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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3,919,799 | [
"https://math.stackexchange.com/questions/3919799",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Prove that the subspace topology is the coarsest topology on <span class="math-container">$Y$</span> for which the inclusion function <span class="math-container">$i:Y \longrightarrow X$</span> given by <span class="math-container">$i(y)=y$</span> is continuous.
</blockquote>
<strong>Attempt</strong>
Def... | <span class="math-container">$$ S = 1 + z^2 + z^4 + ... + z^{2020}= \sum_{r=0}^{1010} z^{2k} = \sum_{r=0}^{1010} (z^2)^{k} =\frac{z^{2022}-1}{z^2-1}=\frac{z.z^{2021}-1}{z^2-1}$$</span>
It's pretty obvious from here
| IF your sum were infinite, then you'd have the right formula. Since the sum is finite, the formula is
<span class="math-container">$$S = \frac{1-z^{2022}}{1-z^2}.$$</span>
Since <span class="math-container">$z^{2021} = 1$</span>, this should be easy to simplify.
| https://math.stackexchange.com |
86,974 | [
"https://softwareengineering.stackexchange.com/questions/86974",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3668/"
] | At the company I work, we are really wanting to get into the agile methodology for developing software. One thing that I'm not excited about is the fact that management wants us to build a custom project management feature inside the company's Intranet.
I think this is a total waste of time. There are many great third... | Well, I've seen similar efforts before, and in general, they didn't turn out too bad. A custom-made tool comes with exactly the features your company needs, no bloat added. They are more flexible than any off-the-shelf product could ever be.
Sure, it looks like a waste of time, and it probably is, but installing, conf... | Ok, maybe I am just paranoid, but this might be a bit of reading the writing on the wall.
Your boss would rather build than buy, are they reluctant to buy other tools and assets? This could be an indication of a cash flow problem. They probably have the cash flow for salaries, but little else.
This might be a time ... | https://softwareengineering.stackexchange.com |
589,675 | [
"https://electronics.stackexchange.com/questions/589675",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/218894/"
] | Consider a separately excited DC motor which is coupled to a shunt dc generator (under no load condition) and acts as a prime mover. If we set the speed of the DC motor to some certain value (for example 1500 rpm) and increase the field current of the generator, there is a slight reduction in the DC motor's speed. What... | When a DC generator is turned, the voltage generated depends on the product of field current and rotation rate.
The internal losses in the generator (capacitive, eddy currents; arcing at the commutator) will increase at higher voltages (even at a fixed rotation rate). This will reflect as a slightly higher load on the ... | I think you are confused because an increment of generator field should rise generator voltage output, and this will cause also a motor speed increment. I can find 2 reasons that can explain the motor speed reduction:
<ol>
<li>If generator field is connected to generator armature, and it is working in magnetic saturati... | https://electronics.stackexchange.com |
27,566 | [
"https://cs.stackexchange.com/questions/27566",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/19273/"
] | I hope I'm in the right section:
I know that if P = NP, then 3-SAT can be solved in P (Cook), but is the opposite valid, too? If P != NP, then 3-SAT is not in P?
Thanks!
| The opposite is valid.
$3SAT$ is an $NP$-complete problem, so every problem in $NP$ can be reduced to $3SAT$.
If $P \neq NP$ and $3SAT \in P$, every problem in $NP$ would be in $P$, contradicting $P \neq NP$. So if $P \neq NP$ then $3SAT \notin P$.
| Mike's proof is correct. I just wanted to add some other details.
Cook's theorem (or Cook-Levin theorem) says that there exists a polynomial time reduction from all problems in $NP$ to $SAT$ (3-$SAT$ or k-$SAT$ with $k>2$ since 2-$SAT$ is in $P$).
More specifically, it states that 3-$SAT$ is $NP$-complete.
Here ... | https://cs.stackexchange.com |
3,939,970 | [
"https://math.stackexchange.com/questions/3939970",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/859116/"
] | So there exist a lot of similar questions which ask the <span class="math-container">$n$</span>th term of <br> <br>
<span class="math-container">$$1^2 , (1^2 + 2^2) , (1^2 + 2^2 + 3^2) ... $$</span>
Which have a simple answer as
<span class="math-container">$$T_n = n^3/3 + n^2/2 + n/6$$</span>
But I want to know what w... | Note that <span class="math-container">$$a^b = e^{b\ln a}$$</span> So we have <span class="math-container">$$ (2x+1)^{x-\sqrt{x^2-2}} = e^{({x-\sqrt{x^2-2}})\ln(2x+1)}$$</span> Also we have <span class="math-container">$$({x-\sqrt{x^2-2}})\ln(2x+1) = \frac{2\ln(2x+1)}{x+\sqrt{x^2-2}}$$</span>Computing the limit using L... | Using equivalents when <span class="math-container">$x$</span> is large
<span class="math-container">$$(2x+1)\sim 2x \qquad \text{and} \qquad x-\sqrt{x^2-2} \sim \frac 1x$$</span>
Now what is the limit of <span class="math-container">$(2x)^{\frac 1x}$</span> ?
| https://math.stackexchange.com |
31,754 | [
"https://mechanics.stackexchange.com/questions/31754",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/16193/"
] | As of lately my car started to make thumping/knocking sounds whilst driving over speed bumps (at regular speed)
I drive a 2001 renault laguna 1.8 16v with about 218,000km (about 135500 miles) on the clock.
It doesn't happen while driving on flat road, i can only hear it when driving over speed bumps.
it kind of sound... | There are too many possibilities when it comes to draw. The compressor clutch could be staying on, alternator voltage regulator, a glovebox light, radio, computer etc...
You're going to need to use an inductive amp probe and a multimeter to voltage drop the fuses. I'd avoid disconnecting battery terminals to hook an... | an easy way to check current draw without an amp meter or any tools: go to the car after dark. pull and replace each of the fuses, 1 at a time. Watch for any kind of spark. If there is a spark then that circuit is drawing power. It could be one thing or a combination of multiple things. Another possibility could b... | https://mechanics.stackexchange.com |
165,330 | [
"https://electronics.stackexchange.com/questions/165330",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37192/"
] | I am using eeprom emulator which writes a page of flash of 60 bytes at once. Data to be written to that page is first stored in a 60 byte buffer (array of 60 elements) in ram and then transferred to flash at once.
Now I want to make my own function above that library which will take address as well as data and store i... | This is not really an electronics or embedded systems question.
If you use C++, you can make write multiple functions under one name, thanks to overloading:
<pre><code>#include <inttypes.h>
void store_data(void *addr, uint8_t data);
void store_data(void *addr, uint16_t data);
void store_data(void *addr, uint32... | It can't. A pointer to 8 bits of data is exactly the same as a pointer to 16 bits of data. You will have to either provide an extra parameter which tells the function how big the data is, or provide two different functions, one for 8 bit and one for 16 bit.
| https://electronics.stackexchange.com |
585,691 | [
"https://electronics.stackexchange.com/questions/585691",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/295235/"
] | Given a USB cable which supports power delivery, does it necessarily support PD 3.0 and QC 3.0? (And only need to power source and device to support these protocols?)
Do I need to check anything other than the maximal wattage it allows to see if it supports either one?
| No, they aren't.
First of all it's only a connector form factor. Which follows previous types A & B. It does not necessarily implement even USB at all. A cable with USB-C connector(s) might not be a full USB 3.1 cable. Some vendors sell cable with only Vusb & GND lines connected, so you definitely can't get any... | To begin, Type-C connection standard explicitly prohibits the use of proprietary power delivery protocols such as QC. Since USB Type-C spec release 1.3:
4.6.2.3 <strong>Proprietary Power Source</strong>
<em>This section has been deprecated. Devices with USB Type-C connectors shall only employ signaling methods defined ... | https://electronics.stackexchange.com |
111,841 | [
"https://stats.stackexchange.com/questions/111841",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/49034/"
] | I ran an ordinal logistic regression in R using the polr function on a survey analysis dataset. The responses of the dependent variable range from Poor to Excellent.
The responses to the independent variables range from 1 to 5 (1 being Poor and 5 being Excellent). I obtained the following result:
<img src="https://i.s... | Remember that you used maximum likelihood estimation which optimizes the likelihood function. Use this to your advantage - it is the gold standard statistical measure, with only penalized likelihood or Bayesian analysis (which also uses the likelihood) being better. Compute the proportion of the total likelihood rati... | There is no general way to do this because the contribution of each variable will be different at different levels of the other variables. This is true in any logistic regression. But you can look at the contribution at particular levels of the other variables. In SAS there is a <code>slice</code> statement that does ... | https://stats.stackexchange.com |
298,636 | [
"https://electronics.stackexchange.com/questions/298636",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/139307/"
] | Is the strength of a DC electromagnet more determined by current or voltage?
For example: if I had one battery at a fixed output that I could step up or down, would it be better to have a higher voltage or current?
I don't want loads of equations as this doesn't have to be accurate. I just need to know if I should st... | Simple answer: Current. The strength of the magnetic field depends on the current that flows in a linear fashion - Double the current, double the magnetic field. Since the resistance of the conductor is the thing that determines the current, you need more voltage to have that current.
| Magnetic field strength is determined by ampere-turns (current multiplied by number of turns). The voltage that results is a consequence of the resistance under static conditions (indeed, if the wire has no resistance there is no voltage, and therefore no power required to maintain the field).
However, under normal (... | https://electronics.stackexchange.com |
55,392 | [
"https://physics.stackexchange.com/questions/55392",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20730/"
] | So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question.
<hr>
<strong>Background</strong>
Greens are a way of solving inhomogeneous differential equations by first solving the response to a unit impulse. I am aware they are... | Good questions; I'm sure a lot of people are confused on this stuff (as I was the first time I used Jackson).
Essentially your confusion boils down to being careful to consider the following fact:
<em>The Green's function for a particular boundary value problem depends on the boundary conditions.</em>
In particular, le... | Just wanted to add a final point to clear this up for you. The potential of a point charge and the Green's function for your problem are the same, up to the normalization constant. In a comment, you say this is by coincidence; It is not, it's physical!
Take your equation $\nabla^2 \Phi = -\frac{\rho}{\epsilon}$, and s... | https://physics.stackexchange.com |
22,956 | [
"https://electronics.stackexchange.com/questions/22956",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6816/"
] | I'm studying electronics in college (I live in Europe), and they are teaching us we should form our reference designations of elements when designing a circuit as according to EN 81346.
This seems absurd to me, because it might be OK for a meat grinder and a generator to have the same designations (G) in some sort of... | Naming all your resistors R... and your diodes R... is silly, yes.
However, you are forgetting the "table 2" that I have heard tell about. (I can't see the exact content of it to get the "real" designators they suggest because I'm not willing to pay for it.)
This allows you to have a second character... so your res... | Reference designations for electrical and electronics parts and equipment, the Unit Numbering Method, has been around since 1949 when the Institute of Radio Engineers (IRE), predecessor of the IEEE, first came out with it. IEEE 200-1975 has been replaced by ASME Y14.44-2008. Apparently the IEEE figured they had bigger ... | https://electronics.stackexchange.com |
144,339 | [
"https://mathoverflow.net/questions/144339",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25643/"
] | On a projective smooth variety $X$ over complex numbers (or rather compact Kahler) we have a specific set of sheaves, namely sheaves of holomorphic forms ${\mathcal \Omega}^p$ of various degrees. The cohomology $H^q(X, \Omega^p)$ of these sheaves "fit" together via Hodge decomposition into cohomology groups of our vari... | I think the situation you are looking for is when $\mathcal F$ is a local system. If $F$ is a locally constant sheaf on $X$, say of $\mathbf C$-vector spaces, then you can put $\mathcal F = F \otimes_\mathbf{C} \mathcal O$ to get a holomorphic vector bundle, which is canonically equipped with a flat connection
$$ \nab... | Suppose $X$ is compact.
