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 |
|---|---|---|---|---|---|
429,082 | [
"https://physics.stackexchange.com/questions/429082",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I am reading about retarded potentials in Griffiths' Introduction to Electrodynamics, and came across the particular case of wires. Griffiths takes wires to be electrically neutral, therefore the retarded scalar potential is zero, which has an integrand proportional to charge density, which he has taken to be zero.
T... | If the positive and negative charges are moving at different velocities, then their contributions to the current density will be different, even if their charge densities are equal and opposite.
For example, in a normal wire, we can usually model the electrons as moving and the positive charges as stationary (though t... | From a microscopic perspective $J=\rho v$ holds, but from a macroscopic perspective it can fail.
Consider two microscopic charge distributions, one with charge density and no velocity and the other with the opposite charge density and some velocity. The current of the first is 0, but the current of the second is non ... | https://physics.stackexchange.com |
410,248 | [
"https://softwareengineering.stackexchange.com/questions/410248",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/87243/"
] | I'm working on a PHP web application that depends on a few 3rd-party services. These services are well documented and provided by fairly large organisations.
I feel paranoid when working with responses from these API, which leads me to write validation code that validates that the responses match the structure and da... | Absolutely. For starters, you never know that somebody hasn't hacked into your connection and the reply you receive doesn't come from the API at all.
And some time in the last two weeks I think Facebook changed an API without notice, which caused lots of iOS apps to crash. If someone had verified the reply, the API w... | Somebody else's API is your external interface. You shouldn't blindly trust anything that crosses that boundary. Your future debuggers will thank you for not propagating the other system's errors into yours.
| https://softwareengineering.stackexchange.com |
144,199 | [
"https://security.stackexchange.com/questions/144199",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/127161/"
] | If I have a client-server web chatroom, is it important for public or private(client-side encrypted) messages to be signed on the client side? Am I correct in assuming (correctly set up)TLS will prevent any MITM risk?
Each user has their own private/public key for pm encryption.
Clarity: I am developing both the cha... | Using TLS doesn't prove the <strong>user's</strong> identity.<br>
When you use a web browser to connect to a chat room, the server doesn't authenticate your web browser. Only your web browser authenticates your server.<br>
If you are using a chat client, it MIGHT use client side authentication. Even in that case it wil... | Message signing and TLS provide different, overlapping guarantees.
TLS guarantees that the data exchanged between your browser and the server is genuine, and the communication between the other guy's browser and the server is genuine. It doesn't protect against a buggy, hijacked, or subverted server. In this scenario,... | https://security.stackexchange.com |
316,167 | [
"https://mathoverflow.net/questions/316167",
"https://mathoverflow.net",
"https://mathoverflow.net/users/119736/"
] | I know a lot of places where the following is sparsely proved, but I remember there was some paper where I read it in basically the same form I write it, but unfortunately I can't remember where it was.
Let <span class="math-container">$\mathcal{H}$</span> be the Hecke algebra of a reductive <span class="math-containe... | The general setting for your question is the theory of types as developped by Bushnell and Kutzko:
Smooth representations of reductive p-adic groups: structure theory via types. Proc. London Math. Soc. (3) 77 (1998), no. 3, 582–634.
First in order that your question make sense, let us clarify a few things.
<span cla... | The existence of the induction functor is general nonsense (tensor-hom adjunction).
When K is the Iwahori subgroup, Borel gives a direct proof in his paper on representations with Iwahori-fixed vectors. For general K, I see no easy way to prove this, but if you have the equivalence of categories from your third point ... | https://mathoverflow.net |
382,611 | [
"https://electronics.stackexchange.com/questions/382611",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54458/"
] | I am working on a FPGA project where a host CPU writes a 10,240 x 16-bit look up table into FPGA logic. To implement this, I've utilized on-chip memory to store the values and read them out when ready.
An external trigger/go pulse kicks off a processing cycle which lasts several hundred thousand clock cycles. Once we... | One possible strategy could be to use stale bits. Dunno if that's standard terminology, but it's similar to a dirty bit. Writing a new entry will clear the corresponding stale bit in the unlocked buffer and set the bit in the locked buffer. After switching buffers, have an internal copy routine transfer every entry mar... | Unless there are power reasons not to do this, I would go for this:
<ul>
<li>Have two buffers of 10240*16 bits</li>
<li>Fill in one of them using the CPU, call this the "configure" buffer</li>
<li>On the Go Pulse, copy the "configure" buffer into the "processing" buffer, there's no reason this cannot be done in one cl... | https://electronics.stackexchange.com |
275,032 | [
"https://physics.stackexchange.com/questions/275032",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/114622/"
] | I understand how to derive the spacetime interval being invariant for Minkowski space, but I've never seen any derivation of it in general curved spacetime. Is the invariance just derived for Minkowski space and then postulated that it holds for all metric tensors in general relativity, or is there a proof to show it i... | Lets look at an arbitrary invertable coordinate transformation: $$ x^\mu \rightarrow x'^{\mu}=x'^{\mu}(x^\nu). $$
The corresponding Jacobian $\Lambda$
$$ \Lambda^\mu_{~~\rho}=\frac{\partial x'^{\mu}}{\partial x^{\rho}}$$ is invertable
$$ \Lambda_{\sigma}^{~~\nu}=\frac{\partial x^{\nu}}{\partial x'^{\sigma}}.$$
A vect... | You cannot derive the invariance of the line element because it is one of the assumptions on which relativity (both flavours) is based. When you say:
<blockquote>
I understand how to derive the spacetime interval being invariant for minkowski space
</blockquote>
I would guess you mean that you can show the Lorentz tran... | https://physics.stackexchange.com |
204,430 | [
"https://softwareengineering.stackexchange.com/questions/204430",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/82254/"
] | I am working on a C# console application that loads the data from a third party and bulk inserts into tables. Basically the code consists of a static method with logging statements. In these scenarios, how does one write the unit test cases?
Example code
<pre><code>void Main(string[] args)
{
// for loop here to r... | Actually, given your case is really that small and simple as it looks like in your example code, I would probably omit any unit test and write an automated integration or system test instead.
Here is my outline of such a test:
<ul>
<li>provide a fixed XML config file as part of your test suite</li>
<li>clear the des... | use a mock data source, mock data interface, and mock log. If your code just reads in data and calls someone else's methods, that's what your unit test.
Feel free to use your unit test framework to test the whole process if possible, but that may be more of an integration test.
| https://softwareengineering.stackexchange.com |
10,635 | [
"https://mathoverflow.net/questions/10635",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2363/"
] | I remember one of my professors mentioning this fact during a class I took a while back, but when I searched my notes (and my textbook) I couldn't find any mention of it, let alone the proof.
My best guess is that it has something to do with Galois theory, since it's enough to prove that the characters are rational - ... | If $g$ is an element of order $m$ in a group $G$, and $V$ a complex representation of $G$, then $\chi_V(g)$ lies in $F=\mathbb{Q}(\zeta_m)$. Since the Galois group of $F/\mathbb{Q}$ is $(\mathbb{Z}/m)^\times$, for any $k$ relatively prime to $m$ the elements $\chi_V(g)$ and $\chi_V(g^k)$ differ by the action of the ap... | I just want to emphasize that this question points at the rationality theory of representations and characters that is exposed so beautifully in Chapters 12 and 13 of Serre's book <em>Linear Representations of Finite Groups</em>.
In particular, one has the following facts.
[Section 13.1, Corollary 1]: The following... | https://mathoverflow.net |
2,300,583 | [
"https://math.stackexchange.com/questions/2300583",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/450157/"
] | I'm sorry if this is a duplicate. I have no idea on what kind of "name" i should give to this, and therefore i have no idea on how to search on the internet for help on understanding it. If it happens that this is a duplicate, i would be grateful if you could link me to where there are any solutions for this.
I need t... | Let $a_0=0$ and $a_{n+1}=\cfrac1{1+\cfrac1{5+a_n}}$.
Prove by induction:
1) $a_n<\dfrac{-5+\sqrt{45}}2$
2) $a_{n+1}>a_n$ i.e. monotone
So that it converges and that it must converge to some $a'$ such that:
$$a'=\cfrac1{1+\cfrac1{5+a'}}$$
(feel free to ask if you need more tips on any steps below, hover on t... | Hint : Simply consider the difference between two successive recurring terms and then it is easy to show that the sequence is monotonically increasing.<br>
Now, $$\frac{1}{5} > 0\\\implies1+ \frac{1}{5} > 1\\\frac{1}{1 +\frac{1}{5}} < 1$$.
Use this argument several times and try to deduce that the given s... | https://math.stackexchange.com |
128,840 | [
"https://softwareengineering.stackexchange.com/questions/128840",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/40251/"
] | We need to do some user documentation for a product we have been working on for the past few sprints. We are now starting a new project in the next sprint and the PO is making the documentation for the product produced previously a User story for this sprint.
I am just wondering your opinion on this approach. Personal... | "As a user of X, I need to know how X works" seems like a legitimate user story to me. This could result in written documentation or online help.
The point isn't just code--it's meeting the users' requirements.
| Ideally, documentation is part of every user story and never builds up. But, in the real world, that often doesn't happen. In that case, you should create a user story for catching up on a specific missing piece of documentation.
You're right, it doesn't produce any code. But it does satisfy a user requirement and sho... | https://softwareengineering.stackexchange.com |
31,308 | [
"https://stats.stackexchange.com/questions/31308",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9562/"
] | How to define a distance function when euclidean distance doesn't apply? For instance, say I have some data involves nationality. I'll probably assign a number to each nation, but for nations that have smaller difference in numbers doesn't mean that they are more prone to be in the same cluster as nations that have big... | <strong>You cannot use k-means then</strong>.
You don't only need to have a working distance function, but you <em>also</em> need to have a way of computing <em>means</em> that is appropriate for the distance function.
The arithmetic mean and the Euclidean distance work together. Their combination makes k-means <em>t... | As with many questions, the answer is most likely "it depends". If your goal is simplicity, then using 0 for matches and 1 for non-matches may be fine. Using something other than 1 can also be thought of as the more general question of how you want to weight each of the variables (<em>nation</em> being only one such ... | https://stats.stackexchange.com |
25,836 | [
"https://datascience.stackexchange.com/questions/25836",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/43541/"
] | If I get 95+ % accuracy in normal models, should I still consider Ensemble models? Why should I choose Ensemble models over normal models?
| Firstly, welcome to the site!
When do we use Ensemble model?
when there are 2 models which perform moderately then we combine their results to get a model which performs better. In your scenario you already have a model which gives you good results what is the point of implementing Ensemble Models?
As @Tagoma said,... | It is a problem specific and data specific problem. For one problem, 95% accuracy may be good, for some other it might not be very good and there might still be room for improvements. Likewise, it might happen that the problem is well defined, your architecture is good but due to a lot of noise in the data, you can't d... | https://datascience.stackexchange.com |
89,280 | [
"https://dba.stackexchange.com/questions/89280",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/35768/"
] | The following is a script I found online that has most of the elements of what I desire in the result set. The only thing missing is how I can get an average of the run times over a decided time period, like a week, 10 days, 23 days, a month, etc.
I've done some searching, but what I've tried has failed in some way o... | Updated to satisfy the new requirement. Note that you may be tempted to use <code>CONVERT(TIME</code>, but resist - this is brittle, in the event any job runs longer than 24 hours.
