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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|---|---|---|---|---|---|
102,713 | [
"https://security.stackexchange.com/questions/102713",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/56061/"
] | The following scenario: I just visited the webpage of an phisshing company of an german service which is here in germany acting at least not unlawfull, but just trying to get money for not even giving something usefull.
After surfing a bit I filled a formular which just gave me a php created response with a lot of pat... | Yes this is possible. One way to do this would be to create a shared folder and share it with a mangled version of your own computers localhost. When cmd.exe tries to list the files in the folder, it will "look them up" over the mangled localhost and you should be able to intercept that network trafic. I don't think th... | An old trick used by viruses to reinfect and execute malicious code would be to replace the directory with a shortcut that both executes your script and opens explorer to the correct path. This of course would only work in the UI, accessing the directory through console would not activate the shortcut as it is technica... | https://security.stackexchange.com |
26,086 | [
"https://dsp.stackexchange.com/questions/26086",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/17451/"
] | I've got the frequency response $H(e^{j\omega}) = \frac{2 + 3.125e^{-2j\omega}}{1-0.9e^{-j\omega}+0.81e^{-2j\omega}}$, and I'm trying to figure out how to plot the magnitude response and the phase response in Matlab. Is there a simple way to do this?
Thank you in advance. This is my first post here, so please tell me ... | Write the frequency response in function of $ z = e^{j\omega} $, we have:
$ H(z) = \frac{2 + 3.125z^{-2}}{1-0.9z^{-1}+0.81z^{-2}} $
You can use the function freqz to plot the impulse response of this transfer function (both magnitude and phase). Here is the code I used:
<pre><code>b = [2 0 3.125]; % numerator coeffi... | @Hal: Unlike MBaz, I realize you weren't asking for information on the theory of signal processing. But, rather, you were asking a Matlab implementation question. I only have an old version of Matlab so I couldn't try Anthony's code. (Anthony was smart to insert that zero-valued coefficient.) But to plot the frequency ... | https://dsp.stackexchange.com |
170,282 | [
"https://math.stackexchange.com/questions/170282",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/18813/"
] | Let $\mathbf{A}=\begin{bmatrix} f(x_1,x_1), & \ldots,& f(x_1,x_n)\\
\vdots&\ddots& \vdots \\f(x_n,x_1),&\ldots, &f(x_n,x_n) \end{bmatrix} $, where $f:\mathbb{R}\times\mathbb{R}\rightarrow \mathbb{R}$. I want to calculate
$\int \mathbf{A}\mathrm{d}\mathbf{x}$, where $\mathbf{x}=\begin{bmatrix}x... | Consider the change
$$ {\rm d} {\boldsymbol y} = {\boldsymbol A}\, {\rm d} {\boldsymbol x} $$
$$ = \left[ \begin{matrix} f(x_1,x_1)\,{\rm d}x_1 + f(x_1,x_2)\,{\rm d}x_2 + \ldots \\
f(x_2,x_1)\,{\rm d}x_1 + f(x_2,x_2)\,{\rm d}x_2 + \ldots \\ \vdots \end{matrix} \right] $$
and its integral
$$ {\boldsymbol y} = \int ... | Well, it seems the result should be the matrix whose $(i,j)$ coefficient is
$$
\int_{\mathbb R^n} f(x_i,x_j)\mathrm dx_1\cdots\mathrm dx_n.
$$
Be mindful though that the diagonal coefficients are undefined as soon as $n\geqslant1$ and the off-diagonal coefficients are undefined as soon as $n\geqslant2$, hence the who... | https://math.stackexchange.com |
52,359 | [
"https://physics.stackexchange.com/questions/52359",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16278/"
] | The following question appears to be extremely straight forward, but I can't seem to be able to obtain the correct answer.
The question is:
<blockquote>
A charge Q1 = 1.3uC is at rest and is located 2.3 cm away from another
fixed charge Q2 = 1.6uC. The first charge is then released. Calculate
the kinetic energy of char... | Your answer is just a little bit off in the last digit, probably due to incorrect rounding. So I would suggest going back and checking the calculation, perhaps including some more significant figures in certain values.
If that doesn't make a difference, then check with your instructor. It's possible that the computer ... | No your answer is incorrect since some amount of energy will be lose in the form of Electromagnetic radiation as the moving charge would accelerate (according to Maxwell's theory)
| https://physics.stackexchange.com |
156,273 | [
"https://electronics.stackexchange.com/questions/156273",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65030/"
] | I have a bike flash light which is consisted of 5 LEDS (red). Which looks like this.
<img src="https://i.stack.imgur.com/Fo215.jpg" alt="enter image description here">
I unsoldered three of them and put it in a series circuit using two AAA bateries. The Leds did not turn on. I assumed that something was wrong with my... | I'd say there are two possibilities.
First, please check the original unit. In addition to the batteries and the LEDs, there ought to be a resistor. This will limit the LED current to safe levels. Without any resistor at all, it's entirely possible that you've simply destroyed one or more LEDs by hooking them directly... | My best guess is that in the original unit, the LEDs were all connected in parallel. Although it is bad practice to run the LEDs from batteries without a current limit resistor, Asian manufacturers do it all the time.
In the schematic that you show, you have connected the LEDs in series. Assuming that these are Red ... | https://electronics.stackexchange.com |
13,413 | [
"https://mathoverflow.net/questions/13413",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3637/"
] | Given a variety V and a locally free (coherent) sheaf $\mathcal{F}$ of rank 1 (equivalently a line bundle $L$), I can do a Cech cohomology on it. Then $H^0(V; \mathcal{F})$ are just global sections. Is there a similarly understandable meaning to elements of $H^1(V; \mathcal{F})$?
Thanks!
| $H^1(V;\mathcal{F})$ is the space of bundles of affine spaces modeled on $\mathcal{F}$. An affine bundle $F$ modeled on $\mathcal{F}$ is a sheaf of sets that $\mathcal{F}$ acts freely on as a sheaf of abelian groups (i.e., there is a map of sheaves $F\times \mathcal{F}\to F$ which satisfies the usual associativity), a... | $H^1$ is the first derived functor of the functor $H^0$ of global sections.
In the Cech cohomology construction, note that we look whether the local sections glue together to form global sections. On an affine space, this is indeed true. But, not so in general. We would like to address the obstruction using algebraic ... | https://mathoverflow.net |
130,119 | [
"https://softwareengineering.stackexchange.com/questions/130119",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/43211/"
] | The following principles of Agile development makes it look like Agile is mostly suited for services companies:
<ul>
<li>Customer satisfaction by rapid delivery of useful software</li>
<li>Welcome changing requirements, even late in development</li>
<li>Working software is delivered frequently (weeks rather than month... | Agile (and any iterative) method is even more helpful for product development companies as opposed to service industry.
In one of my first assignment in a product development start-up, we went with the management a very detailed (including fine print) scope and my boss threw out most of it and trimmed down the requir... | Define who you believe your customers to be. Are they the people who buy your company's products, are they the people within your company who might use and test your code, or are they perhaps both? When you write your code and submit it for testing, do you complete the entire product first, or do you deliver it in sta... | https://softwareengineering.stackexchange.com |
13,958 | [
"https://softwareengineering.stackexchange.com/questions/13958",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4459/"
] | I am a Software Engineer and over the past few years I have become the de-facto software project manager simply because there isn't one. So to keep our sanity in the R&D/Engineering department, customers have become accustomed to coming to me with their requests. I have no experience in this realm so it is my first... | What we ended coming up with was we would now have bi-monthly sales/engineering meetings to discuss current projects and upcoming or future feature requests. The sales engineers will become project managers and at least they will be in tune with the latest product offerings. In the past it was just easy to pass it alon... | I've found that the more a customer complains about how urgent their request is, unless they are also a developer in their own right, it's usually a good sign that the request isn't urgent at all. One of my professors in college always used to tell us not to let the urgent interrupt the important.
I usually classify ... | https://softwareengineering.stackexchange.com |
66,691 | [
"https://dsp.stackexchange.com/questions/66691",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/39794/"
] | I know that discrete signals have finite precision. But <strong>does that means that those signals can have only integer values(for example,2,3,4 etc) but not decimal values(for example 2.1,3.2,4.2 etc)?</strong>
| There might be a confusion in the discreteness.
It can apply to the ordinal variable of the data: time for signals, space for images. Here <em>discrete</em> is the opposite of <em>continuous</em>. Which is not often well-defined. A common way is to consider that samples are finite in quantity, or enumerable: you can ... | They can very well have decimal values, represented as either fixed point or floating point numbers.
| https://dsp.stackexchange.com |
122,077 | [
"https://cs.stackexchange.com/questions/122077",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/26345/"
] | Suppose we have file A that has been compressed by the the method B and the output-file is C, now if I am not wrong We can not compress C more by method B, but there might another method=algorithm D that might compress C more and produce compressed file E.
Is this kind method of using more than one compression-method... | Here's a partial "yes" answer to your question.
Consider a file containing:
<pre><code>0000000000
0000000001
0000000010
0000000011
0000000100
...
1111111111
</code></pre>
That is, it is all binary numbers that are <span class="math-container">$b$</span> bits long (in this case <span class="math-container">$b=10$</sp... | The essential problem is that most files are NOT compressible (see the counting argument). And an already compressed file is much less likely to be compressible.
| https://cs.stackexchange.com |
614,650 | [
"https://physics.stackexchange.com/questions/614650",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/105209/"
] | Physically speaking, "pseudo-vectors" are vectors <span class="math-container">$v\in \mathbb{R}^3$</span> which transform as <span class="math-container">$ v'= (\det {R})v$</span> if the "system were to transform as <span class="math-container">$R\in O(3)$</span>". However, what does this mean mathe... | Exactly as @Claudio Saspinski says. I was about to write an answer in those same terms when I saw his excellent answer.
Think of the metal as an extraordinarily dense "fluid" in which particles moving (electrons) almost immediately acquire their limit velocity. The faster they want to go, the more resistance ... | It is a analogic useful way to understand the resistive circuit, in the meaning that the electric expression <span class="math-container">$V = RI$</span> has the same form as the mechanical <span class="math-container">$F = kv$</span>, in an environment where the drag force is proportional to the velocity.
In the case ... | https://physics.stackexchange.com |
125,752 | [
"https://cs.stackexchange.com/questions/125752",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/63681/"
] | Suppose I have 3 sets of 2 elements: <code>[A, B], [C, D], [E, F]</code>, and I wanted to generate all possible combinations of 1 element from each set, such that the result of the algorithm would be:
<pre><code>[A, C, E], [A, C, F], [A, D, E], [A, D, F], [B, C, E], [B, C, F], [B, D, E], [B, D, F]
</code></pre>
What ... | You can use recursion.
<pre><code>def recursive_generate(S):
IF #S = 1:
s <-- the single set in S
return {{item} | item \in s}
END IF
S' <-- {}
s <-- some selected set from S
FOR item in s:
For r in recursive_generate(S\{s}):
S' <-- S' \union (r \unio... | If you have <span class="math-container">$n$</span> sets of <span class="math-container">$k$</span> elements, your problem is equivalent to that of generating all numbers with up to <span class="math-container">$n$</span> digits in base <span class="math-container">$k$</span> (where the <span class="math-container">$i$... | https://cs.stackexchange.com |
96,395 | [
"https://physics.stackexchange.com/questions/96395",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/38763/"
] | How is this formula derived (it is present in one of the hundred pages of my textbook about physics and fundamental physics) <img src="https://i.stack.imgur.com/l5bZ3.png" alt="enter image description here">
In the case of a system of particles $P_i$, $i = 1, …, n$, each with mass <em>mi</em> that are located in space ... | The centre of mass is the point at which our collection of objects will balance if we put a pivot there. Let's call this point $\bf R$. The vector joining the point $i$ to $\bf R$ is simply $\bf r_i - \bf R$. The force acting at this point is $m_i \bf g$, so the torque at the point $i$ is:
$$ \bf T_i = m_i \bf g \time... | That is nothing but the <strong>definition</strong> of the position ${\bf R}$ of the center of mass. Indeed it is equivalent to:
$$\sum_i m_i {\bf r}_i = \left( \sum_i m_i \right) {\bf R}$$
namely:
$${\bf R} = \frac{\sum_i m_i {\bf r}_i}{\sum_i m_i}\:.$$
The last formula is perhaps the most familiar one.
| https://physics.stackexchange.com |
151,374 | [
"https://physics.stackexchange.com/questions/151374",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/48784/"
] | If a force is applied to a body which does not act through its centre of mass, it rotates about its centre of mass and not any other point. Why?
| The idea is that if there are no forces on an object, then no matter how it rotates, its center of mass must move at a constant velocity. Then in the frame of the object, the center of mass appears stationary and everything else rotates around it. In general this cannot be said of any other point in the object.
