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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27,627 | [
"https://quant.stackexchange.com/questions/27627",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/22099/"
] | The London Interbank Offered Rate (LIBOR) is an indicative average interest rate at which a selection of banks (the panel banks) are prepared to lend one another unsecured funds on the London money market.
LIBOR is currently calculated for 5 different currencies, including the USD.
If LIBOR denominated in USD is calc... | It depends on the purpose for which you want to use LIBOR. If you want to use it as a measure of risk free rate, then it is not a good idea, because it included premiums for interbank lending credit risk and liquidity risk. You should use the rate on short term US treasuries for risk free rate (again it depends on the ... | Yes, in general it is. If you take a look at the banks that contribute to the Libor you'll see why:
<ul>
<li>Bank of America </li>
<li>Bank of Tokyo-Mitsubishi UFJ </li>
<li>Barclays Bank </li>
<li>BNP Paribas </li>
<li>Citibank NA </li>
<li>Credit Agricole CIB </li>
<li>Credit Suisse </li>
<li>Deutsche Bank</li>
<li>... | https://quant.stackexchange.com |
514,686 | [
"https://physics.stackexchange.com/questions/514686",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70544/"
] | It is my understanding that observers outside the black hole wouldn't ever see some infalling object enter the black hole, as the object's clock would be running so slow in the observer's reference frame that it would essentially freeze near the event horizon.
However, it is also my understanding that the "gravitatio... | Although I haven’t seen any calculation of this, I think that the gravitational field of a small perturbing mass outside a black hole actually becomes centered on the hole, not on the small mass, as the mass approaches the event horizon.
I think this because something similar happens with a point charge held stationar... | Oh, this is an interesting calculation I once did. To start off, lets imagine we have a box with a photon of wavelength <span class="math-container">$\lambda$</span>. Now we'll have a spherical shell of mass and shrink it down from infinity to a smaller finite size. It will envelope the box and give it time dilation <s... | https://physics.stackexchange.com |
38,344 | [
"https://mathoverflow.net/questions/38344",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4903/"
] | Of course, no continuous real valued non-constant function can attain only rational or irrational values, but can there be a pair of nowhere-constant continuous functions f and g such that for all x, at least one of f(x) and g(x) is rational? Or maybe a countable collection of continuous functions, {f1, f2...} such tha... | If you allow the functions to be constant on some intervals, then there are some easy examples, and Ricky has provided one.
But if you rule that out, then there can be no examples, even with countably many functions. To see this,
suppose that $f_n$ is a list of countably many continuous functions which are never cons... | Since your functions are locally non-constant, the preimage of any (rational) point is nowhere dense (in $\mathbb{R}$; if a preimage of a point with respect to a continious function is dense on an interval, then the function is constant on this interval). Hence the union of all preimages of all rational points is of Ba... | https://mathoverflow.net |
451,422 | [
"https://physics.stackexchange.com/questions/451422",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/205198/"
] | Sorry if there this is a duplicate but I can't find anything that deals with this.
I have a point charge <span class="math-container">$q$</span> sitting at the origin. It takes no work for me to put it there.
Then, I bring <span class="math-container">$-q$</span> out from infinity and spread it around over a sphere o... | A stiffer spring (larger <span class="math-container">$k$</span>) means that for a given extension the force exerted by the spring is larger than for a less stiff spring (smaller <span class="math-container">$k$</span>).<br>
This in turn means that the acceleration of the mass is larger for a stiffer spring and so the ... | A stiffer spring means more force is needed to extend/compress it. Hence, the restoring force of the spring back to its equilibrium position is greater; acceleration is greater. Hence period is definitely lower, as the spring moves faster.
| https://physics.stackexchange.com |
140,235 | [
"https://softwareengineering.stackexchange.com/questions/140235",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12697/"
] | For example, there are some key-value configuration in .properties file. Such like <code>someFeatureEnable=true</code>. It must be bool type value which will be parsed by framework, in my case it's typical Java Spring configuration. Spring will handle the configuration and throw Exception when users set <code>someFeatu... | If a property is trivial (i.e. it merely returns a value), no, I don't write a unit test for it.
Instead, I rely on the unit tests that prove that the framework parser works, and unit tests that prove that the code that depends on the property settings works.
If there is a problem reading the properties (because on... | I beleive that you should write tests for the accepted properties that you've defined (i.e. The enum of properties that are valid). However, as these can be changed on the fly at runtime a far mor eimportant test is an integration style test (perhaps unit depending on your design) that tests your property parsing cod... | https://softwareengineering.stackexchange.com |
7,705 | [
"https://dsp.stackexchange.com/questions/7705",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/1894/"
] | I'm trying to create a seamless loop using a "non-periodic" signal using interpolation to smooth out the beginning and the end but I'm still getting a click at the beginning when it loops and I listen to it. Can interpolation do this?
Please Note that the equation is done this way to create a "non-periodic" signal t... | Not sure if I understand it correctly, but assuming this is your problem:
<code>I have a signal that i want to repeat, but the beginning is not at the same level as the end</code>
The solution can be quite straightforward:
Calculate the trend <code>(end-begin)/length</code> of interval and correct the sound value at ... | An alternate method is to create an array of two copies of your input signal
<pre><code>y = [ x , x ] % MATLAB
y = hstack(( x , x )) # NUMPY
</code></pre>
Run $x[k]$ through a LPF. Then slice $N$ samples from the "middle" of $y[k]$ where $N$ is the length of $x[k]$.
<pre><code>xsmooth = y( o : o + N - 1) % ... | https://dsp.stackexchange.com |
26,015 | [
"https://cs.stackexchange.com/questions/26015",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/17884/"
] | I am having trouble giving the description of a Turing machine that goes for
$L = \{0^n 1^m 0^n 1^m \mid m,n \geq 0\}$. What I have so far is:
If we start with a blank, the string is empty and it should accept, if not, start reading $0$s and I thought marking the $0$s with $X$ and the $1$s with $Y$ would be OK. After ... | What I tend to do when it comes to counting with a tape is to go back and forth on the tape, marking the relevant portions of the tape as I'm reading new input.
<strong>Example</strong><br>
To recognize the language $0^n1^n$ with a Turing machine (not that you'd need the power of a Turing machine, but for illustrati... | Turning Machine compares such numbers by zig-zaging across the tape. It can mark first 0 from first $0^n$ and go to all the way across 1s to mark first 0 from second $0^n$, then return back to first $0 ^n$ to mark second 0 and so on.
And yes, you don't need extra tape alphabet Y. X can do fine for 1s too without confl... | https://cs.stackexchange.com |
417,493 | [
"https://mathoverflow.net/questions/417493",
"https://mathoverflow.net",
"https://mathoverflow.net/users/475617/"
] | A copy of the Cantor set is a space homeomorphic to <span class="math-container">$2^{\omega}$</span>.
Suppose that <span class="math-container">$X$</span> is a Hausdorff space that contains a copy <span class="math-container">$C^{\prime}$</span> of the Cantor set. Let <span class="math-container">$U$</span> be a nonemp... | To answer the question: every point of <span class="math-container">$U$</span> is an accumulation point of <span class="math-container">$D\cap U$</span>, hence there are continuum many accumulation points. The ambient space <span class="math-container">$X$</span> plays no role here; everything takes place in the Cantor... | If <span class="math-container">$A\subseteq X$</span>, denote by <span class="math-container">$A^{\mbox{d}}$</span> the set of accumulation points of <span class="math-container">$A$</span>. Thanks to YCor, Saúl Rodríguez Martín and KP Hart. Putting together the previous ideas and being more explicit, we have that:
As ... | https://mathoverflow.net |
3,278,518 | [
"https://math.stackexchange.com/questions/3278518",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/494340/"
] | I'm a noob in abstract algebra. So, I beg pardon for all my mistakes and misconceptions ahead.
My confusion actually arises considering vector space. As far as I know a vector space V over a field F is just an abelian group which must have one special function: "scalar multiplication" defined.
Now is a vector space o... | In a slight variant on @MinusOne-Twelfth's comment,<span class="math-container">$$\frac{\partial}{\partial\beta_i}(y-X\beta)_j=-X_{ji}\implies\frac{\partial}{\partial\beta_i}\sum_j(y-X\beta)_j^2=2\sum_jX_{ij}^T(X\beta-y)_j=2(X^\prime X\beta-X^\prime y)_i.$$</span>Setting this to <span class="math-container">$0$</span> ... | Our goal is to minimize
<span class="math-container">$$
f(\beta) = \frac12 \| X \beta - Y \|^2.
$$</span>
Notice that <span class="math-container">$f = g \circ h$</span>, where <span class="math-container">$h(\beta) = X \beta - Y$</span> and <span class="math-container">$g(u) = \frac12 \| u \|^2$</span>. The derivative... | https://math.stackexchange.com |
78,713 | [
"https://physics.stackexchange.com/questions/78713",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23094/"
] | I'm confused by my books treatment of the Schrödinger equation. In steado f listing my questions at the end of my post, I'll add them as questions in parentheses after the line in question.
For a free particle:
$$i \hbar \left| \dot{\Psi} \right \rangle = H\left| \Psi \right \rangle = \frac{P^2}{2m}\left| \Psi \rig... | Just adding some precisions to @AlfredCentauri 's answer.
When you use a ket notation $|p\rangle$, or $|E\rangle$, or $|x\rangle$, <strong>by definition</strong>, these kets are eigenvectors of their corresponding operators :
$P|p\rangle=p|p\rangle, \quad H|E\rangle = E |E\rangle, \quad X|x\rangle = x|x\rangle$
... | <blockquote>
(where did the potential go?)
</blockquote>
A potential implies a force and a <em>free</em> particle is not under the influence of a force (else it wouldn't be <em>free from force</em>).
<blockquote>
this follows from the eigen-equation, where the eigenvalue must be
equal to E?
</blockquote>
It is... | https://physics.stackexchange.com |
328,339 | [
"https://softwareengineering.stackexchange.com/questions/328339",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/180222/"
] | If I met all requirements on version 1.0 and go on working towards version 2.0, new features would be 1.1, 1.2, 1.3, and so on. What do I version the commits that represent an important fix or a forgotten feature which is required in version 1.0? Even if I didn't version fixes on version 1.0, there would still be two v... | The way to look at this is not a matter of copy vs. move vs. immobility. It's two separate questions:
<ol>
<li>Mobility vs. immobility. Do you want it to be able to transfer the contents of the object to another object in some way?</li>
<li>If it's mobile, then is it fully copyable or move-only?</li>
</ol>
The thing ... | You are correct that determining whether a type should be copyable or not is usually pretty straightforward. For example, it makes no sense to copy an object that represents an open network connection.
For moveability, the important question to ask yourself is whether you expect users to maintain multiple long-lived r... | https://softwareengineering.stackexchange.com |
9,405 | [
"https://stats.stackexchange.com/questions/9405",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/4098/"
] | I have two random poisson variables $x_1$ and $x_2$ with value 10 and 25 respectively. I am interested to use likelihood ratio test to test the null hypothesis: $\lambda_1=\lambda_2$, versus alernate hypthesis $\lambda_1$ not equal to $\lambda_2$.
I want to use simulation to calculate power and alpha values. I would w... | As we have strong reasons to believe that the cooling will follow the $y(t) = a + e^{-kt}$ function for each beaker I would first check if this model fits the data well indeed.
If it does I wouldn't bother with analysing the autocorrelation at all, but focus on the estimation of $k_1$, $k_2$ and $k_3$, and testing the... | If I understand your question correctly, you should be able to achieve what you want to do using a non-linear mixed-effects model. If you use R, you can use the <code>nlme</code> package. Basically as fixed factors you have a covariate (a) and a factor (substance or $i$ in $k_{i}$). You also have a random effect (indiv... | https://stats.stackexchange.com |
187,470 | [
"https://softwareengineering.stackexchange.com/questions/187470",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/81816/"
] | I know that profiling is useful to identify bottlenecks and determining what parts of the code require how much time to execute. The latter isn't always very easy to track in the midst of other paths being executed, so once I decide what I want to optimize it might be problematic to see the improvement in numbers. This... | <blockquote>
once I decide what I want to optimize it might be problematic to see
the improvement in numbers.
