qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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493,642 | [
"https://physics.stackexchange.com/questions/493642",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/58886/"
] | So in many applications like Optical Coherence Tomography, LIDAR, a mechanical scanning mirror is often used to reflect the laser to outside and also reflect the back scattered light to detector.
Since light has a constant speed, when the light hits the mirror at scan angle A and goes out side, then gets back scattered... | Photons are elementary particles, massless, they travel at speed c when measured locally in vacuum.
Now photons travel along lightlike worldlines, that is as long as the photon exists(between emission and absorption) it travels a spacetime distance of 0.
The emission and absorption are casually connected for the phot... | From light's perspective, if it had one, it would see no distance or time, it would just arrive instantaneously. But since time is relative, it sees what you think of as the past and future as the same time. So in the lab frame, light can be sent from a source that misses an object if it doesn't make it there in time.
| https://physics.stackexchange.com |
207,051 | [
"https://mathoverflow.net/questions/207051",
"https://mathoverflow.net",
"https://mathoverflow.net/users/39936/"
] | Let $X$ be a smooth quasi-projective variety over $\mathbb{C}$ and $Z$ be a closed subvariety of codimension $k$.
Q1. How to define a cycle class $[Z]\in H^k(X,\Omega_X^{k})$ ?
Q2. More general, which are necessary conditions to have a "good" cycle class map of this type? The "good" means it is coincide with the usua... | Denoting by $R(\lambda)$ the resolvent and $\mathcal{F}$ the Fourier transform for the sake of legibility (if needed), we have
\begin{equation}
\mathcal{F}\left( \mathrm R(\lambda) u \right)(\xi) = \frac{\hat{u}(\xi)}{\lambda + |\xi|^{\alpha}}.
\end{equation}
Thus,
\begin{equation}
\|\mathrm R(\lambda) u\|_{L^2} \... | As explained by Hachino, the problem is for $\lambda$ near 0. You may get a uniform estimate for low frequencies only if you put some cutoff for large $x$. Indeed, the operator $w(x)R(\lambda)w(x)$ is bounded uniformly for all $\lambda$ if $w(x)$ is a cutoff or more generally a smooth function which decays as $|x|\to\i... | https://mathoverflow.net |
235,140 | [
"https://softwareengineering.stackexchange.com/questions/235140",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2036/"
] | Here's the situation:
I have a "common" Data Access assembly that contains classes used in all my projects. Some of those are abstract classes that are only implemented by my data access layers for each project.
In my projects I have a layered approach - separated data access, business layer, and UI. My data access... | From what I understand your question to be, it seems like your Data Access Layer classes were accessing the Common Assembly and then your Business Layer accessed your Project Specific Data Access Layer.
Now you want to put some of your Common Data Access layer classes into the Common Assembly. You think it is no longe... | Consider using delegates instead of abstract classes. The Template Method pattern is mostly a hack to work around a language's lack of first-class functions. So instead of overriding "execute", pass it in as an argument. That aside, why don't you want dependencies between assemblies? What good is your Common assembly i... | https://softwareengineering.stackexchange.com |
1,624,274 | [
"https://math.stackexchange.com/questions/1624274",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/307490/"
] | This question I am asking right now comes from the Khan Academy practice task entitled 'Solve quadratic equations by using structure', so the credit goes to them.
So, if $m = 6x + 5$, then what equation is equivalent to $(6x + 5)^2 - 10 = -18x - 15$ in terms of $m$? I have been thumping my head on this, but it just d... | $$\displaystyle\frac{\frac{1}{x}}{e^{1/x}-1}$$
Now, it is in $\frac{\infty}{\infty}$ form.
| Putting $x = \frac1t$ you get
$$
\lim_{x\to 0^+} \frac{1}{x(e^{1/x}-1)} = \lim_{t\to\infty} \frac{t}{e^t-1}
$$
which you may find easier to handle.
| https://math.stackexchange.com |
1,991,621 | [
"https://math.stackexchange.com/questions/1991621",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/365230/"
] | A continuous function $f : \mathbb{R} \to \mathbb{R}$ such that $f(i) = 0$ where $ i$ are all integers, can the image of this function be not closed?
| If $g : [0, \infty) \to [0, \infty)$ is a bounded <em>strictly</em> increasing funtion with $M = \sup g$, then the function
$$f(x) = \begin{cases}
0, & x \le 0 \\
|\sin (\pi x)| \ g(x) , & x > 0
\end{cases}$$
is continuous, is trivially $0$ for negative integers and is again $0$ for positive integers becau... | Your question title asked for a function with open image, so I'll provide an example of such. Let
$$f(x) = \begin{cases} 0 & x \leq 0 \\
\frac{1}{2} \sin(\pi x) & 0 \leq x \leq 2 \\
\frac{3}{4} \sin(\pi x) & 2 \leq x \leq 4 \\
\vdots \\
\left( 1 - 2^{-k} \right) \sin (\pi x) & 2k - 2 \leq x \leq 2k \\
\... | https://math.stackexchange.com |
29,139 | [
"https://mechanics.stackexchange.com/questions/29139",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/17008/"
] | I have a 2001 Chevy Malibu and have replaced the engine coolant in it twice in the last six months after the low coolant warning light came on, and the light has recently come on again. The climate is mild here so there's no risk of freezing, and I do keep an eye on the temperature gauge - it doesn't seem to go very f... | "Is it safe to continue driving with low coolant as long as I continue to watch the temperature gauge? "
No, the temp sensor reads coolant temperature, if the coolant gets low enough to be below the temp sensor, now the sensor is reading metal temperature of the area it is screwed into (usually cylinder head), by the ... | <strong>If you do not have any leaks</strong>, then your coolant is most likely getting burned and/or going into your oil. My guess is going to be a problem with your head gasket or some crack or warping in the head.
I believe coolant in oil used to turn oil more brown and make it more foamy or milky. These days, th... | https://mechanics.stackexchange.com |
463,090 | [
"https://stats.stackexchange.com/questions/463090",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/211739/"
] | This might be a simple issue.
I consistently come across internet sources that say that a population parameter is "fixed" and cannot change. However, if we define, for example, our parameter to be the average age of living UK citizens, it could currently be, for example, 40.21292... years, which interestingly could ea... | A population parameter is a fixed value, however, a population may not be fixed - if the population changes, so may the parameter that describes it. Given some population of individuals, we typically try to estimate some parameter by taking a sample of that population. At any point in time, we have some fixed, mostly u... | The population described here represents a distribution, and the one you have as UK population is a sample from it, which is why the parameter changes while for the population it is fixed.
In this sense, although you use the entire UK population to estimate the average age of living, it'll only represent an <em>estim... | https://stats.stackexchange.com |
17,021 | [
"https://security.stackexchange.com/questions/17021",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/11150/"
] | I've looked at a number of question/answer threads and docs about PCI compliance, including various results on Google and have not found a definitive answer to this question:
Does a web app fall under PCI compliance rules/regs if it collects the bank account-routing number combination via a web form and passes it alon... | Since PCI stands for Payment <em>Card</em> Industry the short answer is no.
However that information is sensitive so you should treat it like any other sensitive data and store and transmit it in a secure, encrypted form.
PCI is a great baseline for dealing with any secure data so it certainly wouldn't hurt to treat... | First off - thanks for asking the question. Second, the respondent that stated its PII and should be protected is accurate.
At a minimum I'd employ field level encryption. Along with N tiered architecture for an app on a site managing this - or consider outsourcing payment management to a third party, avoiding many i... | https://security.stackexchange.com |
218,121 | [
"https://physics.stackexchange.com/questions/218121",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/96867/"
] | In general relativity we have no general conservation of energy and momentum. But if there exists a Killing-field we can show that this leads to a symmetry in spacetime and so to a conserved quantity. Thats what the mathematic tells us.
But I don't understand what's the meaning of an timelike/spacelike/lightlike Killi... | A physical system in GR is never <strong>isolated</strong>, in general, as it interacts with the curved metric, i.e., the gravitational background. (However a notion of <em>isolated system</em> can be given in the particular case of an asymptotically flat spacetime as discussed in auxsvr's answer.)
Apparently this fac... | Valter Moretti's answer is very nice, and I learned some things from reading it. This answer is meant to be a lower-level explanation of the basics of this topic, giving a treatment in the same style that is found when most GR texts introduce this topic.
<em>Definition of a Killing vector</em>
A Killing vector $\xi$ ... | https://physics.stackexchange.com |
101,187 | [
"https://softwareengineering.stackexchange.com/questions/101187",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18497/"
] | I don't know why, but I always feel like I am "cheating" when I use reflection - maybe it is because of the performance hit I know I am taking.
Part of me says, if it is part of the language you are using and it can accomplish what you are trying to do, then why not use it. The other part of me says, there has to be ... | No, it's not cheating - it is a way to solve problems in some programming languages.
Now, it is often not the best (cleanest, simplest, easiest to maintain) solution. If there is a better way, use that one indeed. However, sometimes there isn't. Or if there is, it is just so much more complex, involving a lot of code ... | It's not cheating. But it is usually a bad idea in production code for at least the following reasons:
<ul>
<li><strong>You lose compile-time type safety</strong> - it's helpful to have the compiler verify that a method is available at compile time. If you are using reflection, you'll get an error at runtime which mig... | https://softwareengineering.stackexchange.com |
9,798 | [
"https://security.stackexchange.com/questions/9798",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/5501/"
] | Is it bad not to validate length of user input to text field at server side. May it lead to such vulnerabilities as buffer overflows and other?
I think it depends on programming language of application. So, please describe it for PHP, Java, .NET, Ruby etc.
| It does depend on the programming language being used. Keep in mind that if there is a buffer overflow for a language that manages strings, that overflow will generally occur at levels that you cannot reach. I think you might be more concerned about situations where you are going to pass the string into another domai... | While it's true that what happens during a buffer overflow has a lot to do with the development context in which the overflow occurs (ie, what language, what operating system, and even what type of hardware) - it's also a general good practice to check the size and syntax.
I'd be impressed if anyone has both the time ... | https://security.stackexchange.com |
184,638 | [
"https://physics.stackexchange.com/questions/184638",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/81509/"
] | When a ballerina pulls her arms in, her rotational kinetic energy increases because angular momentum is conserved. That means that work must have been done on her. I saw somewhere that there is work done because she has to pull her arms in against a centrifugal force.
Actually, the particular example is from the Feyn... | <blockquote>
How does the kinetic energy of a ballerina increase?
</blockquote>
Conservation of angular momentum:
$$L_1=L_2 \implies I_1\omega_1=I_2\omega_2\quad\quad (1)$$
Pulling in your arms reduces moment of inertia $I$, since the same mass is now distributed over a volume closer to the spin centre, $I=\sum mr... | Let's consider two ships passing each other. When they pass, a rope is thrown from a ship to the other ship. Then then rope is pulled sharply. That causes the ships to collide, the rears of the ships hit each other and the ships start to spin.
In the previous scenario part of the energy used to pull the rope became ro... | https://physics.stackexchange.com |
34,406 | [
"https://electronics.stackexchange.com/questions/34406",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5542/"
] | I'm working on a case design. There is rectangular switch. I am trying to open a rectangular hole on the metallic case to fix it in there. I'm not doing a good job, if it goes on like this it looks like I'm going to ruin the case at all.
How do I open this hole?
<img src="https://i.stack.imgur.com/L9BM3.jpg" alt="Swi... | There is the tool exactly for this, named nibbler.
They sell it for $10 in Radioshack.
<img src="https://i.stack.imgur.com/paead.jpg" alt="enter image description here">
<img src="https://i.stack.imgur.com/Vf2tR.jpg" alt="enter image description here">
Specialized hole punch for specific shapes:
<img src="https://i... | I installed a very similar switch (single not dual) into an Altoids tin. I used a Dremel with a cutoff wheel. Very easy, it took two minutes.
| https://electronics.stackexchange.com |
269,402 | [
"https://softwareengineering.stackexchange.com/questions/269402",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/163761/"
] | When searching for online code editors (out of interest how all the course sites such as Codecademy has been made) I noticed they are all been written in JavaScript.