To se... | It happens I think because rotation about axes which do not pass through the center of mass are usually inherently unstable and hence the rotation tends to "decay" to a more stable axis, i.e the one passing through its center of mass. Also, the moment of inertia of a body is usually the lowest through a certain princip... | https://physics.stackexchange.com |
171,409 | [
"https://physics.stackexchange.com/questions/171409",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75851/"
] | Two observers – A & B - conduct a single double slit experiment and watch the same detector screen for the appearance of an interference pattern.
A separate detector records which slit each particle passes through, but the data from this detector is only available to observer A.
As I understand it the wave funct... | Imagine a free-standing battery (not connected to any wires) and take a closed loop through the battery, out one terminal, and back in the other terminal. The total work done in moving a test charge around that loop must vanish. For this to happen, the change in electric potential outside of the battery must equal th... | First let's establish the situation in which the result actually holds. Voltage itself is only well defined in electrostatics, and this result only holds in a steady state.
In an ideal battery, there is no energy loss inside the battery during operation, and in the steady state just as much charge flows into the bat... | https://physics.stackexchange.com |
707,671 | [
"https://physics.stackexchange.com/questions/707671",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/321537/"
] | According to what I have learnt, there is always a potential difference across a resistor in a circuit (having a battery).
Considering a simple 'resistor' circuit, when we apply an e.m.f in the circuit, we know that electrons that have yet to pass the resistor are at high potential, and electrons in the resistor are lo... | It is not the electrons themselves that carry the energy in the circuit. They do not gain any energy overall in the battery, and nor do they lose any in the resistor, overall.<br />
The electrons undergo random motion, with a net "drift" opposite the direction of the electric field (set up by the battery in t... | The free electrons in a circuit distribute themselves to give a large charge density gradient (and strong electric field) in regions of high resistance and low gradient in regions of low resistance. This produces the required continuity of current flow.
| https://physics.stackexchange.com |
184,742 | [
"https://security.stackexchange.com/questions/184742",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/176778/"
] | Is it possible to inject and run malware on Windows 10 by knowing the victims IP address only?
| Generally, no. Having someone's IP address is enough to try attacks but unless your system is vulnerable, it shouldn't be possible to execute code remotely. That being said, Windows may have vulnerabilities.
| This is like if you know someones street address ... can you eat pizza out of their fridge?
It is way too broad and depends on too many things. Are the people home? Do you know how to pick locks? Do they even lock their doors? Do they have a dog? Do they have a doggy door? Do you want to physically eat the pizza or... | https://security.stackexchange.com |
34,776 | [
"https://stats.stackexchange.com/questions/34776",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13472/"
] | I have some survey data, where the first question is something like, "rate how you are feeling on a scale of 1 - 5". The next group of questions are something like, "do you smoke?" or "how much exercise do you get per day: 0, 15, 30, 45, 60, 60+?"
I'm looking for a way to visualize this data, where each question is ... | Try the <code>lattice</code> package and maybe box-and-whisker plots.
<pre><code># Make up some data
set.seed(1)
test = data.frame(feeling_scale = sample(1:5, 50, replace=TRUE),
smokes = sample(c("Y", "N"), 50, replace=TRUE),
exercise_frequency = sample(seq(0, 60, 15),
... | I am thinking that you could simply summarize the data in a contingency table. The columns could be the question numbers and the rows the specific answers. The ij$^t$$^h$ cell would contain the number of responses to question i with response j.
| https://stats.stackexchange.com |
606,404 | [
"https://physics.stackexchange.com/questions/606404",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266925/"
] | I know that in finding the partial derivative of certain thermodynamics property such as <span class="math-container">$H=H(P,V)$</span>, we can hold the other variable as constant. But what will happen if the relation have more than two variables? For example, if a certain thermodynamics property of pure substance is g... | When you evaluate that partial derivative, you do not need to consider other properties, U and S, as constant. You have <span class="math-container">$$d(T\ \Gamma)=TdS+SdT-dU+VdP+PdV$$</span>But, <span class="math-container">$$dU=TdS-PdV$$</span>Therefore, <span class="math-container">$$d(T\ \Gamma)=\Gamma dT + Td\Gam... | My conclusion is the same as in Chet Miller's answer. Still, in this case, I would have better start from the guideline of identifying the two independent variables an expression like <span class="math-container">$\Gamma$</span> is a function of. It makes explicit a step that has implicitly been used in Chet Miller's s... | https://physics.stackexchange.com |
347,774 | [
"https://mathoverflow.net/questions/347774",
"https://mathoverflow.net",
"https://mathoverflow.net/users/61536/"
] | Let <span class="math-container">$\Pi$</span> be the set of odd prime numbers and let <span class="math-container">$\mathcal P(\Pi)$</span> be the Boolean algebra of subsets of <span class="math-container">$\Pi$</span>.
For a number <span class="math-container">$x$</span> denote by <span class="math-container">$\Pi(x... | <span class="math-container">$2^{11}-1=2047=23\cdot 89$</span> and neither prime divides a smaller such number. So <span class="math-container">$23 \mid 2^n-1$</span> exactly when <span class="math-container">$n=11m.$</span> Similarly <span class="math-container">$89 \mid 2^n-1$</span> exactly when <span class="math... | No. The gcd (greatest common divisor) of <span class="math-container">$\{ 2^{n_i}-1\}_{i=1}^{k}$</span> can be seen to be <span class="math-container">$2^{\gcd(n_1,\ldots,n_k)}-1$</span>, by an application of the Euclidean algorithm. If <span class="math-container">$p$</span> divides this expression, then <span class="... | https://mathoverflow.net |
126,557 | [
"https://electronics.stackexchange.com/questions/126557",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39152/"
] | In quite a lot of PCBs that I have seen, they often have these small metal bars going across from one point to another.
Here is an image of what I am talking about. In this example it is a charger: <img src="https://i.stack.imgur.com/FuHSa.jpg" alt="Charger with points">
J2 and J3 are what I am talking about
For re... | These are called "jumpers" or "jumper wires" and simply connect two parts of the PCB together. They are common for single-sided PCBs to make a connection that may not be routable. The alternative would be to have a double-sided PCB, but that would be more expensive.
| In addition to the direct answer already given by others, I want to point out that this is a different circuit board construction optimized for high volume. What you probably think of as normal PCBs are at least two layer, and the copper is etched and plated with the holes drilled and the outside shape of the board ro... | https://electronics.stackexchange.com |
578,935 | [
"https://physics.stackexchange.com/questions/578935",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/175183/"
] | I just read "Newton's law of gravity says that the gravitational attraction of a star is exactly one quarter that of a similar star at half the distance" and this sentence doesn't make sense to me. Shouldn't the gravitational force be increased by 4 times when the distance is halved?
| I have drawn the figure of the condition
<img src="https://i.stack.imgur.com/60ZdI.jpg" alt="enter image description here" />
The sentence says that the gravitational force between point <span class="math-container">$A$</span> and <span class="math-container">$S_2$</span> is one quarter of the force between <span clas... | It's a badly written sentence that is hard to parse, but parsed the intended way it's correct. It's saying
<span class="math-container">\begin{align}
\text{gravitational attraction of a star of mass $M$ at distance $d$} = \frac{1}{4} \text{gravitational attraction of a star of mass $M$ at distance $\frac{d}{2}$}
\end{a... | https://physics.stackexchange.com |
110,078 | [
"https://mathoverflow.net/questions/110078",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27379/"
] | Let $0< \alpha< n$, $1 < p < q < \infty$ and $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}$. Then:
$ \left \| \int_{\mathbb{R}^n} \frac{f(y)dy}{|x-y|^{n-\alpha} } \right\|_{L^q(\mathbb{R}^n)}\leq$ $C\left\| f\right\| _{L^p(\mathbb{R^n})}$.
| This is the standard Hardy-Littlewood-Sobolev inequality(or the theorem of fractional integration).A more direct approach is write
$$
\int{f(x-y)|y|^{\alpha-n}dy}=\int_{|y|<R}+\int_{|y|\ge R}
$$
For the second term on the RHS,using Holder inequality,and easy to see that it's dominated by $\|f\|_{L^p}R^{-\frac{q}{... | The function $\vert x\vert^{\alpha-n}$ is radial homogeneous of degree $\alpha-n$, so its Fourier transform is radial homogeneous of degree $-(\alpha-n)-n=-\alpha$ (both locally integrable since $\alpha >0$ and $-\alpha>-n$ so both are distributions which are easily seen as temperate: Fourier transforms make sens... | https://mathoverflow.net |
100,903 | [
"https://softwareengineering.stackexchange.com/questions/100903",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I'm not talking about working overtime for a project, but R&D, or test bed applications that benefit the company. These would become teaching tools, and eventually sales tools. I know it sounds crazy to even ask, but I'm seeing a trend in this industry with regard to rapidly changing technology, and a problem with ... | <blockquote>
and a problem with getting programmers to bring the after hours
knowledge gained in house.
</blockquote>
The problem is that you're not paying them to do that.
<blockquote>
You would think it would spill over naturally,
</blockquote>
No I wouldn't, free time is free time. If somebody chooses to sp... | Many developers (perhaps, younger developers) are motivated by "fame" and recognition of their peers at least as much as by monetary compensation.
For example, while the '20%' projects done by developers at Google are, in the end, owned by the company, if the project spins off and becomes successful (like GMail), the ... | https://softwareengineering.stackexchange.com |
10,064 | [
"https://datascience.stackexchange.com/questions/10064",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/8820/"
] | Today, in a lecture it was claimed that the direction of edges in a Bayes network doesn't really matter. They don't have to represent causality.
It is obvious that you cannot switch any single edge in a Bayes network. For example, let $G = (V, E)$ with $V = \{v_1, v_2, v_3\}$ and $E=\{(v_1, v_2), (v_1, v_3), (v_2, v_3... | TL;DR: sometimes you can make an equivalent Bayesian network by reversing arrows, and sometimes you can't.
Simply reversing the direction of the arrows yields another directed graph, but that graph is not necessarily the graph of an equivalent Bayesian network, because the dependence relations represented by the rever... | This might be a bit unsatisfying, so feel free not to accept this answer, and apologies in advance.
In a Bayes net, nodes represent random variables, and edges represent conditional dependences. When you interpret the nodes a certain way, conditioning flows a certain way naturally. Arbitrarily reversing them doesn't ... | https://datascience.stackexchange.com |
23,483 | [
"https://electronics.stackexchange.com/questions/23483",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6211/"
] | In many cases when I am designing a circuit, I use transistors, ICs, etc, by using calculations. But when I go to the market I have to ask the product by its name which I don't know. <code>How do I get the name of device,I am looking for?</code> Is there any simple way? Or I have to memorize hundreds of datasheets?
| Determining the exact part numbers is part of doing electrical design. After a while, you will get to know some parts, particularly general purpose ones. For example when I need a "jellybean" transistor, I generally use a MMBT4401 for NPN and MMBT4403 for PNP. These are widely available, cheap, with reasonable specs... | A not uncommon approach is to start by seeing what parts others have used for tasks with similar requirements. This can be especially true if you are buying support components for one main device that has a manufacturer's reference design.
With time, you build up some personal or organizational knowledge of preferred... | https://electronics.stackexchange.com |
252,748 | [
"https://softwareengineering.stackexchange.com/questions/252748",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23059/"
] | This is something that's been troubling me for a while now. Is it actually worth unit-testing an API client?
