qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
3,566,538 | [
"https://math.stackexchange.com/questions/3566538",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | How can I solve this:
<span class="math-container">$$\int \frac{x}{x^{2}-5x+4}dx$$</span>
I have tried to write with this method <span class="math-container">$$\int \frac{x}{(x-4)(x-1)}dx = \int \frac{A}{x-1}dx+\int \frac{B}{x-4}dx$$</span>
so I get <span class="math-container">$A=-\frac{1}{3}$</span> and <span cla... | Both answer are identical.
<span class="math-container">$$\log(x^2-5x+4)=\log(x-4)+\log(x-1)$$</span>
and
<span class="math-container">$$\log\frac{x-4}{x-1}=\log(x-4)-\log(x-1).$$</span>
A common trap.
<hr>
The answer in the book was probably obtained via
<span class="math-container">$$\int\frac x{x^2-4x+5}dx=\fra... | Your integrand is continuous at <span class="math-container">$(-\infty,1), (1,4)$</span> and <span class="math-container">$ (4,+\infty)$</span>, so it has antiderivative at each of these intervals given by
<span class="math-container">$$F_i(x)=\frac{-1}{3}\ln(|x-1|)+\frac 43\ln(|x-4|)+C_i$$</span>
| https://math.stackexchange.com |
392,909 | [
"https://electronics.stackexchange.com/questions/392909",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/196968/"
] | As I have read, that power supply should be equal to demand. As it can't be stored .So basically this means power is generated in real time.
Consider an area where power comes from a Substation A, which receives power generated from power plant B.Of this area suppose each device is currently switched off till now powe... | In order to meet changes in demand, the generation authority always has more generators running at any time than is needed to meet the present consumption.
Assume we just have rotating generators. The instant a load is switched onto the grid, the current that flows creates a braking torque in the generators, and they ... | To look at power generation in an elementary way, assume there is one small generator and one load. Assume that the generator is driving by an engine. The engine and generator can be running without a load. The generator produces voltage but no current is flowing. The engine is burning some fuel. but it is producing on... | https://electronics.stackexchange.com |
180,310 | [
"https://security.stackexchange.com/questions/180310",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/171346/"
] | How secure is it to pass in to a Stripe website (external, not our own site) some data to prefill a form through the query string? It's an external site so we can't just pass it in encrypted like we would with our own sites data.
I would assume it wouldn't be too bad considering its only usage is to prefill the form a... | I assume by "passing data" you meant "redirecting the end user's browser to the following Stripe.com URL"?
How secure you ask?
If you are concerned about eavesdropping on the communication, the fact that you are redirecting to HTTPS means the query string will travel encrypted between the user's browser and the Strip... | The question is what you consider "bad" in this case. Since I can only guess what is considered bad in your use case:
<ul>
<li>Stripe will have access to the data in the GET request without further intervention from the user if you load it the way your example works: this might be a privacy regulation issue depending ... | https://security.stackexchange.com |
141,741 | [
"https://softwareengineering.stackexchange.com/questions/141741",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/46101/"
] | I run a site which has a couple of million photos and gets over 1000 photos uploaded each day. Up to now, we haven't kept the original file that was uploaded to conserve on space. However, we are getting to a point that we are starting to see a need to have high-res original versions. I was wondering if its better to s... | Yep, as everyone has noted, store the large images in a filesystem (and possibly thumbnails as well). You can hash or UUID them or something to get a reasonable location/unique name, then you can store this (as well as the matching thumbnail or other resolutions if required) location in the database. Then the DB does t... | Without knowing it the question you are asking is very closely related to content management. Part of the domain of content management is managing attributes of that content - that is your problem here.
Store the images wherever you like that serves your purposes. What you need to do is develop a model for defining ... | https://softwareengineering.stackexchange.com |
244,749 | [
"https://mathoverflow.net/questions/244749",
"https://mathoverflow.net",
"https://mathoverflow.net/users/95296/"
] | On $S^4$, we know that rank 2 complex vector bundles are classified by $\pi_3(U(2))=\mathbb Z$. Any element $g\in\pi_3(U(2))=\mathbb Z$ determines a complex vector bundle $E$ over $S^4$.
<strong>Question</strong>: Can we say that the corresponding second Chern class $c_2(E)$ equals $g$, i.e. $\left<c_2(E),[S^4]\ri... | Choose a homotopy equivalence $U(2)\simeq \Omega BU(2)$ to use as an identification and let $g:S^3\rightarrow U(2)\simeq \Omega BU(2)$ represent a homotopy class in $\pi_3U(2)$. Then the $U(2)$-bundle $E\rightarrow S^4$ corresponding to $g$ is classified by the map $\tilde{g}:S^4\rightarrow BU(2)$ which is adjoint to $... | You can identify $c_2$ with an element of $H^4(BU(2))$. Let $BU(2)\to K({\mathbb Z}, 4)$ be a map that classifies $c_2$. It induces a homomorphism
$\pi_4(BU(2))\cong [S^4, BU(2)]_*\to [S^4, K({\mathbb Z}, 4)]_*\cong H^4(S^4)$. If I understand correctly, your first question is equivalent to asking whether this homomorph... | https://mathoverflow.net |
3,103,424 | [
"https://math.stackexchange.com/questions/3103424",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/642364/"
] | I have to make a combinatorial argument for this equation:
<span class="math-container">$ _{n}P_{k} = _{n-1}P_k + k∙ _{n-1}P_{k-1} $</span>
I cant seem to find examples without binomial theorem. I really dont know where to start with an argument for this. Any help would be appreciated.
| <strong>Edit:</strong> At the bottom there's an argument using Zorn's lemma instead of explicit transfinite recursion.
