qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
23,081 | [
"https://physics.stackexchange.com/questions/23081",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5477/"
] | Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the particles?
| The factor of two is coming from the place you identified.
Think about throwing out that factor of two, so you're considering only the bottom hemisphere. When you make your Gaussian shell and have it enclose charge in the bottom hemisphere only, the charge is no longer uniformly distributed inside your Gaussian shell.... | If you are off by a factor of two, it's probably because the volume of a sphere is
$\frac{4}{3}\pi r^3$ and not $\frac{2}{3}\pi r^3$
| https://physics.stackexchange.com |
496,706 | [
"https://physics.stackexchange.com/questions/496706",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/207658/"
] | I understand that the universe is generally agreed to be expanding based on observations. What I have read is that space itself is expanding. My question is why does this expansion of space affect the spectra of light itself?
It has been observed countless time since Hubble that light from distant galaxies arrive to ... | Here is simple explanation:
<ul>
<li>Suppose a light source and a observer are in an expanding space. </li>
<li>Now think of two subsequent crests of wave emitted by the lightsource.</li>
<li>The second crest is emitted slightly later than the first one, hence the space has expanded slightly in the meantime. </li>
<li... | here is a layman's explanation:
There is a toy called a <em>Slinky</em> which is a loosely-wound coil spring made of either plastic or flat wire- if you haven't seen one, search on it to get the idea of how it looks.
We imagine the Slinky resting horizontally on a smooth floor, with its ends pulled apart to some con... | https://physics.stackexchange.com |
675,224 | [
"https://physics.stackexchange.com/questions/675224",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/137933/"
] | Would it be possible to express a quadrupole as an expansion of dipoles? Because a possible definition of a quadrupole seems to be: an electric field equivalent to that produced by two electric dipoles.
| You seem to mix up two things here: Which charge distributions generate what multipole fields and how multipole-expansion works.
Yes, you can reach a pure quadrupole field by a limiting procedure involving two dipoles (just take two anti-parallel dipole sources and let their distance go to zero from above).
But that do... | Actually, for any kind of magnetic field or electric field when a multipole expansion is done in different poles, as dipole, quadrupole, sextupole, octupole and so on, it is like a Taylor expansion:
<span class="math-container">$$ B_z(x) = \overbrace{B_{z0}}^{dipole} +\overbrace{\frac{dB_z}{dx} x}^{quadrupole} + \frac{... | https://physics.stackexchange.com |
42,506 | [
"https://mechanics.stackexchange.com/questions/42506",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/15628/"
] | I know this is a highly contentious question and I am bound to get a number of answers about turning rotors at every pad replacement, but this is going to be a simple replace or keep question as I don't like turned rotors.
I have had a brake pad wear all the way down to metal and it has scored the inside side of the ro... | Yes, if they have been scored such that you can feel or see it you should replace it.
I'm not sure if that model has a retaining screw for the discs, but you don't need to fit it. It is only there to make work easier when the wheel is off. After that, it's redundant. You can use a wheel nut without the wheel to do hol... | I agree with @DizzyFool here, but wanted to add some context.
Overall, since you don't like to cut the old rotors, if you can feel the ridges your only option is to replace the rotors. The reason why you want to replace the rotors is so they will work optimally.
When you put new pads on a worn rotor, the braking sys... | https://mechanics.stackexchange.com |
14,448 | [
"https://electronics.stackexchange.com/questions/14448",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4317/"
] | I'm currently writing a physics report of an experiment, which is about optical fiber.
One of experiments was about compare input & output signal of optical fiber, and the result was this:
<img src="https://i.stack.imgur.com/YY3b4.png" alt="enter image description here">
As you can see, there's difference (6ms) ... | How long is your fiber, what is the switching time of your emitter and where are you measuring?
You would get a 6ms delay on a 1800km long fiber due to the speed of light.
Another source of delay is afterburn in the LED phosphor. If you are using LEDs designed for fiberoptic transmission they would typically have sw... | LEDs switch very fast, typically faster than a microsecond. If they are special-purpose LEDs for communication they should even be much faster than that.
As always you should take a look into the data sheet for the LEDs.
So compared to 6ms this is insignificant.
| https://electronics.stackexchange.com |
349,441 | [
"https://softwareengineering.stackexchange.com/questions/349441",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/273154/"
] | I would like to know how I should go about splitting up the work into tasks/stories for developing a web application?
I created an in-house organization tool for the company I work at just to make things a bit easier for our day to day operations. It was very rough and ready, I developed it without much planning and j... | There won't be any one single answer to this, although there seem to be those that think there is. They may be right, but my gut says "nope". Here are some opening thoughts.
<strong>I) General Goals for Life During the Development Process</strong>
The approach you choose must allow you to fulfill the following goals:... | <blockquote>
I would like to know how I should go about splitting up the work into tasks/stories for developing a web application?
</blockquote>
<ol>
<li>Start with setting up the framework for the code, build scripts, continuous integration, and automated deployment. To do an end to end test you need at least one page... | https://softwareengineering.stackexchange.com |
61,781 | [
"https://dba.stackexchange.com/questions/61781",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/28367/"
] | I have a complete curious situation with a postgres dbms. I have installed the database and due to a misconfiguration of my installation scripts I made the superuser role to be a regular user. Now I have a completeley fresh installation of postgres with only the template database and a single user 'postgres' that can d... | Superuser rights aren't in any config file, they're part of the <code>pg_catalog.pg_authid</code> database table, which is shared between all databases in a PostgreSQL install.
You need to stop the PostgreSQL server, then restart it in <em>single user mode</em>, where it's always running as superuser.
There, you ca... | For Windows it is necessary to:
<ul>
<li>create a local user called 'postgres'</li>
<li>assign write rights for this user on the data folder</li>
<li>stop the postgres service from services</li>
<li>open a command prompt as postgres user (e.g. <code>runas /user:postgres cmd</code>)</li>
<li>run postgres in single user... | https://dba.stackexchange.com |
8,755 | [
"https://chemistry.stackexchange.com/questions/8755",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/4061/"
] | As we know that $\ce{KOH}$ absorbs $\ce{CO2}$, then why can't it be used to remove the excessive $\ce{CO_2}$ present in the atmosphere?
| $\ce{KOH}$ is produced by electrolysis of aqueous $\ce{KCl}$ solutions. Taking into account that the electrical energy still mostly comes from power plants that burn fossile fuels, it doesn't look like the most clever idea to release $\ce{CO2}$, just in order to capture it from the atmosphere again.
While it doesn't m... | KOH can affect us when inhaled and by passing throught the skin.It is a highly corrosive chemical and contact can severely irritate and burn the skin and eyes leading to eye damage.Inhaling it can irritate the lungs. Highly exposures may cause a build-up of fluid in the lungs (pulmonary oedema) a medical emergency.In ... | https://chemistry.stackexchange.com |
115,953 | [
"https://mathoverflow.net/questions/115953",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2191/"
] | I would like to calculate Picard groups of certain schemes over fields; I'm mostly interested in the question whether $Pic(X)$ is infinitely $l$-divisible, i.e. whether $Pic(X)/l=0$, $l$ is a prime distinct from the base field characteristic (the latter could be $0$). I would like to have a characterization of this van... | $Pic(X)$ mod $l$ injects into $H^2(X,\mu_l)$ with cokernel the group of elements of order $l$ in the Brauer group of $X$. Depending on your $X$, the Brauer group may be known, or it may be as mysterious as a Tate-Shafarevich group. For example, for a complete smooth surface over a finite field, the Brauer group is conj... | In characteristic zero, Hodge theory is the best way to approach this. Hodge theory would express $H^2(X,\mathbb \mu_l)=H^2(X,\mathbb Z/l)$ in terms of $H^2(X,\mathbb Z)$. You then use the fact that the classes in $H^2(X,\mathbb Z)$ that come from holomorphic line bundles are exactly Hodge classes, so you try to find t... | https://mathoverflow.net |
259,636 | [
"https://stats.stackexchange.com/questions/259636",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/113777/"
] | What is the null model in regression and what's the relationship between the null model and the null hypothesis?
From my understanding, does it mean
<ul>
<li>Using "an average of the response variable" to predict the continuous response variable?</li>
<li>Using the "label distribution" in predicting... | No, I would say "null model" essentially has the same meaning as "null hypothesis": the model if the null hypothesis is true. What this means, in a particular case, of course depends upon the concrete null hypothesis.
Your interpretations as "the average value" (you probably want to say "the marginal distribution... | A null model is related to a null hypothesis. Take the following univariate model:
$Y=\alpha+\beta_{1}X + \epsilon$
My null hypothesis would normally be that $\beta_{1}$ is statistically no different from zero.
$H_{0}: \beta_{1}=0$ (null hypothesis)
$H_{A}: \beta_{1}\neq 0$ (alternative hypothesis)
For a univariat... | https://stats.stackexchange.com |
164,598 | [
"https://dba.stackexchange.com/questions/164598",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36165/"
] | I had this query:
<pre><code>SELECT YEAR(datetime) AS Year, WEEK(datetime) AS Week, COUNT(*) AS total
FROM table
GROUP BY Year, Week;
</code></pre>
The result is:
<pre><code>+------+------+-------+
| Year | Week | total |
+------+------+-------+
| 2016 | 49 | 14 |
| 2016 | 50 | 20 |
| 2016 | 51 | 19 |... | You can accomplish this with the DATE_FORMAT function,
<pre><code>SELECT YEAR(datetime) AS Year, DATE_FORMAT(datetime, '%b %e') AS Week, COUNT(*) AS total
FROM table
GROUP BY Year, Week;
</code></pre>
| Accepted solution didn't work for me as it doesn't group per week but it can get rows within the same week, example:
<pre><code>year, week, total
2021, Mar 23, 1
2021, Mar 24, 2
</code></pre>
Using a subquery seems to be working:
<pre><code>SELECT
YEAR(ADDDATE(your_datetime, INTERVAL 1-DAYOFWEEK(your_datetime) DAY... | https://dba.stackexchange.com |
191,621 | [
"https://dba.stackexchange.com/questions/191621",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/137507/"
] | I am trying to replace NULL values in table by using SELECT with one (randomized?) string from the set that I provide to the compiler.
Example:
<pre><code>|id | date |
+---+------+
| 1 | 2017 |
| 2 | NULL |
| 3 | NULL |
</code></pre>
I want the <code>NULL</code> values to be '2015', '2012', etc, taken randomly f... | You can use something like
<pre><code>SELECT Id,
ISNULL(Date, (SELECT TOP 1 *
FROM (VALUES(2015),
(2012)) R(Ryear)
ORDER BY CRYPT_GEN_RANDOM(DATALENGTH(Id))))
FROM YourTable
</code></pre>
The reference to <code>Id</code> in the ... | Alternatively you can use <code>NEWID()</code> in combination with BINARY_CHECKSUM()
<pre><code>declare @t table(id int,dates varchar(20))
insert into @t VALUES (1,'2017'),(2,NULL),(3,NULL)
declare @parameter table(para varchar(20))
insert into @parameter VALUES ('2015'),('2012')
SELECT Id,
ISNULL(Dates, ... | https://dba.stackexchange.com |
314,711 | [
"https://softwareengineering.stackexchange.com/questions/314711",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/175434/"
] | I have been trying to figure out an efficient algorithm that can check if a list of values contains a list of values. Both lists are sorted in ascending order.
For example:
Check if
<code>var listToSearch = [1,2,3,4,5,6,7]</code>
contains
<code>var searchValues = [1,2,3]</code>
Without iterating through the list... | Your company isn't following standard agile practices.
