial parameter values but use different batches, you're likely to get a different estimate of the gr... | We move in the direction of the negative gradient, but the gradient is different, because in (full-batch) GD and in (batch) SGD the data are different!
And that's the point: SGD adds randomness so that it can more easily escape local minima.
| https://stats.stackexchange.com |
74,756 | [
"https://cs.stackexchange.com/questions/74756",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/46799/"
] | How to compute the run-time of distributed algorithms in message passing systems? I was reading across and found it very weird that any computation done in each node is considered to take $\mathcal{O}(1)$ time due to the unreliability in the time it takes to pass messages. Since this approach is not practical at all, I... | You understood it right. The standard models of distributed computing typically assume that local computation is free. It follows that in the LOCAL model of distributed computing, you can solve any graph problem in time $O(n)$, and in the CONGEST model of distributed computing, you can solve any graph problem in time $... | Time complexity is always measured relative to some model. For example, the $\Theta(n \log n)$ bound on sorting is the number of comparisons performed. If comparisons are not constant time, then the total number of operations will be higher.
Because of the high variability, and the overall time taken, often distribut... | https://cs.stackexchange.com |
28,842 | [
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] | Would this be a valid equation to calculate kinetic energy created from a drop from a height:
$$E_{kinetic} ~=~ v_{vertical}tmg$$
Velocity multiplied by time gives distance. Distance multiplied by gravitational force acting on it provides kinetic energy. Would this equation be valid?
| No.
You are correct that the kinetic energy is equal to the change in the potential energy, $mgh$, where $h$ is the distance fallen, but because the object is accelerating $h$ is not simply velocity times time. If the object starts at rest then (ignoring air resistance):
$$h = \frac{1}{2} g t^2 $$
so substituting th... | For a body of mass m in a <em>uniform specific-force field $g$</em>:
$$E_{kinetic} = \frac{1}{2} m g^2 t^2 $$
For two mutually interacting bodies of masses M and m: $$E_{kinetic} = \frac{G(M+m)}{r_1}-\frac{G(M+m)}{r_0} $$
where $r_0$ and $r_1$ are the initial and final separations of the two bodies.
Since uniform... | https://physics.stackexchange.com |
395,284 | [
"https://physics.stackexchange.com/questions/395284",
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] | In the derivation of the Rayleigh-Jeans law, using the Equipartition theorem the number of modes per unit frequency per unit volume is multiplied by $kT$, which implies each electromagnetic resonant mode has two degrees of freedom.
I've considered them being the amplitude of the electric field and the amplitude of the... | This is a nice question, glossed over in many textbooks! Let's start with the electromagnetic field Hamiltonian,
$$H \sim \frac12 \left(E^2 + B^2\right).$$
Naively one would say that $\mathbf{E}$ and $\mathbf{B}$ are the two degrees of freedom, giving the factor of two. But as you noted, this isn't correct. The fields ... | The classical equipartition theorem for a one-dimensional harmonic oscillators gives a mean kinetic energy of $\frac{k}{2}$ and a mean potential energy $\frac{k}{2}$ so that the total mean energy is $k$. Analogously, the electromagnetic modes can be considered as harmonic oscillators which have a total mean energy (kin... | https://physics.stackexchange.com |
18,580 | [
"https://dsp.stackexchange.com/questions/18580",
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] | I'm creating windowed sinc filters to apply them to certain signals that I'm dealing with. To design the filters, I'm using the approach described in the book "The Scientist and Engineer's Guide to DSP". Here's a brief resuming:
\[h[i] =
\left\{
\begin{matrix}
Kw(i)\frac{\sin(2\pi f_c(i - \frac{M}{2}))}{i - M/2} &a... | You don't pad it in the frequency domain, you pad it in the time domain (i.e. before you calculate the FFT). You can put the zeros either symmetrically or after the filter. Either way works, it just results in a shift in the output.
| You will have to pad both $h[i]$ and the signal $x[i]$ with zeros so that both their lengths are <em>atleast</em> $M+N+1$ where $N$ is the length of $x[i]$. You can pad more so that the length of the padded vectors are powers of $2$.
This has to be done to ensure that circular convolution behaves like linear convoluti... | https://dsp.stackexchange.com |
66,480 | [
"https://softwareengineering.stackexchange.com/questions/66480",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22500/"
] | I work in a small company as a solo developer. I'm the only developer at the company in fact. I have several (relatively) large projects I've written and maintain regularly, and none of them have tests to support them. As I begin new projects I often wonder if I should try a TDD approach. It sounds like a good idea... | <blockquote>
A lot of the examples I've seen of tests get down to the minutiae, covering all facets of the code.
</blockquote>
So? You don't have to test <strong>everything</strong>. Just the relevant things.
<blockquote>
Since I'm the only developer and I'm very close to the code in the entire project, it is ... | Imagine that you had a suite of tests that could run in an eyeblink and would light up a green or red light. Imagine that this suite of tests tested <em>everything</em>! Imagine that all you had to do to run the suite of tests was to type ^T. What power would this give you?
Could you make a change to the code witho... | https://softwareengineering.stackexchange.com |
464,559 | [
"https://stats.stackexchange.com/questions/464559",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/221202/"
] | I'm reading Chapter 5 of the CLRS Algorithms book. Specifically, it discusses the <strong>hiring problem</strong> in which we want to assess the expected number of hires given that candidates arrive in random order and each candidate has a distinct rank. All permutations of candidates are deemed equally likely.
As an... | Suppose there are <span class="math-container">$n$</span> individuals; we will ignore the ranks and consider the random permutation <span class="math-container">$\pi \colon \{1,\ldots, n\} \rightarrow \{1,\ldots, n\}$</span>, with the interpretation <span class="math-container">$\pi(k)$</span> is the position of indivi... | Feel free to edit your post with the exact wording (verbatim) of the hiring problem if this does not address it. Instead of explaining in a way that will basically be a re-statement of what you wrote, which you intuitively get but formally don't yet, I'll try a different approach. I think the difficult part is separati... | https://stats.stackexchange.com |
483,295 | [
"https://physics.stackexchange.com/questions/483295",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99217/"
] | I'm trying to understand the unit conversions when one unit is obtained by shifting the value of another one by some constant. In particular, the unit conversions from Kelvin to Celsius scale:
<span class="math-container">$$T(\mathrm{^\circ C}) = T(\mathrm K) - 273.16.$$</span>
I want to find the value of <span class... | <strong>Short Answer:</strong> <span class="math-container">$1\ \mathrm{^\circ C}$</span> is <span class="math-container">$274\ \mathrm K$</span>. Does that mean <span class="math-container">$2\ \mathrm{^\circ C}$</span> is <span class="math-container">$2 \times 274\ \text{K} = 548\ \mathrm K$</span>? It is not, becaus... | The universal gas constant tells you how much the energy of a gas <em>changes</em> when you change the mass, the number of particles, or the temperature.