For simplicity, first assume that $\mathcal F$ is a holomorphic verctor bundle.
Then we can organize the numbers $h^q=dimH^q(X, \mathcal O(\mathcal F))$ as follows:
$$\chi(X,\mathcal F):=\sum_{q=0}^{dim X}(-1)^qh^q.$$
Then by Hirzebruch-Riemann-Roch theorem:
$$\chi(X, \mathcal F)=\int_X ch(\mat... | https://mathoverflow.net |
7,245 | [
"https://scicomp.stackexchange.com/questions/7245",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/3980/"
] | When FEM-discretizing and solving a reaction-diffusion problem, e.g.,
$$
- \varepsilon \Delta u + u = 1 \text{ on } \Omega\\
u = 0 \text{ on } \partial\Omega
$$
with $0 < \varepsilon \ll 1$ (singular perturbation), the solution of the discrete problem will typically exhibit oscillatory layers close to the boundary. ... | In the case you show, the solution has a boundary layer. If you can't resolve it because your mesh is too coarse, then for all practical matters the solution is discontinuous to the numerical scheme.
Now, if you just apply a standard discretization to this problem, the discrete solution is the result of applying a lin... | <strong>TL;DR:</strong> Your options are limited 1) go brute force adaptive for accurate and expensive solution 2) use numerical diffusion for a less accurate but stable solution or (my favorite) 3) leverage the fact that this is a singular perturbation problem and solve two inexpensive inner/outer problems and let mat... | https://scicomp.stackexchange.com |
4,620,611 | [
"https://math.stackexchange.com/questions/4620611",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1049697/"
] | I came across this question in my self-study through Gallian's book with an explanation stating that since <span class="math-container">$|(a_1 a_2 a_3 a_4)(a_5 a_6)|=4$</span> then such an <span class="math-container">$x$</span> has order 8. With no further explanation as to why such an <span class="math-container">$x$... | If <span class="math-container">$y=(x_1x_2x_3x_4)(x_5x_6)$</span> has order <span class="math-container">$4$</span> and if there exists an <span class="math-container">$x \in S_{10}$</span> such that <span class="math-container">$x^2=y$</span>, then <span class="math-container">$x^8 = (x^2)^4=y^4=e$</span> and so the o... | Clearly <span class="math-container">$x^8=(x^2)^4=e$</span>, and so the order divides <span class="math-container">$8$</span>. But it also can't be any proper divisor of <span class="math-container">$8$</span>. For then we would have <span class="math-container">$x^4=e$</span>, and so <span class="math-container">$(x^2... | https://math.stackexchange.com |
126,926 | [
"https://electronics.stackexchange.com/questions/126926",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52185/"
] | Coach bus with a 24V system of 2x12V 120Ah batteries for aux load. I need 12V for IT stuff. Is it ok to take it from a single battery or is it a bad idea? Right now I have a crappy 12V->24V converter that I would need to replace if this is a bad idea.
Update: Great answers. Sadly I could pick only one although all 3 a... | If you plan using the two 12V batteries again in series, I'd not recommend it. Because you will generate charge asymmetry between the two. The one you use alone will have less charge than the idle one.
So if you plug them back together, the one you used will be depleted earlier than the other one, and even be undercha... | That's probably a bad idea.
Hooking your... IT stuff to a single battery will discharge it faster than the other, especially if you're planning on using your devices when the engine is off.
If your devices power consumption is low compared to the battery size then you are good to go, but a 24V->12V DCDC converter (th... | https://electronics.stackexchange.com |
9,548 | [
"https://chemistry.stackexchange.com/questions/9548",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/2433/"
] | Why is a sugar solution pre-treated with ammonium hydroxide before analyzing? And why is it specifically ammonium hydroxide instead of sodium hydroxide or calcium hydroxide?
| If I'm not wrong, this is about polarimetry, not polarography. (No dripping mercury, but optical rotation).
If your sugar is a hexose, the following species will exist in aqueous solution:
<ul>
<li>open form (a bit)</li>
<li>furanose (traces)</li>
<li>pyranoses (major amount)</li>
</ul>
The pyranoses will adopt the... | Do you see a potential corresponding to the sugars, or to their Schiff bases, or to said imines' trimers? Perhaps ammonia gives you a nice pH buffer, as opposed to alkali hydroxides that will wildly swing pH and allow Cannizzaro disproportionation of reducing sugars' aldehyde groups at high pH. Ammonia does not reduce... | https://chemistry.stackexchange.com |
110,878 | [
"https://electronics.stackexchange.com/questions/110878",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25255/"
] | I've written the following question here:
<blockquote>
I've learned some basic rules to draw Bode plots and when it comes to Phase plot, some of them are:
<ul>
<li>a single zero located in the left half of s-plane has a contribution of 0 degrees near origin and +90 degrees on high frequencies;</li>
<li>a si... | Any complex number \$Z\$ can be represented in rectangular coordinates or polar coordinates
$$Z = x + jy = A\angle\phi$$
where, \$A = \sqrt{x^2+y^2}\$ and \$\phi = atan2(y,x)\$ where, \$atan2(y,x)\$ is defined as
<img src="https://i.stack.imgur.com/EbZPp.png" alt="atan2">
As you can see your conversion formula is va... | This error occurs whenever the real part is negative. This problem can be corrected by testing the real and imaginary parts after the phase has been calculated. If both the real and imaginary parts are negative, subtract 180° (or π radians) from the calculated phase. If the real part is negative and the imaginary part ... | https://electronics.stackexchange.com |
170,522 | [
"https://softwareengineering.stackexchange.com/questions/170522",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53462/"
] | I see more and more articles about logging in JSON. You can also find one on NodeJS blog. Why does everyone like it so much? I can only see more operations getting involved:
<ul>
<li>A couple new objects being created.</li>
<li>Stringifying objects, which either involves calculating string length or multiple string al... | JSON logging gives you the ability to parse the log file programmatically even if the format <strong>has changed in time</strong>.
A good example is Apache logs. By default Apache uses <code>common</code> format for access.log:
<pre><code>"%h %l %u %t \"%r\" %>s %b"
</code></pre>
Say that you have built an offlin... | If your machine runs so close to its limits that such issues really would matter, you most likely have more serious problems. While there may be exceptional situations where this makes some difference, many applications (maybe most) run on machines for which the difference if you log JSON, simple text or records to a d... | https://softwareengineering.stackexchange.com |
592,263 | [
"https://physics.stackexchange.com/questions/592263",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266050/"
] | If a person were to touch a live wire while on an insulated platform, the resistance shoukd prevent any current flow. However, I have read that there is capacitative coupling voltage. I have studied capacitors but there is probably something I am missing here since even if I consider my body and the ground as capacitor... | The current through a capacitor is
<span class="math-container">$$i = C \frac{dv}{dt}$$</span>
i.e the current is proportional to the CHANGE in voltage. If there is AC voltage, then there is always change in voltage and hence current will flow through the capacitor (and through the person, which is part of the circuit... | <blockquote>
If a person were to touch a live wire while on an insulated platform,
the resistance should prevent any current flow.
</blockquote>
If a person were to touch an ac live wire while on an insulated platform, the resistance of the platform would prevent current flow, but its capacitance would permit current f... | https://physics.stackexchange.com |
143,888 | [
"https://mathoverflow.net/questions/143888",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5420/"
] | The Teichmüller space $T_g$ of genus $g$ Riemann surfaces can be parameterized in terms of Fenchel-Nielsen coordinates, taking values in $\mathbb{R}^{3g-3}\times \mathbb{R}_+^{3g-3}$.
The Teichmüller space $T_g$ also has a natural complex structure.
Could someone suggest a reference where the complex structure is g... | Fenchel-Nielsen coordinates are real-analytic but not holomorphic. One indirect way to see this is as follows. Royden proved that besides a few exceptions the group of biholomorphisms of Teichmueller space is equal to the mapping class group. In particular it is discrete and countable. This shows that the Fenchel-Niels... | Although Fenchel-Nielsen coordinates do not give a complex-analytic parameterization of Teichmuller space, they do extend to give a complex-analytic parameterization of $T_g\times \overline{T}_g$ on a subset. This follows from Bers' simultaneous uniformization theorem, which parameterizes quasi-fuchsian groups by the T... | https://mathoverflow.net |
3,623 | [
"https://electronics.stackexchange.com/questions/3623",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/819/"
] | I want to simulate the load regulation of a power-supply. I'm sure I remember being able to vary the value of a resistor over the course of a simulation in LTspice, but I can't remember how. Anyone?
| Use the SpecialFunctions/Varistor.asy component with a time-varying voltage source
<img src="https://i.stack.imgur.com/CdUOr.png" alt="Screenshot">
| Unfortunately using a varistor will not work, as a varistor itself has a dependence on the voltage across it. Much simpler is to right click onto an existing resistor, and to enter a formula. E.g.
<pre><code>R=11-100*time
</code></pre>
will linearily reduce the resistance from 11Ohm to 1Ohm over the time of 100ms. Yo... | https://electronics.stackexchange.com |
2,037,167 | [
"https://math.stackexchange.com/questions/2037167",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/394532/"
] | I know how to calculate the Fourier Transform using the main formula and integrals calculations. But i want to calculate the Fourier Transform of
$ f(x)=xe^{{-x}^2} $
using the following formula :
for $f(x)=e^{{-ax}^2} (a>0) $ then $ \mathbb{F}(f)=\frac{1}{\sqrt{2a}} e^{{{-\omega}^2}/4a} $
How can i do th... | Your explanation is correct. Note the binomial coefficient
\begin{align*}
\binom{n}{j}=\frac{n(n-1)\cdots(n-(j-1))}{j!}
\end{align*}
has according to the $j$ factors of $j!=j(j-1)\cdots 3\cdot 2\cdot 1$ also $j$ factors in the numerator.
<blockquote>
We obtain
\begin{align*}
\binom{j+r-1}{j}&=\binom{r-1+j}{j}\... | It is just fitting introduction of signes and inversion of a decreasing and consecutive (finite) sequence of factors. Look at the following example:
$$\binom 75=\frac{7\cdot6\cdot5\cdot4\cdot3}{5!}=(-1)^5\frac{(-3)(-4)(-5)(-6)(-7)}{5!}$$
Notice now that $(-3)(-4)(-5)(-6)(-7)=-3(-3-1)(-3-2)(-3-3)(-3-4)$ which is the n... | https://math.stackexchange.com |
627,050 | [
"https://physics.stackexchange.com/questions/627050",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/235858/"
] | Suppose I have a string with uniformly distributed mass <span class="math-container">$\mu$</span>. The instant before I introduce a perturbation which produces a wave, Bob adds an additional mass <span class="math-container">$M$</span> a distance <span class="math-container">$x$</span> from my end of the string. Now it... | The speed of light affects some things in the string, but there is more to it.
Atoms in the string exert forces on each other. If you pull on one, it pulls on the next, which pulls on the next, etc. This is what holds the string together. If you pull on one end, the other end will follow because of this.
The forces bet... | The time <span class="math-container">$x/c$</span> is not particularly meaningful in this scenario. The mass density of the string is still <span class="math-container">$\mu$</span> and the wave propagation speed will still be determined by that. When the wave reaches <span class="math-container">$x$</span> then at <sp... | https://physics.stackexchange.com |
560,865 | [
"https://physics.stackexchange.com/questions/560865",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/164488/"
] | If for an isolated system in thermodynamic equilibrium all the accessible microstates are equally probable, why do the gas molecules in an isolated container, never accumulate at one corner of the box or say, on the right half of the box? I emphasize that my question is about the validity of the postulate of equal a pr... | There are way more microstates where the gas particles aren't in the corner than there are microstates where the gas is in the corner. So if you're talking the probability of "in the corner" vs "not in the corner" they latter is going to win out.
| In principle, if you observed the isolated gas-filled container for long enough, you <strong>would</strong> occasionally see a state in which all gas molecules were congregated on the right side of the box. But you would likely have to wait for an exceedingly long time, well in excess of the expected life-time of the v... | https://physics.stackexchange.com |
5,068 | [
"https://mathoverflow.net/questions/5068",
"https://mathoverflow.net",
"https://mathoverflow.net/users/997/"
] | Hello
I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one?
| Chern's book "Complex manifolds without potential theory" is a good book, and it does explain Dolbeault Cohomology. But it's a short book, and it explains it concisely. If you need more details, you could also try Griffiths-Harris (but I greatly prefer Chern's book).