The developers should be the one estimating, in whatever units you use (hours or Story Points or something else). If you are doing the work, you should be involved in estimating it. In fact, everyone who is required to complete the Story needs to be involved in est... | While I agree with Thomas Owens answer, I think this needs a more strongly worded answer. The process you describe is completely missing some of the most important parts of agile management and these are the parts that managers should care the most about. (full disclosure: I'm a manager.)
In order to improve predicti... | https://softwareengineering.stackexchange.com |
358,162 | [
"https://stats.stackexchange.com/questions/358162",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/189617/"
] | The AR(1) process is
<blockquote>
$$
X_t = \phi X_{t-1} + \varepsilon_t
$$
</blockquote>
if we use this formula recursively, we get
$$
X_t = \phi(\phi X_{t-2} + \varepsilon_{t-1}) + \varepsilon_t = \phi^2X_{t-2} + \phi\varepsilon_{t-1} + \varepsilon_t = \cdots = \phi^k X_{t-k} + \sum_{j=0}^k \phi^j\varepsilon_{t-j}... | The usual sense in which convergence is understood in this case is in <em>mean square</em>:
$$
E[Y_t-(\epsilon_t+\phi\epsilon_{t-1}+\phi^2\epsilon_{t-2} +\ldots+\phi^j\epsilon_{t-j})]^2=\phi^{2(j+1)} E[Y_{t-j-1}]^2
$$
If $Y_t$ is stationary
$$
E[Y_{t-j-1}]^2=\gamma_0+\mu^2
$$
Hence
$$
\lim_{j\to\infty}E[Y_t-(\epsilon_... | You are right to be suspicious of this step, and in fact, without further assumptions to limit the size of $X_{-\infty}$ you cannot get the required form. Remember that the recursive equation for the AR model is insufficient to yield the joint distribution of the process. (You need to impose a distribution for the er... | https://stats.stackexchange.com |
2,000 | [
"https://dsp.stackexchange.com/questions/2000",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/1211/"
] | I was wondering about super simple applications of linear or logistic regression to signal processing (image processing specifically)?
I'm a math guy that's been asked to explain some mathematical methods to signal/image processing people, and I'd like to be able to use a couple simple examples that are related to the... | In image processing all I can think of is using linear regression to fit a plane to the intensity surface of an image, and using logistic regression for some kind of supervised thresholding...
You might be better off using an example from computer vision instead. For example texture classification or object recogniti... | In Hyperspectral imaging linear regression is often used for target identification.
| https://dsp.stackexchange.com |
553,718 | [
"https://physics.stackexchange.com/questions/553718",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/260164/"
] | I'm putting together some charts and the time axis in one shows billions of years, the time axis in another shows millions of years. I've seen in various publications <span class="math-container">$my$</span> and <span class="math-container">$myr$</span> (also <span class="math-container">$ma$</span>) for millions of y... | It depends on the field. There is an ISO standard to use <strong>a</strong> from latin annus, but in astronomy and cosmology <strong>yr</strong> is far more normal. I think the same is true in geology and paleontology. The metric symbols should be capitals, <strong>M</strong> not <strong>m</strong> (which stands for mi... | It's Ma for million years and Ga for billion years.
| https://physics.stackexchange.com |
412,673 | [
"https://softwareengineering.stackexchange.com/questions/412673",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35682/"
] | I am an amateur developper and I deploy my (home oriented) code to containers. This is usually Python and JavaScript.
JavaScript, when saving dependencies for a further <code>npm install</code>, will pin the libraries to exact specific versions. It is also possible (and recommended) to do that in Python via <code>requi... | The trade-off being made is highly reproducible builds over having the latest dependencies.
Why would you want highly reproducible builds? There are a lot of reasons.
You can't rely on the versioning of the dependency. Although Semantic Versioning has rules, there's no guarantee that the third-party dependency is follo... | You are right that pinning the exact version of dependencies forecloses many advantages:
<ul>
<li>Getting a bug fixed without intervention.</li>
<li>Getting a performance upgrade without intervention.</li>
<li>Getting a feature upgrade without intervention.</li>
<li>Having an easier time matching the dependencies versi... | https://softwareengineering.stackexchange.com |
665,006 | [
"https://physics.stackexchange.com/questions/665006",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/313400/"
] | I am having a question regarding significant figures in calculating average of two masses. For example adding two masses 7 kg and 8 kg gives 15 kg, both inputs 7 and 8 have only one significant figure but final answer 15 has two significant figures.
Now if I take average of the masses 15/2 gives 7.5, (Note: the number ... | The question which was asked was <em>Can adding two numbers increase the significant figures?</em><br />
In this context the question is misleading in that when values range over a value of . . . . . <span class="math-container">$0.1$</span> or <span class="math-container">$1$</span> or <span class="math-container">$10... | Consider what the number of significant figures indicates:
The number written as <span class="math-container">$7$</span> has <span class="math-container">$1$</span> significant figure; the number is somewhere between <span class="math-container">$6.5$</span> and <span class="math-container">$7.5$</span>
The number wri... | https://physics.stackexchange.com |
3,777,736 | [
"https://math.stackexchange.com/questions/3777736",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/743498/"
] | General question - if I want to show that a sequence of random variables <span class="math-container">$(X_n)_{n \ge 1}$</span> converge almost surely to a constant, is it sufficient to show that <span class="math-container">$\lim_{n \to \infty}$</span>Var<span class="math-container">$(X_n) = 0$</span>? If not, under wh... | "I'm trying to use the Intermediate Value Theorem but with no luck."
Use it an infinity number of times.
<blockquote>
It should be intuitively obvious that on the interval <span class="math-container">$[2k \pi, 2k\pi + \frac \pi 2]$</span> that <span class="math-container">$\sin x$</span> takes on all values ... | I believe you meant to write <span class="math-container">$\sin \dfrac 1x$</span>.
The function <span class="math-container">$f(x) = \sin \dfrac 1x$</span> oscillates between <span class="math-container">$1$</span> and <span class="math-container">$-1$</span> infinitely many times in the interval <span class="math-cont... | https://math.stackexchange.com |
168,684 | [
"https://mathoverflow.net/questions/168684",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23964/"
] | Given the divergent integral
$$ \int _{0}^{\infty}dx \int_{0}^{\infty}dy \frac{x^{2}y+1}{1+x+y} $$
how can I apply Hadamard's finite part to give a finite meaning to it ?
It is just made by applying the itetrated finite part first to '$dx$' and then '$dy$'?
| The Hadamard finite part description is strictly defined only for $1$-dimensional integrals. Also, it is usually defined for singularities within the domain of integration or at a finite boundary. On the other hand, your integrals is divergent at infinity. It is of course possible to try to do something similar in this... | Rather than a simple numerical value, one might consider a more meaningful interpretation of the integral as an attempt to evaluate the Fourier transform of the integrand (restricted to the positive quadrant) as tempered distribution, at $(0,0)$. Any "regularization scheme" compatible with that is a-priori guaranteed t... | https://mathoverflow.net |
170,592 | [
"https://electronics.stackexchange.com/questions/170592",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1380/"
] | Using a couple of 240V mains step down transformers, undecided whether to use E/I laminated or toroidal, one 22VA the other 7VA. How to mount them in the case, so that they're not affected by each others magnetic fields?
This is unless I can find one ready made with separate secondaries of 22-0-22 and 7-0-7.
| Toroids have very little magnetic leakage, so if you can find two of those, that would be ideal. There are many toroidal transformers for sale on eBay, give that a try. E-I laminants are pretty good also. Is this for a high-end audio amplifier? Magnetic flux dissipates inverse-square with distance, so even a few inches... | Try putting in a piece of steel sheet (contains iron) in between the transformers, never tried it myself but it should provide a low reluctance path for the magnetic flux, so the flux should concentrate inside the steel sheet and provide isolation between the two. But you'll get eddy currents induced in the steel sheet... | https://electronics.stackexchange.com |
72,111 | [
"https://physics.stackexchange.com/questions/72111",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25617/"
] | There are two types of Dirac equations:
<span class="math-container">$(p_\mu\gamma^\mu - m)\Psi(x) = 0$</span> and <span class="math-container">$(p_\mu\gamma^\mu + m)\Psi(x) = 0$</span>.
Here <span class="math-container">$p$</span> are the momentum operators.
The fermion propagator is defined in the equation <span clas... | The two equations would lead to equivalent physics but only one of them may be right: the correct equations of motion for Dirac spinor fields are first-order in derivatives. The convention is that only the first equation is right for the Dirac field $\Psi$. The second equation is simply incorrect and doesn't follow fro... | Mathematically speaking, the first equation for the Dirac spinor field $Ψ$ is the same as the second equation for the Dirac spinor field $γ_5 Ψ$ where $γ_5$ is the parity-odd gamma matrix, so yes, they are both correct, both follow from the same Lagrangian, both have the same conserved quantities (energy and spin, as w... | https://physics.stackexchange.com |
86,579 | [
"https://dba.stackexchange.com/questions/86579",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | At work, we are sharing oracle credentials among many developers. Often time team runs heavy adhoc queries on the database and it is causing lot of trouble to oracle server. We are working to fix this issue permanently by creating readonly replica instance. Mean time I wanted to find out if I can quickly identify who ... | Please try the below query to see if it's helps:
<pre><code> select
c.owner,
c.object_name,
c.object_type,
b.sid,
b.serial#,
b.status,
b.osuser,
b.machine
from
v$locked_object a ,
v$session b,
dba_objects c
where
b.sid = a.session_id
and
a.object_id = c.object_id;
</code></pre>... | first you have to connect as 'sys' and execute this query
<pre><code>select
c.owner,
c.object_name,
c.object_type,
b.sid,
b.serial#,
b.status,
b.osuser,
b.machine
from
v$locked_object a,
v$session b,
dba_objects c
where
b.sid = a.session_id
and
a.object_id = c.o... | https://dba.stackexchange.com |
6,827 | [
"https://physics.stackexchange.com/questions/6827",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/667/"
] | Why do optical fibers usually have a cladding? Ok, if you put make a bundle of optical fibers this prevents that light leaks from one fiber to another fiber in contact. However, are there other reasons to use claddings? Are there applications of optical fibers without claddings?
(I am mainly interested in optical fibr... | For a fiber to guide light, even considering the situation using only geometrical optics, there must be total internal reflection (TIR) at the boundary of the fiber core. For TIR to occur, the angle of incidence of the light must be greater than the critical angle $\theta_c$. If the material before the boundary has ind... | Do you think a fiber that worked until is got some water on it would be acceptable?
In order for the fiber to have a reliable, known behavior (transmission speed, attenuation, wavelength acceptance) in all environments, it is necessary to the total internal reflection to happen against a well defined external materia... | https://physics.stackexchange.com |
371,937 | [
"https://electronics.stackexchange.com/questions/371937",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/187610/"
] | I am running a 3KW motor on a big 24Vdc power supply (Meanwell RST-5000), through a frequency drive.
When stopping the motor, however, I occasionally get a regenerative backcurrent that trips the internal overvoltage protection in my power supply. The voltage ramps up to about 28.5V. The supply is protected against thi... | In the end, I went with a 140Ah Lead-Acid battery bank, because we had that in stock and it was easiest to mount for me. It is connected in parallel to the power supply, fused seperatly with a 200A slow blow fuse.
I let the system run on batteries only for a bit to drain them to +- 24V, and then switched on the power ... | I've implemented 3 solutions to this problem:
<ol>
<li>A capacitor bank sized large enough to absorb the worst-case regen energy without tripping the OVP. In your case it might be expensive and huge, but has minimal losses.</li>
<li>A resistor bank with a comparator. Also big, less expensive but you waste the energy... | https://electronics.stackexchange.com |
180,884 | [
"https://physics.stackexchange.com/questions/180884",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42178/"
] | In my lecture notes there is a step that i cannot follow:
$$\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}] (\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})=: \sigma^{\mu\nu}F_{\mu\nu}=i\vec{\alpha} \vec{E}-\vec{\sigma}\vec{B}$$
Can somebody please help me with this step?