Why are all those code editors such as CodeMirror or Ace written in JavaScript and not in PHP or Java for web applications?
| PHP and Java are processed Server-Side. JavaScript is processed by the web browser.
If you were processing in real-time with PHP, you would need a piece of JavaScript (such as an AJAX POST) to send the entire chunk of code to the server for re-processing, wait for a return and then replace the entire display with newly... | PHP or Java Servlets are purely server-sided technologies. They can't do anything unless the user clicks on a link. When you want any interactivity while the website is displayed, you need Javascript, at least for an AJAX call to a PHP/JSP backend.
When you want an application like a code editor the user is interactin... | https://softwareengineering.stackexchange.com |
342,514 | [
"https://electronics.stackexchange.com/questions/342514",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/170348/"
] | I have a 36V 800W DC brushed motor (MY1020).
It is controlled by a 10-50V 40A motor controller (Cytron SmartDrive40) and an Arduino UNO.
I use a 36V 34A 1200W power supply (AC/DC).
the user's manual of the driver says the following:
<em>"If a power supply that cannot sink current is being used (example: bench top and ... | The reason that they suggest a battery is <em>efficiency</em> (And back-EMF protection, cheers Tony).
The battery can store the energy generated from regeneration, and then it can be used when you next demand power. You could configure a capacitor bank for the same thing, however the quantity of stored charge would re... | The controller spec recommends as follows:
<blockquote>
<pre><code> 6 – 18 cells NiMH or NiCd battery.
3 – 6 cells LiPo or Li-Ion battery.
10V – 45V sealed lead acid battery.
10V – 45V power supply (Must be in parallel with a battery with same voltage).
</code></pre>
</blockquote>
Since you are using 36Vdc 3... | https://electronics.stackexchange.com |
111,315 | [
"https://dba.stackexchange.com/questions/111315",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/72973/"
] | I have one SQL statement as:
<pre><code>SELECT ARTICLES.NEWS_ARTCL_ID, ARTICLES.NEWS_ARTCL_TTL_DES,
ARTICLES.NEWS_ARTCL_CNTNT_T, ARTICLES.NEWS_ARTCL_PUB_DT,
ARTICLES.NEWS_ARTCL_AUTH_NM, ARTICLES.NEWS_ARTCL_URL,
ARTICLES.MEDIA_URL, ARTICLES.ARTCL_SRC_ID, SOURCES.ARTCL_SRC_NM,
MEDI... | Try the following:
<pre><code>SELECT ART.NEWS_ARTCL_ID, ART.NEWS_ARTCL_TTL_DES,
ART.NEWS_ARTCL_CNTNT_T, ART.NEWS_ARTCL_PUB_DT,
ART.NEWS_ARTCL_AUTH_NM, ART.NEWS_ARTCL_URL,
ART.MEDIA_URL, ART.ARTCL_SRC_ID, SRC.ARTCL_SRC_NM,
MED.MEDIA_TYPE_DESCRIP, LIK.TOTAL
FROM RSKLMOBILEB2E.NE... | I'm a little rusty on Oracle but I think that the above answer might fail if there are no likes on an article and those articles might fail to be brought back.
Should the join between:
ART.NEWS_ARTCL_ID = LIK.NEWS_ARTCL_ID
be a left outer join, so that the query would read:
<pre><code> SELECT ART.NEWS_ART... | https://dba.stackexchange.com |
85,713 | [
"https://stats.stackexchange.com/questions/85713",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/39664/"
] | I had this question on an exam, and I was positive that the answer was A.
<blockquote>
The Beck Depression Inventory is a scale intended to measure
depression levels, with higher scores indicative of higher levels of
depression. If this were a valid measure of depression, we would
expect that:
A) the resu... | On multiple choice exams you're supposed to pick The Right Answer. (C) is definitely correct as all it says is that the test is valid - using other words. So if you know what validity is, you should pick (C). Anything you might say about (A) depends on a number of interpretations and assumptions -- it is not the most u... | The answer is (C), because that is exactly what the question stated: Higher scores indicate higher levels of depression. If this is a valid measure, then those who score higher are in fact more depressed than those who score low.
Your reasoning for (A) is not correct. A valid measure is not <em>necessarily</em> rel... | https://stats.stackexchange.com |
94,422 | [
"https://security.stackexchange.com/questions/94422",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6918/"
] | Running below command in as admin from Windows :
C:\Windows\system32>netsh wlan show profile name=MY_WIRELESS_NAME key=clear
Outputs :
<h2>Security settings</h2>
<pre><code>Authentication : WPA2-Personal
Cipher : CCMP
Security key : Present
Key Content : PASSWORD_OF_MY... | The network you've set up uses pre-shared secret authentication. If you're already on the network, then you know the password so seeing it in plain-text isn't that much of a big deal.
In most enterprise environments, they use 802.1x authentication so there's not much to be worried about.
<blockquote>
Could I access... | It is not a security risk if you are able to read your own WiFi key since whether you are running Windows or UNIX like operating systems, there are many ways, including through a GUI, to get it if you are connected to your hotspot at least once.
If you are worried about security then you can log to your router and ch... | https://security.stackexchange.com |
253,233 | [
"https://mathoverflow.net/questions/253233",
"https://mathoverflow.net",
"https://mathoverflow.net/users/38145/"
] | Let $G$ be a connected reductive group defined over a perfect field $F$. The <em>split component</em> $A$ of $G$ is the unique maximal $F$-split subtorus of the radical of $G$. For an algebraic group $H$ over $F$, let $X(H)$ denote the abelian group of rational characters $H \rightarrow \mathbf{G}_m$, and let $X(H)_F... | This is much easier than it looks. The point is that any reductive group $G$ is isogenous to the product of its radical, which is its centre $Z(G)$, and its commutator subgroup, which is a semisimple group. Since Hom into $\mathbb{R}$ will kill all torsion, it is sufficient to prove the statement when $G$ is either sem... | The following is a mild and perhaps too-detailed variant on David Loeffler's answer. To adhere to Borel's textbook notation, I will write $X_F(G)$ for what you denote by $X(G)_F$ and will write $X_{\mathbf{Q}}$ to denote $X \otimes_{\mathbf{Z}} \mathbf{Q}$ for any $\mathbf{Z}$-module $X$.
Firstly, the intervention of ... | https://mathoverflow.net |
168,478 | [
"https://security.stackexchange.com/questions/168478",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/108723/"
] | I have a requirement to force MFA for all non-console administrative access to our Windows AD servers. I've sorted out log ins with RSA, but that does not prevent a domain admin from mapping a drive or connecting via \servername\share and making changes that way.
This is the PCI MFA requirement 8.3.1, for those that a... | I know, two answers to one question isn't cool - but after I posted the first answer I discussed this with some friends in the industry because it really is a question that I believe wasn't thought about when the standard was drafted (and if you think htf can you say this then look at my profile).
So I think the inten... | That's a really great question. My guess is that to allow this you must be trusting domains between the CDE and non-CDE, in which case I’d expect the admin to have logged in initially using MFA.
But it is a great question and I’d actually encourage you to submit it to the PCI SSC - I don't expect you will get a quick ... | https://security.stackexchange.com |
535,272 | [
"https://physics.stackexchange.com/questions/535272",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/255638/"
] | Why do we take pseudo-force to pass through center of mass of a rigid body while calculating torque on the body using a non-inertial frame of reference?
I was just told this fact in my class and never understood intuitively as to why only center of mass is the point at which the resultant pseudo force is applied in th... | <blockquote>
The distance between two points... it’s derivative is relative velocity.
</blockquote>
No, it isn’t. The derivative of the separation distance is the <em>component</em> of the relative velocity along the line between the two objects, not the relative speed (i.e., the magnitude of the relative velocity).... | In the first case:
<span class="math-container">$$\mathbf v_1 - \mathbf v_2 = \frac{ d\mathbf r_1}{dt} - \frac{d\mathbf r_2}{dt} = \frac{d(\mathbf r_1 - \mathbf r_2)}{dt}$$</span>
In the second case:
<span class="math-container">$$\frac{d|\mathbf r_1 - \mathbf r_2|}{dt}$$</span>
Clearly they are different. The sec... | https://physics.stackexchange.com |
185,911 | [
"https://mathoverflow.net/questions/185911",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5498/"
] | Let $m \ge 1$ be an integer, let $k$ be a field of characteristic $0$, and let
$$
1 \rightarrow \mathrm{GL}_n \rightarrow E \rightarrow \mathbb{Z}/m\mathbb{Z} \rightarrow 1
$$
be an extension of $k$-group schemes. Since $E$ acts on $\mathrm{GL}_n$ by conjugation, there is an induced $k$-group scheme homomorphism $\math... | To make my comment more precise, suppose that $k$ contains no primitive $2m$-th roots of $1$, where $m=2^j$ for some $j \ge 1$. Then we can form the <em>central product</em> of $G={\rm GL}_n(k)$ with a cyclic group $\langle x \rangle$ of order $2^{j+1}$, where we amalgamate $-I_n$ with the element of order $2$ in the c... | In the category of commutative group schemes over a field $k$, $Ext^1(\mathbb{Z}/m\mathbb{Z},\mathbb{G}_m)=k^\times/k^{\times m}$ (write the $Ext$ sequence for
$0\to \mathbb{Z}\to \mathbb{Z}\to \mathbb{Z}/m\mathbb{Z}\to 0$). This takes care of the case $n=1$, and the argument in Holt's answer suggests that the genera... | https://mathoverflow.net |
253,646 | [
"https://softwareengineering.stackexchange.com/questions/253646",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/24664/"
] | The title says "Circular Dependency", but it is not the correct wording, because to me the design seems solid.<br>
However, consider the following scenario, where the blue parts are given from external partner, and orange is my own implementation. Also assume there is more then one <code>ConcreteMain</code>, but I want... | What you can do is to create a factory, MainFactory that returns an instance of ConcreteMain as IMain.
Then you can inject this Factory into your Runner constructor.
Create the Main with the factory and pass inn itself as a parameter.
Any other dependencies on the ConcreteMain constructor can be passed into the My... | Some IOC containers (for example Spring or Weld) can solve this issue using dynamically-generated proxies. Proxies are injected on both ends and the real object is only instantiated when the proxy is first used. That way, circular dependencies aren't an issue unless the two objects call methods on each other in their c... | https://softwareengineering.stackexchange.com |
319,068 | [
"https://dba.stackexchange.com/questions/319068",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/44412/"
] | I'm attempting an in place upgrade from SQL 2014 to SQL 2017, Standard Edition on Windows 2012 R2 (Yes, I know...) The issue is that the installer never presents me with a screen to select the instance and under Select Features, there are no options, just greyed out entries for Shared Features and Redistributable Feat... | Back to answer my own question.