</blockquote>
One has to wonder whether you've really found a bottleneck, and also whether you've really eliminated one, if you can't see the effect in the profiler.
<blockquote>
This is especially true... | <blockquote>
In such cases, can I somehow use a profiler to determine improvement [...]?
</blockquote>
Of course. The timings you get not only help to determine improvement but you can see how hotspots move around in the process, getting very informed feedback of how your changes are affecting critical execution pat... | https://softwareengineering.stackexchange.com |
185,015 | [
"https://mathoverflow.net/questions/185015",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24942/"
] | So we've been using summations at least since the dawn of calculus. I'm wondering how the process of summing a function came to be known? Are there events that led to the invention of the summation operation? Can we attribute summations to a particular person, or persons?
How did mathematics evolve to include summa... | according to this <A HREF="http://jeff560.tripod.com/operation.html" rel="nofollow noreferrer">source</A>, the summation symbol <span class="math-container">$\Sigma$</span> was first used by Leonhard Euler in 1755:
<em>Quemadmodum ad differentiam denotandam usi sumus signo <span class="math-container">$\Delta$</span>,... | We've been adding things up since the dawn of arithmetic. The Pythagoreans knew all about figurate numbers, and how these were built up from gnomons: all they lacked was our current terminology and notation.
| https://mathoverflow.net |
326,065 | [
"https://stats.stackexchange.com/questions/326065",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/148774/"
] | I am playing with convolutional neural networks using Keras+Tensorflow to classify categorical data. I have a choice of two loss functions: <code>categorial_crossentropy</code> and <code>sparse_categorial_crossentropy</code>.
I have a good intuition about the <code>categorial_crossentropy</code> loss function, which i... | Both, categorical cross entropy and sparse categorical cross entropy have the same loss function which you have mentioned above.
The only difference is the format in which you mention <span class="math-container">$Y_i$</span> (i,e true labels).
If your <span class="math-container">$Y_i$</span>'s are one-hot encoded, u... | I have no better answer than the links and me too encountered the same question. I just want to point out, that the formula for loss function (cross entropy) seems to be a little bit erroneous (and might be misleading.) One should probably drop the 2nd term in the bracket to have simply <span class="math-container">$$J... | https://stats.stackexchange.com |
174,435 | [
"https://electronics.stackexchange.com/questions/174435",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35875/"
] | I'm starting to investigate Altera's Cyclone IV FPGA to use in my projects. Now I borrowed from neighboring company a real device with USB Baster Rev.C. I'd try to use one instead of evaluation board which I don't have for the moment.
Before I will put any code into the device I'd like to download original firmware to... | To read the device configuration, you have to connect to X5 instead of X4 (as pointed out by @Simon Richter). Change your settings to match what is shown below:
<img src="https://i.stack.imgur.com/9BaDH.png" alt="ready to examine configuration">
Click "Start" to read the configuration. When it finishes, you can set a... | There is no way to read back the current configuration.
If your development board is wired for JTAG mode, as it looks like from your screenshot, then simply writing a new configuration will update the FPGA only and leave the configuration flash alone, so a power cycle will reload the flash and everything is back to as... | https://electronics.stackexchange.com |
39,858 | [
"https://engineering.stackexchange.com/questions/39858",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/30377/"
] | Why a technology like freewheeling not used in cars to save fuel? We all know that when we move to neutral gear (coasting), the car travels farther than when it is in gear because there is no engine braking effect. I understand there is a safety issue there - but is that the only reason for not using it? What I am tryi... | If you are going down a hill, I believe coasting actually uses more fuel. The reason is that with modern fuel injection, leaving the engine in gear allows the engine to keep running without fuel being injected where as if you put the transmission in neutral (or use the clutch) the engine needs fuel to keep running at i... | I assume because added complexity of the already complex transmission and you don't spend that much time actually coasting when driving because you are usually trying to maintain a constant speed which necessitates offsetting the frictional losses.
The only time I coast is down hills when I am already accelerating due ... | https://engineering.stackexchange.com |
3,088,161 | [
"https://math.stackexchange.com/questions/3088161",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/600799/"
] | I've been thinking about the proof. Although it seems very obvious that by the definition of <span class="math-container">$F_\sigma$</span> sets, a set is an <span class="math-container">$F_\sigma$</span> set if it is a countable union of closed sets, so intuitively, a single closed set is also a collection of '1' clo... | It is indeed as trivial as you think. A union of one closed set is a countable union of closed sets.
More interestingly: every open set (in <span class="math-container">$\mathbb{R}$</span> or any metric space) is also the countable union of closed sets.
Also an open set is a <span class="math-container">$G_\delta$</... | A closed set is, by definition, the complement of an open set. A closed set is indeed an <span class="math-container">$F_\sigma$</span> set, as it is a countable union of closed sets, exactly as you said!
as for the part about singletons, well singletons are usually not open (for instance in <span class="math-containe... | https://math.stackexchange.com |
47,729 | [
"https://cs.stackexchange.com/questions/47729",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/40138/"
] | I was just thinking today that the best approach to find two smallest numbers in any array would be to first sort(ascending order) it with some efficient algorithm like <code>Quicksort</code>(Average case complexity: <code>nlogn</code>) and then access the first two members of the array in <code>O(1)</code>.
Is my app... | If you keep track of the 2 smallest elements you have seen so far as you traverse the array, then you only need to go through the array once, and for each element you compare to the larger of the 2 current smallest and if the new element is smaller, then you replace the larger of the 2 current smallest with the new ele... | No, it's not optimal. Do you know an efficient way of finding the smallest number in an array? Knowing the smallest number, could you adapt that method to find the second smallest?
| https://cs.stackexchange.com |
3,253,841 | [
"https://math.stackexchange.com/questions/3253841",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/395239/"
] | It is said that "the symplectic geomtery is rather loose, like that of rubber sheet which may be stretched by different amounts in different directions and still retain its geomtery".
But the scaling transformation, in general, is not a symplectomorphism. For example, for <span class="math-container">$(x,\xi)\in \m... | The symplectic form in <span class="math-container">$\Bbb R^2$</span> is the area form, so any scaling done in one direction must be undone in the other direction, as to preserve area. Such a scaling will be a symplectomorphism if and only if <span class="math-container">$b = 1/a$</span> (in view of your calculation, t... | In you example, if you are stretching the two directions, one with <span class="math-container">$a$</span> and the other with <span class="math-container">$1/a$</span>, then the "geometry is preserved". In this sense, it only means that the symplectic form is preserved (which means the area is preserved, in two dimensi... | https://math.stackexchange.com |
25,584 | [
"https://security.stackexchange.com/questions/25584",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | I have a digital certificate that I use to exchange messages with peers, my certificate expiration date is due next year, suppose I renew this certificate before it expires, will I be able to open the received messages signed/encrypted with the old certificate? Will my peers be able to open the sent messages signed/enc... | It would depend on what is involved in the certificate renewal. Certificate expiration prevent a compromised key from being used forever. It may be possible to reuse the same private/public key for another valid period or it may not be depending on the CA, since they may prefer to assume that a private key may have b... | What "opens" (decrypts) a message is not the certificate, but the <em>private key</em>. The certificate contains the public key, which is mathematically linked with the private key, and is used to <em>encrypt</em> messages.
When the certificate is expired, people stop using it; that is, they will stop encrypting new m... | https://security.stackexchange.com |
4,863 | [
"https://dsp.stackexchange.com/questions/4863",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/3203/"
] | Hi I am just toying around with compression now that we are learning about Fourier transforms in my class (compression is not a part of the class but I became a bit curious). Trying to do this with a wav file and I have some questions.
Assume I don't know the sampling rate of the signal (.wav) how can I figure out wha... | As some comments have pointed out, there are a couple of practical ways to find out the sampling rate:
<ul>
<li>Read the sampling rate information from the WAV file header</li>
<li>Look for mains hum in the recorded audio, which you'd see as a peak in the FFT response in the frequency bin corresponding to 60 Hz (or ma... | "Is there any clever trick in storing the coefficients of a real signal (wav)? "
Yes, there was a variation of the FFT called the Hartley transform that enjoyed modest popularity some years ago, but overall didn't actually save any trouble or clock cycles.
The key was to use a 45-degree shifted sine wave, not cos or... | https://dsp.stackexchange.com |
342,062 | [
"https://softwareengineering.stackexchange.com/questions/342062",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/261951/"
] | I have 3 types of users who might login to my website: Admin, Instructor, Student.
I already have tables for Students and Instructors , and each one has its unique properties .
Now I want to create the login page. Many tutorials use role-based authentication in similar cases, but In my case , I have already create... | Do the simplest thing that could possibly work. If the user in itself also dictates the role it has, then spend no further effort separating them. Can always do that later.
You could add an 'account' table and create foreign keys towards it, you'd have one table to check login name and password and thereafter you can... | People are just people.
An instructor can take a class, and thus, be a student. An admin may also instruct. A student may take several classes, and thus have several instructors. So, it is best not to conflate the notions of a person's identity with the role(s) they play and to accommodate that roles they play ar... | https://softwareengineering.stackexchange.com |
126,266 | [
"https://electronics.stackexchange.com/questions/126266",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/34488/"
] | I'm relearning things I lost since college. I remember you have to flip the sign in \$1/(j\omega C)\$ if you want to turn it to \$j/(\omega C)\$, but I do not remember why.
Is there an empirical method for understanding this, so I don't just "do"?
Is there a comprehensive review source for everything DSP, filters, et... | This is more of a question for math.stackexchange, but remember that \$j = \sqrt{-1}\$. Therefore, \$\frac{1}{j} = \frac{1}{\sqrt{-1}}= \frac{\sqrt{-1}}{-1}=-\sqrt{-1}=-j\$. Note that I multiplied by \$\frac{\sqrt{-1}}{\sqrt{-1}}=1\$ to get rid of the square root in the denominator.
| Since, by definition
$$j \cdot j = -1$$
we have
$$-j \cdot j = 1$$
thus
$$-j = \frac{1}{j} $$
| https://electronics.stackexchange.com |
670,618 | [
"https://physics.stackexchange.com/questions/670618",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/307108/"
] | While I was trying to derive Kepler's third law of planetary motion, I tried the gravitational force for the Earth method which goes something like this:
<span class="math-container">$$\frac{mv^2}{r}=\frac{GMm}{r^2}$$</span>
<span class="math-container">$$\Rightarrow\frac{4\pi r^2}{T^2}=\frac{GM}{r}$$</span>
From furth... | Clearly, <span class="math-container">$L$</span> varies with <span class="math-container">$r$</span> somehow. So, let's work from first principles; in fact, let's not restrict ourselves to circular orbits. The Binet equation proves closed orbits are elliptical with semi-latus rectum <span class="math-container">$\ell=\... | Even though the argument is completely general, let me confine to the simple case of circular motion.
The first derivation mentioned in the question is valid. The starting formula, equating the expression of the modulus of acceleration in a uniform circular motion to the acceleration due to Newton's force, is valid for... | https://physics.stackexchange.com |
75,966 | [
"https://dsp.stackexchange.com/questions/75966",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/58033/"
] | I have a couple of datasets that show a peak around the 50-60 Hz range (mostly around 55Hz and in some cases at their harmonics i.e. 100-120Hz.) In some datasets the spike is significant in comparison with other frequencies.