The $\gamma^{\mu}$ are the dirac- gamma matrices, A is... | So the torque from the back wheel causes a net torque about the centre of mass counterclockwise. This means the back wheel exerts a greater reaction force on the ground so when we resolve forces the reaction force exceeds mg, causing a net force up on the centre of mass.
| Sorry if I'm missing a detail here - but how can you choose the center of mass? Isn't that determined by the shape/mass distribution of the bike? And the axis of rotation ought to be the center of the rear tire, no?
Just imagining a wheelie I can see that the center of mass should move upwards to some degree, as the w... | https://physics.stackexchange.com |
11,201 | [
"https://mechanics.stackexchange.com/questions/11201",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/6357/"
] | I've heard that a larger wheel (diameter) in the front can produce quicker turns on a motorcycle. How much larger should a front wheel be than a rear wheel on a road bike (if at all)? Will this affect the odometer/speedometer readings? Gas mileage?
| A larger front wheel is more stable than a smaller one, so theoretically should keep you more stable in high speed turns. But, you'll be messing up the front fork geometry (rake and trail) which may have unforeseen consequences with the suspension and steering.
You'll definitely have more trouble in parking lots.
| Dirt bikes and enduros do this. Choppers too. Their frames and suspension styles are built around the wheel sizes though. So, unless you are riding a bike that comes "stock" with two different sized wheels, I would not recommend it. On any bike that goes highway speed, you should be especially careful, since you may pl... | https://mechanics.stackexchange.com |
257,720 | [
"https://physics.stackexchange.com/questions/257720",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56184/"
] | For operators with pure point spectra it is clear how to count number of states corresponding to a given eigenvalue - one can just calculate the dimension of eigenspaces. I am wondering how to do it for continuous spectra. What I usually saw in my undergrad classes is the classical trick of putting the system into an a... | For the <em>absolutely continuous</em> part of the spectrum of a self-adjoint operator $H$, the "density of states" is provided by the Radon-Nikódym derivative of the spectral measure of $HP_{ac}$ with respect to Lebesgue measure, where $P_{ac}$ is the orthogonal projection onto the absolutely continuous subspace of th... | I am not sure I understand perfectly you question but formally in the canonical ensemble we can write the partition function $Q(\beta)$ as being:
\begin{equation}
Q(\beta) = \int\cdot \cdot \int d\mu(x)\: e^{-\beta H(x)} = \int_0^{+\infty} dE \: \rho(E)e^{-\beta E}
\end{equation}
where $d\mu(x)$ is the volume measure... | https://physics.stackexchange.com |
33,736 | [
"https://scicomp.stackexchange.com/questions/33736",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/32679/"
] | As we know, for a symmetric positive definite (SPD) matrix <span class="math-container">$\mathbf{A}$</span>, there is a theorem about the <strong>Cholesky factorization</strong> <span class="math-container">$\mathbf{A}= \mathbf{L}\mathbf{L}^T$</span>, where <span class="math-container">$\mathbf{L}$</span> is a lower tr... | Let <span class="math-container">$P$</span> be the anti-diagonal permutation matrix,
<span class="math-container">$$P = \begin{bmatrix}
& & & 1 \\
& & 1 \\
& 1 \\
1
\end{bmatrix}$$</span>
so that <span class="math-container">$PAP$</span> is the version of <span class="math-container">$A$</span> ... | Yes, for an SPD matrix <span class="math-container">$\mathbf A$</span> there are a variety of Cholesky-like decompositions, you can derive the <span class="math-container">$\mathbf A = \mathbf L^T \mathbf L$</span> variant by first writing down an educated/structured guess..
<span class="math-container">$\begin{bmatri... | https://scicomp.stackexchange.com |
3,540 | [
"https://dba.stackexchange.com/questions/3540",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2249/"
] | Currently when executing the <code>imp</code> command with the following parameters: <code>file=my.dmp log=my.log fromuser=myuser touser=myuser</code>
The following errors occur:
<pre><code>IMP-00058: ORACLE error 12560 encountered
ORA-12560: TNS:protocol adapter error
IMP-00000: Import terminated unsuccessfull... | Your problem might very well have to do with incorrect versions or wrong default connection. Make sure that you use the exp utility from the 10g installation and the imp utility from the 11g installation.
Also make sure that the environment variables like ORACLE_HOME are correct and that PATH is adjusted for the correc... | A 10g file can be loaded into an 11g database. It is throwing a networking error and TNSPING doesn't go all the way to the database, just as far as the listener port. I suspect you'd have the same trouble connecting via SQLPLUS.
Check your tnsnames.ora and that the database and listener are available
| https://dba.stackexchange.com |
190,650 | [
"https://physics.stackexchange.com/questions/190650",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/83533/"
] | I had a homework problem with this graph of F(Newtons) vs x(meters).
The graph has a straight line (constant slope) from (0,0) to (8,10).
And the slope ((10-0)/(8-0)) came out to be 1.25, making the function of the graph be F = 1.25x.
Then the question was to find the "Work done by force during the displacement".
W... | The slope you calculated is $\frac{10 \rm N}{8\rm m}=1.25\,{\rm \frac Nm}$, so the force function becomes $F=1.25\,{\rm \frac Nm}*x$. Hence, the work is
$$
W=\int{(1.25\,{\rm \frac Nm}\times x)dx}=1.25\,{\rm \frac Nm}\int{xdx}=0.625\,{\rm \frac Nm}x^2
$$
(If $F(0)=0$). Because the unit of $x^2$ is $\rm m^2$, then the ... | Since the scales of the graph are in Newton and meters, your answer is fine.
Think of integration as simply adding small individual work for small displacements.
For a displacement ds, work done will be
dw=F.s
Its unit will be in J (or Nm), right. Integrating dw will not change the unit, as adding doesnt change th... | https://physics.stackexchange.com |
129,345 | [
"https://electronics.stackexchange.com/questions/129345",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11869/"
] | Our hand-held blender stopped working and I took it apart to see if I could fix it (no, as it turned out).
The circuit was simple; a switch and a 0.47 Ohm (R47) resistor in series with a full bridge rectifier whose DC output was connected directly to the motor.
The wattage is 200 W and the voltage 120 V, so the volt... | It may be a fusible resistor designed to protect the wiring in case of a short in the bridge rectifier or the motor.
<strong>It may also be a simple fuse</strong>. If it is open, then it either has opened early or it has done its job. The 200W rating would seem to indicate a higher amperage of fuse, but perhaps that'... | It could be a ntc - for softstart.
It could also have a capacitor parallel to it as an energy saving or a speed control mechanism: the capacitor shorts out the resistor in start up but after the resistor is there to lower the current to control speed for example.
The 2nd approach is quite common for relays. Btw.
| https://electronics.stackexchange.com |
251,199 | [
"https://physics.stackexchange.com/questions/251199",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/61964/"
] | I don't really know any quantum mechanics. But in our class, we were introduced to Bohr's model of the atom with his postulate that the angular momentum of an electron in the $n$-th orbit is $\frac{nh}{2\pi}$
Recently I read that electrons could jump from one orbit to another, by absorbing energy (through light or hea... | In short, you must consider the total elements of the system for conservation of momentum. In this case, nearly all of the momentum is exchanged between the electron and a photon that is absorbed or radiated away (the light). Momentum is conserved, and is largely balanced by this electron-photon interaction, although... | Angular momentum is conserved only if there's no external forces, in this case the electron gains energy by light or by heat wich is kinetic energy. They are both external forces so the conservation of angular moment does not apply.
| https://physics.stackexchange.com |
651,068 | [
"https://electronics.stackexchange.com/questions/651068",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/315371/"
] | From my knowledge from classical books of computational and digital systems, an ASIC is a category of full-customized or semi-customized integrated circuit (IC) tailored to a specific application.
Then, off-the-shelf ICs, such as an FPGAs, would not be an ASIC since it can be reprogrammed many times to perform differen... | <blockquote>
Is there a ambiguity over the expression ASIC?
</blockquote>
No. There isn't any ambiguity in practical usage.
<blockquote>
Can a digital system be considered an ASIC regardless its physical implementation?
</blockquote>
What it really comes down to is money: specifically whether you need a custom mask for... | ASIC stands for "Application Specific Integrated Circuit". If all integrated circuits were ASICs, then the term "ASIC" would be a useless distinction, and you would simply use the term "integrated circuit".
The key thing that makes an ASIC and ASIC is some sort of silicon-level customizat... | https://electronics.stackexchange.com |
52,936 | [
"https://electronics.stackexchange.com/questions/52936",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17023/"
] | <img src="https://i.stack.imgur.com/y2QmR.png" alt="relay in situ circuit diagram">
Here I have an automotive relay (from a scan of a workshop manual I'm afraid) which is rather more complexly wired up than the relays I'm familiar with. In this diagram:<br>
L/Y - +12V<br>
L - From the relay's switched live (a switch i... | The resistor across the coil is a snubber, which will dissipate the extra energy and make sure the coil voltage never exceeds I*R, where I is the relay's "on" current.
Depending on R and I, you are completely safe, or you might see a controlled low-going transient at relay switch off. Notice high-going spikes won't b... | For a one-off project or prototype, markrages' answer is probably correct. According to the schematics, the <em>specified</em> relay has a snubber resistor that should typically be enough protection, although you'd have to measure to be sure the voltage stays within the maximum ratings of your transistor.
Cars and the... | https://electronics.stackexchange.com |
654,878 | [
"https://electronics.stackexchange.com/questions/654878",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2951/"
] | I have a kid's electric toy car with a 12 V battery and 2 DC motors (Model: RS380/6 V & 12 V with 15000 RPM) connected to battery in parallel and to wheels using gearboxes. For some reason, the 6 V motor burned out. I replaced it with another 6 VDC motor, but it met the same fate within an hour (the other 12 V moto... | <blockquote>
Is this possible to use 12v motor with a different rpm(12v/15000 rpm & 12v/18000rpm),
</blockquote>
Possible, yes. But they'll act differently. Is that OK?
<blockquote>
will this put stress on battery and make it drain faster.
</blockquote>
Compared to what? If compared to two identical 12 V motors: no... | According to Ohm's law there's 12 V and two resistances (active or reactive it doesn't matter I think). In one branch there's one value of current. I think the 6 V motor died because of overcurrent (it can be another reason such as mechanical wear of brushes if it is a brush motor) and there's overcurrent on the other.... | https://electronics.stackexchange.com |
302,862 | [
"https://softwareengineering.stackexchange.com/questions/302862",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/192524/"
] | I'm starting work a new personal project to send out emails using different email services (like mailchimp, for example). I just started coding and I have a base class called Email:
<pre><code>public class Email
{
private string _to;
private string _from;
private string _body;
private string _templateN... | An interface and a parent (or base) class solve different problems, so it depends on the problem you're trying to solve.
An interface defines a contract. This is handy when you want to manipulate a variety of concrete implementations in a consistent, well-defined manner. They're great for hiding the gory details that ... | We should inherit if there is a 'is a relation'. We should use aggregation if there is a 'has a relation'.
There is no need to inherit 'Email' class in every email sending implementation classes. Your 'Email' class is a model class. Email sending logic implementation classes should only implement the 'IEmail' interfac... | https://softwareengineering.stackexchange.com |
105,018 | [
"https://softwareengineering.stackexchange.com/questions/105018",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8029/"
] | I know most people hate flat and long functions, and hate when code is not full of ISomethings.
The problem is that I guess my mind works in different way, and I always have problems with that type of code in any non-trivial solution.
So, since most of people enjoy explosive number of functions, can you describe what... | Sounds like some inappropriate coupling is going on.
