qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
322,363 | [
"https://softwareengineering.stackexchange.com/questions/322363",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/111862/"
] | I wouldn't call myself a superstar dev, but a relatively experienced one. I try to keep code quality to a high level, and am always looking to make improvements to my coding style, try to make code efficient, readable and consistent as well as encouraging the team to follow a patterns & methodologies to ensure cons... | <h2>Types of reviews</h2>
There is no one true way to do peer reviews. There are many ways in which to judge whether code is of a sufficiently high quality. Clearly there is the question of whether it's buggy, or whether it has solutions that don't scale or which are brittle. Issues of conformance to local standards a... | People comment on code formatting and typos because they are easy to spot and don't require much effort from them.
This part is easy to fix - almost any language have a linter or style checker tool. Plugin it in you build process, so that it would fail the build if there is a redundant space. As a result there will b... | https://softwareengineering.stackexchange.com |
2,332,779 | [
"https://math.stackexchange.com/questions/2332779",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/287621/"
] | I know that if this function is injective, then for $(a, b)$ and $(c, d)$ in the set $\mathbb{Z}\times\mathbb{Z}$, then $f(a, b) = f(c, d)$ implies that $a = c \wedge b = d$:
$f(a, b) = f(c, d)$
$2b - 4a = 2d - 4c$
$b - 2a = d - 2c$
And now I'm stuck as to how I should proceed, as there doesn't seem to be any obvio... | Hint: $f(m+k, n+2k) = f(m,n)$ for $\forall k \in \mathbb{Z}$.
| This is clearly not injective. Let's take $(-2,-1), (2,1)$ These are two different couples going to $0$, so the Kernel is not trivial.
| https://math.stackexchange.com |
64,208 | [
"https://stats.stackexchange.com/questions/64208",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8451/"
] | I imagine that the larger a coefficient on a variable is, the more ability the model has to "swing" in that dimension, providing an increased opportunity to fit noise. Although I think I've got a reasonable sense of the relationship between the variance in the model and large coefficients, I don't have as good a sense ... | In the regularisation context a "large" coefficient means that the estimate's magnitude is larger than it would have been, if a <em>fixed model specification</em> had been used. It's the impact of obtaining not just the estimates, but also the model specification, from the data.
Consider what a procedure like stepwise... | One very simple answer without looking into your details: When you are overfitting, the parameter estimators tend to get large variances, and with large variances large values are just what you should expect!
| https://stats.stackexchange.com |
710 | [
"https://quant.stackexchange.com/questions/710",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/451/"
] | If orders are filled pro rata, is there still incentive to engage in HFT? Because pro rata nullifies the time precedence rule, my intuition is no, but I figure there could be other aspects to it I'm unaware of.
| The Eurodollar market is partially pro-rata. And there is a lot of HFT on it. Getting out of the book when conditions are not right is very much HFT.
| My guess is you are right in that it will be unprofitable to be a liquidity provider because of the lack of time priority.
However, liquidity taking strategy (taking out an order that is mis-priced) is still a speed game.
| https://quant.stackexchange.com |
44,814 | [
"https://physics.stackexchange.com/questions/44814",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16197/"
] | If we look at $P=VI$, we see that if the current doubles then the potential difference is halved<br>
but this doesn't seem to make sense according to $V=IR$. If we look at that equation, since the resistance remains constant, doubling the current should increase the potential difference. Can someone explain what I'm mi... | When you say "we see that if the current doubles then the potential difference is halved," you're assuming that $P$ is fixed, whereas when you say "doubling the current should increase the potential difference" you're assuming $R$ is fixed. But in fact, it isn't possible to change the current while keeping both of thes... | Your confusion probably stems from the fact that you are not looking at $P$ being fixed.
If you double the current, but want power to remain constant, then voltage must be halved.
Sometimes the mechanics of the math alone can cause confusion, but if you try to relate it to what is physically going on, it helps to cle... | https://physics.stackexchange.com |
69,262 | [
"https://electronics.stackexchange.com/questions/69262",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20711/"
] | This question is about high speed digital transmission on a transmission line,
I need to know about how does the
(1) impedance of the transmission line and the
(2) source impedance and
(3) termination impedance,
effect the (1) cable length when we want to transmit a fixed high data rate,
and also
(2) effect data... | I understand you asking these sort of questions and I've tried to answer in the format that you presented the questions. Please forgive if I have misconstrued something.
<strong>Q1 - cable length when transmitting high data rate: -</strong>
(1) Impedance of the transmission line is independent of cable length
(2) So... | Q3: Termination is needed at the far end to stop reflections, especially for high data rates and long cables. The termination should be from the receiving end to ground.
| https://electronics.stackexchange.com |
15,712 | [
"https://softwareengineering.stackexchange.com/questions/15712",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3044/"
] | For those of you who work in big-design-up-front/waterfall groups: how much critical thinking and design is skipped in your design phase and left to your implementation phase? How complete and detailed are your functional and technical specifications delivered at the end of the design phase?
It seems to me that there'... | i'm a huge fan of rapid prototyping, rapid incrementation, and rapid iteration. evolution rather than "intelligent design". you're writing software to solve problems for people and people tend to change their minds and needs over time, even short periods of time.
it's nice to get requirements, a birds-eye view, and "... | There is always something missed in the design phase. People are imperfect, and even with a perfect management that permits lots of design phase time without the pressure to move on to implementation, there will be things you missed.
Likewise, in design, you enter a point of diminishing returns. For example, if design... | https://softwareengineering.stackexchange.com |
186,908 | [
"https://mathoverflow.net/questions/186908",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16702/"
] | The definition of a <strong>gerbe on a smooth manifold</strong> that I know is that - after fixing an open cover $U_i$, a gerbe consists of the data of line bundles $L_{ij}$ on two-fold-intersections $U_{ij}$, isomorphisms $\alpha_{ijk}: L_{ij} \otimes L_{jk} \longrightarrow L_{ik}$ on three-fold intersections that sat... | There is a canonical equivalence of $2$-categories
$$St\left(Man/M\right) \simeq St\left(Man\right)/M$$
between stacks on the large site of $M$ and stacks on the site of manifolds equipped with a map to $M$ (regarding $M$ as a representable sheaf). Given a map $\pi:\mathscr{Y} \to M$ for $\mathscr{Y}$ some stack on m... | Your question has been answered by Reimundo Heluani but let me spell out things in full detail. Suppose you have a gerbe on a smooth manifold $M$ in your sense, given by $(U_i,L_{ij},\alpha_{ijk})$. Here is a procedure for cooking up a stack out of this data:
i) Let $P_i = U_i \times \mathrm{BGL}(1)$ for all $i$. A ma... | https://mathoverflow.net |
135,234 | [
"https://softwareengineering.stackexchange.com/questions/135234",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11107/"
] | I couldn't write a book on Agile. I have worked in several shops that call their process Agile. One of the main points of Agile development is regular client involvement. After a sprint, the work can be demo'd to the client to obtain their feedback. Rinse and repeat.
The problem I come across is that many clients ... | How could it? The very nature of the technique dictates some sort of feedback loop between the customer and the developer.
Parts of your team can, however, act as "proxy" customers (a similar process to "eating your own dog food") so that you can "pretend" to be agile, although that won't be as satisfactory as gett... | The short answer to your question is 'no'. Here are comments on some parts of your question. To be accurate most of the answers are based on my personal experience and observation.
<blockquote>
In my experience, waterfall does not work.
</blockquote>
Waterfall is a sound methodology for delivering systems of varyin... | https://softwareengineering.stackexchange.com |
127,720 | [
"https://mathoverflow.net/questions/127720",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10779/"
] | Let $C(\mathbb{R};{U}(n))$ denote the topological group of continuous functions $\mathbb{R}\to {U}(n)$ with pointwise multiplication and compact-open topology. My question is:
<strong>Are these groups isomorphic for different values of $n$?</strong>
I suspect the answer is no (it feels like it should be obvious), but... | How about this argument? If I remember correctly, the irreducible representations of $U(n)$ are either 1-dimensional or at least $n$-dimensional. Suppose that there was an isomorphism $\phi\colon C(\mathbb{R}; U(m)) \rightarrow C(\mathbb{R}; U(n))$ for $n < m$. We have the embedding $i\colon U(m) \rightarrow C(\math... | Here is another proof. The elements of $C(\mathbb{R};U(n)) $ satisfying $f^2=1$ are functions whose values (under the standard representation of U(n)) are self-adjoint unitaries. There are $n+1$ conjugacy classes of such unitaries (each self-adjoint unitary can be represented as a diagonal matrix of 1s and -1s and coun... | https://mathoverflow.net |
91,493 | [
"https://physics.stackexchange.com/questions/91493",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35915/"
] | I have recently been wondering, with respect to which quantities (covariant or contravariant) one should vary QFT Lagrangians and whether there is some rule regarding this. Let me give an example which will hopefully clarify what my problem is.
Let's take the source-free EM Lagrangian:
$$
\mathcal{L}=-\frac{1}{4}F^{\mu... | Let us suppose that we are in a Minkowski (flat) space-time with a diagonal (symmetric) metrics $\eta_{\mu\nu} = Diag(-1, 1, 1, 1)$, and $\eta^{\mu\nu} = Diag(-1, 1, 1, 1)$,
The standard Euler-Lagrange equations for a Lagrangian $\mathcal L(A_\nu, \partial_\mu A_\nu)$, is : $\partial_\mu \dfrac{\partial\mathcal{L}}{\p... | Varied is the correct word. Finding the equations of motion, as you have, is done by applying calculus of variations to the action and demanding that the variation be an extremum. If you were to do precisely that then you would not encounter choices and the confusion you highlight.
However you have applied the con... | https://physics.stackexchange.com |
60,476 | [
"https://stats.stackexchange.com/questions/60476",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3488/"
] | I've run a regression on U.S. counties, and am checking for collinearity in my 'independent' variables. Belsley, Kuh, and Welsch's <em>Regression Diagnostics</em> suggests looking at the Condition Index and Variance Decomposition Proportions:
<pre><code>library(perturb)
## colldiag(, scale=TRUE) for model with intera... | Yes, this is usually the case with non-centered interactions. A quick look at what happens to the correlation of two independent variables and their "interaction"
<pre><code>set.seed(12345)
a = rnorm(10000,20,2)
b = rnorm(10000,10,2)
cor(a,b)
cor(a,a*b)
> cor(a,b)
[1] 0.01564907
> cor(a,a*b)
[1] 0.4608877
</cod... | I've found the following publications on this topic useful:
Robinson & Schumacker (2009): Interaction effects: centering, variance inflation factor, and interpretation issues
'The effects of predictor scaling on coefficients of regression equations (centered versus uncentered solutions and higher order interactio... | https://stats.stackexchange.com |
135,307 | [
"https://stats.stackexchange.com/questions/135307",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/67641/"
] | Suppose that $X$ is distributed as a finite mixture of normals
$$\sum_{j=1}^k w_j \phi(x;\mu_j,\sigma_j^2).$$
Is $\exp(X)$ distributed as a finite mixture of log-normal distributions?
| When operating a change of variable from $X$ to $Y=\exp(X)$, the density gets transformed as follows:$$f_Y(y)=f_X(x\{y\})\times\left|\dfrac{\text{d}x(y)}{\text{d}y}\right|=f_X(\log\{y\})\times\left|\dfrac{\text{d}\log\{y\}}{\text{d}y}\right|=f_X(\log\{y\})=f_X(\log\{y\})\frac{1}{y}$$which translates into$$f_Y(y)=\sum_{... | When formulated in the most general way, this result can be made obvious. In full generality the mixture components could be any distributions (not even continuous ones) and the mixture need not even be finite. This approach forces us to reason with the most basic tools available (cumulative distribution functions)--... | https://stats.stackexchange.com |
106,207 | [
"https://cs.stackexchange.com/questions/106207",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/102223/"
] | I'm reading Sipser's Introduction to the Theory of Computation (3rd edition). In chapter 0 (pg. 2), he says we don't know the answer to "<em>what makes some problems computationally hard and others easy</em>," however, he then states that "<em>researchers have
discovered an elegant scheme for classifying problems accor... | <strong>That's what you get when you distill a whole bunch of theory to a wider audience.</strong>
In his book, Sipser addresses a general audience at the undergraduate level, possibly with no notion of computability theory; hence, he can only hint at concepts which are to be given a more formal treatment later on in ... | <blockquote>
HOW is it possible to classify problems according to their computational difficulty, if we don't even know what makes a problem computationally easy/hard in the first place?
