qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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1,393,432 | [
"https://math.stackexchange.com/questions/1393432",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/131857/"
] | Suppose $f$ $\in$ to $L(C^{10},C^{10}) $ linear functions and has only one eigenvalue say λ .
Suppose $g=f-λid $. And
$$\dim(\text{Ker}(g))=4$$
$$\dim(\text{Ker}(g^2))=7$$ $$\dim(\text{Ker}(g^3))=9$$ $$\dim(\text{Ker}(g^4))=10$$.
Find the Jordan matrix of the $f$ subject to λ.!!
Help if it is possible .I know ... | Hints (justifications omitted):
<ul>
<li>There is only one eigenvalue $\lambda$ so the matrix's diagonal elements are all $\lambda$. The question is how large the Jordan blocks are (i.e., where to put the $1$s above the diagonal).</li>
<li>$\dim(\ker(g))=4$ implies that there are four Jordan blocks.</li>
<li>more gene... | I'll try to sketch why $\dim(\ker g^i)-\dim(\ker g^{i-1})=r_i$, the number of Jordan blocks of size $\ge i$. In particular, the number of Jordan blocks is $r=r_1$. We'll suppose we work in $\mathbf C^n$.
First note the matrix of $g$ is block-diagonal matrix of the form:
$$J_l=\begin{pmatrix}0&1&0&\dots&... | https://math.stackexchange.com |
85,993 | [
"https://mechanics.stackexchange.com/questions/85993",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/68807/"
] | I may or may not be overthinking. I'm new to motorcycles and I bought a new motorcycle. Here's the full thing:
<hr />
So we don't have a showroom in my city. So someone I knew rode it personally to deliver it to me. I was with him as a pillion.
The motorcycle is <strong>110 cc</strong> and at some points he rode at the... | When it comes to running procedures the guidance in the owners manual overrides generalized advice on the internet. If the manufacturer intended for there to be speed restriction (or more likely an engine RPM one since <em>engine</em> speed is what matters not road speed) during running in they'd specify it there.
From... | In the modern manufacturing context, the "run-in" procedure is intended more to prevent damage to the rider and not to the bike.
Like 30 years already, the surfaces in the engine are precise enough not to need any run-in. You are not doing any significant good to your engine by running it at low throttle and ... | https://mechanics.stackexchange.com |
229,168 | [
"https://softwareengineering.stackexchange.com/questions/229168",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/120052/"
] | I'm trying to automate the process of sending many domain name lookup requests.
I tried to do this by sending for example http request to domain registry site like Whois.net, but I notice they block you after several attempts.
others like networksolutions adds token to the page to avoid automated requests.
Is there ... | You are currently going through middlemen (remote web servers) instead of querying the information more directly.
There's a program on your host system called <code>whois</code> (which is what that whois.net site is named after!) which you can call as a subprocess, and the information out of it isn't usually too hard ... | While whois is often used as a method to determine domain name availability, it is not always real-time or accurate.
The best and proper way to do this would be to become an accredited registrar for the TLDs in question and use the registry's APIs (which usually work with the extensible Provisioning Protocol (EPP)) to... | https://softwareengineering.stackexchange.com |
95,087 | [
"https://softwareengineering.stackexchange.com/questions/95087",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31673/"
] | I'm currently working as a software developer and studying for a software engineering degree (the former whilst not doing the latter).
I'm confident in my ability to do my job competently, but I feel I could do it better. I know my greatest pitfall is in my business skills; for example, I often don't understand at fir... | I agree with several others here: it sounds like you need to learn more about how to learn the business domain quickly. Journalists do this a lot.
When I was in your position a long time ago, I picked up a couple of textbooks on journalism and reporting. I learned a lot from them. Background reading is important; in... | Always try to understand the business domain before writing any code. Read a book on it and talk to the users/domain experts until you are confident you truly understand your task. Depending on the business domain, this isn't always easy, especially in the beginning. But as time passes and you gain more experience you'... | https://softwareengineering.stackexchange.com |
141,920 | [
"https://chemistry.stackexchange.com/questions/141920",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/85881/"
] | Since entropy is a state function so it doesn't depends on the path followed. So will the entropy change be equal if a state change be first brought about reversibly and then irreversibly.
| If the initial and final states of systems are the same for both reversible and irreversible process, the entropy change for the systems will be the same.
But the entropy change for the surrounding will not be the same, as the final states will be different. The surrounding for the irreversible process will end with hi... | Yes, that is how we determine the entropy change of a system for an irreversible process . We determine the entropy change for a reversible path between the same two end states.
| https://chemistry.stackexchange.com |
494,173 | [
"https://stats.stackexchange.com/questions/494173",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/172825/"
] | I'm wondering how to get variance of exp. distribution from the raw variance computed using the moment generating function. Here's my line of reasoning:
PDF of Exponential distriution is
<span class="math-container">$$
p_X(x) = \lambda \cdot e^{-\lambda x}
$$</span>
for <span class="math-container">$x > 0$</span>, a... | <span class="math-container">$M_X^{(2)}(0)$</span> is not a variance, it is <span class="math-container">$E(X^2)$</span>. So the variance can be obtained by
<span class="math-container">$$Var(X) = E(X^2) - E(X)^2 = M_X^{(2)}(0) - [M_X^{(1)}(0)]^2 = \frac{1}{\lambda^2}$$</span>
| The second moment gives you
<span class="math-container">$$E[X^2]$$</span>
and the variance is defined as
<span class="math-container">$$E[X^2]-E[X]^2$$</span>
so that you get
<span class="math-container">$$2/\lambda^2-(1/\lambda)^2$$</span>
which will then give you the desired result.
| https://stats.stackexchange.com |
61,704 | [
"https://mathoverflow.net/questions/61704",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4622/"
] | I hope this isn't too narrowly focused. I have a question concerning the inverse of the Bott map as defined in Atiyah's paper, <em>Bott Periodicity and the Index of Elliptic Operators.</em> On page 122 he defines it as the composition
$$K^{-2}(X) \to K(S^2 \times X) \stackrel{\text{index} \bar\partial}{\longrightarr... | Your argument against your definition is not convincing. You say you are writing down an exact sequence for your first map, but in fact you write down one for your second map. The second map is not necessarily injective. We only need it to be injective on the image of the first map.
The definition you write looks fin... | Actually I think I found a better way to look at the map, which shows that it is injective. Consider the pair $(S^2 \times X, \{pt\} \times X)$. Then since $\{pt\} \times X$ is a retract of $S^2 \times X$, the 6-term sequence in $K$-theory splits to give a short exact sequence
$$
0 \to K(S^2 \times X, \{pt\} \times X... | https://mathoverflow.net |
2,326,072 | [
"https://math.stackexchange.com/questions/2326072",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/178698/"
] | We define 3 sequences $(a_n),(b_n),(c_n)$ with positive terms so that
$$ a_{n+1}\leq\frac{b_n+c_n}{3}\ ,\ b_{n+1}\leq\dfrac{a_n+c_n}{3}\ ,\ c_{n+1}\leq\dfrac{a_n+b_n}{3} $$
Check if any of $(a_n),(b_n),(c_n)$ converge, and if they do find their limit.
PROOF
My part of the proof is this: By adding the above inequaliti... | Yes because you have the "sandwiched" inequality $0 < a_{n} < x_{n} \rightarrow 0$, so $a_{n} \rightarrow 0$.
EDIT: Of course, you have to make sure that $x_n \rightarrow 0$ in the first place, but you have that it is bounded by a geometric sequence which converges to zero which implies the stated convergence.
| To prove that $x_n$ converges to $0$ you need to take the limit
$$
0\leq x_{n+1}\leq \frac{2}{3}x_n \implies 0\leq l\leq \frac{2}{3}l \implies l=0
$$
| https://math.stackexchange.com |
312,704 | [
"https://dba.stackexchange.com/questions/312704",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/137986/"
] | I have a date as varchar (dont ask why). I need to select Max(date). However, date can be faulty, like 2034-34-34. I would like to select max date that is valid and not greater than today. It's t-sql.
I tried:
<pre><code>create table #tmp (
dt varchar(10)
)
insert into #tmp values ('2022-02-15'),('2034-34-34')
selec... | This is what I have for now:
<pre><code>create table #tmp (
dt varchar(20)
)
insert into #tmp values ('2022-02-15'),('2034-34-34'),('2022-03-14'),(null)
select top 1 dt from #tmp
where isdate(dt)=1
order by dt desc
</code></pre>
The result:
2022-03-14
<strong>Update</strong>:
Thank you all, I have a solution from you... | Your <code>HAVING</code> clause was the issue in your post's example query. <code>HAVING</code> is usually used to filter with aggregates <em>within</em> a group of values. Also your were evaluating if the max value was a date in the order of events in that <code>HAVING</code> clause, rather than filtering out non-date... | https://dba.stackexchange.com |
4,480,745 | [
"https://math.stackexchange.com/questions/4480745",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1025098/"
] | Let <span class="math-container">$s \in[a, b]$</span> and <span class="math-container">$x \in \mathbb{R}$</span> be fixed and consider the following SIE:
<span class="math-container">$$
X_{t}=x+\int_{s}^{t} \sigma\left(u, X_{u}\right) d B(u)+\int_{s}^{t} f\left(u, X_{u}\right) d u, \quad s \leq t \leq b
$$</span>
Use <... | Essentially, the equation <span class="math-container">$P(X_t^{s,Z} \le y | Z) = P(X_t^{s,x}\le y)|_{x=Z}$</span> is just stating that <span class="math-container">$X_t^{s,Z}$</span> has the Markov property.
The value <span class="math-container">$P(X_t^{s,x} \le y)$</span> is fully deterministic, and can be thought of... | Since <span class="math-container">$P\left(X_{t}^{s, Z} \leq y\right)$</span> is a function of <span class="math-container">$x$</span>, we have
<span class="math-container">$P\left(X_{t}^{s, Z} \leq y\right)=\left.P\left(X_{t}^{s, x} \leq y\right)\right|_{x=Z}$</span>, thus, <span class="math-container">$P(X_{t}^{s, Z}... | https://math.stackexchange.com |
233,562 | [
"https://electronics.stackexchange.com/questions/233562",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/109438/"
] | Professor was teaching us the basics of opamps today, he went quite quickly over the frequency-dependency of opamps.
He said the gain response to frequency was approximately a "first order response", can someone explain what it is and why this is true for opamps?
| <ol>
<li>just substitute Vc in the above equation. name it "eq1"</li>
<li>at t=0, Vc=0
now you get V2-K1=K2(R2C2L+1) (L is lambda) :"eq2"</li>
<li>return to "eq1" and substitute V2-K1 to obtain an expression with only L and K2. you can factorize and solve with 2 possible solutions: L=-1/R2C2 or K2=0</li>
<li>for the fi... | Substitution is easy and straight forward but here is the second method : this requires you to rearrange the equation as shown and then apply integration on both sides to get the voltage across the capacitor with respect to time.
$$\frac {dv_c}{v_2-v_c}=R_2C_2 dt$$
this is the rearranged equation.
You may be able to... | https://electronics.stackexchange.com |
349,020 | [
"https://physics.stackexchange.com/questions/349020",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/164889/"
] | By definition a matrix representing a Lorentz transformation is orthogonal, so that its inverse is equal to its transpose.
Consider a pure boost in the t-x plane;
$$\Lambda_x=\begin{pmatrix}
\cosh(\gamma) && \sinh(\gamma) && 0 && 0\\
\sinh(\gamma) && \cosh(\gamma) && 0 &&am... | The matrix representing a Lorentz boost is orthogonal <em>with respect to the Minkowski metric</em> $\eta = \mathrm{diag}(-1,1,1,1)$ (or reversed signs), which means
$$ \Lambda \eta \Lambda^T = \eta \text{ or } \Lambda^{-1} = \eta \Lambda^T\eta.$$
| This is quite a common problem, and I feel it's usually made a bit clearer by using indices.