Let's say you're creating a small class to abstract-away the calls to a petshop REST API. The petshop is a very simple API, and it has a basic set of methods:
<ul>
<li><code>listProducts()</code></li>
<li><cod... | The job of a remote API client is to issue certain calls - no more, no less. Therefore, its test should verify that it issues those calls - no more, no less.
Sure, if the API provider changes the semantics of their responses, then your system will fail in production. But that isn't your client class's fault; it's some... | <strong>Short answer:</strong>
All methods should be unit-tested.
<strong>Long answer:</strong>
Yes. It is worth it.
These are some things unit tests on those API-calling methods should test:
<ul>
<li>That you are passing well-formed or correct parameters to the API calls.</li>
<li>That you are responding accordin... | https://softwareengineering.stackexchange.com |
115,784 | [
"https://security.stackexchange.com/questions/115784",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/102590/"
] | I have an iOS app that uses a web service to get data from my server. It grabs the data and echoes a JSON feed to the web page, and the iOS app interprets it. I have SSL so I am not worried about the data not being secure in transit.
My problem is that anybody can access the web service page and read the JSON data. It... | It simply sounds like you need to add authentication to the web service.
From your description it appears that the request goes like follows:
<pre><code>App --> Web site --> Web service
</code></pre>
If users have to register for your service, then when they log into the app it should authenticate with the web... | <h1>One Big Problem:</h1>
Allowing anyone access to your data without authorization, especially <strong>sensitive data</strong> is a HUGE no-no!
<hr>
That being said if the only way to access this server is with an application, then the easiest thing to do is to use an application specific SSL certificate that unles... | https://security.stackexchange.com |
2,573,715 | [
"https://math.stackexchange.com/questions/2573715",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/279147/"
] | From Charles George Broyden. Basic Matrices. The Macmillan Press Ltd, 1975.:
<blockquote>
We have already seen, in chapter 2, that if <strong>A</strong> is square and nonsingular a unique solution of the equation <strong>Ax</strong> = <strong>b</strong> exists for any arbitrary <strong>b</strong>. Equations of this ... | A linear dynamical system may be described by a differential system of equations like this:
$$\frac{d\vec x}{dt}=\dot {\vec x}=A\vec x$$
To find the solution we are interested in those values for which a vector $\vec x$ is tranformed by A in a vector multiple of $\vec x$:
$$A\vec x=\lambda \vec x\implies (A-\lambda ... | $A-\lambda I$ is singular iff $det(A-\lambda I)=0$, which means that $\lambda$ is an eigenvalue of $A$.
If the system is linear, then you can easily determine its behaviour using these eigenvalues.
If the system is non-linear, then you can approximate its behaviour in a small neighbourhood.
| https://math.stackexchange.com |
21,960 | [
"https://dba.stackexchange.com/questions/21960",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10639/"
] | I am trying to back up a pretty big database and I keep getting this error:
<pre><code>Msg 3271, Level 16, State 1, Server {Server Name}, Line 1 A
nonrecoverable I/O error occurred on file "{Backup File Location}:"
112(failed to retrieve text for this error. Reason: 1815). Msg 3013,
Level 16, State 1, Server {Server N... | So after many google searches and realizing that there was very little space left on the drive that I was trying to back up to, I found the issue.
Resolution: There is not enough space on the drive to fit the backup.
That seems like something that would be pretty easy to display Microsoft!!
Hope this helps someone e... | Well the one more reason for this Error i.e. SQL Server VSS Writer.
When disk volume is backed up via Windows Server; a replica also known as “Volume Shadow Copy Snapshot” is developed for the same volume. Further, it calls upon the associated VSS Writer and if an error is encountered via any of corresponding VSS Writ... | https://dba.stackexchange.com |
16,162 | [
"https://quant.stackexchange.com/questions/16162",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/15039/"
] | I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a <strong>functions</strong> of a low-dimensional <strong>Markov</strong> process (say 1 or 2).
This gives to the model the ability to calibrate ... | it's difficult to say that they are not popular. Some people definitely use them for live pricing. I'd say the real question is "why are they not popular in the academic literature"?
One answer would simply be that most the questions that arise in their use are ones of fiddliness which do not make good papers.
| In context of Bermudan Options, I believe that since the model determines everything exogenously, calibrating to swaptions may give you cases where the implied forward rate is negatively correlated to swap rates. Note this will never happen in an endogenous model where the short rate equation constrains this possibilit... | https://quant.stackexchange.com |
3,598,979 | [
"https://math.stackexchange.com/questions/3598979",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/764544/"
] | I'm studying Timothy C. Urdan's, <em>Statistics in Plain English</em>, and want to verify my understanding of his definition of a normal distribution. Per volume three,
<blockquote>
"<strong>Normal distribution:</strong> A bell-shaped frequency distribution of
scores that has the mean, median and mode in the mid... | We can provide a more elementary approach, assuming the limit exists.
By Stolz-Cesaro, the discrete version of L'Hôpital's rule, we have
<span class="math-container">$$\lim_{n\to\infty}\frac{\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}}1=\lim_{n\to\infty}\frac{\sqrt[n]{n!}}n=\lim_{n\to\infty}\sqrt[n]{\frac{n!}{n^n}}$$</span>
and... | Brute force, but from the Stirling formula
<span class="math-container">$$
n! = \left( {\frac{n}{e}} \right)^n \sqrt {2\pi n} \left( {1 + \mathcal{O}\!\left( {\frac{1}{n}} \right)} \right),
$$</span>
one has
<span class="math-container">$$
\sqrt[n]{{n!}} = \frac{n}{e}\exp \left( {\frac{1}{2n}\log (2\pi n)} \right)\left... | https://math.stackexchange.com |
264,998 | [
"https://electronics.stackexchange.com/questions/264998",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/121453/"
] | I want to determine the threshold voltage of an NMOS from a bvsim3v3 model in LTSPICE(Not a specific one I'm asking generally for this model). I can't get it directly from the parameters so I want to know how to. It doesn't have to be the exact value, I know it can be changeable but a good approach would be sufficient ... | A boost converter stores energy (in the first half of the switching cycle) in an inductor and then releases that energy to the load in the second half of the switching cycle. The energy it stores (and how often it repeats this process every second) HAS to match the power required by the load in order to sustain the cor... | This circuit does not have any feedback to stabilize the voltage output, so it just pumps voltage higher and higher until some parasitics stops it.
If you are serious, you should use any of industry offerings of boost converters, with internal voltage reference etc. There are plenty at Digi-Key.
If you are more ser... | https://electronics.stackexchange.com |
7,326 | [
"https://chemistry.stackexchange.com/questions/7326",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/3919/"
] | <img src="https://i.stack.imgur.com/bnWO5.jpg" alt="enter image description here">
I'm confused about how this chair conformation was constructed and why that particular Cl leaves. Why is one of the Cl's drawn axial while the others are drawn equatorial (it seems like the others could have been drawn axial as well)? A... | Well, distillation is almost certainly the best method. However, since you've explicitly ruled that out, there are only a few alternatives I can think of:
<ol>
<li>Ethanol can be separated from water with reasonable efficiency (at least on the microscale) by a process of "salting out." The ethanol/water mixture is sat... | Take the mixture of AcOH and ethanol and make it super saturated with bicarbonate, extract with ethyl acetate to remove ethanol and then acidify aqueous layer acidic and extract with 5-10% DCM in MeOH to remove acetic acid.
| https://chemistry.stackexchange.com |
7,348 | [
"https://electronics.stackexchange.com/questions/7348",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/771/"
] | Most microcontrollers (e.g. AVRs,MSP430s, PICs, etc) support a number of different sleep modes. The "deepest" sleep mode is the one that purports the lowest power draw (e.g. "Power Down", "Shut Down"), but all the clock systems are typically halted in these modes and it seems to me that the only way to "wake up" from t... | Most micros support a low-power 32.768 kHz watch crystal oscillator with some kind of prescaler and timer interrupt. Set the prescaler so the timer is counting slowly and the interrupt happens at the period you desire.
Some micros also have a built-in low-power RC timer if exact timing isn't critical.
The datasheet ... | Some parts have pretty low-power oscillators (a few uA) for wakeup, and some PICs also have hardware to allow a very slowly rising voltage on a pin to wake - this can be from an external capacitor set up before sleeping to charge over the required wake period.
| https://electronics.stackexchange.com |
319,327 | [
"https://physics.stackexchange.com/questions/319327",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/145936/"
] | <img src="https://i.stack.imgur.com/MW1Mt.jpg" alt="enter image description here">
This problem has bothered me for quite some time and I can't solve it. I have even tried to make a construction, but it sometimes tips to the left and sometimes tips to the right :).
When we submerge the body in the water the water pus... | The balance will be maintained because there is no EXTERNAL force applied on left or right side. This is because of the same reason you can't push a car while sitting in it!
| <strong>The scale will not move.</strong>
You don't need to think about buoyancy at all to answer this question. In the first picture, the scale is balanced, because the net force on each side (the weight) is equal. No mass is added to or removed from either side, so the net forces remain the same.
| https://physics.stackexchange.com |
3,841,127 | [
"https://math.stackexchange.com/questions/3841127",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/655928/"
] | <span class="math-container">$$\lim\limits_{x\to -\infty} (e^{-x} \cos{x})=\lim\limits_{x\to -\infty} \left(\dfrac{\cos{x}}{e^x}\right)$$</span>
From there, I see that <span class="math-container">$e^x$</span> approaches <span class="math-container">$0$</span> while <span class="math-container">$\cos{x}$</span> oscilla... | Yes your idea is right, to show that in a rigorous way let consider that for <span class="math-container">$x_n= -2\pi n \to -\infty$</span> as <span class="math-container">$n\to \infty$</span>
<span class="math-container">$$e^{-x_n} \cos{x_n}=e^{-x_n}=\infty$$</span>
and for <span class="math-container">$x_n= -\pi n$</... | Take <span class="math-container">$x=\frac{\pi}{2}+\pi k$</span>, where <span class="math-container">$k$</span> is integer and <span class="math-container">$k\rightarrow-\infty$</span>.
We see that <span class="math-container">$e^{-x}\cos{x}=0.$</span>
In another hand, for <span class="math-container">$x=\pi k$</span> ... | https://math.stackexchange.com |
1,384 | [
"https://cstheory.stackexchange.com/questions/1384",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/1171/"
] | Lets say that I have 50 events that generate some unique number (you are free to choose the number, but they should all fit in a 32 bit variable). I want to combine those numbers into a single number(32 bit), which can be used to find the absence of an event (i.e. a number).
If it was just ~10 events, I could have jus... | Well, is it only one missing event you want to detect? It you need to be able to detect the presence or absence of all 50 events, this means distinguishing between $2^{50}$ possibilities which obviously cannot be done with 32 bits. However if you wish to just detect a single missing event, here is a way that will work.... | You can use "binomial encoding" (I forgot the real name). As Joe suggested, we can store the information "the set contains all numbers but for those in S" for any S of size at most 9. The question is how to find a bijection between subsets of $[50]$ of size at most 9 and numbers between 0 and 13432735555 (as it happens... | https://cstheory.stackexchange.com |
35,027 | [
"https://dsp.stackexchange.com/questions/35027",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/16238/"
] | The derivative of $\sin(\omega_o t)$ is $\cos(\omega_o t)$.
The Fourier transform of $\sin(\omega_o t)$ is $\frac{\pi}{j}[\delta(\omega-\omega_o) - \delta(\omega+\omega_o)]$.
Differentiation in the time domain is equivalent to multiplying the transform by $j\omega$.