</blockquote>
I think the point that the piece is trying to make is that we know how to determine whether individual problems are ... | https://cs.stackexchange.com |
164,567 | [
"https://math.stackexchange.com/questions/164567",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/34051/"
] | Here is my steps of finding the integral, the result is wrong but I don't know where I made a mistake or I may used wrong method.
$$
\begin{align*}
\int \frac{dx}{16x^2+20x+35}
&=\frac{1}{16}\int \frac{dx}{x^2+\frac{20}{16}x+\frac{35}{16}} \\
&=\frac{1}{16}\int \frac{dx}{x^2+\frac{20}{16}x+\frac{10}{16}+\frac{... | Your problem is this step:
$$\frac{1}{16}\int \frac{dx}{x^2+\frac{20}{16}x+\frac{10}{16}+\frac{25}{16}}
=\frac{1}{16}\int \frac{dx}{(x+\frac{\sqrt{10}}{4})^2+(\frac{5}{4})^2}$$
for which you use this equality:
$$\textstyle x^2+\frac{20}{16}x+\frac{10}{16}+\frac{25}{16}
=(x+\frac{\sqrt{10}}{4})^2+(\frac{5}{4})^2$$
but t... | You want to complete a square. So, remember that
$$
(x+\alpha)^2 = x^2 + 2 \alpha x + \alpha^2.
$$
You have
$$
2\alpha = \frac{20}{16},
$$
i.e. $\alpha = 5/8$. Hence
$$
x^2 +\frac{20}{16}x = \left( x + \frac{5}{8} \right)^2 - \frac{25}{64}.
$$
Can you go further, now?
| https://math.stackexchange.com |
156,911 | [
"https://dba.stackexchange.com/questions/156911",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/111887/"
] | I want to select last X rows from a table, so what I did was:
<pre><code>SELECT * FROM table ORDER BY id DESC LIMIT 120
</code></pre>
and it worked, but I want it to be ordered ascending, so I tried with:
<pre><code>SELECT * FROM table ORDER BY id DESC LIMIT 120 ORDER BY id ASC
</code></pre>
expecting that it would... | Even this will work:
<pre><code>( SELECT ... ORDER BY ... LIMIT ... ) ORDER BY ...;
</code></pre>
That is, no need in the syntax for the outer <code>SELECT</code>.
| You might be able to do something like this.
<pre><code>SELECT t.*
FROM (SELECT * FROM table ORDER BY id DESC LIMIT 120) AS t
ORDER BY t.id ASC ;
</code></pre>
Another alternative would be to load the results into a temp table, then query that for the desired order.
| https://dba.stackexchange.com |
154,666 | [
"https://math.stackexchange.com/questions/154666",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/10326/"
] | My problem is how to find all groups which have one exactly non-proper subgroup.
Thanks
| <strong>Groups with only one <em>proper</em> subgroup</strong>
A nontrivial group $G$ has no proper subgroups except the trivial group iff $G$ is finite and of prime order.
| Obviously and as Matt noted, your group cannot be infinte. Moreover there are not two distinct prime numbers $p$ and $q$ which divide the order of $G$. (Why?). So the order of group is $p^n$ for some $n≥2$. Now think of the possibilities of $n$ (Hint: apply sylow first Theorem).
| https://math.stackexchange.com |
258,170 | [
"https://softwareengineering.stackexchange.com/questions/258170",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/125534/"
] | I'm learning about Domain Driven Design and struggling with the question if a particular object should be handled as entity or value object.
All possible surname prefixes are kept in a database table. (The data is used in a combo box). Since there are records kept of all these prefixes, should Prefix be seen as an ent... | You already gave the answer yourself in your comment to the other question: If two <code>Prefix</code> objects with the same content are interchangeable, then <code>Prefix</code> is (probably) a value object.
Another rule of thumb is: "Domain first, infrastructure second", i.e., don't let infrastructure concerns (her... | I thought the difference was the linkage with the database. So an Entity object has state that maintains its place in the DB, whereas a value object simply contains the data.
Writing the object back to the DB ends up as a update call in both cases, however the entity will use the internally-held key to refer back to t... | https://softwareengineering.stackexchange.com |
20,264 | [
"https://electronics.stackexchange.com/questions/20264",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1319/"
] | I have a stepper motor powered by a breakout board that uses the A4983 stepper motor driver (http://www.sparkfun.com/products/10735).
Sometimes when the power is disconnected and the drive wheels are back driven, all the LEDs on the the boards light up and it seems like the system is being powered by the stepper motor... | The voltage coming out of your motor probably is AC, but that is being rectified by the kickback catch diodes in the driver circuit. Assuming this circuit was designed and wired up correctly, only the correct polarity voltage will be fed back onto the DC power input net. As long at this voltage doesn't exceed what th... | Accidental powering of a board by motor-generators is often not physically harmful, provided that the motor isn't driven so fast as to subject the board to excessive voltage, but even when it is not harmful it can be a nuisance. It can be somewhat distracting, for example, if turning a motor that's attached to a power... | https://electronics.stackexchange.com |
88,803 | [
"https://cs.stackexchange.com/questions/88803",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/81319/"
] | Given two NP-Complete languages A and B, show that the language:
$L = A\bigoplus B =\{a\bigoplus b \mid a \in A, b \in B, |a|=|b|\}$
is not necessarily NP-Complete.
Remember $a\bigoplus b$ when $|a|=|b|$ gives 0 when they have the same digit and 1 otherwise.
Example: 0110$\bigoplus$ 0101 = 0011
I have tried to s... | $A\bigoplus B$ can be empty (and thus definitely not $NP$-complete) if we pick $A$ and $B$ carefully. For instance, if all strings in $A$ have even length and all strings in $B$ have odd length then $A\bigoplus B$ is empty.
It is fairly easy to modify any $NP$-complete language $L$ to have either only even (resp., odd... | First, notice that $A \oplus B = A \space \Delta \space B = \big( A \space \backslash \space B \big) \cup \big(B \space \backslash \space A \big)$.
To prove that it is not always the case that$\space A \space \oplus \space B \in NP-COMPLETE \space$ you only need to provide one example that falsifies the statement.
T... | https://cs.stackexchange.com |
22,568 | [
"https://softwareengineering.stackexchange.com/questions/22568",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5095/"
] | The situation is that a client requested a number of changes about 9 months ago which they then put on hold with them half done. They've now requested more changes without having made up their mind to proceed with the first set of changes. The two sets of changes will require alterations to the same code modules.
I'... | Explain it like writing two research papers. You might want to go with several different thoughts. In order to do this you create a copy and continue work on the "branches" simultaneously. This issue comes up when you have work done on various different papers and you need to "merge" them into a deliverable.
This exp... | It probably not that important to explain branching. What is important is that you explain the <em>impact</em> of their non-decision.
In this case the impact is if they decide they want the first set of changes down the road it will increase the cost then if you implement the change now. One nice way they will get th... | https://softwareengineering.stackexchange.com |
682,498 | [
"https://physics.stackexchange.com/questions/682498",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/321954/"
] | I have an atom in the ground state for a harmonic potential. At time <span class="math-container">$t = 0$</span> the parabolic potential is switched off.
How can I derive the time evolution of the wave function <span class="math-container">$\psi(t; x)$</span> during the free evolution?
I know that, in order to calculat... | Your difficulty is that the parabolic potential has discrete eigenstates, and in particular your atom is in the ground state, which has a positive energy eigenvalue. When the potential is removed, the eigenstates are planar waves.
But the ground state eigenstate (the square modulus of which is integrable) can be expand... | What you are describing is known as a quantum quench, where an initial quantum state belonging to some Hamiltonian <span class="math-container">$H_{0}$</span> is suddenly evolved by a different Hamiltonian <span class="math-container">$H'$</span> after some switching time <span class="math-container">$t=0$</span>. The ... | https://physics.stackexchange.com |
178,465 | [
"https://physics.stackexchange.com/questions/178465",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/78776/"
] | There is one property of electric lines of forces which states that:
<blockquote>
Electric field lines start and end at 90 degree at the surface of the conductor.
</blockquote>
But why is that so? Is there any proof for this statement or is it observed by any experiment?
<img src="https://i.stack.imgur.com/x58Ia.j... | The reason is the same as why the electric field inside a conductor is zero: if it isn't zero, the free electrons undergo a force and move (rearrange) until they don't feel a net force any more (sum of all forces equals zero). If the electrons don't feel a force, the electric field must be zero.
At the surface of a con... | The surface of the conductor has constant electrostatic potential $V$ and the electric field is proportional to the gradient of the potential: $\nabla V$. By definition the gradient of a scalar quantity is always perpendicular to the level curves (surfaces).
| https://physics.stackexchange.com |
4,036,949 | [
"https://math.stackexchange.com/questions/4036949",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/679645/"
] | The notion of a manifold with boundary has just been introduced in my script. If <span class="math-container">$\mathbb{R}^n_+$</span> is defined as <span class="math-container">$\mathbb{R}^n_+ := \{ (x^1, \ldots, x^n) \in \mathbb{R}^n \; | \; x^n \geq 0 \}$</span>, then a manifold with boundary <span class="math-contai... | Get rid of that image of a manifold given by an embedding into some <span class="math-container">$\Bbb R^n$</span>. An atlas describes the manifold without reference of any surrounding space (if such a space exists at all). Think of a classical atlas of the (surface of the) Earth: Nowhere do you work with three-dimensi... | In addition to Hagen von Eitzen's great answer, let me add something basic.
<span class="math-container">$\newcommand{\R}{\mathbb{R}}$</span>
<span class="math-container">$\newcommand{\B}{\mathbb{B}}$</span>
<span class="math-container">$\newcommand{\pl}{\partial}$</span>
<span class="math-container">$\renewcommand{\S}... | https://math.stackexchange.com |
171,556 | [
"https://physics.stackexchange.com/questions/171556",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59168/"
] | A satellite rotates around the earth; a ball on a string rotates around my hand. Each of these things experiences a <strong>net force</strong> equal to $ mv^2/r = F_{centripetal}$. Why does no object end up at the center of their circular paths?
An attempted answer: An object experiencing a centerwards force at every ... | <blockquote>
Why does no object end up at the center of their circular paths?
</blockquote>
If the path is <em>circular</em> then, by definition, the particle maintains a constant distance from the center of the path. Perhaps you're asking why the particle has a circular path?
<blockquote>
Would someone have a r... | The object has to have an inertia that's pulling it away from the center. Otherwise it would end up at the center as you say. That's why orbiting objects have to constantly move. If the planets stopped orbiting the sun, there would be no inertia of their paths to keep them in place and they'd fall right into the sun... | https://physics.stackexchange.com |
276,722 | [
"https://dba.stackexchange.com/questions/276722",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1754/"
] | I have a query that i am writing to convert some heap tables with primary keys into clustered tables, but the string that i'm generating truncates on objects past a certain length it seems.
<pre><code>SELECT
--t.name,
-- t.schema_id,
-- t.type,
-- t.type_desc,
-- i.name,
-- i.type,
-- i.type_desc... | The reason for this is that the default Results to Text option's maximum number of characters displayed is set to 256 characters. That's why the rest of the text output is truncated.
Try results to Grid, and you should be a happy camper :-)
| So I found two ways to fix this, with @FlogDonkey sending me down the right path.
There is an option for Results to Text for the max characters displayed, i overwrite that from 256 to 1000 and it worked.
I also found that in Results to Grid you can set it to Retain CR/LF on copy or save.
I did, however, have to restart... | https://dba.stackexchange.com |
11,611 | [
"https://dba.stackexchange.com/questions/11611",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6159/"
] | I have a virtual machine (virtualbox) with Windows Server 2003 and SQL Server 2008, running with 4 cores. I wanted to use 6 cores, but when I changed the machine configuration, for some reason SQL Server stopped working. I couldn't start the service - it was giving me an unhandled exception without any extra data.