The Lorentz Group is $SO(1,3)$, not $SO(4)$, since (using the $(-+++)$ convention) the line element has an extra negative sign:
$$\text{d}s^2 = -c^2\text{d}t^2 + \text{d}x^2 + \text{d}y^2 + \text{d}z^2 $$
which is why Lorent... | https://physics.stackexchange.com |
36,777 | [
"https://dba.stackexchange.com/questions/36777",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/21304/"
] | <blockquote>
[backstory] I have a simple database of our current Widget inventory. It averages just dozen columns across five or six tables, but has a huge number of records already.
Some Widgets came with caps, some did not, but we've actually never kept track before. Now management wants users to be able to keep trac... | In most DBMSs, or at least the ones I have dealt with, a Bool is really a trinary. You have 1, 0 and NULL. NULL is specifically there for "I haven't entered any data yet." Depending on how you code it your checkbox should default to unchecked for 0 or NULL. Then 1 for checked of course. However in your reporting y... | When Codd formalised the null marker he wrote that it is a way of dealing with MISSING and INAPPLICABLE data. What you have here is a clear case of MISSING.
As Kenneth correctly points out, it is not really a tri-predicate system, it is a bi-predicate system where you might not actually know the value. The null is not... | https://dba.stackexchange.com |
152,030 | [
"https://electronics.stackexchange.com/questions/152030",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65716/"
] | Im trying to understand the source of ringing at the termination point of a PCB traces before i delve into actually designing a PCB. For example, by 'termination point', I mean a clock signal terminating at the input of an IC.
Some online sources point to ringing caused by reflections due to an impedance mismatch at ... | For short traces, ringing is caused by parasitic inductance / capacitance effects. For long traces, it can be caused by impedance mismatch / reflection or parasitic inductance / capacitance effects, or both. For digital signals, a trace is long if the round-trip propagation time to the load and back to the source is ar... | They are the same thing, or different ways of looking at the same thing, if you prefer. A pc board trace will indeed have parasitic (or intrinsic, if you prefer) inductance and capacitance, and the combination can be expressed as a characteristic impedance.
And no, it is not common for a terminating resistance (in th... | https://electronics.stackexchange.com |
362,134 | [
"https://softwareengineering.stackexchange.com/questions/362134",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/60729/"
] | I have a large class with complex properties. I'd like to introduce a default implementation, allow the user to override part of the default implementation and also make sure the user calls a sync method so that the object is always at a consistent state.
<pre><code>public class Complex {
public int Id { get; set;... | You can use builder pattern. The "WithX" stuff is not really main purpose of builder and is just syntax sugar to make some usage simpler.
Your code, using builder, could very well look like this :
<pre><code>var build = new ComplexBuilder(); // all default values set
build.Custom1.Name = "newName";
Complex a = build... | If you don't want to use builder pattern, and you want to get fancy, you could use setting-changing delegate. I saw something similar in configuration of ASP.NET Core.
<pre><code>public class Complex {
public int Id { get; set; }
public CustomComplex1 Custom1 { get; set; }
public CustomComplex2 Custom2 { g... | https://softwareengineering.stackexchange.com |
37,519 | [
"https://stats.stackexchange.com/questions/37519",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | I'm trying to apply a time series to quarterly sampled data (animal biomass) over a 10 year period with 3 reps per quarter. So 40 dates but 120 total observations.
I have read up to SARIMA'a in Shumway and Stoffer's Time Series Analysis and it's Applications as well as skimmed Woodward, et. al.'s Applied Time Series ... | The adaboost method gives the predictions on logit scale.
You can convert it to the 0-1 output:
<pre><code>gbm_predicted<-plogis(2*gbm_predicted)
</code></pre>
note the 2* inside the logis
| You can also directly obtain the probabilities from the <code>predict.gbm</code> function;
<pre><code>predict(gbm_algorithm, test_dataset, n.trees = 5000, type = 'response')
</code></pre>
| https://stats.stackexchange.com |
361,066 | [
"https://math.stackexchange.com/questions/361066",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I found the following problem interesting but do not know how to tackle it.
<blockquote>
If $A$ and $B$ are different matrices satisfying $A^3=B^3$ and $A^2B=B^2A$.Then find $\det (A^2+B^2)=?.$
</blockquote>
Can someone point me in the right direction?
| Since $(A^2+B^2)(A-B)=A^3-A^2B+B^2A-B^3=0_n.$ Since $A \neq B,$ this shows that $A^2+B^2$ has a zero divisor.Hence it
is not invertible. So its determinant is $0.$
| <strong>Hint</strong>
$$A^3-A^2B+AB^2-B^3=(A^2-B^2)(A+B) $$
| https://math.stackexchange.com |
2,419,058 | [
"https://math.stackexchange.com/questions/2419058",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/478017/"
] | If a complex matrix $X=X_1 +jX_2$ is positive definite, what can we say about its real and imaginary parts? Are they also positive definite?
| Real part? Always. Imaginary part? Never.
The real part of a positive definite matrix $A$ is just the average of two positive definite matrices $A$ and $\bar{A})$ and hence it is positive definite.
The imaginary part of a positive definite matrix is a matrix with a zero diagonal. Hence it cannot be positive definite.... | No. Take $X_1=\left(\begin{smallmatrix}1&0\\0&1\end{smallmatrix}\right)$ and $X_2=\left(\begin{smallmatrix}0&0\\0&0\end{smallmatrix}\right)$. Then $X=X_1+iX_2$ is positive definite, but $X_2$ isn't.
| https://math.stackexchange.com |
7,915 | [
"https://softwareengineering.stackexchange.com/questions/7915",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11/"
] | I have been offered an interesting job, but there's a big caveat for me: they use pair programming.
I hate the idea of pair programming, and I'm probably not suited for it: I like to do frequent pauses, I hate to see someone programming (I would constantly poke the pair away to code myself), I have to be in full contr... | Based on your various comments here, you seem to to have a similar outlook/disposition to myself on the subject. And I <em>have</em> experienced "Pair Programming". And I certainly wouldn't join a company that required me to bite a scorpion. :)
What I'd recommend is: Go with your gut.
If the company would force you t... | Guess what - <strong>nobody likes pair programming at first</strong>.
When I first tried pair programming I was against the idea and I had tons of objections similar to yours. I don't like to watch someone else coding, I like to listen to music, I feel I'll be quicker working on my own, I don't want to stop and expla... | https://softwareengineering.stackexchange.com |
55,029 | [
"https://softwareengineering.stackexchange.com/questions/55029",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12750/"
] | COBOL is still (heavily?) used for financial computing. It is an old language, and AFAIK most programmers hate, or at least dislike, COBOL. This brings a question: is the only reason COBOL is still used that legacy software uses it, or does it have any real advantages over other programming languages?
Just curious.
| It's mostly legacy now. Many critical business systems are still in COBOL simply for the fact that they are so big and integrated that the cost of rewriting doesn't seem worth it. Writing a new system in COBOL is probably not feasible anymore, as most COBOL developers are so scarce that they can pull in a considerabl... | <blockquote>
COBOL is still (heavily?) used
for financial computing.
</blockquote>
Is it?
It depends on what you call financial computing. If you call all the code that is run by financial institutions yes, it probably is. Most have business rules written in the 60s and 70s. The risk+cost of upgrading systems lik... | https://softwareengineering.stackexchange.com |
3,411,493 | [
"https://math.stackexchange.com/questions/3411493",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/711963/"
] | Please advise on how to arrive at solution for determining the power of 17 in the prime factorization of 2890!
Also, is there a short-cut?
So far I know:
Prime factorization of 2890 = 2 x 5 x 17^2
Thank you!
| <strong>Hint:</strong> use your factorization to answer the following questions.
How many multiples of <span class="math-container">$17$</span> are there in the numbers up to <span class="math-container">$2890$</span> (which are multiplied to get <span class="math-container">$2890!$</span>) ?
How many multiples of <... | What I would do is think about all of the numbers between 1 and 2890 that are divisible by 17. Hence, those numbers would have 17 as a prime factor of themselves. Next, I would think about the numbers that could be represented as 17^2 x 2 x 5 or smaller while still having 17^2 as a prime factor. There are only 10 total... | https://math.stackexchange.com |
147,195 | [
"https://physics.stackexchange.com/questions/147195",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/64558/"
] | I was learning to make a car game and came across this situation where my car is on an inclined plane. It's initial velocity is 0. Now, the problem is that my memory serves me this formula to calculate the final velocity
$$v_f^2 - v_i^2 = 2as$$
Since, $v_i = 0$, the equation would be
$$v_f^2 = 2as$$
For an inclined pl... | You can cast your problem in terms of what is the velocity of the car at any instant of time after it started. The answer is $v = a_{\rm eff} t$ from the first kinematical equation. In the same time, the car would've traveled a distance $s = (1/2)a_{\rm eff} t^2$ from the second kinematical equation.
The other option... | If i understood your question correctly, you seem to not know the displacement of the car but you still need to increase the velocity of the car.
Velocity of the car has to be expressed in terms of a quantity. I suggest you use velocity as a function of time,
$$v_f = v_i + at$$
$a = g \sin \theta $ as you told corre... | https://physics.stackexchange.com |
597,023 | [
"https://physics.stackexchange.com/questions/597023",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275310/"
] | <span class="math-container">$a^ta=n$</span> where <span class="math-container">$a^t$</span> is the raising operator. While doing the harmonic oscilaltor I encountered these. I could get that <span class="math-container">$n$</span> and Hamiltonian commute and if <span class="math-container">$|n\rangle$</span> the commo... | To show this we need the following properties:
<ol>
<li>The number operator is <span class="math-container">$\hat{n}=\hat{a}^{\dagger}\hat{a}$</span>.</li>
<li>The raising and lowering operators obey this commutation relation: <span class="math-container">$[\hat{a},\hat{a}^{\dagger}]=1$</span>.</li>
</ol>
It then follo... | Use <span class="math-container">$[a, a^\dagger] = 1$</span> here like this:
Since you agree that <span class="math-container">$a^\dagger|n \rangle$</span> is an eigenstate of <span class="math-container">$a^\dagger a$</span>, it means
<span class="math-container">$$
a^\dagger a (a^\dagger |n \rangle) = \lambda a^\dag... | https://physics.stackexchange.com |
513,447 | [
"https://physics.stackexchange.com/questions/513447",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | While studying kinematics I came to the definition of acceleration which is <span class="math-container">$a = \frac {dv}{dt}$</span>. But from this equation we can derive that <span class="math-container">$ a = v \frac {dv}{ds} $</span> which when I evaluate at <span class="math-container">$v=0ms^{-1}$</span> (here as ... | If you examine the equation <span class="math-container">$ a = v \frac{dv}{ds} $</span> when <span class="math-container">$v \rightarrow 0$</span>, then it turns out that, <span class="math-container">$ \frac {dv}{ds} \rightarrow -\infty$</span>. So when <span class="math-container">$v $</span> is exactly <span class="... | If you have a parabolic trajectory
<span class="math-container">$$
s = \frac{1}{2} g t^2
$$</span>
with velocity
<span class="math-container">$$
v = \frac{ds}{dt} = gt
$$</span>
then note
<span class="math-container">$$
v = \sqrt{2gs}
$$</span>
and
<span class="math-container">$$
\frac{dv}{ds} = \frac{\sqrt{g}}{\sqrt{... | https://physics.stackexchange.com |
127,110 | [
"https://physics.stackexchange.com/questions/127110",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/55696/"
] | We measure distances in universe by the units of light year/s or parsec. Which means distance traveled by light in one year equals one light year. Thus the lights we receive from the distant stars or galaxies are coming from many light years away.