<pre><code>SELECT
job_name = name,
avg_sec = rd,
avg_mmss = CONVERT(VARCHAR(11),rd / 60) + ':' + RIGHT('0' + CONVERT(VARCHAR(11),r... | Updated Script
<pre><code>DROP TABLE IF EXISTS #Temp;
SELECT
h.job_id,
msdb.dbo.agent_datetime(run_date,run_time) as RunDate,
CONVERT(int, SUBSTRING(RIGHT(REPLICATE('0', 6) + CAST(run_duration as varchar(6)), 6),5,2))
+ CONVERT(int,SUBSTRING(RIGHT(REPLICATE('0', 6) + CAST(run_duration as varchar(6)), 6),3,2)) * ... | https://dba.stackexchange.com |
90,146 | [
"https://mathoverflow.net/questions/90146",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19829/"
] | Let $\beta X$ - is a Stone-Čech compactification of $X$. $I=(-1,1)$ - is an interval of the real line. Is it true that $\beta \mathbb R\setminus I = \beta(\mathbb R\setminus I)$? In other words, it means that a finite interval does not affect on the "compactification of infinity".
<strong>Update</strong>:
Great thanks... | I can show the following (which Anton was asking about in comments). Let <span class="math-container">$X$</span> be locally compact and Hausdorff, and <span class="math-container">$U\subseteq X$</span> open. Let <span class="math-container">$X_\infty$</span> be the one-point compactication, so <span class="math-conta... | More generally: if $X$ is normal and $A$ is closed in $X$ then, by the Tietze-Urysohn theorem, the closure in $\beta X$ of $A$ <em>is</em> $\beta A$. In the example above $X=\mathbb{R}$ and $A=\mathbb{R} \setminus (-1,1)$.
As the closure of $(-1,1)$ in $\beta\mathbb{R}$ is just $[-1,1]$ the desired equality follows. ... | https://mathoverflow.net |
406,230 | [
"https://softwareengineering.stackexchange.com/questions/406230",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/315865/"
] | I am working on building a API and SDK for a web service. My question is what is the correct practice for logging. Should the SDK do logging for the API methods? All the SDKs I have seen do not do this so I am just wondering is that the recommended best practice?
| If you don't write code directly for end users but for other developers, I would generally not make assumptions about the needs of these developers unless you have to. Whenever you have the choice, leave the final choice to the people that will later on use your code.
If there are meaningful messages that can be logge... | A dependency which sole purpose is to offers special behavior that other classes use because of business logic (or use cases) should not contain a use case inside of itself.
What?
Your SDK is a <code>tool</code> for others to use during their use case. Whatever is relevant "logged" information will depend on the Use C... | https://softwareengineering.stackexchange.com |
138,256 | [
"https://chemistry.stackexchange.com/questions/138256",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/80684/"
] | Given a closed (air tight) container (Volume <span class="math-container">$V_0$</span>) held at the room temperature (<span class="math-container">$T_0$</span>) and pressure (<span class="math-container">$P_0$</span>). The container contains 100% saturated water vapor with no air (at <span class="math-container">$T_0$<... | If water is introduced in an empty container, the water will slowly evaporate. The pressure <span class="math-container">$p$</span> will slowly increase from <span class="math-container">$0\ \mathrm{Pa}$</span> to a maximum which is <span class="math-container">$3167\ \mathrm{Pa}$</span> at <span class="math-container"... | There will be no water vapor in the container if you apply "room pressure" on it (~1 atm, applied with for instance a piston) at room temperature.
If you want to have coexistence between liquid water and its vapor you can set T or p but the remaining intensive variables (including density) are then fixed.
The... | https://chemistry.stackexchange.com |
206,445 | [
"https://softwareengineering.stackexchange.com/questions/206445",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/98081/"
] | Firstly, I'm not new to this. I've written desktop applications for Windows going back to 1991 with Visual Basic 3.0. I've used C/C++ and Win32 API, VB3-6, C# 1.0-4.0 and currently knock out web applications in ASP.Net MVC. However I haven't touched desktop stuff since 2000 in depth bar playing around with some ClickOn... | As I am somewhat in your situation (currently developing a PHP-based CMS) I hope that my experience can help you.
Testing is key. Repeat that until you believe. It depends on the programming language though how easy it is. As I am developing in PHP I will give some examples on that.
<h2>Developing</h2>
The most impo... | Unit testing is what your project needs for several different reasons.
<ol>
<li>Allows you to test your application's basic functionality. </li>
<li>Allows you to ensure that new features are not causing regressions. </li>
<li>Good unit tests give consumers and maintainers an idea of what your application is capable ... | https://softwareengineering.stackexchange.com |
2,216,406 | [
"https://math.stackexchange.com/questions/2216406",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/431351/"
] | A is a matrix such that $(x_1,x_2,…,x_{117})A$=$(x_{117},x_1,x_2,…,x_{116})$. <br/>
Find $detA$ <br/>
Is the answer 1?
| $$
\begin{align}
x^{T} \mathbf{A} & = \hat{x} \\
%
\left[ \begin{array}{ccccccc}
x_{1} & x_{2} & x_{3} & x_{4} & x_{5} & x_{6} & x_{7}
\end{array} \right]
%
\left[
\begin{array}{c|cccccc}
0 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 & ... | <em>Hint:</em> What does $A^{2}$ do? What does $A^{117}$ do?
| https://math.stackexchange.com |
1,266,200 | [
"https://math.stackexchange.com/questions/1266200",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/224713/"
] | Is $f: \mathbb{R^m} \rightarrow \mathbb{R^n}$ defined by $f(\vec x) \equiv 0 $ considered a linear map? If the definition for linear map is one that satisfies additivity and homogeneity, then $f$ obviously is a linear map. But I'd to confirm $f$ is not specifically excluded in the usual definitions of linear mappings. ... | Yes, the zero function is indeed a linear map.
Any function that is additive and homogeneous is a linear map by definition, and in your case:
<ul>
<li>$f(x+y) = 0 = 0+0 = f(x) + f(y)$</li>
<li>$f(\alpha x) = 0 = \alpha \cdot 0 = \alpha f(x)$</li>
</ul>
So $f$ is both homogeneous and additive.
In fact, as one commen... | Yes, $f:\mathbb{R}^m \to \mathbb{R}^n, x \mapsto 0$ is a linear map.
Linearity:
$$
f(\lambda x + \mu y) = 0 = \lambda 0 + \mu 0 = \lambda f(x) + \mu f(y)
$$
for arbitrary $\lambda, \mu \in \mathbb{R}$ and $x, y \in \mathbb{R}^m$.
The linear maps from $\mathbb{R}^m$ to $\mathbb{R}^n$ can be represented as $n \times ... | https://math.stackexchange.com |
111,826 | [
"https://dba.stackexchange.com/questions/111826",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/73313/"
] | i have Mongodb server and mysql server. i want to use mongodb for "write" and mysql for "read".
so i am looking for some tool or some process by which we can tranfer mongodb to mysql server on regular interval.
also i need to know the steps for mapping of mongo collection and mysql tables.
I cant find something simi... | <pre><code> create table index_test(id number, idx number);
insert into index_test (id, idx) values (1,0);
insert into index_test (id, idx) values (1,1);
insert into index_test (id, idx) values (1,2);
insert into index_test (id, idx) values (1,3);
insert into index_test (id, idx) values (1,4);
inse... | Try:
<pre><code>select id
from tab
where id not in (select id
from tab
where index=0)
group by id
having max(index)+1!=count(*)
order by id;
</code></pre>
Preventing that the combination of id and index is unique
| https://dba.stackexchange.com |
512,912 | [
"https://physics.stackexchange.com/questions/512912",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | The principle is often stated as self explanatory ....
The sentence " the laws of physics are the same in all inertial frames" could mean 2 very different things ( at least from my point of view).
(1) Does it mean that there is a special class of frames that are "inertial" ( and some that are not) , and that, in th... | The correct interpretation is (1). The principle states that, when writing the laws of physics using coordinates (spatial and temporal) of reference frames, the form of the laws turn out to be <em>identical</em> in every <em>inertial</em> reference frame.
<em>Invariant</em> is used here as <em>of identical form</em>... | I am not sure what distinction you are making, but the answer is that your paragraph labelled (1) is correct.
You must bear in mind that reference frames are fictitious abstractions that we overlay on reality to allow us to keep track of distances and elapsed times. Reality remains the same regardless of which frame w... | https://physics.stackexchange.com |
313,130 | [
"https://softwareengineering.stackexchange.com/questions/313130",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/88841/"
] | Which data structure are used for commenting text and which algorithms take care for updating the comment position? A commenting feature is present in every good word processor such as Microsoft Word, Google Docs etc.
I can imagine two approaches: One would be surrounding the commented text with some sort of markup (e... | I would do it with a simple collection of tuples containing the position and length of text to be annotated, and the annotation text.
For example
<pre><code>public class Annotation {
public int Position;
public int Length;
public string Text;
}
</code></pre>
In C#, the most favorable collection appears t... | Based on your comment to Robert Harvey's answer, you could do a combination of both.
The markup/xml tag would hold the position along with some some sort of identifier to an item in the array. This way the tag is reduced in size since it doesn't have to hold the contents of the comment and can easily move along as ite... | https://softwareengineering.stackexchange.com |
11,487 | [
"https://dsp.stackexchange.com/questions/11487",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/4360/"
] | I don't quite understand why the textbooks say it is impossible to implement an ideal low pass filter.
If I was to take the FFT of a discrete signal x[n], with Matlab's fft function I'd be returned with a complex sequence X[n] which represents the magnitude of each frequency from 0 to n/2 and is repeated. If I was to ... | If you only have a finite number of samples and are using a finite length FFT, then you will end up with a finite number of FFT frequency result bins. Each bin has a one-to-one relationship ONLY with frequencies that are exactly integer periodic in the FFT length. Any other spectrum frequencies that are not exactly p... | <em>Is removing values from FFT result same as filtering?</em>
<strong>Yes</strong>, as one would expect intuitively. Taking the FFT of a signal will give you a frequency domain interpretation of the signal, if you then modify the magnitude of frequency bins and take the inverse FFT you will have a signal which is 'fi... | https://dsp.stackexchange.com |
285,606 | [
"https://physics.stackexchange.com/questions/285606",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/129945/"
] | I'm trying to use LED's as a point source of light for a project I have. a crucial idea is that the intensity of the light of the led falls off as 1 over the distance squared as we move away from it. i.e. it should obey the inverse square law. I ran some measurements on an LED and tried to fit the results on a curve bu... | The first possibility is that the response of the probe is non-linear?
Another possibility is that there is an error in the way that you have interpreted the distance you measured between the led and the probe.<br>
What I mean is that is that there may possibly be a constant error at the probe end because you do not e... | LEDs can be pretty directional, so right there they are not point sources. A small incandescent filament should be a pretty good point source if the detector isn't too close and the glass around it doesn't add distortion.
I wouldn't expect the brightness vs distance to change that much because of this, but having str... | https://physics.stackexchange.com |
309,608 | [
"https://electronics.stackexchange.com/questions/309608",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/127483/"
] | I am using STM32VL discovery board(STM32f100rb6)..
I wrote following code for NVIC:
<pre><code>void Interrupt_Init(void)
{
__enable_irq();
/*Core Base(NVIC)*/
//set priority to 0
//NVIC->IP[6] &= ~((uint32_t)0xff00);
//Activate Interrupts
NVIC->ISER[0] |= BIT6;
//Enable Pending... | Finally, I found the mistake. Priority is the problem.
Use <code>NVIC_SetPriority(EXTI0_IRQn, 1);</code> to set SysTick to a higher priority level than EXTI0_IRQn. Then everything goes OK.
| When you enter the interrupt routine, you need to clear the interrupt source flag. If you do not clear the flag, when you exit the interrupt routine it will just re-enter the routine. This way you will always be stuck in EXTI0_IRQHandler.
| https://electronics.stackexchange.com |
238,890 | [
"https://softwareengineering.stackexchange.com/questions/238890",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/130143/"
] | I've the following Interface.
<pre><code>public interface ValueInterface
{
long getValue();
}
</code></pre>
And the class:
<pre><code>public class ValueCreator implements ValueInterface
{
private static long value = 0;
public void setValue(long valueInDollar)
{
value= valueInDollar;
}
@Override
... | No, it is not a good idea to have a non-static getter for a static field.