Do... | Check the version of SQL Server. Enterprise version may be required.
| <blockquote>
it was giving me an unhandled exception without any extra data
</blockquote>
Who was giving an unhandled exception? You app code? Your VM?
SQL Server will restart on 6 cores perfectly fine, you shouldn't have to do anything. It may not <em>use</em> all the cores, but it will restart just fine. If SQL Se... | https://dba.stackexchange.com |
123,356 | [
"https://softwareengineering.stackexchange.com/questions/123356",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15241/"
] | When you are being interviewed by potential future employers, it is of course of benefit to both parties to discuss what your previous job entailed (ie, what you have been doing for the last few years). What if the technology (and the ideas behind the technology) that you have been working on is sensitive and confiden... | I don't think you need be vague:- you can be very specific up-front about what you are -and are not- prepared to discuss. A good (prospective) employer will appreciate your honesty.
Remember that if you're applying for a job with a direct competitor you have a more compelling moral and legal problem if you get the job... | I've frequently had to use phases such as "I can't go into any more detail due to {security/confidentiality/NDA}" at an interview. For every project that I'm working on, I know exactly what is classified, what is competition sensitive, what is covered by an NDA, and what can be shared and who it can be shared with. If ... | https://softwareengineering.stackexchange.com |
301,924 | [
"https://electronics.stackexchange.com/questions/301924",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/147463/"
] | So my question is, if there is a way to use a FM transmitter and send a signal on the same frequency as the local Radio, so that radios only play my signal. Or will it just be interference. In other words: Are FM recivers able to choose a stronger signal over a weaker one, or will they display both?
Thanks in advance.... | FM receivers have a "capture effect" with the stronger signal overriding the weaker signal.
| As others have mentioned FM receivers lock-in to the strongest signal in the vicinity, within limits. This is different from AM where one channel will just mix with the other.
This is one of the reasons FM if much more prevalent than AM. You can pack way more stations into a given bandwidth and the stations with the s... | https://electronics.stackexchange.com |
317,421 | [
"https://physics.stackexchange.com/questions/317421",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/147960/"
] | A mass $m$ is thrown horizontally on a ice rink with speed $v$. From the point of view of the thrower, the initial kinetic energy is $\frac12 mv^2$. Finally the mass stops a certain distance away thanks to the ice friction. He concludes that the energy dissipated by action of the friction is $\frac12mv^2$.
The same th... | So due to Newton's third law there is an equal and opposite force on the ground. Treat this as an object with very large mass $M$, your hockey puck has mass $m$. The puck travels over the ice with speed $v$, the observer moves over the ice in the opposite direction with speed $u$. To this observer the puck seems to hav... | The two observers will observe different kinetic energies of the ice rink. When the ice rink slows down the mass, it must do so by giving itself momentum, even if only a very tiny amount. The difference in the kinetic energy of the ice rink observed by the two observers makes up for the difference in energy that you ... | https://physics.stackexchange.com |
41,327 | [
"https://cs.stackexchange.com/questions/41327",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/30580/"
] | Could someone, in plain english, explain the distinction between the fundamental matrix and the essential matrix in multi-view computer vision?
How are they different, and how can each be used in computing the 3D position of a point imaged from multiple views?
| Both matrices relate corresponding points in two images. The difference is that in the case of the Fundamental matrix, the points are in pixel coordinates, while in the case of the Essential matrix, the points are in "normalized image coordinates". Normalized image coordinates have the origin at the optical center of t... | I want to add one thing to @Dima's answer, just so things are absolutely clear:
<span class="math-container">$E = (K')^TFK$</span> (note the transpose)
You can see how this also captures that the fundamental matrix takes image coordinates as inputs and not normalized 3D points. Let <span class="math-container">$x$</spa... | https://cs.stackexchange.com |
184,202 | [
"https://mathoverflow.net/questions/184202",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34919/"
] | Let $0\le x,y,z,u,v,w\le n$ be integer numbers obeying
\begin{align*}
x^2+y^2+z^2=&u^2+v^2+w^2\\
x+y+v=&u+w+z\\
x\neq& w
\end{align*}
(Please note that the second equality is $x+y+v=u+w+z$ NOT $x+y+z=u+v+w$. This has lead to some mistakes in some of the answers below)
How can the solutions to the above eq... | This system is well studied. You can find full description of solutions in
"Introduction to the theory of numbers" by Leonard E. Dickson. (See Theorem 47).
If all the variables are between $1$ and $P$ then the number of solutions is
$$\frac{18}{\pi^2}P^3\log P+O(P^3),$$
see "An asymptotic formula for the number of ... | This may not give all the solutions, but it does give a 3-parameter family. Choose positive integers $a,b,c,d$ such that $$a+b=c+d,\quad a+c<b<a+d,\quad2a<b$$ Then $$b^2+(b-a-c)^2+(a+d-b)^2=c^2+d^2+(b-2a)^2$$ and $$b+(b-2a)+(a+d-b)=c+d+(b-a-c)$$
| https://mathoverflow.net |
34,016 | [
"https://dba.stackexchange.com/questions/34016",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/9156/"
] | I have a Windows Azure database which I wish to add/remove tables to, and yesterday I witnessed a colleague do this online, on what looked like a web based SQL management studio, but I can't find it anywhere.
I can see a <strong>Manage</strong> button in the toolbar at the bottom of the page, but all this seems to do ... | The Manage button is correct. It should bring up a page in a new window/tab that prompts for the user name and password to connect to the database. If that isn't working, there's something wrong with your web browser configuration (does it allow popups from the Azure site?).
Alternatively, the database <em>server</em>... | This is the format of your managment portal.
Substitute the yoursqlservername (usually something like bhjjeliwwk :)
<pre><code>https://yoursqlservername.database.windows.net
</code></pre>
It's the same as in your connection string.
| https://dba.stackexchange.com |
35,373 | [
"https://astronomy.stackexchange.com/questions/35373",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/31971/"
] | For a high-school students, what are the ways to become an astrophysicist?
What should he/she take in college?
What is the career path to become an astrophysicist?
| In addition to the answer of James K, who outlines the most straight forward way into astrophysics, there's many paths. Some others include:
There are people who did a BSc and/or MSc in Engineering subjects (rocket science of course being a favourite one), and then changing into astrophysics via instrumentation - or j... | Different education systems differ, however
At school you would take maths and physics courses, at least covering calculus.
As an undergraduate, taking (or majoring in) physics. Also probably doing some more maths and perhaps some astrophysics courses.
As a postgraduate doing Masters study in astrophysics leading t... | https://astronomy.stackexchange.com |
801,553 | [
"https://math.stackexchange.com/questions/801553",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/51434/"
] | To be specific, suppose $X_1$ and $X_2$ are independent exponential random variables with parameters $\lambda_1$ and $\lambda_2$; what is $P(X_1 = X_2)$?
According to section 5.2.3 of the book "Introduction to Probability Models" by Sheldon M.Ross (the 10th edition), $P(X_1 < X_2) = \frac{\lambda_1}{\lambda_1 + \la... | It can be confusing to think of an event such as $\{X_1=X_2\}$, since both sides are random; perhaps it will be easier to think about it a little differently.
Instead of considering the event that $X_1=X_2$, let's consider the (clearly equivalent) event that $X_1-X_2=0$. Note that $X_1-X_2$ is just another random var... | <ol>
<li>Yes.</li>
<li>Yes.</li>
<li>Your confusion appears to be the following. If $X_1,X_2$ are continuously distributed random variables then $X_1-X_2$ may or may not be continuously distributed. If $X_1-X_2$ is continuously distributed then $\Pr(X_1=X_2)=0$. If it is not continuously distributed then it can be a... | https://math.stackexchange.com |
484,656 | [
"https://physics.stackexchange.com/questions/484656",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/233944/"
] | The reasoning in my statistical physics book is as follows:
<span class="math-container">$\cdot$</span> The basic postulate of Statistical Mechanics is that for a system with a fixed energy, particle number and volume, each microstate is equally likely to occur.
<span class="math-container">$\cdot$</span> For a certa... | <blockquote>
I have heard people say that based on our current understanding and ideas for possible/current technology no person would ever be able to even travel at a solid (70-80%) the speed of light because getting up to that speed fast would kill the person inside (pizza) because first, the spaceship will acceler... | The concept of "instantly" is problematic in physics, but we can ask whether our bodies could tolerate an arbitrarily high acceleration (say a trillion times g) if all atoms were accelerated at exactly the same pace: you would indeed tolerate it perfectly well, in fact you would feel weightlessness! The problem is that... | https://physics.stackexchange.com |
681,658 | [
"https://physics.stackexchange.com/questions/681658",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/295499/"
] | According to Newton's Second Law,
<span class="math-container">$F=ma$</span>
which is based on the fact that force is proportional to acceleration for a constant mass.
But how will someone measure force to confirm this?
Suppose one observed that for a certain push(force), object accelerated by <span class="math-contain... | I don't know if this what you are looking for, but one can go to dimensionless position and momentum operators (<span class="math-container">$\tilde{p} = p/\sqrt{\hbar m \omega}$</span>, <span class="math-container">$\tilde{x} = \sqrt{ m \omega/\hbar}\;x$</span>) and have the Hamiltonian as
<span class="math-container"... | To add to the answer by @yyy:<br />
Once we have written Hamiltonian in dimensionless representation,
<span class="math-container">$$H=\frac{\hbar\omega}{2}(\bar{p}^2+\bar{x}^2),$$</span>
one can see that the equation is the same in position and momentum representation, where position and momentum (and hence potential ... | https://physics.stackexchange.com |
120,243 | [
"https://cs.stackexchange.com/questions/120243",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/107162/"
] | So I'm looking for a bit of an abstract algorithm and I'd appreciate any references to read up on. This is a bit tough to explain but I'll try my best.
Suppose we have 2 arrays of <code>RGB</code> pixel tuples-
A -> <code>{(56, 39, 75), (125, 222, 32), (156, 201, 102)}</code>
B -> <code>{(125, 195, 93), (53, 31, 67)... | A unary language (i.e., a subset of <span class="math-container">$0^*$</span>) <span class="math-container">$L$</span> is regular iff the set <span class="math-container">$S = \{ n : 0^n \in L \}$</span> is eventually periodic. In particular, if <span class="math-container">$L$</span> is regular then either <span class... | Suppose for contradiction that <span class="math-container">$L = \{0^{2n \choose n} : n \in \mathbb{N}\}$</span> is a regular language. Then by the definition of a regular language there exists a deterministic finite automaton (DFA) that recognizes <span class="math-container">$L$</span>. Let <span class="math-containe... | https://cs.stackexchange.com |
276,770 | [
"https://math.stackexchange.com/questions/276770",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/43601/"
] | I was reading elementary number theory when I came across the theorem that $ a≡b \pmod{N}$ and $N=nm$ implies that $a\equiv b\pmod{m}$. And as a consequence of it, $a ≡ b \pmod{r}$ and
$a \equiv b \pmod{s} \implies a \equiv b \pmod{ lcm(r,s)}$. But I could not think of a proof of it. Could some one please help me with ... | There is a way to complete your argument, although the work is a little tedious. Observe that
$$
x \cdot \ln \left( \frac{2 \cdot {\tan^{-1}}(x)}{\pi} \right) =
\frac{\ln \left( \dfrac{2 \cdot {\tan^{-1}}(x)}{\pi} \right)}{\left( \dfrac{1}{x} \right)}.
$$
As
$$
\lim_{x \to \infty} \ln \left( \frac{2 \cdot {\tan^{-1}}(x... | <strong>Hint</strong> Make change of variables
$$
1+t=\frac{2\arctan(x)}{\pi}
$$
and recall that
$$
\cot\alpha\sim\frac{1}{\alpha}\quad\mbox{for}\quad\alpha\to 0
$$
| https://math.stackexchange.com |
12,612 | [
"https://ai.stackexchange.com/questions/12612",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/26070/"
] | The MSE can be defined as <span class="math-container">$(\hat{y} - y)^2$</span>, which should be equal to <span class="math-container">$(y - \hat{y})^2$</span>, but I think their derivative is different, so I am confused of what derivative will I use for computing my gradient. Can someone explain for me what term to us... | The derivative of <span class="math-container">$\mathcal{L_1}(y, x) = (\hat{y} - y)^2 = (f(x) - y)^2$</span> with respect to <span class="math-container">$\hat{y}$</span>, where <span class="math-container">$f$</span> is the model and <span class="math-container">$\hat{y} = f(x)$</span> is the output of the model, is
... | <blockquote>
The MSE can be defined as <span class="math-container">$(\hat{y} - y)^2$</span>, which should be equivalent to <span class="math-container">$(y - \hat{y})^2$</span>
</blockquote>
They are not just "equivalent". It is actually the exact same function, with two different ways to write it.