Before I analyse the data, I need to ensure that these spikes are not interfering with my analy... | Well, if I were doing this from scratch, I would do this with biquad notch filters with very high Q and adjustable coefficients. Two or three of them with frequencies that are harmonically locked. An algorithm could be measuring the difference between the notches and a "wire" and very slowly adjust the fund... | RBJ's answer is a good suggestion but can potentially result in significant phase distortion. If that's a problem, here is an alternative approach:
<ol>
<li>Use a PLL to track the line frequency. Since line frequency only varies slowly over a very small amount, a fairly simple PLL will do</li>
<li>Track amplitude and p... | https://dsp.stackexchange.com |
212,734 | [
"https://softwareengineering.stackexchange.com/questions/212734",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102854/"
] | Sometimes when I create an API that should enable getting a single value or all values I use the following pattern (passing <code>NULL</code> to the API, means get all rows):
@Usernames - comma separeted list of users
<pre><code>CREATE PROC GetUsers (@Usernames VARCHAR(100) = NULL)
AS
BEGIN
SELECT *
FROM User... | Your question title is different from the question within your posting, so I try to answer both questions.
IMHO it is a perfectly valid idiom to have a function with an optional filter condition, and when you leave that filter out, you get the full unfiltered result set. That's true for SQL as well as for many other p... | Create another procedure named <code>GetEmployeesDetails</code>.
Your procedure is named <code>GetEmployeeDetails</code>, so the procedure should only do one thing: get the details of an employee.
You're making it do other things than what its name says if it returns something else than the details of <em>one</em> em... | https://softwareengineering.stackexchange.com |
247,898 | [
"https://mathoverflow.net/questions/247898",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34951/"
] | In a recent research work, I have come across the following nice identity, where the entries $a,b,x$ belong to an arbitrary commutative unital ring:
$$\begin{vmatrix}
2 & a & b & ab-x \\
a & 2 & x & b \\
b & x & 2 & a \\
ab-x & b & a & 2
\end{vmatrix}=(x^2-abx+a^2+b^2-4... | Here's a method for calculating the determinant, explaining at least why it ends up as a product. I don't know if there's any significance to your determinant being a square.
Define
$$H=
\frac{1}{\sqrt{2}}
\begin{pmatrix}
1 & 1 & 0 & 0 \\
1 & -1 & 0 & 0 \\
0 & 0 & 1 & 1 \\
0 & 0... | The following answer is inspired by Colin's.
As noted by Colin MacQuillan, the matrix under consideration turns out to be similar to<br>
the block matrix
$\begin{bmatrix}
A & C \\
C & B
\end{bmatrix}$
where $A=2I_2+x K$, $C=a I_2+ b K$, $B=2 I_2+(ab-x) K$, with
$K:=\begin{bmatrix}
0 & 1 \\
1 & 0
\end... | https://mathoverflow.net |
279,842 | [
"https://mathoverflow.net/questions/279842",
"https://mathoverflow.net",
"https://mathoverflow.net/users/57020/"
] | Consider the following $n \times n$ upper triangular matrix with a particularly nice structure:
\begin{equation}\mathbf{P} = \begin{pmatrix}
1 & \beta & \alpha+\beta & \dots & (n-3)\alpha + \beta & (n-2)\alpha + \beta\\
0 & 1 & \beta & \dots & (n-4)\alpha + \beta & (n-3)\alpha +... | Let $A$ be the nilpotent matrix $$\begin{pmatrix}0 & 1 & 1 & \cdots & 1 \\ & 0 & 1 & \cdots & 1 \\ & & \cdots & \cdots & \cdots \\ & & & 0 & 1 \\ & & & & 0\end{pmatrix},$$ then the matrix $P$ is equal to $1 + \beta A + \alpha A^2$.
This gi... | Working out the the details of the answer given by user WhatsUp, the elements of the inverse of $\mathbf{P}$ are given by
\begin{equation}
p^{(-1)}_{i,j} =\begin{cases}
0, &i>j,\\
1, &i=j,\\
\frac{\lambda^2(1+\lambda)^{j-i-1}-\mu^2(1+\mu)^{j-i-1}}{\lambda-\mu},&i<j.
\end{cases}
\end{equation}
| https://mathoverflow.net |
211,677 | [
"https://security.stackexchange.com/questions/211677",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/190529/"
] | Is the botnet controlled broiler of servers or personal PCs?
We know the botnet can be controlled to DDoS attack, but what's the main constituent part of botnet?
I know the botnet's element maybe PC, Servers, and mobile devices, but what's the main constituent part of a botnet in general? I mean, which type element h... | It depends entirely on the botnet. Some botnets are made up entirely of IoT devices, some are entirely made up of webservers, some are all PCs, some are a mix of everything.
There is no answer to your question without further defining what you are asking about.
| From wikipedia:
<blockquote>
A botnet is a logical collection of internet-connected devices such as computers, smartphones or IoT devices whose security has been breached and control ceded to a third party.
</blockquote>
the botnet can contain many types device who can connect to Internet.
but at the present stag... | https://security.stackexchange.com |
144,321 | [
"https://physics.stackexchange.com/questions/144321",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57317/"
] | Can it ever be possible that a light ray going inside a triangular prism of refractive index n having refracting angle A undergo total internal reflection thrice before emerging out?
Note:I know it "may" be possible if the medium surrounding the prism from the three sides is different but I am asking for the case whe... | The answer is YES. See diagram:
<img src="https://i.stack.imgur.com/1lLfN.png" alt="enter image description here">
The key here is that you can write down the expressions for the angles $a_2, a_3, a_4$ in terms of the angles of the prism $\alpha, \beta, \gamma$ and the first angle $a_1$. Now $\alpha + \beta + \gamma... | This is not a complete answer, just a possible way to handle the problem.
I assume that the transversal section of your prism is a triangle with all the angles equal to 60⁰. Let's denote by A, B, C, the three corners of this triangle. Let's denote by $P_1$ the point of incidence on the prism, and then by $P_2$, $P_3$,... | https://physics.stackexchange.com |
53,331 | [
"https://biology.stackexchange.com/questions/53331",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/27739/"
] | Is spermatozoa (ie human) technically considered bacteria? I've been told it is and I've been told it isn't. Would it meet the definition? If not what is sperm considered?
| The sperm cell is a eukaryotic cell. All bacteria are prokaryotic. (doesn't necessarily mean all prokaryotic cells are bacteria). Whoever told you that it's technically considered a bacteria, must have used it as a figure of speech referring to it's characteristics.. example, the sperm cell has a flagellum, which some ... | Complement: it's not even a real being: it can't reproduce, it's almost not functioning (I'm not even sure than his DNA material is in a transcriptible form. Basically, it's a dedicated half-cell of a multicellular organism, frozen genetic packed content + a flagellum + mitochondria + enough energy to make it beat for ... | https://biology.stackexchange.com |
289,978 | [
"https://dba.stackexchange.com/questions/289978",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/228105/"
] | I am taking a SQL course and am completely stumped on this question.
Using a subquery have a query that returns:
CustomerID, EmailAddress, FirstName, LastName, '#3: Customers who have ordered than 1 product' as
queryInfo
The subquery from this query will be: All customers with who have ordered more than 1 product
Note:... | Your code has a number of issues:
<ul>
<li>You can simplify to a <code>COUNT(DISTINCT</code> here as you want the number of distinct products</li>
<li>The subquery returns <code>ProductID</code> you would need <code>CustomerID</code> instead. Since you need the grouped count, you are better off with an <code>EXISTS</c... | What is wrong? From your point of view?
But:
<ol>
<li>the subselect returns productid instead of customerid which means the data returned is wrong
</li>
<li>the customer table and product table in subselect is bot needed. You can group by productid in orderitems table and return customerid from orderheader
</li>
</ol>
| https://dba.stackexchange.com |
3,731,861 | [
"https://math.stackexchange.com/questions/3731861",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/284494/"
] | Consider two vectors <span class="math-container">$v,w \in \mathbb{R}^n$</span> and a matrix <span class="math-container">$A \in \mathbb{R}^{n \times n}$</span>. What conditions need to be imposed on the matrix <span class="math-container">$A$</span> such that <span class="math-container">$v^T A w > 0$</span>?
I und... | There is no matrix <span class="math-container">$A$</span> for which <span class="math-container">$v^TAw > 0$</span> holds for all choices of <span class="math-container">$v,w$</span>. In particular, for any choice of <span class="math-container">$w$</span>, the vector <span class="math-container">$v = -Aw$</span> i... | Assuming you're talking about a fixed pair of <span class="math-container">$(v,w)$</span>, if <span class="math-container">$A$</span> is positive definite, and if <span class="math-container">$v,w$</span> can be written as a positive linear combination of eigenvectors of <span class="math-container">$A$</span> (e.g. <... | https://math.stackexchange.com |
110,748 | [
"https://physics.stackexchange.com/questions/110748",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45596/"
] | A probe wavefunction in the variational method is <span class="math-container">$$\psi(r_1, r_2) =\frac{\alpha^6}{\pi^2}e^{-\alpha(r_1+r_2)}.$$</span> In <span class="math-container">$\left<\psi \right|H\left|\psi\right>$</span> with <span class="math-container">$$H = \frac{p_1^2+p_2^2}{2m} - \frac{Ze^2}{r_1}-\fra... | Of course, just after a day I've found the way to do it in two of my books at once
You should rewrite the denominator as follows:
$$\sqrt{r_1^2+r^2_2-2r_1r_2\cos{\theta}},$$
where $\theta$ is the angle between vectors. Then you fix Z axis collinear with $r_1$, for instance, and integrate the $\phi$-part, so you get so... | There are two ways to carry out this integral.
<strong>Method I</strong>
Write
<span class="math-container">$$
\frac{1}{|\vec{r}_1 - \vec{r}_2|} = \begin{cases}
\frac{1}{r_2}\sum_{n=0}^\infty\left(\frac{r_1}{r_2}\right)^nP_n(cos\theta) & \;\text{if}\; 0 < r_1 \le r_2 \\
\frac{1}{r_1}\sum_{n=0}^\infty\left(\fra... | https://physics.stackexchange.com |
37,639 | [
"https://electronics.stackexchange.com/questions/37639",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8376/"
] | I am thinking about building a capacitor bank between the PSU and load to smooth out current surges from electric motors. However, if the capacitors are discharging rapidly during a current surge, does that mean the PSU also experiences a current surge in order to recharge the caps, thus negating the point of a capacit... | In the end, all of the current must come from the power supply-- regardless of how many caps you have in your cap bank. What the cap bank will do is average (a.k.a. smooth) out the current over a longer and longer period of time. Ideally the cap bank would average out the current over a time period that is much large... | If the current from the PSU to the caps is not limited at all, and the PSU is capable of supplying the current, then yes, it will experience a surge of current (if there is zero resistance then the caps will do nothing - the PSU will supply the surge current)<br>
As long as the current is safely limited in some way tho... | https://electronics.stackexchange.com |
321,742 | [
"https://softwareengineering.stackexchange.com/questions/321742",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/232698/"
] | I am developing internal Android apps for the company I work for. In various places in the apps I need to connect to an internal server. This server is shutdown for maintenance for a period of time every night so there are times when it is not available. There may also be times when the wi-fi connection on the tablet ... | You are leaving the radios turned on practically the whole time and this will undoubtedly use up battery.
I do see your motivation, however. A decent compromise is to assume that the app is online unless it turns out not to be. If it turns out not to be, <em>and it would like to be</em>, then poll for a connection at... | Using a background service won't really help you. The problem is that after a succesful check for wi-fi and server you can't be sure that they are still online while you make your call to get the online data because they may went immediately offline after the succesful check.
A better alternative would be to just try ... | https://softwareengineering.stackexchange.com |
18,923 | [
"https://electronics.stackexchange.com/questions/18923",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3876/"
] | Sanity check: I need to measure the junction temperature (or as close as possible) of an SMD LED. Can I solder the tip of a thermocouple to a leg of the part? Assuming there is no ground loop (the meter is battery operated, standalone), is there anything I should be aware of?