The problem is that you can have multiple instances of <code>ValieCreator</code>, but they will all share the same static <code>value</code> field, so all instances will always return the same value and if you change the value through one instan... | FindBugs does not actually find bugs (or at least not only bugs). It finds things that are strange.
So if what you really want is have that value static and need to implement interface that gets value and it should return that value, you cannot do differently than non static method accessing static field.
If setter is ... | https://softwareengineering.stackexchange.com |
10,353 | [
"https://cogsci.stackexchange.com/questions/10353",
"https://cogsci.stackexchange.com",
"https://cogsci.stackexchange.com/users/6415/"
] | Can someone please explain this to me because it's driving me bonkers. In cognitive research when one group of participants are exposed to a number of crossed factors manipulated by the researcher, is it a quasi-experimental design or a true experiment?
All the sources I read always mention random assignment and rando... | If the researcher randomly samples individuals from the population of interest and randomly assigns them to different experimental treatments, then it is a true experiment. Quasi-experimental design occurs when there is no random assignment to treatments.
In general, true experiments can make claims about causality. S... | The real issue is equivalence of groups. As Josh implies above, it is a game of probabilities when randomly assigning to groups, but it is considered very improbable that non-equivalence of groups will occur through random assignment when the number of assignments is relatively high (no less than 30 per group). So in a... | https://cogsci.stackexchange.com |
137,990 | [
"https://mathoverflow.net/questions/137990",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14024/"
] | A word $w$ on the alphabet $A := \{0, 1\}$ is <em>factorable</em> if
\begin{equation}
w = u^k \mbox{ where } u \in A^* \mbox{ and } k \geq 2.
\end{equation}
Let $L$ be the language of the set of factorable words on $A$ and $f(t)$ be its generating series, that is
\begin{equation}
f(t) := \sum_{n \geq 0} |L \ca... | Suppose $[F : R] = n$ is finite. I first claim that the integral domain $R$ is a subfield of $F$. For if $0 \neq \theta \in R$, then we have inclusions of $R$-modules
$$R \subset R \cdot \theta^{-1} \subset R \cdot \theta^{-2} \subset \ldots$$
where in each case $R \cdot \theta^{-j-1}/R \cdot \theta^{-j} \cong R\cd... | Related result (W. R. Scott, “On the multiplicative group of a division ring” <i>Proc. Amer. Math.Soc.</i> <b>8</b> (1957) no. 2, 303–305): given a division ring $F$ (commutative or otherwise) and a division ring $R \subsetneqq F$, we have $$[F^{\ast} : R^{\ast}] = |F|$$ where $R^{\ast}$ and $F^{\ast}... | https://mathoverflow.net |
622,775 | [
"https://physics.stackexchange.com/questions/622775",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/253144/"
] | I know that the throttling device reduces pressure of the gas but that's it. I can't somehow imagine how the change in cross-sectional area can affect how the particles of gas to lose energy and see a decrease in pressure?! Can someone perhaps visually, using a diagram, even if it's just doodles, explain how the indivi... | A throttling device is basically a flow restrictor which, when flow is asserted through it, exhibits a <em>pressure drop</em> the same way pushing current through an electrical resistor develops a voltage drop across it.
Take the example of a throttling valve on a compressed air tank that is exhausted to ambient pressu... | The pressure decreases as a result of viscous friction, starting with the no-slip (zero velocity) boundary condition at the wall(s) of the throttling device and propagating into the fluid. This is a dissipative process which results in viscous heating of the fluid, to offset the pressure decrease as a result of expans... | https://physics.stackexchange.com |
2,179,926 | [
"https://math.stackexchange.com/questions/2179926",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/387077/"
] | Give an example of a map $T:\mathbb{R}^2\rightarrow\mathbb{R}^2$ with both of the following properties:
a. $T(kx)=kT(x)$ for all $x\in \mathbb{R}^2, k\in \mathbb{R}$
b. $T$ fails to be a linear transformation
I am really stuck on this. I can only find matrices that are not linear transformations and don't fulfill th... | $$T(x_1,x_2) = \big((x_1^2x_2)^{1/3},x_1+x_2\big)$$
| $f(x,y) = \begin{cases} \frac {x^2}{y} & y\ne 0 \\ 0 & y = 0\end{cases}\\
f(kx,ky) = kf(x,y)$
Here we have a non-linear map from $\mathbb R^2 \to \mathbb R$
now find a $g(x,y)$ along similar lines (or even a linear $g(x)$ at this point.)
and $h(x,y) = f(x,y),g(x,y)$ will do what you need it to do.
| https://math.stackexchange.com |
333,323 | [
"https://physics.stackexchange.com/questions/333323",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/143460/"
] | When we shift the system's time from $t=0$ to $t = t$, we can define the following operator $\hat{U}$.
$$\hat{U} = e^{- i \hat{H} t / \hbar} \, .\tag{1}$$
So many (as far as I read, almost all of) documents assume $\hat{H}$ is Hamiltonian and $\hat{H} = \hat{H}^\dagger$ to prove that $\hat{U}$ is unitary.
I don't un... | <strong>1st point of view:</strong>
If you accept the Schrödinger equation
$$ \mathrm i\hbar\, \partial_t \psi = \hat H \psi $$
with self-adjoint $\hat H$, then your equation 1 follows directly and $\hat U$ is unitary.
<strong>2nd point of view:</strong>
Time evolution must have the following properties:
<ul>
<li>$... | The assumption is that the wave function is a probability amplitude. In particular, it's a vector that is normalized. In Dirac's notation, this is the statement:
$$\langle \psi |\psi\rangle = 1.$$
This can be made more concrete with:
$$\begin{align}
\mathrm{ordinary\ vectors\ } &\sum_{i} \psi^\star_i \psi_i = 1, \\... | https://physics.stackexchange.com |
199,351 | [
"https://stats.stackexchange.com/questions/199351",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/107036/"
] | I am having trouble calculating the standardized errors of a GARCH(1,1) model.
Since $\epsilon_t = \sigma_t z_t$ with $z \sim \text{N}(0,1)$, the standardized error is $z_t = \frac{\epsilon_t}{\sigma_t}$. However, I don't know how to generate the $\sigma_t$. In Stata, I stumbled upon residuals that are described as "p... | <blockquote>
I don't know how to generate the $\sigma_t$
</blockquote>
The fitted standard deviations $\hat\sigma_t$ should be part of the output of a GARCH model. I do not work with Stata so I am not sure how to extract them, but they should be accessible. Given those, the standardized residuals will be $\hat z_t=\... | Just run as below after <code>garch</code>
<pre><code>predict res, resid
predict h, var
gen stdres=res/h
</code></pre>
| https://stats.stackexchange.com |
121,194 | [
"https://cs.stackexchange.com/questions/121194",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/115366/"
] | Consider the following code snippet:
<pre><code>for(int i=0;i<n;i++)
</code></pre>
The question I have is: whether this loop is executed <span class="math-container">$n$</span> times or <span class="math-container">$(n+1)$</span> times?
According to what I understand: when <span class="math-container">$i=n$</span... | <blockquote>
Consider the following code snippet:
<pre><code>for(int i=0;i<n;i++)
</code></pre>
The question I have is: whether this loop is executed <span class="math-container">$n$</span> times or <span class="math-container">$(n+1)$</span> times?
</blockquote>
This loop executes <span class="math-con... | A for loop contains a header specifying the iteration and body that executed once per iteration. What you consider is the header. You must run at least the assignment and comparison once to decide to enter the loop or not. A clever compiler can skip a loop if it is not entering if the values are available on the compil... | https://cs.stackexchange.com |
745,283 | [
"https://physics.stackexchange.com/questions/745283",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/97850/"
] | In explaining <span class="math-container">$C_v = \left(\frac{\partial u}{\partial T}\right)_V$</span>, my textbook first writes that <span class="math-container">$\delta q = du$</span> for a constant volume process, and then that that <span class="math-container">$dq=C_v dT$</span> 'from the definition of <span class=... | Your book has it backwards. The definition of <span class="math-container">$C_v$</span> is <span class="math-container">$$C_v=\left(\frac{\partial U}{\partial T}\right)_V$$</span>From Gibbs phase rule, if you have a single phase, then U is a function of two parameters, in this case T and V. But if V is constant, then... | A thermal (entropy) reservoir, e.g., a large metal block, a "calorimeter", by definition, is a device whose interaction with its environment is characterizable by its <em>experimental</em> temperature change. Now starting at a given temperature one can measure the effects of a small (ideally infinitesimal) te... | https://physics.stackexchange.com |
211,293 | [
"https://physics.stackexchange.com/questions/211293",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/92346/"
] | Does a collapsing and re-establishing magnetic field impart a force on a stationary charged particle? Does the charge particle get repelled and or attracted? Does it move or spin?
| Yes, it will create a force. The force is directed solenoidally around the change in a magnetic field.
To see this, look at Maxwell's equation <span class="math-container">$\nabla \times \mathbf{E} = -\partial_t \mathbf{B}$</span>. This is analogous to the equation from magnetostatics: <span class="math-container">$\na... | In the absence of any charge motion and current density then a changing magnetic field is accompanied by a changing electric field. From Ampere's law we can say that
<span class="math-container">$$ \vec{E} = \frac{1}{\epsilon \mu} \int \nabla \times \vec{B}(t)\ dt$$</span>
This electric field will exert a force <span c... | https://physics.stackexchange.com |
187,718 | [
"https://electronics.stackexchange.com/questions/187718",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/77735/"
] | When thinking about signal conversion in temperature sensors how could the non-linear temperature-resistance characteristics be a problem ?
| One problem with very nonlinear sensors such as thermistors is that the resolution (or SNR if analog) at temperature extremes may be insufficient with normal signal conditioning.
For example a 10K thermistor might change 450 ohms for one degree at 25 C but less than 5 ohms for 1 degree C at 150 C.
This is not a pro... | Not such a problem at all, you can compute the corrected temperature with a polynomial equation. The real problem is to make a good PCB layout for ADC, and good ADC like TI's ADS1248.
| https://electronics.stackexchange.com |
127,846 | [
"https://security.stackexchange.com/questions/127846",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/31232/"
] | Me and a colleague were discussing the fact that due to licensing we need to disclose a couple of libraries we used in the development of an Android app we make. I said, from a security standpoint it would probably be better to disclose the bare minimum.(So not disclosing the libraries that didn't specifically require ... | <blockquote>
If someone were to find a vulnerability that would affect a specific library that could maybe pose a threat to our app
</blockquote>
The defense against that is not to use the library. Using the library and not documenting it does not change the fact that your application is vulnerable.
Not documenting... | There may be a potential risk if you disclose libraries with known or later to be discovered vulnerabilities. This is no different than a website using WordPress and a popular image plugin that becomes comprised to allow shell uploads or an OS that has a program that allows someone remote access through an exploit. If ... | https://security.stackexchange.com |
87,238 | [
"https://cs.stackexchange.com/questions/87238",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/66724/"
] | I was reading about the differences standards and specifications for C.<br>
I understood that programming languages are usually stadardized and I learnt that there are different approches to stadardization.<br>
Anyway I did not understand yet what this terms refer to.<br>
If I think to C, I believe it refers to a stan... | A standard for a programming language is a document defining the syntax and semantics for that language. Usually, for real-world languages, this document involves a (hopefully) precise description in intuitive terms, rather than a formal semantics, written in mathematical terms.
Still, this document acts as a contract... | Standardization is the process of developing, promoting and possibly mandating standards-based and compatible technologies and processes within a given industry.
Standards for technologies can mandate the quality and consistency of technologies and ensure their compatibility, interoperability and safety. Standards org... | https://cs.stackexchange.com |
120,606 | [
"https://softwareengineering.stackexchange.com/questions/120606",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5184/"
] | Prematurely introducing complexity by implementing design patterns before they are needed is not good practice.