<span class="ma... | https://ai.stackexchange.com |
231,738 | [
"https://electronics.stackexchange.com/questions/231738",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/32995/"
] | I am looking to setup a 40w (or similar) solar panel on my SUV to charge a 12v deep cycle (AGM) battery for use when we're camping and that sort of situation. I am unsure as to what sort of charge controller and what amperage charge controller I am going to need for such a setup.
Could anyone please suggest what sort ... | You can purchase an inexpensive USB microscope that can work very well. The main drawback of the inexpensive unit that I use is a small lag when displaying the image. But I quickly got used to the delay.
There are many such microscopes available. I have two identical units purchased from eBay and I assume that Asian ... | To get good magnification at a distance, you need optics with multiple lenses, essentially small telescopes attached to glasses. These are often used by dentists and surgeons. You can find these by searching for "loupe glasses". You'll see many for $200 and up and a few in the $20-$60 range. Look for ones that specify ... | https://electronics.stackexchange.com |
1,013,692 | [
"https://math.stackexchange.com/questions/1013692",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/190908/"
] | I want to determine which group $(\mathbb{Z}/24\mathbb{Z})^{*}$ is isomorphic to.
$\mathbb{Z}/24\mathbb{Z}$ contains the 24 residue classes $z + 24\mathbb{Z}$ of the division mod 24. For brevity, I will identify them with $z$, so $\mathbb{Z}/24\mathbb{Z} = \{ 0, 1, ..., 23\}$. For $(\mathbb{Z}/24\mathbb{Z})^{*}$, I ha... | Very nicely posed question, and some good work on your part. For the first part, identifying the elements of $(\mathbb{Z}/24\mathbb{Z})^{\star}$, note that an element of $\mathbb{Z}/24\mathbb{Z}$ is a unit if and only if it is relatively prime to $24$. You can see this by noting that if $\gcd(\alpha, 24) = 1$, then the... | Every finite <em>abelian</em> group is a product of cyclic groups. If every element has order two, then it has to be a product of copies of $\mathbf{Z} / 2$.
I believe your conjecture is true for finite abelian groups, but false for general finite groups (and false for infinite abelian groups). But it's been a long ti... | https://math.stackexchange.com |
144,050 | [
"https://mathoverflow.net/questions/144050",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40924/"
] | Is it true that if a module $M$ has finite uniform dimension then the same is true for its homomorphic images ?
| Here is a (very easy) counterexample.
The rationals $\mathbb{Q}$ form a uniform module over $\mathbb{Z}$, and thus $\mathbb{Q}$ has uniform dimension $1$, but
$\mathbb{Q}/\mathbb{Z}$ is an infinite direct sum of its $p$-torsion parts and thus has infinite uniform dimension.
| Here is a counterexample.
Let $\Bbbk$ be a field and let $A=\Bbbk [x_0,x_1,x_2,\ldots]$ be the polynomial ring in countably many variables with its natural grading. Consider the ideal $I$ generated by $\{x_i x_j \mid i,j\in \mathbb N, i \neq j\}$, $\{x_i^2-x_j^2 \mid i,j\in \mathbb N, i \neq j\}$ and all monomials of ... | https://mathoverflow.net |
112,930 | [
"https://cs.stackexchange.com/questions/112930",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/108656/"
] | I was watching a lecture video and the Professor states that it would be very rare to see the order of a Btree to be even. I was hoping for an explanation but he cut it off there and moved on with the lecture.
| I don't think there's a right answer to this but you could argue for a preference either way.
Let's define B-tree order <code>m</code> like this
<ul>
<li>max children/values <code>m</code></li>
<li>min children/values <code>m/2</code></li>
<li>max keys <code>m-1</code></li>
<li>min keys <code>Math.ceil(m/2)-1</code>
... | One thing that distinguishes real-world B-trees from "lecture B-trees" is that real B-trees tend to have nodes and leaves where the size <em>in bytes</em> is fixed. So the "degree" of a B-tree is determined by the number of keys that will fit on a page.
So if the keys vary in size (e.g. strings), the "degree" of diffe... | https://cs.stackexchange.com |
860,291 | [
"https://math.stackexchange.com/questions/860291",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/81908/"
] | I have N elements (numbered from 0 to N-1) and I must choose one but without the same probability. For example, I need that the 0 must happen 50% of times, 1 with a 25%, 2 with a 12.5%, etc.
I don't care what happen with the remain probability, it can be assigned to the first element. For example with N=3, I have 0 =>... | Pick a random number between 0 and 1, and calculate $\lfloor-\log_2(x)\rfloor$
| Could also use a monte carlo approach. Pick two random numbers ($x$ and $y$) and define a function ($f$) that gives you the pdf. If $f(x)\geq y$ then accept the point, otherwise pick again. Then it's just a matter of finding the right scaling for the function you use (I'm not familiar with the Java Random class).
| https://math.stackexchange.com |
4,849 | [
"https://scicomp.stackexchange.com/questions/4849",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/1738/"
] | In finite difference theory, you learn, that you have to use upwinding for equations with high convection, like Burgers' equation. What does the finite volume equivalent look like? What if the convection is nonlinear like in Burgers' equation?
| You need to solve a <strong>Riemann problem</strong>, perhaps approximately. For a linear system of equations, the solution to the Riemann problem is just upwinding applied to the characteristics. An "exact" Riemann solver for nonlinear problems resolves the full wave structure (consisting of <em>shocks</em>, <em>raref... | Read any textbook on FV, for example Ferziger and Peric, or Wesseling <img src="https://i.stack.imgur.com/ruDqR.jpg" alt="">!<img src="https://i.stack.imgur.com/lbVR2.jpg" alt="">!
| https://scicomp.stackexchange.com |
1,088 | [
"https://dsp.stackexchange.com/questions/1088",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/1124/"
] | I've read up a lot about this, but haven't been able to piece everything together successfully, so I'm looking for some help.
I need to filter 50 Hz from a signal. It looks like the best options are either a notch filter or a LMS filter, but I don't have a copy of the noise so a notch filter seems to be the best choic... | I'm not sure what iirnotch does, but this is how to design the notch filter by hand.
<pre><code>fs = 20000; % sampling rate
f0 = 50; % notch frequency
fn = fs/2; % Nyquist frequency
freqRatio = f0/fn; % ratio of notch freq. to Nyquist freq.
notchWidth = 0.1; % width ... | You can just type help iirnotch and then see the following example:
<pre><code>% Design a filter with a Q-factor of Q=35 to remove a 60 Hz tone from
% system running at 300 Hz.
Wo = 60/(300/2); BW = Wo/35;
[b,a] = iirnotch(Wo,BW);
</code></pre>
If you replace the 60 with 50 Hz and then do:
<pre><code>Y = filter(... | https://dsp.stackexchange.com |
670,025 | [
"https://physics.stackexchange.com/questions/670025",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/85883/"
] | Given a central potential <span class="math-container">$V(r)$</span>, for any particle subject to this potential, we have its angular momentum not changing with respect to time because <span class="math-container">$\frac{d\mathbf{L}}{dt}=\frac{dm}{dt}\mathbf{x}\times\mathbf{\dot x}+m\mathbf{\dot x}\times\mathbf{\dot x}... | The formula: <span class="math-container">$\tau = I\alpha$</span> is valid for a rigid body rotating around one of its axis of inertia. It is the derivative of <span class="math-container">$L= I\omega$</span>.
But if the radius changes, the system is not a rigid body, so the notion of the dependency of torque for an an... | I think the main question is "how did that radius change?" Whatever force caused that to happen would be responsible for the alteration in angular speed and overall momentum
| https://physics.stackexchange.com |
134,016 | [
"https://dba.stackexchange.com/questions/134016",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39151/"
] | Scenario is this, prod is two two node FCI with mirroring (primary/disaster DC). This is working just fine. New hardware is coming and a version upgrade to SQL Server 2012 (from 2008 R2) in the form of two two node FCI in primary with async AG to get the data over to the second FCI. (DR is all SAN mirroring with identi... | You can't log ship from the principal mirror to a database that's live in an AG, but to another DB you could then make an AG later. Enabling the AG feature and having other AGs has nothing to do with what you're trying to do unless I am misinterpreting.
| If you want to ensure you minimize the amount of time you are without HA during your migration, here's a trick I recently used:
<ul>
<li>Set up the AG with a "dummy" database so that your AG is ready in advance. </li>
<li>Log ship the database(s) to both your primary & secondary AG replicas--at this point, the log... | https://dba.stackexchange.com |
4,475 | [
"https://chemistry.stackexchange.com/questions/4475",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1400/"
] | This one is troubling me, and I even got it wrong in my exam:
<blockquote>
at equilibrium the mass of reactants and products are equal, does that mean the reaction stops?
</blockquote>
Please explain this one.
| At equilibrium, the reaction continues, but the rate of the forward reaction is equal to the rate of the backward reaction.
Let's consider the first order reaction $\ce{A <=>[k_f][k_b] B}$
So, the rate of the forward reaction is $k_f[A]$, and the rate of the backward reaction is $k_b[B]$. Initially, $[B]=0$, an... | A reaction at equilibrium never stops (by itself), it rather remains in a <em>dynamic</em> equilibrium where forwards and reverse reactions occur <em>at the same rate.</em> However, macroscopically you cannot differentiate between a reaction that stopped and a dynamic equilibrium.
Also another note: It is <strong>wron... | https://chemistry.stackexchange.com |
51,339 | [
"https://mathoverflow.net/questions/51339",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3659/"
] | The following problem optimization problem arose in a project I am working on with a student. I would like to minimize the quantity:
$$ M=\frac{1}{12} + \int_0^\frac{1}{2} \left( \tfrac{1}{2}-x \right)^2 Q(x)^2 \ dx - 4 \left[ \int_0^\frac{1}{2} \left( \tfrac{1}{2}-x \right) Q(x) \ dx\right]^2 $$
over all continuousl... | I'll change the variable $y=\frac 12-x$ to make typing easier. Since, as Peter already observed, the condition $Q(0)=0$ is worthless and since $\frac 1{12}$ is just an additive constant, we are just to minimize $\int_0^{1/2}y^2Q^2-4\left(\int_0^{1/2}yQ\right)^2$ under the condition $\int_0^{1/2}Q^2=1$. Since everything... | Here's an interesting/natural observation which might be useful.
Let $U$ be a uniform$(0,1/2)$ random variable, so that $U$ has density function $f(x)=2$, $0 \lt x \lt 1/2$, and define a function $Y$ by $Y(x)=(1/2-x)Q(x)$, $0 \lt x \lt 1/2$. Then, $M=1/12 + \frac{1}{2}{\rm E}(Y^2 ) - {\rm E}^2 (Y)$. (Interestingly, a ... | https://mathoverflow.net |
264,159 | [
"https://dba.stackexchange.com/questions/264159",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/203694/"
] | how can i make monthid column values appear as example: 201901, not 20191.