I am assuming that the thermocouple being... | Solder a type T thermocouple to whichever pin of the LED has a better thermal conductive path to the LED die.
Type T thermocouples are copper-constantan, and are solderable, whereas the more common type J and type K are of metals that do not form a solder joint.
| Two things. First, a thermocouple is not the best way to measure LED temperature. Thermocouple signals are very small. The main advantage to thermocouples is that they are simply two metals, and as such can stand high temperatures. Thermistors give you much bigger signals and can still cover the temperature range o... | https://electronics.stackexchange.com |
222,760 | [
"https://security.stackexchange.com/questions/222760",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/219493/"
] | New to buffer overflow through image parsing. How can one design a secure library that parses images, and ensure there are no security vulnerabilities in it? It is common knowledge that image parsing libraries are vulnerable to Buffer Overflow, so I would appreciate it if someone could specifically explain how to secur... | There are a couple of obvious things which are not limited to image parsing libraries:
<ul>
<li><strong>Don't assume that the input is well-formed</strong> but actually check it. It is actually a common problem with image or video libraries that they were not designed with deliberately malformed input in mind but whic... | To expand on one point from Steffen's answer: whenever you have code that is consuming untrusted input and considered an exploitation risk - such as an image library consuming files from untrusted sources - you should look at sandboxing that code. There are a number of ways to do this, varying by things like language, ... | https://security.stackexchange.com |
1,972 | [
"https://stats.stackexchange.com/questions/1972",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1029/"
] | I have a bunch of variables organized into 10 different levels of a grouping factor. I'm doing some ANCOVA on particular variables and also plotting the data using boxplots. I'd like to add 84% confidence intervals to all the groups (since non-overlapping 84% CIs indicate a significant difference at alpha .05 - at leas... | It sounds a reasonable solution <strong>if this is what important for you to present in the plot</strong>.
What this will give you (besides many questions, in case you are working with people who like statistics less then you), is a CI that is applicable to your situation which requires correction for multiple hypoth... | For nearly equal sample sizes you can translate <em>Tukey's HSD</em> (Google it) into a set of individual CIs. For unequal sample sizes your approach may be doomed, because all pairwise comparisons cannot be reduced to pairwise comparisons of intervals: check out the literature on the <em>Tukey-Kramer Method</em> for ... | https://stats.stackexchange.com |
14,526 | [
"https://physics.stackexchange.com/questions/14526",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5164/"
] | Third Newton's law, $F_{1->2} = -F_{2->1}$
So, how does a body react with the same force that it's receiving from the acting body? Is it the electric interactions at the subatomic level? When we sit on the chair, does that mean we are just bringing our electrons in contact with the electrons of the chair and get... | If you have charge on a ball in water, and current leaves the ball, then it is completely obvious that the exact same current enters the water. This is Newton's third law for charge--- the loss of charge for body 1 is equal to the gain in change for body 2. The reason this is always true is because charge is conserved.... | Newton's third law is equivalent to conservation of momentum, which arises, by Noether's theorem, from translation symmetry in space.
This may sound abstract and not much of an explanation, but the trouble is that the concept of <em>forces</em> is not exactly useful anymore at a subatomic level.
| https://physics.stackexchange.com |
388,506 | [
"https://physics.stackexchange.com/questions/388506",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/186020/"
] | Assuming we had a spacecraft that could accelerate up to 10% of the speed of light, what speed could be realistically reached without breaking its structure given current material science? Space debris can be ignored for this question.
| Acceleration is very different from speed. Yes, acceleration can cause stresses. But your vehicle can get to any given speed with anything from a very low acceleration (like 1 km/hour per second) to a very high acceleration (like a million km/hour per second). In the first case it takes one second to reach 1 km/hr. ... | For reaching a final speed of 10% of the speed of light, the above answers are completely correct. Speed doesn't matter, acceleration does, and even then, acceleration only matters when different parts of your ship are accelerating at different rates.
But this is only true up to a (very hard-to-reach) point, due to th... | https://physics.stackexchange.com |
418,861 | [
"https://mathoverflow.net/questions/418861",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78173/"
] | In interpolation theory, given a compatible couple of Banach spaces <span class="math-container">$(X_0, X_1)$</span> one considers the <span class="math-container">$J$</span> and <span class="math-container">$K$</span>-functionals, defined as follows:
If <span class="math-container">$x \in X_0 + X_1$</span> and <span c... | I found the motivation in Luc Tartar's book <em>An Introduction to Sobolev Spaces and Interpolation Spaces</em>. It is in the first page of Chapter 24.
I quote:
<blockquote>
The K-method is the natural result of investigations which originated in questions of traces: if <span class="math-container">$u \in L^{p_0} (R_+;... | The idea of introducing K-functional is described in R. A. DeVore's article <em>Nonlinear approximation</em> p. 85.
| https://mathoverflow.net |
76,409 | [
"https://cs.stackexchange.com/questions/76409",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/73221/"
] | I am a beginner in coq and want to prove the following theorem t1. First I used <code>induction i</code> and <code>destruct j</code>, but it got bogged down in the middle.
I would like some hints for this problem.
Function f takes two arguments of nat and returns Prop (e.g., f 2 4 = x 2 ∧ x 3 ∧ x 4 ∧ x 5).
Theorem t... | First of all, let's simplify <code>f</code> just a little bit, keeping the special case when it doesn't let the trailing <code>/\ True</code> to appear in the generated proposition (I also renamed the parameter names to make them correspond to the ones used by the theorem below):
<pre><code>Fixpoint f' (i j : nat) : P... | You are making your life difficult by defining things in convoluted ways. Here's how a better definition of the same thing makes the proof easy.
<pre><code>Fixpoint f_better n0 len : Prop :=
match len with
| 0 => True
| S k => x n0 /\ f_better (S n0) k
end.
Theorem t1_better: forall n0 len,
x n0 /\ f_... | https://cs.stackexchange.com |
1,072,103 | [
"https://math.stackexchange.com/questions/1072103",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/114222/"
] | $
\sin ^2 \alpha = \frac{\tan ^2 \alpha}{1+\tan^2 \alpha}
$
$
1+\tan^2 \alpha = \frac{\tan ^2 \alpha}{\sin ^2 \alpha}
$
It is said that these two equations are equivalent. How can that be? I know that for two equations to be equivalent they must have the same set of solutions. But here the first one has solutions f... | Whenever two equations are said to be equivalent, it is worth exploring the process of going from one equation to another. In this case, we can consider performing the following sequence of operations on the first equation:
<ol>
<li>Divide both sides of the first equation by $ \sin^2\alpha $.</li>
<li>Multiply both si... | If you multiply the second equation by $$\frac{\sin^2\alpha}{1 + \tan^2 \alpha}$$ you have the first equation. Since $\tan^2 \alpha\geq 0$, this multiplication gives us no need to exclude any solutions that aren't excluded in original equation.
The second equation does have $\sin^2\alpha$ in the denominator, so we nee... | https://math.stackexchange.com |
166,397 | [
"https://security.stackexchange.com/questions/166397",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/1850/"
] | I'm just trying out <code>hashcat</code> v3.6.0 on an up-to-date Arch Linux laptop.
<code>hashcat -I</code> shows me this:
<pre><code>OpenCL Info:
Platform ID #1
Vendor : Intel(R) Corporation
Name : Intel(R) OpenCL
Version : OpenCL 1.2 LINUX
Device ID #1
Type : CPU
Vendor ID : 8
... | This message is straight from Intel's OpenCL, and hashcat just passes it along.
Intel's OpenCL has some known issues - so much so that there is usually a warning from hashcat if Intel's OpenCL is being used, which notes that errors can be overridden with <code>--force</code>. Did you see anything like that? You may be... | I encountered the same issue. Try doing <code>hashcat -I</code>, and listing how many devices you have. I found that when using <code>--opencl-device-types 1,2,3 --force</code> produced the same issue with this error:
<pre><code>clCreateContext(): CL_INVALID_PLATFORM
</code></pre>
so I didn't use device 1, and it wa... | https://security.stackexchange.com |
22,913 | [
"https://dsp.stackexchange.com/questions/22913",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/7931/"
] | I kind of expected this to of been asked before, so if this is duplicate please point me in the right direction, however I couldn't find anything.
I am currently experimenting with low pass filtering. I take an image and apply a 2-dimensional fast Fourier transform to the image, next I apply a shift such that the zero... | If your processed 2D FFT is conjugate symmetric, then any imaginary components in the complex IFFT result are just numerical noise or rounding errors. Thus using them to compute an absolute value is mostly a waste of CPU cycles.
| I happened to need solving the same question, so thanks for sharing this (although a while ago).
However I'd like to complement or even somehow correct the accepted answer. There's a big difference between abs and real: real is a linear operator, abs is NOT. Say you want to combine 2 filters by multiplying your real-si... | https://dsp.stackexchange.com |
13,165 | [
"https://security.stackexchange.com/questions/13165",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/7493/"
] | I have an account in an online banking system and they have the FAQ with something like this:
<blockquote>
<h2>How secure is the <em><Online Banking System Name></em>?</h2>
Each page you view and any information submitted on <em><Online Banking System Name></em> is encrypted between the client's com... | <blockquote>
Is it alright to tell everyone your encryption information?
</blockquote>
It's not just alright, it's actually a design feature of modern ciphers. The whole concept of cryptography is that you can freely publish the algorithm used, but must keep secret a specific piece of information, called the key.
... | The information that they're providing is relatively standard stuff. In the case of protecting data in transit, 128-bit SSL is a standard mechanism and knowning that it's in use wouldn't provide an attacker significant benefit.
On the encryption of sensitive data, apart from a niggle that they're describing hashing an... | https://security.stackexchange.com |
2,689 | [
"https://cs.stackexchange.com/questions/2689",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/2121/"
] | <h3>Definition: Karp Reduction</h3>
A language <span class="math-container">$A$</span> is Karp reducible to a language <span class="math-container">$B$</span> if there is a polynomial-time computable function <span class="math-container">$f:\{0,1\}^*\rightarrow\{0,1\}^*$</span> such that for every <span class="math-con... | No. First note that Levin reduction only makes sense with respect to classes which certificate has a meaning, e.g. $\mathsf{NP}$ while Karp reduction is general. The word "certificate" for a problem makes sense only when a verifier is fixed. Levin's reduction assumes that the verifiers are fixed. You cannot change the ... | A quick counterexample for your proof: suppose that $x_1, x_2 \in L_1$, $f(x_1) = f(x_2) \in L_2$, and $w$ is a valid certificate for $x_1$ but not for $x_2$
$M_1'(x_1,\langle 0,w \rangle)= M_1(x_1,w)=1$
$M_1'(x_2,\langle 0,w \rangle)= M_1(x_2,w)=0$
By definition $g(x_1,\langle 0,w \rangle) = \langle 1,x_1,w \rangl... | https://cs.stackexchange.com |
44,721 | [
"https://astronomy.stackexchange.com/questions/44721",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/40935/"
] | I am not able to find the diameter of the moon. I have the following question in my physics textbook:
<blockquote>
During a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.