But if you follow all (or even most of) the SOLID principles and use common design patterns you will introduce some complexity as features and requirements are added or changed to keep your design as maintai... | In some ways, I think this is largely a business decision and not necessarily based on the code itself. Some things to consider:
<ul>
<li>Are you getting paid to make the changes?</li>
<li>Does the code currently function as expected?</li>
<li>Are there any security or performance issues with the code as is?</li>
<li>... | Isn't removing this code and replacing it with something simple for future ease of coding a feature the client needs to consider and pay for?
You may have something useful another developer could learn from, but the odds of finding another client's app to plug it into, is not likely.
Gossiping about competitor's code... | https://softwareengineering.stackexchange.com |
2,050,666 | [
"https://math.stackexchange.com/questions/2050666",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/307530/"
] | Let $F: C[0,L] \to C[0,L]$ be a linear operator defined as $Fu(x) = \int_0^x u(y)dy$. We wish to show this operator is continuous, one-to-one, find it's norm, and find it's eigenvalues.
I've already proved the first three properties, but I have never found the eigenvalues of functions before, only matrices.
I've se... | You have to distinguish between two cases. First, assume that $\lambda \neq 0$. Then the equation
$$ (Fu)(x) = \int_0^x u(t) \, dt = \lambda u(x) $$
together with the fact that $f$ is continuous and the fundamental theorem of calculus implies that if $u$ is an eigenvector (often called eigenfunction, for obvious reas... | Since $ u $ is continuous , $Fu $ is differentiable and $(Fu)^{'}=u $.
Hence you have the equation $u= \lambda u'$
your turn!
| https://math.stackexchange.com |
351,866 | [
"https://softwareengineering.stackexchange.com/questions/351866",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/276700/"
] | I'm a software developer recently in charge of entire project (project manager). The project I'm working on (with 6 other persons) is a complex Java-based application that's being developed for over 5 years. The entire time we were using SVN, without branching. Now, I would like to switch to Git as I do believe Git wil... | IMHO you are approaching this from the wrong side. You probably need first and foremost a better workflow, utilizing branches, and <strong>not necessarily another tool</strong>. Why not start using feature branches <strong>with SVN</strong>? If you are going to develop two major features in parallel, just create indivi... | It seems to me from your post that you are not making the best use of source control.
Additionally you say you don't have much experience of using git.
I think its fairly well accepted that git has become the dominant source control software. Possibly you could argue that the git flow branching strategy is the most p... | https://softwareengineering.stackexchange.com |
459,221 | [
"https://physics.stackexchange.com/questions/459221",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222038/"
] | I was wondering how it is possible for overtones to co-exist at the same time. When one pulls a string, it starts to oscillate and forms a standing wave with frequency <span class="math-container">$$f_0 = f$$</span>
Additionally, infinite overtones oscillate at integer multiples of the fundamental frequeny:<span class=... | Your mistake is in your initial assumption:
<blockquote>
When one pulls a string, it starts to oscillate and forms a standing wave with frequency <span class="math-container">$$f=f_0$$</span>
</blockquote>
The only way this is true is if you could start the string with length <span class="math-container">$L$</span>... | If there are overtones, then the "wave" is not just of the main frequency, but is more complicated. In the linear approximation the tone and overtones may come together - in a superposition, due to linearity of the wave equation (which admits very complicated "wave" profiles).
You may excite any overtone without excit... | https://physics.stackexchange.com |
1,906 | [
"https://dsp.stackexchange.com/questions/1906",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/1172/"
] | I want to write a MATLAB program for simple object recognition using bag of features. In short, I want to first extract the features from an image, create a visual library using those features, then cluster up the features belonging to one part together, hence creating different parts. now use these parts for matching.... | The native sampling frequency of iOS devices is 44100 Hz, while Android devices can operate at either 8, 16, 24, 44.1 or 48 kHz. Support of all of these depends on Android device manufacturer, however most Android support all of them.
| The maximum limit is probably like <span class="math-container">$20$</span> kHz because that’s the human top limit and there is no point in having a higher frequency speakers unless you want to use it as an animal repeller so in that case some manufacturers may chose to add a second special piezoelectric speaker (metal... | https://dsp.stackexchange.com |
9,444 | [
"https://dba.stackexchange.com/questions/9444",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5213/"
] | We are synchronizing tables between two databases (yes, it needs to be done by our software and not by replication etc.)
Both databases are identical with many foreign-key constraints on tables.
Within a transaction we insert rows to various tables. The whole transaction will leave the tables in a state where all con... | No, server checks Foreign keys for every statement inside transaction
The way is to disable all the FKeys in target DB just after the beginning of transaction and enable them back just before commit.
Useful script:
<pre><code>DECLARE @sql NVARCHAR(MAX) = ''
SELECT @sql = @sql + N'ALTER TABLE [' + OBJECT_SCHEMA_NAME... | No, thats not supported!
You should try to arrange your statements in the correct order which avoids FK violation.
| https://dba.stackexchange.com |
46,067 | [
"https://mechanics.stackexchange.com/questions/46067",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7952/"
] | <strong>Car: 2010 Mazda 3 GT 2.5L Manual 160,000KMs</strong>
I purchased the car 3 months ago not knowing the history of the battery, I wanted to test it.
I measured the voltage across my battery using a voltmeter directly connected to the battery terminals. The following are the readings under different conditions:... | I wouldn't worry too much. You can go a little deeper in checking the system. But you will need a load tester. I wouldn't worry about 0.4v. You could turn on as many loads ad you can.
Head lights/hi and low beam, a.c., blower motor, and radio. And check the voltage.
| Its normal. No need to worry. Anything else we can look into?
| https://mechanics.stackexchange.com |
160,872 | [
"https://mathoverflow.net/questions/160872",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3621/"
] | Lately I've begun to suspect that a certain ternary relation might play a role in <span class="math-container">$\bf{C}$</span> analogous to the role played by the binary relation <span class="math-container">$>$</span> in <span class="math-container">$\bf{R}$</span>, namely, the relation that the oriented triangle
... | A too long waste of bits in three parts. The core of the answer is the summary at the end of part 2 section 2.
<h1>Part 1. Orientation.</h1>
Before treating the aspects on which I agree, let me say one aspect where I disagree (but quite probably only about terminology).
I would not say that orientation in the [compl... | Given your two axioms, the relation is determined for all cycles by its value on cycles of the form $(0,1,z)$, on which it should divide $\mathbb C$ into the upper half plane, the real line, and the lower half plane. For $x \in \mathbb R$ you get the order relation on $\mathbb R$ by considering $(0,1,ix)$. So one way ... | https://mathoverflow.net |
4,352,959 | [
"https://math.stackexchange.com/questions/4352959",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/799923/"
] | Prove the periodic function <span class="math-container">$f :\mathbb R \to \mathbb R$</span> s.t. <span class="math-container">$f(x)=|x|$</span> on <span class="math-container">$[-1,1]$</span> with period <span class="math-container">$2$</span> is Lipschitz continuous.
Here is my proof. I'm stuck in the last part.
<hr ... | Take it one step at a time.
f(x) = mod(x, 3) gives the series [0, 1, 2, 0, 1, 2, ...]
f(x) = mod(x + 1, 3) shifts that to [1, 2, 0, 1, 2, 0, ...]
f(x) = 2 - mod(x + 1, 3) is a winner [1, 0, 2, 1, 0, 2, ...]
| <span class="math-container">$$f(x)=1-\frac2{\sqrt3}\sin\frac{2\pi x}3$$</span>
| https://math.stackexchange.com |
1,813 | [
"https://dba.stackexchange.com/questions/1813",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1012/"
] | We are planning on setting a static port for SQL Server 2005/2008 failover clustering. Any guide on what port to choose/select for 4 nodes of each cluster?(Active/Active)
I am also thinking some applications need to know about the static port. What is the best way of knowing which application is setup to use default ... | The port number you select doesn't matter. Static port numbers should only be needed if you need to specify holes through a firewall which isn't on the local server. All SQL Server client drivers can convert the instance name to the TCP port number automatically using the SQL Server Browser.
The nice thing about usi... | <ul>
<li>Sequential port numbers for each instance. Just pick some.</li>
<li>Port numbers that match instance name (eg xxx1 = InstanceA, xxx2 = InstanceB)</li>
<li>No app this century should require "default" port 1433. They should resolve instance name. Only the default instance (which won't apply here) should use 143... | https://dba.stackexchange.com |
594,264 | [
"https://physics.stackexchange.com/questions/594264",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275724/"
] | In quantum mechanics, the kinetic energy of a particle described by the wave function <span class="math-container">$\psi$</span>, is related to the curvature of the <span class="math-container">$\psi$</span>. This is easily seen, but I have confused my self with the negative sign. That is: <span class="math-container">... | In Riemannian geometry, there are in principle two fundamental quantities: the metric <span class="math-container">$g$</span> and the connection <span class="math-container">$\nabla$</span>. Each one may be chosen independently of the other, or even be left undefined (that is, you can have only the metric, or only the ... | In general, you seem very focused on the scalar curvature. The scalar curvature is just one measure of curvature. A spacetime can be curved and have zero scalar curvature, as in, e.g., a gravitational wave.
<blockquote>
For a given g, can R be any choice of arbitrary, possibly smooth, function...
</blockquote>
No. R ca... | https://physics.stackexchange.com |
153,880 | [
"https://electronics.stackexchange.com/questions/153880",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35875/"
] | I'd like to make a device combined two controllers: ATMega64 I already familiar with and ARM Cortex-M0 STM32F051 I'd like to be familiar with.
I'd like to directly connect GPIOs of two controllers. I hope that I will be able to choose which controller is now operating just providing the power to the one I need.
<stro... | No, in general you can not assume anything about GPIO pins of an unpowered chip, unless this is explicitly stated in the datasheet.
What will <em>likely</em> happen is that the protection diodes in the chip will try to power the 'unpowered' chip from any pin that is high.
| Yup, i think you can assume that (all GPIO in Z-state). But of course you can force some state (0 or 1) by use pullup or pull down resistors.
| https://electronics.stackexchange.com |
1,696,084 | [
"https://math.stackexchange.com/questions/1696084",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/313010/"
] | I would like to solve the inequality $|\int_{\gamma} \frac{1}{z^2}dz|\leq 2$ where $\gamma$ is the line $[i,2+i]$. I thought about using the Cauchy theorem in closing the path between $i$ and $2+i$, but I don't know if this is allowed.
Is it possible to proceed in this manner? Otherwise, is anyone could give me a sim... | Hint: integral $\le$ (bound of $|$integrand$|$)(length of path).
| Just use the Fundamental Theorem of Calculus. If $F$ is an antiderivative of $f$ in a neighbourhood of $\gamma$, then
$\int_\gamma f(z)\; dz = F(end
(\gamma)) - F(start(\gamma))$.
| https://math.stackexchange.com |
2,197,853 | [
"https://math.stackexchange.com/questions/2197853",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/395478/"
] | I have an exam question to solve the following PDE:
$$
x^2y^{''}-4xy^{'}+6y=21x^{-4}
$$
This problem is supposed to be solved by the variation of parameter method(Wronskian). For finding the solution of the homogenous part I used the Euler cauchy method, but it turns out it gets very computationally intensive. What i... | Assuming that the problem is $$x^2y''-4xy'+6y=21x^{-4}$$ For the homogeneous equation, assume $y=x^a$ and replace. This let you with $$(a-3) (a-2) x^a=0$$ So, you have $$y=c_1x^2+c_2x^3$$
| After you find the solutions to the corresponding homogeneous ODE, you can find $y_p$ by variation of parameters, then the general solution to the original ODE is the sum of $y_p$ and a general linear combination of the $x^2$ and $x^3$.
Alternatively, you assume that the general solutions is something like $y=v*x^2$ (... | https://math.stackexchange.com |
72,992 | [
"https://mathoverflow.net/questions/72992",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16981/"
] | I understand that my question is probably elementary to someone well-versed in model categories, but the subject is very deep and I wonder whether there is a much simpler answer.