Let's say that we wanted to convert <span class="math-container">$R$</span> to <span class="math-container">$\frac{J}{g*mol*K}$</span>. The value of <span class="mat... | https://physics.stackexchange.com |
1,931,976 | [
"https://math.stackexchange.com/questions/1931976",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/300243/"
] | This is one of my linear algebra problems:
<blockquote>
Prove that polynomials of degree $n$ <strong>does not</strong> (The professor made these words bold intentionally) form a vector space.
</blockquote>
From what I read, the set of polynomials of degree $n$ should be a vector space, because:
<ol>
<li>There is a... | Polynomials of degree $n$ <strong>does not</strong> form a vector space because they don't form a set closed under addition.
For instance:
$$X^n-X^n=0$$
which is not of degree $n$.
So, don't get confused with the set of polynomials of degree <strong>less or equal</strong> then $n$, which form a vector space of dim... | Polynomials of degree $n$ is a set which is not closed under addition. For example, if $n=3$, then $x^3+x^2$ and $-x^3$ are both $3$rd degree polynomials but their sum is not:
$$
x^3+x^2-x^3=x^2
$$
(which is not a $3$rd degree polynomial).
| https://math.stackexchange.com |
84,049 | [
"https://electronics.stackexchange.com/questions/84049",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9983/"
] | I'm using a digital pin as a supply to a sensor (should draw ~7mA).
Unfortunately, the sensor pulls the voltage of the digital pin down from 3.3v to 3.0v, which isn't enough for the sensor.
Can I tie two digital pins together and enable both of them to keep a higher voltage? Or will it release the magic smoke from m... | Yes, but no.
Yes, you can use two pins to source more current, or in your case, source less current out of each. This is a common practice, but not often used on Microcontrollers. Devices like led drivers, or ULN2803 Motor Drivers, or connecting multiple transistors in parallel. Even multiple resistors in parallel. On... | You could.... but it's a bad idea.
Typical microcontroller pins can easily source or sink up to 40mA (at least, this is typical of the AVR chips most Arduino boards are built around). So, current draw is not likely the problem.
It is also common for the pins set as digital outputs to be a few to a few dozen millivolt... | https://electronics.stackexchange.com |
62,541 | [
"https://dba.stackexchange.com/questions/62541",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36699/"
] | I'm the lone user of my computer. I haven't changed my MYSQL root user password, but it is somehow changed to empty password. Help me out !
My default sakila db is also gone. I specified engine=innodb for one of the tables.Would there be any effect
| The mess was because I was in middle of a crash recovery. It is good now. No ghosts,no hackers.
| This, literally, is impossible as you've described it. What has happened is something else. Either you have changed something in your installation, or some other condition has changed.
Here's how to get to the bottom of it. The MySQL database has a table, user, that lists all the users and their details. Run <code>'SE... | https://dba.stackexchange.com |
2,114 | [
"https://bioinformatics.stackexchange.com/questions/2114",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/982/"
] | I have a binary matrix of gene presence or absence which looks like: [roary output]
<pre><code>Gene sample1 sample2 sample3 sample4
fliI 1 1 1 1
patB_1 1 1 1 1
pgpA 1 1 1 1
osmB 1 1 1 1
cspA 1 0 ... | It's not a fasta file, but:
<pre class="lang-r prettyprint-override"><code>> m
sample1 sample2 sample3 sample4
fliI 1 1 1 1
patB_1 1 1 1 1
pgpA 1 1 1 1
osmB 1 1 1 1
cspA 1 0 1 1
>... | One could also use <code>cut</code> and a pair of Python scripts:
<em>transpose.py</em>
<pre><code>#!/usr/bin/env python ... | https://bioinformatics.stackexchange.com |
328,606 | [
"https://stats.stackexchange.com/questions/328606",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/170946/"
] | Let's say $x \in \mathbb{R}$ is normally distributed so that $x \sim \mathcal{N}(\mu,\sigma^2)=p(x)$. I want to simplify the following integral, which includes arbitrary, but fixed integration limits $a\in \mathbb{R}$ and $b\in \mathbb{R}$.
$I := \int_{a}^{b} x^2 p(x)dx$.
In the case of $a=-\infty, b=\infty$ the inte... | Thanks for the hint @sarwarte. Here's what I got so far:
$ I := \int_a^bx^2p(x)dx = \frac{1}{\sqrt{2\pi\sigma^2}} \int_a^bx^2\exp(-\frac{(x-\mu)^2}{2\sigma^2})dx.$
Sidenote: Using the Substituation $z := \frac{x-\mu}{\sigma}$, and therefore $dx = \sigma dz$.
$I = \frac{1}{\sqrt{2\pi}} \int_{(a-\mu)/\sigma}^{(b-\mu)/... | Hint: Since $\frac{\mathrm d}{\mathrm dx}\phi(x) = -x\phi(x)$ where $\phi(x)$ is the pdf of the standard normal variable, it is possible to find the anti-derivative of $x^2\phi(x)$ by writing it as $x\cdot (x\phi(x))$ and then using the integration by parts formula:
$$\int u\, \mathrm dv = uv - \int v \,\mathrm du$$ w... | https://stats.stackexchange.com |
203,559 | [
"https://softwareengineering.stackexchange.com/questions/203559",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34841/"
] | While developing a product, I've come across a situation where my group wants to store meta data for data entry forms (questions, layout, etc) in a different database then the database where the collected data is stored. This is mostly for security because we want to be able to have our meta data public facing, while ... | Well, the bigger problem is that effectively prevents you from maintaining consistency between the data sets. If you store the data like this, it <em>will</em> break.
I would probably store the metadata in the internal database alongside the data and set up <em>replication</em> of the metadata only to another server i... | Depending on how secure the data needs to be, if the web service is restricted to using a Database User account that only has security set up to access the specific data that is needed, then that may be enough to satisfy concerns. MSSQL has pretty robust security.
I don't think this is a superior solution to replicat... | https://softwareengineering.stackexchange.com |
14,423 | [
"https://chemistry.stackexchange.com/questions/14423",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7163/"
] | How does the electron from the 2s orbital "jump" to the 2p, thus leaving 4 unpaired electrons to form four covalent bonds?
Also, does the octet rule not apply to carbon? If it does, how can it bond with only two electrons? It would lack two more.
| The octet rule does apply to carbon. In order for carbon to form a complete octet, it must either gain 4 electrons, lose 4 electrons or form 4 covalent bonds. Placing 4 units of charge on such a small nucleus would be exceedingly difficult, so carbon typically binds in a covalent manner.