The solution in this case was to do a command prompt upgrade. The command was as simple as this:
setup.exe /Q /ACTION=UPGRADE /IACCEPTSQLSERVERLICENSETERMS /INSTANCENAME=MSSQLSERVER
In my case, because there was still an SSRS 2014 instance on the server, we had to go through the whole u... | Could it be that your SQL 2014 is 32-bit? SQL 2017 is only available as 64-bit:
SQL Server 2017 (14.x) is only available for 64-bit platforms. Cross-platform upgrade is not supported. You cannot upgrade a 32-bit instance of SQL Server to native 64-bit using SQL Server Setup. However, you can back up or detach databases... | https://dba.stackexchange.com |
686,976 | [
"https://physics.stackexchange.com/questions/686976",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/324529/"
] | Imagine a tree that stands 100 feet tall. If the tree gets cut at the point parallel to the ground, it will fall over in a specific direction. However, the base of the tree will not move, simply the top will fall over in a circular path before it hits the ground. How would we calculate the potential energy of the top o... | The plate would have to have initially been <em>negatively</em> charged. When the UV light is shined on the plate, negative photoelectrons leave it so that the plate overall becomes neutral (negative charge leaving a surface induces a positive charge resulting in electrical neutrality if the surface was already negativ... | The discoveries by Hertz led to a series of investigations by Hallwachs,[28][29] Hoor,[30] Righi[31] and Stoletov[32][33] on the effect of light, and especially of ultraviolet light, on charged bodies. Hallwachs connected a zinc plate to an electroscope. He allowed ultraviolet light to fall on a freshly cleaned zinc pl... | https://physics.stackexchange.com |
329,818 | [
"https://stats.stackexchange.com/questions/329818",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/54923/"
] | I am fitting a Weibull distribution to some data in Stan. I am trying to reproduce some published values of parameters from a paper. However I am running into problems because I believe the normalizing constant does not match. The paper gives the pdf equation as follows:
$p(x|\mu,\nu) = \frac{1}{K} (\frac{x}{\nu})^{\m... | Perhaps the answer you are looking for is to change your likelihood statement to
<pre><code>for (i in 1:N) x[i] ~ weibull(mu, nu) T[L, ];
</code></pre>
where <code>L</code> is the lower truncation point. But you should not actually do it that way. Stan arrives at that answer by subtracting the logarithm of the compli... | If you can get easy access to it the book <em>The Weibull Distribution: A Handbook</em> by Horst Rinne covers the general three parameter Weibull down to the one. There is also a section on the truncated Weibull distributions. You may want to consult it for how different parameterizations are derived.
| https://stats.stackexchange.com |
350,924 | [
"https://stats.stackexchange.com/questions/350924",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/186272/"
] | Let
$$X_i\sim \mathcal{N}(0,\sigma^2)$$
than we know that
$$\sum_{i=1}^N\frac{X_i^2}{N}\sim\Gamma(\frac{N}{2},\frac{2\sigma^2}{N})$$
that the empirical variance follows a Gamma distribution. How do we reconcile this, with the fact the the inverse gamma is being used for the prior on the variance? I know that inverse ... | No reconciliation is needed. In one case you are referring to the sampling distribution of the maximum likelihood <em>estimator</em>, which is a function of the <em>data</em>. In the other, you are referring to the posterior distribution of the actual model <em>parameter</em>. Two different referents; two different ... | Eventhough this question was posted 4 years ago, I will make a post since it seems that there is a misconception in the comments of the other post. The question "So, the fact that Gamma is the sampling distribution of the MLE estimator, has nothing to do with the fact that we use the InverseGamma as a prior on the... | https://stats.stackexchange.com |
74,513 | [
"https://physics.stackexchange.com/questions/74513",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26419/"
] | <blockquote>
A postage stamp is placed on a surface and a glass cube of refractive index $1.5$ is placed over it. When observed through the cube, the stamp appears at a height of $1.5cm$ from the bottom of the table. Another glass cube made of different material and same thickness is then placed over the first glass ... | I don't know if my solution is right, since it is much simpler!
The refractive index formula is
<span class="math-container">$$\mu = \frac{real \ depth}{apparent \ depth}$$</span>
Now, let the thickness of the cube be <span class="math-container">$s$</span>
For the bottom cube,
<span class="math-container">$1.5 = \frac... | I believe you made a mistake at $\tan \angle NGI = \frac{IN}{d} \Rightarrow IN = d \tan 60$. It should be $\angle NGI = 30$ and not $\angle NGI = 60$.
If you use $\angle NGI = 30$, you get $d - 1.5 = \frac{d \tan 30}{\tan(\arcsin\frac {3\sin 30}{2})}\approx 0.5 d $ and $d\approx 3.1 cm$.
| https://physics.stackexchange.com |
251,711 | [
"https://physics.stackexchange.com/questions/251711",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65843/"
] | If there is a hot cup of tea and we were asked to add milk and sugar, which mixing order would make the hottest tea?
I personally think that the order doesn't matter, since sugar wouldn't change the temperature of the tea before or after milk. Is it true?
| The fact that sugar does not change the temperature can be true but this means that the time it takes to dissolve the sugar is important. The coffee will cool down exponentially all the time. Then, you drop the milk, which additionally reduces the temperature. But, mixing milk with coffee takes no time. So it will me i... | <h2>Edited because I had misread the question</h2>
If the goal is to keep the tea hot, you add the milk first. This will bring the temperature of the tea down by some amount $\Delta T$, and the cooler tea will now lose heat more slowly while you dissolve the sugar. I am assuming that since you cannot see the sugar in ... | https://physics.stackexchange.com |
151,900 | [
"https://softwareengineering.stackexchange.com/questions/151900",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18348/"
] | (I will show examples using php and phpunit but this may be applied to any programming language)
The case: let's say we have a method <code>A::foo</code> that delegates some work to class <code>M</code> and returns the value as-is.
Which of these solutions would you choose:
<pre><code>$mock = $this->getMock('M');... | I would choose 3rd solution for two reasons:
<ol>
<li>Having it defined as
<code>$result = ...</code>
makes it possible to assign a different value to $result later.</li>
<li>Precisely because second method is too tricky. I think its important for code to be readable and understandable by others as much as possible w... | IMHO all the 3 approaches are fine<br>
considering all three cases<br>
1. You return a value ('baz') and then apply the assertion using the same value.<br>
2. You are returning a variable which you are assigning while returning the same.<br>
3. You have a previously assigned variable ($result ='baz') which you return a... | https://softwareengineering.stackexchange.com |
24,034 | [
"https://mathoverflow.net/questions/24034",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1508/"
] | More generally, can the zero set $V(f)$ of a continuous function $f : \mathbb{R} \to \mathbb{R}$ be nowhere dense and uncountable? What if $f$ is smooth?
Some days ago I discovered that in this proof I am working on, I have implicitly assumed that $V(f)$ has to be countable if it is nowhere dense - hence this question... | Here's a semi-explicit construction for a smooth function f that is zero precisely on the classical Cantor set. By this set I mean the one that is obtained from $I_0 = [0,1]$ by repeatedly removing the middle third of any ensuing interval. So let's denote by $I_n$ the
$n$-th set in this process.
Now let's make a smoot... | The continuous function is very easy to construct: it's the distance to the closed set.
| https://mathoverflow.net |
2,755 | [
"https://quant.stackexchange.com/questions/2755",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/89/"
] | The derivation of the Black-Scholes model assumes no counterparty risk. Does the presence of counterparty risk invalidate the argument behind the model?
EDIT: The question is about options in general, not just the exchange-traded ones. BS model is used to price FX options, or -- in a modified form known as "Black 1976... | Options are actually some of the least susceptible securities to the adverse impact of counterparty risk. I refer to listed options, such as those cleared through the OCC (Options Commodity Clearinghouse) in Chicago, IL. The OCC is a true <strong>central clearing counterparty</strong> (CCC) because it bears all default... | Keep in mind that most futures, equity, and index options, at least, are traded on exchanges where the counterparty risk is so tiny as to be negligible.
In general, adding extra variables like this fails to invalidate the model. For example, the fact that interest rates or volatilities are not constant just ends up l... | https://quant.stackexchange.com |
312,729 | [
"https://softwareengineering.stackexchange.com/questions/312729",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/220443/"
] | We are using SonarQube for code quality testing. It tests the quality of code, and not the function of code. It has the concept of quality gates, so you can set for instance a 90% quality gate, meaning that anything over 90% quality is considered a pass.
Some folks here like this idea and have decided to apply it to f... | A test suite should only pass if all tests pass. Otherwise, the tests become worthless. What is an important failure, what is a failure that can be ignored? The result would be that all test failures would be ignored after a while. Bad.
There is one exception to this: a test suite may contain tests that are known to f... | I'd add something to amon's good answer:
<blockquote>
...the tests themselves are the quality gate.
</blockquote>
They are <em>a</em> gate of your production code, but tests themselves can have their own (potential) quality measurements, including:
<ul>
<li>Is common setup/teardown code cloned in each test? Or is ... | https://softwareengineering.stackexchange.com |
711,628 | [
"https://physics.stackexchange.com/questions/711628",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/281285/"
] | According to my notes the Standard deviation in QM is defined as:
<span class="math-container">$$(\Delta A)^2 = \langle \psi| A^2|\psi\rangle -\langle\psi|A|\psi\rangle^2$$</span>
Now I stumbled on the following claim: <span class="math-container">$$(\Delta A)^2 = \langle\psi|(A-\langle A\rangle)^2|\psi\rangle$$</span>... | <blockquote>
For example, imagine that a laser pointer is aimed at me at 1 lightsecond away. Then, I move away from it at a speed of 0.5c. Does the laser still take 1 second to reach me?
</blockquote>
It takes 2 seconds according your buddy that you leave behind standing still. Because the buddy sees the distance shrin... | The answer to your first question is that in your frame of reference the light will take one second to reach you. The answer to the second is that B will measure a longer time than you did, because light has had further to travel in B's frame.
Those effects arise from the relativity of simultaneity. If you are moving r... | https://physics.stackexchange.com |
86,443 | [
"https://electronics.stackexchange.com/questions/86443",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/13834/"
] | On our main front door at the Stack Exchange offices we have a glass door with a magnetic lock installed. As is common at offices, visitors can ring a doorbell and then our receptionist will press an RTE button to release the door lock and allow them to open it.
The problem we have is that the maglock does not make t... | Use a linear solenoid and a bell.
It will work with the same principle holding your door locked. The pull-type solenoid will hold the plunger down while the power is on. When the power is disabled, the plunger is released and sprung forward to strike the bell. When the lock is reengaged, the plunger is pulled down rea... | At some lowish voltage the mechanism will release. You don't have to totally remove power for this to happen. This means that a low voltage detector can still harvest enough energy to make a decent "sound" to indicate the door is now unlocked. A small printed circuit board should be fittable somewhere near the lock tha... | https://electronics.stackexchange.com |
208,717 | [
"https://stats.stackexchange.com/questions/208717",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/113113/"
] | I didn't find any similar question so I just post the question here.
Suppose after training and validation, the model performs poorly on the test set. Then what we do is to consider another model (Is it true? correct me if I'm wrong). When it still performs poor on the test set after training and validation, we head t... | Yes this will result in overfitting to the train + "test" set.
<ul>
<li>Data-driven model selection is part of the training process: <em>any</em> kind of data used in order to obtain the final model is involved in training. </li>
<li>The fact that you select the model manually (instead of letting an optimization rout... | Yes, if you will repeat this process multiple times you will overfit the test set.
It happens in many Kaggel competitions when the group submit their results multiple times and try to tweak their models to produce better results on the public test set. Then when the competition ends and the private test set scores are ... | https://stats.stackexchange.com |
112,848 | [
"https://physics.stackexchange.com/questions/112848",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42249/"
] | I am reading Schroeder's book "Thermal Physics". One calculation in the text was not quite clear to me. The entropy of an ideal gas is given by the Sackur-Tetrode equation:
$$
S=Nk\left[\ln\left({V\over N}\left(4\pi m U\over 3Nh^2\right)^{3/2}\right)+{5\over 2}\right]
$$
Also, the chemical potential is given by:
$$
\mu... | No, there is not. As you wrote down yourself, the definition of the chemical potential is
$$\mu=-T\left(\frac{\partial S}{\partial N}\right)_{U,V} $$
The subscript $U$ and $V$ mean that, in calculating this partial derivative, $U$ and $V$ are held fixed. Thus, you should disregard the fact that $U$ depends on $N$.
| U is assumed to be a state function of the independent variables S,V,N. Inverting S and U, S now becomes a state function of the independent variables U,V,N.
| https://physics.stackexchange.com |
224,682 | [
"https://mathoverflow.net/questions/224682",
"https://mathoverflow.net",
"https://mathoverflow.net/users/48438/"
] | Suppose $(a_n)_{n=1}^\infty$ and $(b_n)_{n=1}^\infty$ are two decreasing sequences of positive numbers such that
$a_1<b_1$ and
$$\sum_{k=1}^\infty a^p_k\leq \sum_{k=1}^\infty b^p_k<\infty$$ for $p=2,3,\cdots.$
Does it follow that
$$\sum_{k=1}^\infty a^p_k\leq \sum_{k=1}^\infty b^p_k$$
for all real $p\geq 2$?