If you localize a ring, some elements get identified, so I assume the same will happen when we localize a category.
Suppose we start with ... | If we localize at all weak equivalences, the localization $L^W(Top)$ will be equivalent to the homotopy category of CW-complexes $Ho(CW)$. This can be seen using the fact that for each topological space there is a weakly equivalent CW-complex (the cellular approximation) and the fact that on CW-complexes the weak equiv... | I'm not sure if I'm reading your question correctly. Are you asking for a proof of the following statement?
If $f, g \colon X \to Y$ are homotopic map of topological spaces, then they are identified in the localization of the category of spaces with respect to homotopy equivalences.
The proof is completely elementary... | https://mathoverflow.net |
395,525 | [
"https://stats.stackexchange.com/questions/395525",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/239833/"
] | Notation: <span class="math-container">$\pi(x)$</span> is the target density. <span class="math-container">$(x_n)_{n=1}^{N}$</span> is the chain generated by the MCMC method.
At the moment, I am doing some research in MCMC methods. Before, I was planning to dive into the recently developed non-reversible MCMC methods,... | I will elaborate on Xi'an's response.
Metropolis-Adjusted Langevin Algorithm, as its name implies, is based on the Langevin diffusion that is represented by the following stochastic differential equation (SDE):
<span class="math-container">$ d X_t = - \nabla f(X_t) dt + \sqrt{2} d B_t $</span>,
where <span class="ma... | There is no theoretical constraint in using a Gaussian random noise when looking at the discrete-time version directly, since the Metropolis-Hastings correction validates its stationary distribution as <span class="math-container">$\pi(\cdot)$</span> in (almost) any case but it feels natural to use a Gaussian noise giv... | https://stats.stackexchange.com |
2,150,480 | [
"https://math.stackexchange.com/questions/2150480",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/337982/"
] | I need help understanding this proof:
<blockquote>
Prove that <span class="math-container">$$\lim_{x\to 0}\frac{e^x-1}{x}=1.$$</span>
For <span class="math-container">$x>0$</span> and <span class="math-container">$n\in\Bbb N$</span>: <span class="math-container">$$1\leq\frac{(1+\frac {x}{n})^n -1}{x}=\frac{1}{n}[(1+... | <strong>HINT:</strong> $$\lim_{n \to 0} \left(1 + \frac{x}{n}\right)^n = e^x$$
| Let $e^x-1=y$.
Hence, $y\rightarrow0$ and since $\ln$ is a continuous function, we obtain:
$$\lim\limits_{x\rightarrow0}\frac{e^x-1}{x}=\lim\limits_{y\rightarrow0}\frac{y}{\ln(1+y)}=\lim\limits_{y\rightarrow0}\frac{1}{\ln(1+y)^{\frac{1}{y}}}=1$$
| https://math.stackexchange.com |
98,269 | [
"https://electronics.stackexchange.com/questions/98269",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/34021/"
] | I have a lot of old analog video equipment and my trusty Apple IIe Color Monitor is finally dying. Since CRT's aren't produced anymore, and because I just am interested in how it is done, I obtained a decent plasma monitor (I can't get enough of those deep black tones). I want to know if an analog signal can be deinter... | Interlaced scan composite video signal isn't easily convertable to similar progressive-scan signal. You need to store the whole frame into some kind of memory and resend it at different speed using progressive scan. The simpliest way you will need a DAC-ADC pair with Fq about 6.5 MHz, an SRAM or ADRAM unit capable of r... | Conceptually, there is no reason why an LCD or other such display should interpret a non-interlaced signal as interlaced, rather than simply doubling every scan line [upon receipt of two or more "even" fields, start assuming that each "odd" field matches the even one until an "odd" field is received; do the reverse upo... | https://electronics.stackexchange.com |
1,498,218 | [
"https://math.stackexchange.com/questions/1498218",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/284003/"
] | I need to solve this complex equation:
$$
(c + id)^2 = 1
$$
where $i^2=-1$.
What am I supposed to calculate here? Just $c$ and $d$?
| $$(c+id)^2=1 \Rightarrow c^2+2cdi+i^2d^2=1 \Rightarrow c^2+2cdi-d^2=1 \Rightarrow (c^2-d^2)+2cdi=1+0i$$
The real part of the LHS must be equal to the real part of the RHS and the imaginary part of the LHS must equal to the imaginary part of the RHS.
So, you have to solve the following system : $$c^2-d^2=1 \\ 2cd=0... | Your post says $i^2=1$, surely you mean $i^2=-1$ the complex unit, no?
Well assuming $i^2=-1$, firstly
$$(c+id)^{2}=(c+id)(c+id)$$
After multiplying we find
$$c^{2}+2icd+(id)^{2}=1$$
Since $i^{2}=-1$
$$c^{2}-d^{2}+2icd=1$$
Since $1$ is real and there is no imaginary part on the r.h.s we can split to two equations
\be... | https://math.stackexchange.com |
381,010 | [
"https://softwareengineering.stackexchange.com/questions/381010",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/317388/"
] | We are currently in the process of building a service (a REST API) which is called on by our primary application. The primary application contains a users/permissions/roles set up which is used to verify if the user is able to complete tasks on the application. The user-roles relationship is one-to-many.
The third par... | Put the permissions and authentication on a separate Auth service.
This checks the username/password and issues a signed token containing all the roles the user is in.
You microservices can then check the signature of the token against the public key and compare the users roles with the required role for the method t... | Who is able to access this REST service? If the answer is, "only your application," then it may be perfectly justifiable for your service to simply trust its client.
But, if the REST service must <em>obtain trust</em> in order to successfully carry out one of its prescribed objectives, it may be necessary to (e.g.) ... | https://softwareengineering.stackexchange.com |
64,839 | [
"https://mathoverflow.net/questions/64839",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11395/"
] | Let $X$ be a hyperelliptic curve and let $i:X\to X$ denote the hyperelliptic involution. Once we fix a point $x_0\in X$ we get the Abel-Jacobi map $AJ:X\to J$ where $J$ denotes the Jacobian variety. Now the Jacobian is also equipped with an involution, namely $x\mapsto x^{-1}$. Is it possible to choose the base point $... | Yes, pick $x_0$ to be a Weierstrass point, i.e. a fixed point of the hyperelliptic involution.
Let $\sigma$ denote the hyperelliptic involution on $X$. Under the Abel-Jacobi map we have $x \mapsto [x-x_0]$ and $\sigma(x) \mapsto [\sigma(x) - x_0]$. Now $[x + \sigma(x) - 2x_0]$ is the divisor of a function, since it i... | Another way to think of this is the following (at least over $\mathbb{C}$).
Consider the diagram
$$
\begin{array}{ccccc}
X & \xrightarrow{AJ \times AJ \circ \sigma} & J \times J & & \\\\
\downarrow & & \downarrow & & \\\\
\mathbb{P}^1 & \to & Sym^2J & \xrightarrow{+} & ... | https://mathoverflow.net |
4,504,017 | [
"https://math.stackexchange.com/questions/4504017",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/87430/"
] | <strong>Question:</strong>
If <span class="math-container">$\theta\in[-\frac{5\pi}{12},-\frac\pi3]$</span> and maximum value of <span class="math-container">$\frac{\tan(\theta+\frac{2\pi}3)-\tan(\theta+\frac\pi6)+\cos(\theta+\frac\pi6)}{\sqrt3}$</span> is <span class="math-container">$\frac ab$</span> (where <span clas... | Expanding on @Claude Leibovici's answer, rewrite as
<span class="math-container">$$A=\cos(x)-2\csc(2x)$$</span>
Now, <span class="math-container">$$A'=-\sin(x)+4\csc(2x)\cot(2x)=\frac{4\cos(2x)-\sin^2(2x)\sin(x)}{\sin^2(2x)}$$</span>
<span class="math-container">$$\implies A'=\frac 4{\sin^2(2x)}\cdot \left( {\cos(2x)-\... | <strong>Hint</strong>
At least, you could start simplifying the expression writing
<span class="math-container">$$A=\tan(\theta+\frac{2\pi}3)-\tan(\theta+\frac\pi6)+\cos(\theta+\frac\pi6)$$</span> as
<span class="math-container">$$A=\cos \left(\theta +\frac{\pi }{6}\right)-\tan \left(\theta +\frac{\pi
}{6}\right)-\c... | https://math.stackexchange.com |
73,774 | [
"https://electronics.stackexchange.com/questions/73774",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16711/"
] | Let's say that we have capacitor with two identical plates - but one of them (let's call it plate A) is 50% of the size. Let's put a current through this capacitor so that there is some voltage V.
Questions:
<ol>
<li>Will the electrical charge between those two plates be the same?</li>
<li>Will electromagnetic curre... | Why you would want to have the plates different areas escapes me but here goes.
<img src="https://i.stack.imgur.com/SFNtb.png" alt="enter image description here">
The charge on the plates will be the same.
The electric field between the plates will essentially follow the geometry as the charge on the smaller and la... | <blockquote>
Will the electrical charge between those two plates be the same?
</blockquote>
If you're asking if the magnitude of electric charge on each is equal then I think the answer must be yes. You're charging the capacitor with a current. Let's assume for simplicity the current is some constant I during some... | https://electronics.stackexchange.com |
127,101 | [
"https://dba.stackexchange.com/questions/127101",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/78238/"
] | I have a table with about 300 columns and about 10<sup>7</sup> rows and I have to retrieve changed rows only, ordered by time (not distinct, but changed). The result set may be limited to 100 rows as well.
I've tried the following query with <code>lag</code> window function:
<pre><code>-- Suppose, we want to retrieve... | If the version was 9.3 or newer, I would try this rewrite of the query:
<pre><code>SELECT
w.stamp,
w.column1,
w.column2,
w.column3
FROM
"table_name" AS w
JOIN LATERAL
( SELECT p.column1, p.column2, p.column3
FROM "table_name" AS p
WHERE p.stamp < w.stamp
AND p.stamp &g... | There's probably no better way to get the expected result.
Some remarks:
You don't have to repeat the <code>w.stamp BETWEEN '01.12.2015 00:00' AND '23.01.2016 00:00'</code> in the outer query.
Are you sure that a missing <code>w.obj_id = 42</code> is correct? If this was part of the Derived Table the existing index ... | https://dba.stackexchange.com |
97,524 | [
"https://dba.stackexchange.com/questions/97524",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | I have a question related to the limiting of the access to a database network for the users that are allowed to log on to it.
The problem is that the databases are huge (they contain hundred of millions of records) and without a few precautions, letting the logged-in users do whatever they want creates chaos.
For ins... | Allowing even trusted users to login to what appears to be a production database is in my mind a big no-no. The solutions you mention above may provide you with a sense of security/relief but they their own have side effects.
I would be particularly worried about your statement
<blockquote>
Manual updating and in... | Use read-only copies of subsets of the data to service users. Combine with views/stored procedures and you have solid control over who can how much data and through what means.
Refresh the data periodically to suite the needs of the users.
| https://dba.stackexchange.com |
114,881 | [
"https://mathoverflow.net/questions/114881",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22980/"
] | Let $f:\mathbb{R}\to\mathbb{R}$ a <em>convex decreasing</em> function. Let $x_0 < x_1 < x_2$.
Studying the behaviour of the difference quotient, it is clear that
$$f(x_0)-f(x_2) \leq M (f(x_0)-f(x_1))$$
with $M=\frac{x_2-x_0}{x_1-x_0}>0$.
Now take $F:\mathbb{R}^2\to\mathbb{R}$ <em>convex</em> and <em>decreasi... | You can use the triangle inequality to solve this by looking at each coordinate separately.