Let's imagine an experiment ... | Look up "orbital hybridization". It says that atomic orbitals can be combined to make new orbitals for bonding purposes. Carbon can take 1 s and 3 p orbitals to make 4 sp3 orbitals that can make 4 bonds.
| https://chemistry.stackexchange.com |
64,318 | [
"https://mechanics.stackexchange.com/questions/64318",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/14881/"
] | Our 2008 Chrysler 300c has 2 batteries instead of the usual one. This is common on boats and RVs but not on cars. It has a large battery in the back far away from the starter motor and a smaller battery in the front close to the starter motor. When Barbara left the lights on we went out and jump started the car on the ... | The battery is located in the trunk next to the spare. There is a positive battery terminal in the engine compartment located next to the fuse box. Maybe this is what you are referring to as a smaller second battery? It's just a convenient place to access the positive battery connection from the engine compartment.
| the 1 at the engine is for starting. the other (called deep cycle), is for supporting all the electronic components that draw a lot of current even if the engine is not running, and otherwise drains the starter battery faster. the starter has more thinner plates, and is more effective for it purpose. the other has less... | https://mechanics.stackexchange.com |
30,118 | [
"https://electronics.stackexchange.com/questions/30118",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5872/"
] | I'm reading the Xilinx Spartan 6 user guides. They seem to make the distinction between a <em>Spartan 6 FPGA device</em> and a <em>Spartan 6 FPGA package</em>.
I'm assuming that an FPGA <em>package</em> contains an FPGA <em>device</em>. What exactly is are FPGA packages, and what is the need for the package/device dis... | "Device" is a <em>functional</em> perspective, i.e. the thing which does the actual work.<br>
"Package" is a <em>mechanical</em> perspective, i.e. how it is mounted and connected.
| The device is the silicon itself, and the package is the black plastic moulding with metal pins or solder balls. The same device may be available in different packages (BGA, QFN, TQFP, etc.).
| https://electronics.stackexchange.com |
382,389 | [
"https://mathoverflow.net/questions/382389",
"https://mathoverflow.net",
"https://mathoverflow.net/users/173121/"
] | I have a collection <span class="math-container">$\{v_1,...,v_k\}$</span> of vectors in <span class="math-container">$\{\pm 1\}^n$</span> with the property that for all <span class="math-container">$i\neq j$</span> we have <span class="math-container">$\langle v_i, v_j \rangle \le c\log_2(n)$</span>. I am looking for a... | This is an interesting twist on the usual question.
Relevant results are due to Welch, Kabatianski, Levenshtein, Sidelnikov. Welch's applies to arbitrary vectors, real or complex. The others apply to vectors constructed from complex roots of unity of some finite order.
Welch's bound states (I will apply it to <span cla... | Whilst kodlu gave a highly informative response to my question, I don't think it quite provided a direct answer, but following the references that were provided did, so I have accepted the answer.
The problem is that my bound is on the inner products <span class="math-container">$\langle v_i, v_j \rangle$</span> rather... | https://mathoverflow.net |
40,672 | [
"https://chemistry.stackexchange.com/questions/40672",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/22885/"
] | How can I prepare $\ce{Cu2S}$ powder?
I have some idea about preparing the ternary composition containing copper, but copper sulfides are difficult due to the large difference between their melting points (Cu: 1084°C, S: 119°C).
| The crucial point which explains this is that there are two different forms of conduction happening here.
The first kind of conduction, and the one we are most familiar with is electronic. This is a flow of electrons, and is the conduction which flows in the wire and through the load (a motor, LED etc).
The second ki... | Electrical current will follow the path of least resistance (i.e. it will flow through whichever material is a better conductor); in this case, the external circuit. The conductivity of the electrolyte will depend on what's dissolved in it. I.e. pure water has very poor conductivity, while sea water (dissolved NaCl etc... | https://chemistry.stackexchange.com |
314,195 | [
"https://stats.stackexchange.com/questions/314195",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/107618/"
] | I have a list of 1D values, like this:
<pre><code>x = [20 21 30 31 200 201]
</code></pre>
These values have corresponding weights:
<pre><code>w = [100 100 100 100 1 1]
</code></pre>
I know that there are $k = 2$ clusters in this dataset. Using regular k-means results in
<pre><code>centroids = [25.5, 200.5]
</code>... | You could simply make multiple copies of the points proportional to their weights and then run k-means. Here is an R implementation of that.
<pre><code>## Your data
x = c(20, 21, 30, 31, 200, 201)
w = c(100, 100, 100, 100, 1, 1)
WeightedX = rep(x, w)
kmeans(WeightedX, 2)
Cluster means:
[,1]
1 20.50000
2 32.18... | You can trivially modify k-means to support weights.
When computing the mean, just multiply every point with it's weight, and divide by the weight sum (the usual weighted mean).
$$\mu = \frac{1}{\sum_{i\in C} w_i} \sum_{i\in C} w_i x_i$$
This needs to happen <em>in</em> k-means, at each iteration when it is recomput... | https://stats.stackexchange.com |
33,116 | [
"https://engineering.stackexchange.com/questions/33116",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/5967/"
] | I've got a flashlight with a 3.7 V 18650 cell that charges with a 3.5 mm barrel plug. They provided adapter that says 4.2 V +/- 0.5. Can I use a 5 V USB to barrel plug adapter to charge it?
UPDATE
So the adapter clearly says +- .5 v. Is this an obvious misprint. It must be .05 right?
| I think maybe, definitely NOT do this. Measurement shows the provided adapter/charge controller ranges 4.0 to 4.3 v and current at 200-220 mA.
Plugging into an un charge controlled 5 v 1A power supply immediately drives the current to 1.1 A.
Certainly leading to overheating, possibly venting and leaking, venting lea... | Check the current rating on the existing power adapter. The amperage it draws should not be greater than the source you are considering to use with the 5v usb to barrel plug adapter. If, for example, your existing adapter lists 300 ma and your available source is 1000 ma, you will not overload that new source. If the e... | https://engineering.stackexchange.com |
3,910 | [
"https://security.stackexchange.com/questions/3910",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/2075/"
] | I'm currently studying for the CISSP exam and would like to ensure that I'm using proper terminology when referring to models. I'm a little confused because I'm coming across generic and specific labels; all of which seem to be referred to as "models".
For example, there are terms like <strong>Information Flow</str... | Information flow, state machines and non-interference are more like 'theoretical concepts'.
You can say that the Bell LaPadula model is an implementation of an information flow concept and BIBA is a model build on a state machine concept.
I don't know if this helps.
| I don't think it's important to know whether these are "models". (I know nothing about CISSP, but if that's the kind of thing CISSP wants you to memorize, CISSP is inane.)
That said, yes I'd say that Bell-Lapadula and Biba might well be called theoretical security models. Non-interference is in the same territory. ... | https://security.stackexchange.com |
66,772 | [
"https://electronics.stackexchange.com/questions/66772",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11709/"
] | Say I have a uC active for 1s every 100s, sleep otherwise. This will lead to 1% duty cycle.