So how do we know the age of the light so that we determine the distance... | We actually measure the distance, and infer the age of the light from the distance. There are many answers on the site discussing how cosmological distances are measured.
| You can misure the redshift <span class="math-container">$z$</span>, from which <span class="math-container">$z=\frac{1}{a_e}$</span> you obtain the Scale Factor <span class="math-container">$a_e$</span> that the Universe had when that light was emitted. But the scale factor is directly related to the age of the univer... | https://physics.stackexchange.com |
63,700 | [
"https://chemistry.stackexchange.com/questions/63700",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/31614/"
] | According to <em>Chemistry the Central Science 13 Edition</em>, these ions are isoelectronic:
$\ce{Ca^2+}$ (18 electrons); $\ce{Cs+}$ (54 electrons); $\ce{Y^3+}$ (36 electrons)
Furthermore, the textbook states that the caesium ion is the largest.
Now, every definition I've looked up, including from the book, stat... | Core Electrons don't count. It's the valence electrons that are counted (outermost shell). The valence shell of all 3 is empty. So they all have 0 electrons in their valence shell.
| 1) They all have the configuration of a noble gas with a full P sublevel as the highest sublevel.
2) Nuclear charge is inversely proportional to anion radius within a given period.
| https://chemistry.stackexchange.com |
552,895 | [
"https://physics.stackexchange.com/questions/552895",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/264745/"
] | Why don't charges pile up at the vicinity of resistor as charge flowing out of resistor is slow at one side of resistor but on the other side charge starts to pile up to enter resistor?
| Because the current flowing out is <em>not</em> faster than the current flowing in.
If charges moved faster when exiting the resistor, then they will soon deplete. They will all soon have left that end of the resistor. Then we'll have to wait until a new charge has flown through before we see another one moving fast a... | Yes, when electric charge flows in a closed circuit, the current remain same everywhere in it.
The electric charge leaving one end of a conductor is equal to the charge entering the other end of the conductor. Thus no charge stores or piles up in a conductor when an electric current flows through it. This also satisf... | https://physics.stackexchange.com |
7,886 | [
"https://mechanics.stackexchange.com/questions/7886",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4034/"
] | My 2007 Ford Focus ZX3 SES (65k miles ) has a vibration at all engine speeds. Other research has led to a high probability that this is from worn out motor mounts.
I have read after market replacements will typically wear out again in a few months and that I should get them from Ford. True?
I have also read that al... | <h1>Safety First</h1>
Check the condition of your tires and brakes before the trip. They will be working overtime pulling a trailer. Check brake pads and rotors and/or shoes and drums, and consider a brake fluid flush, which should be done every couple of years regardless. Check tire pressure regularly during the trip... | Auto or manual it is allways wise when towing a heavy load (particularly when going
uphill) to engage a lower gear
| https://mechanics.stackexchange.com |
146,246 | [
"https://softwareengineering.stackexchange.com/questions/146246",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/42599/"
] | I would like to know the ideas that are being used for explaining to the client the limitations of the language used for enhancement of the existing project.
Given a scenario was that the project existed in VC++ 6.0 and the client had asked for enhancement that could include transparency (alpha) component in the col... | Take a step back and think about your requirements:
<blockquote>
Given a scenario was that the project existed in VC++ 6.0 and the
client had asked for enhancement that could include transparency(
alpha) component in the color part(currently using gdi).
</blockquote>
See that your tasks were very technical to b... | Well as you are really not talking about a "language" but an upgrade of your development environment its a no brainer.
"The current version of xxxx does not support the features you want we need to upgrade to the latest version".
I know VC 6.0 for C++ to VS 2010 is a big upgrade but its still just an upgrade.
| https://softwareengineering.stackexchange.com |
350,133 | [
"https://mathoverflow.net/questions/350133",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | <strong>Motivation.</strong> My elder son played the following game. He had a bunch of coins, all with heads up, arranged in a circle. He flipped one coin, so that it showed tails, then he moved <span class="math-container">$1$</span> position clockwise, flipped that coin, then moved <span class="math-container">$2$</s... | Only a partial answer: Assume that <span class="math-container">$n$</span> is not a power of <span class="math-container">$2$</span>. Then there is a prime <span class="math-container">$p | n$</span> with <span class="math-container">$p > 2$</span>. First we consider the case <span class="math-container">$n = p$</sp... | To complete the proof of Dieter Kadlka:
For <span class="math-container">$n=2^m$</span>, we are looking for <span class="math-container">$a\neq b< n$</span> such that <span class="math-container">$$ b^2+b=a^2+a+l 2^{m+1} $$</span> for some <span class="math-container">$l\in \mathbb{N}$</span> and then <span class="m... | https://mathoverflow.net |
2,719,143 | [
"https://math.stackexchange.com/questions/2719143",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I am studying PDEs using the book "<em>PDEs An Introduction 2nd edition</em>" by Walter A. Strauss. In Chapter 2, a "geometric method" is described in order to solve linear PDEs of the type:
$$ (x,y)\mapsto u_x + yu_y = 0 $$
This is said to be equivalent to the directional derivative of $u$ in the direction of the ve... | I cannot see where you found an impossibility or an exception in the rules.
I the case of $\quad yu_x-xu_y=3x \tag 1$
$$\frac{dx}{y}=\frac{dy}{-x}=\frac{du}{3x}$$
A first family of characteristic curves comes from $\quad\frac{dx}{y}=\frac{dy}{-u}\quad$ which leads to $$x^2+y^2=c_1$$
A second family of characteristic ... | You can't have this:
$$\frac{du}{dx} = 3x/y ==> u (x,y) = 3x^2/y + f(C)$$
Because you have a differential equation ( du,dx) but three variables namely x,y,u. Y shouldnt be there...Apart for that mistake you did a very good job.
<strong>Usisng the method of characteristics:</strong>
$$\frac {dx}{y}=\frac {dy}{-x}=... | https://math.stackexchange.com |
185,942 | [
"https://electronics.stackexchange.com/questions/185942",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29920/"
] | If I buy a full reel of components (let's say resistors) with the intention of sending it to an assembler later so they can assemble my product, is it OK to use components from the reel when I'm soldering at home, or will this make it difficult/more expensive if I later send that partially used reel to the assembler?
| The assembler is going to have to pull some of the tape from the reel regardless, so any components that are under the end of the tape will likely be wasted anyways. Using them for your own purposes instead of letting them fall on the floor should not be a problem. Just make sure to not cut off any of the reel or tape ... | Full reels come with 2-3 turns of extra cover tape at the beginning of the reel. If you want to harvest some parts do not cut this extra cover otherwise assembly house would have to make it, wasting parts in the process.
| https://electronics.stackexchange.com |
19,144 | [
"https://chemistry.stackexchange.com/questions/19144",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5084/"
] | Suppose I have a phenyl Grignard and methyl benzoate.
If I react the two, can I expect benzophenone and a triphenylmethoxide ion as my products?
I ask because I know that Grignards react with ketones and aldehydes. So as the benzophenone is generated, couldn't more Grignard attack the benzophenone as well as the or... | Reaction of a Grignard reagent with an ester is a standard method for producing tertiary alcohols where at least two of the substituents (the "$\small\ce{R_2}$" group attached to the Grignard) are the same. Judicious choice of the starting ester allows for the preparation of a tertiary alcohol where all 3 substituents... | Yes, that is exactly what happens. And since ketones are typically more reactive than esters, you should expect that the tertiary alcohol (after workup) will be the predominant product.
In order to access the ketone, add the Grignard to a nitrile, which will give an imine (after protonation) that can be hydrolyzed to ... | https://chemistry.stackexchange.com |
7,244 | [
"https://stats.stackexchange.com/questions/7244",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3253/"
] | Lets say I have a website which gets 100 hits per day (mu = 100). Yesterday my website got 130 hits (x = 130). If I assume a Poisson distribution, then the probability of getting 130 hits is:
<pre><code>> dpois(130, 100)
[1] 0.0005752527 # about 0.06%
</code></pre>
So this tells me that getting 130 hits is quite u... | There are two points to make:
<ol>
<li>It is not the specific value of 130 that is unusual, but that it is much larger than 100. If you got more than 130 hits, that would have been even more surprising. So we usually look at the P(X>=130), not just P(X=130). By your logic even 100 hits would be unusual, because <code>... | First, note that <code>dpois(130, 100)</code> will give you the probability of <em>exactly</em> 130 hits if you are assuming that the true rate is 100. That probability is indeed very low. However, in the usual hypothesis testing framework, what we calculate is the probability of the observed outcome or an even more ex... | https://stats.stackexchange.com |
429,100 | [
"https://electronics.stackexchange.com/questions/429100",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/136601/"
] | While thinking about how to reduce stray capacitance on my pcb, I got triggered by the question:
Should the stray capacitance depend on the voltage difference?
Acccording to the equation of capacitance(parallel plates:)
<span class="math-container">$$C = \dfrac{\varepsilon \cdot A}{d}$$</span>
Where <span class="ma... | Should the stray capacitance be dependent on the voltage difference?
No, it shouldn't; it's a physical property related to physical dimensions and the electric permittivity of the materials.
The electric field being higher is immaterial.
<blockquote>
capacitance is entirely independent of the voltage
</blockquote>... | Normally the capacitance is independent of voltage. It's a function of geometry and material properties - as can be seen in the equation for a parallel plate capacitor that you cited yourself:
<span class="math-container">$$
C = \varepsilon_{r}\varepsilon_{0} \frac{A}{d}
$$</span>
The capacitance can only depend on ... | https://electronics.stackexchange.com |
2,476,870 | [
"https://math.stackexchange.com/questions/2476870",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/477343/"
] | I have two <em>main</em> conjectures relating to the Pythagorean Theorem that I desperately want to find out if they are true or not. Could somebody please help me?
<blockquote>
<blockquote>
<ul>
<li>If <span class="math-container">$ \ a^2 + b^2 = c^2 \ $</span> for which <span class="math-container">$c$</span> is a pr... | Suppose that is $c=4k+3$. Then $c|a^2+b^2$ and since it is prime $c|a$ and $c|b$. Thus $a=mc$ and $b=nc$. But then we get $m^2+n^2=1$ which is impossible if $mn\ne 0$.
| The accepted answer covers the first conjecture.
The second and third conjectures are in fact related. To solve,
$$\big(x^2 + (x + 1)^2\big)^2 = y^2+z^2$$
$$a^2+b^2 = (b+1)^2$$
and turns out to have the solution,
$$\big(x^2 + (x + 1)^2\big)^2 = (2x + 1)^2+(\color{brown}{2x^2 + 2x})^2 =(\color{brown}{2x^2 + 2x}+... | https://math.stackexchange.com |
132,897 | [
"https://mathoverflow.net/questions/132897",
"https://mathoverflow.net",
"https://mathoverflow.net/users/26222/"
] | As we know, by universal coefficient theorem, $H^{1}(X,\mathbb{Z})$ is torsion-free. My question is:
for cup product $H^{1}(X,\mathbb{Z})\otimes H^{1}(X,\mathbb{Z})\rightarrow H^{2}(X,\mathbb{Z})$
could $a\cup b$ be a torsion element in $H^{2}(X,\mathbb{Z})$.
| An example is given by a 3-manifold. Specifically, for any $n$ other than $0$ or $\pm 1$ we can take the real Heisenberg group $G$ of $3 \times 3$ real matrices of the form
$$
\begin{bmatrix}
1 & a & b \\\\
0 & 1 & c \\\\
0 & 0 & 1
\end{bmatrix}
$$
where $a,b,c \in \mathbb{R}$. We then take th... | Here's an example that's a 2-dimensional CW complex. Start with a 0-cell, then attach three 1-cells labeled $a$, $b$, $c$ to get a wedge of three circles, then attach a 2-cell via the word $aba^{-1}b^{-1}c^n$ for a fixed integer $n>1$. From the cellular cochain complex one then reads off that the resulting complex $... | https://mathoverflow.net |
645,055 | [
"https://physics.stackexchange.com/questions/645055",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/269418/"
] | Just like it says in the question title. I have heard that photons are force carriers of electromagnetism.