Here's what I believe is a correct proof - would have included the details in my previous post on the topic except that something, I don't recall what, was bothering me about the transfinite recursion... | Some mitigating facts:
<ol>
<li>If <span class="math-container">$X$</span> is an infinite dimensional Banach space, then <span class="math-container">$|X|=\dim X$</span>, this is because the dimension of an infinite dimensional Banach space is at least <span class="math-container">$2^{\aleph_0}$</span>, and therefore ... | https://math.stackexchange.com |
43,986 | [
"https://mathoverflow.net/questions/43986",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9871/"
] | Let $V$ be an infinite dimensional topological vector space and consider the natural application $\iota\colon V\to V^{**}$. The space $V$ is said to be reflexive if $\iota$ is an isomorphism.
Are there examples where $\iota$ fails to be an isomorphism but $V$ and $V^{**}$ are nevertheless isomorphic?
Can one find an ... | Yes, the James space.
This is a good question, and R. C. James is rightly praised for this example.
<blockquote>
MR0044024 (13,356d)<br>
James, Robert C.<br>
A non-reflexive Banach space isometric with its second conjugate space.<br>
Proc. Nat. Acad. Sci. U. S. A. 37, (1951). 174–177.
</blockquote>
| James' construction can be iterated, in order to produce a countable family of pairwise non-isomorphic Banach spaces with the same property.
Look at the following paper:
Marek Wójtowicz - "Finitely Nonreflexive Banach Spaces"
Proceedings of the American Mathematical Society
Vol. 106, No. 4 (Aug., 1989), pp. 961-965... | https://mathoverflow.net |
538,706 | [
"https://stats.stackexchange.com/questions/538706",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/331377/"
] | Let's say I have a blackbox function <code>generate_number()</code> that generates a random number between 1-N; and assume <code>N</code> is known. Each function call is independent from each other and carries no state.
I use this to generate <code>X</code> numbers; let's say these numbers are not stored anywhere so i ... | This is the birthday problem in another form.
With <span class="math-container">$d$</span> equally likely days and <span class="math-container">$n$</span> independent draws, the expected number of distinct days drawn is <span class="math-container">$d(1-(1-\frac1d)^n)$</span> which in your case of <span class="math-con... | With <span class="math-container">$N = 365$</span> and <span class="math-container">$x = 23,$</span> randomly generated numbers, your vetting procedure is similar to the famous birthday problem, in which one would expect matching numbers among the <span class="math-container">$x$</span> a little more than half the time... | https://stats.stackexchange.com |
102,946 | [
"https://cs.stackexchange.com/questions/102946",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/-1/"
] | I am trying to get better at solving recurrence relations, so I am making my own simple relations and try to solve them. I have made the following recurrence:
<span class="math-container">$$T(n) = 3T(n-1) + 2, \quad\quad T(1) = 1$$</span>
My work at solving it:
<span class="math-container">$$\begin{align*}
T(n) &... | As Apass.Jack hinted at in the comments, you were a bit careless when multiplying and adding everything. Here is a hint for you:
<span class="math-container">$$\begin{align*}
T(n) &= 3T(n - 1) + 2 \\
&= 3^2 T(n - 2) + 2 \cdot 3 + 2 \\
&= 3^3 T(n - 3) + 2 \cdot 3^2 + 2 \cdot 3 + 2 \\
&= 3^4 T(n - 4) + 2 ... | Let us add <span class="math-container">$1$</span> to both sides of your recurrence:
<span class="math-container">$$
T(n) + 1 = 3T(n-1) + 3 = 3(T(n-1) + 1).
$$</span>
This shows that
<span class="math-container">$$
T(n) + 1 = 3^{n-1}(T(1) + 1),
$$</span>
and so
<span class="math-container">$$
T(n) = 2 \cdot 3^{n-1} - 1... | https://cs.stackexchange.com |
58,446 | [
"https://electronics.stackexchange.com/questions/58446",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | I have a mono audio signal which I want to output on two boxes. Can I just connect the speakers in series or parallel (which?) or do I have to do something more advanced (and if so, what)?
| A <strong>ganged potentiometer</strong> is two or more variable resistors of the same or sometimes different value, ganged together on one adjusting shaft, normally used on stereo systems as a volume control so that one can vary the volume of both channels at the same time.
<img src="https://i.stack.imgur.com/AuHIX.jp... | Aside from Ganged, other common names are Quad Potentiometer, or 4 Channel Potentiometer.