There are some tools out there that make this a little easier. In C# I use CodeRush, which includes a handy navigation utility to "jump to implementors" for an interface definition, and similar.
| <strong>You don't</strong>. This is the point in writing code that way.
You don't need to know about any of those implementations. You just have to know about what you're adding.
Now you say that you need to add a method to IFoo. Why do you? Is it some functionality you need to call in every class which implements IF... | https://softwareengineering.stackexchange.com |
46,767 | [
"https://mechanics.stackexchange.com/questions/46767",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/21546/"
] | I have a 2007 Ford V6 Mustang that has a stuck high-side A/C Schrader valve.
The system is evacuated and without pressure but the schrader valve will not turn. I've ruined two tools because the little arms just twist off. Even putting the tips of needle nosed pliers down there and turning just doesn't budge it.
Is th... | It sounds to me like you need a better Schrader valve core removal tool. It's going to cost a few more denaro, but will take out the core without shearing off the little nibs. If they are built right, the metal will withstand the torque and the outside of the valve (the brass part you thread the core into) will help su... | duh---its not that simple. 134A is very corrosive and the schrader valve is STUCK. Obviously if it were not- he could and would have been able to get it off. I would put a few drops of the correct oil on top of the valve core- and heat up the area from the outside- where the schrader valve is. Then keep making an e... | https://mechanics.stackexchange.com |
375,884 | [
"https://physics.stackexchange.com/questions/375884",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/177136/"
] | I've heard of $\beta^-$ decay,
$$n \rightarrow p^+ + e^- + \bar \nu_e$$
$\beta^+$ decay,
$$p^+ \rightarrow n + e^+ + \nu_e$$
and electron capture,
$$p^+ + e^- \rightarrow n + \nu_e$$
but every time I've googled "positron capture," which I assume would probably happen as
$$n + e^+ \rightarrow p^+ + \bar \nu_e$$
... | Positron capture is not possible, and here is why: The "capture" part refers to the fact that the electron is taken from its atomic orbit around the nucleus containing the proton with which it reacts. Since a positron cannot for a bound state with a nucleus--it can't be captured.
Nevertheless, $e^+p(n, \bar{\nu}_e)$, ... | "Positron capture" does not normally happen. However if temperatures are high and pressures are high(like in the sun) it is possible for positron capture to occur. This could be a way that occasionally neutrons turn into protons.
| https://physics.stackexchange.com |
21,157 | [
"https://electronics.stackexchange.com/questions/21157",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5849/"
] | Am I correct in that the IC extraction is used to extract an IC from a DIP socket for swap/extraction in a safe manner? Or is it used for something else?
I doubt I will need this behaviour, however if I damage the socket it is worth a few dollars to own such a tool.
| If there is adequate clearance, a typical screwdriver will work very nicely for removing DIPs from sockets. Insert the blade between the socket and the chip (not under the socket!), then twist gently in alternate directions to raise the two sides of the chip. Apply gentle pressure on the side of the chip opposite the... | Yes, you can use an extraction tool for removing ICs from DIP sockets (you can get them for PLCCs too) but something like a screwdriver wiggled underneath gently at both ends works fine.
The main thing to avoid is lifting one end up too high and bending the pins, so you lift one side a mm or two, do the same with the... | https://electronics.stackexchange.com |
4,511,544 | [
"https://math.stackexchange.com/questions/4511544",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/990012/"
] | I know that a Lie Group representation <span class="math-container">$\rho: G \rightarrow GL(V)$</span> gives rise to a Lie Algebra representation: <span class="math-container">$\rho_*: \operatorname{Lie}(G) \rightarrow \mathfrak{gl}(V)$</span>. I don‘t understand, however, how these <span class="math-container">$\rho_*... | If someone is interested here an answer based on Qiaochu Yuan‘s suggestions and definitions:
„Exercise 1a“:
<span class="math-container">$\forall g \in G \ \ \forall w \in W \ \ \forall X \in \mathfrak{g} $</span>
<span class="math-container">$ \rho(g)w \in W \Rightarrow \ \frac{d}{dt}\rho(\exp(tX))|_{t=0}w \in W$</spa... | Here is the answer in the form of a two-part exercise.
<blockquote>
<strong>Exercise 1a:</strong> Let <span class="math-container">$G$</span> be a connected Lie group, <span class="math-container">$\rho : G \to GL(V)$</span> be a finite-dimensional representation of <span class="math-container">$G$</span> over <span cl... | https://math.stackexchange.com |
874 | [
"https://softwareengineering.stackexchange.com/questions/874",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | In my current job it feels like we have a lot requirement changes. We are an "Agile" shop, so I get that we are supposed to adjust and what not, but sometime the change is large and nothing trivial.
My question is, how do you effectively communicate the cost of the change? Because of being agile, if a change is big e... | @Joe "We are an "Agile" shop, so I get that we are supposed to adjust and what not, but sometime the change is large and nothing trivial. "
If your process doesn't allow you to control the rate of change in requirements, your process is not agile, but haphazard. Agile does not mean "taking anything that comes my way."... | From what you described, you don't have a problem. They ask for a change and are either willing to wait until you say it can be done or are willing to postpone another feature. Seems like a balance between: time, resources and requirements.
| https://softwareengineering.stackexchange.com |
2,676,657 | [
"https://math.stackexchange.com/questions/2676657",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/502334/"
] | Medians $\overline{AD}$ and $\overline{BE}$ of a $\triangle ABC$ are perpendicular. If $AD= 15$ and $BE = 20$, then what is the area of $\triangle ABC$?
Note: A lot of my work can have inaccuracies and is based off a diagram. It is very helpful if you draw a diagram first
Let's call the centroid of $\triangle ABC$, $... | Let $AD$ and $BD$ meet at $G$ = gravity center. Remember that $AG:GD =2:1$ so $AG=10$.
Area of the triangle $ABD$ which is half of the area of whole triangle $ABC$ is $${EB \cdot AG \over 2} = {20 \cdot 10\over 2} =100$$ so the whole triangle has area $200$.
| These following equalities are using the fact that area of triangle with same vertex and equal base are same.
$$\text{Ar}(ABC) = 2\text{Ar}(ABD) = 2[\tfrac{3}{2}\text{Ar}(AGB)] = 3\text{Ar}(AGB)$$
Now $\triangle AGB$ is right triangle with $AG = \frac{2AD}{3} = 10$ and $GB = \frac{2BG}{3} = \frac{40}{3}$.
Required a... | https://math.stackexchange.com |
2,362,039 | [
"https://math.stackexchange.com/questions/2362039",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/173420/"
] | I am investigating insofar to the general solution of a basic problem. From what I've researched, I need to use a special method to solve the following differential equation
$$y''-y'-2y = e^{3x}$$
We have a complementary solution of
$$y_c = c_1e^{2x} + c_2e^{-x}$$
with $a=2, b=1$ by quadratic (or factoring). We pr... | Instead of $p(x)$ as a function. Make it a constant.
$y_1 = p e^{3x}\\
y_1' = 3p e^{3x} \\
y_1'' = 9p e^{3x}$
now plug these into the original diff eq.
$y_1''-y_1' - 2y_1 = 4pe^{3x} = e^{3x}$
and solve for $p$
$p = \frac 14$
$y = c_1 e^{-x} + c_2 e^{2x} + \frac 14 e^{3x}$
| To eliminate the exponential term, and get an easier equation, begin by putting
$$y=ze^{3x} $$
$$y'=(z'+3z)e^{3x} $$
$$y''=(z''+6z'+9z)e^{3x} $$
the equation becomes
$$z''+5z'+4z=1$$
the characteristic equation is
$$r^2+5r+4=0$$
the roots are
$$r_1=-4 \;,\;r_2=-1$$
a particular solution is
$$z_p=\frac {1}{4} $$
the ... | https://math.stackexchange.com |
274,107 | [
"https://physics.stackexchange.com/questions/274107",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/127116/"
] | I'm studying black bodies for IB Physics and I'm having trouble understanding the full concept of black body radiation. I understand that a black body in thermal equilibrium with its surroundings will emit all radiation that is incident upon it. My question is, why must this radiation be emitted at all? Why can't the o... | The definition of thermal equilibrium is that at equilibrium there is no net transfer of heat, so it is this requirement that forces the blackbody to emit as much energy as it absorbs.
In general an object can heat up (or cool down) by absorbing (respectively emitting) radiation, but then the object is not in thermal... | As long as a body has temperature it will radiate energy. All the way down to absolute zero. If the electrons are excited (accelerated) they will radiate photons. If energy goes in faster than it can radiate then the body will heat up. The hotter it gets the higher the frequency of the photons. But more to your questio... | https://physics.stackexchange.com |
3,969,397 | [
"https://math.stackexchange.com/questions/3969397",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I want to find a general integral for <span class="math-container">$xz_x + yz_y = z^2 + 1$</span>, where <span class="math-container">$z = z(x,y)$</span> is implicitly a function of two variables. I'm not sure how to go about this.
| <span class="math-container">$$\dfrac {dx}{x}=\dfrac {dy}{y}=\dfrac {dz}{z^2+1}$$</span>
First DE gives us:
<span class="math-container">$$d \ln x = d\ln y \implies \dfrac x y=C_1$$</span>
Second DE gives us:
<span class="math-container">$$ d\ln y=d \arctan z$$</span>
<span class="math-container">$$\ln y = \arctan z +C... | Elaborating on my comment, the complete Lagrange-Charpit equations read
<span class="math-container">$$ \frac{\mathrm{d}x}{x} = \frac{\mathrm{d}y}{y} = \frac{\mathrm{d}z}{1+z^2} = \frac{\mathrm{d}p}{(2z-1)p} = \frac{\mathrm{d}q}{(2z-1)q}, $$</span>
with <span class="math-container">$p=z_x$</span> and <span class="math... | https://math.stackexchange.com |
384,534 | [
"https://physics.stackexchange.com/questions/384534",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/177855/"
] | Title says it all. From a physics point of view, gravity is a conservative force and so the amount of work done should be the same, and yet one option is a lot more tiring than the other. It's especially odd if we consider friction, since rolling friction is less than static friction, which should imply that cycling up... | The bike's gears are set so that a large force over a shorter distance at the pedal gives a smaller force over a longer distance at the wheel. This is the opposite to most machines, eg. a screw-jack or winch where you put in a smaller force over a longer distance to move a much heavier load.
Normally when you are cruis... | Being a 65-year-old cyclist who lives at the top of a steep hill, I am well-familiar with this problem. When you are pushing a bike up a hill on foot, you are moving uphill very slowly and the power required to do this is less than that required to ride the bike (i.e., go fast enough to keep the bike upright) up the sa... | https://physics.stackexchange.com |
381,573 | [
"https://physics.stackexchange.com/questions/381573",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/182379/"
] | My physical intuition is rather poor so I would appreciate any help.
If a string is vibrating and is heavier towards one end and gradually gets lighter towards the other, I find after plotting the eigenfunctions that the standing waves have a smaller amplitude and smaller wavelength on the heavier end. I assume the re... | The wave velocity on a string is $v =\sqrt{T/\varrho}$ where $T$ is the tension and $\varrho$ mass per unit lenngth. Tension is the same everywhere in the string. So in lighter parts wave speed is faster, wavelength shorter.
| You assumed that the frequency of oscillation is constant down the length of the string when you assumed a standing wave; combining that criteria with boundary conditions (e.g. fixed string ends) results in standing waves.
You <em>could</em> have different frequencies of oscillation in different parts of the string i... | https://physics.stackexchange.com |
459,775 | [
"https://math.stackexchange.com/questions/459775",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/85297/"
] | <blockquote>
What is the order of group of automorphisms of $\mathbb Z_{15} \times\mathbb Z_3$?