The transform of $\cos(\omega_o t)$ is $\pi[\delta... | I assume you mean the derivative with respect to $t$. In that case, the derivative of $\sin(\omega_0t)$ is not $\cos(\omega_0t)$ but $\omega_0\cos(\omega_0t)$. And luckily, this is also obtained via the Fourier transform relation you mentioned in your question:
$$\begin{align}\mathcal{F}\left\{\frac{d}{dt}\sin(\omega_... | So, the delta function satisfies:
$$\int_{-\infty}^{\infty} f(x) \delta(x - a)\, \mathrm{d}x = f(a)$$
Now, suppose we substitute $f(x) = x$
$$\int_{-\infty}^{\infty} f(x) \delta(x - a)\, \mathrm{d}x = a = \int_{-\infty}^{\infty} a \delta(x - a)\, \mathrm{d}x$$
This means that multiplying by $\omega$ is the same as mult... | https://dsp.stackexchange.com |
53,584 | [
"https://physics.stackexchange.com/questions/53584",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20378/"
] | Suppose engineers built a cylinder-shaped space ship which rotates to create artificial gravity:
<pre><code> __________________
/<-b \ \
/ \ \ -----> a
\ / /
\_b->/_____________/
</code></pre>
The space ship uses a rocket to travel through space in the direct... | There are two concepts here that may be getting mixed together, namely, conservation of <strong>linear momentum</strong> and <strong>conservation of angular momentum</strong>.
Newtons laws state that an object in motion will say in motion unless acted upon by an external force. So unless interstellar friction is a pro... | If there is no torque acting on the ship, then its rotational velocity would stay constant. The rotation of the ship has no effect on its course.
| https://physics.stackexchange.com |
52,610 | [
"https://biology.stackexchange.com/questions/52610",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/27162/"
] | The effects of coffee as a stimulant are quite well-known. What are the mechanisms by which coffee helps prevent sleepiness? I have heard of the presence of caffeine, but what does it actually do inside our body?
| Drowsiness is caused by the chemical adenosine binding to a nerve cell's adenosine receptor. A compound that binds and elicits a response, in this case a slow down of nerve activity, is called an agonist.
Caffeine is also capable of binding to the adenosine receptor. However, it does not elicit a response and no drows... | Adenosine is a naturally produced hormone. It inhibits neurons and makes you tired. The longer you stay awake, more adenosine is produced.
Caffeine is a competitive inhibitor. It will bind to the adenosine receptors and prevent adenosine from binding. The adenosine is unable to bind and thus you don't get tired.
For ... | https://biology.stackexchange.com |
38,965 | [
"https://stats.stackexchange.com/questions/38965",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11584/"
] | If <code>X</code> is a nonnegative random variable representing the life of a component having distribution function <code>F</code>,the mean residual life is defined by
$$
m(t) = E(X-t | X >t) = \frac{1}{\bar F(t)} \int_t^\infty (x-t) d\nu(x), t\geq 0
$$
In papaer R. C. Gupta and D. M. Bradley (2003)" Represe... | You have a nonnegative random variable $X\newcommand{\E}{\mathbb{E}}$ with distribution function $F$. The mean residual life is defined as
$$
m(t) = \E\left[X - t\mid X >t\right] = \frac{\E\left[ (X-t) I_{\{X>t\}}\right]}{P\{X>t\}} = \frac{1}{1-F(t)} \int_t^\infty (x-t)\,dF(x) \, ,
$$
for $t>0$. But
$$
... | Here is another way you can think about the problem.
<span class="math-container">\begin{align*}
& \mathbb{E}[X - t \, | \, X> t] = \int_0^{\infty} \mathbb{P}(X - t > s \, | \, X > t)ds = \int_0^{\infty} \dfrac{\mathbb{P}(X - t > s, \, X > t)}{\mathbb{P}(X > t)}ds \\
= & \dfrac{1}{\mathbb{P}... | https://stats.stackexchange.com |
2,390,638 | [
"https://math.stackexchange.com/questions/2390638",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/468609/"
] | Let $f$ be Lebesgue-integrable on $[0,1]$. Suppose $\int_a^bf(x)\,dx=0$ for all $0\leq a\leq b\leq 1$. Show $\int_Af(x)\,dx=0$ for every measurable subset $A$ of $[0,1]$.
*Let $A$ be a measurable subset of $[0,1]$. Then $A$ can be written as the union of disjoint, <strong>countable?</strong> intervals. Since $\int_a^... | The Lebesgue measure is regular, and in particular outer regular. Therefore there exists a sequence $(O_n)$ of open measurable sets containing $A$ such that $\lambda(A)=\inf \lambda(O_n)$.
Then $\displaystyle \int_A f(x)\, \mathrm{d}x=\int_{O_n} f(x)\, \mathrm{d}x - \int_{O_n - A} f(x)\, \mathrm{d}x$.
Since $O_n$ is ... | This is a standard application of Dynkin's $\pi$-$\lambda$ Theorem.
Define $\mathcal{P}=\{(a,b]\mid0\leq a<b\leq1\}\cup\{\emptyset\}$
and $\mathcal{L}=\{A\in\mathcal{B}([0,1])\mid\int_{A}f(x)\,dx=0\}$.
It is routine to verify that $\mathcal{P}$ is a $\pi$-class and
$\mathcal{L}$ is a $\lambda$-class. That is:
<ul>... | https://math.stackexchange.com |
715,254 | [
"https://physics.stackexchange.com/questions/715254",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/281431/"
] | Imagine we have the first Maxwell Equation:
<span class="math-container">$$
\nabla \cdot \mathbf E = \frac{\rho}{\varepsilon_0} \\
\mathbf E = -\nabla \phi \\
\nabla \cdot (-\nabla\phi) = \frac{\rho}{\varepsilon_0} \\\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}
$$</span>
We arrive to an equation for finding the potentia... | You can have a non-zero potential -- as long as it is constant in space. This will always generate a zero electric field, since in this case <span class="math-container">$\mathbf{E} = -\nabla\phi = 0$</span>, which is indeed expected for a zero charge density.
Mathematically, you could notice that since the point <span... | Ive been unfortunately trying to apply simple boundary conditions on your equation with no luck, because it's wrong. so First of all, let me correct you:
Laplaces equation for <span class="math-container">$r-$</span>dependance is:
<span class="math-container">$$\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\p... | https://physics.stackexchange.com |
15,505 | [
"https://chemistry.stackexchange.com/questions/15505",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7567/"
] | It is generally said that reactants react so that they can achieve a lower energy state. Then why does a reversible reaction occur in the first place? Since turning reactants into products increases their energy - an undesirable effect from the point of view of reacting molecules.
| First, let's tackle what an irreversible reaction is. Baking a cake, for example, is commonly considered "irreversible." The eggs, flour, milk, etc. which you started with are no longer present in their original forms after the cake has been baked.
Now, can you <em>reconstitute</em> the eggs, flour, milk, etc.? Of co... | There are several reasons for the reverse reaction to be favored; one is temperature. In the following reaction:
$$\ce{2NO_2<=> N_2O_4 + energy}$$
The right is the favored product, unless the temperature is increased. With enough heat, then the reactant is favored.
| https://chemistry.stackexchange.com |
1,998,676 | [
"https://math.stackexchange.com/questions/1998676",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/375991/"
] | I want to prove the following statement:
<blockquote>
Let $H$ be a self-adjoint operator in a Hilbert space $\mathcal{H}$. Suppose that $H^2 = H^3$. Prove that $H = H^2$.
</blockquote>
I tried to prove that proposition and I couldn't.
It seems to be very easy but I think that I need some trick to prove that propo... | Since $H$ is self adjoint, note that $$\left<H^2x-Hx,H^2x-Hx\right>=\left<H^2x,H^2x\right>-\left<Hx,H^2x\right>-\left<H^2x,Hx\right>+\left<Hx,Hx\right>\\=\left<H^4x,x\right>-\left<2H^3x,x\right>+\left<H^2x,x\right>=\left<(H^4-2H^3+H^2)x,x\right>.$$ But, $H^3=H^2$, s... | A proof using spectral theory in the case where $\mathcal{H}$ is complex:
Observe that if $T$ a self adjoint operator on $\mathcal{H}$, then $T$ is bounded (Hellinger- Toeplitz) and for the spectral radius $r(T)$ of $T$ we have
$$ r(T)=||T||.$$
Let us denote the spectrum of $T$ by $ \sigma(T)$
If $H$ is self adjoin... | https://math.stackexchange.com |
135,451 | [
"https://electronics.stackexchange.com/questions/135451",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | Do the logic families such as TTL and CMOS represent only different logical structure? Or do they also use different type of transistors? Latest microprocessor chips with millions of components use CMOS. Is that only because CMOS "operating logic" is superior or also because CMOS family use entirely different transisto... | Here is an awfully incomplete answer :
By doping, oxyding, metallising a slice of sillicon, you can create on the surface several types of components : wires, bipolar transistors (aka BJT), metal-oxyde transistors (aka MOS), resistors, inductors, capacitors... (but it is often easier to create a transistor than these ... | TTL logic uses bipolar transistors and CMOS logic uses, well, CMOS transistors. The structure of gates is also quite different between the two since the two types of transistors are so different and therefore need to be used differently.
| https://electronics.stackexchange.com |
177,564 | [
"https://physics.stackexchange.com/questions/177564",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/66165/"
] | Obviously gravity pulls objects towards the earth's surface. Now suppose I have a refrigerator and a magnet. The magnetic force is perpendicular to the gravitational force. So it is not counteracting it. So why does the magnet not get pulled to the ground since no other force is opposing it?
My instinct is that the m... | As you may know, the friction is proportional to the normal force of an object or in this case the force of attraction between magnet and refrigerator.
If your force is strong enough then the friction will be sufficient and the magnet will not slip (on earth the force of friction must exceed the mass of your magnet mu... | f(friction) directly proportional to N(normal force acting, perpendicular to the plane of fridge in outward direction here) is the force that opposes motion, now friction will in this case be provided by the atomic attraction, only atomic attraction is taken into account here, because repulsion would not even let it at... | https://physics.stackexchange.com |
225,813 | [
"https://mathoverflow.net/questions/225813",
"https://mathoverflow.net",
"https://mathoverflow.net/users/83971/"
] | Let M be a finite dimensional von Neumann algebras with a normal faithful trace. Let e and f be two projections with rank 1. I want to know if e and f have identical traces. (This is obviously true if M is a factor.)
I guess it is false, while i have no counterexample.
| This follows, fairly easily, from the hypothesis of irreducibility and from the "annulus theorem" (see page 130 of Jaco-Shalen's book "Seifert Fibered Spaces in 3-Manifolds"). You can remove the hypothesis of irreducibility if you are willing to use the Poincaré conjecture.
| Although this question has already been answered, I would like to shortly explain the idea on how to prove that $f$ is $\pi_1$-surjective, as it has been established in the comments below my original question. The result then follows from the classification of Haken manifolds (See Hempel's "3 Manifolds", for example). ... | https://mathoverflow.net |
330,733 | [
"https://stats.stackexchange.com/questions/330733",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/108150/"
] | I am wondering why in the Causal Inference literature that the Average Treatment Effect is usually written as $\tau = E[Y_i(1) - Y_i(0) ]$ instead of $\tau_i = E[Y_i(1) - Y_i(0) ]$? In other words, why is it that typically $\tau$ is NOT indexed by $i$?
Is it to be taken that $\tau = E[Y_i(1) - Y_i(0) ]$ is averaging ... | +1 to Dimitriy's answer. To elaborate this a bit more:
The average treatment effect in the population is: $E[\tau] = E[Y^1 -Y^0] = E[Y^1]- E[Y^0]$.