Kodaira's book "Complex manifolds and deformations ... | I like "Hodge Theory and Complex Algebraic Geometry" by Voisin. The focus is on the Kahler case, but the early explanations of Dolbeaut cohomology are for all complex manifolds.
| https://mathoverflow.net |
21,485 | [
"https://electronics.stackexchange.com/questions/21485",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5281/"
] | I'm a student studying computer engineering , I'm in love with hardware stuff /logic gates design ... etc
What I studied till now is :
<ul>
<li>Electronics</li>
<li>IC fabrication</li>
<li>Logic circuits design (sequential , ... )</li>
<li>Error detecting & correction in logic circuits (parity check , ...)
HW d... | Make something. Seriously, make something major. Imagine this: hundreds or thousands of people are exactly in your same predicament of getting out of school with lots of classes. These people are largely indistinguishable from each other. You need to do something that differentiates you from the others, and shows ... | You may want to consider doing a post-graduate degree or some post-graduate degree courses in Embedded Systems Design. You can consult a lecturer who has a post-graduate degree in Embedded Systems/Computer Systems Design to discuss your options based on your qualifications, skills and interests(e.g. what type of embedd... | https://electronics.stackexchange.com |
133,932 | [
"https://security.stackexchange.com/questions/133932",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/121384/"
] | I've set up a public-facing Debian server on a well-known web hosting provider and am trying to determine if hackers are breaking in. I know very little about securing web servers but I am trying to learn. I've configured my server to disallow root logins over SSH and I've also disabled password logins via SSH. All ... | Denial of Service, as its name suggests, is any event which causes service to be denied, either to users or administrators, or any other entity which relies upon the system.
This can include anything from synfloods to smashing the server with a sledgehammer. As such, yes, your example would be considered a denial of s... | Yes, you are correct. That is, by definition, a Denial of Service.
Before Distributed Denial of Service (DDoS) came to the fore, DoS was the staple attack form where malware would, for instance, force excessive CPU or memory usage on the victim server. This is considered a valid Denial of Service as the server is rest... | https://security.stackexchange.com |
13,605 | [
"https://stats.stackexchange.com/questions/13605",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2984/"
] | I have been using R for several years, but I have always used a GUI like Tinn-R, JGR, and most recently R-Studio.
Though I like R-Studio's interface, I feel that for longer programs with few/no graphics, I could code more efficiently by taking advantage of the shortcuts offered by a more basic text editor like Emacs... | First you will need to learn basic text operating with emacs. Since emacs is very sophisticated finding out how to simply select text and copy might be a challenge. So invest some time in finding out how to do that efficiently. Reading the manual might help. For Mac OS X use Aquamacs, it supports native shortcuts.
Wo... | Depending where you are, this may not work for you, but I found someone down the hall who used it and pestered them with questions. Stick with it, it's worth it!
One tip I found especially useful was to use cua-mode; it makes emacs share some of the most common keyboard shortcuts (like save, cut, copy, etc) with mo... | https://stats.stackexchange.com |
196,008 | [
"https://dba.stackexchange.com/questions/196008",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/142321/"
] | Let suppose I have a query that runs multiple times because it is in a while loop which inserts data into a table.
<pre><code>INSERT INTO <table>( psuiKey, group_id) VALUES ('54ds8a784daEd','1');
</code></pre>
The problem is when two users from different computers add data at same time. So what is happening is... | <blockquote>
book_id is int
</blockquote>
Then your code should say:
<pre><code>WHERE book_id = 15
</code></pre>
And not:
<pre><code>WHERE book_id='15'
</code></pre>
This shouldn't affect performance in <em>this</em> case, but it is a best practice to delimit (or not) correctly. Non-Unicode strings and dates wit... | If the value does not change this eliminates a lock and a trigger
<pre><code>UPDATE books
SET last_read = '2018-12-31 11:23:45'
WHERE last_read <> '2018-12-31 11:23:45'
AND book_id = 15
</code></pre>
| https://dba.stackexchange.com |
1,499,209 | [
"https://math.stackexchange.com/questions/1499209",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/213555/"
] | My book says we can quickly prove the conditional statement $P \implies Q $ when we know $P $ is false. This much I'm fine with as I can show it with a truth table. But then I'm asked to, using vacuous proofs, prove $P (0)$ is true, given if $n > 1$, then $n^{2}$ > $n $. How can $P (0)$ be true? 0 is not greater tha... | It looks like $P(n)$ is supposed to be the statement:
<blockquote>
$n>1\implies n^2>n$.
</blockquote>
When $n\le1,$ we have that $n>1$ is <em>false</em>. So, for example, $P(0)$ is true.
| I'm not sure what your instructor wants.
"Whenever $0 > 1$ then $0^2 > 0$"
Well, this is vacuously true because $0$ is <em>never</em> greater than one.
Or maybe s/he wants this "Prove $P(n) = (n > 1 \implies n^2 > n)$". In which case, you'd say "If $n \le 1$, this is vacuously true and we don't need to ... | https://math.stackexchange.com |
153,014 | [
"https://physics.stackexchange.com/questions/153014",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25555/"
] | <img src="https://i.stack.imgur.com/GRDJ2.png" alt="enter image description here">
Would the speed of 'push' be equal to the speed of sound?
| Of course you know from special relativity that no information can propagate faster than $c$, which includes your directing the Mars end of the stick to move through your Earth end push.
But you don't need to think about SR at all. Simply think carefully about what would happen if you did give the end of this rod a su... | The speed of the push would be roughly the speed of the sound in whatever medium the stick was made of. One thing is certain - it would not exceed the speed of light.
| https://physics.stackexchange.com |
177,577 | [
"https://electronics.stackexchange.com/questions/177577",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35350/"
] | I am using TM4C1230C3PMI controller from Texas instrument in one of my project. It has 32KB of internal flash, which is not sufficient for my application. Higher flash sized micro-controller are available in the market which can be used but I want to go with this micro-controller only. As per my knowledge external EEPR... | You cannot extend the program memory (flash). TI produces the same chip with double the flash and RAM, but nothing else changed: <em>TM4C1230D5PMI</em>.
If you cannot use a chip with larger flash, you will have to reduce your code size:
<ul>
<li>Disable debugging, such as the expensive <code>printf</code> function. ... | You might get the smallest software footprint by using assembler and a Forth-like language designed for your purpose. Another is compressed machine code if there is a lot of almost identical code.
| https://electronics.stackexchange.com |
253,765 | [
"https://softwareengineering.stackexchange.com/questions/253765",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/93050/"
] | Usually, I consider a large number of parameters as an alarm bell that there may be a design problem somewhere. I am using a Generic Repository for an ASP.NET application and have a Controller with a growing number of parameters.
<pre class="lang-cs prettyprint-override"><code>public class GenericRepository<T>... | In my opinion a controller should only be a thin layer around the businesslogic.
If the controller needs several repositories that might be an indicator that the controller is doing too much and
logic should be moved to servicelayers for seperation of concerns:
Instead of having
<pre><code>OrderController(productRe... | I've been playig around with using seperate query and command classes instead of using repositories with multiple methods.
Your UserRepository might a <code>GetByEmail(string email)</code> method. Instead of that, I have a <code>GetUserByEmailQuery</code> class and a <code>GetUserByEmailQueryHandler</code> class.
You... | https://softwareengineering.stackexchange.com |
35,090 | [
"https://mathoverflow.net/questions/35090",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7692/"
] | Normally a 2-sided error randomized algorithm will have some constant error $\varepsilon < 1/2$. We know that we can replace the error term for any inverse polynomial. And the inverse polynomial can be replaced for an inverse exponential. Say that we have an algorithm $A$ with $\varepsilon_A=1/p(n)$ for some polynom... | There seems to be some confusion in your notation. When you says error $\epsilon$, do you mean the probability of failure is $\epsilon$, which means that the algorithm outputs the wrong answer with probability $\epsilon$. In this case, if $\epsilon$ is polynomially small, that's great. If you run it a few times you sh... | You cannot in general replace the inverse polynomial by an inverse exponential unless BPP = PP, which is highly unlikely.
| https://mathoverflow.net |
338,013 | [
"https://math.stackexchange.com/questions/338013",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/61039/"
] | I tried manipulating the terms but I couldn't get anywhere.
The only other thing I can observe is that the minimum must be greater than $1$ since all the terms are non-negative and the range of $\sec^4 x$ is $[1, \infty)$. Also it can't be $1$ since then $\sin^4 x + \cos^4$ must be $0$ which means $\sin x = \cos x = 0... | <strong>Hint</strong>: If you write $\sin^4 x$ as $(1-\cos^2 x)^2$ and $\sec x=\frac{1}{\cos x}$, then what you have is just a function of $\cos^2 x$, so you can set $u=\cos^2 x$ and look for a minimum of $(1-u)^2+u^2+u^{-2}$ under the condition that $u\in[0,1]$.
| For all non-negative $a$, we have the inequality $$\frac{1}{a}+a\geq 2.$$ We can deduce this from the fact that $(a-1)^2\geq 0\Rightarrow a^2+1\geq 2a$, and then dividing both sides by $a$. This inequality implies that $$\sin^4(x)+\cos^4(x)+\sec^4(x)\geq \cos^4(x)+\sec^4(x)\geq 2.$$
By considering $x=0$, we see tha... | https://math.stackexchange.com |
229,218 | [
"https://math.stackexchange.com/questions/229218",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/48194/"
] | Use the modulo version of the quadratic formula and Euler's criterion to decide if the following has a solution or not.
$2x^2+5x+8 \equiv 0\pmod{37}$
I'm not sure how I would use what was being asked of me to decide if this has a solution or not, but I have came to the conclusion that it does not, because I plugged i... | Consider the quadratic congruence $ax^2+bx+c\equiv 0\pmod{p}$, where $p$ is an odd prime. Multiplying through by $4a$, we obtain the equivalent congruence
$$4a^2x^2+4abx+4ac\equiv 0\pmod{p},$$
which, by completing the square, can be rewritten as
$$(2ax+b)^2\equiv b^2-4ac\pmod{p}.\tag{$1$}$$
So in order for the origin... | The modular version of the quadratic formula is, for all practical purposes, just the quadratic formula (provided twice the coefficient of $x^2$ is relatively prime to the modulus). As usual, you wind up looking at $b^2-4ac$, which here is $5^2-(4)(2)(8)=25-64=-39$. Since we're working modulo $37$, we can replace that ... | https://math.stackexchange.com |
2,242,629 | [
"https://math.stackexchange.com/questions/2242629",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/249258/"
] | I was doing the problem $$ A+B=AB\implies AB=BA. $$
$AB=BA$ means they're invertible, but I can't figure out how to show that $A+B=AB$ implies invertibility.
| Consider the expression $$(A-\mathbb 1)(B-\mathbb 1)=AB-A-B+\mathbb 1=\mathbb 1$$
Thus $(A-\mathbb 1)$ and $(B-\mathbb 1)$ are inverse to each other, whence $$\mathbb 1= (B-\mathbb 1)(A-\mathbb 1)=BA - A - B + \mathbb 1$$
It follows that $$BA=A+B=AB$$ and we are done.