... | All we have to do is solve some equations. If I did it right, then:
Let $q \approx 2.45$ satisfy $204q^4-580q^3+867q^2-4028=0$. Let
$$
r = \frac{578}{4323}q^3+\frac{2465}{12969}q^2-\frac{8056}{12969}q+\frac{41905}{2593}\approx 3.20 .
$$
Let
$$
a_1 :=3 ,\qquad a_2 := q,\qquad a_3 := \frac{1}{2},
$$
$$
b_1 := r,\qq... | This is a counterexample for the original question that had $p \ge 1$ instead of $p \ge 2$.
Consider a case where $(a_1, a_2, a_3) = (3,2,1)$. We'll take $$(b_1, b_2, b_3) = \left(2 + \sin(\theta) + \frac{\cos(\theta)}{\sqrt{3}}, 2 - \sin(\theta) + \frac{\cos(\theta)}{\sqrt{3}}, 2 - \frac{2\cos(\theta)}{\sqrt{3}}\rig... | https://mathoverflow.net |
194,350 | [
"https://math.stackexchange.com/questions/194350",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/30881/"
] | The following is problem 19 from page 87 of Saff and Snider's "Fundamentals of Complex Analysis for Mathematics, Science, and Engineering,"
<blockquote>
How would you construct a branch of $\log z$ that is analytic in the
domain D consisting of all points in the plane except those lying on
the half-parabola $\lb... | Just define the half-parabola to be the branch cut and you're done. A branch cut isn't intrinsic to a function, you <em>choose</em> it in whatever way you like that prevents you from circling a branch point. For example, $\log z$ has branch points at $0$ and $\infty$, so <em>any</em> unbounded curve that hits zero (and... | To construct that branch of log $z$, you just define the half-parabola to be the branch cut. This would mean log $z$ = Log|$z$| + $i\theta$ where $\theta$ equals the value of arg $z$ between $\frac{\pi}{2}$ and $2\pi$ for $z$ in the second, third, or fourth quadrant, the value of arg $z$ between $0$ and $\frac{\pi}{2}$... | https://math.stackexchange.com |
2,414,808 | [
"https://math.stackexchange.com/questions/2414808",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/430305/"
] | I know that$\ f$ is convex if
$\ λf(x)+(1-λ)f(y) \ge f(λx +(1-λ)y)$, that is:
$\ λ(2x^2 -x)+(1-λ)(2y^2 -y) \ge 2(λx +(1-λ)y)^2 - (λx +(1-λ)y)$
The last inequality is equivalent to:
$\ 0 \ge (1-λ)(2λxy)+(1-λ)^2 (y^2) +2(λ^2 - λ)(x^2)-(1-λ)(2y^2 -y)$
I'm stuck at this at this point, how can I go on with the proof?
| You can show that the second derivative is positive everywhere.
$$
f(x) = 2x^2 - x\\
f'(x) = 4x - 1\\
f''(x) = 4
$$
| <strong>Hint:</strong>
The sum of two convex functions is convex.
| https://math.stackexchange.com |
3,364,525 | [
"https://math.stackexchange.com/questions/3364525",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/598227/"
] | How is it that we can get two different answers for an integral depending on whether we apply an identity or not?
Typically, <span class="math-container">$$\int \sin x \cos x \ dx = \frac {\sin^2x}{2}+C~.$$</span>
However if we apply the trigonometric identity <span class="math-container">$$\sin A \cos B = \frac12[\... | The same in-definite integral,<span class="math-container">$I(x)$</span> done by different methods could yield different expressions <span class="math-container">$I_1(x), I_2(x), I_3(x)...$</span> which would differ with each other only by a constant. For example
<span class="math-container">$$I(x)=\int \sin x \cos x d... | You're fine, because <span class="math-container">$\frac12\sin^2x+\frac14\cos 2x=\frac14$</span> is absorbed into the integration constant.
| https://math.stackexchange.com |
26,565 | [
"https://astronomy.stackexchange.com/questions/26565",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/22623/"
] | Can a red dwarf star or a white dwarf have enough energy to support life on earth? How it will change the climate and the seasons of earth if it is our only star? (energy source)(Expecting it to change since earths orbital mechanics will also change)
| Certainly a red-dwarf star can have enough energy for a planet around it to be in the goldilocks zone. There are some difficulties with red-dwarf stars and Earth like planets. The planet would need to be very close to the star and as a result, tidally locked. The orbital period would be quite short, so there woul... | Not life as it has evolved on Earth, no. A Red Dwarf emits mostly in in the infrared so the rate of photosynthesis would be very slow, leading to the collapse of food chains even if the temperature was favourable. An old white dwarf that had cooled to Sun-like temperature might be able to support life on Earth for a pe... | https://astronomy.stackexchange.com |
706,095 | [
"https://physics.stackexchange.com/questions/706095",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44621/"
] | I have two straightforward question, and below I introduce more context to interpret them:
<ol>
<li><strong>What is, or is there, an order relation for forms that one can use to make sense of the 2nd law of thermodynamics for processes (reversible or not)? Or is the 2nd law fundamentally given in an integral way?</stro... | For your first question, I guess you could, but it would be a mere translation of the inequalities of integrals. For example, when people write <span class="math-container">$dS\geq \delta Q/T$</span>, they mean <span class="math-container">$\int dS (=\Delta S)\geq \int \delta Q/T$</span> along all paths. Mathematically... | The proper way to deal with Physics, particularly Thermodynamics, is to use Mathematics as a language to say something about the world and not to ask how to make the world fit a particular mathematical formalism.
In thermodynamics, some differential forms appear quite naturally. However, this does not imply that every ... | https://physics.stackexchange.com |
565,335 | [
"https://math.stackexchange.com/questions/565335",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1551/"
] | A friend of mine, who is a high school teacher, called me today and asked the question above in the title. In an abstract setting, this boils down to asking whether an expression like "$f=g$" is regarded as an "identity" when one of their domains is a <strong>proper subset</strong> of the other, and the two functions c... | I've typically seen the term "identity" used to refer to an equation that is true wherever both sides are defined. This would include $\sin x=\tan x\cos x,$ to be sure, but it would also include $x=2x-x.$ Put another way, we say that $f=g$ is an identity iff $f$ and $g$ are identical wherever they are both defined.
| To be precise, a statement $f(x)=g(x)$ should always be accompanied by specifying the range of all free variables involved (in this case, presumably $x$ and only $x$ is free), e.g. "for all real $x$" or - in your example - "for all $\theta\in\mathbb R\setminus(2\mathbb Z+1)\frac\pi2$".
On the other hand, if one works ... | https://math.stackexchange.com |
2,456,759 | [
"https://math.stackexchange.com/questions/2456759",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | The question is:
-How many ways are there for $n$ people to sit around a circular table if two seating arrangements are considered identical if each person has the same left neighbor in them?
I recall from my probability course long ago that for circular arrangements the formula is $(n-1)!$ but that doesn't seem cor... | $(n-1)!$ is correct.
You start by placing the first person anywhere in the table. Any starting placement is identical because of the circular symmetry.
Then you have $(n-1)$ choices for the person sitting to their left. Then $(n-2)$ choices for the person sitting to the left of the second person and so on. Thus $(n-1... | Why wouldn't it be correct?
Take a particular person and count distinct arrangements of the $n-1$ people to hir left (clockwise around the table, wherever zhe may sit). Are there not $(n-1)(n-2)\cdots 1$ ways to so choose left-person successors?
Well, there you go. That is $(n-1)!$
$\blacksquare$
| https://math.stackexchange.com |
351,830 | [
"https://physics.stackexchange.com/questions/351830",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/159887/"
] | Please tell me where i got wrong with my understanding here:
Consider a cylinder fitted with a frictionless and weightless piston having area of cross section $A$. Let it contain gas of volume $V$ and let the pressure of gas inside the cylinder be $P_{int} $. Let the pressure outside be $P_{ext} $.
Now if the external... | The work done by the gas is given by $W= \int F \cdot dl$, which is $\int PA \cdot dl =\int P dV$. The reason it is not what you have stated is because you are using the net force acting on the piston, when in actuality <em>the work done by the gas</em> is just the <em>product of the force exerted by the gas on the pis... | In a quasistatic process (reversible), the difference between the external pressure and the internal pressure is infinitesimal for each infinitesimal change in the volume of the system.
$P_{ext}=P_{int} \pm dP $,
As you know that the term for work in terms of pressure is given by, $dW=PdV$. This means that work obtai... | https://physics.stackexchange.com |
138,286 | [
"https://dba.stackexchange.com/questions/138286",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/90707/"
] | I have two queries that appear to be logically equivalent, yet they return different result sets. I am using the <code>AdventureWorks2012</code> database.
The first query uses an EXISTS clause with a subquery:
<pre><code>SELECT p.FirstName, p.LastName, e.JobTitle
FROM Person.Person AS p
JOIN HumanResources.Employee ... | <code>EXISTS</code> don't actually return any rows. They check for the existence and then move on.
Your problem is probably a duplicate caused by the JOINs to the second two tables. Try running this:
<pre><code>SELECT p.FirstName, p.LastName, e.JobTitle, COUNT(1) AS Cnt
FROM Person.Person AS p
JOIN HumanResources.... | When doing your last test trying to pop out the errant row with an except, you need to do a select of all columns (*) not just the few you want. This will almost certainly reveal something.
Based on the table name it will likely be that an employee was in one department and then moved to another department, and so wi... | https://dba.stackexchange.com |
975,884 | [
"https://math.stackexchange.com/questions/975884",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | What I've tried for this problem is expanding it to $x^3\cos(2x) + \cos(2x)$ and then evaluating the respective functions as separate integrals. The first one uses tabular and the second one is simple u substitution. Is my procedure correct?
| what we want to do is eliminate x for the integral, thus do the integral by parts.
$$
\begin{align}
\int (x^3+1)\cos (2x))\mathrm dx
&=\frac{1}{2}(x^3+1)\sin2x - \int 3x^2\sin 2x\mathrm dx\\
&=\frac{1}{2}(x^3+1)\sin2x ＋\frac{1}{4}3x^2\cos2x-\frac{1}{2}\int 3x\cos2x\mathrm dx\\
&=\frac{1}{2}(x^3+1)\sin2x ＋\... | The first integral must be integrated by parts 3 times to whittle down the $x^3$.
| https://math.stackexchange.com |
54,327 | [
"https://datascience.stackexchange.com/questions/54327",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/56913/"
] | I've been training several <code>auto encoders</code> containing two <code>GRU</code>s as encoder and decoder during last year. It occurred to me that while training there were sequences of epochs which their loss did change just a little bit(less than 0.005 or so). Every time I took this as a sign that my model is not... | Thats the whole point behind early stopping, don’t train the network to too small training error. It is always a bit tricky with early stopping but following framework might help.
When training, also output validation error
• Every time validation error improved, store a copy of the weights
• When validation error n... | Generally we track loss on validation set during training. If the loss is not changing by a large factor for some number of epoch, we stop training.