$F(x_0,y_0)-F(x_2,y_2)=F(x_0,y_0)-F(x_2,y_0)+F(x_2,y_0)-F(x_2,y_2)$ $\leq M_1(F(x_0,y_0)-F(x_1,y_0))+M_2(F(x_2,y_0)-F(x_2,y_1))$. Replacing $F(x_1,y_0)$ with $F(x_1,y_1)$ only increases the right side, and replacing both $x_2$'... | <blockquote>
Here is an answer in the case $F$ is convex and decreasing in each variable --- that is the way I understood the original question.
</blockquote>
Without loss of generality, we can assume that
$$\frac{y_2-y_0}{y_1-y_0}\ge\frac{x_2-x_0}{x_1-x_0}.$$
Let $x_2'$ be the real number number such that
$$\frac{y... | https://mathoverflow.net |
164,728 | [
"https://softwareengineering.stackexchange.com/questions/164728",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/64156/"
] | For example, should I be doing something like:
<pre><code><?php
function output_message($message,$type='success') {
?>
<p class="<?php echo $type; ?>"><?php echo $message; ?></p>
<?php
}
output_message('There were some errors processing your request','error');
?>
</code></pre>... | As longs as it's clear from the name, comments and signature of the function that its purpose is to generate output, there's nothing wrong with it.
What's not good is to have output generation as a side effect of a function that also does something else (like compute and return some data, or write a file), because tha... | If the purpose of the function is to <code>output_message()</code> then I would expect the calling of the function to actually output the message.
If on the other hand, the function was called <code>generate_message()</code> then I would not expect it to do the outputting:
<pre><code><?php
function generate_error_... | https://softwareengineering.stackexchange.com |
2,007,520 | [
"https://math.stackexchange.com/questions/2007520",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/378456/"
] | Consider the sequence $(g_n) \subseteq C[0,1] $ given by $g_n(x) = x^n/n$.
Show that $g_n \rightarrow 0$ in the metric space $C[0,1]$, but $g'_n$ does not converge in $C[0,1]$. The metric space $C[0,1]$ equipped with the metric: $d(f,g) = sup\{|f(x) - g(x)| : x \in [a,b] \}$
| In order to show that $g_n \to 0$ in $C[0,1]$, we need to show that $d(g_n, 0) = \operatorname{sup} \{ |g_n(x) - 0 | ~:~x \in [0,1] \} \to 0$. Now we can note that $d(g_n,0) = \frac{1}{n}$ by observing that $|g_n(x)|$ has a maximum of $\frac{1}{n}$ at $x=1$ for all $n$.
As for $g_n'$, you correctly note that $g_n'(x)... | Theorem : Let $I$ be an interval and a sequence of functions ${f_n}$ be unifromly convergent on $I$ to the function $f$ Let $c$ be a point in $I$ where each $f_n$ is continuous .Then $f$ is continuous at $c$ .
Each $g'_n $ is pointwise convergent on $[0,1]$ to the function $g$ where $g$ is defined as
$g(x)=1$ only at p... | https://math.stackexchange.com |
208,035 | [
"https://softwareengineering.stackexchange.com/questions/208035",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29526/"
] | I'm responsible for creating a presentation to management that details how a system should be refactored or rewritten. We have an existing system that has had production failures and the code base is not in a desirable state.
Here are the current possible options:
<ol>
<li>Rewrite the system using developers that pro... | The business is interested in time, money, and emotion (depending on the product). I dealt with a similar problem, and presented it from a few different perspectives:
<ol>
<li>It is costing us 'X' per month to maintain TerribleApp, adding no value to the business. If we spent 'X' up front, this project would pay its... | <ul>
<li>First estimate the effort required to refactor/rewriting the code.</li>
<li>Then find out the cost implications of all 4 options. </li>
<li>Find out the loss made due to production outages of the legacy system
and then compare the benefit each approach would give comparing it with potential loss if there is a ... | https://softwareengineering.stackexchange.com |
159,117 | [
"https://mathoverflow.net/questions/159117",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29730/"
] | Let $X$ be a projective, normal variety over complex field with canonical singularities. Suppose $|D|$ is a basepoint free linear system, then is it true that the generic elements in $|D|$ are irreducible?
Besides, I noticed that something might related to "free linear system" (see Mori, Kollár "Birational geometry of... | No, the image of the associated morphism, $$\phi_{|D|}:X\to \mathbb{P}^n,$$ might be a curve. If the image has dimension $\geq 2$, then the general member is irreducible. Look up "Bertini theorems".
| Just to illustrate this on a simple example: take on $\mathbb{P}^1\times \mathbb{P}^1$ the divisor $D$ equivalent to $2f$, where $f$ is the fibre of one projection. Then $|D|$ is base-point free but any member is the union of two fibres (computing the intersection with $f$ we get $0$ so it is vertical), so is not irred... | https://mathoverflow.net |
954,207 | [
"https://math.stackexchange.com/questions/954207",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/63050/"
] | <blockquote>
Is <span class="math-container">$\max\left(\frac{A}{B},\frac{C}{D}\right) \ge \frac{\max(A,C)}{\max(B,D)}$</span>?
Given that <span class="math-container">$A,B,C,D>0$</span>.
What about <span class="math-container">$\frac{A}{B},\frac{C}{D}>1$</span>.
</blockquote>
Is there a better bound for the left... | The inequality is true when $A,B,C,D$ are positive (no need to assume
$\frac{A}{B}>1$ or things like that). Let $\mu=\frac{{\sf max}(A,C)}{{\sf max}(B,D)}$
and $M={\sf max}\bigg(\frac{A}{B},\frac{C}{D}\bigg)$.
If $A\leq C$, then
$$
\mu=\frac{C}{{\sf max}(B,D)} \leq \frac{C}{D} \leq M.
$$
If $C\leq A$, then
$$
\m... | What if $A = D = 1$ and $B=C=-1$? Then, $LHS=-1$ and $RHS=1$.
| https://math.stackexchange.com |
213,715 | [
"https://security.stackexchange.com/questions/213715",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/160653/"
] | Suppose we send out email verification to new subscribers that where they have to click on a link to verify their account.
Suppose they forget to verify it, and later try to login.
Should the error message say "Your user name or password is incorrect?", instead of letting them know that they have forgotten to verify ... | What I see most commonly is allowing the authentication and signing the user in, but locking meaningful features away until the email is verified. You should bubble up an error reminding the user to re-send an activation email if they try to access one of the restricted features.
It is poor design to ever lie to a us... | I agree with Buffalo5ix, but email verification should not be considered a part of account security. Email verification:
<ul>
<li>proves the ownership of the address, just to know that the user has entered correct address for you to send <strike>spam</strike> password recovery emails.</li>
<li>serves as a very light d... | https://security.stackexchange.com |
101,234 | [
"https://electronics.stackexchange.com/questions/101234",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | I know that rms of an AC is totally different than its mean. But what if the voltage is not alternating(DC) but varying by time. For example a noise with a huge offset.
How is varying DC measured by voltmeters? Mean or rms? Or as in my question are they the same thing for a varying DC?
| The rms voltage is given by
\$\sqrt{\frac{1}{t_1-t_0}\int_{t_0}^{t_1}v^2(t) \mathrm dt}\$
The mean voltage is given by
\$\frac{1}{t_1-t_0}\int_{t_0}^{t_1}v(t) \mathrm dt\$
As you can see, these are not the same, except in special cases. A pure positive dc voltage is one such special case.
However, if the dc com... | Varying DC <i>is</i> AC.
RMS is "Root Mean Square", which is the square root of the average of the square. The term "average" is a clue that some time judgement is envolved. For a repeating signal, that would usually be the repetion period. For something else, you have to decide over what time interval you are goin... | https://electronics.stackexchange.com |
106,876 | [
"https://mathoverflow.net/questions/106876",
"https://mathoverflow.net",
"https://mathoverflow.net/users/26369/"
] | If we have a Riemann surface with punctures of negative Euler characterstisc, how can one define a complete hyperbolic metric?
I know that in this case the universal cover is the hyperbolic plane and it has a complete metric. Do we project this metric to the puntured surface? If so, why is it complete?
I will dee... | A good reference for this is, say, Kobayashi and Nomizu "Foundations of Differential Geometry". The result you are looking for is: If $M$ is a complete Riemannian manifold and
$p: M\to M'$ is a (locally) isometric covering map to another Riemannian manifold, then $M'$ is also complete. To prove this note that every ge... | To see how you get complete metrics, you should know enough about hyperbolic geometry to know what an ideal triangle is. Once you do, note that any triangulation can be made of ideal triangles (usually in more than one way). Checking completeness is then a mildly challenging exercise. I would suggest you look at Bill T... | https://mathoverflow.net |
174,434 | [
"https://security.stackexchange.com/questions/174434",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/92592/"
] | I had a debate recently regarding whether conducting an Nmap scan through a 3rd party such as pentest-tools.net is considered active or passive. I argued that it is passive since there is no link between the scan and myself.
On the other hand, my friend argued that Shodan and Censys are considered passive which to me... | I tend to take a legal eye when I look that this (IANAL).
An NMAP scan of a target will always be active regardless of who performs the scan. Just because you shift the scanning responsibility to a third party doesn't change that fact.
You might be able to argue that you retrieved the scan data passively, but I woul... | The first question to ask is, "Why does it matter?" What is the reason for needing to label something "active" or "passive"? If the answer is that your Rules of Engagement place some restriction on "active" measures, then you need to improve your rules of engagement to reduce ambiguity about that term.
The action of a... | https://security.stackexchange.com |
215,877 | [
"https://softwareengineering.stackexchange.com/questions/215877",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66745/"
] | If I write something like this:
<pre><code>var things = mythings
.Where(x => x.IsSomeValue)
.Where(y => y.IsSomeOtherValue)
</code></pre>
Is this the same as:
<pre><code>var results1 = new List<Thing>();
foreach(var t in mythings)
if(t.IsSomeValue)
results1.Add(t);
var results2 = new... | LINQ queries are <strong>lazy</strong>. That means the code:
<pre><code>var things = mythings
.Where(x => x.IsSomeValue)
.Where(y => y.IsSomeOtherValue);
</code></pre>
does very little. The original enumerable (<code>mythings</code>) is only enumerated when the resulting enumerable (<code>things</code>)... | The following code :
<pre><code>var things = mythings
.Where(x => x.IsSomeValue)
.Where(y => y.IsSomeOtherValue);
</code></pre>
Is equivalent to nothing, because of the lazy evaluation, nothing will happen.
<pre><code>var things = mythings
.Where(x => x.IsSomeValue)
.Where(y => y.IsSomeOt... | https://softwareengineering.stackexchange.com |
155,631 | [
"https://physics.stackexchange.com/questions/155631",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/37677/"
] | How would we treat an operator of the form $ \hat{\mathbf{A}} \propto \hat{\mathbf{r}} \cdot \hat{{\mathbf{p}}} $ ?
Would it have eigenstates that are also eigenfunctions of position and/or momentum?
<strong>EDIT</strong>:
I am interested in knowing if there exists a common set of eigenstates of both r and p, which... | If you keep the order when expanding the inner product you get terms of the form $x^ip_i$ which are not self-adjoint, due to the fact that $x^i$ doesn't commute with $p_i$. Hence the spectrum of such operator won't lie in $\mathbb R$, nor there is any hope in finding simultaneous eigenstates for both $x^i$ and $p_i$.
... | The operator $\hat{x}^{j}\hat{p}^{j}$ is closely related to the Fourier transform.