Note: here $\mathbb 1$ denotes the appropriate ... | Start with equation:
<span class="math-container">$$A+B=AB$$</span>
replace <span class="math-container">$B$</span> with <span class="math-container">$(B - I) + I$</span> in left side
<span class="math-container">$$A+(B - I) + I =AB$$</span>
<span class="math-container">$$I =AB - A - (B - I)$$</span>
<span class="math-... | https://math.stackexchange.com |
364,260 | [
"https://physics.stackexchange.com/questions/364260",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/172965/"
] | In $\text{Work} = m \times a \times \text{distance}$.
From this equation, How can we know the duration of the force that have been applied
in order to move the object over that distance?
| In the simplest case of a straight line movement with a constant force starting from a zero speed, from energy conservation
$$W=\dfrac{mv^2}{2}=\dfrac{m(2v_a)^2}{2}=2m\left(\dfrac{d}{t}\right)^2$$
Where $v_a$ is the average speed. The solution for time follows
$$t=\sqrt{\dfrac{2m}{W}}\cdot d$$
| First of all: in general you cannot substitute $F_r=ma$ into $W=Fd$, the reason being that the work equation can be applied for any force, while Newton's 2nd law refers to the resultant force $F_r$. Also, if the force $F$ isn't constant, and we are in 3D, then work is calculated as $W=\int \vec{F}\cdot d\vec{x}$.
As f... | https://physics.stackexchange.com |
134,019 | [
"https://dba.stackexchange.com/questions/134019",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/73499/"
] | I have two different databases that both contain a table with the same structure. I have to go across and select the distinct records across both, how is this best achieved? The uniqueness is based on <code>Id</code>. The other columns in the table could have varying data, but <code>Id</code> should be used as the basi... | You can't log ship from the principal mirror to a database that's live in an AG, but to another DB you could then make an AG later. Enabling the AG feature and having other AGs has nothing to do with what you're trying to do unless I am misinterpreting.
| If you want to ensure you minimize the amount of time you are without HA during your migration, here's a trick I recently used:
<ul>
<li>Set up the AG with a "dummy" database so that your AG is ready in advance. </li>
<li>Log ship the database(s) to both your primary & secondary AG replicas--at this point, the log... | https://dba.stackexchange.com |
26,874 | [
"https://mathoverflow.net/questions/26874",
"https://mathoverflow.net",
"https://mathoverflow.net/users/799/"
] | Given a finite group G, its complexified ring of finite-dimensional complex representations is isomorphic to its algebra of class functions, by the trace map $\mathrm{Tr}_\rho: g \mapsto \mathrm{Tr}(\rho(g))$. These class functions can in turn can be shown to correspond to the elements in the center of the group algebr... | Off the top of my head: the representation ring is really indexed by the set of irreps (well, OK, a set of representatives from equivalence classes thereof) and is indeed commutative and semisimple (at least over the complex numbers) so isomorphic to an appropriate direct product of copies of the ground field.
The cen... | The centre of the group algebra has also a basis indexed by irreducible representations, the basis of central irreducible idempotents. But the corresponding natural linear map is not an isomorphism (irreducibles are not usually idempotents) unless you the group is an elementary abelian 2-group. So the natural map is so... | https://mathoverflow.net |
174,016 | [
"https://electronics.stackexchange.com/questions/174016",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/44008/"
] | I have a 74HC14 Schmitt trigger IC. I only use one of its I/O pairs, and everything else is not used.
I understand that in TTL logic the unused inputs should be set to either high or low to prevent floating pins.
But I wonder, can I set the outputs to high instead? Will the effect be the same, i.e prevent floating pins... | The 74HC14 isn't TTL, it's CMOS, and what matters is that the <strong>input</strong> pins be kept from floating.
The reason is because the impedance of the input pins is so high when they're floating that random charges accumulating there can/will cause unpredictable internal behavior in the chip, including oscillatio... | The output pins are being driven by the schmitt trigger; you should never tie a (non-tristated) output to a rail, and it won't do you any good here.
Because these are schmitt triggers, leaving the inputs floating is less harmful than would be the case for regular logic, but it's still a good idea (and free!) to tie th... | https://electronics.stackexchange.com |
296,398 | [
"https://softwareengineering.stackexchange.com/questions/296398",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/194161/"
] | Assume I have following class
<pre><code>class Student{
void method1(){
// Do Something
}
void method2(){
// Do Something
}
</code></pre>
}
And the object of this class is used as monitor in synchronization in some piece of the code as
<pre><code>class ProcessingThread implements Runnable {
... | <blockquote>
What happens when a thread acquires a lock?
</blockquote>
No other thread can acquire that lock until it's released.
Note that this is <strong>all</strong> that happens. Only methods called via <em>other threads</em> are affected. Only other threads that compete for <em>the same lock</em> are affected ... | To ensure safety <em>both threads</em> must go and acquire the lock before messing with the data of student.
If one thread doesn't do that then it's like neither thread acquired the lock.
Part of acquiring the lock is waiting until no other thread has the lock.
| https://softwareengineering.stackexchange.com |
31,963 | [
"https://cs.stackexchange.com/questions/31963",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/22753/"
] | I understand the theory behind the definition of Big-Oh, but when I try a question, I don't get how you would find the $c$ and $n_0$ values.
For example: if $f(n) = n!$ and $g(n) = 2^n$, how would I go about finding the $c$ and $n_0$ values for $g(n) = O(f(n))$?
| In general, you should first set up the inequality and then try to solve for $n$ in terms of $c$. Often, this won't be feasible - there may not be a way to analytically obtain a closed-form solution involving only $c$ and $n$. In such cases, you can usually massage the inequality down to something where solutions can b... | In this particular case, as $n$ increases by $1$, $g(n)$ doubles while $f(n)$ gets multiplied by $n+1$. That means that for $n \geq 1$, $g(n+1)/f(n+1) \leq g(n)/f(n)$, and so you can choose $n_0 \geq 0$ of your choice and $c = g(n)/f(n)$.
In the general case, suppose that you know that $g(n)/f(n) \to \gamma$, where $\... | https://cs.stackexchange.com |
112,536 | [
"https://security.stackexchange.com/questions/112536",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/36623/"
] | I have some sensitive data in the cookie, e.g. it contains the user id that is later on used to execute the query and we trust the cookie because it is encrypted. All communication happens only on https. Is it secure enough with just encryption, or I need to make sure that the cookie authenticity is maintained by e.g. ... | Yes you need a MAC in order to ensure the user hasn't manipulated the value to something else which is a valid user id once decrypted.
Also, rather than MAC <code><userid></code> you should add some context around it, and then mac that.
e.g. <code>userid=<userid></code>
This will prevent a substitution a... | HTTPS only prevents 3rd parties from doing man-in-the-middle attacks and manipulating the connection (including the cookie). HTTPS does not do anything to protect you from a malicious user. The user could edit their own cookie. You need to use authenticated encryption or sign the cookie's contents yourself if you don't... | https://security.stackexchange.com |
3,648,492 | [
"https://math.stackexchange.com/questions/3648492",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/775699/"
] | I am self studying Combinatorics from Richard Brualdi Elementary Combinatorics .
In chapter - System Of Distinct Representatives I am unable to solve this question ( Q no. 11) .
Let > 1 and let = <span class="math-container">${A_1,A_2 , … ,A_n}$</span> be a family of subsets of {1, 2, … , }, with <span class="math-c... | If the permutation <span class="math-container">$\pi$</span> of <span class="math-container">$[n]$</span> is a derangement, <span class="math-container">$\langle\pi(1),\pi(2),\ldots,\pi(n)\rangle$</span> is an SDR: for each <span class="math-container">$k\in[n]$</span> we have <span class="math-container">$\pi(k)\ne k$... | Let the distinct representatives be <span class="math-container">$a_1,a_2,\dots,a_n$</span>. By hypothesis, <span class="math-container">$a_i\neq i,\ i=1,2\dots,n$</span>. That is, <span class="math-container">$a_1,a_2,\dots,a_n$</span> is a derangement of <span class="math-container">$1,2,\dots,n$</span>.
| https://math.stackexchange.com |
262,728 | [
"https://dba.stackexchange.com/questions/262728",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/204043/"
] | I'm using PostgreSQL 9.5.19, DBeaver 6.3.4
I have a table where one row is - user's name, place he attended, time when he was there
I need to select all pairs of places where any user was (if user was at place a and place b i need row like this: user, place a, place b, time at place a, time at place b)
The ponds ta... | Postgresql 9.5.19 has windowing functions that prove helpful in such situation. The lead() function give you access to the next row in a "partition".
You could try something like that :
<pre><code>SELECT
user_name,
place_name AS r1_place,
tm AS r1_tm,
lead(place_name) OVER (PARTITION BY user_name ORDER BY tm)... | Colleague helped me to create window function:
<pre><code>select
subq.*
,EXTRACT(EPOCH FROM (subq.next_tm - subq.tm)) as seconds_diff
from (
select
t1.user_name,
t1.place_name,
t1.tm,
lead(t1.place_name) over w as next_place_name,
lead(t1.tm) over w as next_tm
from example.example as t1
wind... | https://dba.stackexchange.com |
56,705 | [
"https://stats.stackexchange.com/questions/56705",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17503/"
] | I am required to use the Naive Bayes classifier to classify example 8, to see whether it is poisonous or not.
<img src="https://i.stack.imgur.com/SnscY.png" alt="enter image description here">
I gained the following results:
p(x|Poisonous=Y) = 0.0267857 and
p(x|Poisonous=N) = 0.0101989
If I am given extra inform... | Bayes Theorem:
$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
So it seems what you're looking for its:
$P(poisonous=Y|X) = \frac{P(X|poisonous =Y)P(poisonous)}{P(X)}$
Use the law of total probability:
$P(poisonous=Y|X) = \frac{P(X|poisonous=Y)P(poisonous)}{P(X|poisonous=Y)P(poisonous) + P(X|poisonous=N)P(not poisonous)}$
It ... | Think about your extra information as a new prior: $P(\textrm{Poisonous}) = 0.05$. It should be pretty easy to slot that into Bayes' Rule, no?
| https://stats.stackexchange.com |
163,641 | [
"https://softwareengineering.stackexchange.com/questions/163641",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17309/"
] | My coworker and I have different opinions on the relationship between base classes and interfaces. I'm of the belief that a class should not implement an interface unless that class can be used when an implementation of the interface is required. In other words, I like to see code like this:
<pre><code>interface IFo... | <blockquote>
I'm of the belief that a class should not implement an interface unless that class can be used when an implementation of the interface is required.
</blockquote>
<code>BaseWorker</code> fulfills that requirement. Just because you can't directly instantiate a <code>BaseWorker</code> object doesn't mean ... | I'd have to agree with your coworker.
In both examples you give, BaseWorker defines the abstract method Work(), which means that all subclasses are capable of meeting IFooWorker's contract. In this case, I think BaseWorker should implement the interface, and that implementation would be inherited by its subclasses. ... | https://softwareengineering.stackexchange.com |
3,671,025 | [
"https://math.stackexchange.com/questions/3671025",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/787227/"
] | I have a point <span class="math-container">$(x_0, y_0)$</span> at <span class="math-container">$(1, 2)$</span> and a directional vector <span class="math-container">$\vec{v}=\left[\frac{3}{5} \frac{4}{5}\right]$</span>. The corresponding implicit form is <span class="math-container">$$4x - 3y + 2 = 0$$</span> How did ... | <span class="math-container">$ {\left( {\overline A} \right)^{\text{o}}}=\emptyset \iff {\left ( {\left( {\overline A} \right)^{\text{o}}} \right)}^c=X$</span> <span class="math-container">$ \iff {\overline {{(A^c)^{\text{o}}}}}=X$</span>.
Then <span class="math-container">${(A^c)^{\text{o}}}$</span> is dense in <... | Let <span class="math-container">$U\subseteq A\cup B$</span> be open.