We can drop the subscript $i$ not because we assume constant effect but because we assume the expected causal effect of a randomly selected individual from the population... | It is because $$\tau = E[\tau_i]=E[Y_i(1)-Y_i(1)],$$ that is it is the <em>average</em> of the individual-level treatment effects.
| https://stats.stackexchange.com |
836,183 | [
"https://math.stackexchange.com/questions/836183",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/86863/"
] | <strong>Question</strong>
Prove that if $a$ is a real number such that $a^2 \ge 7a$ then $a\le0 \text { or } a\ge7$
<strong>My Attempt</strong>
We are given:
<ol>
<li>$a \in \mathbb{R}$</li>
<li>$a^2 \ge 7a$</li>
</ol>
And need to prove:
$a\le 0 \text{ or } a\ge 7$ is true
Since:
<blockquote>
$a\le 0 \text{ ... | $a^2\ge7a\leftrightarrow a^2-7a\ge0\leftrightarrow a(a-7)\ge0$
The multiplication of two reals can only and only if non-negative, if
<ul>
<li>both of them is non-negative (thus $a\ge0$ and $a-7\ge0$ $\leftrightarrow \underline{\underline{a\ge7}}$)</li>
<li>or both of them is non-positive (thus $a\le0$ and $a-7\le0$ $... | Perhaps an easier way is to notice the following: $$a^2 \geq 7a \iff a^2 - 7a \geq 0 \iff a(a-7) \geq 0$$ Now we only need to use the fact that $ab \geq 0$ iff $a, b \leq 0$ or $a, b \geq 0$.
| https://math.stackexchange.com |
60,759 | [
"https://electronics.stackexchange.com/questions/60759",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10917/"
] | I am currently building a robot (as some of you may know from my previous questions). The current task I a dealing with is that of communication. To keep things simple, assume I have 5 commands to deliver from my ground station to my robot:
<ol>
<li>Drive forward</li>
<li>Drive reverse</li>
<li>Activate servo 1</li>
<... | What I usually do is I try to ensure that the controller doesn't send commands faster than the robot can process. Sending instructions consistently faster than can be processed by the robot will always eventually result in a loss of information with either a FIFO or a LIFO buffer. As a backup to intermittent lag on the... | What I have done in some projects is to use a circular buffer that is filled by an ISR triggered by a UART.
So when the UART receives a byte, an interrupt is triggered and the handler loads that byte to end of the buffer.
Then in the main loop you can check if there is any bytes in the buffer and execute each command... | https://electronics.stackexchange.com |
2,139,961 | [
"https://math.stackexchange.com/questions/2139961",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/413652/"
] | I want to prove that $r(AB) = r(BA)$, where $r$ is a rank. $A$ is a square matrix and $B$ is an invertible matrix.
Can I use this?
$r(AB) \le min \{r(A), r(B)\} = r(A)$, and from the other side
$r(A) = r(BB^{-1}ABB^{-1}) \le min \{r(BB^{-1}), r(AB), r(B^{-1})\} = r(AB)$
hence $\;$ $r(AB) = r(A)$, and
$r(BA) \le m... | Your proof is correct, assuming (of course) you know the fact that $r(AB)\leq \min\{r(A), r(B)\}$. One thing I wonder about is why you write $A=B^{-1}BAB^{-1}B$? Is it not enough to write $A=B^{-1}BA$?
| Image:
$Im(AB)\subset Im(A)=Im(A(BB^{-1}))=Im(AB(B^{-1}))\subset Im(AB)$
So for $B$ invertible we have $Im(AB)=Im(A)$
Kernel:
$x\in Ker(A)\Rightarrow Ax=0\Rightarrow BAx=0\Rightarrow x\in Ker(BA)$
$x\in Ker(BA)\Rightarrow BAx=0\Rightarrow Ax=B^{-1}0=0\Rightarrow x\in Ker(A)$
So for $B$ invertible we have $Ker(BA)=... | https://math.stackexchange.com |
186,140 | [
"https://physics.stackexchange.com/questions/186140",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/82223/"
] | I have a question from the very basics of Quantum Mechanics. Given this theorem:
<blockquote>
For the discrete bound-state spectrum of a one-dimensional potential let the allowed energies be $E_1<E_2< E_3< ...$ with $E_1$ the ground state energy. Let the associated energy eigenstates be $ψ_1,ψ_2,ψ_3,...$. ... | I guess there is not that much to grasp, unless you can really understand dark spots on an electron diffraction pattern. Very roughly explanation would be to interpret wave functions of a particle in a potential well as "standing waves", or as two interfering waves reflected from the walls of the well. Increasing the e... | The physical interpretation behind the increase of energy with the number of nodes can be understood in a very crude manner as follows:
Nodes are points of zero probability densities. Since the wavefunction is continuous, the probability density is also a continuous function. So the regions in the neighbourhood of nod... | https://physics.stackexchange.com |
656,232 | [
"https://physics.stackexchange.com/questions/656232",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/307732/"
] | I am working on two different SHMs:
<span class="math-container">$$P=a\sin\omega t \\ Q=a\sin(\omega t +\phi)$$</span>
where <span class="math-container">$\omega$</span> = angular velocity, <span class="math-container">$\phi$</span> = phase constant, <span class="math-container">$P,Q$</span> = displacement at a instan... | The only difference between the <span class="math-container">$P=a\sin\omega t $</span> and the <span class="math-container">$Q=a\sin(\omega t +\phi)$</span> description is that you are <strong>observing the same motion</strong> but starting the clock, setting <span class="math-container">$t=0$</span>, at difference par... | If you have an object undergoing simple harmonic motion with a position <span class="math-container">$x(t)$</span> given by <span class="math-container">$$x(t) = A \sin (\omega t + \phi),$$</span>
then the velocity of the object is: <span class="math-container">$$v(t) = \frac{\text{d}x}{\text{d}t} = A \omega \,\cos(\om... | https://physics.stackexchange.com |
80,940 | [
"https://mathoverflow.net/questions/80940",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | I would like to know examples of forcing arguments where in order to make the cardinal arithmetic go through one needs to assume something about the size of the continuum or other power sets.
The examples that I know of are forcing to add $\aleph_2$ many Cohen reals (which requires the assumption of CH in the ground m... | Something that happens rather frequently (in my particular field of interest) is that some assumption like CH is needed for the forcing notion to exist at all.<br>
An example is the consistency proof of Todorcevic's Open Coloring Axiom, where the appropriate forcing notion for a single step of the forcing construction ... | There are some odd examples coming from PCF theory, where one begins with assumptions about pcf structures that are not known to be consistent (even if one assumes consistency of large cardinals), and then do some forcing in order to make things happen.
For example, consider the following conjecture of Shelah:
"If $... | https://mathoverflow.net |
30,680 | [
"https://stats.stackexchange.com/questions/30680",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12060/"
] | I need to classify URLs into categories. Say I have 15 categories that I'm planning to zero down every URL to.
Is a 15-way classifier better? Where I have 15 labels and generate features for each data point.
Or building 15 binary classifiers, say: Movie or Non-Movie, and use the numbers I get from these classificat... | First of all, you must ask yourself if your problem is multilabel (i.e. a single URL can belong to several classes) or not (i.e. a single URL can belong to only one class).
If the former, go with a battery of binary classifiers, because this is a default way of doing multilabel problems.
If the latter, the answer d... | This will depend on how your data is dispersed. There is a beautiful example that was given recently to a similar question where the OP wanted to know if a single linear discriminant function would be a better classifier for deciding population A vs B or C or one based on mutliple linear discriminant functions that se... | https://stats.stackexchange.com |
291,090 | [
"https://physics.stackexchange.com/questions/291090",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59234/"
] | If a uniform magnetic field ${\bf{B}}=B_{z}{\bf{\hat{z}}}$ exists in a hollow cylinder (with the top and bottom open) with a radius $R$ and axis pointing in the $z$-direction, then the vector potential
$${\bf{A}}=\frac{BR^{2}}{2r}{\bf{\hat{\phi}}}?$$
using Stokes's theorem.
<hr>
How can you prove this?
| You are given a uniform magnetic field $\vec{B}=B_z\hat{z}$
We have the relation connecting the magnetic field vector $\vec{B}$ and the vector potential $\vec{A}$
$$\vec{B}=\nabla\times\vec{A}\tag 1$$
Now, according to Stoke's theorem, we have
$$\int_S\left(\nabla\times\vec{A}\right)\cdot d\vec{S}=\oint_C\... | Take the curl of ${\bf A}$. If the answer is ${\bf B}$, then you have a valid vector potential. Note, however, that the vector potential is not unique; two different expressions for ${\bf A}$ may have the same curl, and so they correspond to the same magnetic field.
| https://physics.stackexchange.com |
484,963 | [
"https://physics.stackexchange.com/questions/484963",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/211093/"
] | Hello I have a question about rotating coordinate frames. Following the book of Brizard the Lagrangian is given by
<span class="math-container">\begin{equation}
L(\mathbf{r}, \mathbf{\dot{r}}) = \frac{m}{2} \vert \mathbf{\dot{r}} + \boldsymbol{\omega} \times \mathbf{r} \vert^2 - U(\mathbf{r})
\end{equation}</span>
Woul... | We are used to the fact that you get a 180 degree phase shift when a wave impinges on a denser material - for example in the difference between Lloyd's mirror and Young's slits. You do not get one when travelling from denser to less dense, i.e. glass to air.
So it looks like the question forgot this... until you thin... | The solution is flawed, by more than just this. "The minimum distance x for which a maximum occurs at detector, the path length will be <span class="math-container">$\Delta = \lambda$</span>" as a statement has not been justified and is completely untrue. A minimum for x requires a maximum for \Delta which you can see ... | https://physics.stackexchange.com |
31,071 | [
"https://physics.stackexchange.com/questions/31071",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5300/"
] | I understand that when you pluck a guitar string, then a bunch of harmonic frequencies are produced rather than just the frequency of the desired note.
If this is true, why does C2 sound so different from C1? I mean, C2 is a harmonic of C1, and should therefore be heard when C1 is played.
Why are all these harmonics ... | Let's look at frequency instead of notes. Let's say the string has a natural frequency of $100 Hz$ and that harmonics are present when you pluck it. Then, the frequency content of the sound will be of the form:
$a_1 \cdot 100 Hz + a_2 \cdot 200 Hz + a_3 \cdot 300 Hz + ... $
Now, let's say you fret this string halfw... | Frequency is just a way of analyzing a time dependent motion. Consider plucking a string by first pulling one point on the string away from its equilibrium. The string shape will be like a triangle, two straight bits of string coming away from where your finger is holding the string, but meeting at a slight angle whe... | https://physics.stackexchange.com |
18,207 | [
"https://engineering.stackexchange.com/questions/18207",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/5825/"
] | Diesel engines are considered "steady torque", which means that torque is same no matter the revolutions whereas torque depends on revolutions for an engine that runs on Otto cycle.
What is the reason for this?
| The diesel engines are working on diesel cycle. The heat addition(ingnition) is taking place during the constant pressure process.
After added energy is spent by the expansion of piston.
The amount of expansion is fixed in terms of stroke length.
So for given fixed pressure and fixed expansion we ought to get const... | Compared to Otto cycle engines, diesel engines have a smaller rpm range and, as they tend to have more mass (due to the higher compression ratio etc), tend to develop the torque earlier in the rev band and it tends to be a flatter curve through the range.
| https://engineering.stackexchange.com |
26,533 | [
"https://mechanics.stackexchange.com/questions/26533",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4906/"
] | Somebody drove into the back of my 2003 Opel Agila at about 5-10mph.
There is no damage to the bumper apart from a large dent but I'm worried there may be hidden internal damage.
<strong>What can I do to check the car is still safe and not damaged?</strong>
<strong>Should I take it to a garage to check tracking, s... | Not sure how things work were you are. Here if you are rear ended, it is considered to be the fault of the person who hit you, so their insurance will pay for the damage. If this is the case, you might as well take it to a shop and have them take a look at it.
I work on all my own cars, and don't like taking my cars... | Another thing to check immediately that is often not visually obvious is whether your trunk opens, closes and locks easily and reliably. Not much can be damaged at that speed, but even slight damage to the trunk can bend it enough to cause locking difficulty. It would really suck if you let go that careless driver afte... | https://mechanics.stackexchange.com |
190,861 | [
"https://physics.stackexchange.com/questions/190861",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | This is an excerpt from Edward M. Purcell's Electricity & magnetism:
<blockquote>
Suppose a spherical shell of charge is compressed slightly, from an initial radius of $r_0$ to a smaller radius. This requires that work be done against the repulsive force $\dfrac{\sigma^2}{2\epsilon_0}$ for each square meter of ... | <blockquote>
How can the energy required for squeezing be the energy required for assembling the charges?