But what if it is active ones every ten seconds, and once every 100 seconds, and then once every week? Over what period of time do I calculate the duty cycle?
| If I read your question correctly then you have a wakeup at three different intervals simultaneously:
<ul>
<li>Once every ten seconds and</li>
<li>Once every 100 seconds and </li>
<li>Once every week</li>
</ul>
In this case you have to calculate the duty cycle over the longest interval, in this case one week. Then ca... | The duty cycle for a microcontroller is just a figure that helps calculating the average power consumption. If the duty cycle is not fixed, like for example when it's woken up by an asynchronous signal, it doesn't make sense to express it in terms of duty cycle.
You could have an estimate if you could have the average... | https://electronics.stackexchange.com |
223,932 | [
"https://physics.stackexchange.com/questions/223932",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75502/"
] | Stephen Hawking said that black hole also have temperature and it is related to its mass so in other words a black hole can also be shown to have a negative temperature! I know that nothing is colder than absolute zero and negative temperature are hotter than all positive temperature including infinity, in the case of ... | The temperature of a black hole cannot be negative. The temperature is given by:
$$ T = \frac{\hbar c^3}{8\pi kGM} \tag{1} $$
and obviously this cannot be negative as all the quantities on the right hand side are greater than zero.
However the specific heat is negative and I wonder if this is what you are thinking o... | <blockquote>
Stephen Hawking said that black hole also have temperature and it is related to its mass so in other words a black hole can also be shown to have a negative temperature!
</blockquote>
I'm under the impression that your reasoning is the following: black holes have negative mass, mass is related to temper... | https://physics.stackexchange.com |
72,662 | [
"https://mechanics.stackexchange.com/questions/72662",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/40441/"
] | I was wondering why specific coolants or distilled water is used as a heat transfer liquid for engine cooling instead of just using a separate oil circuit with some type of oil as a heat transfer liquid.
Cost issues aside I guess there is (could be created) an oil type available with similar properties (viscosity, hea... | There's a very straightforward answer to this question: Water has a much, much higher capability to transfer heat than oil.
Even if you were able to overcome the safety and design issues brought up in other answers, you'd still have to overcome the fact that water has a huge performance advantage at transferring heat ... | Water has the nice property that it boils at a fairly low temperature, so the vapour pressure rises quickly with temperature and it is easy to design fail-safe over-pressure protection (a simple spring-loaded filling cap). Also, water is not flammable.
Oil does not have those nice properties, and a cooling system fail... | https://mechanics.stackexchange.com |
3,956,637 | [
"https://math.stackexchange.com/questions/3956637",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/837717/"
] | I have that <span class="math-container">$X_i = \mathbb{N}$</span> for <span class="math-container">$i = 1,2...$</span> and let <span class="math-container">$\tau$</span> be the discrete topology in <span class="math-container">$\mathbb{N}$</span>. In the set <span class="math-container">$X_1 \times X_2 \times ...$</sp... | This is indeed a metric on <span class="math-container">$\mathbb N^ \mathbb N$</span> (for the triangle inequality, show that <span class="math-container">$d(x,y) \leq \max \{ d(x,z),d(z,y)\}$</span> ). It's not hard to see that
<span class="math-container">$$ d(x,y) = \begin{cases} 0 \text{ if } x=y\\ \frac{1}{\min{... | HINT: Let the product be <span class="math-container">$X$</span>. Verify that if
<span class="math-container">$$x=\langle x_n:n\in\Bbb Z^+\rangle,y=\langle y_n:n\in\Bbb Z^+\rangle\in X\,,$$</span>
then <span class="math-container">$d(x,y)<\frac1n$</span> if and only if <span class="math-container">$x_k=y_k$</span> f... | https://math.stackexchange.com |
588,762 | [
"https://math.stackexchange.com/questions/588762",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | This is the text of the problem: Let $(X_{j})_{j\geq 1}$ be i.i.d. nonnegative with $E\{X_{1}\}=1$ and $\sigma_{X_{1}}^{2}=\sigma^{2} \in (0, \infty)$, and let $S_{n}=\sum_{j=1}^{n}X_{j}$. Show that $\frac{2}{\sigma}(\sqrt{S_{n}}-\sqrt{n})\to^{\mathcal{D}}Z$, with $\mathcal{L}(Z)=N(0,1)$.
I was given the following hin... | First check for $n=1$, $n=2$. These are trivial. Assume it is true for $n = m$. Now consider $n=m+1$. The graph has $m+1$ vertices with $m$ edges and no cycles. Now by handshake lemma, there exists at least $2$ vertices with degree $1$. Pick on such vertex and remove it from the graph. Now you have graph on $m$ vertice... | You can use the definition that a tree is a simple ( meaning has no cycles) , minimally-connected graph ( meaning that removing any edge disconnects the graph.). Then use induction on the number of vertices: for $n=1$ , it is clear; try for $n=2$ , just to experiment: you have $2$ vertices and $1$ edge, and your graph ... | https://math.stackexchange.com |
812,868 | [
"https://math.stackexchange.com/questions/812868",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/153906/"
] | How to prove that
$$
\begin{cases}
x_1 + x_2 + x_3 & = 0 \\
x_1x_2 + x_2x_3 + x_3x_1 & = p \\
x_1x_2x_3 & = -q \\
x_1 & = 1/x_2 + 1/x_3
\end{cases}
$$
implies
$$
q^3 + pq + q = 0\,\,?
$$
| To make it $X$ seconds long, play it at $\frac{30}{X}\times 100$ per cent speed.
| Since the 50 and 100 refer to "speed" whereas the 30 and 60 refer to "length", it's actually "$100$ is to $1/30$ (i.e., play $1/30$ of the file per second) as $50$ is to $1/60$ (play $1/60$ of the file per second)".
That is,
$$\frac{\mbox{speed factor}}{1/\mbox{desired length}} = \frac{{100}}{1/{30}}.$$
Equivalently,... | https://math.stackexchange.com |
71,803 | [
"https://mathoverflow.net/questions/71803",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6094/"
] | Has the dynamics of billiards in a polygon subject to gravity been
studied?
What I have in mind is something like this:
<br />
<img src="https://i.stack.imgur.com/kqFWm.jpg" />
<br />
Still Snell's Law applies so the angle of incidence equals the
angle of ref... | As fedja notes in the comments, the bounces off the right and left walls can be accounted for by unfolding the unit square into a horizontal strip, so the trajectories can be viewed as the parabolic arcs of an elastic ball that bounces off a floor and is constrained by a ceiling. We may as well start things at (0,0).