Then <span class="math-container">$V=U\setminus \bar A$</span> is open and <span class="math-container">$V\subseteq (A\cup B)\setminus \bar A\subseteq B$</span>, so <span class="math-container">$V=\emptyset$</span>. Thus, <span class="math-container... | https://math.stackexchange.com |
435,597 | [
"https://physics.stackexchange.com/questions/435597",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/149817/"
] | In section 6.1 of Peskin's quantum field theory introduction, right after equation 6.3, the four current density <span class="math-container">$j^{\mu}$</span> is said to be conserved because for any function <span class="math-container">$f \left( x \right)$</span> that falls off at infinity, we have
<span class="math-... | Current conservation is <span class="math-container">$\partial_\mu j^\mu=0$</span>, not integrated over ANYTHING (note the zeroth component of <span class="math-container">$j$</span> is the current density, so this is equivalent to the usual statement of current conservation <span class="math-container">$\dot\rho=-\vec... | I don't know Peskin's book, so I guess. Maybe the author has defined a quantum field as an operator-valued distribution? Then it would make sense to insert a test function, since to say <span class="math-container">$T=0$</span> if <span class="math-container">$T$</span> is a distribution means <span class="math-contain... | https://physics.stackexchange.com |
236,222 | [
"https://electronics.stackexchange.com/questions/236222",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/91853/"
] | I am reviewing about using complex number in solving electrical linear circuits.
I see that the input sinusoidal signal \$ V_m \cdot \cos(\omega t) \$ is replaced \$ V_m \cdot e^{jwt}\$.
Then solve for the complex output voltage with the complex input voltage above.
Finally, output voltage is the real part of "compl... | <blockquote>
Why the imaginary part added to the input doesn't affect the real part of the output voltage?
</blockquote>
Short answer: because of the linearity.
A system may be described as an operator \$\operatorname{L}\$, which takes a function and outputs the transformed function:
$$y(t) = \operatorname{L}(x(t))... | Generally, a sinusoidal waveform may be represented as a complex number by using Euler's identity and freezing time at \$\small t=0\$.
Consider a sinusoid with amplitude, \$\small V_m\$ a phase angle, \$\small \phi\$, which may be written:
$$V= V_m\: e^{j(\omega t+\phi)}=V_m[cos(\omega t+\phi) +jsin(\omega t+\phi)]$$
... | https://electronics.stackexchange.com |
6,740 | [
"https://electronics.stackexchange.com/questions/6740",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | I am trying to develop a very high reliability product, with a MTBF exceeding 100,000 hours, hopefully in the 250,000 hours range. Yep, I know - stupidly high reliability, at least 10 years.
Most LED's I've seen have a reliability rating of only 20,000 hours. What happens after this? Do they reduce in output too much... | Must say I've always been highly sceptical of the meaningfulness of MTBF figures.
LEDs will gradually reduce brightness over time, but it will be many times their stated life before they cease to be useable as a power indicator. Running at well below the specc'd current will increase lifetime many-fold.
And would fail... | I think you are utterly doomed trying to get to MTBF of 250000 hours on any usefully complex product, but then you haven't said what it is, so it might be very simple.
LEDs tend to age faster if they're hotter / driven at higher currents, and the failure mechanism is different for white leds (which are fluorescent) an... | https://electronics.stackexchange.com |
123,157 | [
"https://electronics.stackexchange.com/questions/123157",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/50278/"
] | When the internet appears to have crashed, the service provider invariably gives this advice as a first line remedy: unplug the router from the wall socket, then wait 5 minutes, then plug it back in. Many times this remedy works.
Question: Why does the router care if it's been unplugged from the wall versus simply tu... | What you are waiting can be two things. One is for the ISP to "release" your dynamic IP address, and after 'x' minutes, when powered back on, the MRC (Modem/router combo) will be re-assigned an IP address to its MAC address.
The other reason is to allow a internal capacitor to discharge completely to allow the volat... | If you have a 'hard' on/off switch this should have the same effect as pulling the plug. But a lot of devices nowadays have a 'software managed' switch, which is of course useless when you want to force a hard reset on the software.
The 5 minutes is to make sure that the device has really lost its power. A power suppl... | https://electronics.stackexchange.com |
2,110,430 | [
"https://math.stackexchange.com/questions/2110430",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/266135/"
] | Let's suppose I have a subset $A \subset \mathbb{R}$, then $A$ is bounded as $\sup A$ and $\inf A$ exist in $\mathbb{R}$.
But suppose I have $A \subset \mathbb{R}^k$, how does one define boundedness for this subset?
I've been told that $\sup A$ and $\inf A$ have no meaning in $\mathbb{R}^k$, but I can't see why thi... | Your proof is correct, maybe we can make it slightly faster.
Let <span class="math-container">$z$</span> be a limit point of <span class="math-container">$\overline A$</span>. Every open set <span class="math-container">$U$</span> containing <span class="math-container">$z$</span> must contain a point <span class="math... | If z is a limit point of <span class="math-container">$\bar{A}$</span> and <span class="math-container">$U$</span> is a open set containing <span class="math-container">$z$</span> then it must contain a point in <span class="math-container">$\bar{A}$</span>. But as an open set containing a point in <span class="math-co... | https://math.stackexchange.com |
302,681 | [
"https://stats.stackexchange.com/questions/302681",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/115971/"
] | I'm trying to show that the mode (i.e. the maximum) of a Gaussian distribution is given by its mean.
Consider that the Gaussian distribution is given by Equation 1: $$N(x|\mu, \sigma^2)=\frac{1}{(2\pi\sigma^2)^{1/2}}exp(-{\frac{1}{2\sigma^2}}(x-\mu)^2)$$
where $\mu$ is the mean and $\sigma^2$ is the variance.
To so... | It's not always wise to jump straight into taking derivatives (indeed there are a number of widely used densities where this will be useless, or if you're sufficiently rash in going about it, may lead you to select values that are not the mode).
Let's think a little first. That often pays handsome dividends.
<ol>
<l... | Your intuition is good. Removing constants, you have
$$exp(-(x-\mu)^2/2\sigma^2) (\mu-x) = 0,$$
which is zero if either $ (x-\mu)^2 \to \infty$ or $\mu = x$.
The last step is to take a second derivative in order to distinguish the maximum from the minimum. Since this is a self-study question I'll leave out the equat... | https://stats.stackexchange.com |
237,882 | [
"https://physics.stackexchange.com/questions/237882",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/87129/"
] | Let us consider a circuit made up of connecting wires, a resistor, a switch and a battery. Now, the resistance of the resistor is much higher than that of the wire. Now, intuitively, I am thinking that current flow would be less in the resistor than the wires. But, I have read at many places where they write that the c... | Current is charge per second passing by. Think of the consequences if at one spot more current was flowing than in another spot.
<ul>
<li>If at spot A the current is <em>smaller</em> than in a later spot B, then less is flowing in every second than what is flowing out. After some time there wouldn't be any more charg... | Current is the movement of charges through the wire. Since charge is conserved, it has to be the same at any given point in a closed circuit without branches, otherwise the circuit would be leaking.
An often cited analogy would be a system of water pipes. It might be more difficult for the water to squeeze through nar... | https://physics.stackexchange.com |
24,425 | [
"https://physics.stackexchange.com/questions/24425",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8889/"
] | That's how it's framed in my Physics school-book.
The question (or rather, the explanation) is that of the thrust of rockets and how the impulse is equal (with opposite signs) on the thrust-gases and the rocket itself.
$( m \frac { \Delta v}{ \Delta t} ) = -(v \frac {\Delta m}{ \Delta t} ) = F_i$
I suppose it's a p... | Here is a visualization:
Momentum is mass times velocity, so draw it as the area of a rectangle:
<img src="https://i.stack.imgur.com/ca1oO.png" alt="enter image description here">
If we change the mass and velocity a little, we change the momentum:
<img src="https://i.stack.imgur.com/z2nZ2.png" alt="enter image des... | It's only true when the changes $\Delta t$, $\Delta v$, $\Delta m$ are small and then it is known as the Leibniz rule, the rule for the derivative of a product, which Leibniz (but also Newton) discovered when they invented the calculus 3 centuries ago.
Just look at this proof:
$$\frac{\Delta (mv)}{\Delta t} = \frac{(... | https://physics.stackexchange.com |
51,937 | [
"https://dba.stackexchange.com/questions/51937",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/29619/"
] | I have a table in a database with these columns
<pre><code>id name facility_Type
1 Taluka y,n,n,y,n
</code></pre>
Now I want to retrieve the comma separated values like this
<pre><code>id name Ambulance ward male_doctors female_doctors operation_theator
1 Taluka yes no ... | Some databases would support something like this (Oracle, MySQL, PostgreSQL, SQLite).
<pre><code>select T.id,
T.name,
case substr(T.facility_type, 1, 1) when 'y' then 'yes' else 'no' end as Ambulance,
case substr(T.facility_type, 3, 1) when 'y' then 'yes' else 'no' end as ward,
case substr(... | If your facility_Type is a fixed length, and then a rather static (non-dynamic) method of doing it would just be to identify the letter at position 1, 3, 5, 7 and 9.
You do not mention what database you use, but for <strong>SQL Server</strong> (for example) it could be done something like this:
<pre><code>SELECT
id, ... | https://dba.stackexchange.com |
118,081 | [
"https://electronics.stackexchange.com/questions/118081",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39585/"
] | Can anyone explain to me why there are 2 maximum voltages/amperage for both AC and DC like below ?
10A 250VAC 10A 125VAC
10A 30VDC 10A 28VDC
I was thinking that the one on the left is for normally open and the one on the right for normally closed ?
<img src="https://i.stack.imgur.com/XNsXc.jpg" alt="enter ima... | NC vs NO is is usually a different current at the same voltage (if the ratings are, in fact different).
More likely the differences you cite would refer to compliance with different safety agencies.
For example, this one:
<img src="https://i.stack.imgur.com/AujXg.png" alt="enter image description here">
Should not ... | Don't know about the compliance thing mentioned here however mechanical relays have different AC and DC ratings - this is standard! Now why... When the relay opens there will be an arc between the contacts.
If you are running AC (say 50Hz) the current goes down to 0A A 100 times per second, after this happened once th... | https://electronics.stackexchange.com |
275,706 | [
"https://mathoverflow.net/questions/275706",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | The product
$$
F(s)=\prod_{p}\frac1{(1-p^{-s})^p},
$$
converges for $\mathrm{Re}(s)>2$, when $p$ runs over all primes. Does it admit analytic continuation beyond the line $\mathrm{Re}(s)=2$? Any papers where it has been studied?
| $$P(s) = \sum_p p^{-s}, \qquad \log F(s) = \sum_{p^k} \frac{p^{1-sk}}{k} = \sum_{k\ge 1} \frac{P(sk-1)}{k}$$
<ul>
<li>$P(s) = \sum_{n=1}^\infty \frac{\mu(n)}{n} \log \zeta(ns)$ and $P_N(s) = \sum_{n=N+1}^\infty \frac{\mu(n)}{n} \log \zeta(ns)$ is analytic for $\Re(s) > \frac{1}{N+1}$
so that $$e^{N! P(s)} = e^{N! ... | Let $\sigma:=\mathrm{Re}(s)$, and consider the principal branch of the logarithm. For $\sigma>3/2$ we have
$$\begin{align*}p\log(1-p^{-s})-\log(1-p^{1-s})&=p\left(-p^{-s}+O(p^{-2\sigma})\right)-\left(-p^{1-s}+O(p^{2-2\sigma})\right)\\&=O(p^{2-2\sigma}),\end{align*}$$
hence the "Euler sum"
$$H(s):=\sum_p\left... | https://mathoverflow.net |
236,833 | [
"https://dba.stackexchange.com/questions/236833",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/177795/"
] | I have an assignment where I have to design a logical model.
I have a relation NURSE that has "nurse_id" and "certification". The certification attribute has yes/no values, so, should I move it to another relation, or is it okay to keep it in the same NURSE relation?
And is the suitable data type for that attribute ... | As usual, it depends. Given your description, it seems already decided that certificate is a boolean type and if that's correct there is no reason to create a new relation.