</blockquote>
If $15$ and $3$ were relatively prime I would know how to compute the order, but since they are not, I don't know how to do it.
| Well, note that since $\mathbb{Z}_5$ and $\mathbb{Z}_3^2$ are coprime in orders, that
$$|\text{Aut}(\mathbb{Z}_{5}\times\mathbb{Z}_{3}^2)|=|\text{Aut}(\mathbb{Z}_5)|\times|\text{Aut}(\mathbb{Z}_3^2)|$$
Now, $\text{Aut}(\mathbb{Z}_5)\cong \mathbb{Z}_4$ and $\text{Aut}(\mathbb{Z}_3^2)\cong \text{GL}_2(\mathbb{Z}^3)$.... | We know that $\mathbb{Z}_{15}\times\mathbb{Z}_3\cong\mathbb{Z}_5\times\mathbb{Z}_3\times\mathbb{Z}_3 = G$. All of those are cyclic groups, thus a group homomorphism $G\rightarrow H$ is completely determined by the image of the three generators.
The generator of $\mathbb{Z}_5$ can only be mapped to one of the non-ident... | https://math.stackexchange.com |
26,917 | [
"https://stats.stackexchange.com/questions/26917",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10802/"
] | I am asked to give a lecture on clustering algorithms for an audience that is not very technical. With that in mind, I wanted to do a simple exercise where I will ask the audience to identify groups from a dataset. However, I cannot find good datasets that could be usable for this purpose.
Is there a dataset of custom... | The term you're searching for is 'extrapolation'. The problem is that no matter how much data you have, and how many intermediate levels you have between your endpoints on disk size (i.e., between 5 and 30), it is always possible that there is some degree of curvature in the true underlying function, that you simply d... | Let me add a few points to @gung's excellent answer:
<ul>
<li>Depending on your field, there may be relevant <em>norms</em> (as in DIN/EN or ISO). This is probably not an issue with predicting hard disk reading speed, but e.g. in <strong>analytical chemistry</strong> the rule is <strong>no extrapolation</strong>. Peri... | https://stats.stackexchange.com |
365,738 | [
"https://math.stackexchange.com/questions/365738",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/73267/"
] | I'm trying to jog my memory of calculus from 10 years ago and it's proving a bit difficult. I'm hoping someone can give me a push in the right direction here. I've found a number of good resources online, but they're all either too far abstracted from my problem or too advanced. The concrete problem that I'm trying to ... | Since any neighborhood $(q - \epsilon, q + \epsilon)$ of a rational $q$ contains irrationals, $\mathbb{Q}$ has
no internal points. This implies that $\mathbb{Q}$ is not open. Since every irrational number is the limit of a sequence of rationals, $\mathbb{Q}$ is not closed (for a set to be closed it should contain al... | <strong>Hint</strong>
$$r\in\mathbb{Q},\quad\forall \epsilon>0, (r-\epsilon,r+\epsilon)\not\subset\mathbb{Q}$$
$$x\in\mathbb{R}\setminus\mathbb{Q},\quad\forall \epsilon>0, (x-\epsilon,x+\epsilon)\not\subset\mathbb{R}\setminus\mathbb{Q}$$
$$\displaystyle\mathbb{Q}=\bigcup_{r\in\mathbb{Q}}\{r\}$$
| https://math.stackexchange.com |
422,384 | [
"https://physics.stackexchange.com/questions/422384",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/203838/"
] | On page 21-4 of vol. III of The Feynman Lectures on Physics, he derives the formula for the probability current density. Starting with the Schrödinger equation, he presents the time derivative of the probability density, and then states,
<blockquote>
"The potential terms and a lot of other stuff cancel out. And it t... | Chester Miller points out that my simplistic answer is incorrect. Please see his derivation in the comment section below.
| The force would be simply the product between the pressure and the surface of the hole in the tank, say $F = PS_h$, where $F$ is the force, $P$ is the pressure and $S_h$ the surface of the hole. But the force is changing in time, than it's interesting to see how the force is varying with time.
A solution might be this ... | https://physics.stackexchange.com |
458,065 | [
"https://physics.stackexchange.com/questions/458065",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75085/"
] | Consider an atom modelled as a two level system :
<span class="math-container">$$H=\frac{\hbar \omega}{2} \sigma_z $$</span>
<span class="math-container">$|0\rangle$</span> and <span class="math-container">$|1\rangle$</span> are the ground and excited states that span the Hilbert space.
In the Rabi oscillations stud... | We have a pair of state spaces <span class="math-container">$A$</span> and <span class="math-container">$B$</span>, their combined state space is the tensor product <span class="math-container">$A\otimes B$</span>. Its elements are of the form <span class="math-container">$|a\rangle\otimes|b\rangle$</span> and (limits ... | The representation is for vectors too.
Think of it this way: the formalism is for matrices, of any size. Vectors are matrices with a single column.
| https://physics.stackexchange.com |
290,954 | [
"https://dba.stackexchange.com/questions/290954",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/229148/"
] | I am wondering if the SQL jobs like automating the database backup runs even the machine/server is offline?
| No but you can create a script or a cron job that can take a copy of the files:
<ul>
<li><code>Database_Name.mdf</code></li>
<li><code>Database_Name.ldf</code></li>
</ul>
Such files are stored under <code>C:\Program Files\Microsoft SQL Server\MSSQL15.MSSQLSERVER\MSSQL\DATA</code> and are the actual database.
So if you ... | No SQL Jobs cannot run without the SQL Server & the SQL Agent Service running
| https://dba.stackexchange.com |
233,201 | [
"https://mathoverflow.net/questions/233201",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21339/"
] | It is known that an invertible <em>mpt</em> $S$ is weakly mixing if and only if $S \times T$ is ergodic for any ergodic invertible <em>mpt</em> $T$. Is it more generally true that the invariant $\sigma$-field of $S \times T$ is the product of the trivial $\sigma$-field times the invariant $\sigma$-field of $T$ whenever... | The answer is yes (I am assuming here the spaces are standard and the measures are probability measures).
For this kind of questions I find that it is convenient to think about quotient spaces rather then sub-$\sigma$-algebras. In particular, instead of considering the $\sigma$-algebra of invariants you better conside... | Here I will explain (briefly) the proof of the statement using tensor products of unitary operators.
Recall that a unitary operator $U$ on a Hilbert space $H$ is called <em>ergodic</em> if $H^U=\{0\}$, ie there is no $U$-invariant vector in $H$, and <em>weakly mixing</em> if $U\otimes U$ is ergodic on $H\otimes H$ (he... | https://mathoverflow.net |
6,151 | [
"https://electronics.stackexchange.com/questions/6151",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | I'm trying to repair an 800W power supply (see my previous question on this.) One thing that gets me is that the design has two schottky diode packages (in TO-220) in parallel. I was always told this was A Bad Idea, but since they are thermally coupled to the same heatsink, does it present a problem in this instance? I... | The issue with putting diodes in parallel is that as they heat up, their resistance decreases. As a result, that diode ends up taking on more current then the other diode, resulting in it heating up even more. As you can probably see, this cycle will cause thermal run away causing the diode to eventually burn if you gi... | If you put a low value resistor, for example 1 ohm or 1/2 ohm, something like that, in series with each diode, and then parallel those assemblies, the resistors help to keep the load even between the two diodes. If one diode starts to take more of the load current (as it would with thermal run-away), the IR drop on the... | https://electronics.stackexchange.com |
2,855,689 | [
"https://math.stackexchange.com/questions/2855689",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/60900/"
] | Here's my doubt:
<blockquote>
When we say polynomial regression, do we usually mean linear or non-linear?
</blockquote>
A simple answer would be very helpful.
<hr/>
<sub><sup>This is not a duplicate question. I've read through similar questions and require clarification on the <b>nuances</b> of the terminology.</su... | Polynomial regression usually stands for the fitting of a polynomial to a set of $(x,y)$ points, which is a linear problem when solved by least-squares.
| No. As was already pointed out - the linearity in regression model is defined w.r.t. the parameters $\beta$ and not the variables $x$. Formally, if the gradient vector of (the conditional expectation of the model) is independent of any unknown terms - then it is linear, otherwise non-linear. Namely, for a polynomial re... | https://math.stackexchange.com |
665,019 | [
"https://physics.stackexchange.com/questions/665019",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/313410/"
] | Given two pieces of aluminum, a sphere with diameter <span class="math-container">$d$</span> and a plate, how can we estimate the penetration depth given the initial velocity <span class="math-container">$v$</span> of the sphere? If that proves too complicated due to effects like melting, neglect plastic deformation of... | The question which was asked was <em>Can adding two numbers increase the significant figures?</em><br />
In this context the question is misleading in that when values range over a value of . . . . . <span class="math-container">$0.1$</span> or <span class="math-container">$1$</span> or <span class="math-container">$10... | Consider what the number of significant figures indicates:
The number written as <span class="math-container">$7$</span> has <span class="math-container">$1$</span> significant figure; the number is somewhere between <span class="math-container">$6.5$</span> and <span class="math-container">$7.5$</span>
The number wri... | https://physics.stackexchange.com |
553,174 | [
"https://stats.stackexchange.com/questions/553174",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/299869/"
] | I know AUC is supposed to be independent on the threshold, which means AUC does not change while the threshold changes. However, I'm getting different AUC values while changing the thresholds. I'm using <code>roc_auc_score</code> to calculate the AUC value in Python.
I've got the probability and assigned the group as 1... | I think you might be doing the following: defining a threshold (k), calculating your output accordingly (y_k = 1 if p>k, 0 otherwise ), then calculating AUC from y_k and y_true. This is not the AUC for your initial model, but for a different model which doesn't see probabilities and only sees 1 or 0 depending on the... | AUC is calculated by <em>varying</em> the threshold across the permissible space, e.g., <span class="math-container">$[0,1]$</span>. This varying threshold gives you precision-recall <em>curve</em>. You then calculate the <em>Area</em> <em>Under</em> this <em>Curve</em>.
Thus, it makes little sense to say that "AU... | https://stats.stackexchange.com |
8,748 | [
"https://physics.stackexchange.com/questions/8748",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2536/"
] | Why is it that photons are emitted in bundles?
My physics teacher's answer was "it's complicated"...
| Photons aren't complicated, Instead they're non-sensical! This topic is really about "Quantum Weirdness."
First let's get one thing straight: photons are not emitted in bundles. Instead atoms emit photons one at a time.
I'm guessing here, but I think the teacher was trying to communicate the following: EM wave-e... | In general photons are emitted one by one from individual atoms.
I suspect you were discussing laser photons, and also suspect that you still are in high school. Photons from lasers do come in bunches, and your teacher is correct that it is not simple to explain it. Let me try.
Have you seen the domino set ups, where... | https://physics.stackexchange.com |
4,082,688 | [
"https://math.stackexchange.com/questions/4082688",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/274944/"
] | I am interested in this problem as a novelty; in the direction of constructing <em>known</em> things (which are usually taken to be somewhat fundamental) in terms of other, less-orthodox-to-call '<em>fundamental</em>' things.
In particular, suppose the function <span class="math-container">$s(x) = x^2$</span> is taken ... | No polynomial formed with linear combinations only does contain the term <span class="math-container">$xy$</span>.
A polynomial obtained by squaring a linear combination has an even coefficient of <span class="math-container">$xy$</span>.
The property "has an even coefficient of <span class="math-container">$xy$</... | Instead of working in a situation where <span class="math-container">$x \mapsto x/2$</span> is not 'effectively calculable', why not work in a situation where it is impossible - i.e., in characteristic <span class="math-container">$2$</span>?