</blockquote>
The energy required for squeezing the sphere from initial radius $r_0 \to (r_0-dr)$ is not the energy required to assemble the charges. He merely calculated the change in energy (or the work requir... | <blockquote>
What is actually meant by assembling of charges? To bring the charges to make the desired arrangement, right? In order to find the energy, wouldn't we need to find the work done from bringing the charges from infinity to the desired configuration?? But here, Mr. Purcell just squeezed the sphere & fou... | https://physics.stackexchange.com |
924 | [
"https://mathoverflow.net/questions/924",
"https://mathoverflow.net",
"https://mathoverflow.net/users/570/"
] | In the chapter 6.4 on normal and self-adjoint operators, there is an example of an infinite dimensional inner product space H that has a normal operator but that has no eigenvectors.
The space is the set of functions f_n(t) = e^(int) , t in [0,2pi]
with inner product = 1/2pi * integral_0_2pi(e^(-int) e^(imt))dt
The ... | The space being defined is the <strong>span</strong> of the functions f<sub>n</sub>, and in the definition of the span we only allow finite sums of the basis vectors.
Edit: I should also mention that the notion of infinite sum in an inner product space doesn't make sense unless the space is also complete with respect... | Qiaochu Yuan hit it on the head. To quote Hoffman & Kunze (<em>Linear Algebra</em>):
<blockquote>
Infinite bases have nothing to do with 'infinite linear combinations.' The reader who feels an irresistible urge to inject power series into this example [concerning vector spaces of polynomials] should study the e... | https://mathoverflow.net |
2,386,079 | [
"https://math.stackexchange.com/questions/2386079",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/159793/"
] | I have a question concerning the composition of morphisms in the category $ \textbf{Rel} \ $.
First, for categories generally, it is frequently stated that if $ f \colon A \to B $ and $ g \colon B \to C $ , i.e., if cod(f) = dom (g), the morphisms must compose in order to fit the definition of a category.
However, t... | For all $A$ and $B$, the null set is indeed a subset of $A\times B$, so it fits the definition of a morphism $A\to B$. What else is there to say?
| The composite $S \circ R$ only exists when the codomain of $R$ is the domain<sup>1</sup> of $S$, where the words "composite", "domain", and "codomain" all refer to the category structure of <strong>Rel</strong>.
This does not preclude there being some other operation that extends the category composition operation to ... | https://math.stackexchange.com |
69,560 | [
"https://mathoverflow.net/questions/69560",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8320/"
] | Let $X$ be a finite CW-complex and $A$ an abelian group, and consider the space $Maps(X,K(A,n))$ of continuous maps from $X$ to $K(A,n)$ endowed with the compact-open topology, so that it represents the functor $Y\mapsto C(X\times Y,K(A,n))$. Let $Maps_0(X,K(A,n))$ be the path-connected component of $Maps(X,K(A,n))$ co... | In general, the homotopy groups (based at the trivial map) of a <strong>based</strong> mapping space $Map(X,Y)$ are $\pi_nMap(X,Y)=[\Sigma^n,Y]$, $n\geq 0$, where the brackets denote sets of homotopy classes of maps. If $Y=K(A,n)$ then you get $\pi_1Map(X,K(A,n))=[\Sigma X,K(A,n)]=H^n(\Sigma X,A)\cong H^{n-1}(X,A)$.
| One can sharpen Fernandos answer: there exist models for Eilenberg Mac Lane spaces that are abelian topological groups. Hence the mapping space $Map(X;K(A,n))$ (based or unbased) is a topological abelian group. Topological abelian groups are products of Eilenberg-Mac Lane spaces, and so your mapping space is a product ... | https://mathoverflow.net |
14,881 | [
"https://chemistry.stackexchange.com/questions/14881",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/3793/"
] | From 1,5-diphenylpentan-3-ol (above), how to add the two hydroxy groups in red (below)?<br>
Is there any proven successful synthesis route to 1,5-diphenylpentane-1,3,5-triol with higher yield (40 % or above)?
<img src="https://i.stack.imgur.com/Owk4H.jpg" alt="enter image description here">
| A few possibilities for direct hydroxylation:
<ul>
<li>$\ce{SeO2}$ immediately comes to mind as one potential option; it is well known to selectively oxidize allylic positions to yield alcohols and carbonyl compounds, and there appear to be references suggesting it reacts at the benzylic position as well.</li>
<li>In ... | Actually, hell with that. I recall that organolithium compounds may be carefully oxidated at very low temperatures by different things, namely halogens, sulfur and - tadam! - molecular oxygen.
$\ce{BuLi}$ should selectively deprotonate each benzyl position once, and then the lithium compound may be very carefully oxi... | https://chemistry.stackexchange.com |
2,286,652 | [
"https://math.stackexchange.com/questions/2286652",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/98816/"
] | Suppose we are given two functions $g(x)$ and $f(x)$ where $f(x)$ is monotonous, such that
$$g(x) = af(x) + b,$$
with $a,b$ constant. I was wondering if there is any relationship between their inverses.
| We have
$$
af(x)+b=g(x)=y \iff x=g^{-1}(y),
$$
and
$$
f(x)=\dfrac{g(x)-b}{a}=z \iff x=f^{-1}(z)
$$
Hence
$$
g^{-1}(y)=f^{-1}\left(\dfrac{g(x)-b}{a}\right)=f^{-1}\left(\dfrac{y-b}{a}\right).
$$
The relationship between $f^{-1}$ and $g^{-1}$ is therefore
$$
g^{-1}(x)=f^{-1}\left(\dfrac{x-b}{a}\right)
$$
or equivalently
$... | Letting $y = g(x)$
$$y = af(g^{-1}(y))+b$$
$$f^{-1}\left(\frac{y-b}{a}\right) = g^{-1}(y)$$
and so
$$f^{-1}(y) = g^{-1}(ay+b)$$
| https://math.stackexchange.com |
535,442 | [
"https://physics.stackexchange.com/questions/535442",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236156/"
] | If an object hits a soft surface it will bounce lower compared to the object hitting a hard surface, isn't the impulse in the first case equal to the impulse in the second case, so why does the object bounce lower when it hits a softer surface?
| You need to be careful as to exactly what you mean by the terms "softer" and "harder". It is rather the degree of inelasticity of the collision that determines how high the object bounces.
For example, you can have a spring with a low spring constant that you might consider "softer" than a spring with a higher spring... | When an object bounces off of something, the bounce is not instantaneous, and in fact goes through a sequence of changes.
First, the object slows down to a stop, and both the object and the surface are deformed. If they are both hard, then the deformation will be very small, but it will still exist.
Second, both the ... | https://physics.stackexchange.com |
14,508 | [
"https://mathoverflow.net/questions/14508",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2215/"
] | Suppose that $f$ is a weight $k$ newform for $\Gamma_1(N)$ with attached $p$-adic Galois representation $\rho_f$. Denote by $\rho_{f,p}$ the restriction of $\rho_f$ to a decomposition group at $p$. When is $\rho_{f,p}$ semistable (as a representation of
$\mathrm{Gal}(\overline{\mathbf{Q}}_p/\mathbf{Q}_p)$?
To make ... | The right way to do this sort of question is to apply Saito's local-global theorem, which says that the (semisimplification of the) Weil-Deligne representation built from $D_{pst}(\rho_{f,p})$ by forgetting the filtration is precisely the one attached to $\pi_p$, the representation of $GL_2(\mathbf{Q}_p)$ attached to t... | Since <em>f</em> is potentially semi-stable, you can look at its attached filtered (φ, <em>N</em>, Gal(<em>L</em>/<strong>Q</strong><sub><em>p</em></sub>))-representation (where ρ<sub>f,p</sub> becomes semi-stable when restricted to <em>G</em><sub><em>L</em></sub>). If its <em>N</em> is zero, then it is potenti... | https://mathoverflow.net |
42,914 | [
"https://quant.stackexchange.com/questions/42914",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/28335/"
] | I'm having some confusion doing Engle-Granger Cointegration test and then trade the ratio.
Methodology:
<ol>
<li>Run an OLS fit for A and B price time series without a constant. Therefore,
<span class="math-container">$\hat{Y} = \gamma \cdot P_b + e$</span> where <span class="math-container">$\hat{Y}$</span> is the e... | To avoid "violating the assumptions of the OLS model" it is important to do the regression using returns <span class="math-container">$\frac{P_t-P_{t-1}}{P_{t-1}}$</span> (or logarithmic returns <span class="math-container">$\ln P_t - \ln P_{t-1}$</span>) for both the index and the stock and not the price level <span c... | I have seen this done mostly qualitatively. For example, this is a large cap tech name, so I will benchmark it against the QQQ.
With short time periods of data and a single stock, running a historical regression and choosing a benchmark without taking into consideration your intuition could lead to sporadic results.
... | https://quant.stackexchange.com |
342,051 | [
"https://physics.stackexchange.com/questions/342051",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/160413/"
] | Let's say I want to teach kinetic and potential energy and I'd like to use an example that students can remember. The original idea is to show that speed (being squared) in the kinetic energy formula proves to be very important in the energy being delivered to a body.
If a car travels in a 30 km/h limit zone with 34 km... | There is more than one approximation here. Some apply to mirrors and lenses. Some apply to the propagation of light in general. Lenses are more common that curved mirrors. Much more attention has been paid to lens design than mirror design. But the techniques are similar.
First, the small angle approximation assumes ... | There is a more general (exact) formula for a spherical mirror. This formula was discovered by H. A. Elagha and was published in the journal of the optical society of america in 2012. The paper has the title: "Exact ray tracing formulas based on a nontrigonometric alternative to Snell's law" . This formula ha... | https://physics.stackexchange.com |
1,826 | [
"https://dba.stackexchange.com/questions/1826",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/44/"
] | Is it possible to specify the user_id of a user while creating it?
<pre><code>SQL> create user user1 identified by user1;
User created.
SQL> select user_id, username from all_users where username='USER1';
USER_ID USERNAME
---------- ------------------------------
72 USER1
SQL>
</code></pre>
In... | Not in a supported fashion, no.
Why would you care what the <code>USER_ID</code> of a new user was? That would seem to raise a pile of red flags in my mind.
| If you want to migrate logins and users from a server to another there should be another way then forcing their ids and names.
In SQL Server for example there is a system stored procedure (sp_help_revlogin) that generates the necessary scripts to migrate users between servers. I don't know for Oracle, but I'm sure som... | https://dba.stackexchange.com |
354,542 | [
"https://mathoverflow.net/questions/354542",
"https://mathoverflow.net",
"https://mathoverflow.net/users/146669/"
] | I am about to (hopefully!) begin my PhD (in Europe) and I have a question: how did you learn so much mathematics?
Allow me to explain. I am training to be a number theorist and I have only some read Davenport's Multiplicative Number Theory and parts of Vaughan's book on the circle method. I have briefly seen some vari... | The other answers have some good general advice. Let me try to say something that is specific to the topics of analytic number theory, and number theory generally.
First, there is no such thing as training to be a number theorist. There are many different kinds of number theorists, and very few of him are comfortable ... | It may seem like a mountain. But remember that a few years ago you knew <em>absolutely nothing</em>, and you have mastered a lot of material already! Three or four years is a lot of time, and almost certainly enough to become an expert on <em>one</em> thing (maybe even two). You can always expand later, but it's useful... | https://mathoverflow.net |
7,132 | [
"https://physics.stackexchange.com/questions/7132",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2597/"
] | The professor asked us to do this one:
"..Determine all potentials $V(r,\theta, \phi)$ for which it is possible for find solutions of the time independent Schrodinger equation which are also eigenfunctions of the operator $L_{z}$."
I try to solve this problem by assuming separation of variables, and I get $$\Phi(r,\t... | Try writing out $[L_z,V(r,\theta,\phi)]=0$. In other words, V has to be a function such that:<br>
$L_zV \psi = VL_z\psi$<br>
for absolutely any function $\psi$. Does that tell you anything about V?
| I'm not going to answer your homework problem. Instead I'm going to construct a counter example to the hint $[L_{z},V]=0$, which is wrong.