However, in a real-world situation, there are probably more attributes involved. I can imagine something like:
<pre><code>NURSES:
nurse_id p... | For a logical database design you don’t need to specify TINYINT or CHAR — that’s a physical consideration. Some DBMSes such as Postgres have a BOOLEAN data-type which would be preferred, but again, a physical design.
In your logical model you could assume a binary-valued datatype with Yes and No as the two values (or ... | https://dba.stackexchange.com |
9,290 | [
"https://softwareengineering.stackexchange.com/questions/9290",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | A quality what I would like to develop is to write more concise code. With writing more concise, at least in my opinion, the opportunity to add bugs to the code is smaller. It is easier to read the code for other.
My question is if it is something that just comes with experience or is it something you can do explicitl... | I would say that on the whole it is something that comes with time and experience, but you may find that if you do some work with more terse languages you bring that quality back to your regular working languages.
Certainly after a year or two working with Ruby I found my C# got a lot tauter. I think if I was to unde... | One great way to write less code is to try to <strong>avoid re-inventing the wheel</strong>, and use existing software components when available.
One common answer I get when I ask why people did their own ORM, or their own logging engine, or their own UI components, or their own everything:
<blockquote>
But our is... | https://softwareengineering.stackexchange.com |
43,442 | [
"https://dba.stackexchange.com/questions/43442",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/12917/"
] | I have a single table that contains 4 billions rows that I plan on splitting up in to separate tables for each Quarter of the year. Then I want to create a partitioned view across all tables.
At the moment I have one filegroup for data (where most of the data resides) and one filegroup for non-clustered Indexes (I hav... | If you're going with traditional partitioned views with each table containing a different yearly quarter, then you have a few levels of separation here:
<ol>
<li>Each Table</li>
<li>Each Index on Each Table</li>
</ol>
So in other words, say you have 10 tables that the partitioned view accesses, and you have a cluster... | I see various points to address here:
<ul>
<li>partitioning of a large table</li>
<li>filegroup placement of nonclustered indexes</li>
</ul>
Starting with the second one, separating non-clustered indexes might not be a good idea as a general purpose approach.<br>
Having storage aligned (rows in a table, along with th... | https://dba.stackexchange.com |
561,334 | [
"https://math.stackexchange.com/questions/561334",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $M$ be the following subsets of $\mathbb R^4$:$$M= \{(x,y,z,w), 2x^2+2=z^2+w^2, 3x^2+y^2=z^2+w^2 \}$$
we know $M$ is a submanifold of $\mathbb R^4$,what is the Euler Characteristic of M?
| Let $F:\mathbb{R}^4\rightarrow\mathbb{R}^2$ be defined by $F(x,y,z,w)=(x^2+y^2,z^2+w^2-2x^2)$. Then $M=F^{-1}(2,2)$. I'll assume that you know how to check that $(2,2)$ is a regular value of $F$ (hint: on $M$, $x,y$ do not vanish simultaneously and the same happens for $z,w$). Then $M$ is a surface embedded in $\mathbb... | I'll give another answer without making use of Morse theory. Since we suspect $M$ is a torus we may try to find a diffeomorphism between $M$ and $S^1\times S^1$. The map
$$
\begin{array}{ccc}
M & \longrightarrow & S^1\times S^1\\
(x,y,z,w) &\longmapsto & \left(\left(\frac{x}{\sqrt{2}},\frac{y}{\sqrt{2}}... | https://math.stackexchange.com |
194,782 | [
"https://mathoverflow.net/questions/194782",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50426/"
] | Fix $q$ to be a positive integer. Let $$f : \mathbb{N} \to \{-1 ,0, 1\}$$ be a $q$-periodic arithmetic function such that $$\sum_{n = 1}^q f(n) = 0.$$ If $f$ is not identically zero, is it true that $$\sum_{n=1}^{\infty} \frac{f(n)}{n} \neq 0?$$ I ask this question in attempt to understand how general of a statement i... | Not necessarily. The first counterexample might be
$q=14$ and $f(n)=1, -1, -1, -1, -1, 1, 0, -1, 1, 1, 1, 1, -1, 0$
for $n=1,2,3,\ldots,14$.
| On the other hand, a variant of the question has a positive answer.
This question was raised by Chowla in 1964 in the case that $q = p$ is prime and $f(p) = 0$ (but with $f$ taking arbitrary rational values). This was settled affirmatively in a paper by A. Baker, B. Birch, and E. Wirsing ("On a problem of Chowla," <em... | https://mathoverflow.net |
118,366 | [
"https://cs.stackexchange.com/questions/118366",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/105892/"
] | I am trying to prove the theorem
<blockquote>
A language is Turing-recognizable iff some enumerator enumerates it.
</blockquote>
I proved the "if" part, but I have no idea of proving the "only if" part, so I searched a proof for the "only if" part of this theorem. In the proof that I found, it says
<blockquote>
... | In slightly more detail, what's happening is:
<ol>
<li>Run the machine on input <span class="math-container">$s_1$</span> for one step. If it accepts, list the string.</li>
<li>If the machine didn't halt on the previous step, run the machine on <span class="math-container">$s_1$</span> for one more step and then on <s... | A language is <em>Turing-recognizable</em> (or <em>Recursively enumerable</em>) <em>iff</em> there exists a <em>Turing Machine</em> which will enumerate all valid strings of the language.
What you probably miss in the above proof is the fact that <span class="math-container">$i$</span> can take any value ... when we s... | https://cs.stackexchange.com |
28,750 | [
"https://dsp.stackexchange.com/questions/28750",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/19209/"
] | I just learned following notation for a sine wave:
$A e^{j\phi t}$
A low passfilter and a highpass filter respectively generate a phase shift in the complex plane of the sine wave as follows:
$A e^{-j\phi t}$ and $A e^{+j\phi t}$
I don't understand what phase shifting has to do with letting higher or lower frequenc... | <blockquote>
I just learned following notation for a sine wave: $Ae^{j\phi t}$
</blockquote>
well, that's not really a sine wave; that's a complex sinusoid. The real and imaginary parts of that are cosine and sine, respectively.
<blockquote>
A low passfilter and a highpass filter respectively generate a phase shi... | Because they need a certain time delay in order to "decide" what the output should look like if the output changes a lot. Imagine you see a number series and your brain has to decide what the mean value of these number series is. You will need to look at several numbers to arrive at some reasonable conclusion (let's as... | https://dsp.stackexchange.com |
143,565 | [
"https://electronics.stackexchange.com/questions/143565",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37758/"
] | I have a power supply that has only screw terminals for its AC mains input. Currently I'm using a power cord from a computer that I cut the female end off of and attached fork terminals to (live, neutral, and ground). It works fine but now I'd like to add a rocker-type switch to the cord so I don't have to unplug it ... | ALWAYS switch the live wire(s). If you only switch the neutral, then the entire circuit becomes live when switched off.
Switching the neutral also can add some safety in case the outlet is wired backwards. It would also allow you to give it 120-0-120 split phase later on (240v total), if it's rated for that.
Do NOT... | A SPST-type is ok and you should put it on the live wire (as usual), doing so also provide a protection for you circuit since that there will be no main voltage in the circuit if something short, as long as the switch is open.
In other word, placing the switch on the main will isolate your circuit from the main when t... | https://electronics.stackexchange.com |
35,699 | [
"https://mathoverflow.net/questions/35699",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1/"
] | One very handy (counter)example I often think about is the scheme $Spec(k[a,b,c]/(ab-c^2))$ (where $k$ is a field), which you may also know as $Spec(k[x^2,xy,y^2])$, as $\mathbb A^2/\mu_2$, or as the $A_1$ singularity. As with other (counter)examples, I'd like to be able to say as much as possible about it.
There is a... | It seems to me that in the global case the answer should be $no$ because of the following argument.
Set $S:=Spec$ $k[x,y,z]/(z^2-xy)$. Then $S$ is isomorphic to a quadric cone in $\mathbb{A}^3$. The point is that there are plenty of smooth double covers of $S$, which are pairwise non-isomorphic.
To see this, notice f... | At least in the complete (or henselian) case, this generalizes. Suppose $R$ is a complete regular local ring of dimension at least $2$ and $G$ a finite group of automorphisms of $R$, acting freely on $V=Spec\ R$ outside the origin. Put
$X=V/G$, and suppose $S$ is another complete regular local ring with a finite surje... | https://mathoverflow.net |
218,282 | [
"https://dba.stackexchange.com/questions/218282",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/102996/"
] | <h1>Case of use</h1>
We have a log table without a PK with two columns (date, event);
You inserted a row. Then you want to undo the inserted record.
Is there a way to delete that row (without deleting other rows with the same data), that doesn't use postgres only capabilities?
I want a solution that works in anot... | You should try this one:
<pre><code>SELECT *
FROM
( SELECT tb1.*,
tb3.id AS hasDiscount,
tb2.type,
tb2.amount,
CASE WHEN tb3.id IS NULL THEN tb1.price
WHEN tb2.type = 1 THEN tb1.price -(tb1.price * tb2.amount) / 100
ELSE tb1.price - tb2.a... | Start with that:
<pre><code>select * from products where price > 100 and price < 150;
</code></pre>
Then...
<pre><code>select * from products p
left join discounted_products dp on dp.product_id = p.id
left join discounts d on dp.discount_id = d.discount_id
where (price+IFNULL(d.amount,0)) > 100 and (pr... | https://dba.stackexchange.com |
101,776 | [
"https://dba.stackexchange.com/questions/101776",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/66704/"
] | Please help me figure out why postgresql isn't playing nice with updating. I can't find anything on SO or Google that remedies this problem. This is a production server and a distribution reinstall is not really an option. apt-get install -f and apt-get autoclean/check will tell you to use apt-get install -f.
<pre>... | This is how I fixed my issue:
`dpkg -l | grep postgres
will show you the postgresql packages that have been installed. Run:
<pre><code> sudo apt-get --purge remove
</code></pre>
with each package name, separated by a space, following <em>remove</em>.
<pre><code>root@vps1484:/home# dpkg -l | grep postgres
ii pos... | Go to this location <code>cd /var/lib/dpkg</code>
Delete everything <code>sudo rm -f postgresql-*</code>
Please note that this is not a correct way but it is working. This happened since you haven't properly uninstalled PostgreSQL.
| https://dba.stackexchange.com |
60,137 | [
"https://electronics.stackexchange.com/questions/60137",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17944/"
] | This follows on from another question I'd been asking. Having been 'gifted' dozens of mains LED lamps, I've been blithely assuming that they don't offer much in the way of inductive load.
But, of course, they aren't just a mass of LEDs: there's a rectifier, and perhaps an inverter (though a glance at the wiring of th... | LEDs are a nonlinear load and probably these lamps will not have a power factor correction converter. This means that the current will not be sinusoidal therefore you will have some reactive power flowing. There may be a PFC choke before the rectifier bridge.
If you want to measure the power factor and harmonic conte... | I measured a few LED table lamp bulbs. The PF was 0.86. I also measured some CFLs, and the power factor was 0.90.
| https://electronics.stackexchange.com |
195,181 | [
"https://softwareengineering.stackexchange.com/questions/195181",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51350/"
] | I've seen many lists on the internet that includes many 'ities' (maintainability, scalability, portability, etc), but I'm not sure if animations, screen transitions, and similar features are functional or non functional requirements.
| Animations can be an extremely important part of the user interface. They communicate or hint at things a user can do, guide the user through the application or help build up a well defined mental model of the application inside the user's head. Consider the classic iPod interface, where screens slid from side to side ... | Your question is like "Is the color of a real world object a functional or non-functional property?" and the answer is - it depends.