By reducing modulo <span class="math-container">$2$</span>, you may consider ... | https://math.stackexchange.com |
567,000 | [
"https://math.stackexchange.com/questions/567000",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/36434/"
] | I would like to show the followoing result:
<blockquote>
Every vector bundle over $[0,1]^n$ is trivial
</blockquote>
First, I consider the case $n=1$, so let $E$ be a vector bundle over $[0,1]$. If $\nabla$ is a connexion for $E$, let $\tau_x : E_x \to E_0$ be the parallel transport along the path $p_x : t \mapsto ... | Following Theo Johnson-Freyd's comments, I found:
Let $E \to B$ be a vector bundle and $\nabla$ be a connection. Let $x_0 \in B$ and, for every $x \in B$, let $\gamma_x : [0,1] \to B$ be a path from $x$ to $x_0$. A candidate for a global trivialization is $$\Phi : \left\{ \begin{array}{ccc} E & \to & B \times ... | Theo says in the comments:
<blockquote>
Although not obvious, it is nevertheless true that every vector bundle admits a flat connection. It follows that vector bundles are trivial on manifolds with vanishing $\pi_1$, but not in general.
</blockquote>
This is false. I wouldn't post this as an answer except that it's... | https://math.stackexchange.com |
413,766 | [
"https://mathoverflow.net/questions/413766",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2362/"
] | <span class="math-container">$\newcommand\Sq{\mathit{Sq}}$</span>Recall that a (graded) module <span class="math-container">$V^\ast$</span> over the Steenrod algebra <span class="math-container">$\mathcal A^\ast$</span> is said to be <em>unstable</em> if <span class="math-container">$\Sq^i v = 0$</span> for <span class... | Normally people think about Steenrod comodules as graded <span class="math-container">$\mathbb{Z}/2$</span>-modules equipped with a graded coaction <span class="math-container">$\psi\colon M_*\to M_*[\xi_1,\xi_2,\dotsc]$</span>. However, it is equivalent to consider ungraded modules with coaction <span class="math-con... | Your question seems to be equivalent to asking for a description of the unstable condition in terms of the Milnor basis. This is easy to do: Given <span class="math-container">$r = (r_1,\dots, r_s)$</span>, let <span class="math-container">$P(r)$</span> be dual to <span class="math-container">$\xi_1^{r_1}\cdots \xi_s^... | https://mathoverflow.net |
113,022 | [
"https://datascience.stackexchange.com/questions/113022",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/102713/"
] | I'm training a tree-based model (e.g. xgb). I have some features with more than 90% values constant. Does it add value to the model since the variation in the data is minimal?.
What would be the impact of the same if I were to use a linear regression model?
| Variation is not the key. Notice that 0/1 indicator variables are used frequently and might have mostly 0's (like many missing indicators). The key is where is the variation in relation to what you are predicting and in relation to interactions.
For example, if your column is 0 where target = 0 and not 0 where target =... | Variation does not matter what matters is how good is your variable in predicting the target variable.
in order to know whether linear model is applicable, you have to fit data on linear classification . If the accuracy is good then you can proceed with the linear classification else consider more complicated models l... | https://datascience.stackexchange.com |
38,810 | [
"https://engineering.stackexchange.com/questions/38810",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/19906/"
] | Today as I was filling up a bottle of water, and I could hear the distinctive change in pitch that signals that the bottle is near filling up, I started wondering what equation determines the frequency of the sound.
More specifically, I suspect this is fundamentally a problem in vibration dynamics. I suspect that there... | Most acoustic vibrations of air more or less confined to a given geometry can be explained by two basic models. One is the one-dimensional treatment of the air in a tube, and the other is the lumped-parameter treatment of the air within a volume that has a small hole in its side. The former is called a quarter-wave or... | The frequency of the sound you're hearing is related to the changing resonant frequency of your bottle based on the frequency/velocity relationship of sound waves <code>v=f*λ</code>
Velocity (v) is the speed of sound in air which is nearly constant, typically 343 m/s.
The length of the air column in your bottle is the ... | https://engineering.stackexchange.com |
239,025 | [
"https://softwareengineering.stackexchange.com/questions/239025",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/104647/"
] | In my company, we have had a policy of tagging every release. Someone new joined, and he suggested that instead of formally using a Tag, we could just leave a comment for the release build when it is checked in. I like using a Tag, but, obviously, we can also get to the source code for a build also by looking for the c... | A tag in subversion is technically the same as a branch. It is only convention that keeps you from modifying a tag after it was created.
Last year I had a situation where we were very happy that we use tags in subversion.<br>
We had created a release and tagged that release. In parallel to the acceptance tests on the ... | Some customer who cannot upgrade to a newer version ask you for support for version x.y.z. A tag with that release will help you identify the code you need to inspect. Ask the new guy to search the release using commit comments. Please, do it!
| https://softwareengineering.stackexchange.com |
18,126 | [
"https://cs.stackexchange.com/questions/18126",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/11155/"
] | I am trying to design a context-free grammar for the language $L = \{a^ib^jc^k \mid i\neq j+k\}$ over the alphabet $\Sigma = \{a,b,c\}$.
I know that I can split this up into the union of two cfg's $S_1$ and $S_2$,
<br>where $S_1$ is the case where $\#_a \lt \#_b + \#_c$,
<br>and $S_2$ is the case where $\#_a \gt \#_b... | I would start by finding a CFG that generates the balanced version $\{a^ib^jc^k\mid i=j+k\}$ from nonterminal $C$.
<blockquote class="spoiler">
$C\rightarrow aCc\mid B \\ B\rightarrow aBb\mid\varepsilon$
</blockquote>
Now, as you correctly note, there are two possibilities on how to get the unbalanced version; eit... | The split you made is actually a good design decision.
The language is context-free. Keep a central non-terminal, write $a$'s to the left, and $b,c$'s to the right. If you generate the $c$'s before you generate the $b$'s all letters stay in alphabetic order.
| https://cs.stackexchange.com |
646,490 | [
"https://physics.stackexchange.com/questions/646490",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300178/"
] | I've been having this confusion regarding the <strong>gradient</strong> being a <strong>covariant</strong> vector. Intuitively I seem to have understood the concept. However, mathematically, I'm unable to show this, in a single example.
Let us have our normal cartesian coordinates at the beginning. I don't know what ex... | Consider a scalar function <span class="math-container">$f:M\rightarrow \mathbb R$</span>, where <span class="math-container">$M$</span> is some smooth manifold. You can restrict your attention to <span class="math-container">$\mathbb R^2$</span> or <span class="math-container">$\mathbb R^3$</span> if you only want to... | The chain rule
<span class="math-container">$$
\frac{\partial x^\mu}{\partial y^\nu}\frac{\partial \varphi}{\partial x^\mu} = \frac{\partial \varphi}{\partial y^\nu}
$$</span>
is the change of coordinate transformation for the compoents of a covariant vector:
<span class="math-container">$$
\frac{\partial x^\mu}{\parti... | https://physics.stackexchange.com |
83,705 | [
"https://mathoverflow.net/questions/83705",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11072/"
] | I don't know how to show the following:
Let $A$ be an associative algebra (not necessary finite-dimensional) and $p\colon A\to End(V)$ be it irreducible finite-dimensional representation. Then $p$ in general is not surjective.
The standard textbooks on representation theory don't contain answer on this and googling d... | What's the ground field? Of course if it's $\mathbb{R}$ and $A=\mathbb{R}[t]/(t^2+1)$, then the regular module is irreducible, but the corresponding $p$ is not surjective. Over an algebraically closed field it's true even for infinite-dimensional $A$ though.
| Let $D \ne k$ be a central division algebra of finite dimension over a (commutative) field $k$ say with $\dim_k D = n^2$. Now view
$V = D$ as a left module over itself; then $V$ is an irreducible $D$-module.
Since $\dim \operatorname{End}_k(D) = n^4 > n^2$, the image of the mapping $D \to \operatorname{End}_k(V) =... | https://mathoverflow.net |
20,024 | [
"https://dsp.stackexchange.com/questions/20024",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/11809/"
] | As far as I know, bandwidth is measured in herz or 'radian/second' in digital signal processing or in analog communications. But in computer networking it is measured in 'bits/second'. I don't get how these two are related. Can anybody please help?
| They <em>both</em> define the amount of data you can get through a channel -- the channel bandwidth, together with the SNR, defines the channel capacity $C$, which has the unit of $\frac{\mathrm{bit}}{\mathrm{s}}$ (which, by the way, is simply $1$ binary decision per second), giving you the maximum amount of informatio... | As far as I'm aware, the original use of 'bandwidth' comes from communications engineering and is measured in hertz, and its use predates digital communications. The data (or information) rate in a link is meaured in bits per second. Since the data rate in a link is related to the system's bandwidth, the term was also ... | https://dsp.stackexchange.com |
20 | [
"https://engineering.stackexchange.com/questions/20",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/74/"
] | I'm making a robot for the Sparkfun AVC. I was curious if I could use only the knowledge about
<ol>
<li>How the car is being steered at every time interval,</li>
<li>How many times the wheels have rotated,</li>
</ol>
to get a general sense of where the car is. I would use computer vision to avoid immediate dangers.
... | Taking this in stages, initially lets consider only a single front wheel, with no slip in any direction, where we have an accurate continuous measure of both rotational position and absolute angle. In this case calculating current position (relative to our starting point) is a relatively straightforward trigonometry an... | The main problem which I can see in your idea, that your system will have a cumulative error. Only calculating this won't be enough, you will have to find alternate solutions, too.
In similar (but maybe bigger) scenarios, for example for drones, there is a similar problem.
The solution is using the wheel rotation cou... | https://engineering.stackexchange.com |
321,593 | [
"https://dba.stackexchange.com/questions/321593",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/93409/"
] | I've got a 400 line query in MS SSMS. When I run it I get:
<blockquote>
Msg 8115, Level 16, State 2, Line 1
<br /> Arithmetic overflow error converting expression to data type int.
</blockquote>
Line 1 is just the "Select" statement. Is there anything I can enable in SSMS that will point me closer to the li... | The problem turned out to be one of four "DateAdd" functions. I found it by commenting out half the SQL then progressively commenting/uncommenting lines until I narrowed it down. The failing line was using an "Epoch msec" value. I hadn't read the fine print in the source table docs. The other 3 ... | No.
SQL Server will just tell you the line of the statement that causes the error.
It won't even attempt to try and tie the error back to any particular line in a multiline statement and this wouldn't always be possible anyway.
For this error you likely just need to look for expressions using <code>SUM</code>, <code>CO... | https://dba.stackexchange.com |
466,609 | [
"https://stats.stackexchange.com/questions/466609",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/285177/"
] | I saw this question online as a prep question for stats/data science interviews. I’m familiar with the concept of uniform distributions and joint probability distributions, but I wasn’t able to make sense of this question, I’m wondering if I am interpreting it incorrectly or if this is a concept I’m unfamiliar with. If... | You can include dummies (binary variables that are either 1 or 0) for each year, for each region, and also year times region interaction dummies in your model. So you might have a dummy for year 2019, another dummy for Northeast region, and then a dummy that is 1 for Northeastern region municipalities in 2019, and so o... | The dataset under consideration is a dataset for <span class="math-container">$i=1,...,I$</span> municipalities for <span class="math-container">$t=1,...,T$</span> time periods. The model to be estimated is
<span class="math-container">$$ y_{it} = \mathbf x_{it}^\top \beta + \delta_t + \phi_r + \psi_{rt} + \epsilon_{it... | https://stats.stackexchange.com |
121,546 | [
"https://softwareengineering.stackexchange.com/questions/121546",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5209/"
] | Let's say we have a codebase that is used for many different costumers, and we have some code in it that is relevant only for costumers of type X. Is it better to use preprocessor directives to include this code only in costumer of type X, or to use if statements? To be clearer:
<pre><code>// some code
#if TYPE_X_COST... | I think there is one advantage of using a #define that you didn't mention, and that is the fact that you can set the value on the command line (thus, set it from your one-step build script).