Here the large factor and number of epoch are hyper parameters and you need to tune it according to the dataset.
| https://datascience.stackexchange.com |
1,126,794 | [
"https://math.stackexchange.com/questions/1126794",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/114655/"
] | Let $\{X_n | n \in \mathbb{N} \}$ be a sequence of independent identically distributed random variables with density function:
$$f_X(x) = e^{\theta - x}I_{(\theta, \infty)}(x)$$
with $\theta > 0$. We define the sequence of sample means by:
$$\tilde{X_n} = \frac{1}{n}\sum_{j=1}^nX_j$$
Prove convergence in law of $... | The moment generating function of the random variable $\,\,\dfrac{1}{n}\sum\limits_{j=1}^{n}X_j\,\,$ is (for $\lambda<n$)
$$
\mathbb{E}\left[e^{\lambda\frac{1}{n}\sum\limits_{j=1}^{n}X_j}\right]{}={}\left(1-\lambda/n\right)^{-n}e^{\theta\lambda}.
$$
One way to justify that, as $n\to\infty$, this MGF tends to the MG... | Don't have time for a full answer, but here's an approach that seems to use the hint:
$f_X(x;\theta)= e^{\theta - x}I_{(\theta, \infty)}(x)\implies F_X(x;\theta)=\left(1-e^{\theta-x}\right)I_{(\theta, \infty)}(x):=p_{\theta}\implies e^{\theta-x}I_{(\theta, \infty)}=1-p_{\theta}$
Now take log of both sides:
$$\theta-... | https://math.stackexchange.com |
165,720 | [
"https://softwareengineering.stackexchange.com/questions/165720",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15077/"
] | I'm stating to work on a project that I intend to release as open source via the githubs. What are the advantages of putting the code on github from the outset, as opposed to waiting until the project is in a working state before publishing.
If it matters, this particular project is a C# app/service, and I have only a... | The quicker you make your code publicly available, the quicker you can gain feedback and people to help you. If your intention is to make the project open source from the beginning, then I would recommend starting your project out as public by default.
Github is full of small and unfinished projects so your project s... | There are no disadvantages. As long as you have a readme file that clearly states the project is in flux nobody will hold it against you if you make breaking changes as the project progresses.
| https://softwareengineering.stackexchange.com |
39,837 | [
"https://security.stackexchange.com/questions/39837",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/9616/"
] | So what is the use of protecting the ssh key with password when the notebook has full disk encryption? If someone is able to get the id_rsa then it is able with no effort (?) to get the id_rsa's password from memory, because it's stored in the memory in a cleartext format? (using ex.: ssh-agent)
<strong>Q:</strong> wi... | You asked about if ssh-agent stores the key passwords in cleartext. I think from looking at the code we would probably find that it doesn't store the passphrase used to decrypt it but does store the decrypted key that is then used to establish an SSH connection.
But there's a more important issue in point. If an attac... | <blockquote>
If someone is able to get the id_rsa then it is able with no effort (?) to get the id_rsa's password from memory, because it's stored in the memory in a cleartext format?
</blockquote>
It is not trivial to get access to the full contents of a machine's RAM. But if someone does have access to the content... | https://security.stackexchange.com |
22,233 | [
"https://chemistry.stackexchange.com/questions/22233",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/11537/"
] | What type of material is used in the control rod of a nuclear reactor? (Nuclear power plant)
| <strong>Control Rods:</strong> They have the ability to capture the slow neutrons and can control the chain reaction at any stage. Boron and cadmium are the best absorbers of neutrons.
To start fission in <span class="math-container">$\ce{^{238}U}$</span> we need very fast neutrons having kinetic energies more than ab... | There are various designs and materials for control rods, which are more technically correctly called <em>control assemblies.</em> The choice depends on the type and purpose of the reactor, the size of the core, the availability of other means for power control (e.g. boric acid in the reactor coolant, burnable poison r... | https://chemistry.stackexchange.com |
15,422 | [
"https://electronics.stackexchange.com/questions/15422",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4185/"
] | I'm running a dc motor using PIC16 family microprocessor.
I connect it to my pc, I can send a command to run the motor in certain speed or stop.
It works for small motor (3V, 100 mA). But the moment I use bigger motor (3V, 300 mA), I can only I send 1 command e.g. run fast. After that, the pic refused to process the n... | Federico Russo said it well: "decoupling, decoupling, decoupling". ICs like microcontrollers require smooth power supplies, that is without disturbances. Small negative spikes may cause a reset or cause your software to go bananas. Positive spikes may do the same, and even damage the part. You definitely want to get ri... | Use separate supplies for the PIC and motor and connect the two grounds at only one point. Filtering of the PIC supply should help, with a transient voltage suppressor, if you still have problems.
| https://electronics.stackexchange.com |
148,421 | [
"https://math.stackexchange.com/questions/148421",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/31972/"
] | I apologize if this is a duplicate. I don't know enough about group cohomology to know if this is just a special case of an earlier post with the same title.
Let $G=\langle\sigma\rangle$ where $\sigma^m=1$. Let $N=1+\sigma+\sigma^2+\cdots+\sigma^{m-1}$. Then it is claimed in Dummit and Foote that
$$\cdots\mathbb{Z}... | As $(\sigma-1)(c_0+c_1\sigma+\dots c_{n-1}\sigma^{n-1})=(c_n-c_0)+(c_0-c_1)\sigma+\dots (c_{n-2}-c_{n-1})\sigma^{n-1}$, the element $a=c_0+c_1\sigma+\dots c_{n-1}\sigma^{n-1}$ is in the kernel of $\sigma-1$ iff all $c_i$'s are equal, i.e. iff $a=Nc$ for some $c\in\mathbb{Z}$. Similarly, $Na=(\sum c_i)N$, so here the ke... | I just wanted to elaborate a bit on minu's excellent answer.
Suppose that $\alpha=\sum_{i=0}^{m-1}a_i\sigma^i$ is in the kernel of $\sigma-1$. Then
$$\textstyle(\sigma-1)(\alpha)=\sum\limits_{i=0}^{m-1}a_{i}(\sigma^{i+1}-\sigma^i)=(a_{m-1}-a_0)+(a_0-a_1)\sigma+\cdots+(a_{m-2}-a_{m-1})\sigma^{m-1}=0$$
so that $a_{i-1}-... | https://math.stackexchange.com |
560,780 | [
"https://stats.stackexchange.com/questions/560780",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/345437/"
] | I've read somewhere that generative models are better than discriminative ones to detect outliers in our dataset—why is that true? I think its somehow related to decision boundaries and equiprobability curves, but can't get the entire intuition. Thanks!
| Let <span class="math-container">$x$</span> be your data and <span class="math-container">$y$</span> be some sort of label or decision variable that this data can be mapped to. Discriminative models learn (some approximation of) <span class="math-container">$p(y|x)$</span>. Generative models, depending on who you ask, ... | I would say that you cant really define an outlier is unless you know what sort of data you expect to see. An outlier is an <em>unusual</em> observation. A generative model is essentially a way of specifying the kind of data you expect to see, so if it would be generated with a very low probability by your generative... | https://stats.stackexchange.com |
517,993 | [
"https://physics.stackexchange.com/questions/517993",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247868/"
] | Tensors are objects that are invarient under a change of basis representation and whose coordinates change predictably. The spacetime interval is invarient under a change of coordinate representation caused by a change in frame of reference and the coordinates describing it change predictably with the Lorentz transform... | The answer is technically yes, as has been lined out, but in regards to the second part of the question the answer is an emphatic <strong>NO</strong>. It should never be treated as a tensor because that only works in flat space and will only lead to future misunderstandings and lots of wasted time.
To give a longer an... | Edit: I no longer agree with my answer, and I think it would be appropriate to accept one of the other answers. Depending on what you mean by the spacetime interval, it's either a non-local, non-tensorial thing (if we're talking about <span class="math-container">$\Delta s$</span>), or a 2-form that happens to be prese... | https://physics.stackexchange.com |
122,062 | [
"https://electronics.stackexchange.com/questions/122062",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9402/"
] | Now, I know that this question has been asked so many times that it seems like I'm trolling, but I must point out that I couldn't find the right answer to this question <em>anywhere</em>.
So yeah, CMOS and TTL are different. Logic levels, speed, drive current, power consumption, and so on.
What I'm wondering is what ... | A few arguments:
<ul>
<li>with HC and HCT, the fan-out (at lower frequencies) is essentially unlimited, for LS it s IIRC 10 (or was it 20)?</li>
<li>the HC and HCT families are newer than LS, so my bet would be that they will be around longer than LS</li>
<li>HC and HCT use much less current than LS (except maybe for ... | I'll assume you're talking about 'glue logic' and you're not trying to build a CPU out of logic chips.
I think you're better off using popular types of HC CMOS chips since they'll likely still be available in some years. 4000-series CMOS is too slow when operated from low voltage, and LS TTL is becoming rare, has lowe... | https://electronics.stackexchange.com |
18,491 | [
"https://quant.stackexchange.com/questions/18491",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/13370/"
] | How can I extraction this PDE
\begin{align*}
0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\
+& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma \sigma}b^2(\sigma)+\frac{1}{2}P_{rr}\beta^2(r) \\
+& P_{S\sigma}\sigma Sb(\sigma)\rho _{12}+P_{Sr}\sigma S\beta(\sigma)\rho _{13}+P_{\sig... | First we write dynamic of ${{x}_{t}}=\ln ({{S}_{t}})$
\begin{align}
& d{{x}_{t}}=({{r}_{t}}-\delta -\frac{1}{2}\sigma _{t}^{2})t+{{\sigma }_{t}}d{{W}_{1}}(t) \\
& d{{\sigma }_{t}}=a({{\sigma }_{t}},t)dt+b({{\sigma }_{t}},t)d{{W}_{2}}(t) \\
& d{{r}_{t}}=\alpha ({{r}_{t}},t)dt+\beta ({{r}_{t}},t)d{{W}_{3}... | The PDE only holds in t he continuation region, in the excerise region, P is just the pay off of the function. Let $\tau$ be the first time you enter the stopping region, then by the martingale property of the option price up to the first stopping time
$$\mathbb{E}P(S_{t\wedge\tau},\sigma_{t\wedge\tau},r_{t\wedge\tau})... | https://quant.stackexchange.com |
11,829 | [
"https://scicomp.stackexchange.com/questions/11829",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/9383/"
] | I am using cvx to solve linear programs with constraints of the form $Ax=b,x\ge0$. However the matrix $A$ is rank deficient and cvx returns a warning and finally displays status as 'Infeasible'. Rank deficient systems can have a solution and my guess is that my system does have a solution. Is there a way to make cvx so... | It's known that CVX itself, and to an extent the solvers it uses, have issues with rank deficiency in the equation matrix. (Hence the warnings.) But what is your aversion to doing some sort of LU factorization here? Also, have you tried all of the solvers, or just one?
Another approach is to solve a model that is guar... | Depending on the particular $b$ vector that you have, it may be that the system of equations is infeasible or that there are solutions to $Ax=b$ but no solutions with $x \geq 0$. The solvers used with CVX are perfectly capable of detecting either type of LP infeasibility, so it's most likely the case that your guess i... | https://scicomp.stackexchange.com |
212,697 | [
"https://mathoverflow.net/questions/212697",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22606/"
] | Let $(M,g)$ be a smooth manifold equipped with a metric tensor $g$, and $f\in C^\infty(M)$ a regular function (i.e., with nowhere vanishing differential).
Denote by $\mathrm{Hess}_g(f):=\nabla df$ the Hessian tensor of $f$ with respect to the metric $g$, and by $N_f:=f^{-1}(\{0\})$ the one-codimensional submanifold of... | It is known (say, Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans.Amer.Math.Soc. 117(1965) 251–
275; I am not sure that Tashiro is the first who proved it and there were many later papers which independently prove the same result later. The proof is pretty straightforward.) that the existence ... | It is rare that manifold admits such functions.
Assume $Hess_g(f)=\lambda\cdot g$.
If $\lambda=0$ then it is so called <em>affine function</em> on $M$.
In this case $M$ is isometric to $\mathbb R\times M'$ and the function $f$ depends linearly on the first projection.