The matrix elements of the unitary operator $\exp(i\hat{x}^{j}\hat{p}^{j})$ are,
\begin{equation}
\langle x|\exp(i\hat{x}^{j}\hat{p}^{j})|p\rangle=\exp(ix^{j}p^{j})
\end{equation}
which is the Fourier transform that changes from the mome... | https://physics.stackexchange.com |
22,694 | [
"https://mathoverflow.net/questions/22694",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78/"
] | In coordinate-free language, my question is as follows. Let $M$ be an $n$-dimensional manifold with volume form, and let $\mathcal D$ be a smooth (integrable, if necessary) distribution with constant rank $k\leq m$ (by which I mean that $\mathcal D$ is a subbundle of the tangent bundle, spanned by $k$ many every-linea... | For any non-zero vector field $v$ and a volume form $\omega$ there exists (locally) a positive function $f$ such that $L_{fv}\omega=0$ (Indeed, one can take coordinates such that $v=\frac{\partial}{\partial x_1}$, $\omega=A(x_1,...,x_n)dx_1\wedge ...\wedge dx_n$. In these coordinates the condition $L_{fv}\omega=0$ is e... | As already pointed out in the comments, one does not necessarily have nowhere vanishing vector fields tangent to a foliation.
Although in the differentiable setting this is always the case for orientable one dimensional foliations. But for a foliation $\mathcal F$ to be defined by a divergence free vector field is a v... | https://mathoverflow.net |
67,161 | [
"https://chemistry.stackexchange.com/questions/67161",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/40368/"
] | <blockquote>
A chemist mixed <span class="math-container">$12~\mathrm{g}$</span> of phosphorus with <span class="math-container">$35.5\ \mathrm{g}$</span> of chlorine gas to synthesize phosphorus(III) chloride (phosphorus trichloride). The yield was <span class="math-container">$42.4~\mathrm{g}$</span> of <span class... | The yield is typically calculated according to equation $(1)$.
$$\text{yield} = \frac{\text{actual amount of substance obtained}}{\text{theoretical amount of substance to be obtained}}\tag{1}$$
(Whether it is given in percent or as a fractional number is not important, but percentages are the usual value.) So for any... | I'd of done this using a different approach.
<em>Frankly I'd first try a shortcut of sorts. Such chemistry problems usually consume all of one of the reactants.</em>
Knowing that 42.4 g of $\ce{PCl3}$ were produced
g P = $\dfrac{30.97}{137.3} \cdot 42.4 = 9.56$ grams
the rest must be Cl so
g Cl = 42.4 - 9.6 = 32.... | https://chemistry.stackexchange.com |
19,006 | [
"https://cstheory.stackexchange.com/questions/19006",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/10288/"
] | Are there a complete decidable $\mathcal{L}$-theory, a formula $\phi$ and a proof of $\phi$ for which the Kolmogorov complexity of the proof of $\phi$ is less than the Kolmogorov complexity of $\phi$?
Proofs in the proof systems I have seen so far are of the form:
<ol>
<li><i>mathematical reasoning</i></li>
<li>there... | As I mentioned in the comments, you need to first clarify what you exactly mean by a proof system.
Josh discusses the case where one uses the original definition of a proof system according to Cook-Reckhow.
There is an alternative definition which is also common: a proof system is a binary relation $R$ computable in ... | In most "standard" proof systems, the formula $\varphi$ being proved is usually part of the proof itself by definition of the proof system, in which case for all $\varphi$, $K(\varphi) \leq K(\text{proof}) + O(1)$ (the extra constant is for the part of the program which says, basically, "extract the last line of the pr... | https://cstheory.stackexchange.com |
476,132 | [
"https://electronics.stackexchange.com/questions/476132",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/160923/"
] | In negative feedback Op amp Virtual ground condition is satisfied but in positive feedback it doesn’t why?
| OP Amps, by circuit design, are <strong>linear ONLY when the output is not saturated</strong> which means if the input differential is >>0 there is zero linear gain. ( ie no virtual ground, Vin NOT =0 ).
As soon as the <strong>input >> 0 OR the output goes to the rail</strong>, the closed loop gain must (by definitio... | <blockquote>
why?
</blockquote>
Positive feedback seeks to maximize the voltage difference between Vin- and Vin+ therefore it cannot produce a virtual ground.
Negative feedback seeks to <strong>minimize</strong> the voltage difference between Vin- and Vin+ therefore it <strong>can</strong> produce a virtual ground.... | https://electronics.stackexchange.com |
411,322 | [
"https://physics.stackexchange.com/questions/411322",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/194362/"
] | The energy of light is given by:
$$ E = h\nu = \frac{hc}{λ} $$
which seems weird to me is that the equation has nothing to do with its amplitude. But intuitively, since the light is wave, the energy of wave should dependent on its amplitude.
So I wondered why the energy of light/photon has nothing to to with its amp... | In the scenario you describe, with no heat loss to the environment (perfect insulation), the temperature of the water will rise without limit so long as you keep adding energy to the system, which in the scenario is at a rate of 1 W. Given enough time (and assuming your container doesn't break down) this will exceed th... | Yes, if no heat is lost then the water will ultimately reach the same temperature as the heating element — presumably more than $100\,^\circ\mathrm C$.
Water has a heat capacity of $4200 \,\mathrm{J/(kg\,^\circ C)}$, so a $250 \,\mathrm{cm^3}$ glass of water being heated by $1 \,\mathrm W$ (i.e., $1 \,\mathrm{J/s}$) w... | https://physics.stackexchange.com |
85,606 | [
"https://mathoverflow.net/questions/85606",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3199/"
] | Color the positive integers using just two colors. By van der Waerden's theorem, we can find a $k$-term arithmetic progression as long as we consider a long interval.
I imagine it is possible to find a $k$-term arithmetic progression so that the terms in the progression have minimal gaps by possibly taking an even lo... | They grow very fast. Denote by N(l) the largest integer such that we can color the numbers with two colors from 1 to N(l) without an l-long arithmetic progression. Now if you use this coloring for (k-1)/2-long sequences and put such colorings after each other, then any k-long arithmetic progression will be longer than ... | I believe this question is discussed at great length in Graham Rothschild's/Spencer's "Ramsey Thory" book (page 68 and on), and cannot really be done justice here. The bounds are very, very, very large (recursively computable is about as much as one can say).
| https://mathoverflow.net |
249,050 | [
"https://dba.stackexchange.com/questions/249050",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/181904/"
] | I have two tables projects and project_user_cross. I want to get the projects if the user id exists in either of the two tables
Here is the <code>projects</code> table
<pre><code>Id | project_manager_id | name | description | created_at | updated_at | progress
1 | 1 | p 1 | lorem ipsum | 2019-9-16... | <blockquote>
except the Id is returning null
</blockquote>
You must obtain 2 columns named <code>ID</code>. First - from <code>projects</code> table with value of <code>1</code>, second - from <code>project_user_cross</code> table with value of <code>NULL</code>.
To distinguish them you must replace the asterisk ... | The join happens - logically - before the <code>WHERE</code> clause is applied. You can use an <code>EXISTS</code>, moving the join to a subquery:
<pre><code>SELECT p.*
FROM projects p
WHERE p.project_manager_id = 1
OR EXISTS
( SELECT 1
FROM project_user_cross c
WHERE c.project_id = p.id
... | https://dba.stackexchange.com |
40,474 | [
"https://softwareengineering.stackexchange.com/questions/40474",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2115/"
] | I've been freelancing for a local game development shop. Most of the projects we worked on were brought in by an external contractor. This guy now wants to do business directly with me for some new projects which have nothing to do with games, and thus <em>wouldn't require the skills of my previous clients</em>.
They ... | The only way to keep everyone happy is to get the blessing of your previous client.
I would speak to them and try to <strong>sympathize with their point of view.</strong>
Say that you value their business and you wouldn't want to do anything that might disrupt future business dealings with them. You understand that ... | <strong>You should care and you can't make everyone happy</strong>.
You should care because you are a professional. It would be very difficult for us to give you an objective opinion since we don't have all the details, so all I can say you is:
<blockquote>
Respect your clients.
</blockquote>
It will eventually pa... | https://softwareengineering.stackexchange.com |
682,229 | [
"https://physics.stackexchange.com/questions/682229",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/123113/"
] | I am trying to understand the nature of Maxwell's equations a little more. Am I correct in stating that the constants <span class="math-container">$\epsilon_{0}$</span> and <span class="math-container">$\mu_{0}$</span> in Maxwell's equations must be positive? Is my reasoning below valid?
Consider Maxwell's equations:
<... | Roughly speaking, yes; changing the signs of <span class="math-container">$\mu_0$</span> or <span class="math-container">$\epsilon_0$</span> (or both) can lead to "run-away" solutions.
The easiest way to see why changing the sign of <span class="math-container">$\mu_0$</span> and/or <span class="math-contain... | As for as Maxwell's equations are concerned, changing the signs of both constants is equivalent to changing the signs of <span class="math-container">$\rho,\,\vec{J}$</span>, i.e. charge conjugation. But, as @Javier & MaximalIdeal note, the Lorentz force law will reverse direction. This will lead positive and negat... | https://physics.stackexchange.com |
1,284,982 | [
"https://math.stackexchange.com/questions/1284982",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/241060/"
] | In Multinomial Distribution, we have
\begin{align}
f(x_1,\ldots,x_k;n,p_1,\ldots,p_k) & {} = \Pr(X_1 = x_1\mbox{ and }\dots\mbox{ and }X_k = x_k) \\ \\
& {} = \begin{cases} { \displaystyle {n! \over x_1!\cdots x_k!}p_1^{x_1}\cdots p_k^{x_k}}, \quad &
\mbox{when } \sum_{i=1}^k x_i=n \\ \\
0 & \mbox{o... | A space $X$ is a <em>$k$-space</em> if it has the final topology with respect to all maps from compact Hausdorff spaces to it, in other words, if $A\subseteq X$ is closed if $t^{-1}(A)$ is closed in $K$ for every map $t:K\to X$ where $K$ is compact Hausdorff. Usually, a <em>compactly generated</em> space has the proper... | Some quotations from “General Topology” by Ryszard Engelking:
<img src="https://i.stack.imgur.com/YxxX6.png" alt="enter image description here">
<img src="https://i.stack.imgur.com/Wrh72.png" alt="enter image description here">
<img src="https://i.stack.imgur.com/XjrJN.png" alt="enter image description here">
<img src... | https://math.stackexchange.com |
379,337 | [
"https://physics.stackexchange.com/questions/379337",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/165198/"
] | Well this problem is challenging me, but seems ridiculously simple:
Imagine we have a frictionless hill, and a mass of m
which starts slipping down without an initial velocity from the height h. So when it reaches the horizontal ground at the end, it has the horizontal velocity $$v = \sqrt{2gh}$$ to the right.
Now let... | According to the observer, the hill is moving to the right. The normal force exerted by the hill on the mass has a component pointing to the right. So in this frame, the normal force does work on the mass.
| I just wanted to add the explicit energy balance relation in the moving frame because I found it interesting. The moving frame is not accelerating and so the forces are the same that we have in the fixed frame.
In the moving frame, at $t=0$, the mass moves horizontally with velocity $u$. Let's say the angle of the hil... | https://physics.stackexchange.com |
251,071 | [
"https://softwareengineering.stackexchange.com/questions/251071",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/107200/"
] | I've been trying to develop web applications while at the same time creating the testing. I understand unit testing, I can declare a test method and test specific methods in my application.
But I don't see what is the best way to use selenium web driver for testing. I tried to test the a specific site for broken links... | Unit testing is just one of the multiple types of testing. Basically, you'll find three types of tests:
<ul>
<li>Unit tests.
Each of those tests ensure that a tiny piece of application is working as expected. For example, a unit test will ensure that if, on an e-commerce website, I create an instance of a <code>Produ... | UI testing is hard. For the most part, it doesn't lend itself well to unit testing.
Tools like Selenium are designed to fill this gap. For the most part, they do this by automating the user interface, simulating the operations that a user might perform via mouse clicks and typing. But these tests tend to be brittle... | https://softwareengineering.stackexchange.com |
2,268,425 | [
"https://math.stackexchange.com/questions/2268425",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/328809/"
] | Let $(X,\tau)$ be a topological space. I need to show that if every subset is closed then it is a discrete space.