The color of a car is mostly non-functional, since it has no direct influence in the main functions of a car (you can have cars any color you like, they all can go from A to B, transpor... | https://softwareengineering.stackexchange.com |
1,286,464 | [
"https://math.stackexchange.com/questions/1286464",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/223498/"
] | I first heard of the following problems when I was a freshman, and I remember that my TA showed me a very short and elegant solution which I am unable to recall now. I think I know how to solve it using (quite a lot of) $\epsilon-\delta$. I would like to see solutions which does not involve explicitly $\epsilon-\delta$... | Assume there is a nonconstant continuous $f$ having a local maximum at all points $x\in{\mathbb R}$. Then there is such an $f$ with $f(0)=0$, $\>f(1)=1$.
Define
$$\tau:=\sup\bigl\{t\>\bigm|\>0\leq t\leq1, \ f(t)\leq0\bigr\}\ .$$
Continuity then implies $f(\tau)\leq0$ and $\tau<1$. Since $f(t)>0$ for $\ta... | For the first part, let $a\in\mathbb {R}.$ Then there is $\delta > 0$ such that $f(x)\le f(a)$ for all $x \in [a-\delta, a + \delta].$ Claim: $f$ is constant in this interval. Proof: Suppose $f(b) < f(a)$ for some $b\in (a,a+\delta].$ Let $m$ be the minimum value of $f$ on $[a,a+\delta];$ this minimum value exist... | https://math.stackexchange.com |
280,002 | [
"https://dba.stackexchange.com/questions/280002",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/177400/"
] | In our environment, users were granted read/write/ddladmin permissions on tempdb database (dev/qa/prod).
These permissions will be lost when SQL Services restart, as tempdb rebuilds every time. One solution that is currently in place is - reapply the permissions scripts from a SQL Agent job, when ever SQLAgent starts. ... | An alternative to modifying model <em>might</em> be to create a stored procedure in the master database that contains whatever you need to do. Then you mark this as startup proc (sp_procoption).
You might have to put in a WAITFOR in there in case SQL Server executes this before model has been recovered and tempdb has b... | If you read the top accepted answer on the StackOverflow you linked, it takes a step back and asks the question "why are you creating permissions for users on TempDB"? They're unnecessary for users to create, access, and manage temporary objects in it. The permissions you mentioned are already implicitly gran... | https://dba.stackexchange.com |
179,905 | [
"https://stats.stackexchange.com/questions/179905",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/93914/"
] | I keep running into problems in understanding hazard rates. I know, for example, that in a strict sense a hazard rate is not a probability and it is continually mentioned that because of this the hazard rate has no upper bound.
Am I right in understanding that hazard function values can be interpreted as instantaneou... | The hazard is indeed a rate. It is the expected number of events a person can expect per time unit conditional on being at risk, i.e. not having died before. Say we are studying the time until you get the flu [influenza] , and we measured time in months and we got a hazard rate of .10, that is, a person is expected to ... | This is perhaps best understood by looking at the exponential (time to a single event) distribution with a constant hazard rate $\lambda $, there the probability of an event by time $t$ is $1-e^{-\lambda t}$. So it is always $\in [0,1] $. In contrast the Poisson distribution is the corresponding distribution for recurr... | https://stats.stackexchange.com |
745,880 | [
"https://physics.stackexchange.com/questions/745880",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/321102/"
] | Consider an object rotating about its own axis. If the law of inertia is applicable, the object should keep rotating with the same angular velocity if no external torque is provided, but how is the linear velocity of the particles of the object changing if there is not an external force, (Newton first law?)
Can someone... | <blockquote>
but how is the linear velocity of the particles of the object changing if there is not an external force
</blockquote>
You have to be consistent on what you term as a system.
If the system is the entire object, then there is no external force and the center of mass does not accelerate.
If the system is jus... | Instead of a rigid object, imagine two opposing masses on springs, spinning around the central axis.
The springs are what accelerates the masses, forcing them to go in a circle.
A rigid object is kind of like that, except instead of springs, it's held together by forces between molecules.
| https://physics.stackexchange.com |
225,726 | [
"https://softwareengineering.stackexchange.com/questions/225726",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/116308/"
] | The question is about <strong>typehinting of the role interfaces</strong>.
The <em>code example</em> has two DataMappers which typehint the interface they need in the constructor,
FooDataMapper type hints the Preparable interface. Because it dependens on it and no other method from the dependency.
In the other mapp... | The <strong>consumer</strong> of dependencies is the one responsible for defining them (by means of their interfaces). In your example, <code>BarDataMapper</code> rules. I see two possible scenarios:
<ol>
<li>If <code>BarDataMapper</code> depends on a single object implementing both <code>prepare()</code> and <code>qu... | I think you are standing on one edge case, which can either mean that you have pushed software engineering in some place where PHP can't help you much or that you have some kind of conception problem.
<strong>According to the interface segregation principle</strong> the DataMapper interface should be strict enough for... | https://softwareengineering.stackexchange.com |
25,947 | [
"https://engineering.stackexchange.com/questions/25947",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/17811/"
] | I have a question that I can't solve.
Coefficient of drag= x,
Coefficient of Lift= y,
it is given that x= 0.015 + 0.05*(y^2), FInd Max Lift to drag ratio
and I know that Lift to drag ratio is L/D= Coefficient of lift/Coefficient of drag. Can anyone tell me how to solve this
Thanks in advance
| The lift(y) to drag(x) ratio can be expressed as:
<span class="math-container">$LD_{ratio} = y/x = \frac{y}{0.015 + 0.05*(y^2)}$</span>
You will get the maximum when the denominator is 0, so when:
<span class="math-container">$0.015 + 0.05*(y^2)=0$</span>
Hence, only when
<span class="math-container">$$y = 0. - 0.54... | As has been mentioned above by Eric Shain the correct answer is to take the partial with respect to y= CL and equate it to zero. Let's Call the max L/D, M.
<span class="math-container">$$M = \frac{C_L}{C_D} = \frac{C_L}{C_{D_0} +K*C_L^2}, \quad C_{D_0}=0.015\ and\ K=0.05 $$</span>
<span class="math-container">$$ \fra... | https://engineering.stackexchange.com |
149,531 | [
"https://physics.stackexchange.com/questions/149531",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56452/"
] | Consider this:
you are driving through a tunnel listening to your AM radio and a GPS, all of the sudden AM radio has nothing but statics and your GPS says "reconnecting - please hold".
You say to yourself, this can't be happening, because radio signal would move through the opening of the tunnel to reach your anten... | It is all about wavelength versus tunnel diameter. The wavelength of GPS is about 20cm it would happily propagate in any normal tunnel if it could get in but the earth and other structures absorb it. AM radio (600kHz - 1500kHz) cannot propagate in any normal tunnel because the wavelength is too long (500m-200m) relativ... | Both of these technologies rely on radio frequency waves, which are blocked by dense matter eg, a hill, a building.
| https://physics.stackexchange.com |
383,198 | [
"https://physics.stackexchange.com/questions/383198",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | A body is floating partly immersed in a liquid. The body and the liquid are taken to the Moon. What will happen next? Will its immersed part come out of the liquid? Will it sink? Will it continue to float as before?
| In the usual simple argument based on Archimedes' principle, the volume of fluid displaced is simply $V_{\rm disp}=m/\rho_{\rm f}$ where $m$ is the mass of the object and $\rho_{\rm f}$ is the density of the fluid in which it is floating. The mass of the object obviously doesn't change by moving it to the Moon (though ... | I believe, the volume of ball immersed in water on the moon will be greater than that on earth. It's because, when you say it is partly immersed, buoyancy due to air must also be considered and there is no air on moon. So, the buoyant force experienced by the body on moon will be less, making it get a bit more submerge... | https://physics.stackexchange.com |
23,095 | [
"https://security.stackexchange.com/questions/23095",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10834/"
] | I am using internet by connecting mobile phone to my laptop using usb. From yesterday,my browser (firefox) shows <img src="https://i.stack.imgur.com/Qbdtw.png" alt="like this"> for all most all website. Why this happen? How can i solve this?
| The date/time on your device maybe invalid.
All SSL certificates have a start and end period. Certificates can be compromised and its a good practice to renew them.
| Your mobile provider might be routing everything thru a proxy server that is doing SSL inspection, so it can do content filtering or bandwidth optimisation, which Firefox is detecting as a man-in-the-middle attack.
| https://security.stackexchange.com |
212,995 | [
"https://softwareengineering.stackexchange.com/questions/212995",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/103666/"
] | I have a function that takes in a set of parameters, then applies to them as conditions to an SQL query. However, while I favored a single argument array containing the conditions themselves:
<pre><code>function searchQuery($params = array()) {
foreach($params as $param => $value) {
switch ($param) {
... | IMHO your colleague is correct for the above example. Your preference might be terse, but its also less readable and therefore less maintainable. Ask the question why bother writing the function in the first place, what does your function 'bring to the table'- I have to understand what it does and how it does it, in gr... | My answer is more or less language agnostic.
If the only purpose of grouping arguments in a complex data structure (table, record, dictionary, object...) is to pass them as a whole to a function, better avoid it. This adds a useless layer of complexity and makes your intention obscure.
If the grouped arguments have a... | https://softwareengineering.stackexchange.com |
157,373 | [
"https://softwareengineering.stackexchange.com/questions/157373",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36006/"
] | I know that default arguments are created at the function initialisation time and not every time the function is called. See the following code:
<pre><code>def ook (item, lst=[]):
lst.append(item)
print 'ook', lst
def eek (item, lst=None):
if lst is None: lst = []
lst.append(item)
print 'eek', ls... | I think the reason is implementation simplicity. Let me elaborate.
The default value of the function is an expression that you need to evaluate. In your case it is a simple expression that does not depend on the closure, but it can be something that contains free variables - <code>def ook(item, lst = something.default... | One way to put it is that the <code>lst.append(item)</code> <em>doesn't</em> mutate the <code>lst</code> parameter. <code>lst</code> still references the same list. It's just that the content of that list has been mutated.
Basically, Python doesn't have (that I recall) any constant or immutable variables at all - but ... | https://softwareengineering.stackexchange.com |
370,672 | [
"https://stats.stackexchange.com/questions/370672",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/221723/"
] | I am here to ask something that I think it is interesting, first I just read about the shrinkage using the Ridge or Lasso regression by using the lambda as the penalty to introduce a little bias that reduces a large amount of variance. From here why lambda is doing is it flatter the slope that makes me think what if it... | To consider this, let's look at what the Lasso estimates of the coefficients is trying to minimize. Suppose <span class="math-container">$y_i$</span> is the outcome for observation <span class="math-container">$i=1,\ldots,n$</span> and that <span class="math-container">$x_{ki}$</span> is the value of covariate <span cl... | Let's dumb down this concept, with no complex equations.
Let's say by some magic you have already found an optimal w, now in below equation if you want to tinker with <code>logistic_loss</code> or <code>lasso</code>, you have to either decrease one of them and subsequently increase other one. Right?
<pre><code>optimal ... | https://stats.stackexchange.com |
555,694 | [
"https://electronics.stackexchange.com/questions/555694",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/102975/"
] | I'm performing some operations with fractional numbers in a 16-bit FIXED-POINT processor.
I have to multiply the numbers <span class="math-container">\$ x=-6.35 \$</span>, represented in <span class="math-container">\$ Q_{11} \$</span>, and <span class="math-container">\$ y=-0.1 \$</span>, represented in <span class="... | <blockquote>
I have to multiply the numbers <span class="math-container">\$ x=-6.35 \$</span>, represented in <span class="math-container">\$ Q_{11} \$</span>, and <span class="math-container">\$ y=-0.1 \$</span>, represented in <span class="math-container">\$ Q_{14}\$</span>. So <span class="math-container">\$ x=1100... | What you have done is taken two <em>signed</em> numbers, and multiplied them together using <em>unsigned arithmetic</em>. Signed 2's compliment multiply is different.
In a higher-level language like C, C++ or Rust, make sure that your fractional numbers are sign extended into 32-bit signed integers and multiply them, ... | https://electronics.stackexchange.com |
35,921 | [
"https://dba.stackexchange.com/questions/35921",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/20839/"
] | I am in the process of moving my servers from stand alone hosting to AWS using RDS (MySQL) for database usage.