Is it not true, that when a golf club imparts force on to a golf ball, then the fundamental force involved is the electromagnetic force ? Is yes, then would it be true , that during this interaction, there is some... | The blank assertion that "photons are the force carrier of the electromagnetic force" is sort of true, but a bit misleading if you don't have the technical knowledge to unpack what it is trying to say.
When the golf club pushes the ball, it is correct that the forces are largely electromagnetic. The situation... | What is an electromagnetic force?
We have an electrical interaction between the electrical charges of the subatomic particles and a magnetic interaction between the magnetic dipoles of the subatomic particles.
Furthermore, we have inductive processes in which two of three participants induce the third (electric drive w... | https://physics.stackexchange.com |
9,916 | [
"https://mechanics.stackexchange.com/questions/9916",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/5165/"
] | I recently bought a Pioneer stereo system (FH-X700BT) for my 2008 Hyundai Sonata. The Sonata still has its factory speakers. The factory stereo was working fine, I just wanted something other than a CD player (aux, bt). After I connected the stereo wiring to the wiring harness and plugged it in, the music couldn't even... | Sounds like no amplification. I don't know hyundai and all but I had a similar problem with my volvo, they had a separate amp box that you had to have a special aftermarket harness to wire to to kick in the amp. Otherwise all you got was very faint tinny, no bass sound.
| This may be because your speakers are wired out-of-phase ("+" to "+" on one speaker, and "+" to "-" on another. When this happens, the sound "cancels each other out" to some extent.
To test this, adjust the fader and balance to isolate a single speaker (say, the front-left speaker). Then bring in a second speaker. ... | https://mechanics.stackexchange.com |
117,990 | [
"https://softwareengineering.stackexchange.com/questions/117990",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12893/"
] | If we refer to exceptions as bugs, why not just call it a bug in the first place instead of an exception?
If in the code it's called exception and as soon as it occurs it's called a bug. Then why not call it a bug in the first place?
Thank you for any answer or comment.
| Well, it's pretty simple: not all exceptions are bugs (and similarly, not all bugs manifest themselves as exceptions).
As example of an exception that's not a bug, if you're reading a file from a USB drive and someone yanks the drive out of the socket. That's going to raise an exception (in most languages that support... | Plain and simple, an exception is not (always) a bug!
An exception is thrown (or should be) when something exceptional happens. If there is a problem with my hard drive and a file cannot be written, that is not a bug. That is a failure of the hardware.
A bug is generally a result of bad programming. If an application... | https://softwareengineering.stackexchange.com |
3,364,727 | [
"https://math.stackexchange.com/questions/3364727",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/497284/"
] | <span class="math-container">$Lemma-4.4.2:$</span> If <span class="math-container">$a,b,c$</span> are real numbers such that <span class="math-container">$a>0$</span> and <span class="math-container">$a\lambda^2+2b\lambda+c\geq0$</span> for all real number <span class="math-container">$\lambda$</span>, then <span cl... | The book explicitly specifies that this only applies if the infinite union happens to be in the algebra. If it isn't, then it doesn't assert that the measure of that set exists.
| The condition b) says that if we happen to have a disjoint family of members of <span class="math-container">$\mathcal{A}$</span> such that the union is <em>also</em> in <span class="math-container">$\mathcal{A}$</span> (this is indeed not guaranteed to be the case (algebras are only required to be closed under finite ... | https://math.stackexchange.com |
24,609 | [
"https://mathoverflow.net/questions/24609",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6089/"
] | $\exists p, q \in \mathbb{P}: p^4+1 = 2q^2$? I suspect there is some simple proof that no such p, q can exist, but I haven't been able to find one.
Solving the Pell equation gives candidates for p^2=x and q=y, with x=y=1 as the first candidate solution and subsequent ones given by x'=3x+4y, y'=2x+3y; chances of a prim... | This is not my solution, but I don't remember where I learned it.
Square both sides, subtract $4p^4$, and divide by 4 to obtain
$({p^4-1\over 2})^2=q^4-p^4$.
However, $z^2=x^4-y^4$ has no solutions in non-zero integers.
This is Exercise 1.6 in Edwards's book on Fermat's Last Theorem.
The proof uses the representation... | I don't know if there is a simple proof, but I know one which is easy to do because it lets a computer do all the work (but the work is perhaps complicated): you simply ask a computer to solve Y^2=2X^4+2 in integers for you, like this (in MAGMA, but other packages will do it too):
<pre><code>> IntegralQuarticPoints... | https://mathoverflow.net |
26,122 | [
"https://electronics.stackexchange.com/questions/26122",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/92/"
] | I realize that when you short the terminals of a motor, it stops the motor faster than just turning off the voltage.
I was wondering if putting a large diode across the leads so that when the motor is running current can't flow through the diode, but when the current stops, the diode would short the pins. In other wo... | A typical DC motor may be reasonably well modeled as an ideal motor in series with a certain amount of inductance and resistance. An ideal motor will always have voltage across its leads proportional to rotational speed, and current flowing through it proportional to torque. If a motor with frictionless bearings and ... | This is a more popular method of braking a motor than many people seem to realize. The physics behind it boil down to the fact that an electric motor is a generator (the input power is provided as mechanical power from the shaft, e.g. when braking due to inertia) as well and can 'flip' from one operation mode to the ot... | https://electronics.stackexchange.com |
2,984,040 | [
"https://math.stackexchange.com/questions/2984040",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/119537/"
] | I am reading Walds General Relativity and am looking at Question 8, Chapter 2. In the solutions to this question it states that the metric is determined by the transformation rule
<span class="math-container">$$g_{\alpha\beta}^{'} = \frac{\partial x^{\mu}}{\partial x^{'\alpha}}\frac{\partial x^{\nu}}{\partial x^{'\bet... | My algebra professor taught me this style
<span class="math-container">$$(\forall \varepsilon >0)(\exists N\in\mathbb N)(\forall n\in\mathbb N) (n >N \implies P(n,\varepsilon)) $$</span>
If I were to use the <span class="math-container">$:$</span> symbol as a stand-in for "such that.." I would do the following.
<... | I like to see <span class="math-container">$\forall \varepsilon>0: \exists N: \forall n \ge N: |x_n -x| < \varepsilon$</span> as a description of a game of sorts: if you want to show the limit is <span class="math-container">$x$</span> you get a challenge from your opponent, in the form of some <span class="math-... | https://math.stackexchange.com |
42,812 | [
"https://dsp.stackexchange.com/questions/42812",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/30038/"
] | In a text I am using it states:
<blockquote>
The fourier transform $F(\omega)$ has both positive and negative
frequencies and $F(\omega) = F^*(-\omega)$. <strong>The power spectral
density</strong> $S(\omega)$ is similarly defined to have the positive and
negative frequencies, and the power spectral density i... | It's less about power spectrum and more about Fourier transform of real signals. Let's take an easy signal, $g(x) = \cos(10\pi x)$.
Then:
$$ F(\omega) = \frac{\delta(\omega -10) + \delta (\omega +10)}2.$$
When you ask "what is the energy in the band $ \omega = [9,11]$ you ask what is the energy of that cosine (of cou... | If the power spectral density $S(\omega)$ is defined for both positive and negative frequencies, then the power in the frequency band $[\omega_1, \omega_2]$ <em>in the usual meaning assigned to the expression by engineers</em>
is
\begin{align}P_{[\omega_1, \omega_2]} &=
\frac{1}{2\pi}\int_{\omega_1}^{\omega_2} S(\o... | https://dsp.stackexchange.com |
138,999 | [
"https://physics.stackexchange.com/questions/138999",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21270/"
] | I am reading quantum mechanics from Shankar's Principles of Quantum Mechanics. On page 157 he defines the box potential $V(x)$ as
$$
V(x) = \left\{ \begin{array}{rl}
0 &\mbox{ if $|x|< L/2$} \\
\infty &\mbox{ otherwise .}
\end{array} \right.
$$
<img src="https://i.stack.imgur.com/bsDoJ.jpg" alt="enter imag... | <blockquote>
We all know that $E=k_E + V(x)$; $E$ = total energy, $k_E$ = kinetic energy, $V(x)$ = potential
</blockquote>
One reason why you may be confused by this is that the equation
$$
E = \frac{1}{2}m\dot{x}^2 + V(x)
$$
comes from classical mechanics. When we are solving the Schroedinger equation
$$
H\Phi = ... | Since $k_E \propto \hat{p}^2$ and $\hat{p}$ is Hermitian you may see that this makes $k_E$ positive semidefinite, that is all of its eigenvalues are larger or equal to 0.
In other words when you measure this operator you will always get results which are larger or greater than zero.
This "contradiction" is resolved b... | https://physics.stackexchange.com |
23,985 | [
"https://mechanics.stackexchange.com/questions/23985",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/13968/"
] | <strong>Q1:</strong> When one removes a car battery, why does one start with the minus wire?
Is it because if we remove the plus wire first it may touch the body of the car and close the circuit, causing a short-circuit that leads to ... what?
<strong>Q2:</strong> Why doesn't one get electrocuted when touching the min... | When disconnecting a clamp from a car battery, there is a danger of creating a short circuit with the tools that are in contact with the battery terminal. So a tool in contact with the positive terminal can cause a short circuit if it touches any piece of grounded metal. Starting with the negative terminal removes th... | When you remove the ground cable (-ve in most cars), you are probably touching the body of the car - but the ground terminal is connected to the body, so you don't complete a circuit, and so can't either cause a short or get a shock (though as gbarry's answer points out, you'd barely feel the shock anyway, as the volta... | https://mechanics.stackexchange.com |
72,914 | [
"https://security.stackexchange.com/questions/72914",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/60780/"
] | could an attacker who'd just found out that you're using mysql make an SQL Injection attack with only this information? If you don't know Any table/db name how come you can find it out? Is that even possible and how to avoid that?
Thanks
| In addition to what Philipp said, keep in mind that SQL injection attacks are quite often done without knowing the structure of the DB, but once a vulnerability is exposed, it can be used to determine the structure.
For example, one of the first SQL injection string that was once taught used to be <code>';shutdown--</... | That depends.
<ol>
<li>In some web applications, syntactically incorrect SQL statements result in an error message which might get forwarded to the HTML output the visitor sees. This might give the attacker some information how the query looks. ("You have an error in your SQL query near 'myapp_tbl_users'."). To avoid ... | https://security.stackexchange.com |
30,005 | [
"https://physics.stackexchange.com/questions/30005",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7993/"
] | Firstly, General Relativity states that Spacetime is dynamic and is consonant with the distribution of matter/energy. How does String Theory predict gravity, when it is background dependent, that is it starts off with a fixed, and presumably flat space-time?
Secondly, String Theory predicts the existence of a graviton... | In general relativity the gravitational field is given by the metric tensor in space-time. The metric tensor is the solution to Einstein’s field equations. It is a symmetric tensor with ten degrees of freedom. So fundamental excitation in quantum gravity must have spin two. In string theory the oscillations of the clos... | Someone -- Richard Feynman apparently [nope, I was wrong! see comment by @RonMaimon below] -- decided at some point to see if the massive success of QED theory could also be applied to gravity. Attempting to represent gravity as a force mediated by bosons (force particles) produced spin-2 carriers for the gravitational... | https://physics.stackexchange.com |
267,596 | [
"https://dba.stackexchange.com/questions/267596",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/85703/"
] | Here's a rather simple SQL query:
<pre class="lang-sql prettyprint-override"><code>select source_id
from data_sources
join sources on sources.id = data_sources.source_id
where log_time + interval sources.retention_days day < current_timestamp;
</code></pre>
There are <strong>~800 records</strong> in <code>sources<... | I just validated it. Yes. Not only is it possible, other than using the WITH MOVE to change where the files are located, there's literally nothing special involved. I tested it using a shared volume to get the backup out of my docker instance. I also tested it using the docker file copy command. Both worked just fine. ... | I can reproduce when trying to restore to localdb.