<pre><code>INSERT INTO [dbo].[table2](accountno, monthid, active)
SELECT accountno, CONCAT(YEAR(InsertionDate), month(insertiondate)), active
FROM [dbo].[table1]
</code></pre>
| <pre><code>DECLARE @t TABLE(InsertionDate datetime);
INSERT @t(InsertionDate) VALUES(GETDATE()), ('20190125');
SELECT CONVERT(char(6), InsertionDate, 112) FROM @t;
</code></pre>
Result:
<pre><code>202004
201901
</code></pre>
| Not sure it is the best way but you could cast the date as a string and then use the "Right" to get only the month like so:
<pre><code>declare @date datetime = getdate()
select @date
select MONTH(@date)
select right(CONVERT(varchar(7),@date,102),2)
</code></pre>
If there is a lot of data, this will not be a performan... | https://dba.stackexchange.com |
518,722 | [
"https://electronics.stackexchange.com/questions/518722",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/222530/"
] | I have two 7.4V batteries. I want to use the series 14.8V voltage to drive a load but I also want to use them paralleled to drive a lower-voltage load.
So would it be possible to connect an isolated 1:1 DC/DC converter to one of the batteries and connects its Vout+ and Vout- to the + and - of the other battery?
There's... | <blockquote>
So would it be possible to connect an isolated 1:1 DC/DC converter to one of the batteries and connects its Vout+ and Vout- to the + and - of the other battery?
</blockquote>
Trying to do so with an off-the-shelf converter would just lead to trouble and frustration -- without a specially-built circuit eith... | <blockquote>
<em>So would it be possible to connect an isolated 1:1 DC/DC converter to
one of the batteries and connects its Vout+ and Vout- to the + and -
of the other battery?</em>
</blockquote>
Step in the buck regulator - feed it from your 14.8 volt (series battery) and it should very efficiently step down to provi... | https://electronics.stackexchange.com |
432,603 | [
"https://softwareengineering.stackexchange.com/questions/432603",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/400032/"
] | I've noticed that most AST tree implementations use classes for nodes instead of something like a vector. I want to ask, why do most people use classes? Are there issues to using vectors to make AST trees?
| To add to the existing answer, the classes (or algebraic types) represent the "node of the tree". Or rather, they represent the <em>kind of node</em> in the tree.
Being able to have more than one type of a node means that language implementors can allow for lots of variety. That means a tree's definition can ... | And what do you put in the vectors? Since it is a tree, you need to model depth. In languages with declarative types, that means a <code>vector<vector<vector<vector</code>… infinitely which isn’t actually denotable. Hence the recursive class.
| https://softwareengineering.stackexchange.com |
51,471 | [
"https://cs.stackexchange.com/questions/51471",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/44416/"
] | I'm volunteering for a non-profit, and was asked to write a program for this problem, but I'm having a little trouble tackling it. Here's the problem:
So they're a daycare, and they get paid by the government depending on specific ratio's of staff to children. Here are the possible ratios and their pay:
<ul>
<li>one ... | You haven't specified your computation model, so I will assume the comparison model.
Consider the special case in which the array $B$ is taken from the list
$$
\{1,2\} \times \{3,4\} \times \cdots \times \{2n-1,2n\}.
$$
In words, the $i$th element is either $2i-1$ or $2i$.
I claim that if the algorithm concludes that... | This answer considers a different model of computation: the unit-cost RAM model. In this model, machine words have size $O(\log n)$, and operations on them take $O(1)$ time. We also assume for simplicity that each array element fits in one machine word (and so is at most $n^{O(1)}$ in magnitude).
We will construct a l... | https://cs.stackexchange.com |
365,838 | [
"https://softwareengineering.stackexchange.com/questions/365838",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/193669/"
] | We're completely remodelling a system at the company for which I am currently working. We're applying DDD and for the very first time I have actually got someone on my team who has some prior experience with DDD as well (yay!)
This new system is extremely user-centric, i.e. pretty much every operation within the syste... | First of all. If you want to follow DDD then one of the rules for creating aggregates is that the transactions should not cross aggregate boundaries. But in your approach if a UserWithActiveAccount has a new accessible account then you will have to delete UserWithActiveAccount and create a new UserWithAccessibleAccount... | I'm not a fan of your smaller aggregate approach. You are over-valuing small at the expense of a large overhead of slightly different classes that repeat themselves a lot. However, I think both of you are too focused on user and aren't fleshing out other domain objects properly.
Based on your three rules user should b... | https://softwareengineering.stackexchange.com |
119,746 | [
"https://cs.stackexchange.com/questions/119746",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/114582/"
] | I am solving a graph problem, which can be formulated as an integer programme. Based on computer experiments, it seems that the branch and bound method works well. I would like to analyse the running time, and wonder whether there have been other problems where branch and bound method was used and the theoretical bound... | Interval graphs are chordal graphs, so you can use a linear time algorithm for finding max clique in a chordal graph. This can be done by first finding a perfect elimination ordering, and then using the fact that every time a vertex is eliminated it forms a clique together with its neighbors that are not eliminated yet... | <pre><code>def mex(m):
for i in [0 ..]:
if not(m.contains(i)):
return i
def maxCliqueOfIntervals(intervals):
maxClique = []
map = {}
for interval in intervals.sort():
// map should only contain intervals that overlap with the current interval
map.filter(lambda x: overlaps(x, interval));
/... | https://cs.stackexchange.com |
262,074 | [
"https://mathoverflow.net/questions/262074",
"https://mathoverflow.net",
"https://mathoverflow.net/users/104830/"
] | Suppose that
<ul>
<li>$X$ is the $n \times n$ matrix of all ones</li>
<li>$Y$ is an arbitrary $n \times n$ matrix with zeroes on the diagonal and all other entries equal to $0$ or $1$</li>
<li>$0 < \delta < 1$</li>
</ul>
Let $Z = -X - \delta Y$. If $Y$ has any ones, then does $Z$ have an eigenvalue with positi... | Suppose that $Y_{ij} = 1$ for some $i, j$. Construct a vector $x$ with $n$ coordinates such that $x_t = 1+\frac{\delta}{n}$ if $t = i$ and $x_t = 1$ otherwise.
Note that $\frac{(-Zx)_t}{x_t} > n$ for each $1 \leq t \leq n$. By the Collatz-Weilandt formula, the Perron-Frobenius eigenvalue of $-Z$ exceeds $n$.
Sin... | In the case $n=3$, try $Y = \pmatrix{0 & 0 & 0\cr 0 & 0 & 1\cr 1 & 0 & 0\cr}$. The characteristic polynomial of $Z$ is $\lambda^3+3 \lambda^2-2 \delta \lambda+\delta^2= \lambda^3 + 2 \lambda^2 + (\lambda - \delta)^2$, which has no positive real roots for any real $\delta$.
| https://mathoverflow.net |
2,128,933 | [
"https://math.stackexchange.com/questions/2128933",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/356308/"
] | Prove that, if $S = \{$real numbers $x > 0 : x^2 < 2\}$, then for every real number $\epsilon > 0$, there is an element $x \in S$ such that $x^2 > 2 − \epsilon$.
<hr>
<strong>My Proof</strong>
<strong>Proposition:</strong> If $S = \{$real numbers $x > 0 : x^2 < 2\}$, then for every real number $\ep... | Most of this post was a discussion about how to properly go from a solution to a sufficient condition that will prove a result, and how not to assume the conclusion to verify a hypothesis. And the result was how to back track from a conclusion to find a correct range of values to test.
But none of my previous answer ... | The idea lurking behind this question might be to use an iteration procedure $x\to A(x)$ converging monotonically to $\sqrt2$, for example,
<blockquote>
$$A(x)=\frac{4x}{2+x^2}$$
</blockquote>
That is, define $x_0=1$ and, for every $n$, $$x_{n+1}=A(x_n)$$ Since every $x_n$ is positive, the goal becomes to show th... | https://math.stackexchange.com |
480,937 | [
"https://electronics.stackexchange.com/questions/480937",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88557/"
] | I know the question might sound slighly basic, but stay with me here.
Kirchoff's Current Law states that
<blockquote>
"The algebraic sum of currents in a network of conductors meeting at a
point is zero."
</blockquote>
But how do we know that no charge gets "stuck" in the junction? Usually, I see people justify... | <blockquote>
"The algebraic sum of currents in a network of conductors meeting at a
<strong>point</strong> is zero."
</blockquote>
It's a <em>point</em>, so no charge can get 'stuck' there because there is no place for it to get stuck in. This point has no capacitance, inductance, resistance or length, so any curr... | The economist George Box once said that "all models are wrong; some are useful". If you asked a physicist they might be able to describe a particular set of circumstances...electric field, magnetic field, quantum effects, whatever...that would cause a temporary nonuniformity in the carrier concentration in a wire.
But... | https://electronics.stackexchange.com |
8,975 | [
"https://physics.stackexchange.com/questions/8975",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <blockquote>
An object is undergoing simple harmonic motion with period 1.2s and amplitude 0.6m. At <span class="math-container">$t=0$</span>, the object is at <span class="math-container">$x=0$</span>. How far is the object from the equilibrium position when <span class="math-container">$t=0.480$</span>s?
</blockquo... | The initial phase $\phi$ should be $-\pi/2$, or in other words, the solution should be $A\sin(\omega t)$ because $\cos(\theta-\pi/2)=\sin(\theta)$. How did you find that $\phi$ is zero? You're supposed to use the fact that $x$ is zero when $t$ is zero. Which is what let's you set $\phi $ to $-\pi/2$ (modulo $\pi$).
| Also remember that the "displacement equation" you refer to could just as well be:
\begin{equation}
x(t) = A \sin{\left(\omega t + \phi\right)}
\end{equation}
The phase angle $\phi$ is a measure of when you decide to start your stopwatch, i.e. when you set $t=0$. For an easy way to remember this, just remember the grap... | https://physics.stackexchange.com |
2,247,383 | [
"https://math.stackexchange.com/questions/2247383",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/417020/"
] | Prove that
\begin{equation*}
\int_{-\infty}^{\infty} e^{-(x - i\alpha)^2}dx = \sqrt{2\pi}.
\end{equation*}
How can I prove it using contour integration & residue theorem? could anyone give me a hint?
| The following solution uses differentiation under the integral.
Write$$f(\alpha)=\int_{-\infty}^\infty e^{-(x-i\alpha)^2}dx.$$ Then$$\frac{df}{d\alpha}=\int_{-\infty}^\infty2i(x-i\alpha)e^{-(x-i\alpha)^2}dx=-i\int_{-\infty}^\infty-2(x-i\alpha)e^{-(x-i\alpha)^2}dx.$$The latter is just $$\left.-ie^{-(x-i\alpha)^2}\right... | Alternative approach: $e^{-z^2}$ is an entire function, hence its integral over the rectangle having its vertices at $-R,+R,+R+i\alpha,-R+i\alpha$ is simply zero. On the other hand the contribute given by the integral over the line segment from $R$ to $R+i\alpha$ (over line line segment from $-R+i\alpha$ to $-R$) is ne... | https://math.stackexchange.com |
82,453 | [
"https://mathoverflow.net/questions/82453",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7455/"
] | Let $X$ be a non-singular complex variety with a big line and base point free bundle $M$ on it. My question is can we say that for any locally free sheaf $F$ on $X$, $F \otimes M^n$ is globally generated for $n \gg 0$.
Motivation: If $M$ were an ample line bundle then all we need is that $F$ is coherent sheaf. But si... | In general the answer is no, even $F$ is a line bundle itself. It is easy to see that a globally generated line bundle is nef, and if $F$ is not nef, and the segment between $F$ and $M$ does not intersect with the ample cone in $N^{1}(X)$, then $F \otimes M^{n}$ is numerically propotional to a divisor lies in the inter... | Here is a simple counterexample (of the form Zhengyu Hu suggested). Take $X$ to be the blowup of a point in $\mathbb P^2$, $M$ the pullback of $\mathcal O(1)$ under the blowup map, and $F$ the line bundle associated to the exceptional divisor $E$. Sections of $F\otimes M^n$ are rational functions which may have a pole ... | https://mathoverflow.net |
337,727 | [
"https://electronics.stackexchange.com/questions/337727",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/167729/"
] | This is the question from a very important assignment I am working on: "A load is being driven by an AC source. At a particular time, the voltage across the load is 120cos(wt+50) and the current through the load is 20sin(wt-10). Calculate the average power in Watts dissipated by the load."