One of the first things RDS states is that in order to use their backup, and snapshot features of RDS the tables must be using InnoDB.
My site has always run on MyIsam, probably mainly because 10+ years ago,... | Without knowing your dataset size, or your usage (read or write heavy? queries per second?), here are some generalities:
<ul>
<li>InnoDB has improved drastically in even the last few years performance-wise. This, along with the (mostly) ACID compliance and row-level locking, is why it's now the default in 5.5+</li>
<l... | Also keep in mind InnoDB tables are backed up automatically daily, and recovery for InnoDB is painless, but MYISAM tables will be unrecoverable.
| https://dba.stackexchange.com |
4,836 | [
"https://robotics.stackexchange.com/questions/4836",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/7038/"
] | My yaw angle varies from -180 degree to 180 degree.
<pre><code> -170 170
-135 135
-90 90
45 45
... | The problem is here:
<blockquote>
Since, for PID <code>ERROR = SETPOINT - INPUT</code>
</blockquote>
This is only true for linear systems. In your system, your error never exceeds $180^\circ$ no matter how many times you rotate -- modular arithmetic is affecting your calculation. (For the PID to work properly f... | While the books give general formulas, you need to have enough understanding to adjust them based on your specific application. The textbook definition of error is:
<pre><code>error = goal - position
</code></pre>
where <code>position</code> is your current state and <code>goal</code> is the state you wish you were a... | https://robotics.stackexchange.com |
89,140 | [
"https://cs.stackexchange.com/questions/89140",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/78296/"
] | How can we know that a specific ILP problem is solvable in polynomial time or not given the constraints?
| First of all, let me start by making clear that the notion of 'solvable in polynomial time' is something defined on a <em>class</em> of problem instances. It makes no sense to speak of polynomial time for a <em>single</em> problem as any single problem can be solved in $O(1)$!
That said, there is a notable class of IL... | There are instances of size n that can be solved in time $t ≤ 2n+2$, $t ≤ (2n+2)^2$, $t ≤ (2n+2)^3$, $t ≤ (2n+2)^4$ etc. <em>Every</em> instance can be solved in $t ≤ (2n+2)^k$ if we pick k large enough for that instance.
Let $I_k$ be the class of all instances that can be solved in $t ≤ (2n+2)^k$, where n is the ins... | https://cs.stackexchange.com |
191,061 | [
"https://security.stackexchange.com/questions/191061",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/127498/"
] | Can I prove that someone used an executable that connected to the Internet (not necessary a harmful one) on my Windows 10 PC? Especially when the program was installed on a removable device such as a USB stick and not on the PC itself?
The only thing that came to mind was the Windows Event Log. But, as far as I know (... | <blockquote>
Is there a way to prove that a program was executed on my Windows PC?
</blockquote>
Regarding program execution: Some programs will copy themselves to a temporary directory on the Windows machine when executed from a USB stick, you could look for a program with the same name in temporary files directory... | With a network capture or proxy server log, otherwise I don't believe so.
| https://security.stackexchange.com |
3,322,102 | [
"https://math.stackexchange.com/questions/3322102",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/489735/"
] | I am taking a first course in functional analysis but I am unable to understand the difference between <span class="math-container">$\|x-y\|$</span> and <span class="math-container">$|x-y|$</span> ?
I have doubt that if <span class="math-container">$|x-y|$</span> is defined as the distance between x and y ,then why to... | In this case, the notation <span class="math-container">$f^{-1}(7)$</span> <em>does not</em> mean the <strong>number</strong> obtained by applying the inverse of <span class="math-container">$f$</span> to 7; what it actually refers to is the <strong>set</strong>
<span class="math-container">$$f^{-1}(7) = \{x \in {\Bbb ... | The restriction of your function to <span class="math-container">$f:[0,+\infty) \rightarrow [3,+\infty): x\mapsto x^2+3$</span> is bijective and for this function you can determine <span class="math-container">$f^{-1}(7)$</span>.
| https://math.stackexchange.com |
2,616,915 | [
"https://math.stackexchange.com/questions/2616915",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/160307/"
] | Let <span class="math-container">$A$</span> be a subset of <span class="math-container">$\ell^\infty(\mathbb R)$</span> defined by
<span class="math-container">$$
A=\{(a_n)_{n\in\mathbb N}:|a_n|\leq 2^{-n}\},
$$</span>
that is, each coordinate <span class="math-container">$a_n$</span> is bounded by <span class="math-co... | To continue the OP's approach: For the "diagonal subsequence" $(m_n)_{n\in\mathbb N}$ all coordinate sequences $a_k^{m_n}$ converge to $c_k$ and it is enough to show that then $a^{m_n} \to c=(c_1,c_2,c_3,\ldots)$ in $\ell^\infty$. Given $\varepsilon>0$ take $k_0\in \mathbb N$ with $2^{k_0-1}<\varepsilon$. For $k\... | Yes, $A$ is compact. Note that $\ell^\infty$ is complete. Since $A$ is closed, it is complete.
Now, I shall prove that $A$ is totally bounded. Take $r>0$. Take $n\in\mathbb N$ such that $2^{-n}<c$. Let$$A_n=\left\{(a_1,\ldots,a_{n-1})\in\mathbb{R}^{n-1}\,\middle|\,(\forall i\in\{1,2,\ldots,n-1\}):|a_i|\leqslant ... | https://math.stackexchange.com |
1,843,738 | [
"https://math.stackexchange.com/questions/1843738",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/300836/"
] | Consider the following equation
$\lambda (a+Pu)=\lambda^* (a+Pu^*)$,
where $\lambda$ and $u$ are the variables, $\lambda,\lambda^* \in \mathbb{R}$, $u, u^* ,a \in \mathbb{R^n}$ and $P \in \mathbb{R^{n \times n}}$.
Can we conclude that $\lambda=\lambda^*$ and $u=u^*$ is the only solution for this problem?
If not, w... | As Dark mentions in the comments,
$$e^y = 1+y+\frac{y^2}{2!}+\frac{y^3}{3!}+\cdots$$
works for <strong>any</strong> $y\in \Bbb R$. In particular, you can substitute $y=-x^2$ and that should give you the result!
$$e^{-x^2} = 1+\left(-x^2\right)+\frac{(-x^2)^2}{2!}+\frac{(-x^2)^3}{3!}+\cdots$$
There's no need of using ... | That is easier than what you think.
General expansion:
$$e^A = 1 + A + \frac{1}{2}A^2 + \frac{1}{6}A^3 + \cdots$$
So if $A = -x^2$ you get
$$e^{-x^2} = 1 - x^2 + \frac{1}{2}(-x^2)^2 + \frac{1}{6}(-x^2)^3 + \cdots$$
So
$$e^{-x^2} = 1 - x^2 + \frac{x^4}{2!} - \frac{x^6}{3!} + \cdots$$
To find the general series ex... | https://math.stackexchange.com |
39,435 | [
"https://mathoverflow.net/questions/39435",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9402/"
] | You're playing pinball. When you first shoot a ball it randomly comes down through 1 of 3 gates. When you go through an unlit gate, it lights up. Similarly, a lit gate will go out. What is the expected number of balls you have to throw for all 3 gates to light up?
For example, ball A could go through gate 2, B through... | This is the average time it takes for a random walk on the 1-skeleton of a cube to reach the opposite vertex. There are more general theories for such values, but you can determine this particular one with a simple set of linear equations. Let $T_i$ be the expected time from when $i$ lights are lit. You want to determi... | After 3 balls you are either at all lit up, or 1 lit up. Hand calculations give these probabilities at 2/9ths and 7/9ths respectively.
If you throw another ball you can't be all lit up, so throw 2 more in.
There are 9 ways these 2 balls can land.
3 of these options will take all lit up to all lit up (namely they both f... | https://mathoverflow.net |
103,762 | [
"https://softwareengineering.stackexchange.com/questions/103762",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/16322/"
] | I've recently been approached to do some development work for a start up.
The fellow has requested my terms and conditions.
Being new to the industry, what sort of information would/should I include in this?
Obviously pay rate and maybe information about ownership of Intellectual Property perhaps.
Is there anything... | Don't forget liability. Do what you can to prevent them from being able to sue you when it doesn't work, or when it turns out that you violated a patent on organizing source code using line breaks.
| I would determine maintenance up-front: Are you expected to maintain the code once you've completed your tasks? Along with that, cost of maintenance (i.e., if you're charging a lump sum for the project and would be charging hourly for maintenance).
| https://softwareengineering.stackexchange.com |
51,628 | [
"https://security.stackexchange.com/questions/51628",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/36184/"
] | A comment posted on one of my questions the other day raised a question in my head. I know that many site admins appreciate users reporting bugs and security holes, and as a user I appreciate people who do this. I often try to find and report them in sites and apps to which I use frequently or hand sensitive data. I am... | In a web app pentesting course I took recently, the instructor opined that anything you can do <em>passively</em> - looking at the raw source the server and client is exchanging, without changing anything - is on the ethical side of the line. As soon as you <em>insert</em> 'malicious' strings (like SQL injection tests... | I agree with gowenfawr. The unfortunate truth is that penetration testing and bug testing do more harm than good in many cases even when you're doing them accidentally. The laws haven't caught up yet, so you could go to jail for just trying to help. Maybe in a couple decades when there are more lawmakers and fortune 50... | https://security.stackexchange.com |
40,129 | [
"https://mechanics.stackexchange.com/questions/40129",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/16085/"
] | I forgot the lights on overnight on a 2016 Volkswagen Jetta and 16 hours later when I came back to the car the lights were still on but the car wouldn't start.
Can't the car check the battery level and automatically turn off lights if it had been stopped for a long while so as to prevent the battery from completely dr... | All of these other answers go into weird philosophical directions...
The answer is much simpler than that:
Yes, it is possible to have the car turn off the headlights when the car turns off - many cars have an "Auto" setting for the headlights, and it does just this. They usually have a manual mode too, for those cas... | This is another of those questions that can <strong>only</strong> be answered by a few people at VW, clearly the car could turn the headlights off after it is stopped; or after it is stopped and a certain amount of time has elapsed; or, as you suggest, by monitoring the battery and not allowing the battery to drain pas... | https://mechanics.stackexchange.com |
7,699 | [
"https://electronics.stackexchange.com/questions/7699",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | Both my microcontrollers on my project (dsPIC33FJ128GP804 and PIC24FJ64GA004) support JTAG boundary scan testing. Should I wire these up and expose a JTAG port for hackers? The product is intended to be open hardware and as such be modified. ICSP and ICD ports will also be exposed. Of course these ports and traces take... | How expensive is half a square inch of board space? Bring out the traces to some small pitch pads. Those who are interested can solder their own header adapter.
(EE who says "yes please")
| JTAG is very rarely used with those devices. All you need is the usual connector for an ICD 2/3 or PICkit.
| https://electronics.stackexchange.com |
461,606 | [
"https://physics.stackexchange.com/questions/461606",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208374/"
] | After I finished studying and trying to test my knowledge to see what I have learned, I realized I am confused about the centripetal force formula:
<span class="math-container">$$F_c= \frac{mv²}{R}$$</span>
which I know is also equal to
<span class="math-container">$$F_c= m\omega^2R$$</span>
because <span class="math... | As mentioned in the comments, it all depends on what is constant in your system. For example, if the linear velocity <span class="math-container">$v$</span> is constant as you move outward from the center of rotation, then <span class="math-container">$\omega=v/R$</span> must be decreasing. So, if you wanted to see how... | An example might be helpful: consider a car going in circles.
<ul>
<li>Assume the car has constant speed <span class="math-container">$v$</span>. In sharp curves (small <span class="math-container">$R$</span>), the centripetal force that is required to keep the car on the road is large and for large <span class="math... | https://physics.stackexchange.com |
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