Restoring on a full SQL Server works fine.
| https://dba.stackexchange.com |
212,196 | [
"https://mathoverflow.net/questions/212196",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50128/"
] | Let $G=GL(n,\mathbb{C})$ and let $U\subset G$ be a maximal unipotent subgroup. (For example,assume that U is the set of upper triangular matrices with ones in the diagonal.) Now let $X=M_{n}(\mathbb{C})$ be the space of $n$ by $n$ complex matrices and consider the usual action of $U$ on $X$ given by left multiplication... | Here is a coordinate-free description of the affine hull of the quotient of $G=\text{Aut}_k(V)$ by the right action of the unipotent radical $U$ of a Borel subgroup $B$. The group $B$ is the stabilizer of a flag of $k$-linear subspaces, $$\{0\} = F^0 \subsetneqq F^1 \subsetneqq \dots \subsetneqq F^r \subsetneqq F^n = ... | Questions of this type can be approached from the direction of algebraic geometry (in a suitable generality) or from the direction of invariant theory involving algebraic group actions. I'd point especially to Chapter 3 in the 1997 monograph by Frank D. Grosshans, <em>Algebraic homogeneous spaces and invariant theory... | https://mathoverflow.net |
2,557 | [
"https://mathoverflow.net/questions/2557",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78/"
] | In "Quantum field theory and the Jones polynomial" (Comm. Math. Phys. 1989 vol. 121 (3) pp. 351-399), Witten writes:
<blockquote>
A representation <em>R<sub>i</sub></em> of a group <em>G</em> should be seen as a quantum object. This representation should be obtained by quantizing a classical theory. The Borel-Weil... | Look at the orbits of <code>G</code> on <code>g*</code> the dual of the Lie algebra. These 'coadjoint orbits' have a canonical symplectic structure. Each of these orbits intersects the positive Weyl chamber exactly once; consider those intersecting it at a 'positive weight' (i.e. the the elements of <code>g*</code> th... | The most concrete example of this is just <code>SU(2)/S^1 = S^2</code>. Depending on which point in <code>su(2)*</code> this <code>S^1</code> is stabilising, the <code>S^2</code> has various different volumes. When that volume is an integer k, there's an associated line bundle <code>O(k)</code>, sections of which are t... | https://mathoverflow.net |
441,058 | [
"https://stats.stackexchange.com/questions/441058",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/197188/"
] | Suppose that, for a given <span class="math-container">$n \in \mathbb{N}$</span>, I draw points <span class="math-container">$x_1,...,x_n$</span> uniformly in <span class="math-container">$[0,1]$</span> and independently from each other.
What would be the <strong>distribution</strong> of the empirical frequency of poi... | Let <span class="math-container">$X_1,\dots,X_n \sim \mathcal{U}_{[0,1]}$</span>.<br>
For <span class="math-container">$a \in [0,1]$</span>, <span class="math-container">$\mathbb P(X_i \leq a)=a$</span>.
Thus, <span class="math-container">$$Y_n = \sum_{i=1}^n I_{X_i \leq a} \sim \text{Bin}(n,a).$$</span>
The support ... | If I understood the question correctly, it's a Beta distribution, where parameters are:
<span class="math-container">$\alpha$</span> is the count of items < <span class="math-container">$a$</span>,
<span class="math-container">$\beta$</span> is the count of items >= <span class="math-container">$a$</span>.
You ... | https://stats.stackexchange.com |
71,930 | [
"https://electronics.stackexchange.com/questions/71930",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22757/"
] | I'm trying to code an exponential function for use on a PWM signal.
My question is, does anyone know how to do a power function on an ARM cortex-M (STM32F4 in this case, which has an FPU) microcontroller. Or would a taylor series approximation do the trick better.
I know this is question is very much programming rela... | Generating a PWM signal in an embedded application generally involves a limited number of bits in the counters used to generate the signal timing. This could be as few as 8 bits or 10 bits depending upon your PWM hardware. Keep in mind too that the binary representation of the PWM values establishes a fixed universe of... | The standard lib function for power on float data type is <code>float powf(float, float)</code>. It appears to be well supported on my gcc-based STM32F4 setup. Given the performance of this MCU and its hardware FPU support for <code>float</code>, this function probably has excellent performance (it is likely using some... | https://electronics.stackexchange.com |
158,272 | [
"https://stats.stackexchange.com/questions/158272",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/27662/"
] | For my (binary) classification problem I'm developing several features and tune them with ROC curves.
At some point, I want to combine them with in classifier.
How well should the features perform, for example in terms of AUC, to discriminate my data "good enough" and build a powerful classifier out of them?
This is... | Your question starts from a wrong premise, being that the performance of a classifier is always directly contingent on the performance of individual features. It is perfectly possible to build very good models based on (individually) bad features.
Consider a double helix, with features $x_1$, $x_2$ and $x_3$, as depic... | You could use a backward feature selection algorithm: provide all possible features to your classifier, assess its performance (for instance with the auroc you mentioned). Then remove the features one by one and each time assess the performance of your classifier and the p-value between your previous classifier (or the... | https://stats.stackexchange.com |
139,582 | [
"https://softwareengineering.stackexchange.com/questions/139582",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/49643/"
] | Is there any recommended/generally accepted coding style for handling situations where a function returns a tuple of values but only one of those values is used afterwards (note that this is mostly meant for library functions I can't change -- writing a wrapper around the call is probably a bit of overkill…)?
Instead o... | Using the underscore for unused variables is definitely acceptable. Be warned though, in some codebases it's not an option as that identifier is reserved as shorthand for <code>gettext</code>. This is the most frequent objection to this style (though it's not an issue for the majority as far as I can judge). I'd still ... | Pylint has gotten me in the habit of doing it this way:
<pre><code>widget, _parent, _children = f()
</code></pre>
That is, unused results have a descriptive name prefixed by _. Pylint regards locals prefixed with _ as unused, and globals or attributes prefixed with _ as private.
| https://softwareengineering.stackexchange.com |
177,959 | [
"https://security.stackexchange.com/questions/177959",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/168503/"
] | If you have a fully end-end encrypted app, should the push messages sent to the APNS or GCM also be encrypted.
The payload only contains message ids, from uid n conversation gid. Is there a major risk if we don't encrypt this ?
How do other Apps like WhatsApp or Signal do it ? I read Signal only sends a wakeup call ... | No, this is not possible. Among other things, the value provided for CVV online (such as a one-time use credit card number) is a CVV2 value, similar to what's printed on the back of a Visa/Mastercard. (And is generally used for any "Card not present" transactions.)
On the other hand "card present" transactions requi... | You can however use a number of services, which issues you a physical card that charges all transactions to another card which can be virtual. Google "prepaid charge card".
| https://security.stackexchange.com |
77,957 | [
"https://dba.stackexchange.com/questions/77957",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/47912/"
] | I have the following scenario:
A table containing more than a million records. I need to create a loop that deletes 10'000 rows per execution (loop) based on the column number of the rows. So if in the end of the execution the column has 500 rows for example, then i need to delete all these rows.
So I imagined that t... | Ok I got the answer.
I used the following:
<pre><code>EXEC sys.sp_cdc_add_job
@job_type = N'cleanup'
,@start_job = 0
,@retention = 52494800;
</code></pre>
This adds the cleanup job but does not start it immediately i.e. start_job set to 0 does the magic. Retention can be set accordingly (100 years in my case as we ... | I don't have hands-on with this but have observed someone else go through the same thing. To keep the old history you <em>might</em> want to migrate it to a separate table.
When the jobs get created, the default retention period is 72 hours. Unfortunately I don't know how to change that because the system procedures ... | https://dba.stackexchange.com |
43,237 | [
"https://dba.stackexchange.com/questions/43237",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/24283/"
] | I know I have to write <code>SUM</code> twice, if I wish to use it in a <code>HAVING</code> clause (or use a derived table otherwise):
<pre><code>SELECT id,
sum(hours) AS totalhours
FROM mytable
GROUP BY id
HAVING sum(hours) > 50;
</code></pre>
My question now is, whether or not this is suboptimal. As a p... | The sum is only computed once.
I verified this using
<pre><code>create table mytable (id int, hours int);
insert into mytable values (1, 60);
select sum(hours) from mytable group by id having sum(hours) > 50;
</code></pre>
and then used a debugger to check how many times <code>int4_sum</code> (the transition func... | Compare your query
<pre><code>explain
select sum(counttodo)
from orderline
group by orderlineid
having sum(counttodo) > 100
</code></pre>
To this equivalent one an check in what they differ
<pre><code>explain
select *
from (
select sum(counttodo) counttodo
from orderline
group by orderlineid
) s
where... | https://dba.stackexchange.com |
79,743 | [
"https://mechanics.stackexchange.com/questions/79743",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/60370/"
] | I have noticed a distinct rattling sound coming from my tail pipe when I am parked and idling. After some experimenting I realized it only happens when the AC is on. If I turn the AC off it immediately stops. It will also stop if I apply a little gas so the engine is no longer idling.
This was all I could find from Goo... | Thanks to everyone for their knowledge regarding why the exhaust would vibrate when the AC was on. To paraphrase when the AC was on the engine was under a slight load, lowering the RPM and causing the vibration.
As to the source of the rattling, I was able to investigate this weekend and it turns out my car has a tip o... | The refrigerant compressor attached to your motor via rubber belt adds load to the engine. This in turn can lower your engine RPM, causing an object to reverberate as the frequency matches it's length or is otherwise able to excite the material, similar to a guitar's string. That's the rattle. It could be any part, any... | https://mechanics.stackexchange.com |
65,900 | [
"https://mathoverflow.net/questions/65900",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14812/"
] | Okay, so an automorphic form $f$ on a reductive group $G/ \mathbb{Q}$ and arithmetic subgroup $\Gamma$ is a smooth function satisfying the following conditions:
(a) invariance with respect to left $\Gamma -$ translations.
(b) Right $K -$ finiteness.
(c) Annihilated with respect to a finite co-dimension ideal of the... | These conditions have technical/subtle interactions. It probably suffices to think about automorphic forms on a Lie group, and not think of the interaction with finite places.
For example, on each K-isotype, the Casimir element is an elliptic operator, but it is not elliptic without specifying the behavior under K. F... | I am no expert in the general theory, but let me share some thoughts. In some sense (c) accounts for the fact that $K$ does not have enough open subgroups (unlike at nonarchimedan places), so that the usual convolution definition of Hecke operators is too crude. Instead, one needs to work with the convolution algebra o... | https://mathoverflow.net |
61,328 | [
"https://physics.stackexchange.com/questions/61328",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22916/"
] | Are Cartan structural equations equivalent to Einstein's equations
$$G_{\mu\nu}=T_{\mu\nu}$$
and why (in the case of torsionless geometries, of course)? Does it also apply with a non-null cosmological constant?
| The covariant exterior derivative of Cartan structure equations imply the Bainchi identity: By starting with
\begin{align}
T^a &= de^a + \omega^a_{\phantom a b}\wedge e^b \tag{1}\\
R^a_{\phantom ab} &= d\omega^a_{\phantom a b}+\omega^a_{\phantom ac}\wedge \omega^c_{\phantom cb}
\end{align}
Then operate them... | No. The structure equations give expressions for torsion and curvature in terms of the spin connection. In contrast, Einstein's equations tell you how the curvature responds to energy-momentum and vice versa.
<strong>Addendum: 4 April 2013.</strong>
The structure equations can be written in a non-coordinate basis (... | https://physics.stackexchange.com |
1,474,201 | [
"https://math.stackexchange.com/questions/1474201",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/242446/"
] | For $x\in \mathbb{R}$, let $\lfloor x \rfloor$ denote the largest integer that is less than or equal to $x$. For example, $\lfloor 3 \rfloor=3$ and $\lfloor \pi \rfloor=3$. Define $f:\mathbb{R}\to \mathbb{R}$ by $f(x)=x-\lfloor x \rfloor$. Determine those points at which $f$ has a limit and justify your conclusion.