... | Here is the rather interesting result I get in Maple for a square of side 1 tilted at 30 degrees, acceleration of gravity = 1, initial position at the top left corner and moving horizontally with speed 1. This plot goes up to $t=300$. The trajectories appear to fill up a rectangular region (the top right boundary bein... | https://mathoverflow.net |
77,935 | [
"https://dba.stackexchange.com/questions/77935",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/40938/"
] | When we did a rebuild on a clustered index on a table that have about 15gb data in it and the datasize shrunk to 5gb, how can this be? What kind of "data" is removed?
Data size i mean the "data" column of DBCC sp_spaceused
<blockquote>
<strong>Before Rebuild on clustered index:</strong>
<pre><code>name ... | When a table has a clustered index, the index <em>is</em> the table data (otherwise you have a heap type table). A rebuild of the clustered index (any index in fact, but the space wouldn't be counted as "data" for a non-clustered index) will result in partially used pages being merged into a more full form.
As you ins... | The <code>sp_spaceused</code> stored procedure is not examining the total culmulative size of the rows in the database. It is reporting the size of space allocated to hold that data in the cumulative size of the extents allocated for the data.
If there is significant freespace available, such as from many deleted row... | https://dba.stackexchange.com |
126,817 | [
"https://chemistry.stackexchange.com/questions/126817",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/69193/"
] | Consider a reaction
<span class="math-container">$$\ce{A + B <=> C + D}. \tag{R1}$$</span>
Now <span class="math-container">$\Delta G$</span> for the forward reaction is
<span class="math-container">$$\Delta G_\mathrm{fwd} = \Delta H - T\Delta S. \tag{1}$$</span>
For the reverse reaction <span class="math-contain... | The Gibbs energy of reaction <span class="math-container">$\Delta_\mathrm{r} G$</span> determines in which direction equilibrium lies, i.e. in which direction there has to be a net reaction (with a change in concentrations) to reach equilibrium.
When equilibrium has been reached already, there is no net reaction (i.e. ... | I feel Koushal has not seen the difference between <span class="math-container">$\Delta G$</span> and <span class="math-container">$\Delta G°$</span>, because <span class="math-container">$G$</span> of all reactants and products change during the reaction. <span class="math-container">$G$</span> and <span class="math-c... | https://chemistry.stackexchange.com |
92,511 | [
"https://mathoverflow.net/questions/92511",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16934/"
] | Take $n\geq 1$, and $m_{ij}\in [0,1], 1\leq i,j \leq n$. Under what conditions is it possible to find measurable subsets $X_1,...,X_n$ of, say, $[0,1]$, such that $leb(X_i\cap X_j)=m_{ij}$?
Some relations are necessary, like $m_{ii}\geq m_{ij}$, or the fact that the matrix $(m_{ij})$ must be semi-definite positive, bu... | Here's a counterexample with $n=d=3$.<br>
Let $C$ be the rational curve $\lbrace (x,y,z) = (t,t^4,t^6) \rbrace$.
Then the space $S$ of cubics that vanish on $C$ is the span of
$\lbrace x^2 y - z, x^2 z - y^2, y^3 - z^2 \rbrace$.
But all such cubics vanish also on the line $y=z=0$. Therefore
we can take $V$ to be the z... | Edit: the first version of this was completely wrong, I hope this one works.
Take a line $L$ in $\mathbb P^3$, and two general surfaces of degree $d > 3$ passing through $L$; it is not hard to see that the only line contained in $S_1$ is $L$. Their intersection is the union of $L$ with an irreducible curve $C$ of d... | https://mathoverflow.net |
389,775 | [
"https://physics.stackexchange.com/questions/389775",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/67685/"
] | I do understand why the horizontal order matters for indices on the same vertical position, e.g.:
$$T\left(V_{(1)},V_{(2)}\right) = T_\color{red}{\mu\nu}V^\mu_{(1)}V^\nu_{(2)} \neq T_\color{red}{\nu\mu}V^\mu_{(1)}V^\nu_{(2)} = T\left(V_{(2)},V_{(1)}\right)$$
But I don't understand why $T^\mu{}_\nu \neq T_\nu{}^\mu$ i... | $T^\mu{}_\nu$ and $T_\nu{}^\mu$ are both maps from a vector and a dual vector to $\mathbb R$, true. But they aren't necessarily the <em>same</em> map as each other.
Mathematically, you can see this by considering the difference explicitly:
$$ T^\mu{}_\nu-T_\nu{}^\mu $$
You can use the metric to raise/lower one of th... | The difference is $(T^{\mu\rho}-T^{\rho\mu})g_{\rho\nu}$.
| https://physics.stackexchange.com |
1,340 | [
"https://dsp.stackexchange.com/questions/1340",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/852/"
] | Hi I am a little confused on what the notation of the following statement means.
$$ H_{k}(z)= H(W_{4}^{k} z), k = 0,...,3$$
It comes from a question in which I have designed a FIR low-pass filter $H(z)$ and my goal is to implement a DFT filter bank scheme like this:
<img src="https://i.stack.imgur.com/MZMVd.png" alt... | Hk are modulations of the low pass filter (band pass instead of low pass).
$$
(W_{4}^{k}) = e^{-2j\pi k /4}.
$$
For $z = e^{j\omega}$: $$H(W_{4}^{k} z) = H(e^{j(\omega-2\pi k/4)})$$
This means that the filters $H_k$ are shifted in frequency- these are the band pass filters you want to get using your filter bank.
For... | You are going to end up with 4 filters.
$$
H_0(z), H_1(z), H_2(z), H_3(z)
$$
These are constructed by taking your original filter W(z) and dividing it into 1/4ths.
I believe this terminology is telling you to take W(z) and skip every 4th item, starting at the kth item.
$$
H(W_{4}^{k} z), k = 0,...,3
$$
Although... | https://dsp.stackexchange.com |
8,097 | [
"https://earthscience.stackexchange.com/questions/8097",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/6080/"
] | I'm aware that andesite consists of about 60 percent silica and as for minerals, pretty sure it's usually pyroxene and plagioclase. What form would these take on if they were to be separated? Especially interesting, I think, is what would happen to the silica: would it be in its "commercial" powdered form?