</blockquote>
Similar question from my textbook:
... | Draw a picture of Sun, moon, observer, as viewed from the side:
<pre><code>SSSSSSSSSSSS
\ /
\ /
\ /
\ /
MMMM
\/
</code></pre>
Since the triangles formed by the diameter of the sun and the observer, and the diameter of the moon and the observer are similar, you can write down the... | If a sphere with a radius <span class="math-container">$R$</span> lies at a distance <span class="math-container">$d$</span> away from you, it can be covered exactly by an sphere with radius <span class="math-container">$\frac{1}{2}R$</span> lying away<span class="math-container">$\frac{1}{2}d$</span> away from you. Th... | https://astronomy.stackexchange.com |
74,633 | [
"https://electronics.stackexchange.com/questions/74633",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25925/"
] | I'm trying to protect a receiver from spikes on the antenna from a nearby transmitter by using a PIN diode from the center conductor of the feed line (RG6, 75 ohms) to gnd. the receiver input limit is 1 dBm (1.3 mw}. Will Z × W = V<sup>2</sup> give me the correct breakdown voltage spec?
| Adding as a seperate answer because the new question is different from the original:
Your Manchester decoding is correct but the bit order is b8-b7 etc to b0 so you have the bit decoding backwards. The set bits are b2 = arc power ON and b4 = Fade is running. These make sense as you have sent broadcast DAPC to level 0x... | First check your physical layer setup before attempting to get the right query. Check that you are using an appropriate power supply (DALI requires a 11.5V to 20.5V d.c. power supply current limited to less than 250mA) which connects to your control device and the control gear (ballast).
Then send queries which you kn... | https://electronics.stackexchange.com |
684,108 | [
"https://physics.stackexchange.com/questions/684108",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I was trying to make my own capacitor and found it hard to make it even equal to <span class="math-container">$1\mu F$</span> of capacitance.
<span class="math-container">$ C= \epsilon A/d$</span>
What i can do to have large capacitance is to have large <span class="math-container">$\epsilon $</span> value and large Ar... | The electric field inside a conductor is zero.
Let's consider the alternative. If there were a field at some point in the conductor that means there would be a force on the electrons there - and they would move. They would redistribute themselves until the field became zero.
The books are talking about a scale bigger... | Physically, they will continue to move, until there is no field.
Mathematically,
For a conductor following ohms law:
<span class="math-container">$J=\sigma E$</span>
Taking the divergence of both sides
<span class="math-container">$\nabla \cdot \vec{J} = \sigma \nabla \cdot E$</span>
Sub in gauss law
<span class="math... | https://physics.stackexchange.com |
261,439 | [
"https://dba.stackexchange.com/questions/261439",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/135293/"
] | We are running kea DHCP server with MySQL DB and today we encounter following error and after googling everyone saying it could be MySQL bug so wanted to see if it's really a bug or implementation issue.
MariaDB-server-10.2.15-1.el7.centos.x86_64 (3 node galera cluster)
<pre><code>2020-03-07 01:59:16.484 INFO [kea... | This is likely to be a problem with daylight saving time: In the US (and possibly other places) the hour between 02:00am and 03:00am on 8th March 2020 does not exist because the clocks are moved forward one hour at 02:00am to 03:00am.
| Use <code>TIMESTAMP</code> instead of <code>DATETIME</code>. That converts your system time into UTC for storing, then converts back when fetching.
| https://dba.stackexchange.com |
41,170 | [
"https://physics.stackexchange.com/questions/41170",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/14171/"
] | After a hot shower, the mirror in my bathroom steams up. When I try to clear it with a towel, it immediately refogs. Yet once I use my hair-dryer, it will clear the fog and the mirror will stay clear.
I'd like an answer to the mechanics behind this difference. I suppose it got something to do with the heat, and maybe ... | The water vapor in the bathroom will condense preferentially on the coldest spots around the bathroom. When you wipe the mirror with a towel the water vapor readily condenses on it again because you have not changed the mirror temperature. When you use the hair dryer, the temperature of the mirror is now higher and ... | Beyond the principle of the car defogger example, you may notice in some 5-star hotels, that the mirrors are always fog free regardless of how much steam there is in the washroom. They have put a heater plate behind the mirror, and the surface is warm and prevents fogging.
| https://physics.stackexchange.com |
123,792 | [
"https://dba.stackexchange.com/questions/123792",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/3379/"
] | Next to the actual data I have in a table, I need to save some data about those fields. I'm hesitant to call it metadata, because while it is exactly that, metadata has a specific meaning within databases sometimes, and this is not exactly what I mean.
Example: I have a table, and for each field I want to know some so... | The biggest issue I have here is that I really want to be able to separate the meta-data from the normal data. There is something special to the data we're saving in two ways: one is that it is of a different type (metadata) then the other data, the other is that it 'belongs' to another column.
Both of these facts ar... | <blockquote>
I have a table, and for each field I want to know some sort of state. Lets say 'unchecked', 'ok', 'faulty' etc. I could just double the columns, add a new 'status-field' per column, but that feels wrong.
</blockquote>
To me, this feels right ;-) In order to prevent typos, I think that this could (and s... | https://dba.stackexchange.com |
426,356 | [
"https://physics.stackexchange.com/questions/426356",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/135334/"
] | I have a physical picture of hydrostatic pressure ($dp/dh = \rho g$) in liquids, interpreting it as the weight of the water column.
Now in a gas, the molecules are much further apart than in a liquid. Still the same hydrostatic pressure exists in gases (e.g. air) as well.
How am I to imagine the "weight of an air col... | When a gas is too dilute, you cannot use hydrodynamics anymore and you are going to have to rely solely on statistical mechanics.
This sets the difference between the <em>continuum</em> and <em>molecular</em> régimes.
Hydrodynamics in this case is an ‘equilibrium’ state where you assume the gas has a homogenous densit... | You say: "I have a physical picture of hydrostatic pressure (dp/dh=ρg) in liquids, interpreting it as the weight of the water column."
Calculationwise that's a shortcut, seeing as that it only 'holds water' in a gravity field. We basically live in a huge column of gas that reaches up to the top of the atmosph... | https://physics.stackexchange.com |
128,977 | [
"https://dba.stackexchange.com/questions/128977",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/69522/"
] | We have a table in one of our databases with approximately following structure:
<pre><code>Field1 int primary key
Field2 int foreign key A
Field3 int foreign key B
Field4 int foreign key C
Field5 ... Field70 diverse data types, for the "payload"
</code></pre>
There are indices on the foreign key columns, albeit only ... | The problem arises because the aliases defined in the <code>SELECT</code> list are not visible by the same level <code>WHERE</code> clause - and the reason behind this is the order of logical execution of queries (which is roughly <code>FROM -> WHERE -> GROUP BY -> HAVING -> SELECT -> ORDER BY</code>, om... | <em><sub>Community Wiki answer to document the answer originally edited into the question by the question author.</sub></em>
<hr>
I used a variable to hold the subquery value:
<pre><code>SET @A =
(
SELECT TT1.EmployeeName
FROM [dbo].[Tb_OPL_Employee] AS TT1
JOIN [dbo].[Tb_MKT_SKD] AS TT2
ON TT2... | https://dba.stackexchange.com |
34,072 | [
"https://security.stackexchange.com/questions/34072",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/16206/"
] | When a user has logged in to a system using their primary password, is there any value in asking for a distinct second password when performing sensitive functions?
Does it provide any benefit over asking for their primary password again?
I consider a second password to not be two factor authentication (2FA), but in... | Agreed. Definitely not two factor.
The three factor classes are something you know (a password), something you have (a security token of some sort) or something you are (iris pattern, fingerprint etc).
Whether a second password is of any use depends on your application and environment.
In many ways the 2nd password... | A 2nd password (ie. Security Question) can ensure extra security when used properly. For example, RBC uses 3 security questions, chosen at random during login. This is a sort of safety net that if the password has been compromised (sniffing, brute force, etc.) the 2nd password is unrelated, "unpredictable" and could pr... | https://security.stackexchange.com |
290,814 | [
"https://physics.stackexchange.com/questions/290814",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/126696/"
] | Usually these terms are used interchangeably. But It seems Thermal energy is the average kinetic energy of all of the particles in the system, while Heat is the transfer of energy. So we can't say that a system have "Heat content". Correct?
What is the difference between the two? And how we define them exactly?
| You already have all the ingredients for an answer.
Internal Energy ($U$) is a property of the system (e.g. the gas has a definite energy) while heat ($Q$) is transfer of energy (e.g. if i put two systems with different temperature together they will exchange some energy and we call that heat).
Everything is linked to... | The terms are used interchangeably only outside of a scientific context, for example, in your kitchen, in the popular press or poor blogs, and even a few bad textbooks.
In a scientific context, you have it almost correct. Heat is the energy that enters or leaves a system on account of a difference in temperature (... | https://physics.stackexchange.com |
580,048 | [
"https://math.stackexchange.com/questions/580048",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/100106/"
] | Solve the equation:
$xdy=(x^5+x^3y^2+y)dx$
My attempt at a solution:
I've tried to check if this was an exact differential equation or if I could reduce it to one, so
$xdy=(x^5+x^3y^2+y)dx \iff xdy-(x^5+x^3y^2+y)dx=0$. If I call $M(x,y)=-(x^5+x^3y^2+y)$ and $N(x,y)=x$, the equation is exact if and only if $\dfrac{\p... | Hint: Let:
$$y = v x \rightarrow y' = v + x v'$$
Substitute this into the ODE and solve. It will reduce it to a separable equation and you can use integration of both side.
It may also be possible to get this in Riccati form.
| The exact form is easy to observe
<span class="math-container">$$xdy=(x^5+x^3y^2+y)dx \implies \frac{xdy-ydx}{x^2 +y^2}=x^3dx$$</span>
<span class="math-container">$$d\left(\arctan\left(\frac{y}{x} \right) \right)=x^3 dx$$</span>
On integration we get
<span class="math-container">$$\arctan\left(\frac{y}{x} \right)=\fra... | https://math.stackexchange.com |
14,814 | [
"https://scicomp.stackexchange.com/questions/14814",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/3309/"
] | I am doing a nondimensional Navier-Stokes simulation, but it's not exactly clear what values to use for the various gas constants: $R$, $C_v$, and $C_p$. Obviously, once I know one of these and $\gamma$, I can define the others. A colleague of mine is using the formula
$$C_v=\frac{1}{\gamma*(\gamma-1)M_\infty^2}$$
but ... | If you are using an ideal gas equation of state, only the ratio of specific heats should appear in the nondimensional governing compressible Navier-Stokes equations. Knowing that you want to simulate (say) air, which provides gamma, is sufficient.
If this is your setting and my answer unclear, please let me know and ... | It would probably be instructional if you went through the process of non-dimensionalization yourself, starting from the dimensional equations for which it is always clear which constant to use where. This way, you will discover which combinations of constants appear where.
| https://scicomp.stackexchange.com |
185,839 | [
"https://mathoverflow.net/questions/185839",
"https://mathoverflow.net",
"https://mathoverflow.net/users/56913/"
] | I am trying to find the asymptotic behavior of the sum:
$$ \sum^n_{i=0} \begin{pmatrix} 2n \\ i \end{pmatrix} x^i y^{2n-i}$$
as $n\rightarrow\infty$. Here $x$, $y$ are complex numbers and I have $|x|\leq1$ and $|y|\leq1$. I also know that $|x+y|\leq1$ and $|4xy|\leq1$.
One of the approaches I thought about was to ap... | Assuming that $|x+y|<1$ and $4|xy| \le 1$, here's a proof of the decay.
First suppose that $|x|> |y|$. The desired sum is
$$
\le \binom{2n}{n} |xy|^n \sum_{j=0}^{n} |y/x|^j \le
\binom{2n}{n} |xy|^n \frac{1}{1-|y/x|}.
$$
Since $\binom{2n}{n}$ is of size about $4^n/\sqrt{n}$, the desired decay follows in th... | This is a comment to Lucia’s answer that doesn’t fit into the comment box.