Consider first, for simplicity, a spherically symmetric potential $V(r)$ and a product solution
$\Psi(r,\theta,\phi)=R(r)\Theta(\theta)e^{im\phi}$
to the time independent Schro... | https://physics.stackexchange.com |
7,679 | [
"https://physics.stackexchange.com/questions/7679",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/661/"
] | Most textbooks on basic quantum mechanics tell you that when your initial Hamiltonian $H_0$ has degenerate states, then before you can do (time independent) perturbation theory with a perturbation matrix $V$ on it, you have to first diagonalize $H_0 + V$ in the subspace of the degenerate states.
Sounds nice enough, b... | First, just to be sure about the answers to this particular problem: the eigenvalues of the $4\times 4$ matrix are
$$0,\quad U\quad {\rm and}\quad U/2\pm \sqrt{(U/2)^2+4t^2}$$
When expanded to the first nontrivial order, the last two eigenvalues are
$$ 0 - \frac{4t^2}U \quad {\rm and} \quad U+\frac{4t^2}U. $$
Note th... | <strong>This answer is basically what I learned from the Lubos Motl's answer(hopefully I understand it right), with a little bit generalization</strong>.
<h2>Question raised</h2>
We want to solve a Hamiltonian $H=H_0+\lambda V$ perturbatively . What we know is the solution of $H_0$, whose eigenstates are $|n^0\rangle... | https://physics.stackexchange.com |
657,498 | [
"https://physics.stackexchange.com/questions/657498",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/310683/"
] | My understanding goes like this: an x-y plane (or flat 2-dimensional surface) is an infinite set of lines, each one dimensional. The x-y-z space (or 3d volume) is an infinite set of 2-dimensional planes. So the 4th dimension must be an infinite set of 3-dimensional volumes, right?
My question is, if we see the world li... | Yes, you can think of it this way. You could also have started with 1 dimension and stated that it is an infinite set of points. With regard to the flow of time, this is indeed one of the challenges of General Relativity (GR). One of the interpretations within GR is that the flow of time is simply a collection of ev... | The picture of physical events which you are referring to here is called the "block universe". If basic physical patterns ("laws") are all deterministic then the block universe picture makes a lot of sense. If the basic physical patterns ("laws") are not entirely deterministic then the fut... | https://physics.stackexchange.com |
84,911 | [
"https://softwareengineering.stackexchange.com/questions/84911",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22417/"
] | I am mostly developing on ASP.NET MVC and sometimes on ASP.NET WebForms. But when I hit a PHP web site, I always think that;
<blockquote>
Should I learn PHP?
</blockquote>
Assuming answer here is yes, where would be the first place to start and where should I go from there?
| I would suggest try taking a page you've developed in MVC and seeing if you can do the same page, but in php.
You already understand the mechanics of the page as you've done it once before. This would allow you to make parallels between the two different solutions and help you gain a better understanding.
You look ... | I would say coming from ASP.NET MVC to immediately dive into a PHP framework like Zend (not really a "framework", more like the .NET libraries, but it calls itself a framework) or Symfony (the only ones I'm familiar with, there are others obviously). Trying to use raw PHP will be like pulling teeth (speaking from expe... | https://softwareengineering.stackexchange.com |
78,940 | [
"https://math.stackexchange.com/questions/78940",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/9450/"
] | In a text I am reading, the author defines two norms on a vector space $X$ to be <em>equivalent</em> if they induce the same topology on $X$. The text does not define what it means however for two topologies to be equivalent. The only definition I can think of that seems reasonable is that two topologies $T_1$ and $T_2... | Given two topologies $\tau,\tau'$ on a set $X$, we say $\tau$ is <em>coarser</em> (or <em>weaker</em>) than $\tau'$ iff $\tau\subset\tau'$. Accordingly we say $\tau'$ is <em>finer</em> (or <em>stronger</em>) than $\tau$.
Equivalently, this means $\tau$ has more (read:not less) opens, or equivalently ... | Two norms are equivalent if they induce <strong>the same</strong> topology. So it does not matter whether the author of your book defines the notion of "equivalent topologies", since he does not need it (at least not here). I.e., you work here with equality of topologies. (Which is reflexive, symmetric and transitive, ... | https://math.stackexchange.com |
16,284 | [
"https://softwareengineering.stackexchange.com/questions/16284",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/92/"
] | I'm learning about the open source web based project management tool Trac and I'm a bit confused about its role in the area of reporting defects vs bug tracking.
For those unfamiliar with Trac itself, it has a Ticket system which is the tool used to report issues, and you can choose between reporting a task, an enhan... | Trac is a tool to keep track of things, assign them to people, and report on progress through state and comments.
Software development shops often have QA keep track of all the problems they've encountered (defects) and assign them to developers to fix.
Enhancments and other incidentals can also be kept track of as w... | I use it to track features and tasks in addition of defects.
I use the <strong>Defect</strong> option when the item I'm adding is a defect.
(I'm using Task option when it's a task, and Enhancement when it's a feature)
| https://softwareengineering.stackexchange.com |
92,736 | [
"https://mathoverflow.net/questions/92736",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6862/"
] | Let $V_{\lambda}$ and $W_{\lambda}$ be the irreducible representations of $S(n)$ and $\mathfrak{su}(N,\mathbb{C})$ associated to the partition $\lambda \in \mathbb{Y}$ of size $| \lambda |=n$ and length $l(\lambda) \leq N$. The following limit $$\frac{\dim V_{\lambda}}{n!} = \lim_{N \rightarrow \infty} \frac{\dim W_{\... | This is an answer to Alexander's combinatorial reformulation of the question in comments to Bruce's answer.
dim $V_\lambda$/$n$! is the chance that you will get a standard Young tableau if you assign the values 1 to $n$ to the boxes of a tableau of shape $\lambda$ according to a random permutation.
dim $W_\lambda/N... | The $q$-analogue of $\dim W_\lambda$ is the specialisation $s_\lambda(q,q^2,\ldots ,q^n)$ and the $q$-analogue of $\dim V_\lambda$ is the principal specialisation $s_\lambda(q,q^2,\ldots )$ which is manifestly given by taking $n\rightarrow\infty$. In fact in Enumerative Combinatorics II by Stanley this is how the hook ... | https://mathoverflow.net |
8,633 | [
"https://dba.stackexchange.com/questions/8633",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4552/"
] | The indexes are affecting the ADD/UPDATE operations however I was wondering whether the redundant indexes will affect the <code>SELECT</code> query performance or not?
How the redundant indexes are handled by the SQL Server in case more than one indexes are eligible to use by the select query?
| If you want to really split hairs, at the very least they affect the compilation time, since the optimizer has more indexes to consider. They also consume time to load and memory to store their metadata. It may seem a trivial amount, but consider the extreme case of an index with 16 columns over 1000 partitions: it req... | The only overhead for indexes are on DML statements (<code>INSERT</code>, <code>UPDATE</code>, and <code>DELETE</code>). The reason this causes overhead is because it makes the database engine update the indexes due to the inserted/updated/deleted data.
Because <code>SELECT</code> doesn't modify data, there is no ind... | https://dba.stackexchange.com |
163,654 | [
"https://mathoverflow.net/questions/163654",
"https://mathoverflow.net",
"https://mathoverflow.net/users/42695/"
] | Do You know any successful applications of the geometric group theory in the number theory? GTG is my main field of interest and I would love to use it to prove new facts in the number theory.
| To expand on my answer above, consider the sequence $\dots\subset Y_2\subset Y_1$
of spaces where $Y_i=X_i$ for $i\leq n$ and $Y_i=X_n$ for $i>n$.
Milnors proof proceeds by taking $M_i$ to be the mapping cylinder of $X_{i+1}\rightarrow X_i$ and $M_0$ the cone over $X_0$ with vertex $t$. Then one takes the union $... | Here is a counterexample, which is probably not "nice". Let $X$ be the Warsaw-circle. Let $X_n$ be the obtained from the Warsaw-circle by thickening the limit inverval by $1/n$. The intersection of all the $X_n$'s is the Warsaw-circle, and its first homology vanishes.
Each $X_n$ is homotopy equivalent to $S^1$ and th... | https://mathoverflow.net |
188,465 | [
"https://electronics.stackexchange.com/questions/188465",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/83675/"
] | I couldn't really figure out this issue. Raspberry Pi 2 has 1GB of RAM, 900 Mhz Quad Core ARM Cortex-A7 processor and so on. On the other side we have Cortex-4 processor 256Kb RAM. Other peripherals also points to Raspberry pi. However they have almost the same price.
Please do not judge me, because I think I am missi... | RPi is a full-featured, ready-to-use product. It is mass-produced and used widely mostly by individuals. Contrary, Discovery boards , as many of other evaluation boards are <em>development tools</em> used, as named, for evaluation of a specific technology in order to make <em>another</em> product, potentially with much... | To expand a bit further than Eugene's answer of price being dependent on manufacture quantity, which is very astute and correct (100's of thousands RPi vs 1000's at best of Experimenter boards per edition),
There is a big difference in the application of a Cortex-M series core and a Cortex-A series (multi-)core.
An A... | https://electronics.stackexchange.com |
6,737 | [
"https://scicomp.stackexchange.com/questions/6737",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/110/"
] | I'm implementing a very simple Susceptible-Infected-Recovered model with a steady population for an idle side project - normally a pretty trivial task. But I'm running into solver errors using either PysCeS or SciPy, both of which use lsoda as their underlying solver. This only happens for particular values of a parame... | You've identiifed the key problem. Certainly the primal <em>can</em> be solved directly by, say, a quadratic programming solver. But typical QP solvers often don't scale well to large problem sizes. A projected gradient method can often scale to significantly larger problems---but only if the derivatives and projection... | I would guess that the main reason for solving the max margin task in the dual is that the dual formulation permits the use of kernel functions. And therefore it is easy to transfer the input points implicitly to some other feature space where the two classes are separable. In your above formulated task (hard margin) t... | https://scicomp.stackexchange.com |
559,715 | [
"https://physics.stackexchange.com/questions/559715",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/267509/"
] | I'm looking for a short explanations describes the difference between the magnetic flux and magnetic flux density in the most easiest way.
| An atom and a quark are very different objects. A quark is a fundamental particle, whereas an atom is a made up of many fundamental particles (quarks and electrons) which are continually exchanging other fundamental particles such as photons and gluons.
To keep things simple, let's suppose your hypothetical universe ju... | With Quantum Mechanics (actually quantum field theory) there is no single elementary particle, but "the electron field", the "quark field" etc and their excitations (little waves in the field that we call elementary particles). OK, you can remove the "quantum fluctuations" (namely the brot... | https://physics.stackexchange.com |
29,262 | [
"https://stats.stackexchange.com/questions/29262",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11577/"
] | A researcher knows that the probability that a person will respond his letter is 10%
If the researcher sends a post-paid letter the probability that the reciever will respond is 40%. The researcher sends 5 post-paid letters and 5 non post-paid letters.
What is the probability that he recieves less then 3 responses?
A... | Think of it this way - overall, there's a significant difference, but it's a little hard to say exactly which two are significantly different. Alternatively, consider the chances of having three p-values less than 0.1 (even though they aren't independent of each other) - pretty small, right? So, again overall, we mig... | The same thing can happen with the ANOVA test when normal distributions can be assumed. The differences beteween the three is apparently just large enough to see that they are different but not quite large enough to distinguish the difference between pairs. Note the overall p-value is a little less than 0.05 and each... | https://stats.stackexchange.com |
548,021 | [
"https://physics.stackexchange.com/questions/548021",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167103/"
] | Suppose a mass of <span class="math-container">$M$</span> kg is hanging from a spring in earth. The mass will stretch the spring about <span class="math-container">$x$</span> m. So the change in the gravitational potential energy is <span class="math-container">$mgx$</span> J (supposing <span class="math-container">$x$... | Imagine that when you attach the mass to the unstretched spring you are holding the mass in you hand. You then gently lower the mass until the uplift <span class="math-container">$kx_{\rm max}$</span> of stretched spring just balances the dowward weight <span class="math-container">$mg$</span> of the mass. Gravity... | If there is <em>just</em> the (ideal) spring and a mass, i.e., if there is no dissipation, the total energy <span class="math-container">$E$</span> of the system is constant and is the sum of three terms:
<span class="math-container">$$E = mgh + \frac{1}{2}kz^2 + \frac{1}{2}m\dot{z}^2 = U_g + U_s + T$$</span>
where <... | https://physics.stackexchange.com |
352,453 | [
"https://softwareengineering.stackexchange.com/questions/352453",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/275260/"
] | So far I have used to write interfaces to those classes I want to mock/fake. Reason for that is that those classes don't have any virtual method to overwrite. But resently I have figured out that I could use virtual methods also.