We... | If $(x,y) \in \mathbb{R}^{2}$ such that $|y| \leq |x|$, then
$$
|5x^{3} - x^{2}y^{2}| \leq 5|x^{3}| + x^{2}y^{2} \leq 5|x^{3}| + 2x^{2} = x^{2}(5|x| + 2);
$$
if $|x| \leq 1$, then $x^{2}(5|x|+2) \leq 7x^{2}$;
taking any $\varepsilon > 0$, we have $7x^{2} < \varepsilon$ if $|x| < \varepsilon/\sqrt{7}$. We have ... | By definition, we are required to show that, for each $\epsilon>0$, there is some $\delta>0$ such that, for all points (x,y), if $|(x,y)-(0,0)|<\delta$, then $|5x^3-x^2y^2-0|<\epsilon$. In particular, we must be careful to avoid any dependencies between x and y, so as not to inadvertently miss important lim... | https://math.stackexchange.com |
24,093 | [
"https://datascience.stackexchange.com/questions/24093",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/21560/"
] | I developed a machine learning model with Python (Anaconda + Flask) on my workstation and all goes well. Later, I tried to ship this program onto another machine where of course I tried to set up the same environment, but the program fails to run. I copied the program to other machines where it also runs smoothly.
I c... | First of all this is a Python/Anaconda question and should probably be asked in a different stack exchange subsite.
<hr>
As for the question itself - you can export your Anaconda environment using:
<pre><code>conda env export > environment.yml
</code></pre>
And recreate it using:
<pre><code>conda env create -f ... | First export environment configuration of your current conda environment using:
<pre><code>conda-env export -n your_env_name > your_env_name.yml
</code></pre>
example:
<pre><code>conda-env export -n base> base.yml
</code></pre>
After running above command their should be yml configuration file in your curre... | https://datascience.stackexchange.com |
1,931,770 | [
"https://math.stackexchange.com/questions/1931770",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/354115/"
] | Middleschool mather here.
When solving for <code>p</code> in the proportion equation below our teacher tells us to handle the variable in the denominator first -- as if order of rationalization matters here:
$$\frac{8}9 = \frac{12}p$$
<strong>School Solution</strong>
First multiply both sides by $\frac{p}1$: $$\fr... | Adding the first $n$ rows to the last $n$ rows and then adding the negative of the last $n$ columns to the first $n$ columns we obtain via the formula for a triangular matrix per blocks:
$$\det\begin{bmatrix}
A & B \\
B & A
\end{bmatrix}=\det\begin{bmatrix}
A & B \\
... | Both sides of the equation above are polynomials in $\mathbb{Z}[A_{ij}, B_{ij}]$, where $A_{ij}$ and $B_{ij}$ are the entries of $A$ and $B$, respectively. If they agree over characteristic $p\not = 2$, then they also agree in characteristic $2$.
| https://math.stackexchange.com |
304,215 | [
"https://softwareengineering.stackexchange.com/questions/304215",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/126663/"
] | I think I'm in the minority on this but would be curious to see other perspectives.
A lot of times I see people talk about the Data Layer like having functions like UpdateCustomer() or Summarize(). I really feel like the Data Layer should be more abstract than that. I currently use a generic Repository pattern on top ... | It's a matter of definition of the terms Data and Business. Your perspective seems to be that the Data Layer is dealing with data generically and the Business Layer tells the Data Layer which data.
Another perspective is to consider the Data Layer as consisting of the collection/attributes of data classes and the Busi... | That's not exactly an uncommon scenario.
You can certainly implement your DAL in such a manner, but you will likely want another layer of abstraction between that and your business layer. I've seen it referred to as a Repository or Service layer in the past.
Your DAL offers very generic functions for finding, retriev... | https://softwareengineering.stackexchange.com |
78,385 | [
"https://physics.stackexchange.com/questions/78385",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/27376/"
] | "If a wire loop is completely in magnetic field no current is induced as voltage induced is balanced by an equal and opposite voltage. "
My guess for this statement is that the loop wire must be stationary and that voltage is zero if its equal on both sides of the wire
my question is if current will stil be induced if... | Electrical generators work by moving loops of conductive material through magnetic fields. These conductors never leave the fields.
Saying that a wire loop is "completely" inside a magnetic field is rather inane. The condidtion that has to be met is that either the field is uniform, the object is stationary, or both. ... | when a straight conductor is moved in and out of magnetic field,a potential difference is setup because when conductor is in magnetic field,force is exerted on free electrons and work is done by them (elctric potential) and when conductor is out of magnetic field,no force is acting on charges and so work done is zero.I... | https://physics.stackexchange.com |
1,604 | [
"https://electronics.stackexchange.com/questions/1604",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/399/"
] | Here's the circuit I'm working on, it's a robotic stringed musical instrument thing, that uses 6 DC motors and an Arduino Duemilanove -
<img src="https://i69.servimg.com/u/f69/14/39/80/39/pictur10.png" alt="Circuit">
The resistors are 0.25w 1KΩ
The transistors are TIP122 Darlington PNP
The diodes are N5401
The mot... | If you are sure of the motor voltage and currents and all the motors
may need to be on at the same time you really want two voltages.
Using a single a 7V supply you would need to drop
4V to power a 3V motor. 4V * 1.17A * 6 motors = 28W. That is
a lot of power to dissipate.
You can get dual output wall warts. Get one... | You could use a small DC-DC converter to convert the 3V supply to something the Arduino can use.
| https://electronics.stackexchange.com |
109,432 | [
"https://cs.stackexchange.com/questions/109432",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/97870/"
] | If G has a unique minimum spanning tree, does that mean the edge weights in G are also unique? if yes why and if no why?
| If <span class="math-container">$G$</span> is a tree, it has a unique MST whatever its weights are. The weights could be unique, all the same, anything.
| The question is: If <span class="math-container">$G$</span> has a unique MST, then are the edge weights necessarily distinct?
The answer is no. If <span class="math-container">$G$</span> is a tree with all edges having the same weight, then <span class="math-container">$G$</span> has a unique MST.
More generally,... | https://cs.stackexchange.com |
608,511 | [
"https://physics.stackexchange.com/questions/608511",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/207730/"
] | My textbook states that translational KE and rotational KE are completely analogous. The author states "They both are the energy of motion involved with the coordinated(non random) movement of mass relative to some reference frame. I can understand why this applies when comparing rotational velocity and translatio... | Keep in mind what an analogy is. It's a comparison of forms, not of identical quantities. So if we look at the two forms, <span class="math-container">$$\frac{1}{2}mv^2 \text{ and } \frac{1}{2}\mathcal{I}\omega^2, $$</span>
we see that there are two <em>types</em> of quantities in the first form: a mass, which is indep... | <strong>Well this is how i understand this.</strong>
The function that <strong>inertial mass</strong> has in translational motion is same as that of <strong>moment of inertia</strong> in rotational motion. Mass gives me an idea of translational inertia while the later gives me an idea of rotational inertia. So, in a se... | https://physics.stackexchange.com |
166,914 | [
"https://physics.stackexchange.com/questions/166914",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60080/"
] | If no light can escape black holes, in my mind they would act as a greenhouse, collecting radiation from the stars or CMB or anything. Or is all this energy just absorbed by the black hole?
| The energy of any infalling mass is absorbed by the black hole. Classically, the temperature of a black hole is absolute zero, since it is a perfect absorber.
If you include quantum mechanical effects, as Stephen Hawking did, you can show that black hole horizons will emit radiation in such a way that is consistent... | Simply because the Second Law of Thermodynamics states:
<pre><code>Entropy > 0 (always)
</code></pre>
(think of taking a basketball and squeezing it into a golf ball)
so that the density gets larger as the mass gets smaller.
therefore,
Entropy will always increase in a black hole, gaining Entropy [heat] as it g... | https://physics.stackexchange.com |
88,988 | [
"https://mathoverflow.net/questions/88988",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6849/"
] | We note $G$ a connected algebraic group, $T$ a maximal torus in $G$, $B$ a Borel subgroup containing $T$. We put also, $N=N_{G}(T)$ the normalizer of $T$ in $G$. We know that $(B,N)$ is a BN-pair of $G$. How we prove that every parabolic subgroup of $G$ containing $B$ is of the form $P=BW_{T}B$, where $W$ is the Weyl g... | Combine Theorem 6.43 (1) pg. 315 in Abramenko-Brown "Buildings" together with Proposition 6.36 (6) on pg. 310.
These are two steps:
As you mention, $BW_T B$ is a subgroup (Proposition 6.36).
$BW_TB$ contains $B$, any subgroup containing the Borel subgroup is parabolic, and any parabolic is conjugate to a subgroup con... | To provide a more balanced context for the question (and the answer by pm), it's useful to separate the elementary notion of BN-pair from the far more sophisticated structure theory of algebraic groups. Following Chevalley's 1955 Tohoku paper on finite simple groups of Lie type and his 1956-58 Paris seminar on classi... | https://mathoverflow.net |
3,472,801 | [
"https://math.stackexchange.com/questions/3472801",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/336499/"
] | Let <span class="math-container">$f \in L^{p}$</span> for <span class="math-container">$p \in [1, \infty)$</span> and <span class="math-container">$E= \lbrace x \in X \: | \: |f(x)| \neq 0 \rbrace$</span>. If <span class="math-container">$$E_{n}= \lbrace x \in X \: | \: |f(x)| \geq n \rbrace$$</span>, prove that <span... | A fuller exposition of solutions to <span class="math-container">$a^x+a^y=b^2$</span>
WLOG, let <span class="math-container">$x\le y$</span> <span class="math-container">$$a^x+a^y=b^2 \Rightarrow a^x(a^{y-x}+1)=b^2$$</span>
Now <span class="math-container">$\gcd(a^x,a^{y-x}+1)=1$</span>, and since <span class="math-co... | My try:
Let <span class="math-container">$x=1, y=1$</span>, and you have <span class="math-container">$2a=b^2$</span>, where <span class="math-container">$a=8,b=4$</span>.
Let <span class="math-container">$a=7$</span>, and <span class="math-container">$a^x$</span> and <span class="math-container">$a^y \equiv 1$</span... | https://math.stackexchange.com |
32,194 | [
"https://datascience.stackexchange.com/questions/32194",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/52738/"
] | While using Keras' <code>flow_from_directory</code> method to train my model on a multi-class image classification problem, the <code>predict_generator</code> function gives the class probabilities.