In the case $|x|=|y|=1/2$, put $\omega=x/y$, and
$$S_k=\sum_{j=0}^k\omega^j=\frac{1-\omega^{k+1}}{1-\omega}.$$
Then by partial summation,
$$\sum_{k=0}^n\binom{2n}kx^iy^{2n-i}=y^{2n}\left[\binom{2n}nS_n-\sum_{k=0}^{n-1}S_k\left(\binom{2n}{k+1}-\... | https://mathoverflow.net |
465,227 | [
"https://physics.stackexchange.com/questions/465227",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/221932/"
] | I have found a polaroid from an old LCD device. It is rectangular in shape and does not have any markings on it. I wanted to somehow determine its axis, maybe not exact. I have tried to use it in front of a TV and phone screen, but I can't understand anything from that. I also know about polarised blue sky, but I don't... | Polarized light results from reflection on transparent objects. Find a
plate of glass, and look at a reflection in it, at about 45 degrees. The orientation
of the polarizer that dims the reflection the most, is with the polarization
axis of the polarizer antiparallel to the plate ( most nearly aligned with the
per... | Well, I know answer by @Whit3rd is best, but for reference, which I think I found by some study:
On a clear day, put your polaroid in front of blue sky, a little bit away from the Sun. Rotate the polaroid in such a position such that brightness of sky is least. And now, the line from Sun to the polaroid becomes the ax... | https://physics.stackexchange.com |
50,632 | [
"https://astronomy.stackexchange.com/questions/50632",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/47602/"
] | If the phases of the moon and the moon's perigee are just dependent on the point that the moon is in through it's orbit, why can perigee happen at different phases of the moon?
My thinking is this:
<ul>
<li>The phases of the moon take one lunar orbit to complete</li>
<li>A lunar perigee will occur at the same point thr... | The orbit of the Moon is not exactly simple. First, it’s an ellipse, as you probably know already. The Earth is at one focus of the ellipse; this is why sometimes the Moon is closer, sometimes it’s farther.
This ellipse is tilted with respect to the <em>ecliptic</em>, <strong>not</strong> the Earth’s equator (it’s one ... | While the Moon orbits the Earth, the Earth orbits the Sun. So, by the time the Moon completes one orbit around the Earth, the Earth will have completed about 1/13th of its orbit around the Sun. This means the Earth-Moon-Sun angle will be different from one apogee to another, so the phase will be different.
Put anothe... | https://astronomy.stackexchange.com |
168,484 | [
"https://chemistry.stackexchange.com/questions/168484",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/74624/"
] | Exothermic reaction has negative enthalpy change because energy is flowing out of the system. Isolated system means no energy is flowing in and out of the system. If you have an exothermic reaction in an isolated system, is enthalpy change 0?
Also, assume
Substance 1: initial enthalpy of isolated system (i.e. reactant... | An exothermic reaction is one in which you need to remove heat from the reaction mixture in order to hold the temperature constant. The amount of heat you need to remove to hold the temperature constant is minus the the enthalpy change for the reaction.
If you have an exothermic reaction of an ideal gas mixture in an ... | Enthalpy is defined as <span class="math-container">$$H = U + pV$$</span>
Isolated systems are implicitly of constant volume, otherwise they can exchange energy by volume mechanical work.
Isolated systems have therefore constant <span class="math-container">$U$</span> and <span class="math-container">$V$</span>.
<span ... | https://chemistry.stackexchange.com |
265,749 | [
"https://security.stackexchange.com/questions/265749",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/42053/"
] | I use an old AirPort Extreme to provide WiFi in my home. It provides a 2.4 and 5.0 GHz network with a good password, only available to me and my wife. It also provides a separate guest network without password. The benefit is that visitors can have WiFi in my home without needing my password so I don’t need to hand my ... | There is no inherent unavoidable risk in this approach which would put your private WiFi in danger. But ...
These networks are served by the same router. This means their implementation and configuration are only separated by software. And software can have bugs. For example if the attacker manages to exploit your rout... | I think that besides the technical security risk (which probably is not that critical if the system only works for your visitiors and you trust them), the major problem will be that <em>anybody</em> near your home can use that network.
This means, even if your hard- and software don't have any flaws, the next guy from ... | https://security.stackexchange.com |
128,082 | [
"https://softwareengineering.stackexchange.com/questions/128082",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4701/"
] | Are there any specific reasons for a developer that deals with web applications (let's say writing html and js) to download a browser's source code (like Chromium) and learn how the engine works (renderer, javascript vm, network processing, etc.)?
| It is more important to understand HTTP, client server, web standards and specifications (HTML 4, XHTML, HTML 5, CSS 2.0, CSS 3.0, Javascript) and the differences between the different browsers and browser versions.
Understanding the inner workings of a single browser engine can be useful in the same way that understa... | Complete waste of time. What is important to have at hand is the standards, and perhaps some documents explaining browser peculiarities. But not the source code of the browser! It would be like hoping to get better at drawing pictures by studying the source code of Photoshop.
| https://softwareengineering.stackexchange.com |
992,580 | [
"https://math.stackexchange.com/questions/992580",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/103063/"
] | This is an example I read around closed graph theorem. Let $Y=C[0, 1]$ and $X$ be its subset $C^\infty[0, 1]$. Equip both with uniform norm. Define $D: X \to Y$ by $f \mapsto f'$. Suppose $(f_n, f_n') \to (g, h)$ in $X \times Y$. Thus, $f_n \to g, f_n' \to h$ both uniformly on $[0, 1]$. It is well known that $g' = h$. ... | <ol>
<li>The topology on $X\times Y$ is given by the norm $\|(x,y)\|=\max\{\|x\|,\|y\|\}$. So if $(f_n,f_n')\to(f,g)$, this means that $\|f_n-f\|\to0$, $\|f_n'-g_n\|\to0$, i.e. $f_n\to f$, $f_n'\to g$ uniformly. </li>
<li>Fix $x\in X$. Then
\begin{align}
\left|\frac{f(x+h)-f(x)}h-g(x)\right|
&\leq\left|\frac{f(x+h... | <strong>3.</strong>
$D(t^n) = nt^{n-1}$. But $\|t^n\| = 1$ and $\|D(t^n)\| \to \infty$.
So $D$ is not a bounded operator. You know, right, that for linear operator on normed spaces, continuity holds iff the operator is bounded?
| https://math.stackexchange.com |
29,873 | [
"https://electronics.stackexchange.com/questions/29873",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5780/"
] | We have a lab that wants us to simulate an RC and RL circuit, and then a CR and LR circuit (series). From reading it is my understanding that reversing order of components results in reversing the action (ie frequency selection curve). In other words
LR=RC
CR=RL
Why is this?
| There is a lot you implied or are assuming that you didn't state. The order of two components in series only matters if you access the node between them. It doesn't matter either if they are in parallel. You really should be more careful in explaining what you are talking about than just "RC and RL circuit". There ... | <img src="https://i.stack.imgur.com/N8QDG.png" alt="enter image description here">
<blockquote>
\$ V_{OUT} = V_{IN} \cdot \dfrac{Z_C}{Z_C + R} \$
</blockquote>
If the impedance of \$C\$ is much higher than \$R\$ this equation will approach 1. This is the case for low frequencies, for DC the impedance will be infi... | https://electronics.stackexchange.com |
14,842 | [
"https://mathoverflow.net/questions/14842",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1353/"
] | Given a formal power series $f \in k[[X]]$, where $k$ is a commutative field, is there any good way to tell whether or not $f\in k(X)$?
Edit: To clarify, "good way to tell" means "computable algorithm to tell".
Edit 2: I really screwed up this question, so I am recusing myself from accepting an answer. I will accept... | Continued fractions!
To motivate this answer, first recall the continued fraction algorithm for testing whether a real number is rational. Namely, given a real number $r$, subtract its floor $\lfloor r \rfloor$, take the reciprocal, and repeat. The number $r$ is rational if and only if at some point subtracting th... | Whether a power series corresponds to a rational function or not is independent of any finite initial segment of its coefficients; accordingly, (as some power series are and others are not given by rational functions), one has to know infinitely many coefficients of the power series in order to tell whether it is given... | https://mathoverflow.net |
4,009 | [
"https://chemistry.stackexchange.com/questions/4009",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1069/"
] | To my knowledge, metalic ions only precipitate from a solution as salts & and a process that could possibly produce monocristalline metal would be very interesting indutrially - I've never heard of one, so I don't think it is possible.
But: is it not conceivable to dissolve a metal in an acid (or maybe base), and ... | IIRC, the solubility of virtually all gases in water decreases with temperature. This is the reason why heating water will result in bubble nucleation, and this can be exploited to produce very clear ice by boiling water, perhaps several times, before putting it into the trays.
| To minimize the air bubbles in ice, either 1) hold the water under a vacuum or 2) 'degas' the water with an ultrasonic cleaner before freezing.
1) Holding the water under a vacuum will pull the dissolved gases out of solution. The will diffuse to the air-water surface, and then be vacuumed away.
2) An ultrasonic cle... | https://chemistry.stackexchange.com |
76,377 | [
"https://mathoverflow.net/questions/76377",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18064/"
] | Hi all,
I am encountering a problem in calculating the sum of multinomial coefficients. The original problem is about a signal source with $k$ symbols under uniform distribution, i.e.
$p_0=p_1=\cdots=p_{k-1}= \dfrac{1}{k}$.
My problem is to find an appropriate string length $N$ with two concerns:
<ul>
<li>The pr... | The probability that a sequence does not contain all symbols is bounded above by the expected number of symbols omitted, $k (\frac{k-1}{k})^N \approx k \exp (\frac{-N}{k})$. You can ensure this is small by choosing $N$ to be large relative to $k \log k$.
You can get an exact probability easily using inclusion-exclusio... | Here is how to estimate
$$Q(n,t) = \sum \binom{n}{k_1,\ldots,k_t}$$
with the sum over $k_1,\ldots,k_t\ge 1$ such that $k_1+\cdots+k_t=n$.
Let $X_1,\ldots,X_t$ be independent random variables with truncated Poisson distribution
$$Pr(X_i=q) = (e^{\lambda}-1)^{-1}\frac{\lambda^q}{q!},~~~q\ge 1.$$
Define $X=\sum_{i=1}^t X_... | https://mathoverflow.net |
65,006 | [
"https://electronics.stackexchange.com/questions/65006",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20711/"
] | An ideal current source is able to change its potential difference at the output to keep the same current at the output regardless of the load imepedance there. Real current sources are able to do this till a limit, I think. I wish to know how do they do it?
Also, what exactly does "load" mean in circuits, when a comp... | <blockquote>
An ideal current source is able to change its potential difference at the output to keep the same current at the output regardless of the load imepedance there.
</blockquote>
Some current sources, like the one you can make from a 3-terminal voltage regulator, operate like pjc50 says by using feedback co... | Real constant current sources usually consist of a feedback system that senses the current consumption and adjusts either the voltage supplied or the resistance of some component in the circuit (usually a transistor).
Inductive sources (generators, alternators) behave like varying current sources. A moving magnetic fi... | https://electronics.stackexchange.com |
368,718 | [
"https://softwareengineering.stackexchange.com/questions/368718",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/301792/"
] | People say that "talking about TDD hardly works, if you want to convince someone to TDD, show them results". However, I'm already getting great results without TDD. Showing me that people who use TDD get good results won't be convincing, I want to see that people who write both TDD and not-TDD get better results with T... | Yes.
Proofs are fine when they're available, but even at the best of times they only prove that a single bit of code will work as expected (for all inputs? accounting for interruptions in the middle of any operation? what about running out of memory? disk failure? network failure?).
<strong>What happens when it chan... | We don't know. We cannot answer your question.
While you spend lots of time explaining that process you have now seems to work to everyone's satisfaction, you are telling us only small sliver of what is actually happening.