For finite $X$, let $S$ be a subset of $X$. Since $S$ is closed, $X \setminus S \in \tau$. But $X \setminus S \subseteq X$. Therefore, $X \setminus S$ is closed and $S$ is open. Since the choice of $S$ wa... | Your proof looks good to me. Actually you did not use the fact that $X$ is finite. The same logic applies to any $X$.
$\forall s \subset X$, $X \setminus s \subset X$, and thus $X \setminus s $ is closed. Thus $s \in \tau$. - we are not involving anything about the finiteness of $X$.
| Let $x$ be a point of $X$, $X-\{x\}$ is closed so its complementary subset $\{x\}$ is open. Thus every subset is open since it is the union of its elements.
| https://math.stackexchange.com |
16,922 | [
"https://biology.stackexchange.com/questions/16922",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/6512/"
] | Let's take a quote from Wikipedia about zebroids.
<blockquote>
Donkeys are closely related to zebras and both animals belong to the horse family. These zebra donkey hybrids are very rare. In South Africa, they occur where zebras and donkeys are found in proximity to each other. Like mules, however, they are generall... | A critical step in meiosis is the formation of tetrads. In diploid organisms like donkeys, they have a paternal version and a maternal version of each chromosome. Two chromosomes 2, for instance. During prophase 1, these two "matching" or homologous chromosomes form a tetrad and cross over, swapping alelles. There is n... | I am a little bit out of practice but i researched the genetics of the horse tribe during the 1990s at the start of the Internet.
Male hybrids of the diverse equine species are all infertile.
However, a fairly large number of fertile female mules have been observed for over a century and much genetic research has been ... | https://biology.stackexchange.com |
300,437 | [
"https://physics.stackexchange.com/questions/300437",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57218/"
] | In a nutshell, what exactly is 'tension' in a string or spring etc, and its properties?
I was wondering this because I read that if you have a spring in equilibrium and you know there is a force $F$ applied to one end, then as it is in equilibrium the net force in any point in the spring is 0 and therefore the force F... | Take a string and hold it tight between your hands. And just hold it there. Tight.
No net force on any piece of the string, of course. But a net force at the ends? <strong>Also no</strong>! Otherwise they would move (accelerate).
Here is the line of thought:
<ul>
<li>One hand pulls in one end. Since that end doesn... | You are correct that the net force at any point on the spring must be zero when the spring is in equilibrium - if it were not zero, something would have to be moving. This is always the case any time you're considering different forces acting on an object - if the net force works out to be non-zero, then the object mus... | https://physics.stackexchange.com |
1,115,094 | [
"https://math.stackexchange.com/questions/1115094",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/209790/"
] | I spent too many time trying to solve this problem...and finals are coming. Please help me!
I just can't see a method to do this demonstration:
"For an $A_{n \times n}$ matrix, demonstrate that a function f:$R^n$\{0} $\rightarrow$ $R$
defined by
\begin{eqnarray}
f(x)=lim_{t\rightarrow \infty} \frac{1}{t}log\|e^{At}x... | A connected smooth $1$-manifold is either a line or a circle. The above Helix is a line. The Trefoil is a circle. Both can be smoothly embedded in the plane.
| Sometimes you want to study the properties of the embedding in the sense that you want to study the embedded manifold together with its surrounding. Notice that knot theory is not equivalent to the classification of closed 1-manifolds!
Every connected 1-manifold (being either an interval or $S^1$) embeds in a standard... | https://math.stackexchange.com |
633,497 | [
"https://physics.stackexchange.com/questions/633497",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24452/"
] | In Sakurai's book Modern Quantum Mechanics, p276 chapter 4, near equation(4.4.59), there is a theorem saying:
<blockquote>
Therorem. Suppose the Hamiltonian is invariant under time reversal and
the energy eigenket <span class="math-container">$|n>$</span> is nondegenerate; then the corresponding
energy eigenfunction... | A Hamiltonian is invariant under time reversals if <span class="math-container">$[H , T ] = 0$</span>. Remember that <span class="math-container">$T$</span> is an anti-unitary operator. Now, consider the state <span class="math-container">$|n\rangle$</span> which satisfies
<span class="math-container">$$
H|n\rangle = E... | The condition on the theorem is necessary.
If you have two independent real eigenfunctions <span class="math-container">$\psi_1$</span> and <span class="math-container">$\psi_2$</span>, then the eigenfunction <span class="math-container">$\psi_1 + \mathrm{e}^{\mathrm{i}\alpha}\psi_2$</span> for <span class="math-contai... | https://physics.stackexchange.com |
538,810 | [
"https://physics.stackexchange.com/questions/538810",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45613/"
] | I thought I could simply Google this question and get a straight, simple answer. Everything but.
Is it simply that the mean velocities of the molecules are increased (so molecular kinetic energy) as pressure increases?
Or is energy going anywhere else internally? I'm discounting possible heat transfer across the cons... | If we assume a monatomic ideal gas then the internal energy of the gas is simply the kinetic energy of the gas particles, and the average kinetic energy of a single gas particle is dependent only on the temperature:
<span class="math-container">$$ KE = \tfrac32 k_B T \tag{1}$$</span>
If you have some fixed volume <sp... | There are two pressure effects on a gas that relate to the temperature and
stored energy. The first, is that when applying pressure, one accelerates
a few atoms as they bounce off the moving piston. This causes
adiabatic heating (Diesel engines and clever little fire-starting devices
put this effect to good use). ... | https://physics.stackexchange.com |
3,846,155 | [
"https://math.stackexchange.com/questions/3846155",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/727735/"
] | <blockquote>
<strong>Question:</strong> Let <span class="math-container">$ (\varOmega,\mathcal{F},\mathbb{P}) $</span> be a probability space and <span class="math-container">$ F\in \mathcal{F} $</span> event such that <span class="math-container">$ \mathbb{P}\left(F\right)>0.$</span>
Define <span class="math-contai... | Since <span class="math-container">$B^c\in\mathcal{F}$</span>,
<span class="math-container">$$
F\setminus A =F\setminus (B\cap F)=F\setminus B=F\cap B^c \in \mathcal{F}|_F.
$$</span>
| <span class="math-container">$F\backslash (B\cap F)=F\cap(B\cap F)^c=F\cap(B^c\cup F^c)=(F\cap B^c)\cup \underbrace{(F\cap F^c)}_{=\emptyset}=F\cap B^c\in\mathcal{F}|_F.$</span>
| https://math.stackexchange.com |
64,925 | [
"https://mathoverflow.net/questions/64925",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12301/"
] | Suppose $G$ is a group and $V$ an irreducible representation of $G$. One has that $V\otimes V\cong \Lambda^2(V)\oplus Sym^2(V)$. It is well-known that if the trivial representation appears as a subrepresentation of $\Lambda^2(V)$ then $V$ is of quaternionic type; while if the trivial representation appears as a subrepr... | The trivial representation appears in $\wedge^2 V$ if and only if the representation $V^{\ast}$ has a $G$-invariant alternating bilinear form (because $\wedge^2 V\cong\wedge^2\left(\left(V^{\ast}\right)^{\ast}\right)$ is isomorphic to the $G$-module of all alternating bilinear forms on $V^{\ast}$, and $G$-invariant for... | This is essentially what Darij wrote, but without mentioning the bilinear forms. (I had written it out before reading far enough into Darij's post to see that he was really doing the same thing, after the part about bilinear forms.) Think of $V\otimes V$ as $\text{Hom}(V^*,V)$. An occurrence of the trivial represent... | https://mathoverflow.net |
112,830 | [
"https://physics.stackexchange.com/questions/112830",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46410/"
] | A wind turbine produces a power $P$ when the wind speed is $v$. Assuming that the efficiency of the turbine is constant, the best estimate for the power produced when the wind speed becomes $2v$ is
(1) $2P$
(2) $4P$
(3) $6P$
(4) $8P$
My doubt here is that power, $P= F.v$ and basically ... | No, it is not an operator, at least with the same status as that of the Hamiltonian operator! The states are described by vectors in a Hilbert space, in this case $L^2(\mathbb R^3)$, i.e. functions $\psi=\psi(x)$ with integrable squared absolute value: $\int_{\mathbb R^3}|\psi(x)|^2 d^3x < +\infty$. Operators repres... | Yes, the operator you are referring to is the <strong>energy operator</strong>,
$$\hat{E}=i\hbar \frac{\partial}{\partial t}$$
| https://physics.stackexchange.com |
619,000 | [
"https://physics.stackexchange.com/questions/619000",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/277576/"
] | Apparently there is a lack of resources regarding inertia in the web. I have already asked 2 similar questions in this site, but still I have a problem with inertia. My question -
<blockquote>
What is value of inertia of a box placed on the floor of an accelerating bus?
</blockquote>
I know the standard explanations; b... | The ball will slow down to terminal velocity. This is because the force of air drag increases with increasing speed. Terminal velocity is the speed where the force of air drag equals the force of gravity, so the total force is zero and the object travels at a constant speed. If the ball has a higher speed, then it will... | Terminal velocity is achieved when the drag force <span class="math-container">$f=Dv^2$</span> (where <span class="math-container">$D$</span> is a constant and <span class="math-container">$v$</span> is the object's speed) equals the gravitational force <span class="math-container">$F_g=mg$</span>. Equating these force... | https://physics.stackexchange.com |
318,915 | [
"https://physics.stackexchange.com/questions/318915",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/148748/"
] | Okay, so in Griffiths' <em>Introduction to Electrodynamics</em>, Griffiths clearly defines surface current density as follows:
<blockquote>
when charge flows over a surface, we describe it by the surface current density, <span class="math-container">$K$</span>.
Consider a 'ribbon' of infinitesimal width dL running... | You are wrong that google results say that surface current density is a current per unit area. I did my own google search, and that was not said in any of the results.
My guess is that you have no problem with an infinitely concentrated charge being a zero-dimensional point, and a current happening along a line. Noti... | Let's start with charge density $\rho$ which is the charge per unit volume. To get the amount of charge on some object, we'd integrate over the volume. Current is defined as charge per unit time crossing some surface. So to describe a charge density moving, we get a current density $J$ which is amount of charge per a... | https://physics.stackexchange.com |
49,978 | [
"https://mechanics.stackexchange.com/questions/49978",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/33963/"
] | <strong>Disclaimer 1</strong><br>
Before I begin explaining my issue, I want you to know that I am definitely planning on taking my car to the mechanic. I just want to know what I am getting myself into so I don't get ripped off.
<strong>Discalimer 2</strong><br>
I am a car noob and not a mechanic by any chance. I am ... | I can give you some help.
The brake hydraulic system is a sealed system that should never leak. This isn't the good 'ol days where you had to top of the master cylinder. In a modern car, you should never have to add fluid. The fluid level will drop as the brake pads wear, but the reservoir is designed to hold enoug... | also when torquing the wheel lug nuts,if they are not evenly torqued, over time it can cause rotors to slowly warp. I bought a big torque wrench so i am sure mine are all even. Also very possible if a shop does it there air guns could be off and not apply even torque too all lug nuts,regardless of what they tell you.
| https://mechanics.stackexchange.com |
385,722 | [
"https://softwareengineering.stackexchange.com/questions/385722",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/326130/"
] | I am currently writing a memoire on the evolution of developing tools. Among them is of course the programming languages. I made some researches, and a lot of the most popular languages are scripts languages like Javascript, Python or Ruby But when comparing performances, they are not as efficient as VM languages or co... | You are looking in the wrong direction:
<blockquote>
But when comparing performances, they are not as efficient as VM languages or compiled languages.
</blockquote>
The criterium you are using to answer this question is too narrow.
<em>Performance</em> - whatever you may subsume under this term - seems to be no ... | Script languages and compiled languages have different purposes so it is pointless to compare them in terms of "better" or "efficient". Note that execution speed is very different from efficiency.
Script languages are typically command languages used to string up program modules in order to perform complex tasks. It i... | https://softwareengineering.stackexchange.com |
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