If $\lambda\ne 0$ the picture is similar, but yo... | https://mathoverflow.net |
62,803 | [
"https://physics.stackexchange.com/questions/62803",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22810/"
] | For example, I have a mass, m = 0.1kg and I square root it, giving me m = 0.316 (3s.f.) does the unit still stay as kg, or does it change?
| As the other answers (and dmckee's comments) note, yes, if you take the square root of a dimensional quantity then you need to take the square root of the units too:
$$ \sqrt{4\;{\rm kg}} = 2\;{\rm kg}^{\frac12} $$
And no, I can't think of any meaningful physical interpretation for the unit ${\rm kg}^{\frac12}$ eithe... | Yes, the dimension of a quantity changes if it is square-rooted. If $m$ is a mass with dimension $[m]=\textrm{kg}$, $\sqrt{m}$ is not a mass, but another quantity with dimension $[\sqrt{m}] = \textrm{kg}^{1/2}$.
More generally, if $[a] = A$ and if $[b]=B$, then $[a^n b^m] = A^nB^m$ etc.
| https://physics.stackexchange.com |
136,233 | [
"https://mathoverflow.net/questions/136233",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33757/"
] | The study of algebraic geometry usually begins with the choice of a base field $k$. In practice, this is usually one of the prime fields $\mathbb{Q}$ or $\mathbb{F}_p$, or topological completions and algebraic extensions of these. One might call such fields <b>$0$-dimensional</b>. Then one could say that a field $K$ is... | I think you are lumping too many disparate kinds of fields together under the heading "zero-dimensional". As Jason says in his answer, there <em>are</em> some precise definitions of dimensions of fields (e.g. cohomological dimension but also other definitions of a field-arithmetic nature).
Another important comment i... | The usual definition of "dimension" for fields is "cohomological dimension". The list of fields you gave have quite different cohomological dimensions. You can read much more about this in Serre's "Galois Cohomology".
| https://mathoverflow.net |
24,661 | [
"https://mechanics.stackexchange.com/questions/24661",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4551/"
] | As I've been learning more about cars, I keep hearing about how manufacturers are conservative with ECU settings.
For someone who isn't into racing, but would like a bit better performance out of his daily-driver, what's the cost of reprogramming the ECU to do things like improve the air/fuel mixture, and/or adjusting... | You can't necessarily re-program an ECU that is stock from factory. There are a few aftermarket ECUs that you can buy though.
On that particular vehicle it won't make too much difference. You can tune the crap out of it, but it won't increase torque or horsepower by much.
In general from my experience the only tim... | As I understand it, a "performance" tune for an unmodified, normally-aspirated engine basically consists of a slightly more aggressive ignition advance curve and a higher (200-500 RPM) redline. Depending on your engine you might see some single-digit horsepower gains, but IMHO it's not worth it for the $200+ you'll spe... | https://mechanics.stackexchange.com |
318,938 | [
"https://softwareengineering.stackexchange.com/questions/318938",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/223064/"
] | I have around 30 not-changing "objects" (the amount of them is final, no more can be added or removed). Each object has an id as well as some booleans describing what the object is and what it isn't. Now, each objects has a variable that must be changed at runtime. Most of these variables are just an integer, but some ... | I'd define a class containing all of the common stuff (is the list of booleans the same among these objects?) and their getters and setters, then subclass depending on the type of the changeable item within, then put them all into a container optimized for how you look up these things (id, probably).
This way, you hav... | For me you have 2 way :
<ul>
<li>A registry : a class that will contains all your global variable from itself and will have getter on read-only proerty and getter/setter on read/write property.</li>
<li>Use a framework that provides dependency injection, for instance Spring. By default every bean instantiated by Spri... | https://softwareengineering.stackexchange.com |
137,392 | [
"https://dba.stackexchange.com/questions/137392",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/93730/"
] | I've been working with a a relational model for a work project over the last few months, and I've gotten to the point where I'm wondering if I've made a mistake in my model's design or implemented things incorrectly. I can't go into specifics about the model because it's for work, but I'll try my best to elaborate.
Th... | Modeling and performance are related but not quite the same thing. Performance and scalability will have a lot to do with what DBMS you are actually using.
Queries which seem to be slow and difficult to execute against MySQL might fly when run against Postgres for instance. This has everything to do with how intel... | Performance combines a lot of things: physical database design, yes, but also hardware resources and DBMS implementation. You want to look at how your query optimizer is dealing with your slow-running queries, and what the DBMS reports about its resource constraints, things like disk I/O queues. You might need new in... | https://dba.stackexchange.com |
317,127 | [
"https://mathoverflow.net/questions/317127",
"https://mathoverflow.net",
"https://mathoverflow.net/users/117762/"
] | In the study of nonlinear conservation laws a lot of time I work on the two problems given bellow:
<span class="math-container">$$(1) \hspace{1cm} \begin{cases}
u_t+(f_{1}(u))_x=\lambda \cdot g(u) \\[2ex]
u(x,0)=h_{1}(x)
\end{cases}
$$</span>
<span class="math-container">$$(2) \hspace{1cm} \begin{cases}
u_t+(f... | When <span class="math-container">$n=1$</span>, you can always do this, at least near <span class="math-container">$t=0$</span>, by solving a single inhomogeneous, linear first-order PDE; you can even arrange that <span class="math-container">$h_2 = h_1$</span>. When <span class="math-container">$n>1$</span>, there... | Here's one possible solution, but this may or may not be what your professor had in mind.
<hr>
Since <span class="math-container">$\lambda$</span> is a constant, we can ignore it by absorbing it into <span class="math-container">$g$</span>.
Assume <span class="math-container">$u$</span> is scalar (takes value in <... | https://mathoverflow.net |
18,443 | [
"https://physics.stackexchange.com/questions/18443",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5129/"
] | In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is meaningless."
He measures the length of a student and an aluminium bar both in their vertical and horizontal positions respective... | Do you even know what you mean by "ignoring the uncertainties"? I don't.
You may <em>neglect</em> uncertainties sometimes. That doesn't so much have anything to do with a particular measurement of a quantity $x$ being exceptionally precise, but with putting that measurement in a calculation / comparing it with another... | Two recent examples of where an understanding of your uncertainties would be the superluminal neutrino report and the possibility of the 120 GeV Higgs.
If the experimentalists have no sense of the ability of their machines to report accurately then neither result should be taken very seriously. It is only the apparen... | https://physics.stackexchange.com |
2,305 | [
"https://mechanics.stackexchange.com/questions/2305",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1107/"
] | I'm starting down the DIY-automotive path and was reading about how some people use bubble balancers to balance their own tires at home. Can anyone speak to the accuracy of these balancers? Does anyone use them, and if so, how you found them to be precise enough for everyday use?
| Long before the spin balancer was invented all tires were balanced by a bubble balancer. If done properly, the 4 point static balance is as good and accurate as any other method.
The most effective bubble balance is accomplished on both inner and outer portions of the tire rim. This is called a 4 point balance, and ... | A bubble balancer is only able to balance the tire in one plane, as if it were a flat disc. A dynamic balancer is able to detect and correct for balance in both that plane as well as the axial dimension. You'll notice that wheels balanced on a dynamic machine often wind up with weights added on both the inside and ou... | https://mechanics.stackexchange.com |
78,664 | [
"https://electronics.stackexchange.com/questions/78664",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/26864/"
] | I cannot understand how this IC works from the block diagram given in the datasheet. I understand the concept of an H-bridge, but cannot figure how this one operates.
I drew on the schematic to illustrate my confusion.
To run a motor in the given way (red path) you would need to enable the transistor in the top lef... | If you take the logic step by step, let's say:
ENA = 1, IN1 = 1, IN2 = 0
(left is the IN, right the EN input, ~ stands for inverted by the bubble)
So the top left AND gate:
1 + 1 = 1
bottom left AND gate:
~1 + 1 = 0
Top right AND gate:
0 + 1 = 0
Bottom right AND gate:
~0 + 1 = 1
So in this case the top left ... | The two IN connections determine the direction of the motor.
<img src="https://i.stack.imgur.com/aJP8e.png" alt="enter image description here">
The <strong>ENABLE</strong> is connected to the 4 AND gates so when <strong>ENABLE</strong> is HIGH all the gates will be enabled.
Note that <strong>ONE of the inputs to ea... | https://electronics.stackexchange.com |
137,720 | [
"https://softwareengineering.stackexchange.com/questions/137720",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/45125/"
] | I would like to understand why do some people like open source and some others like closed source? Let me be more specific and make my question about web development. If I build my site using an open source server side language what are the benefits for me? and if I build it using a closed source server side language, ... | <strong>Initial Cost has a role to play</strong>. Open Source is generally cheaper on both the hosting and the tooling. The only way that closed source competes is by trying to provide better tools, sometimes even free tools. If your input costs are low open source can be an excellent option.
Microsoft will give away ... | This has probably been discussed to death, but...
Choosing between an open-source and a closed-source <em>language</em> probably won't matter much to you. However, choosing between an open-source and a closed-source <em>framework</em> might.
For example, if you found a bug in the framework, and it was open source, we... | https://softwareengineering.stackexchange.com |
69,620 | [
"https://mathoverflow.net/questions/69620",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15587/"
] | In "On definable susbsets of p-adic fields", Macintyre 1976, he states the following fact that, let $x\in Q_p^*$ such that $v(x) = 0$ (where $v$ is the p-adic valuation) and $k\in N$ then there exists $n\in Z$ such that $x/n\in (Q_p)^k$ (ie the $k$-th powers).
This property is evident if $k$ is prime to $p$ by Hensel'... | The basic idea is that it is possible to extract $k^\mathrm{th}$-roots of elements of $\mathbb{Z}_p$ that are close enough to 1. This is because you can compute explicitely the radius of convergence of the series $(1+X)^{1/k}$ (because you know the $p$-adic valuation of the factorials, hence of the binomial coefficient... | There are many different ways of attacking this, and though I have nothing against series, I always prefer a polygon argument, when one exists. First, by dividing by a suitable $n_0$, you can assume that $v(x-1)\ge1$; second, since Silvain has already taken care of the question when $k$ is prime to $p$, you can assume ... | https://mathoverflow.net |
360,866 | [
"https://softwareengineering.stackexchange.com/questions/360866",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/74713/"
] | I am working on figuring out the architecture for putting together a complex modular system that has Orders, Customers, Projects and Quotes.
The customer can have multiple projects. For each project there will be at least one order or quote associated but there is the possibility of having multiple quotes and orders o... | Certainly inheritance or inheritance based design patterns are not required for your current requirement. We can create the classes <code>Customer</code>, <code>Project</code>, <code>Order</code> and <code>Quote</code> right away. We need to carefully identify the relations between them so that we can decide about plac... | <blockquote>
It seems like the Customers class should be extended some how to add these items [...]
</blockquote>
Why? Extension/inheritance is used when you want to centralize common code between similar objects. This would be a great way to define multiple types of <code>Customers</code> where you could have one whic... | https://softwareengineering.stackexchange.com |
307,204 | [
"https://physics.stackexchange.com/questions/307204",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/130290/"
] | Let's say we have a really simple circuit consisting of a capacitor sandwiched between two resistors, all in series. When the switch flips, which resistor does the capacitor charge through? I feel like the intuitive answer is that it charges through the "downstream" resistor because electrons move in the opposite direc... | The same current flows through both resistors and the capacitor at the same time.
When the capacitor is being charged, +ve and -ve charges accumulate at the same time on opposite plates of the capacitor. Electrons flow towards the -ve plate and away from the +ve plate at equal flow rates, so that it looks like they a... | Current will flow through both resistors. Remember that the charge on both plats of plate capacitor are same but of oposite sign. So if before switching the switch the capacitor was not charged, the same amount of charge should flow to each plate and thus through resistors.
| https://physics.stackexchange.com |
1,359 | [
"https://astronomy.stackexchange.com/questions/1359",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/294/"
] | I am a complete novice when it comes to astronomy, but someone asked me the above question casually. It seems as though planets are all roughly spherical, whereas other celestial bodies aren't necessarily. Is there are particular reason for this?
| That's mainly because of the gravity, and of size. Small objects, e.g. a stone, create only a very weak gravitation. The stone is much harder than necessary to withstand this force caused by its own gravity.