Other than that, it is generally better to avoid macros. They don't respect any scoping and that can cause problems. Only very ... | As for many questions, the answer of this question is <em>it depends</em>. Instead of saying <em>which is better</em> i have rather given examples and goals where a one is better than other.
Both preprocessor and constant have their own places of appropriate usage.
In case of pre-processor, the code is removed befo... | https://softwareengineering.stackexchange.com |
251,619 | [
"https://security.stackexchange.com/questions/251619",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/248179/"
] | When using 2-factor-authentication using plain TOTP, the secret is stored on both the client and the server. This in turn means, that anyone with access to the database (and a key for it) knows the 2fa-secret of all the users. Why is this acceptable? Storing plaintext passwords has been deemed unacceptable a long time ... | There are a few issues with your scheme that I can think of:
<ul>
<li>the server would have to store several keys per user, where the current scheme needs just one secret to be stored for multiple client authenticators</li>
<li>the authentication scheme shifts the responsibility of generating and maintaining the secret... | 2FA is not one thing. It's a general concept, where you have two factors. The factors may be a shared secret you have, or it may be a PKI certificate the user has. It may be U2F.
If you have concerns over the database of secrets, don't use TOTP; use U2F or some other 2FA which doesn't require you to have this database.... | https://security.stackexchange.com |
211,953 | [
"https://dba.stackexchange.com/questions/211953",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/155091/"
] | I'm designing the schema for a database and have a question about primary key choice. There aren't any natural keys available in the tables we're looking at now although there's interest from my team in using more "readable" keys to see relations between tables a bit easier.
The current proposed solution is to have ... | You <em>could</em> do this - but I <em>wouldn't</em>. Here's why:
I generally try to avoid using "human meaningful" values as keys - because humans may decide they want the value to be something else. Since your key is partly a human meaningful value, there will be a temptation to change it.
For instance, "Alex" deci... | Keys first and foremost should be designed to satisfy business requirements. You need to understand what the business process is and how people (customers? or employees? or something else?) need to be identified as part of that process. Then you can design a suitable key strategy to support those needs.
You have said ... | https://dba.stackexchange.com |
170,731 | [
"https://electronics.stackexchange.com/questions/170731",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/76604/"
] | Question: Design a state machine that would output the sequence 0 1 7 1 and then 1 7 1 1 7 1 and so on. A reset will make the machine go to the which outputs 0?
What I've managed to do so far:
Since the sequence has four numbers so we use two Flip Flops. And states would be: 00, 01, 11, 10
And I'm considering "reset... | Voltage droop is a result of cable resistance over large runs. Resistance adds up the longer and thinner the cable. And as your current load increases, the voltage you see at one end of the cable will decrease. Basic ohms law. In this case you will see the leds down the line look dimmer and dimmer until they stop light... | The higher amperage that your supply <strong>can</strong> produce is irrelevant. Ohms law dominates and if the volt drop down a conductor due to the current taken by the LEDs causes the LEDs to get progressively dimmer then you might have to re-inject power at the half way point (assuming you apply power at both ends).... | https://electronics.stackexchange.com |
137,103 | [
"https://softwareengineering.stackexchange.com/questions/137103",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/48198/"
] | I'm new at computer science and programming, and I was wondering, is there a difference between computer science and programming? and do you get to choose to study only one of them at the university, or both of them?
| Computer science is the study of what computers [can] do; programming is the practice of making computers do things.
Take a look at the courses/syllabi offered by universities you're interested in to find out whether the course is a CS course, a programming course, something else (for example Software Engineering) or ... | A caveat: 'Computer Science' has become a muddied field in modern times because (at least in the United States) universities do not have degrees in "programming". This means that people interested in programming must sign up for Computer Science degrees, and as a reaction to that the Computer Science programs emphasi... | https://softwareengineering.stackexchange.com |
45,731 | [
"https://mathoverflow.net/questions/45731",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3902/"
] | The concept of a subobject classifier is of course standard and ubiquitous. But is there any nontrivial example of an unrestricted slice classifier?
Specifically, what I mean by this is, is there any non-preorder category with pullbacks with a morphism m into an object X such that ALL other morphisms can be taken as a... | It looks like such categories may be rather easy to construct. The following example should give the general idea: take the category of sets $V_\alpha$ of cardinality less than or equal to $\alpha$, for some infinite cardinal $\alpha$. The morphism classifier will be the set $C$ of cardinals up to and including $\alpha... | I claim that a such category exist:
Let $\mathcal{C}$ any category, build a full immersion $\mathcal{C}\subset \mathcal{C'} $ adding to $\mathcal{C}$ the new objects: $\coprod_f d_0(f), \ \coprod_f d_1(f) $ and the no-identity new arrows: $\coprod_f f: \coprod_f d_0(f) \to \coprod_f d_1(f)$ and for any $f: X\to Y$... | https://mathoverflow.net |
548,703 | [
"https://physics.stackexchange.com/questions/548703",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262977/"
] | I know that friction in pure rolling is zero.But in some questions friction is included such as on an inclined plane while in others friction is not included . I am very much confused with friction in pure rolling. Can anybody clarify me what actually happens and where I am going wrong?
Should we include friction or n... | I think your confusion is due to the fact that <strong>there are two types of friction</strong>.
<ul>
<li>One is always zero. That is <strong>kinetic friction</strong> (it only appears when something slides, which isn't the case for rolling).</li>
<li>The other is <em>not</em> always zero. That is <strong>static frict... | <strong>Frictional force is not zero in a rolling motion</strong>
An object is able to roll only because friction prevents the bottom part from slipping. Else the body would simply slip through the floor. It is true for all kinds of surface-flat, inclined, cicular...
<strong>Work Done by frictional force, during a pu... | https://physics.stackexchange.com |
14,456 | [
"https://quant.stackexchange.com/questions/14456",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/17133/"
] | Suppose I model the forward swap rate lognormal
$$dS_t = \sigma_{ln}S_tdW_t$$
On the other hand we could model it simply by a normal assumption:
$$dS_t = \sigma_{n}dW_t$$
I would like to know if there is a relationship for the volatilities $\sigma_n,\sigma_{ln}$? A friend told me, that he saw the approximation
$$\... | It might help to look at the solutions of the SDEs that you have there.
In the first case
$$
S_t/S_0 = \exp(-\sigma^2/2 t + \sigma B_t) \quad \quad (1)
$$
Thus if you take the log then $\sigma$ is the volatility of the log-returns (assume that $t=1$ time step),.
In the second case
$$
S_t = S_0 + \sigma B_t \rightarrow... | For any normal variable, you have $$aX\sim N(a\mu,a^2\sigma^2).$$ So a linear transformation preserves the distribution type (note that $dW_t\sim N(0,dt)$).
When you want to approximate $dS_t$ by setting $dS_t=dS_t$, canceling the $dW_t$ you get:
$$\sigma_{ln}S_t=\sigma_n$$
| https://quant.stackexchange.com |
178,944 | [
"https://physics.stackexchange.com/questions/178944",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/79039/"
] | My question in the title might not be very descriptive so I am re-writing it here:
If there is a truck in motion and it has stack of hay (lets suppose) on the back. Now if the truck comes to a sudden stop will it stop faster if the force exerted by the truck on hay had overcome the friction force (another wording: wil... | On the whole, static friction is higher than dynamic friction. This means that if you can brake without your wheels skidding, you will come to a halt more quickly. So let's assume that the truck brakes without skidding, and see where that gets us.
Let's assume that your truck has weight $W = Mg$ with a haystack with a... | Not to detract from Floris' answer, but I think this is an instance where it is nice to think in terms of limits.
If the hay is tied down, you're stopping an object with mass (truck + hay).
If the hay isn't tied down, but on a sufficiently sticky surface such that it doesn't move, it should be the same as stopping it... | https://physics.stackexchange.com |
1,744,899 | [
"https://math.stackexchange.com/questions/1744899",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/154929/"
] | <blockquote>
We have $10$ bags of candies each with $10$ colorful candies It is
known that <strong>at least</strong> $1$ of the bags contains <strong>exactly</strong> $5$ red
candies
We get $1$ candy from <strong>each</strong> bag what is the probability that we get
an even($0$ is considered even) numbe... | Somewhat unexpectedly, it turns out that you don't need any information about the distribution of colors in the remaining bags. This, of course, is a property of symmetry...if you replace the $5$ in your problem with anything else, then the question can not be answered without additional information.
Suppose we know ... | The problem as stated is not well posed, as we don't know what is the probability that a bag contain exactly $n$ candies. We could have for example that each candy has probability $\tfrac{1}{p}$ of being red for some $p$, or that the probability for a bag to contain exactly $n$ red candies is exactly $\tfrac{1}{10}$, a... | https://math.stackexchange.com |
116,643 | [
"https://security.stackexchange.com/questions/116643",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/81513/"
] | An automatic login URL is a mechanism whereby an existing but logged out user of your website or application can click a link with a random token and be automatically recognized and logged-in to your website. Often these mechanisms are used in other fashions such as password resets.
I am wondering what some "defense i... | In addition to ensuring a token is single use, has a short expiration and that the token is sufficiently random and long:
<ul>
<li>I'd recommend limiting the number of valid tokens in existence at any given time (preferably to 1). That way your exposure to compromised codes is limited to a fixed number.</li>
<li>Havin... | If possible, learn where you user typically comes from (geo-locate their IP addresses). If that single-use token is used from an unusual location, don't authenticate them.
This way you can hopefully prevent account compromises from email account hijacking, or MiTM of the emails (which are plaintext, remember!).
(Idea... | https://security.stackexchange.com |
36,735 | [
"https://mathoverflow.net/questions/36735",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2384/"
] | In Peter J. Cameron's book "Permutation Groups" I found the following quote
<blockquote>
It is a slogan of modern enumeration theory that the ability to count a set is closely related to the ability to pick a random element from that set (with all elements equally likely).
</blockquote>
Indeed, one can count and sa... | Yes, there is formal way of saying this using complexity theory. I think the statement is something like: For all self-reducible relations, the problems of approximate sampling and approximate counting are equivalent (with polynomial time reductions). More specifically, for such problems, the existence of an FPRAS (ful... | If you have an algorithm that produces uniform and independent samples from a set of object, you can estimate the total number of objects as follows. First, construct a subset of the objects to be counted, if possible quite large, in a way such that you know the size of the subset and you can check easily if a given el... | https://mathoverflow.net |
2,795 | [
"https://mechanics.stackexchange.com/questions/2795",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/433/"
] | What's the need for car battery chargers that I often see on display in auto parts shops?
I mean a battery is sold charged (and if it discharges too much it just dies and can't be restored) and every car has an alternator for charging the battery and if the battery is empty and can't start the engine then jump-startin... | <blockquote>
Why and when would one use such charger?
</blockquote>
To my mind, the major needs fall into two major categories:
<ol>
<li>You have a vehicle that does not get driven enough to keep the battery up to charge against its passive drain. Common examples would include the summer-only car or the utility ve... | E.g., driving only short distances may make it difficult for the alternator to keep up (low running-engine-time to number-of-starts ratio.) Connecting a battery charger when the car is parked can keep the battery fully charged and eliminate the need for occasional jump-starts.
| https://mechanics.stackexchange.com |
199,838 | [
"https://softwareengineering.stackexchange.com/questions/199838",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3417/"
] | I have an SVN repository set up like so:
<ul>
<li>trunk</li>
<li>branches
<ul>
<li>UAT</li>
<li>QA</li>
<li>DevelopmentTeam</li>
<li>programmer1</li>
<li>projectA</li>
<li>projectB</li>
<li>programmer2</li>
<li>projectC</li>
<li>projectD</li>
<li>programmer3</li>
<li>projectE</li>
<li>projectF</li>
<li>projectG</li>
<... | Conflicts occur because two people change the same part of the code in different, incompatible ways. If you see a lot of them, this should raise some questions about your basic development methodology.