So, my query is how to get the corresponding class-labels for those class probabilities?
| You just take the class with the maximum probability. This can be done using numpy argmax function.
| I realize this question was raised some time back but came across this and thought will share what I have done
It is better to use predict_classes function from the keras model rather than predict_generator - I have run into issues while using this with the time it takes to complete. However, the input data to this fu... | https://datascience.stackexchange.com |
1,076,997 | [
"https://math.stackexchange.com/questions/1076997",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/79762/"
] | By Stone-Weierstrass one has: $f\in\mathcal{C}(K):\quad p_n\to f$
Now, for analytic functions this is just Taylor:
$$f\in\mathcal{C}^\omega([a,b]):\quad f(x)=\sum_{k=0}^\infty a_kx^k$$
But, how does this work for other examples like:
$$K:=[-1,1]:\quad f(x):=|x|$$
$$L:=[-1,-\frac12]\cup[\frac12,1]:\quad g(x):=\frac{1}... | <em>As mentioned by Pedro Tamaroff Bernstein Polynomials do the job.</em>
Consider for example:
$$f:[-1,1]\to\mathbb{R}:f(x):=|x|$$
Then the first six polynomials are:
$$B_1(x)=1$$
$$B_2(x)=\frac12(1+x^2)$$
$$B_3(x)=\frac12(1+x^2)$$
$$B_4(x)=\frac{1}{8}(3+6x^2-x^4)$$
$$B_5(x)=\frac{1}{8}(3+6x^2-x^4)$$
$$B_6(x)=\frac{... | <blockquote>
how does this work for other examples
</blockquote>
<strong>Not</strong> via a Taylor series, that's for sure. The difference between
<ol>
<li>$f$ is the limit of a uniformly converging power series, </li>
</ol>
and
<ol start="2">
<li>$f$ is the limit of a uniformly converging sequence of polynomi... | https://math.stackexchange.com |
120,011 | [
"https://security.stackexchange.com/questions/120011",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/107045/"
] | I'm doing due diligence on a company. They are entirely cloud based and need to collect lots of personal information from users (including SSN). Is this something I should be majorly concerned with? They say they are using encryption, and Azure is a secure platform. I'm unfamiliar with how securely reliable cloud stora... | Given the current state of public cloud, I would argue that in many cases it is in fact <em>more</em> secure than on-premise storage. Granted I work for Microsoft, but my opinion both pre-dates my employment, and extends to competitors like Amazon and Google as well. Companies whose business models are built on data ... | To add to Xander's answer, there are a few things to consider:
<ul>
<li>Company policy</li>
<li>IaaS, PaaS, and SaaS multi-tenancy</li>
<li>Key management</li>
<li>Current internal security posture</li>
</ul>
<h2>Company policy</h2>
Some companies are okay with *aaS, some companies say a certain level of PII is okay... | https://security.stackexchange.com |
266,290 | [
"https://softwareengineering.stackexchange.com/questions/266290",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/128394/"
] | In several of our company's applications, we use a custom logger. It's fairly robust, though we may replace it with something like NLog in the future. One of the logger's tasks is to log any exceptions encountered in the application.
One concern I've always had is that the exception handling <em>within the logger</em>... | When you encounter exceptions within the logger itself, you shouldn't use the logger to log its own exceptions. The reason for that is that:
<ul>
<li>You may be stuck in an infinite loop. Imagine that within your logger, you have a conditional branch which wasn't tested (and generates an exception). Imagine that once ... | If logging is critical to your application, then one should stop the application if logging fails.
If not critical, then being somewhat defensive one could have a secondary component to handle logging failures that logs/alerts to a secondary source. But even that is not fool proof and you will have to consider what h... | https://softwareengineering.stackexchange.com |
598,357 | [
"https://physics.stackexchange.com/questions/598357",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | In learning the Lagrangian formalism and now Feyman diagrams, when we look at Feynman diagrams
we are told contruct terms at each vertex and propagator terms etc to calculate the overall
amplitude and so on. But since the Lagrangian describes the physical processes, is there a way
to get all the physics from the Lagran... | <blockquote>
is there a way to get all the physics from the Lagrangian instead of using Feyman diagrams?
</blockquote>
All the Feynman diagrams are <em>literally</em> represented by terms in the Lagrangian. Each term in the Lagrangian has a corresponding Feynman diagram. Usually you will see terms up to quadratic power... | <blockquote>
In learning the Lagrangian formalism and now Feyman diagrams, when we look at Feynman diagrams we are told contruct terms at each vertex and propagator terms etc to calculate the overall amplitude and so on. But since the Lagrangian describes the physical processes, is there a way to get all the physics fr... | https://physics.stackexchange.com |
4,886 | [
"https://stats.stackexchange.com/questions/4886",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2101/"
] | I have a data set that I need to analyze in R. A simplified version of it would be like this
<pre><code>SessionNo. Objects OtherColumns
A 2 .
A 3
B 4
C 1
D 2
D 1
D 2
D 3
E 5
</code>... | Perhaps this might help:
<pre><code>tapply(df$Objects, df$SessionNo., sum)
</code></pre>
| If I am reading your question correctly, something like the following should do it:
<code>aggregate(x$Objects,by=list(x$SessionNo.),sum)</code>
where <code>x</code> is the data frame containing your data. This will give you, for each unique session number, the sum of the object counts.
You can of course substitute o... | https://stats.stackexchange.com |
4,495,553 | [
"https://math.stackexchange.com/questions/4495553",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/642739/"
] | Let <span class="math-container">$n \in \mathbb{N}$</span>.
I want to know how one can find out that
<span class="math-container">$$\lim_{n \to \infty} \bigl( 1+ \frac{1}{3n} \bigr)^{2n} = e^{2/3}$$</span>
I know that
<span class="math-container">$$\lim_{n \to \infty} \bigl(1 + \frac{x}{n} \bigr)^n = e^x$$</span>
But w... | Let <span class="math-container">$u = 3n$</span>. Then
<span class="math-container">$$\lim_{n \rightarrow \infty} \left( 1 + \frac{1}{3n} \right)^{2n}$$</span>
<span class="math-container">$$= \lim_{u \rightarrow \infty} \left( 1 + \frac{1}{u} \right)^{(2/3)u}$$</span>
<span class="math-container">$$= \left( \lim_{u \... | More generally,
<span class="math-container">$\begin{array}\\
\left(1+\dfrac1{an}\right)^{bn}
&=\left(1+\dfrac1{an}\right)^{(b/a)an}\\
&=\left(\left(1+\dfrac1{an}\right)^{an}\right)^{b/a}\\
&\to e^{b/a}\\
\end{array}
$</span>
Your case is
<span class="math-container">$a=3, b=2
$</span>
so
<span class="math-... | https://math.stackexchange.com |
210,675 | [
"https://dba.stackexchange.com/questions/210675",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/154176/"
] | I have a stored procedure which is called by Console Application (C#), the sp do nothing much just checking the existing of the record and update it:
<pre><code> ALTER PROCEDURE [dbo].[sp_Update_StaffTable]
@OldStaffId nvarchar(100)
,@NewStaffId nvarchar(100)
,@FirstName nvarchar(100)
... | If it's the first UPDATE that times-out then I'd look closer at your physical reads.
If [staffid] isn't indexed then you'll be performing a full table scan and pulling the entire table from the IO subsystem through to the buffer.
After the first UPDATE most of the table's pages will be in the buffer and subsequent UP... | Nah, I would guss that StaffID is unique and if estimated row is 1 then it it pretty much on target. Perhaps blocking is the cause for the timeouts?
| https://dba.stackexchange.com |
131,547 | [
"https://mathoverflow.net/questions/131547",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4177/"
] | In ZF we have the two relations $A \leq B$ and $A \leq^\ast B$ which relate the size of sets: the first says there is an injection from $A$ to $B$, the second that there is a surjection from $B$ to $A$, or $A=\emptyset$. In topos theory people consider the relation '$A$ is a subquotient of $B$' (usually in the non-bool... | In $\sf ZF$ injections can be split, so if $A\leq B$ then we have $A\leq^\ast B$ as well. For this reason I prefer to use a slightly modified (but equivalent) definition for $\leq^\ast$:
<blockquote>
$A\leq^\ast B$ if there is some $C\subseteq B$ such that there is a surjection from $C$ onto $A$.
</blockquote>
This... | Assuming that the topos is boolean and well-pointed (which is the case in ZF) if $A$ is a nonempty subquotient of $B$ then $A$ is a quotient of $B$. In other words $A$ is a subquotient of $B$ iff $A = \varnothing$ or $A \leq^\ast B$. So the subquotient relation fixes the "defect" of $\leq^\ast$ that prevents $\varnothi... | https://mathoverflow.net |
305,483 | [
"https://dba.stackexchange.com/questions/305483",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/245465/"
] | I'm working in a company that has two legacy data warehouses, which have evolved to unmaintainable monoliths throughout the time. Therefore, they are in dire need of re-form.
I'm investigating a reform of the current data architecture into an architecture that is more in line with the principles of a data mesh, like ad... | First, you seem to be missing a few zeros in the numbers you mentioned before you should start seeing problems (IMO)
Second, I've only seen Kafka as part of a data loading solution for ingesting data from multiple IoT devices.
In these instances, Kafka was used to solve the IoT problem.
ACID Compliant databases have pr... | Data volume is one of the last criteria for choosing the ingestion pipeline implementation. You choose the tool for what it can do that your current tool cannot, and <em>then</em> you test it to see if can handle the volume (spoiler alert: it can; the database will be the bottleneck in 99.9% of the cases).
| https://dba.stackexchange.com |
540,894 | [
"https://electronics.stackexchange.com/questions/540894",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/273032/"
] | I intend to serialise two DC power supplies (12V/16A and 36V/1A) to achieve 48V.
Q1: how much current can I draw from such a combination? 1A, 16A, 17A...?
Q2: I understand that grounds must be isolated on the DC side, does this apply to the AC side of the PSUs? (Earth/ground or neutral?)
| A1: 1A.
A2: No, regardless of what kind of AC input it has, earthed or not, the DC output on at least one supply must be floating/isolated from ground/earth.
But I would not recommend connecting these in series. If you exceed the 1A limit then the 1A supply might shut down. If one of the supplies is off, the other supp... | <blockquote>
<em>I intend to serialise two DC power supplies (12V/16A and 36V/1A) to
achieve 48V.</em>
</blockquote>
That makes no sense - use only the 12 volt / 16 amp supply with a boost converter to produce 48 volts at a maximum current of maybe 3.5 amps. Forget about the 36 volt supply.
| https://electronics.stackexchange.com |
101,623 | [
"https://softwareengineering.stackexchange.com/questions/101623",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11932/"
] | In the case of a newly designed functional language, consider e.g. the <em>not equals</em> operator, spelled <code>/=</code> as is common among functional languages.
Of course this operator is also known as <code>!=</code> in C family languages, and <code><></code> in SQL et al. It would be easy to make the pars... | I believe that when learning a language, the biggest issue is not learning the operators. This is (usually) only a fairly small part of the syntax, which in itself is the smaller part of the whole task. Most competent programmers can write syntactically correct code in a new language after a couple of hours or days. Ho... | I have pondered much the same thing in the past. While learning Haskell, I simply <em>could not</em> remember that <code>/=</code> didn't mean "divide by and assign back to". But, you make the mistake... compile, curse the language, recompile, rinse, repeat, until... suddenly, one day, you aren't cursing the compiler... | https://softwareengineering.stackexchange.com |
320,403 | [
"https://mathoverflow.net/questions/320403",
"https://mathoverflow.net",
"https://mathoverflow.net/users/134361/"
] | I'm curious whether lacunary functions (functions in the complex plane that are holomorphic in some open ball about the origin, but cannot be analytically extended past that ball) are typical or the exception.
<strong>Are lacunary functions dense in the space of functions that are holomorphic on the open unit ball?</... | I'm going to prove density in compact-open topology, i.e. that for any <span class="math-container">$f$</span> holomorphic on the disk there is a sequence of lacunary functions convergent to <span class="math-container">$f$</span> uniformly on compact sets.
Take any function <span class="math-container">$g$</span> lac... | Much more is true: the "non-lacunary" series are very rare, from the point of view of
Baire's cathegory, in various natural topologies, and from the point of view of probability.
These results go back to Polya and Hausdorff, and a nice survey of them is
contained in chapter 4 of the book of Bieberbach, Analytische Fort... | https://mathoverflow.net |
65,864 | [
"https://mathoverflow.net/questions/65864",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13559/"
] | Lets assume an elliptic curve intersect a curve inside a projective space. How does the graph of an elliptic curve (complex curve) locally look like at the point of intersection. For example how does it look like inside a line bundle of $\mathbb{P}_2$ at the point of intersection?
| I'm not quite sure about the formulation of the question: but there is something worth saying anyway, since it isn't often emphasised in basic texts. The points of order 3 can be identified with the inflection points of a plane cubic E (or, more accurately, taking one inflection point as origin on E for the group law, ... | Let $E$, $C$ be your curves and suppose they intersect at a point $P$. I think asking for a description of $E$ "locally" at $P$ must mean that you want to understand the closed subscheme of $\mathcal{O}_{C, P}$ which is defined by an equation for $E$ in an affine neighborhood of $P$, say $f(\underline{x}) = 0$. Of co... | https://mathoverflow.net |
195,493 | [
"https://softwareengineering.stackexchange.com/questions/195493",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/88713/"
] | I put up a webpage advertising a particular birthday party. A simple html page served by apache2 on ubuntu server 12.04. I have a link on the page to a cgi script-Python-that asks the requester to submit text values that will be formatted and relayed in an email to the bithrday boy. What's a simple way to authenticate ... | I assume that you are sending this site as a link to the invitees. Why not have the link be something like <code>www.yourbirthdaysite.com/24387921854781987458714590349839849394</code>? Only accept connections to that address, not the root address. This is an effective way to keep content private when you don't need ... | I'd try something that's trivial and based on the page, but requires context so a standard bot won't pick up on it.