| By definition andesite is mainly plagioclase (mostly variety andesine),and pyroxene with either quartz or olivine (not both), and minor amounts of magnetite, ilmenite, zircon, apatite, possibly biotite mica, and maybe a few traces of rarer minerals. The pyroxene is probably a mixture of orthopyroxene and augite. In add... | I'll add a bit to Gordon's answer. Andesite usually contains several large crystals (that can be pyroxene, plagioclase, olivine, or any combination of these). Their sizes can be up to several mm. These crystals will be set in a groundmass (also called matrix) of either very fine crystals of all of the other minerals Go... | https://earthscience.stackexchange.com |
383,002 | [
"https://physics.stackexchange.com/questions/383002",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/183093/"
] | I would like to know how gamma rays from cosmic rays are blocked by the earth's atmosphere. I know that the sun's gamma radiation don't usually reach the earth so I wouldn't be worrying much about it. I have did some research and I only see that ozone will block uv radiation but not gamma radiation. So I am wondering h... | Your first two sentences are correct. But then you go astray. A Carnot cycle is indeed less than 100% efficient, yet it is an ideal (reversible) cycle without friction or any other 'dissipative' processes. Its inefficiency is a case of the Second Law of Thermodynamics: no cyclic process can take in heat at one temperat... | No, this is not the way to think about this. In the Carnot cycle some heat is, necessarily deposited in the low temperature reservoir, rather than being used to do work, but this is <em>not</em> due to friction and does <em>not</em> represent some sort of irreversibly. Your last sentence is true in the sense that it es... | https://physics.stackexchange.com |
70,625 | [
"https://softwareengineering.stackexchange.com/questions/70625",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23496/"
] | I wonder whether PERT/CPM is still being used, or, is it an ancient methodology for the world of today? Thanks.
| Microsoft Project (and a variety of other project management tools) offer Gantt charts, which as far as I can tell are equivalent to PERT charts.
I use them on 6-12 month tasks building complex software systems. We usually define several hundred tasks, that do have many order dependencies.
This is a completely dif... | Although I had never heard of CPM (Critical Path Method) and PERT (Programme Evaluation Review Technique) and thought you were asking about an old operating system it appears that these techniques are still in use or at least still taught.
Doing and advanced search on Google and limiting the query to the last year re... | https://softwareengineering.stackexchange.com |
518,486 | [
"https://physics.stackexchange.com/questions/518486",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249159/"
] | I am reading Goldsetein's Classic Mechanics 3rd edition in Chapter 1 it says,
<blockquote>
If work done in moving form point 1 to 2 denoted by <span class="math-container">$W_{12}$</span>, is independent of the path it should be possible to express it as a change in quantity that depends only on the positions of end... | We know that <span class="math-container">$F_s=\vec{F}\cdot \vec{u}_s$</span> moreover <span class="math-container">$\vec{F}\cdot \vec{\mathrm{d}s}=\vec{F}(\mathrm{d}s\cdot \vec{u}_s)=(\vec{F}\cdot \vec{u}_s)\mathrm{d}s=F_s\mathrm{d}s$</span> and according to your third equation: <span class="math-container">$\vec{F}\c... | <strong>F</strong>.<strong>ds</strong> is the product of the component of F in the direction described by ds and ds itself so it is F<sub>s</sub>ds. Now dividing both sides by ds gives equation (2). I'm not sure of the mathematical rigor, but I think the use of the partial derivative is because, as you say, V depends o... | https://physics.stackexchange.com |
234,181 | [
"https://electronics.stackexchange.com/questions/234181",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/92777/"
] | Cranking Amps: 675
Im trying to find a good battery for a project.
That part where it says "20hr" keeps making me rethink what i sorta hope it means.
| No, it means that you'll get a <em>total</em> of 65 amp-hours out of the battery when you discharge it over a 20-hour period. This would correspond to a current of
$$\frac{65 \text{ amp-hours}}{20 \text{ hours}} = 3.25 \text{ amps}$$
during the 20-hour discharge.
Battery capacity usually varies with the discharge ra... | 65A per hour is written as 65A/h, not 65Ah.
That's Ampere-hour, or the product of time and current.
The 20 hour just means that you can take more energy out slowly. If you drain 65A it'll only last 30minutes, probably, because the higher the current, the lower the amount of energy you get out.
The 20 hour is just ... | https://electronics.stackexchange.com |
477,531 | [
"https://stats.stackexchange.com/questions/477531",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/291539/"
] | I am trying to derive the covariance of two sample sums.
Some notation and details:
<span class="math-container">$x_i$</span> and <span class="math-container">$y_i$</span> are numeric values of two characteristics corresponding to member <em>i</em> of a finite population of N members.
<span class="math-container">$w_i$... | To help make the ideas clear, I will use capital letters for random variables.
Everything follows from the restriction <span class="math-container">$\sum W_i=n,$</span> because that implies this sum has zero variance. Since each <span class="math-container">$W_i$</span> is a Bernoulli variable,
<span class="math-contai... | Based on some of the methods whuber used in his answer, I decided to derive this covariance again, but this time in the way that I originally attempted the derivation (starting by showing the covariance as an expectation and going from there). I get the right answer now:
<span class="math-container">$$Cov\left(\sum_{i... | https://stats.stackexchange.com |
5,711 | [
"https://mathoverflow.net/questions/5711",
"https://mathoverflow.net",
"https://mathoverflow.net/users/401/"
] | The Fell-Doran problem is a problem in functional analysis. It goes as follows: Let $A$ be a complex unital algebra, $X$ a locally convex space, and $L(X)$ the algebra of all continuous endomorphisms of $X$. Suppose that we have a representation of $A$ on $X$, by which we simply mean an algebra homomorphism
$$
T : A \... | I don't agree with Andrew: more specifically, if $A$ is the algebra of compact operators on a Hilbert space $H$, then let $T\in L(H)$. If, say, $H$ is separable, then let $(e_n)$ be an orthonormal sequence, and let $P_n$ be the orthogonal projection on the span of $e_1,\cdots,e_n$. Then $P_n$ is compact, and $P_n(x)\... | I don't know, but I would be very surprised if a topology made the problem any easier since I would imagine that you could always use the induced topology from $L(X)$ on $A$ so if you can answer it in the topological setting then you can answer it in the discrete setting. More specifically, the question is about the <... | https://mathoverflow.net |
316,518 | [
"https://physics.stackexchange.com/questions/316518",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/128264/"
] | I was recently introduced to the concept of probability as a conserved quantity in the context of QM, and the mathematics behind using the continuity equation on probability, specifically the free-particle equation:
$$
\nabla \cdot \mathbf{J} + \frac{\partial |\psi|^2} {\partial t} = 0
$$
Eventually, we came to the we... | Like any other wavefunction, a real wavefunction evolves according to the Schrödinger equation $$i\hbar \partial_t \psi = \hat{H} \psi.$$
Thus a real wavefunction will in general not stay real, and in the case that $\mathbf J = 0$ holds at $t = 0$, it will in general not hold at $t > 0$.
However, suppose that $\psi... | It is possible that the wave function is real, i.e., $\psi(\textbf{r}, t) = \psi^{\ast}(\textbf{r},t)$, at one particular moment $t$. Then, as you have correctly observed, $\textbf{J}(\textbf{r}, t) = 0$, and $\partial\psi/\partial t = 0$, but only at that moment. At later (or earlier) times, $\text{J}$ will become non... | https://physics.stackexchange.com |
2,335,940 | [
"https://math.stackexchange.com/questions/2335940",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/372201/"
] | <blockquote>
Find all $k$ such that the inequality
$$2^{\frac{2\pi}{\arcsin x}}-2(k+2)2^{\frac{\pi}{\arcsin x}}+8k<0$$
holds for at least one real $x$.