First, you appear to be abusing branching rather severely. Giving every developer their own repository basically de... | Your problem is you aren't working on the same codebase. Each dev has their own codebase, which is apparently being allowed to diverge significantly from the trunk (if it wasn't diverging, you wouldn't have this problem).
I think the existence of the 'programmer' branches is really the problem here. You should probabl... | https://softwareengineering.stackexchange.com |
49,973 | [
"https://electronics.stackexchange.com/questions/49973",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16454/"
] | Over the next two weeks, I'm going to be building a greenhouse fan system. It's not for a real greenhouse, though. It's just for fun. Anyway, my plan is to use the Dragon12+ board that I have, an LM34 temperature sensor, and a little 5V fan.
My goal is to read the temperature, convert it with the A to D converter,... | You don't limit what the sensor sees. The sensor reports what it sees. Your question is kind of like asking "I'm only interested in hot women. How can I adjust my eyes to not see ugly women?" You have no control over what the sensor sees.
Similarly, the ADC resolution (and sensor accuracy/resolution) will determine ho... | Instead of focusing on your sensor display range, why not focus on your control circuit.
If you change the control to a proportional control, the fan speed will indicate air temperature and you can tell by the RPM of the noise.
The RED line shows your implementation. The others are hypothetical.
The dotted line shows ... | https://electronics.stackexchange.com |
176,293 | [
"https://mathoverflow.net/questions/176293",
"https://mathoverflow.net",
"https://mathoverflow.net/users/50191/"
] | I have the following function for two matrices ${\bf A}$ and ${\bf B}$:
$f({\bf A}, {\bf B}) = \| {\bf Y - XAB} \|_F^2 = trace\{({\bf Y - XAB)}^T({\bf Y - XAB)}\}$
where matrices ${\bf X}_{n \times p}$ and ${\bf Y}_{n \times q}$ are fixed, and matrices ${\bf A}_{p \times r}$ and ${\bf B}_{r \times q}$ are the variabl... | $f$ is convex separately for $A$ or $B$ but is not (in general) for the couple $(A,B)$.
Proof: The Hessian of $f$ in $X,Y$ is the following QUADRATIC form:
$Q(H,K)=2(||XHB+XAK||^2+2trace((XAB)^TXHK))-4trace(Y^TXHK)$.
Then $Q(H,0)=2||XHB||^2$ and $f$ is convex for $A$ (and similarly for $B$) - One must say a little ... | Did you try the case $n=q=p=r=1$? Consider $Y=0$, $X=1$, $(A,B) = (1,0),$ $(1/2, 1/2)$ and $(0,1)$. Yes, I know you said $r < \min(p,q)$, but you can easily throw in some irrelevant dimensions.
| https://mathoverflow.net |
87,441 | [
"https://cs.stackexchange.com/questions/87441",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/-1/"
] | Let $L$ a language over $X = \{a\}$ defined as follow :
$$L = \{ a^{n!} \ | \ n \geq 0 \}$$
I want to prove that $L$ isn't regular, I have searched in the forum for an equivalent question, but I found nothing. If it's a duplicate, I apologize and I'll be glad if you provide me the link of the duplicated question.
I... | The easiest way is probably to use the pumping lemma on the complement language $\overline{L} = \{ a^m : m \neq n! \}$. Suppose that $L$ were regular. Than $\overline{L}$ would be regular. According to the pumping lemma, there is a pumping length $p$ such that every word $w$ of length at least $p$ in $\overline{L}$ has... | It is a little confusing that you seem to have used $k$ in two different ways. First in the pumping lemma $xy^kz$, then to fix the length of $xy$.
Rather than trying to prove that deleting $y$ from the string $\omega$ (pumping with $k=0$) will give a string outside the language, perhaps it is easier to add a copy of $... | https://cs.stackexchange.com |
2,293 | [
"https://mathoverflow.net/questions/2293",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1095/"
] | I've recently started to look at elliptic curves and have three basic questions:
<ol>
<li>Is it correct to say that elliptic curves $E$ in the projective plane are in <strong>bijective</strong> correspondence with lattices $L$ in the complex plane via $E$ <--> $C/L$. </li>
<li>If so, is there an explicit expressio... | What you want in terms of the relation between lattices and elliptic curves over C is proposition I.4.4 of Silverman's Advanced topics in the arithmetic of elliptic curves. Additionally, to go from a lattice to the equation of the elliptic curve (explicitly), you use Eisenstein series as in Corollary I.4.3 of that book... | <ol>
<li>No, for any cubic curve in the plane, there is a family of cubic plane curves (<strike>3 or 4 dimensional - I forget</strike> <b>Edit:</b> 8-dimensional, with a transitive action of PGL<sub>3</sub>) that are isomorphic as curves. For any lattice in C, there is a 1-dimensional family of lattices that form isom... | https://mathoverflow.net |
161,475 | [
"https://physics.stackexchange.com/questions/161475",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/71561/"
] | Let us define an inertial frame as a frame of reference where the laws of physics take their usual form, as opposed to non intertial frames where one has to introduce pseudo-forces.
We can further define an equivalence class which contains other inertial frames as the class of frames of reference moving of constant ve... | What follows is a version of the statement you want to prove which assumes that any two frames are related by a spacetime transformation that leaves time invariant up to translation and that preserves Euclidean distances. Because of these hypotheses, the statement below is a Newtonian answer to the question. I'm conf... | Consider time reversal or parity transformations.
Because some physics doesn't have this symmetry, there are separate in-equivalent classes of inertial frames.
In each class, the physics will appear the same, and you can rotate, translate, or boost from one inertial coordinate system to another in the same class. Bu... | https://physics.stackexchange.com |
702,797 | [
"https://physics.stackexchange.com/questions/702797",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/318939/"
] | Suppose I want to model a system described by a Hamiltonian <span class="math-container">$H_0$</span> to which I give a quick kick at time <span class="math-container">$t = 0$</span>.
I would use the time-dependent Hamiltonian <span class="math-container">$$ \mathcal{H}(t) = H_0 + \bar{V} \delta (t)$$</span> with <span... | I've been thinking about this problem again and I want to propose an other answer, which I think is more correct than the previous one. We have to be more careful when we integrate <span class="math-container">$\delta (t)$</span> from <span class="math-container">$0$</span> to <span class="math-container">$t > 0$</s... | <strong>Solution using a basis set expansion</strong>
Let <span class="math-container">$H_0|n\rangle=E_n|n\rangle$</span> and lets make the following ansatz for our time dependent state,
<span class="math-container">$$
|\psi(t)\rangle = \sum_n c_n(t) \exp\left(-\frac{i}{\hbar }E_nt\right)|n\rangle .
$$</span>
Inserting... | https://physics.stackexchange.com |
366,465 | [
"https://softwareengineering.stackexchange.com/questions/366465",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/157448/"
] | Many of Laravel's build-in framework libraries use closures as arguments. What is the primary purpose of this coding style? Is it just to gain more control over the configuration of the function, to use "functional style", or does it provide dependency inversion of some sort?
I'm curious because I wonder whether I sh... | The Laravel route directives actually do accept a string as the second parameter:
<pre><code>Route::get('/user', 'UserController@index');
</code></pre>
This is parsed by the Laravel router to call the desired action in the desired controller, and then inject whatever the action controller returns into the actual resp... | The primary reason is so that Route does not have to depend on View. By passing in the function, I am able to reduce dependencies between objects, observe separation of concerns and make each class more testable.
| https://softwareengineering.stackexchange.com |
109,333 | [
"https://cs.stackexchange.com/questions/109333",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/105300/"
] | I have the following statement. I would say it's correct as it's either equal or higher than <span class="math-container">$\Omega(\log^{10}(n))$</span>.
Because:
I know <span class="math-container">$\log(2^n) = n$</span>.
By that I would guess the same goes for <span class="math-container">$\log(n^{10})$</span> unimpo... | The "assembly writer" in that book is a human software developer who writes code in assembler language.
| <blockquote>
In VLIW architecture, the compiler/and or assembly writer chooses instructions that can be executed in parallel
</blockquote>
The meaning of this sentence is that in VLIW architecture, assembler (machine) code defines which instruction will be executed in parallel, so it's fixed at the time assembly co... | https://cs.stackexchange.com |
114,529 | [
"https://stats.stackexchange.com/questions/114529",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/52898/"
] | I am doing multiple imputation using chained equations in Stata to deal with item-missing data. One of the variables on which I did imputation was income. However after I did imputation, the imputed values of income contain negative values though the mean and standard deviation of income after imputation are almost sim... | I think you just continue with your analysis. For one thing, negative income is not impossible. If you lose money (e.g. on investments) and don't make any, that would be negative income.
| If you are using Royston's <strong>ice</strong> package to do the multiple imputation, you can truncate the distribution of income at 0 with the <code>interval()</code> option. For example, if you wanted to bound income between zero and some maximum:
<pre><code>ice income x1 x2 x3, saving(imputed) m(5) interval(income... | https://stats.stackexchange.com |
26,428 | [
"https://chemistry.stackexchange.com/questions/26428",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/14536/"
] | I'm taking a first year university chemistry course, and I am reading a lot of contradicting things. Some people say that ionic compounds that are soluble in water are <em>always</em> electrically conductive, others say that it <em>maybe</em> conductive. Which one is it?
I have this problem to think about:
<blockquo... | DavePhD is right! Your material is an organic compound.
In order to be soluble in water, it should have some polar substituents. I'd however exclude carboxylic acids or phenolic $\ce{OH}$ (except maybe in the proximity of a carbonyl group) since these will partly dissociate and yield to minor conductivity.
If the me... | All soluble ionic compound conduct according to Debye-Hückel-Onsager theory.
Think of something molecular.
| https://chemistry.stackexchange.com |
4,248,417 | [
"https://math.stackexchange.com/questions/4248417",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/966200/"
] | If it were true, how would one prove it? In my textbook the definition of a basis for V is simply that it is linearly independent and V is dependent on it. There is no mentioning of it being a subset relation so I think the subset relation to be logically implied by those two conditions.
I want to use the result to pro... | When a basis of <span class="math-container">$V$</span> is defined I think it's normally stated that the basis is a subset of <span class="math-container">$V$</span>. The question is if we take the following as the only given properties of a set <span class="math-container">$\{x_1, x_2, ... x_n\}$</span> is that suffi... | How about: Let <span class="math-container">$\{v_1,...,v_n\}$</span> be a basis for the vector space <span class="math-container">$V$</span>. Then, for any scalars <span class="math-container">$a_1,...,a_n$</span> we have that:
<span class="math-container">$$a_1v_1+a_2v_2+...a_nv_n \in V$$</span>
We want to show that e... | https://math.stackexchange.com |
316,812 | [
"https://softwareengineering.stackexchange.com/questions/316812",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/218080/"
] | I am approaching a project where I'll be having to implement a database with my boss; we're a very small start up so the work environment is deeply personal.
He had given me one of the company databases before and it completely went against what I was taught (and read about) in school for RDBMS. For example, there are... | The performance argument is usually the one which is most intuitive. You especially want to point out how it will be difficult to add good indexes in an incorrectly normalized database (note: there are edge-cases where denormalization can in fact <em>improve</em> performance, but when you are both inexperienced with re... | <blockquote>
I'll be having to implement a database with my boss ...
</blockquote>
Using dedicated Database Management <em>software</em> might be considerably easier (sorry; couldn't resist).
<blockquote>
lngStoreID | vrStoreName | lngCompanyID | vrCompanyName | lngProductID | vrProductName
</blockquote>
If t... | https://softwareengineering.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.