When should I use virtual methods rather than interfaces?
Should I even make most of me... | How would virtual methods help? The idea of mocking is that you rip out a class <em>completely</em> from your application and plug in a completely different mocked class, with the only thing in common that they both implement the same interface. Inheritance doesn't come into the game at all.
| I favour making methods virtual over extracting an interface. The performance hit is negligible. In Java, where methods are virtual by default, people don't worry about this nearly as much.
I've seen far far too many codebases where every class has a corresponding interface in the same namespace. It makes the project c... | https://softwareengineering.stackexchange.com |
552,060 | [
"https://electronics.stackexchange.com/questions/552060",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/278690/"
] | Im trying to read/write EEPROM byte by byte but if i dont put an enough delay(~1ms) between read/write tasks, im getting or writing wrong value to the EEPROM. But this delay is taking a significant time when there is a many bytes to read/write and 400kHz losing its meaning. Am i missing something ? or its a nature of b... | Yes, you are missing the time it takes to write anything, even if the bus is 400kHz.
The first page of 24LC64 says that a page write is max 5ms. You can write one byte or up to 32 bytes (a full page) at once but it can still take up to 5ms.
So after a write operation, the EEPROM will be busy writing the data and will n... | EEProms require some minimum amount of time to write a page or single byte to memory. Most production code will poll the device (WB bit) to see when this write has finished. In your case, the 1ms probably allows this time to finish.
It is going to be more efficient to write by pages rather than bytes, you only have t... | https://electronics.stackexchange.com |
441,609 | [
"https://softwareengineering.stackexchange.com/questions/441609",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/421693/"
] | I have an interface that looks like this:
<pre><code>public interface IInterface<T> where T : IParameterType
{
void InterfaceMethod(T param);
}
</code></pre>
And a lot of implementations of this interface, each with a different derived type for T.
I can't change the interface.
Now I want all the implementatio... | I suppose the canonical way to do this would be to derive the implementations from a common base class.
<pre><code>public class InterfaceBase<T>
{
// Constructor
public Interface<T>()
{
// Call your common method here ...
CommonMethod();
}
public virtual void InterfaceM... | I've added this answer in response to your comment:
<blockquote>
I am OK with making the implementors derive from a base class but was hoping to avoid making them have to remember to call <code>base.InterfaceMethod</code>
</blockquote>
You can enforce this behavior without requiring derived classes to manually call the... | https://softwareengineering.stackexchange.com |
67,144 | [
"https://softwareengineering.stackexchange.com/questions/67144",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22667/"
] | We are trying to develop a website that automate an organisation process. This company, let's called it Acme Limited, usually ask their clients to submit paper form and have the clerks to manually enter those form into the internal system. At the moment they have 60 clients across the state.
Now, Acme Ltd wants their ... | You need customer <em>representation</em>. That's an important word. Agile development doesn't mean get all your users in the process of creating the app. A core component is getting your client involved--but your client and your users are many times different groups of people. Your client has business goals they w... | You need to incorporate the customer in any process, but if your end user is the general public or a large population of remote clients you usually won't actually have them in person. Instead you will have someone like a program manager or business analyst who represents the customer to the rest of the team. It is the ... | https://softwareengineering.stackexchange.com |
132,097 | [
"https://electronics.stackexchange.com/questions/132097",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54530/"
] | I'd like to know if there is some magnet in the rotor or in the stator of the generator? Or neither of those (rotor & stator) need a magnet for the current to flow?
| If you need a bandwidth of B=440-220=220 Hz the center frequency will be app. at Fo=311 Hz. As a consequence, the required <strong>quality factor</strong> of your bandpass will be <strong>Q=311/220=1.4</strong>
Please note that it is NOT possible to realize a bandpass with such a selectivity based on the mentioned app... | If you put the low blocking stage first, your first capacitor will be very close to zero impedance to the higher frequency signal being cut off by your high blocking capacitor.
If you put your high blocking stage first, your high blocking will be close enough to high impedance to at low frequencies to have little effe... | https://electronics.stackexchange.com |
314,101 | [
"https://electronics.stackexchange.com/questions/314101",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/153730/"
] | I am completely new to assembly, and I must develop a counter using PIC16F628A, a push button, and a display. Additionally it there will be an external oscillator (555).
I made some progress on this, but I think I need some help from you people.
At first I did a delay based on decrements in order to be able to watch n... | Since you cannot use a timer (gathered from comments you've made), you need a suitable delay routine to provide a specific period of time. I like the period of \$8\:\textrm{ms}\$, from prior experience. But you can use any period you feel is appropriate. Assuming that your processor is using the factory calibrated \$4\... | You need to "debounce" your switch. This can be done in hardware by adding a small capacitor across the input or in software by checking that the switch maintains its state for long enough.
<blockquote>
Now the other problem is that I need to add the value of 1 once and only once while pressing the button. Imagine t... | https://electronics.stackexchange.com |
230,598 | [
"https://security.stackexchange.com/questions/230598",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/176187/"
] | I work in a Software Company. Currently, we don't have any security software to secure our data in an employee laptop. Now we want to make a policy where any data stored or created on the company laptop and server must not get outside of the internal network. This includes securing these scenarios:
<ul>
<li>Any data f... | First, you are dealing with developers. They are known to sidestep and bypass everything that stands in their way. No matter what protections you setup, a developer will bypass it sooner or later. And tell the others.
<blockquote>
Data can be a copy or moved inside the company internal network
</blockquote>
You ca... | Your plan is full of holes. and these cannot be fixed.
if you allow PDFs out you allow anything that can be converted to pdf out.
if you allow any email out source code can be copied and pasted into an email.
if you allow web access source code can be copied and pasted into gmail.
I think the only solution is to ke... | https://security.stackexchange.com |
113,027 | [
"https://cs.stackexchange.com/questions/113027",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/22714/"
] | Suppose we have a set of variables <span class="math-container">$V$</span>. We also have a set of equations <span class="math-container">$E$</span>, which are sets of at least two variables. We don't know anything about these equations, except if we know all but one of the variables in an equation, we can deduce the mi... | <blockquote>
Can anything change in a computer without the user modifying something, also while not having internet connection?
</blockquote>
Yes, definitely - computers update their own states all the time, and some of these changes will be persistent from one boot cycle to the next.
The computer itself is a compl... | <blockquote>
Can anything change in a computer without the user modifying something
</blockquote>
Yes, definitely. Most obvious example: the clock, it changes all the time!
Other examples of environmental factors that change without the user actively manipulating them, are temperature and humidity. Temperature infl... | https://cs.stackexchange.com |
179,850 | [
"https://dba.stackexchange.com/questions/179850",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/126277/"
] | This is my update query :
<pre><code>Update fa set dynamicl52 = 0
where catno in (0,1,2,3,4,5,6,7,8,9,10,11) and year in (201605,201606);
Update fa set dynamicl26 = 0
where catno in (0,1,2,3,4,5,6,7,8,9,10,11) and year in (201611,201512);
Update fa set dynamic_l13_weeks_flag = 0
where catno in (0,1,2,3,4,5,6,7,8... | It might some help you.
<pre><code>-- Sample Data
DROP TABLE new_test.fa;
CREATE TABLE new_test.fa(
id INT PRIMARY KEY AUTO_INCREMENT,
catno INT,
`year` INT,
dynamicl52 INT,
dynamicl26 INT,
dynamic_l13_weeks_flag INT,
dynamiclm1 INT,
KEY (`year`),
KEY (catno));
INSERT INTO new_test.fa(catno,year,dynamicl52,dynamicl2... | here below is an example
<pre><code>-- example table with data
create database if not exists test ;
use test;
drop table if exists test.table1;
CREATE TABLE if not exists test.table1 (
id INT(10) NOT NULL,
value INT(10) NOT NULL,
PRIMARY KEY (id));
insert into table1 values (1,1);
insert into... | https://dba.stackexchange.com |
73,146 | [
"https://physics.stackexchange.com/questions/73146",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26419/"
] | Ohm's Law tells us that $V = IR$. This implies that $I \propto \frac{1}{R}$. But, $R \propto l$, where l is the length of the conductor. This would mean that $I \propto \frac{1}{l}$. But this does not fit with the definition of current that says that current is the amount of charge $Q$ passing through a given point per... | For a <em>fixed</em> voltage $V$, it is true that the current in a conductor having a fixed resistivity and cross-sectional area will decrease as the inverse of its length as you have indicated. Thus, under these circumstances, the statement
<blockquote>
Clearly, the amount of charge passing through a given point p... | The main form of the Ohm's Law (which is valid in some specific conditions) is actually the following:
$$\vec J=\sigma \vec E\tag{1}$$
where $\sigma$ is the conductivity of the medium (usually an inherent property of the matter, so a constant in our calculations) and $\vec J$ and $\vec E$ are current density and electr... | https://physics.stackexchange.com |
63,137 | [
"https://physics.stackexchange.com/questions/63137",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23922/"
] | I have a homework question that I'm completely stumped on and need help solving it.
I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at $25\, \mathrm{C}$.
No heat is lost to the surroundings and there is negligible heat loss to the container. I have to fin... | For the melting process You should use $Q=mc\Delta T_1+mL_f + mc\Delta T_2$, assuming that after the ice cube melts, there is still heat exchange between the warm water and the cold water (former ice cube) and $\Delta T_2$ is the temperature difference between the final temperature of the mixture and the melting temper... | The actual way hinges on the fact there is infinitesimal change in temperatures if they are not undergoing phase changes. Hence there will be $dT$ term inside the integral if they are not undergoing phase change. Otherwise the entropy chage is simply $Q/T = mL_{f}/T$.
So Hint: Hence you would end up seeing 2 terms (a... | https://physics.stackexchange.com |
1,470,344 | [
"https://math.stackexchange.com/questions/1470344",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/197270/"
] | Can someone explain how the homomorphism $\phi : S_4 \to S_3$ works?
Artin defines the partitions $\pi_1 : \{1,2\} \cup \{3,4\} $, $\pi_2 : \{1,3\} \cup \{2,4\} $, $\pi_3 : \{1,4\} \cup \{2,3\} $. Then he defines the map $\phi$ from $S_4$ to the group of permutations of the set $\{ \pi_1, \pi_2, \pi_3 \}$.
What I do ... | Let's examine more closely how $p$ acts on the different $\pi_i$s:
$$p(\pi_1)=p \left( \{1,2\} \cup \{3,4\} \right)=\{p(1),p(2)\} \cup \{p(3),p(4)\}=\{2,3\} \cup \{4,1\}=\{1,4\} \cup \{2,3\}=\pi_3 $$
Similarly, one can show that
$$p(\pi_2)=\pi_2 $$
and $$p(\pi_3)=\pi_1.$$
Thus, when viewed as a permutation of $\{\... | Let $\{a, b\}\cup \{c, d\}$ be one of $\pi_1, \pi_2, \pi_3$, where $\{a, b, c, d\} = \{1, 2, 3, 4\}$. Then $\phi$ is defined by
$$\phi(p) (\{a, b\}\cup \{c, d\}) = \{p(a), p(b)\} \cup \{p(c), p(d)\}.$$
For example, if $p = (1234)$, then
$$\begin{split}
\phi(p) (\pi_1) &= \phi(p) (\{1, 2\} \cup \{3, 4\}) \\
&am... | https://math.stackexchange.com |
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