</blockquote>
$\bf{My attempt}$ Let $2^{\frac{\pi}{\arcsin x}}=t>0.$ Then $t^2-2(k+2)t+8k<0$
$$t^2-2(k+2)t+(k+2)^2+8k-(k+2)^2<0$$
$$\bigg(t-(k+2)... | Following your steps, with corrections:
$\int\frac{{\sqrt {25-x^2}}}x\,dx$
I see that it is the form $a-x^2$.
Let $x = 5\sin\theta$
Then $dx=5\cos\theta d\theta$
Then substitute this $x$ and $dx$ value in and
get $\int\frac {\sqrt {25-(5 \sin\theta)^2}}{5 \sin\theta}\, 5\cos\theta d\theta $
Using the trig identit... | If $x = 5\sin\theta$ then $dx = 5\cos\theta\, d\theta.$ That was neglected.
You also replaced $\sqrt{25 - (5\sin\theta)^2}$ with $5 - 5\sin\theta.$ That is also not correct. Notice that, for example,
$$
\sqrt{5^2 - 3^3} = \sqrt{25-9} = \sqrt{16} = 4 \ne 5-3, \text{ so } \sqrt{5^2-3^2} \text{ differs from } 5-3.
$$
| https://math.stackexchange.com |
179,571 | [
"https://security.stackexchange.com/questions/179571",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/170466/"
] | For example, if a client submits a file to a server, and the server opens the file in read-mode with Python:
<pre><code>with open(uploaded_file, "r") as f:
# Do something
</code></pre>
Could the act of opening a file be abused with a cleverly-crafted file from the client? Does it depend on the language used by t... | No.
If the filename is controlled by the user, then you might open yourself up to vulnerabilities (e.g. an attacker might try to read config files with the database password). But just opening a file handle for an uploaded file can't do much.
Perhaps if the underlying mechanism would try to read the whole file for bu... | Operating systems generally have a limited number of files they can open at once (specifically, a limited number of file descriptors or <code>fd</code>s in Unix-like systems, or <code>HANDLE</code>s in Windows). If you allow people to open an arbitrary number of those without closing them, then it might be possible to ... | https://security.stackexchange.com |
284,401 | [
"https://mathoverflow.net/questions/284401",
"https://mathoverflow.net",
"https://mathoverflow.net/users/116446/"
] | Let $G$ be a connected simple graph with two distinct edges $e,f \in E(G)$. Choose a random spanning tree $T\subseteq G$, my question is whether there are any known upper bound for the following
\begin{equation} \frac{\mathbb{P}(e\in E(T))\mathbb{P}(f\in E(T))}{\mathbb{P}(e,f\in E(T)) } \end{equation}
for all possible... | There is no constant upper bound, as shown by the following example. Take two vertices $v, u$ and connect them with $n \geq 2$ edge-disjoint paths of two edges. This graph has $n 2^{n - 1}$ spanning trees. The number of spanning trees containing any fixed edge $e$ is $(n + 1)2^{n - 2}$. However, for any $v-u$ path $e, ... | I claim an upper bound on this ratio is $O(D)$ where $D$ is the maximum degree of the graph. In a simple graph, this also implies the bounds $O(n)$ and $O(m)$ where the graph has $n$ vertices and $m$ edges.
Recall that the probability $\mathbb P(e\in T)$ is equal to the effective resistance between the ends of $e$, ... | https://mathoverflow.net |
267,319 | [
"https://mathoverflow.net/questions/267319",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16877/"
] | Let $I$ be the category with objects points of $[0,1]$ with unique morphism for every pair of objects.
Let $C$ be a complete category, suppose that there is an isomorphism $m: a \to b$, $m \in C$ when does there exist a functor $F: I \to C$, with $I(0)=a$, $I(1)=b$, and such that the following holds. Let $D(t)$ denot... | This is a bit of a boring answer, but such a functor always exists. We can use the functor that sends $0$ to $a$, every thing else in $[0,1]$ to $b$ and then sends the morphisms to $\mathrm{id}_a$, $\mathrm{id}_b$ or $m$ as appropriate.
| Yes, certainly. For instance, you could define $F(t)=a$ for $a<1$ and $F(1)=b$, with the obvious choice of morphisms (the identity whenever possible, and otherwise $m$).
More generally, if $I=A\cup B$ is any partition of $I$ such that every element of $A$ is less than every element of $B$ (so $A$ and $B$ are (poss... | https://mathoverflow.net |
264,113 | [
"https://dba.stackexchange.com/questions/264113",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/134116/"
] | I have a table that contains a file path column containing data like this.
<pre><code>C:\ABC\Files\AA.dat
C:\ABC\Files\AA.Unbound.qp
C:\DEF\AA\GGG Build 1 Modules\Random123.qpp
C:\DEF\AA\GGG Build 1 Modules\Random456.qpp
C:\GH\DC.Random789.qpp
C:\IJK\Random987.qpp
</code></pre>
I need to replace the file path to a ... | One possible approach is to reverse the full filenames and find the actual file names.
Table:
<pre><code>CREATE TABLE Data ([FileName] varchar(100))
INSERT INTO Data([FileName])
VALUES
('C:\ABC\Files\AA.dat'),
('C:\ABC\Files\AA.Unbound.qp'),
('C:\DEF\AA\GGG Build 1 Modules\Random123.qpp'),
('C:\DEF\AA... | I have written something that has worked, gives me just the file name after the final \ character. So I should be able to build an update statement.
SELECT Column1
,Column2
,FilePath
,RIGHT(FilePath,CHARINDEX('\',REVERSE(FilePath))+0) file_name
FROM TableName
Open to advice if this is bes... | https://dba.stackexchange.com |
474,399 | [
"https://physics.stackexchange.com/questions/474399",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228999/"
] | I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite.
Kepler's third law gives the equation <span class="math-container">$P^2 = a^3$</span> where <span class="math-container">$P$</span> is ... | that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can't be equal.
Instead, I'd be checking whether <span class="math-container">$T^{2}/a^{3}$</span> is constant for differ... | The general form of Kepler's period law is <span class="math-container">$T^2 = \frac{4\pi^2}{G(M+m)}a^3$</span>. Often, we make the simplifying assumption that <span class="math-container">$M\gg m$</span>, so that <span class="math-container">$M+m \approx M$</span>.
Kepler's period law only takes the form <span class... | https://physics.stackexchange.com |
223,942 | [
"https://security.stackexchange.com/questions/223942",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/224754/"
] | Hacker is trying to attack the site by using the following SQL injection query to get the SQL version.