Specific suggestions:
<ul>
<li>Type the birthday boy's name backwards</li>
<li>Type the birthday boy's initials</li>
<li>What is the name of the birthday boy's mother?</li>
<li>What day is the birthda... | https://softwareengineering.stackexchange.com |
570,919 | [
"https://physics.stackexchange.com/questions/570919",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214881/"
] | In the double slit experiment (with electrons), physicists wanted to know which of the two slits the electron passed through. Of what use is knowing which slit the electron passed through?
| There is no use in knowing which slit the electron went through. The whole experiment is used to highlight experimental effects that classical mechanics cannot explain.
Showing an interference pattern indicates that electrons behave like a wave. But electrons also often behave like particles. Which one is true? Classic... | It is not so clear what you mean with "use" in your question. But in a scientific context, the information through which slit the electron went serves for the understanding of the experiment. Physicists want to know what is going on. However, it turns out that if one tries to check through which slit the elec... | https://physics.stackexchange.com |
631,386 | [
"https://electronics.stackexchange.com/questions/631386",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/193983/"
] | Let's say I have a flash memory that has a 100,000 write cycle endurance. Each segment is 512 bytes, and as usual has to be erased fully to be rewritten to.
If I want to save the amount of elapsed seconds (and therefore perform a write cycle each second), I will have to start using an other segment after every 100,000 ... | Each segment is 4096 bits. Erasing turns all the bits to ones. Writing can only set bits to zero.
If you store the erase timestamp in the first 64 bits, that leaves 4032 bits. If you set a bit to zero every second without erasing the page, each page can last for 4033 seconds. So that multiplies your endurance calculati... | You can use something called FRAM, it runs at memory speed and will support trillions of cycles. A small cap would keep it up while you write. You could also save your results in several locations, whatever works for you. The ones I use are 32K x 8 and cost less than $5 US. You could also place each write into a new lo... | https://electronics.stackexchange.com |
117,268 | [
"https://electronics.stackexchange.com/questions/117268",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/46541/"
] | I have a few projects I want to get started on (not for patent: only for me) I wanted to know what types of tools I need to get some components and other salvageable parts from things like a PS2 controller, or other console related devices. Any help is appreciated.
| You might try the TDA7050 (5V) or TDA7052 (18V max). Both are bridge amplifiers, so they don't require a large speaker coupling capacitor. And they don't require a load cell / boucherot network either (R+C parallel to the speaker).
| The LM386 seems to be a appropriate chip for this application, so there is no need for a replacement. If you can't get it to work, the problem is in you circuit. Since you haven't shown us your circuit, there is little more than can be said.
Whatever you are doing wrong would be just as likely to happen to a replace... | https://electronics.stackexchange.com |
34,343 | [
"https://security.stackexchange.com/questions/34343",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/22627/"
] | My unpatched PC running Windows is connected to a network which contains other "infected" computers, can I get infected by viruses without any interaction on my part?
| Absofrickenlutely.
All the other infected PC(s) have to do is find a vulnerability in an unpatched application visible on the network on your PC and exploit it with vulnerabilities they know about.
This doesn't just apply to Windows either. Any OS that is network facing and has exploitable vulnerabilities can be atta... | Yes you can, these type of virusses are known as Worm virusses and may try to exploit vulnerabilities in services you are running which are network facing.
| https://security.stackexchange.com |
62,110 | [
"https://chemistry.stackexchange.com/questions/62110",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/30246/"
] | In the dehalogenation of vicinal dihalides why can't sodium be taken as a reagent?
I understand that zinc is taken because it is reactive and rate of reaction would be considerably high and it doesn't form complexes. Because of this many other metals can't be used including magnesium as it forms complexes. But I do... | You mean something like the following right
$$
\mathrm{R-X ~+~ Na \longrightarrow R\cdot ~+ ~NaX}
$$
and we add a proton source like an alcohole to transfer an H atom to $\mathrm{R\cdot}$:
$$
\mathrm{R\cdot~ + ~R'-H} \longrightarrow \mathrm{R-H}
$$
Well, its in principle possible. But a) you don't want an explosion rig... | Dehalogenation can be effected with many metals, e.g. zinc, magnesium, lithium and sodium in ammonia. Other reagents are sodium naphthalenide, phenyllithium, lithium aluminum hydride, chromium(II) chloride, sodium iodide, sodium sulfide and sodium selenide.
Usually good yields are obtained in these reactions; however... | https://chemistry.stackexchange.com |
52,768 | [
"https://physics.stackexchange.com/questions/52768",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | As we know the eigenfunctions for a particle of mass $m$ in an infinite square well defined by $V(x) = 0$ if $0 \leq x \leq a$ and $V(x) = \infty$ otherwise are:
$$\psi_n (x) = \sqrt{\frac{2}{a}} \sin \left(\frac{n\pi x}{a} \right).$$
How does the ground state wave function look like in momentum space? As far as I r... | Seems good to me. You are right integrating only from 0 to $a$ because $\psi$ is zero in the region of infinite potential.
The solution would be
$\psi(p)=\frac{1}{\sqrt{a\pi h}}\int_o^ae^{-ipx/\hbar}\sin(\pi x/a) dx=\frac{\sqrt{a\pi \hbar^3 }}{\pi^2 \hbar^2 - p^2 a^2 } (e^{-ipa/ \hbar }+1)$
As for the other question, ... | This question is not well-posed from scratch. There is <strong>no</strong> Momentum Operator for the problem you are considering. Your geometric space is a bounded region of the real axis, so <strong>no translation group can be defined</strong> and no self-adjoint generator of translation (the momentum observable) exis... | https://physics.stackexchange.com |
3,707,104 | [
"https://math.stackexchange.com/questions/3707104",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/736008/"
] | <blockquote>
<strong>Lemma</strong>
If <span class="math-container">$X$</span> path connnected then for any <span class="math-container">$x_0$</span> there exist a path such that connect <span class="math-container">$x_0$</span> with any other point <span class="math-container">$X$</span> of <span class="math-co... | The statement is not quite true: if <span class="math-container">$X=\{x_0\}$</span>, then <span class="math-container">$X$</span> is path connected, and its only point is isolated. It can also fail if <span class="math-container">$X$</span> is not <span class="math-container">$T_1$</span>. Let <span class="math-contain... | A space with two or more points that is <span class="math-container">$T_1$</span> and connected, cannot have an isolated point. Proof: otherwise the singleton of that point is nontrivial clopen. The separation axiom is needed: a two point Sierpiński space is path-connected but has an isolated point.
| https://math.stackexchange.com |
328,193 | [
"https://physics.stackexchange.com/questions/328193",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/152508/"
] | I am currently working on a project where we use syringes to extrude some viscous materials. I will explain what I am trying to do and I just want to know what size of tubing would be better for me. I have a 10 cc syringe connected to 3/32" tubing with luer lock and at the very end, it is attached to either a 27 gauge ... | A stream of photons which is reflected by a perfect mirror doesn't, in spite of the radiation pressure, do any work on the mirror unless the mirror moves (possibly due to the radiation pressure). There is no transfer of energy from the photons to the mirror. This is similar to the pressure of gas molecules on the wall ... | Don't try and calculate it using forces, do it using energy and momentum instead. First conserve momentum:a number of photons strike a mirror on the earth and recoil. Technically they change their frequency by a tiny amount, but as far as conservation of momentum goes that is negligible. The mirror (plus the planet it ... | https://physics.stackexchange.com |
3,450 | [
"https://softwareengineering.stackexchange.com/questions/3450",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/594/"
] | Long winding <code>if</code> conditions should be avoided if at all possible, yet sometimes we all end up writing them. Even if it's a very simple condition, the involved statements are sometimes simply very wordy, so the whole condition ends up being very lengthy. What's the most readable way to format those?
<pre><c... | Often, a long if condition is the sign of code that needs refactoring, but sometimes you can't avoid it. In those cases, I prefer the first:
<pre><code>if (bar || baz || quux) { ... }
</code></pre>
Because you're able to tell what's going on with one line. However, I'd much rather do something like this, when possib... | I like keeping the operators at the end to indicate continuation:
<pre><code>if (the_function_being_called() != RETURNCODE_SUCCESS &&
the_possibly_useful_recovery_strategy() == RETURNCODE_EPICFAIL &&
this_user_has_elected_to_recieve_error_reports)
{
report_error();
}
</code></pre>
| https://softwareengineering.stackexchange.com |
395,456 | [
"https://softwareengineering.stackexchange.com/questions/395456",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/342391/"
] | I have a class with a (simplified) method which returns a string like this :
<pre><code>private String doStuff(String currencyCode, BigDecimal amount){
StringBuilder sb= new StringBuilder();
NumberFormat format = NumberFormat.getInstance(Locale.FRANCE);
Currency currency = Currency.getInstance(currencyCode... | <ol>
<li>No, the .lib file is not the same in both cases. You can see that from the file sizes: unless it's a very small library, the .lib file in the static case will be significantly larger than the .lib file in the dynamic case. The first one contains all code, the second only just enough for linking with the dll.</... | When you use a DLL, as the name implies, you have to dynamically link to its functions. You do that by first calling <code>LoadLibrary</code> or <code>LoadLibraryX</code> to load its code into memory. Then, you call <code>GetProcAddress</code> to find the entry point to the function. You then cast the result of the pro... | https://softwareengineering.stackexchange.com |
234,731 | [
"https://mathoverflow.net/questions/234731",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Suppose $G, H$ are finite, simple, undirected graphs and there is a bijection between the vertex sets $\varphi:V(G) \to V(H)$ such that for all $v\in V$ we have $$\text{deg}_G(v) = \deg_H(\varphi(v)).$$
Does this imply that $\chi(G) = \chi(H)$?
| Let $G$ be a 6-cycle and let $H$ be two 3-cycles.
Or, if you want them connected, let $G$ be a 6-cycle with an extra edge between vertices 1 and 3, and $H$ a 6-cycle with an extra edge between vertices 1 and 4.
| There is also a general principle one can apply: If you have any parameter <span class="math-container">$\alpha$</span> of graphs so that there is an efficient (polynomial-time) algorithm to compute <span class="math-container">$\alpha (G)$</span>, then it is extremely implausible that <span class="math-container">$\a... | https://mathoverflow.net |
166,650 | [
"https://electronics.stackexchange.com/questions/166650",
"https://electronics.stackexchange.com",
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] | I have a small microcontroller (VoCore, runs Linux, has wifi and GPIOs) and i want to use it to hook into another system (basically a doorbell) to make the state of the doorbell-buzzer available over the network.
The system I want to hook into runs on 8V DC, there is a buzzer in it which normally doesn't get any power... | <blockquote>
how is detecting voltage on some line with different voltage than my
microcontroller typically done?
</blockquote>
Normally people use an opto-coupler; an LED and photodiode in close proximity sealed into one package: -
<img src="https://i.stack.imgur.com/enKr3.png" alt="enter image description here"... | Since the I/O pin input to your microcontroller is pretty high impedance you could simply use a voltage divider as follows to convert the 8V buzzer signal to a 3.3V level suitable for the MCU.
<img src="https://i.stack.imgur.com/3kQBB.png" alt="enter image description here">
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