My working:
I first convert ... | <blockquote>
An online calculator gave me a complex number with the real part twice the value that I found.
</blockquote>
Be careful with online calculators and the inputs they expect. Many AC formulas expect RMS values.
Assuming the voltage and current given in your problem are <em>not</em> RMS, you've done it rig... | <blockquote>
Negative power in a resistor? Where did I go wrong?
</blockquote>
The load is not a resistor. If it were a resistor, there would be no phase difference between the current and voltage waveforms.
In general, a negative power is possible --- it means the load has a power source within it and it is delive... | https://electronics.stackexchange.com |
147,907 | [
"https://physics.stackexchange.com/questions/147907",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42337/"
] | The propagator of a free particle in 1d is
$$ K(x_b, t_b; x_a, t_a ) = \sqrt{\frac{m}{2\pi i \hbar (t_b-t_a)}} \exp \left [ \frac{i m (x_b-x_a)^2}{2 \hbar (t_b-t_a)} \quad \right ] .$$ It looks nice.
But, here we have a square root of $i$. Between the two roots, which one should be taken? Based on what rule?
| That propagator is nothing but the analytic continuation of the Green function of heat equation from real positive to imaginary values of $t_b-t_a$. The cut in the complex plane to make single valued the square root has therefore to be put along the negative real axis, or however in the semiplane $x<0$. With this c... | Define $\Delta t := t_b-t_a$ and $\Delta x := x_b-x_a$.
One should ensure that
$$\tag{1}{\rm Re}(i\Delta t)~>~0$$
is positive in order for the exponential factor
$$\tag{2}\exp \left [- \frac{ m}{2 \hbar}\frac{(\Delta x)^2}{ i\Delta t} \right]$$
to be exponentially damped.
Equivalently, one should perform... | https://physics.stackexchange.com |
11,428 | [
"https://physics.stackexchange.com/questions/11428",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4034/"
] | If a fan that is using 50 watts is moving 1 m³/min of air. Lets say the walls are the same temperature as the air so there’s no heat dissipation there. How do I know if the fan is putting in more energy in to the room than its dissipating?
If the walls are 10 deg cooler than the air will this be sufficient for the mol... | Assuming no heat transfer from a cooler outside to a warmer inside, a fan always adds more energy than it dissipates (because it dissipates no energy). However, by introducing a breeze, it accelerates evaporation off your skin, which in turn cools you off. (This is related to the wind chill factor meteorologists talk a... | From my empirical experience, to dissipate 2kW of power in a room, one need 18C temperature difference above walls with one fan.
So to dissipate 0.05kW, walls need to be cooler by ~0.45C only.
| https://physics.stackexchange.com |
2,075,186 | [
"https://math.stackexchange.com/questions/2075186",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/356211/"
] | I was recently considering the problem of determining if one string is a rotation of another. It's a fairly common software engineering problem, but since I recently finished taking abstract algebra I was inspired to ask this from a more algebraic perspective.
First, if we represent the alphabet as a = 0, b = 1, etc.,... | No, this is not true. For the sake of simplicity, allow me to work on $[-\pi, \pi]$ instead of $[0,1]$. Let $f(x) = \cos x$. Clearly, $\| f \|_\infty = 1$. Notice that, in general, $L(x) = (f(\pi) - f(-\pi))x + f(-\pi)$ so, in this case, $L(x) = \cos (-\pi) = -1$. It follows that $\| f - L \| _\infty \ge 2$ because $(f... | Take $f$ defined by the graph $(0,0), ({1 \over 2}, -1), (1,1)$. Then
$L(x) = x$, $\|f\|_\infty = 1$ and
$\|f-L\|_\infty =
{3 \over 2}$.
| https://math.stackexchange.com |
294,684 | [
"https://dba.stackexchange.com/questions/294684",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/230708/"
] | I'm using Visual Studio 2019 to build sql project.
The issue is that building and deploying the dacpac to our database takes up most of our deployment time, when a lot of times, there are no changes to the database.
Is it possible to not have the dacpac build when there are no changes to the database?
| Pick a very good password and then don't share it with any other accts and don't leak it. Hackers generally break into cloud postgresql servers by guessing crappy passwords, not by guessing good ones. Then open up pg_hba to everyone, or at least the entire range of your isp.
Better yet, do this only for your nonsupe... | This will let all ip adresses starting with 127.113.122
<pre><code>host all all 127.113.122.0/24 scram-sha-256
</code></pre>
This will let all ip addresses starting with 127.113
<pre><code>host all all 127.113.0.0/24 scram-sha-256
</code></pre>... | https://dba.stackexchange.com |
260,588 | [
"https://softwareengineering.stackexchange.com/questions/260588",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/153175/"
] | I read that Scrum meetings should be less than 15 minutes long. Is this how long they usually are, or do they depend on the size of the development team? Must every team member speak in these?
| <blockquote>
Is this how long they usually are, or do they depend on the size of the development team?
</blockquote>
No. In my experience, they're either <10 minutes for a manageable team or like 30 minutes because the team is too large or there's nobody (good) in charge. Once you get over 10 minutes, people get ... | The Scrum meetings should mainly involve
<ol>
<li>What is the progress from the last meeting?</li>
<li>What do you plan to do next?</li>
<li>Do you see any blockers?</li>
</ol>
The actual time depends on the team size and should be short and quick.
This is mainly a technique in agile world where you want to dynamical... | https://softwareengineering.stackexchange.com |
1,181,269 | [
"https://math.stackexchange.com/questions/1181269",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/155687/"
] | I have a function $f(x)=x+\sin x$ and I want to prove that it is strictly increasing. A natural thing to do would be examine $f(x+\epsilon)$ for $\epsilon > 0$, and it is equal to $(x+\epsilon)+\sin(x+\epsilon)=x+\epsilon+\sin x\cos \epsilon + \sin \epsilon \cos x$.
Now all I need to prove is that $x+\epsilon+\sin ... | Let $f(x)=x+\sin x$. Then $f'(x)=1+\cos x\geq 0$ and:
$$ f(x+h)-f(x) = h\, f'(\xi),\quad \xi\in(x,x+h) $$
by Lagrange's theorem, hence $f(x+h)-f(x)\geq 0$.
In order to prove that the inequality is strict,
we can notice that:
$$ f(x+h)-f(x-h) = 2h + 2\cos x \sin h $$
can be zero only if $\cos x=-1$ and $\sin h=h$, i.... | differentiate: you get $ 1 + \cos (x)$ this is positive except on a discrete set of points. Integrate it and you get a strictly increasing function.
| https://math.stackexchange.com |
10,535 | [
"https://electronics.stackexchange.com/questions/10535",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3112/"
] | Many farms use electric fences to discourage animals breaking through to neighbouring paddocks.
These electric fences have regular (say once per second) high-voltage spikes of between around 100 V and 120 kV.
Would it be possible to "harvest" this as a power supply for remotely-deployed electronics? e.g. a coil wrapp... | I'd try connecting a small transformer (one designed for a flyback power-supply) with a high step-down ratio between the energized cable and ground, you could then rectify the output and do whatever with it. The HV coil impedance should be high enough to avoid a tremendous draw on the cattle killer, but I don't know m... | Possibly.
I live on a small horse farm and recently made a fence tester using a resistor and a small neon bulb. Even with 10k resistor, I get a really bright flash from the bulb: clearly visible in broad daylight.
The thing I'd want to be careful with is how you get power off the line: intuition says wrap a few turns... | https://electronics.stackexchange.com |
72,641 | [
"https://mechanics.stackexchange.com/questions/72641",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/53616/"
] | <strong>Background:</strong>
I've been having an issue with my car recently where the battery will "die" when I attempt to start my car the morning after an extremely cold night (<32 F). I drive a 2013 Hyundai Genesis, 3.8L V6, 4 door sedan. I live in Indiana (US) so it gets pretty cold but we aren't talking about... | Sounds like your battery terminal connectors are stretched to the point that they are loose even when the bolt is fully tightened. Best fix would be to replace them with new connectors. Alternatively you could add a thin shim of metal between the post and the connector.
Since the metal lead (battery post) has a high... | Clearly there is an electrical connection problem, either external to the battery or internally.
First of all, check the battery cables, both the (+) and (-) connectors. Disconnect them, clean off any debris or corrosion, make sure the terminals are clean, and reconnect the cables and tighten the bolts securely.
T... | https://mechanics.stackexchange.com |
1,169 | [
"https://dba.stackexchange.com/questions/1169",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/873/"
] | I have an Oracle database (10.2.0.1.0 I believe) on a Windows 2003 server that I believe has successfully crashed the OS itself twice. Debates on platforms and stability aside, the evidence suggests that the server becomes unresponsive to any remote access (ports open but services don't respond) due to what I can only... | The first thing to look at would be the database's alert.log file. If the database was having problems at the times that were identified, you'll get error messages in the alert.log and, most likely, you'll get pointers to detailed trace files.
Are you licensed to use the AWR? Is statspack installed? If none of th... | If you believe that the Oracle process had caused trouble to the OS, then maybe you should take a look also in the Event Viewer of that server. System and Application hives should be the ones to check for any error messages.
| https://dba.stackexchange.com |
265,299 | [
"https://mathoverflow.net/questions/265299",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6129/"
] | There are several conventions for the definition of the Fourier transform on the real line.
1 . No $2\pi$. Fourier (with cosine/sine), Hörmander, Katznelson, Folland.
$ \int_{\bf R} f(x) e^{-ix\xi} \, dx$
2 . $2\pi$ in the exponent. L. Schwartz, Trèves
$\int_{\bf R} f(x) e^{-2i\pi x\xi} \, dx$
3 . $2\pi$ square-ro... | The version number 2 is the only one that makes the Fourier transform both a unitary operator on $L^2$ and an algebra homomorphism from the convolution algebra in $L^1$ to the product algebra in $L^\infty $.
It is not, however, of widespread use in analysis as far as I know. From the point of view of semiclassical an... | I would like to add the point of view from a more general aspect.
In the general situation, the Fourier transform can be defined for any locally compact abelian group $G$.
Let $G$ be a locally compact abelian group. Let $\hat{G} = \mathrm{Hom}_{\mathrm{cont}}(G, \mathbb{S}^1)$ be the Pontryagin dual of $G$, where $\m... | https://mathoverflow.net |
13,986 | [
"https://ai.stackexchange.com/questions/13986",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/21158/"
] | I read these comments from Judea Pearl saying we don't have causality, physical equations are symmetric, etc. But the conditional probability is clearly not symmetric and captures directed relationships.
How would Pearl respond to someone saying that conditional probability already captures all we need to show causal... | Perhaps the shortest answer to this question is that Bayes' Theorem itself allows us to easily change the direction of a conditional probability:
<span class="math-container">$$
P(A|B) = \frac{P(B|A)P(A)}{P(B)}
$$</span>
So if you have <span class="math-container">$P(B|A)$</span>, <span class="math-container">$P(A)$<... | <blockquote>
But the conditional probability is clearly not symmetric and captures directed relationships.
</blockquote>
One needs to consider the kinds of directed relationships that is captured by conditional probability. It surely does capture <em>some</em> kind of association or dependence which could be directe... | https://ai.stackexchange.com |
212,388 | [
"https://stats.stackexchange.com/questions/212388",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/110036/"
] | My question is related to the exercise 2.9, p. 79 in Brockwell & Davis, <em>An Introduction to Time Series Analysis and Forecasting</em>, 2nd edition, New-York, Springer, 2002 (It is also related to exercise 3.5, same reference).
Let {$Y_t$} be a process defined by
$$ Y_t = X_t + W_t,$$ where $\{W_t\}\sim \mbox{WN... | Rather than working through the auto-covariance function, it is simpler to perform the analysis as an algebraic exercise working with the initial recursive equations for the two levels of the model. Taking time back by one unit in the upper process gives the equation:
<span class="math-container">$$Y_{t-1} = X_{t-1} ... | Here is my answer, feel free to comment and or correct. By assuming the invertibility of the process, I can discard one of the two solutions of the equation in $\lambda$.