Earth is much larger. The gravity at the surface causes the weight we feel. A huge mountain on Earth would be f... | When a planetary system is born, most material to build bodies is in fine dust(gas state/plasma) because it has termo-dynamic high , thus is easy that gravity force create regular spherical forms width very weight materials as iron (earth center) after that system planetary is yougest (lower termo-dynamic),it has plane... | https://astronomy.stackexchange.com |
4,908 | [
"https://math.stackexchange.com/questions/4908",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Sometime back i watched the documentary of Andrew Wiles proving the Fermat's Last theorem. A truly inspiring video and i still watch it whenever i am in a depressed mood. There are certain things(infact many) which i couldn't follow and i would like it to be explained here.
The first is:
<blockquote>
The Taniyama-S... | The elliptic curve is not a modular form. The idea that there is
a modular form $f$ associated to $E$. It satisfies
$$f(z)=\sum_{n=1}^\infty c_n q^n$$
where $q=\exp(2\pi i z)$, $c_1=1$ and (with finitely many exceptions)
for prime $p$, the equation $y^2=x^3+ax=b$ has $p-c_p$ solutions $(x,y)$
considered modulo $p$. It ... | The starting point of the link between elliptic curves and modular forms is the following.
From a topological point of view, elliptic curves are just (2-dimensional) tori, i.e. products $S^1\times S^1$, where $S^1$ is a circle.
A torus has always an invariant never vanishing tangent field. Dually, one can find a non-... | https://math.stackexchange.com |
8,105 | [
"https://mechanics.stackexchange.com/questions/8105",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3479/"
] | <b>UPDATE</b>: I bought a scan tool and downloaded the torque app. I don't get any error codes. I decided to drive it again today. I drove about a quarter mile and barely got to 20MPH. I turned around and pushed the gas pedal to the floor and car never made it above 25 MPH in about a quarter mile. The RPMs fluttered a ... | It sounds like the catalytic converter might be plugged. If it has self destructed, it could be causing a blockage and not allowing your engine to exhaust the gasses as it should, thus not allowing the engine to rev as high as it normally should. You can test it by tapping it with a hammer (not hard) and listening to s... | Your engine management is in 'limp home mode'. You need an OBD2 scan to check for any fault codes, and recification carried out.
The coolant level sensor is not OBD2, it is an info light.
| https://mechanics.stackexchange.com |
51,628 | [
"https://physics.stackexchange.com/questions/51628",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/19948/"
] | Can a body be limitlessly charged? Suppose a sphere of radius $R$. Can it be charged limitlessly?
| A complement to Jerry's answer:
A real body (a metallic sphere) will discharge in vacuum much earlier than at $Q$ sufficient to produce electron-positron pairs. If the body is charged negatively, the excess of electrons will be emitted due to cold emission. If the body is charged positively, the excess of positively ... | If it is in air (or any other substance), there is a limit where the electric field of the object is going to be enough to ionize the surrounding medium, and the resulting current will drain the object of its charge.
Similarly, if the object is immersed in vacuum, you will eventually have an electric field sufficient ... | https://physics.stackexchange.com |
98,892 | [
"https://mathoverflow.net/questions/98892",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4325/"
] | Let $S$ be a closed incompressible surface in a finite volume hyperbolic 3-manifold $M$ without cusps. Let $N$ be the cover of $M$ associated to $\pi_1(S) \subset \pi_1(M)$. The cover $N$ is homeomorphic to $S\times\mathbb{R}$ and has two ends. An end is <em>convex cocompact</em> if it has a neighborhood whose inter... | It follows from Thurston's Covering Theorem that there are no such examples.
The covering theorem says that if a degenerate end is infinite-to-one under a covering map, then you are (virtually) in the fibered case. See R.D. Canary, A covering theorem for hyperbolic 3-manifolds and its applications, Topology 35:3 (1996... | To answer your question about allowing $M$ to have infinite volume, there exist such examples on $M=S \times \mathbb{R}$ itself. These were originally constructed by Bers, his "singly degenerate" groups.
| https://mathoverflow.net |
444,925 | [
"https://physics.stackexchange.com/questions/444925",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214901/"
] | I'm confused about resistance's relationship to current and power.
Scenario:
<strong>CIRCUIT A</strong>
<ul>
<li>10 V battery</li>
<li>100 W incandescent light bulb</li>
</ul>
<em>Calculate resistance</em>:
I = P/E<br>
I = 100/10<br>
I = 10 amps<br>
R = E/I<br>
R = 10/10<br>
R = 1 ohm<br>
<strong>CIRCUIT B</stro... | The trick to this is that a "100W" bulb is a bulb that will consume 100W when plugged into a standard wall socket voltage (120V in the US). For most calculations people want to do (such as "how much power are might lights consuming when I leave them on?" or "how bright is this bulb anyways?") this is convenient. Howe... | Mathematically you are correct, but the question seems strange when considering common usage.
Usually when you buy a lightbulb rated for 100 W, the manufacturer assumes that you are going to plug it into a standard set voltage. If you put it at a much lower voltage it will not make full use of its capabilities and wi... | https://physics.stackexchange.com |
645 | [
"https://cs.stackexchange.com/questions/645",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/106/"
] | I have used the technique of dynamic programming multiple times however today a friend asked me how I go about defining my sub-problems, I realized I had no way of providing an objective formal answer. How do you formally define a sub-problem for a problem that you would solve using dynamic programming?
| The principle of dynamic programming is to think top-down (i.e recursively) but solve bottom up. So a good strategy for designing a DP is to formulate the problem recursively and generate sub-problems that way.
| As @Suresh pointed out, once you know that your problem can be solved by DP (i.e. it exhibits optimal substructure and overlapping subproblems), you may think of a divide and conquer recursive solution.
Of course, divide and conquer will be highly ineffecient because every subproblem encountered in the associated rec... | https://cs.stackexchange.com |
161,836 | [
"https://physics.stackexchange.com/questions/161836",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56452/"
] | I was surprised to asked this on an exam. The reason being the probability density is described by $\psi^*\psi$ where $\psi$ assumes the form of ~ $cos(kx)exp(-iwt)$
and when we perform $\psi^*\psi$ the time term cancels out.
So what does it meant by time evolution of probability density when there is no time term?
| Generally speaking we use the term <em>adsorption</em> when we're talking about a specific molecular interaction. In contrast the term <em>condensation</em> is really a phase transition of a bulk fluid.
Consider the interaction of water with a silica surface (this is a system I studied about 30 years (!!!) ago). A cle... | Adsorption can catalyse condensation, but it's a distinct process. Molecules adsorb to a surface and then act as a (heterogeneous) nucleus for the gas-to-liquid phase transition (i.e. condensation).
| https://physics.stackexchange.com |
9,889 | [
"https://physics.stackexchange.com/questions/9889",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3550/"
] | My understanding is that dark matter cannot be (or is at least highly unlikely to be) an exotic form of any known particle. On the other hand, articles about particle accelerators seem to say that the Higgs is the last piece missing in the Standard Model jigsaw puzzle.
<em>If</em> dark matter is determined to be some... | The conventional wisdom about dark matter is that it is likely to be a new kind of particle that is not part of the standard model. Basically, the reason for this is that most of the stable standard model particles interact electromagnetically (and so wouldn't be "dark").
The exception is neutrinos, and for a long ti... | Let me address this part of the question, as the physics part is covered by Ted Bunn.
<blockquote>
If dark matter is determined to be some form of new particle, what are the certain implications? Might such a discovery "stand to the side" of the Standard Model or would it certainly change the foundations?
</blockq... | https://physics.stackexchange.com |
266,336 | [
"https://physics.stackexchange.com/questions/266336",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/64108/"
] | So, lets say that I am an ant living on a 2-D spherical surface that is stretching to the equator...like half a sphere. I can not describe this surface in terms of the outside coordinates only someone living in the outside world can do this. So, can I really determine that I am in fact living on a spherical and not fla... | If an inhabitant of a spacetime <em>couldn't</em> measure its curvature, then there would be no general relativity, because general relativity is the study of how the curvature of our spacetime affects us...
Your intuition is correct that <em>some</em> geometric aspects of curvature cannot be measured from "inside" th... | You could construct a circle of radius $r$ and measure the circumference $c$. In a flat space, $c=2\pi r$. However, in a positively (negatively) curved space, $c<2\pi r$ ($c>2\pi r$).
Alternatively, you could pick three non-collinear points and measure the three angles that they form. In a flat space, the sum of... | https://physics.stackexchange.com |
51,304 | [
"https://stats.stackexchange.com/questions/51304",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17124/"
] | I am using the coin package in R to do a permutation test and it gives output that looks like this:
<pre><code>> pvalue(pt)
[1] 0.1479615
99 percent confidence interval:
0.1450811 0.1508754
</code></pre>
Why would one want a confidence interval for a p-value? How should it be interpreted, and how should it be use... | The theory of permutation tests (and bootstraping) is based on the idea of looking at every possible permutation. If you can look at every possible permutation then you have an exact p-value.
For most cases it is impractical to compute every possible permutation so instead we sample from the "population" of possible ... | The <em>pure</em> frequentist interpretation: If your were to do this experiment $N$ times, you should expect $X$ percent of the time (99% in your case) or $N * X$ times, that the true $p$ value falls inside the range provided by this 99% confidence interval that percentage or number of times.
| https://stats.stackexchange.com |
11,157 | [
"https://softwareengineering.stackexchange.com/questions/11157",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2861/"
] | It is easy for managers and customers to appreciate what they can see.
I have seen many GUI developers who are average programmers with minimal knowledge of design principles or other programming idioms. However, these shortcomings often go unnoticed, specially by management and customers, if the programmer can creat... | I think I see your point, but I suspect that there is also an opposite issue to consider.
Essentially, I believe you are suggesting that, because the UI is the element of the application 'in the face' of the end users, the UI developers enjoy a higher visibility than the team members working in deeper layers of the ap... | For a person who doesn't deal with programmers any, I can confidently say that they would believe this kind of stuff. They don't know the amount of work that goes in the background, all they see is a bunch of buttons/textboxes/menus/[insert GUI element] and the speed it takes to accomplish what the button started. So i... | https://softwareengineering.stackexchange.com |
143,203 | [
"https://mathoverflow.net/questions/143203",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40504/"
] | Suppose that $G$ is a linear group of positive dimension, defined over some field $k$. Is that true, that $G$ admits a (closed) one-dimensional subgroup?
I'm pretty much sure this is true in characteristic 0, or at least for $k=\mathbb{C}$. It seems that the main obstacle in positive characteristic is that there may n... | Every positive dimensional linear algebraic group $G$ over an algebraically closed field has a one dimensional subgroup.
<b>Case 1</b> $G$ is reductive. In that case, $G$ contains a torus $T$. Since we are over an algebraically closed field, $T \cong \mathbb{G}_m^r$ for some $r>0$. In particular, $\mathbb{G}_m \su... | Here is a counter-example for $k$ not algebraically closed (for simplicitly I assume that $k$ is perfect). Recall that there is an anti-equivalence of categories between the category of algebraic tori over $k$ and the category of free $\mathbb{Z}$-modules with a continuous action of $Gal(\overline{k}/k)$ (given by the... | https://mathoverflow.net |
105,990 | [
"https://physics.stackexchange.com/questions/105990",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I was out target shooting with a friend of mine, and about 2 hours into it I commented how my accuracy seems to be going down the longer we shoot. He (a fire arms instructor in the Navy, so I tend to believe him) said when a barrel heats up, the gun becomes less accurate.