Using URL site. example:
<pre><code>www.abc.com/?queryParamString=(SELECT 9701 FROM(SELECT COUNT(*),CONCAT(0x71787a7171,(SELECT (ELT(9701=9701,1))),0x71767a6271,FLOOR(RAND(0)*2))X FROM INFORMATION_SCHEMA.CHARACTER_... | Best practice, server and client-side: always, always sanitise your inputs, outputs, and use prepared statements.
You could look at using a WAF (web application firewall) which will detect attempted SQL attacks etc and offer a layer of protection and also customise responses if they are detected. Other than stopping ... | Based on the query string, that is sqlmap, not scanning for a vulnerability, but extracting data, suggesting that there either is a vulnerability or it's a false positive. However it is using error based extraction, which is not very prone to false positives.
I suggest you investigate this further. Although you may be... | https://security.stackexchange.com |
52,924 | [
"https://quant.stackexchange.com/questions/52924",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/34173/"
] | When the price of an asset's future contract is at a certain level, does that mean investors as a whole expect the actual underlying asset to reach that price level in the future?
| It depends. But generally for a <em>storable commodity</em> and as long as there is no shortage of storage capacity or temporary problems with the supply of the spot commodity, the answer is NO.
Gold is an example. You have <span class="math-container">$F > S$</span> but that is because of the financing and storage... | For a purely financial product, with no pent-up investor sentiment for buying or selling (i.e. no supply/demand concerns), the futures market is purely a function of the discounted cash flow in 'carrying' the current spot price forward. Now, if markets are efficient, today's product spot price is a function of the dis... | https://quant.stackexchange.com |
53,067 | [
"https://softwareengineering.stackexchange.com/questions/53067",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18774/"
] | I've worked mostly with interface building tools such as xCode's Interface Builder and Visual Studio's environment to place forms and position them on screens. But I'm finding that with my latest project, placing controls on the form through a graphical interface is not going to work. This more has to do with the num... | It all depends on what your ultimate objective is.
<ul>
<li><strong>Do you want to let your users resize the window?</strong></li>
<li><strong>Is it worth the time?</strong></li>
</ul>
Depending on the project you'll find setting a fixed windows size is much more cost effective, especially if this is an internal tool... | I'm not sure how IB does it, but if I need to create controls that will move or resize if the form they're on in Delphi, I can do that with the controls' <code>Align</code> and <code>Anchors</code> properties.
<code>Align</code> lets you set a control to take up the entire space available, or all space available along... | https://softwareengineering.stackexchange.com |
1,308,524 | [
"https://math.stackexchange.com/questions/1308524",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/189062/"
] | Is it right that the range of convergence is here $1 < x < 3$:
$$\sum_{n= 1}^\infty \frac{e^n + e^{-n}}{n^2} (x-2)^n$$
Just like you do with the geometric series? Or what is this radius of convergence? Thanks!
update:
i got until now:
$$\frac{\frac{(e^{n+1}+e^{-(n+1)})*(x-2)^{n+1}}{(n+1)^2}}{\frac{(e^n+e^{-n... | Using the Ratio Test, we have
$\displaystyle\lim_{n\to\infty}\frac{e^{n+1}+e^{-(n+1)}}{(n+1)^2}\lvert x-2\rvert^{n+1}\cdot\frac{n^2}{(e^n+e^{-n})\lvert x-2\rvert^n}=\lim_{n\to\infty}\frac{e^{n+1}+e^{-(n+1)}}{e^n+e^{-n}}\cdot\frac{n^2}{(n+1)^2}\cdot\lvert x-2\rvert$
$\displaystyle=\lim_{n\to\infty}\frac{e+e^{(-2n+1)}}... | According to WolframAlpha, the interval of convergence is as follows.
<img src="https://i.stack.imgur.com/EdM1X.png" alt="Radius of Convergence">
You can see it plotted as so:
<img src="https://i.stack.imgur.com/RRAfT.png" alt="Plot of interval of convergence">
Unfortunately I'm not sure how one would go about find... | https://math.stackexchange.com |
142,721 | [
"https://stats.stackexchange.com/questions/142721",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/52092/"
] | Certain names are used for structures or node relationships that appear in acyclic, directed graphs (DAGs). Often these DAGs are interpreted causally. Here's a partial list for relationships that nodes might have to each other in such DAGs:
<ol>
<li>Instrument (eg, $Z$ is an instrument for $X$)</li>
<li>Cause (eg, $... | After some thought, I would say that the core relationships are (1) cause; (2) mediator; (3) collider; and (4) confounder. DAGs to illustrate these relationships and the instrument since you asked about it are below.
<ol>
<li>Cause
$X \rightarrow Y$
X is a cause of Y. X and Y are marginally associated in this DAG, b... | @AzulaR. has provided a great answer. Let me add one more, less common, possible situation that is sometimes discussed.
<ol start="6">
<li>Suppression
Here is the scenario: You are interested in estimating the relationship between X and Y, but you do not have direct access to X. You do have data on P, which can ... | https://stats.stackexchange.com |
3,416 | [
"https://cstheory.stackexchange.com/questions/3416",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/2335/"
] | 1) Is it possible to have a parsimonious reduction from a #P-complete problem #A to a counting problem #B when (the decision version) A is NP-complete and the B is in P?
For example, can there be a parsimonious reduction from #SAT to #B, when B is in P?
2) If B is in P, what are the different possibilities for the c... | If you insist on parsimonious reductions (where the number of solutions is preserved) you cannot have such a reduction unless P = NP because the decision algorithm for non-emptyness of solutions for B will give you a decision algorithm for non-emptyness of solutions for A. On the other hand, if you allow other kind of ... | The answer to the question 2 is that the complexity of the counting problem #B can be basically anything (not even necessarily computable). More precisely, the restriction that the decision version is in P does not have any implication on the complexity of the counting version. This is because you can add a dummy sol... | https://cstheory.stackexchange.com |
165,254 | [
"https://dba.stackexchange.com/questions/165254",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/108119/"
] | How to change <code>CHAR</code> (17 byte) to <code>CHAR</code> (16 byte) when there is already a data?
Values are something like this:
<code>012345-000-00001</code>
<ul>
<li>There is a space at the end.</li>
</ul>
I tried to trim it first before altering the column size but still gets the error due to column is al... | Your screen images leave out details that would show up in <code>SHOW CREATE TABLE</code>. But I will make some guesses.
You need, but don't have, a "composite" <code>INDEX(cityCode, tvlDate)</code> on <code>etm</code> and/or a similar index on the other table.
Other issues:
<ul>
<li>Comparing a <code>DATE</code> t... | Looking on Your pictures, I can guess - for run subquery You also use MySQLWorkbench. Most of software - not return to You back all rows from dataset, by default it filter up to 1000 records (some less)
So select without ORDER BY start work and immediately stop after first XXX rows.
In case of create table:
<ol>
<li... | https://dba.stackexchange.com |
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