We remind the second order equation for $\lambda$:
$$\phi \lambda^2 + (k^2 + \phi^2 +1)\lambda + \phi. $$
The discriminant of this equation is simp... | https://stats.stackexchange.com |
28,601 | [
"https://physics.stackexchange.com/questions/28601",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8923/"
] | In mathematics there is the concept of <em>infinity</em> meaning that whenever you pick a number and say that it is the smallest/Largest there is a way to further reduce/increase that number by subtracting/adding any other number.
But in physics or chemistry, I see that the absolute temperature does not have a negative... | In physics, temperature and other concepts in "thermodynamics" (that was known for centuries from macroscopic analyses of the heat engines and similar systems) is given by a more fundamental theory, the so-called "statistical mechanics". According to statistical mechanics, the thermal phenomena are explained by the mo... | Zero kelvin is the temperature at which there is no thermal motion. Since temperature by definition is the average thermal motion (really kinetic energy) of an ensemble of molecules, then it is a matter of definition that there can not be a lower temperature than that zero K--because there is no such thing as "negativ... | https://physics.stackexchange.com |
244,758 | [
"https://softwareengineering.stackexchange.com/questions/244758",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/136389/"
] | In my early days of programming I often used to get memory related fatal errors in the following format:
<pre><code>Fatal error: Allowed memory size of <some big number> bytes exhausted
(tried to allocate <some small number> bytes) in /path/to/filename.php
on line <some line number>
</code></pre>
... | Your program has 67108864 bytes (~67MB) available to it at runtime, all of which it has filled. The specific allocation which took the total memory usage from <67MB to >67MB was an allocation of 4000 bytes, which happened within the expression on line 34.
Basically, you're using too much memory, and all the interpr... | 67108864 bytes are also known as 64 MiB (Mebibyte).
Many softwares like PHP still identifies 64 MB as 64 MiB, this is an historically grown issue.
Nowaday we define 64 000 000 bytes as 64 MB (Megabyte, 64 * 1000 ^ 2)
and 67108864 bytes as 64 MiB (Mebibyte, 64 * 1024 ^ 2).
| https://softwareengineering.stackexchange.com |
606,588 | [
"https://physics.stackexchange.com/questions/606588",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/261461/"
] | Suppose the polarisation inside a dielectric is given by <span class="math-container">$P$</span>, then is it related to the electric field as <span class="math-container">$\vec{P}=\epsilon_o \chi \vec{E}$</span> where <span class="math-container">$E$</span> is the field inside the dielectric <em>or</em> is is <span cla... | It is a matter of definition. The usual definition of <span class="math-container">$\chi$</span> implies the electric field <span class="math-container">$\bf E$</span> actually present inside the dielectric.
However, one has to notice that in the special case of a dielectric completely filling a large parallel-plates c... | <span class="math-container">$E$</span> is the field inside the dielectric. "Original field" is called "electric displacement" and usually denoted by <span class="math-container">$\mathbf D$</span>, not <span class="math-container">$\mathbf E$</span>.
| https://physics.stackexchange.com |
270,202 | [
"https://softwareengineering.stackexchange.com/questions/270202",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/163849/"
] | A mobile back-end I am building should receive a larger amount of data (some sensor recordings) from an Android phone. The phone does not have much use of it so it was most efficient to store the data into plain files (SQLite can get quite slow with larger amounts). Now when we upload the data to a REST service backed ... | It's perfectly valid, and is usually done in situations like the one you have. Others have suggested message queues, which are nice but they'll either take up memory or wind up writing the data to a backing store anyway, so now you've got another layer of software doing what you could do directly. That said, it may be ... | You may want to consider a Message Queuing service like Rabbit MQ, this would allow you to send data to a server that would simply keep hold of it until you had a consumer/worker available to process it. You would have to consider things like memory usage on the message queue server if your datasets are very large (or ... | https://softwareengineering.stackexchange.com |
28,010 | [
"https://dsp.stackexchange.com/questions/28010",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/17687/"
] | I know this question has been asked here numerous times. But I am still unclear here :(
My book says,
<blockquote>
A linear time-invariant system is stable if its impulse response is absolutely summable. (G. Proakis)
</blockquote>
So that should mean that, <strong>for a stable system, the impulse response h[n] g... | Note that for stable IIR filters, the impulse response does approach zero as $n$ goes to infinity. It just never becomes exactly zero. However, the sum of the absolute values is finite. Just as an example, take the exponential impulse response
$$h[n]=a^nu[n],\qquad |a|<1\tag{1}$$
where $u[n]$ is the unit step func... | IIR filters are stable when the poles are inside the unit circle. The fact the that impulse response is infinite in time doesn't mean it's not absolute summable.
Consider a simple filter like $y[n]= x[n] + \frac{1}{2} \cdot y[n-1]$. The impulse response is 1, 0.5, 0.25 ..., i.e. $h[n] = 2^{-n}$. The absolute sum of t... | https://dsp.stackexchange.com |
130,355 | [
"https://mathoverflow.net/questions/130355",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6779/"
] | Every elliptic curve $E/\mathbf Q$ is modular, in the sense that there exists a nonconstant morphism $X_0(N) \to E$ for some $N$.
It is tempting to extend this definition in a naïve way to an arbitrary projective curve over $\mathbf Q$; if $Y$ is such a curve, we might say that $Y$ is modular if there exists a noncon... | One expects that the majority of algebraic curves over number fields having genus <span class="math-container">$> 1$</span> should not be modular in this sense.
For instance, take a sufficiently general genus 2 curve <span class="math-container">$C$</span> over <span class="math-container">$\mathbf{Q}$</span>. Then ... | A complement to David's very good answer. A necessary condition for a curve <span class="math-container">$C$</span> over <span class="math-container">$\mathbb Q$</span> to be modular in your sense is as follows:
(RM): each simple abelian variety <span class="math-container">$A$</span> that appear at a quotient of the J... | https://mathoverflow.net |
254,115 | [
"https://physics.stackexchange.com/questions/254115",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/116063/"
] | I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated.
But my professor told me the entropy of a single atom also makes sense, without telling me why.
But I cannot find papers introducing the concrete method of ho... | Before talking about entropy, we need to discuss what possible states an atom can be in. I will start by the most general case that consists in considering a single-atom gas in a 3D box. In that case, the microstate of the atom is described by:
<ul>
<li>The definite linear momentum states $| \textbf{k} \rangle$ of the... | The entropy of a single atom does not make sense per se, <em>unless you specify the preparation</em>. The entropy of a single isolated atom, fixed at a point, is indeed not defined – the entropy is, after all, a property of an <em>ensemble</em> not of a system. The entropy of an ensemble of isolated atoms prepared at a... | https://physics.stackexchange.com |
477,396 | [
"https://physics.stackexchange.com/questions/477396",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | As we know <span class="math-container">$p=F/A$</span> where <span class="math-container">$p$</span> is pessure, <span class="math-container">$F$</span> is force and <span class="math-container">$A$</span> is area.
And we know that p is directly proportional to <span class="math-container">$F$</span> .
Now in case of... | <span class="math-container">$$F=PA$$</span>
For a given applied force to your knife, and the smaller the area over which the force is applied (i.e., the sharper the blade), the greater the pressure (force per unit area) that is applied to your vegetable. Higher pressure makes the force more "concentrated" making a sh... | Bob D offered a good answer. Here is a more philosophical one.
You seem to have suggested a false dichotomy: that in any given situation in which pressure is the fundamental quantity of interest, either force is the dynamic variable with area held constant, or vice versa.
| https://physics.stackexchange.com |
528,188 | [
"https://physics.stackexchange.com/questions/528188",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/252914/"
] | I am a bit troubled trying to make connection between energy and work. Image there is a block on frictionless road on x axis with initial velocity of 0 and a force F is applied for some distance d. the work done is equal to change in kinetic energy and this block has some kinetic energy now and with velocity V. What I ... | <blockquote>
I am a bit troubled trying to make connection between energy and work.
</blockquote>
Work is one of two means by which energy can be <em>transferred</em> from one object to another by means of a net force acting on an object through a distance. The other means of energy transfer is heat, which is energy... | "What I do not understand is that this block has energy which means it has ability to do work but how does it do that?" Lasso the block with a rope and hang on to the rope. The block will come to rest exerting a force on you, the holder of the rope, through a distance as your hand is pulled forward. Work is done on you... | https://physics.stackexchange.com |
1,217,631 | [
"https://math.stackexchange.com/questions/1217631",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/133030/"
] | Consider $n$ arbitrary integer numbers $a_1,\ldots, a_n$ and real numbers $x_1,\ldots, x_n$. Can one find a polynomial, $f(x)\in \mathbb{R}[x]$ such that the graph of $f$ path through $(x_1,a_1), \cdots , (x_n,a_n) $, and
<ol>
<li>$\deg(f)=n$ </li>
<li>$\deg(f)=n-1$</li>
</ol>
Any help would be appreciated.
| Assuming that the $x_i$'s are distinct.
Step 1: For any $i$, can you find a polynomial which vanishes at $x_1,\cdots,x_{i-1},x_{i+1},\cdots,x_n$? (And does not vanish at $x_i$).
Step 2: For any $i$, can you take the polynomial discovered in Step 1 and make its value $a_i$ at $x_i$ (and the value $0$ at $x_j$ for $j\... | For degree $n$, it can be done, using a construction along the lines described in the answer by Michael Burr. One needs a little trick to ensure the degree is exactly $n$.
For degree $n-1$, in general it cannot be done. The Lagrange interpolation process produces a polynomial of degree $\le n-1$, but finding a polynom... | https://math.stackexchange.com |
503,202 | [
"https://stats.stackexchange.com/questions/503202",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/306850/"
] | I have been given the task to classify some tweets per topic. I have done a classification based only on the per-document-per-topic probability with LDA. I have been suggested to use BTM instead, so I am working on that too.
The dataset I work on is made of 3 columns:
<ul>
<li>the text,</li>
<li>the username, and</li>
... | This is a fairly strong assumption and one not likely to be true in practice. That assumption being true justifies the use of a linear regression of <span class="math-container">$Y$</span> on <span class="math-container">$D$</span> and <span class="math-container">$p(X)$</span> for estimating the causal effect of <span... | The expectation of <span class="math-container">$Y$</span> given <span class="math-container">$X$</span> is a function of <span class="math-container">$X.$</span> Hence if <span class="math-container">$X$</span> takes value in <span class="math-container">$\{0,1\}$</span> then there always exists <span class="math-cont... | https://stats.stackexchange.com |
944,463 | [
"https://math.stackexchange.com/questions/944463",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/178493/"
] | When I am trying to integrate a composite function $f(g(x))$ that is multiplied by $g'(x)$, then there's a formula for that in my book. It's simply $F(g(x)) + C$.
But what if $g'(x)$ isn't there?
I'm trying to solve a problem like that, and it's obviously pretty easy with $u$ substitution.... but what formula can I... | With $j=k-1$
$$\sum_{k=1}^n {n-1\choose k-1}=\sum_{j=0}^{n-1} {n-1\choose j}=2^{n-1} $$
| $$2^{n-1}=(1+1)^{n-1}=\sum_{k=0}^{n-1}\binom{n-1}{k}\cdot 1^{n-1-k}\cdot 1^k=\sum_{k=0}^{n-1}\binom{n-1}{k}=\sum_{k=1}^{n}\binom{n-1}{k-1}.$$
| https://math.stackexchange.com |
273,492 | [
"https://electronics.stackexchange.com/questions/273492",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/107039/"
] | We have a new LED roof-lamp at our home and I ordered a matching dimmer-switch to replace one switch in a 3-way-switching. To have matching wall-elements, I also ordered a replacement for a normal toggle-switch (for another roof-lamp) and a normal power-outlet in the same "wall-group".
I was able to replace the topmos... | "Until an electrician installes everyhing correctly it might take some days or weeks - is it okay to have all cables loose and unconnected (with the ends protected against touching, off course) in the meantime?"
"Or is there any danger from NOT connecting cables?"