From my experience, what you are describing is extreme rarity and I'm skeptical that it is actu... | https://softwareengineering.stackexchange.com |
264,042 | [
"https://electronics.stackexchange.com/questions/264042",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24564/"
] | I'm designing a small battery powered system, actually I'm battery powering a module which already has all the switching regulators it needs. This provides me with a wide input range of 5-10V. I was thinking of connecting the batteries directly to the module instead of using a regulator because I don't want to pay a... | You haven't said anything about the current draw of your system, how much inrush you expect, nor the type of battery, so the question can't be answered directly. However, it is unlikely that inrush current from occasionally turning something on is going to matter to the battery or the power supply input circuitry. If... | I do not think that there will be any problem when connection your batteries. Even an inrush current of 20 or 30 A does not hurt given the time required to charge your input circuit.
Overheating of the battery will therefore also not take place because therefore the energy loss in the battery is far to low.
| https://electronics.stackexchange.com |
6,510 | [
"https://electronics.stackexchange.com/questions/6510",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | Is it possible to use a digital potentiometer with an SMPS, to adjust the voltage? I'm looking at one with a 2 MHz -3dB bandwidth. What does this mean for a 300 kHz switcher?
| Thomas, This question may be a bit too broad.
There are normally SMPS that will have a set resistance. This can be controlled by a digital pot, very effective at that.
If you are wanting to change components inside the control loop of the SMPS, I would suggest against it.
| Bandwidth is usually not relevant when it comes to a power supply adjustment pot. The value is generally set at a single calibration point and isn't varied. Even if the pot were being varied (by a micro, for example) the adjustment speed has to be significantly lower than the switching frequency to maintain Nyquist sta... | https://electronics.stackexchange.com |
20,116 | [
"https://physics.stackexchange.com/questions/20116",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7376/"
] | It is hard to push the empty upside down mug inside the water as it has air present inside its cavity which prevents the water from entering inside the mug.But when we tilt that mug which is still completely immersed in the water by some angle then water enters inside it accompanying the formation of bubbles.....even t... | This is how I imagine the situation:
<img src="https://i.stack.imgur.com/z3tnY.jpg" alt="enter image description here">
The water level tries to be horizontal, even beneath the tilted mug. That means that in the "lower half" of the mug, the water penetrates inside the mug. The pressure and density of the air stays ne... | A naval engineer would ask you to examine the relationship between the center of buoyancy and the point where you are applying force and suggest you consider the stability (or lack there of) of the arrangement.
If you have access to a vessel with a rigid handle you could try the experiment again while <em>pulling</em>... | https://physics.stackexchange.com |
651,682 | [
"https://physics.stackexchange.com/questions/651682",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/192858/"
] | I am considering the theorem in a statistical mechanics context, but I suppose the question could be extended to other fields where it applies as well.
If we have a system with property <span class="math-container">$A$</span> and apply a small perturbation <span class="math-container">$f_0A$</span> to its Hamiltonian, ... | I think the simplest way is to take into account that the sum
<span class="math-container">$$\frac{1}{2}\sum_i\sum_{j, j\ne i} {\bf F}_{ij}\cdot ({\bf r}_i + {\bf r}_j)
$$</span>
is a sum over all the values of <span class="math-container">$i$</span> and <span class="math-container">$j$</span>, with the only constraint... | Newton's second law states that the force the <span class="math-container">$i^{th}$</span> particle exerts on the <span class="math-container">$j^{th}$</span> is equal in magnitude, but opposite in direction to the force that the <span class="math-container">$j^{th}$</span> particle exerts back on to the <span class="m... | https://physics.stackexchange.com |
349,385 | [
"https://physics.stackexchange.com/questions/349385",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/119217/"
] | I thought that if we use monochromatic source, we can only get one peak, if it exists.
Because Photoelectric Effect allows only the electron that have the corresponding frequency(energy level) that can be excited.
appreciate your help to rectify my understanding.
| Because the X-rays, in the Photoelectron spectroscopy device, excite the electrons from the individual core levels out and as we know the electrons from the individual core levels reside in different energy levels. Thus the amount of energy left after the electrons overcome the individual energy barrier of each level i... | Monochromatic X-rays produce electrons from a multiplicity of orbitals,
producing a range of electron kinetic energies. One can analyze the outgoing electron
energy to produce a spectrum. It's a spectrum of Xray photon energy
minus binding energy of the electron, so for a fixed Xray energy, it's
the electron bindin... | https://physics.stackexchange.com |
38,550 | [
"https://stats.stackexchange.com/questions/38550",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14600/"
] | I am running a series of regressions to eliminate the effects of IQ, language ability and age from my variables (task performance). To do this, the variable is entered as the dependent variable (e.g. EFT in syntax below) in a regression with IQ, language ability and age as predictor variables, selecting for control gro... | It's not clear to me why you want to do this, but anyway... This is a tentative based on what I've understood from your post.
<pre><code>regress eft age iq lang if group1 == 2, vce(cluster clustvar)
predict resid1 if inlist(group1, 0, 1), resid
</code></pre>
Where <code>clustvar</code> is your cluster variable
(Plea... | I don't know what you mean by saying cluster is not available in SPSS. Perhaps you need the MIXED procedure or one of several others that might apply here.
| https://stats.stackexchange.com |
23,911 | [
"https://mathoverflow.net/questions/23911",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5337/"
] | I am teaching a course on Riemann Surfaces next term, and would <strong>like a list of facts illustrating the difference between the theory of real (differentiable) manifolds and the theory non-singular varieties</strong> (over, say, $\mathbb{C}$). I am looking for examples that would be meaningful to 2nd year US grad... | Here is a list biased towards what is remarkable in the complex case. (To the potential peeved real manifold: I love you too.) By "complex" I mean holomorphic manifolds and holomorphic maps; by "real" I mean $\mathcal{C}^{\infty}$ manifolds and $\mathcal{C}^{\infty}$ maps.
<ul>
<li>Consider a map $f$ between manifold... | Any two compact surfaces (without boundary) of the same genus are diffeomorphic. However, if S is a surface of genus g > 0, there are uncountably many non-isomorphic complex (or, equivalently, algebraic) structures on S.
| https://mathoverflow.net |
119,611 | [
"https://physics.stackexchange.com/questions/119611",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21270/"
] | We can use Gauss's law to find out the electric field $\vec{E}(\vec{r})$ due to an infinite cylinder of charge.
<img src="https://i.stack.imgur.com/SNR2j.jpg" alt="enter image description here">
But if the cylinder is of finite length then it is said that $|\vec{E}(\vec{r})|$ is valid at $\vec{r}$ when $r<< R$.... | rodrigo has a good explanation for why this intuitive explanation is useful.
If you wanted to prove it mathematically, you'd have to find the exact field first. Here's an example from Griffiths: If you have a line of charge with linear charge density $\lambda$ on the $x$-axis running from $-L$ to $+L$, the field at so... | It is an intuitive approximation. I guess that you could calculate the exact electric field for a finite cylinder and then see that effectively, it is approximately equal to the infinite one when $ r << R$.
But the idea of using Gauss in the first place is not to have to calculate the finite cylinder case explic... | https://physics.stackexchange.com |
8,621 | [
"https://electronics.stackexchange.com/questions/8621",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2288/"
] | In school, I was told not to leave components in a breadboard for extended periods of time. However, this length of time was never quantified. The reasoning was that the contacts would eventually lose their "springiness"; at some point later in time, you'd be debugging issues with a circuit, only to find out that the... | Here's a picture of a board which had some headers forced into it which were too large, damaging the contacts:
<img src="https://i.stack.imgur.com/RNXWP.jpg" alt="Bad board">
The outer rows of the Sharpie'd area make intermittent contact, so we avoid the whole section. Notice that some of the numbers are rubbed off,... | I've never had any problems, and I've left components in the board for months.
Component leads seem to be quite a tight fit anyway, so whether it's springy or not I think it will make contact anyway.
| https://electronics.stackexchange.com |
4,474,883 | [
"https://math.stackexchange.com/questions/4474883",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1025720/"
] | Let <span class="math-container">$p$</span> be an increasing, continuous function on the interval <span class="math-container">$[t_0.t_1]$</span>. I wish to show the inequality <span class="math-container">$$
\int_{t_0}^{t_1}p(t)\exp (t_0-t)dt\leq \int_{t_0}^{t_1}p(t)\exp(t-t_1)
$$</span>
I have checked this inequality... | For the amended question, we can show the following generalisation:
<blockquote>
Let <span class="math-container">$p$</span> and <span class="math-container">$q$</span> be increasing on <span class="math-container">$[a,b].$</span> Then <span class="math-container">$$ \int_a^b p(t) q(a+b-t) \mathrm{d}t\le \int_a^b p(t) ... | As the function <span class="math-container">$\exp(.)$</span> is increasing, we have <span class="math-container">$\exp(t_0)\leq \exp(t_1)$</span>. If we suppose that <span class="math-container">$\int_{t_0}^{t_1}p(t)\exp (-t)dt \geq 0$</span>, we will get
<span class="math-container">\begin{align*}
\exp(t_0)\int_{t_0}... | https://math.stackexchange.com |
70,142 | [
"https://cs.stackexchange.com/questions/70142",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/66165/"
] | I apologize for the long title, but I really didn't know how to write it different without lacking informations about the content.
I recently had an university exam about Parallel Algorithms. One exercise asked me to write an algorithm to determine if the elements of an array, let's call it <code>A</code>, were repeat... | No, your algorithm doesn't work. Consider if the array A is
A = [1 1 1 1 1 2 2 3 3 3 3 3 3].
Then the array B will be
B = [5 5 5 5 5 2 2 6 6 6 6 6 6].
The sum of B will be 65, and the length of B will be 13, so after division, we'll get the number 5. This is equal to the first element of B, so your algorithm will... | [2,2,5,5,5,5,5,6,6,6,6,6,6] is a counterexample.
how I found that: (The last step of this was a Python script.) For them to <em>not</em> all be equal, there need to be at least two distinct numbers that appear. However, averages are <em>strictly</em> between the min and the max, so to pass your criterion the... | https://cs.stackexchange.com |
1,186,491 | [
"https://math.stackexchange.com/questions/1186491",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/201017/"
] | I tried inclusion-exclusion.
There are $6^{8}$ possible outcomes, subtract off those with only 5 outcomes, add those with 4 outcomes... There are $\binom{6}{5}$ ways to choose those with 5 outcomes, $\binom{6}{4}$ to choose those with 4 outcomes...
so the answer is
$\binom{6}{1}^8 - \binom{6}{5}\binom{5}{1}^8+\binom... | You take
$$
\text{Proj}_{s}(\mathbf{V}) = \mathbf{s}\frac{1}{\|\mathbf{s}\|^{2}}\mathbf{s}^{T}\mathbf{V},
$$
which is indeed what you wrote.
More generally, instead of a single vector $\mathbf{s}$, you could have a $k$-dimensional subspace of $\mathbb{R}^{d}$.
Let $\mathbf{X} \in \mathbb{R}^{d \times k}$ be a matrix w... | You could for instance change the basis where one basis vector includes the direction vector of a line. For instance, if the line has the equation $\vec r = t(1,1,1)$, you could construct a new basis such as
$$f_1=(1,1,1), f_2=(1,-1,0), f_3=(1,1,-2)$$
In this basis, it's much easier to project on either the xy-plane o... | https://math.stackexchange.com |
1,429,000 | [
"https://math.stackexchange.com/questions/1429000",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/269423/"
] | Prove that for any integer $n$, the integer $n^2 + 7n + 1$ is odd.
I have $n=2k+1$ for some $k\in Z$
I really do not how to do this problem. any help in understanding would be greatly appreciated.
| There are only two scenarios here: $n$ is odd or $n$ is even. That alone is enough to determine whether $n^2 + 7n + 1$ is odd or even.