On a side note, he said that when snipers are ... | This sounds like two faces of the same coin - expansion due to heating. In the first set-up, the barrel gets hot because of the friction of the bullet and the exploding charge propelling it. The internal barrel diameter will increase slightly due to the excess heat, giving a chance for some of the force of the charge t... | I would believe you are correct in thinking of expansion of the barrel. Any slight deviation in the physical properties of the barrel would greatly affect any projectiles exiting it. The expansion would not be equal all around as heat is lost on one side more quickly due to the casing being ejected from the side.
| https://physics.stackexchange.com |
243,867 | [
"https://electronics.stackexchange.com/questions/243867",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/115561/"
] | I've recently bought a HC05 Bluetooth module, of which I hoped to use the general purpose input-output pins. The HC05 has loads of them, but I haven't found anywhere a single description on how to use them, except when in AT mode, which, as far as I understand (I may be wrong) can only be used when the device is <em>no... | The HC-05 is a poorly documented module with firmware designed to just be a bluetooth to ttl serial uart interface, to be seamlessly dropped in. The extra features of the radio chip are ignored with the default firmwares. You could try writing a firmware from scratch, as I have not seen the code for the existing firmwa... | Remember that the BT module is essentially just a radio with protocol. It needs to be connected to something to be of any use. A module with power attached sitting by itself will really do nothing.
On to the bigger question. Let's assume you're connected to an Arduino or some other MCU. You can send it AT commands all... | https://electronics.stackexchange.com |
111,794 | [
"https://chemistry.stackexchange.com/questions/111794",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/73856/"
] | I learnt that for a voltaic cell, the value for the <span class="math-container">$E_\text{cell}^\circ$</span> when the reaction is <em>spontaneous</em> is given by
<span class="math-container">$$E_\text{cell}^\circ = E_\text{cathode}^\circ - E_\text{anode}^\circ, \label{eqn:1}\tag{1}$$</span>
so that the difference ... | Take a look at the two half reactions:
<span class="math-container">$$
\begin{align}
\ce{Ag+(aq) + e- &→ Ag(s)} &\qquad E^\circ &= \pu{0.80 V} \\
\ce{Sn^2+(aq) + 2 e- &→ Sn(s)} &\qquad E^\circ &= \pu{-0.14 V}
\end{align}
$$</span>
If there is an electron for grabs (like the ones in the wire of... | <blockquote>
My book tells me to keep the E∘half-cells as they are written in the
tables and simply put them in
</blockquote>
Your book is then one of the few books which teaches electrochemistry properly. The sign of the electrode reduction potential is <em>invariant</em>. If reflects the <em>sign of the electros... | https://chemistry.stackexchange.com |
143,754 | [
"https://security.stackexchange.com/questions/143754",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/82883/"
] | To develop my website I have the pre-installed Apache set up on my Mac and didn't realize until today that the website on my Mac is actually accessible by other devices in the network, too. This is incredibly helpful for me as it makes it easier to develop for mobile devices.
On the other hand, this means, that every ... | You'll never know.
I once happened to input a password. I immediately changed it once I realised this. If your information was a password, you better change it now.
| The answer to your question is <strong>yes</strong>. Not only "can" they, but certain services <em>do</em> collect data (I'll update this answer with references when I get a minute).
Further to this, from using Google Analytics I've seen reports on 'from' where a user came to find my site. So, what they searched in Go... | https://security.stackexchange.com |
3,962,227 | [
"https://math.stackexchange.com/questions/3962227",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Here is a problem in my hand-
<blockquote>
Show that
<span class="math-container">$$
\sum_{n=1}^{\infty} \frac{e^n}{(1+e)(1+e^2) \cdots (1 + e^n)} = 1
$$</span>
</blockquote>
Some facts about this series can be easily observed. Let <span class="math-container">$a_n = \frac{e^n}{(1+e)(1+e^2) \cdots (1 + e^n)}$</span>. ... | Write the <span class="math-container">$n$</span>th term as <span class="math-container">$\frac{1+e^n}{(1+e)\cdots(1+e^n)}-\frac{1}{(1+e)\cdots(1+e^n)}=\frac{1}{(1+e)\cdots(1+e^{n-1})}-\frac{1}{(1+e)\cdots(1+e^n)}$</span>, then telescope.
| Hint:
<span class="math-container">\begin{eqnarray*}
\frac{e^n}{(1+e)(1+e^2) \cdots (1 + e^n)} = \frac{-1}{(1+e)(1+e^2) \cdots (1 + e^n)} + \frac{1}{(1+e)(1+e^2) \cdots (1 + e^{n-1})}.
\end{eqnarray*}</span>
| https://math.stackexchange.com |
108,105 | [
"https://electronics.stackexchange.com/questions/108105",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40958/"
] | I'm new here - computers are my thing, but I could use some electrics help. I have travelled to a small island where I will be for several months.
I managed to bring everything except one power adapter.
I do have something "similar" and want to ask if this will work before blowing myself up.
The power requirement on... | <blockquote>
Does it really mean, for example 10V per V (10V/V)?
</blockquote>
Yes, it does. For every volt the input increases or decreases by, the output increases or decreases by 10 volts. Until it comes near the rails, of course. Note that this amplification is continuous; an input increase of 0.25V will result ... | Gain is a dimensionless quantity .The plots of input voltage to out put voltages are commonly used to find the transfer characteristics of a Device or circuit or a control system .For example in CMOS inverter we use the same for finding the point at which input voltage is high enough so that the circuit act as an inver... | https://electronics.stackexchange.com |
109,511 | [
"https://chemistry.stackexchange.com/questions/109511",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/58571/"
] | Between a 2% (w/v) aqueous solutions of <span class="math-container">$\ce{NaCl}$</span> and <span class="math-container">$\ce{RbCl}$</span>, which will have a higher boiling point.
Here there are two competing factors. First there's the fact that <span class="math-container">$\ce{NaCl}$</span> has a higher concentratio... | Molar mass of <span class="math-container">$\ce{RbCl}$</span> is <span class="math-container">$\pu{120.92 g/mol}$</span>, Molar mass of <span class="math-container">$\ce{NaCl}$</span> is <span class="math-container">$\pu{58.44 g/mol}$</span>. Both compounds are highly ionic and dissociate in water solutions. Thus, 2% s... | Boiling points depend on the strength of the intermolecular forces of the substance.So NaCl has a higher boiling point than RbCl.
| https://chemistry.stackexchange.com |
139,028 | [
"https://physics.stackexchange.com/questions/139028",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21928/"
] | Here is a machine which seems to violate the second law of thermodynamics:
<img src="https://i.stack.imgur.com/H8s9D.png" alt="2 confocal ellipsoids and an annulus">
<ul>
<li>$A$ and $B$ are point black bodies of the <strong>same</strong> temperature (<em>initially</em>).</li>
<li>everything is rotationally symmetric ... | Ingenious. A and B are small, but they cannot be points.The image of B is magnified at A. Therefore if A and B are the same size, some of the light from B will miss A.
| Position yourself on the surface of body A and shoot a ray in any direction. After a certain number of reflections from the mirror surfaces (possibly none) it will hit either body A or body B. Now expand the ray into a very narrow cone, such that all the rays in the cone finish on the same body. Looking into that cone ... | https://physics.stackexchange.com |
287,005 | [
"https://dba.stackexchange.com/questions/287005",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/113433/"
] | Is there a way to query the sql plan cache for all query's using a table variable?
| One way to do it is you could use the system <strong>DMVs</strong> to do a wildcard contains search on the cached <strong>query plans'</strong> text like so:
<pre><code>SELECT databases.[name] AS DatabaseName, Plans.objtype AS ObjectType, PlanText.text AS PlanText
FROM sys.dm_exec_cached_plans AS Plans -- Cached Query ... | As far as I can tell, a real table can still be called <code>[@sometable]</code> the same as a table variable, but this is still a useful filter. The definitive XQuery filter seems to be that there is no <code>@Database</code> attribute on a node named <code>Object</code>.
<pre class="lang-sql prettyprint-override"><co... | https://dba.stackexchange.com |
76,452 | [
"https://physics.stackexchange.com/questions/76452",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29287/"
] | I am trying to find the stagnation point of a fluid flow from a complex potential. The complex potential is given by $$\Omega(z) = Uz + \cfrac{m}{2\pi}\ln z.$$ From this I found the streamfunction to be $\psi=Ur\sin\theta + \cfrac{m}{2\pi}\theta$ and the velocity potential to be $\phi=Ur\cos\theta + \cfrac{m}{2\pi}\ln ... | You are mostly correct (except that $v$ is actually $\frac{\partial \phi}{\partial y}$). However, it is easiest to deal with $\Omega(z)$ directly.
Since the velocity components are $u=\cfrac{\partial \phi}{\partial x}=\cfrac{\partial \psi}{\partial y}$ and $v=\cfrac{\partial \phi}{\partial y}=-\cfrac{\partial \psi}{\p... | The working for that last solution was correct except for the final answer. It should be:
$ z = \frac{-m}{2 \pi U}+0i $
| https://physics.stackexchange.com |
143,130 | [
"https://stats.stackexchange.com/questions/143130",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/68884/"
] | I have a set of experimental parameters and my task it to find reasonable descriptors to describe them (chemistry).
Since I've got descriptors, I checked Pearson correlation for each of experimental parameter and then chose descriptors with P<0.05 for further investigation. But at this step I did not check normalit... | Here is a hint. Let me know if you need more and I'll expand.
Show that (in particular, make sure to check the assumptions; I didn't):
$$
\sqrt{n}\left( (\bar{X}_n,S_n^2)' - (\mu, \nu)'\right)\overset{d}{\to}N(0,\Sigma),
$$
for some constants $\mu,\nu$ and covariance matrix $\Sigma$. Consider then the function $g(x,y... | As you note yourself, $\mathrm{Var}[T_n]$ becomes 1 in the limit, so $T_n$ becomes deterministically equal to $\mu/\sigma$ in the limit. For the exponential distribution, we have that $\mu=\sigma=1/\lambda$, so $T_n\to 1$.
But that is "the limit value" of $T_n$, i.e. for $n=\infty$. When you ask for "the asymptotic di... | https://stats.stackexchange.com |
1,638,613 | [
"https://math.stackexchange.com/questions/1638613",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/134466/"
] | $$2^{x}+3^{x}=6$$
How to find the real number x? I mean it's approximately $1.19$ bur can we write $x$ as the form of $a, b, c$ when $a^{x}+b^{x}=c$ in general. Maybe an infinite sum?
| There is a way to build an (approximate) explicit formula, using Euler's method of substitution (I think Euler was the first to use it anyway).
First, we need to transform our equation. Let's take $3^x=y$ and $\alpha=\frac{log(2)}{log(3)}$ with $log$ being the natural logarithm. Then we have:
$$
y^\alpha+y-6=0
$$
$$... | This kind of equation does not show analytical solution and only numerical methods would be able to solve the problem.
What is nice if that we know the range which contains the bounds $$1 < x < \frac{\log (3)}{\log (2)}$$
However, since the function is quite stiff (it varied very fast), it should be better to c... | https://math.stackexchange.com |
60,375 | [
"https://physics.stackexchange.com/questions/60375",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22895/"
] | I'm trying to gauge the strength of aquarium air pumps, for use in a vertical hydroponic farm. A curious question arose: is it easier to pump water upwards vertically, or is it easier to pump it downwards (assuming a volume like an aquarium)?
Upwards, you fight with gravity -- downwards you are aided by gravity but fi... | Assuming both ends of a pipe are submerged in the same body of water, pumping upwards requires exactly the same force as pumping downwards, at least if the flow is relatively slow. If this wasn't the case, the water would move through the tube by itself if the pump was removed.
This means that when the water isn't mo... | Pumps are used to achieve three things maintain the flow rate, and overcome the head and the resistance in the pipe line, I will assume the pipe line is the same in both cases. If you pump upwards you have to over come the head (pressure) which increases with the height you are trying for the water to reach. If you pum... | https://physics.stackexchange.com |
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