At least one of the four wires you describe will be "... | If they are correctly isolated (using electrical tape, or electrical splice strips), there should be no danger in leaving any wires unconnected.
| https://electronics.stackexchange.com |
1,414,259 | [
"https://math.stackexchange.com/questions/1414259",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/265438/"
] | How would I start to answer this:
<blockquote>
Show that the vectors $(1,0,0,1)$, $(0,1,0,1)$, and $(0,0,1,1)$ form a basis for the subspace $V$ of $\mathbb{R}^4$ which is defined by the equation $x_1+x_2+x_3-x_4=0$.
</blockquote>
I understand that to be a basis the vectors must be linearly independent and generate... | Since
$$
\{ (x_{1},x_{2},x_{3},x_{4}) \in \mathbb{R}^{4} \mid x_{1}+x_{2}+x_{3} - x_{4} = 0\} = \{ (s,t,u,s+t+u) \mid s,t,u \in \mathbb{R} \},
$$
since
$
(s,t,u,s+t+u) = s(1,0,0,1) + t(0,1,0,1) + u(0,0,1,1)
$
for all $s,t,u \in \mathbb{R}$,
and since $(1,0,0,1), (0,1,0,1), (0,0,1,1)$ are linearly independent in $\mathb... | <strong>Hint</strong>: Consider the vector $v = (x_1,x_2,x_3,x_4)$ and the matrix $A$ whose columns are the vectors given. Then $Av = 0$ implies what about $x_1,x_2,x_3,$ and $x_4$?
| https://math.stackexchange.com |
286,798 | [
"https://math.stackexchange.com/questions/286798",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/37459/"
] | <blockquote>
Find the limit $$\lim_{n \to \infty}\left[\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdots\left(1-\frac{1}{n^2}\right)\right]$$
</blockquote>
I take log and get $$\lim_{n \to \infty}\sum_{k=2}^{n} \log\left(1-\frac{1}{k^2}\right)$$
| The identity $k^2-1=(k+1)(k-1)$ shows that
$$
\prod_{k=2}^n\left(1-\frac{1}{k^2}\right)=\prod_{k=2}^n\frac{k^2-1}{k^2}=\prod_{k=2}^n\frac{k-1}k\cdot\prod_{k=2}^n\frac{k+1}k=\frac1n\cdot\frac{n+1}2,
$$
and the value of limit should follow.
| The $r$th term is $\frac{r^2-1}{r^2}=\frac{(r-1)}r\frac{(r+1)}r$
So, the product of $n$ terms is $$\frac{3.1}{2^2}\frac{4.2}{3^2}\frac{5.3}{4^2}\cdots \frac{(n-1)(n-3)}{(n-2)^2}\frac{(n-2)n}{(n-1)^2}\frac{(n-1)(n+1)}{n^2}$$
$$=\frac12\frac32\frac23\frac43\cdots\frac{n-2}{n-1}\frac n{n-1}\frac{n-1}n\frac{n+1}n=\frac12\... | https://math.stackexchange.com |
3,538,058 | [
"https://math.stackexchange.com/questions/3538058",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/633534/"
] | I'm quite at a loss. I would 'expect' it to be equal to <span class="math-container">$1$</span> since <span class="math-container">$\lim\limits_{x \to 0}2\sin(3x) = 0$</span> and <span class="math-container">$\lim\limits_{x \to 0} \Big (\cfrac{\sin x}{x^{10}} \Big)^{10} = 1?$</span>
Hints please! (Preferably not the ... | You want<span class="math-container">$$\lim_{x\to0}\left(\frac{\sin(2\sin^{10}3x)}{x^{10}}\right)^{10}=\left(\lim_{x\to0}\frac{\sin(2\sin^{10}3x)}{2\sin^{10}3x}\lim_{x\to0}2\cdot 3^{10}\left(\frac{\sin 3x}{3x}\right)^{10}\right)^{10}=\cdots$$</span>
| We have
<span class="math-container">$$
\lim_{x \to 0} \frac{\sin^{10}(2\sin^{10}(3x))}{x^{100}} = \left(\lim_{x \to 0} \frac{\sin(2\sin^{10}(3x))}{x^{10}}\right)^{10},
$$</span>
so it suffices to evaluate the limit within the power. Now
<span class="math-container">$$
\lim_{x \to 0} \frac{\sin(2\sin^{10}(3x))}{x^{10}}... | https://math.stackexchange.com |
598,897 | [
"https://physics.stackexchange.com/questions/598897",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | A thief is driving away on a straight road in jeep moving with a speed of 9 m/s. A police man chases him on a motorcycle moving at a speed of 10 m/s. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police to catch the thief?
I have solved the question in this way ... | When you subtracted, What you did here was you found the separation between the thief and the policeman in the LHS, and in the RHS you found the relative speed between them, as you only subtracted the velocities since t is common. Thus it is the alternate method TKA suggested.
When you add the equations we get 100=19t ... | I think I am understanding it a bit now.
It is more of making the distances equal actually.
I did 10t -9t = 100 -0 because let us say if we make a graph of police at origin and theif at 100m =x.
10 t - 9t is the distance.When we get this equal , means they are at same point.
But we need another value because their is s... | https://physics.stackexchange.com |
279,820 | [
"https://physics.stackexchange.com/questions/279820",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41178/"
] | I am following the procedure outlined in the book "Spacetime and Geometry" by Carroll. The objective is to transform a tensor. In the book, he has this example:
We have a (0,2) tensor of the following form:
\begin{equation}
S_{\mu \nu}=
\left(
\begin{array}{cc}
1 & 0\\
0 & x^2
\end{array}
\right)
\end{equat... | I find the notation that you use in your steps a bit confusing, so I suspect that your mistake comes from a wrong interpretation of the tensor transformation formulae. Anyway, this is how I calculate the first component of $S_{\mu'\nu'}$, which I will call $S_{x'x'}$:
$$S_{x'x'}=\frac{\partial x}{\partial x'}\frac{\pa... | Your tensor has two indices down, so just leave it like that. The transformation law would be
$$S_{\mu' \nu'} = \Lambda^\mu_{\ \ \mu'} \Lambda^\nu_{\ \ \nu'} S_{\mu\nu}$$
where
$$\Lambda^\mu_{\ \ \mu'} = \frac{\partial x^\mu}{\partial x^{\mu'}}$$
or, in matrix, notation,
$$S' = \Lambda^T S \Lambda$$
This way is u... | https://physics.stackexchange.com |
2,609,776 | [
"https://math.stackexchange.com/questions/2609776",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <strong>Problem</strong>
<blockquote>
The matrix <span class="math-container">$A \in \mathbb{R}^{4\times4}$</span> has eigenvectors <span class="math-container">$\bf{u_1,u_2,u_3,u_4}$</span> where <span class="math-container">$\bf{u_1}=\begin{pmatrix}1\\1\\0\\1\end{pmatrix}$</span>, <span class="math-container">$\bf{u_... | <strong>HINT</strong>
We can calculate $Aw$ only if we can find $a,b,c$ such that
$$w=a\cdot u_1+b\cdot u_2+c\cdot u_3$$
thus you can easily find that: $b=12, a+c=1, a-c=-5$
| Here $w$ is not a linear combination of $u_1, u_2, u_3$ so with this imformation it is not possible to calculate $Aw$.
| https://math.stackexchange.com |
418,636 | [
"https://softwareengineering.stackexchange.com/questions/418636",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/282688/"
] | I have a function that repeatedly encodes <code>Foo</code>s to string. I'm currently deciding between two ways to implement this:
Return by value:
<pre class="lang-cpp prettyprint-override"><code>std::string encode(const Foo& foo);
void important_function() {
while (1) {
Foo foo = get_foo();
std::string ... | Is it important?
It is good to have those details in mind but is it really important right now in your development to know if a string will be allocated or not and if it will be a bottleneck for your application?
If yes, try both and measure. Chance are the difference is either minimal (compare to other algorithm issue... | <blockquote>
Am I missing something here?
</blockquote>
The as-if rule means that an implementation <em>may</em> treat both cases the same.
In the cases where you don't need to enlarge <code>encoded</code> in the second case, the allocator can easily re-use the same bytes. Otherwise <em>both</em> cases have to allocate... | https://softwareengineering.stackexchange.com |
372,962 | [
"https://physics.stackexchange.com/questions/372962",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/175517/"
] | I'm confused about this formula $H = \frac {g}{2}\cdot t^2$
Imagine the following situation. A ball falls from a wall of $125$m and the fall lasts $5$s.
At the height of $80$m the time is $4$s, at the height of $45m$ the time is $3$s, since $80+45 = 125$, the time required to fall from a height of $125m$ is $4+3=7$, b... | The formula you have given $$H=\frac{gt^2}{2}$$ is correct in the case where the initial velocity is $0$. This means that the time you have calculated is longer, as for the second part you used this equation which incorrectly assumes that at that point the initial speed would be $0$. The full equation should be $$H=ut+... | In the case that throughout the question the initial velocity is zero (i.e. the object is dropped from a height $H$ ):
As the equation requires the time to be squared, the addition of the two times would have to be done like this:
$$t_1^2+t_2^2=t_{total}^2$$
So
$$4^2+3^2=25=5^2$$
| https://physics.stackexchange.com |
29,497 | [
"https://scicomp.stackexchange.com/questions/29497",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/27504/"
] | I've been discretizing PDEs and formulating $Ax=b$ systems, and yet I don't really know what the $A$ and $b$ are in words.
I occasionally call the $A$ matrix the "Jacobian matrix," but for linear PDEs, "Jacobian" doesn't make sense, so I call it the "differential operator matrix." Is there a standard name for this $A$... | $A$ is a discretized version of your differential operator + enforced boundary conditions. The names for $A$ can vary depending on the way the PDE is being discretized. For example, in FEM, it will be <em>stiffness matrix</em>. For integral equation methods (technically not a PDE) applied to Maxwell equations, such a m... | Here is some generic (application-independent) terminology I've seen in papers:
<ul>
<li>$A$: The ``coefficient matrix''</li>
<li>$b$: The ``right hand side''</li>
<li>$x$: The ``unknown''</li>
</ul>
Also, sometimes $A$ may be called the ``coefficient operator'' if it is considered as a linear operator rather than a ... | https://scicomp.stackexchange.com |
1,229 | [
"https://dba.stackexchange.com/questions/1229",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/105/"
] | How do you calculate mysql max_connections ?
What do you take into consideration ?
| Going to post this as an answer, with the relevant information. The basic formulas are:
<blockquote>
Available RAM = Global Buffers + (Thread Buffers x max_connections)
max_connections = (Available RAM - Global Buffers) / Thread Buffers
</blockquote>
To get the list of buffers and their values:
<pre><code>SHOW VARIABLE... | <strong>WARNING! This is from 2011 using MySQL 5.1.x. Use at your own risk</strong>
---- ORIGINAL POST ----
Here's another alternative formula in stored procedure form:
<pre><code>DELIMITER //
CREATE PROCEDURE sproc_show_max_memory ( OUT max_memory DECIMAL(7,4))
BEGIN
SELECT ( @@key_buffer_size + @@query_cache_size ... | https://dba.stackexchange.com |
112,595 | [
"https://mathoverflow.net/questions/112595",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12706/"
] | Consider the familiar Riemann surface
$$ Y_1(N) = \Gamma_1(N) \backslash \mathcal{H} $$
where $\mathcal{H}$ is the upper half-plane and $\Gamma_1(N)$ is the subgroup of matrices in $SL_2(\mathbb{Z})$ which are congruent to $\begin{pmatrix} 1 & * \\\ 0 & 1 \end{pmatrix}$ modulo $N$.
It's a standard theorem t... | In the model you describe, the cusp $\infty$ of $X_1(N)$ is not defined over ${\bf Q}$ (but the cusp $0$ is). A way to see this is that the marked elliptic curve $({\bf C}/({\bf Z}+\tau{\bf Z}),1/N)$ is isomorphic to the marked Tate curve $E_q=({\bf C}^\times/q^{\bf Z},e^{2\pi i/N})$ with $q=e^{2\pi i\tau}$. When you l... | There are in fact explicit equations (at least for the prime level) worked out in arXiv:math/0010272.
| https://mathoverflow.net |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.