<ul>
<li>If $n$ is odd, then so is $n^2$, as well as $7n$. Then $n^2 + 7n$ is even, because two odd numbers add up to an even number. But then there's the $+ 1$, which makes the number... | <strong>Hint</strong>: You should be able to fill in the the following blanks and justify each claim made. We start by noting that $$n^2+7n=n(n+7).$$ If $n$ is an integer, then either $n$ or $n+7$ must be _____ and the other must be _____. Hence, $n(n+7)$ must be _____, and so....
| https://math.stackexchange.com |
389,037 | [
"https://physics.stackexchange.com/questions/389037",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75502/"
] | Imagine the entire matter content of the universe suddenly becomes antimatter, and vice versa, overnight. Would it change the rate at which space is expanding?
| No it would not.
Matter comes into the Friedmann equation as an energy density. Particles and the corresponding antiparticles have the same mass and therefore make an identical contribution to the energy density.
As hinted at in a comment, changing some of the matter to antimatter would make a difference because the ... | <blockquote>
Imagine the entire matter content of the universe suddenly becomes antimatter, and vice versa, overnight. Would it change the rate at which space is expanding?
</blockquote>
What is called matter and what is called antimatter is a definition. In the universe at this time the bulk of masses are composed... | https://physics.stackexchange.com |
190,649 | [
"https://softwareengineering.stackexchange.com/questions/190649",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/57177/"
] | Recently I had a discussion with a colleague regarding code style. He was arguing that your usage of APIs and the general patterns you are using should be as similar as possible with the surrounding code, if not with the the codebase as a whole, just as you would with code appearance (brace positioning, capitalisation ... | To give a more general answer:
In a case like this, you have two programming "best practices" that are opposed to each other: code consistency is important, but so is choosing the best possible method to accomplish your task. There is no one correct answer to this dilemma; it depends on a couple factors:
<ul>
<li><... | Staying consistent has little value in my perspective; continuously making improvements is a must.
Your colleague's position really impedes innovation. The consistency argument gets you into a situation where you can use, for example, LINQ only if you migrate <em>all</em> code to use LINQ. And well, we don't have time... | https://softwareengineering.stackexchange.com |
98,366 | [
"https://mathoverflow.net/questions/98366",
"https://mathoverflow.net",
"https://mathoverflow.net/users/450/"
] | If $X$ is a nonsingular algebraic (or analytic) variety over $\mathbb C$ or $\mathbb R$ then it is certainly $C^\infty$ over the reals.<br>
The converse is false for a silly reason : in the real or complex affine plane with coordinates $x,y$ the variety $x^2=0$ is singular since it is not reduced, but set-theoretica... | <em>NB: This answer is directed to the questions about the real case, not the complex case, which was already treated by Francesco. Added 5 July 2021: Because of some questions I have received over the years since this was written, I have realized that there are a few places where the logic and flow are not completel... | The answer is in fact <strong>no</strong>.
A complex variety $X$ can never be a differentiable manifold (not even of class $C^1$) throughout a neighborhood of a singular point.
You can find a proof in Milnor's book "<em>Singular Points of Complex Hypersurfaces</em>", Annals of Mathematics Studies <strong>61</strong>... | https://mathoverflow.net |
15,323 | [
"https://mechanics.stackexchange.com/questions/15323",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4152/"
] | I have a hose clamp which is continually leaking. I have tightened it until I cannot turn the screw anymore, but it still leaks. Is there a proper way to install a hose clamp? Am I doing something wrong?
| When you install a hose clamp there are a few concerns to ensure it doesn’t leak. First of all, ensure the hose is in good shape on the inside and the outside. If it is cracking anywhere around there, it will probably leak and before long (if it must hold pressure) it may fail completely.
Second, ensure the hose is su... | The one time I had a persistently leaking hose, it was because the hose was too big. I had put a 12mm hose on a 10mm nipple and no matter how tight I made the clamp, coolant would slowly bubble out of it. I actually tightened it so much that the clamp was starting to cut into the rubber.
Needless to say, installing a ... | https://mechanics.stackexchange.com |
79,456 | [
"https://security.stackexchange.com/questions/79456",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/31356/"
] | From time to time one of the websites I browse regularly becomes a victim of a DoS/DDoS attack and usually they solve the problem by switching to https. I cant see the connection between the attack and the defense? TLS encrypts the connection what does this have to do with the number of connections that consume the ser... | The only reason switching to HTTPS might help is if the attack is focused on only HTTP. There is no inherent DOS protection in HTTPS. In contrary, you could probably tie up the resources of the server with HTTPS with even less efforts if you start with a minimal SSL handshake so that the server has something to do but ... | Two things might make a difference here:
<ul>
<li>If you switch from HTTP to HTTPS, you're switchings ports and protocols. It's effectively a different site. So the attacker would have to modify his attack to target the HTTPS site instead. Many DDoS attacks aren't nearly that sophisticated, so switching protocols coul... | https://security.stackexchange.com |
140,553 | [
"https://electronics.stackexchange.com/questions/140553",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/58827/"
] | I want to calculate the cutoff frequency for a specific filter, but I can't find any formula for that.
I know the formula for the cutoff frequency of a low pass filter:
$$f_c=\frac{1}{2\pi RC}$$
But how is that derived in the first place? I don't have a regular low pass filter, but something similar that I want to ... | The specific formula applies only for a first order RC low pass filter. This is derived from its frequency response:
$$H(j\omega)=\frac{1}{1+j\omega RC}$$
The cutoff frequency is defined as the frequency where the amplitude of \$H(j\omega)\$ is \$1\over\sqrt2\$ times the DC amplitude (approximately -3dB, half power p... | For a simple RC low pass filter, cut-off (3dB point) is defined as when the resistance is the same magnitude as the capacitive reactance: -
\$R = \dfrac{1}{2\pi f C}\$
It's a simple math trick to say: -
\$f = \dfrac{1}{2\pi R C}\$
| https://electronics.stackexchange.com |
398,567 | [
"https://softwareengineering.stackexchange.com/questions/398567",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/344386/"
] | If you go to www.htmlbasictutor.ca/character-encoding.htm you will find the following description of character encoding.
<code>Character encoding tells the browser and validator what set of characters to use when converting the bits to characters.</code>
That's all fine and good - but if we were talking about python... | <blockquote>
what would we replace browser and validator with?
</blockquote>
"The python interpreter"
When you call <code>.encode()</code>/<code>.decode()</code> method on as string, the encoding defines how the bits in the file gets translated into Unicode characters.
| Python itself. More specifically string manipulation functions.
Most string manipulation functions are expected to work on characters, not bytes, so they need to know which bytes are to be considered as "one character" to work.
This is of course a problem in any programming language. The only alternative is for the p... | https://softwareengineering.stackexchange.com |
593,636 | [
"https://physics.stackexchange.com/questions/593636",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/279710/"
] | We know that by <span class="math-container">$F=-dU/dx$</span> formula that when force is attractive in nature potential energy increases and when force is repulsive, potential energy decreases. But I don't exactly understand this concept. Whenever i think of repulsive force i feel that the potential energy between two... | The gradient/derivative of the potential energy gives you the in which the force is acting. So, in a one dimensional system, negative potential energy gradient, i.e. <span class="math-container">$-\frac{dU}{dx} > 0$</span> gradient means that it's acting towards the positive <span class="math-container">$x$</span> d... | Imagine two objects with the same electric charge. In a physics classroom you might use a pair of metal spheres on insulating stands. Since they have the same charge, e.g. both negative, There will be a repulsive force between them. If they start a certain distance apart and you want to move them closer together th... | https://physics.stackexchange.com |
13,747 | [
"https://chemistry.stackexchange.com/questions/13747",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5084/"
] | If all chemical processes are equilibria at least to some extent, then where does the energy to overcome the activation energy come from?
Is a process with a very high activation energy (i.e. the ionization of sodium vapor into sodium ion) still considered an equilibrium process at least to some extent?
If so, where... | I don't think the statement that all processes are in equilibrium to some extent is true. By definition, dynamic equilibrium means that the rate of change in one direction is equal to the rate of change in the opposite direction.
This is certainly not true for all <strong>processes,</strong> otherwise there would not ... | Maybe this is another case where semantics enters in. It seems that if a reaction coordinate connects two species, then over time an equilibrium will be achieved between them. "Over time" could mean microseconds or millennia. The kinetic energy distribution of a collection of molecules is described by a Boltzmann d... | https://chemistry.stackexchange.com |
367,675 | [
"https://physics.stackexchange.com/questions/367675",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Is it necessary that masses of two colliding objects be equal, for them to conserve kinetic energy (along with momentum)? I ask this question because I have seen a scenario where the equation implying the conservation of kinetic energy and conservation of momentum has been derived keeping in mind objects of equal mass.... | "Elastic" simply means that no energy is dissipated during the collision, so the total kinetic energy before and after the collision is the same.
There is no reason why the masses should be the same. If you consider the collision of two unequal masses in the center-of-mass (c.o.m.) frame (which always makes collision ... | The masses do not have to be identical for an elastic collision.
| https://physics.stackexchange.com |
4,522,809 | [
"https://math.stackexchange.com/questions/4522809",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/754185/"
] | Statement : In <span class="math-container">$\mathbb{R}^{n}$</span>, if <span class="math-container">$U$</span> is open and <span class="math-container">$C \subset U$</span> is compact, show that there is a compact
set <span class="math-container">$D$</span> such that <span class="math-container">$C \subset$</span> int... | When you integrate with multiple variables involved, your constant becomes a function of the variables you are not integrating with (Because effectively what you are doing is finding an anti partial derivative). So
<span class="math-container">$$\int xdy=xy+f(x),$$</span>
where <span class="math-container">$f(x)$</span... | One more way, this ODE can be re-written as
<span class="math-container">$$\frac{xdy-ydx}{y^2}=-\frac{dy}{y}$$</span>
<span class="math-container">$$\implies -d(\frac{x}{y})=-d(\ln y)$$</span>
Upon integration both sides, we get
<span class="math-container">$$\frac{x}{y}=\ln y+C.$$</span>
| https://math.stackexchange.com |
4,044,128 | [
"https://math.stackexchange.com/questions/4044128",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/80708/"
] | We have the function <span class="math-container">$f(x)=x\cdot \ln (x)$</span>.
I have calculated the Taylor series <span class="math-container">\begin{align*}T(x)&=\sum_{n=0}^{\infty}\frac{f^{(n)}(1)}{n!}(x-1)^n\\ & =\frac{f^{(0)}(1)}{0!}(x-1)^0+\frac{f^{(1)}(1)}{1!}(x-1)^1+\sum_{n=2}^{\infty}\frac{f^{(n)}(1)}... | The first term <span class="math-container">$x-1$</span> has no effect on the radius of convergence. By root test the radius is <span class="math-container">$1$</span>. So the sreis convers for <span class="math-container">$0 <x<2$</span> it is also absolutely convergent for <span class="math-container">$x=0$</sp... | It is well-known that
<span class="math-container">$$\log(z+1)=\sum_{n=1}^\infty(-1)^{n+1}\frac{z^n}{n}$$</span> has the radius of convergence <span class="math-container">$1$</span>. Multiplying by the polynomial <span class="math-container">$z+1$</span> has no effect on that radius.
<hr />
By the way, this establishe... | https://math.stackexchange.com |
15,399 | [
"https://electronics.stackexchange.com/questions/15399",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4647/"
] | I was wondering what the effects of using a lower rating power rated supply for device would be. For example using a 1.52A supply at 19V to power a device where the charger that comes with the device is 4.74A at 19V.<br>
Is doing this likely to damage the device or will it just take longer to charge.
| Normally the device you are trying to charge will not "know" the charger is underrated. So it will not reduce it's current (ampere) usage.
Under high load components in the charger will overheat and fail. All chargers have protection against high loads. There are two kinds of protection:
<ol>
<li>The charger will die... | It won't damage the device. But it is likely to damage the transformer or SMPS, if it does not have over-current, over-temperature or over-power protection. Sometimes supplies have a thermal fuse which prevents a fire, but when it blows it's not easy to replace it (ever tried to take one of those supplies apart?)
| https://electronics.stackexchange.com |
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