Although multi-channel pots are more common in digital IC versions, due to size saving packages they come in, and are easier to construct.
| https://electronics.stackexchange.com |
16,114 | [
"https://dba.stackexchange.com/questions/16114",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7919/"
] | I have many text files, their total size is about 300GB ~ 400GB. They are all in this format
<pre><code>key1 value_a
key1 value_b
key1 value_c
key2 value_d
key3 value_e
....
</code></pre>
each line is composed by a key and a value. I want to create a database which can let me query all value of a key. For example, wh... | I have been in a similar situation and highly recommend looking into MongoDB or HBase for your needs. The others (Cassandra/Redis) are good too, but HBase and MongoDB have been battle-tested in large environments, have a large community, good documentation (MongoDB's is better) and generally fulfill the three requireme... | <ul>
<li>How big are the keys?</li>
<li>How big are the values?</li>
<li>Will the data arrive "continually", or is this a one-time load?</li>
<li>Let's see all the representative queries. You have mentioned only</li>
</ul>
<code>SELECT val FROM tbl WHERE key = 'constant';</code>
Are there others ?
In general key-va... | https://dba.stackexchange.com |
139,253 | [
"https://dba.stackexchange.com/questions/139253",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/95219/"
] | If I have a table with the following information:
<pre><code>ParentID | ChildID
---------+--------
6 | 6
6 | 7
6 | 8
6 | 9
6 | 10
</code></pre>
I need to display the distinct parent with all instances of child in the second column possibly concatonated... | You can use a pattern like this:
<pre><code>SELECT files.database_id, db.name AS DatabaseName,
STUFF((SELECT ', ' + names.name
FROM sys.master_files names
WHERE names.database_id = files.database_id
FOR XML PATH(''),TYPE).value('.','VARCHAR(MAX)')
, 1... | You could try :
<pre><code>select distinct parentId,
substring(( select ','+cast(childId as varchar)
from MyTable t1 with(nolock)
where t1.parentId = t2.parentId
for xml path ('')
),2, 1000) as childId
from MyTable t2
</... | https://dba.stackexchange.com |
165,883 | [
"https://security.stackexchange.com/questions/165883",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/152326/"
] | On my NPS server which is also a Domain Controller, the Issuing CA has for some reason automatically given the Domain Controller a certificate based on the "Domain Controller" certificate template.
I wanted to give the NPS server a certificate based on the "RAS and IAS" certificate template which it could use to authe... | The templates include, among other things, a list of Key Usage (KU) and Extended Key Usage (EKU) fields that you would like in the issued certificate. Outside of very specific Microsoft services, the template field itself is not checked when evaluating a certificate (it is a Microsoft-only field, not a standard), but b... | If NPS server is installed directly on domain controller, then you don't need to use separate certificate from "RAS and IAS server" certificate template, because they are interchangeable in this context.
That is, domain controller certificate can be used for RADIUS, but "RAS and IAS" certificate cannot be used for dom... | https://security.stackexchange.com |
292,022 | [
"https://stats.stackexchange.com/questions/292022",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/144183/"
] | I have a single-stage cluster sample, and I am trying to estimate the hazard ratio of a given exposure after controlling for a confounder. My dataset contains 10 strata, with 20 clusters within each stratum. Furthermore, my dataset contains repeated observations, so I want to obtain a robust variance estimate that acco... | The answers are correct (though they may not be what you want).
When the first stage of sampling is treated as independent (ie, no <code>fpc=</code> argument, what survey statisticians misleadingly call "with replacement"), additional stages have no effect on the variance estimate.
| In your last block of code you have the correct specification of a design, but you use the non-existent function <code>design</code> rather than <code>svydesign</code> and more importantly you don't pass the design object to your function so it doesn't do anything.
You want
<code>
design3 <- svydesign(id=~id_clust... | https://stats.stackexchange.com |
361,962 | [
"https://softwareengineering.stackexchange.com/questions/361962",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/47556/"
] | In the project I work on we use XSD to generate some classes. XSD determines the order of elements, similar to this snippet:
<pre><code><xs:element name="Customer_ID" type="com:Text6"/>
<xs:element name="Customer_Desc" type="com:Text150"/>
<xs:element name="Customer_Name" type="com:Text50"/>
<xs:e... | The fact that you are using XSD is not important. You are creating Java classes and those don't care the order (well, unless there is some dependency that should be dealt with in the constructor or a builder, rather than through setters). Keeping them in order because of the XSD can end being a maintenance nightmare, a... | Whenever I'm doing some tedious task, like making a new X object and setting 20 of its properties I tend to do so in alphabetical order, because that's the order I see things in the IDE's intellisense/code help combo dropdown - helps me avoid missing one. I'd be tempted to sort and update XSDs similarly, inserting new ... | https://softwareengineering.stackexchange.com |
211,858 | [
"https://security.stackexchange.com/questions/211858",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/210186/"
] | I'm actually busy with learning more about buffer overflows. I read some interesting tutorials and just got the basic idea behind it. I tried to produce a vulnerable c++ file to test my knowledge against it, but it seems like I missed some of the concepts...
My code is the following:
<pre><code> #include <iost... | You have to check the addresses of the char arrays, because your assumption that yy starts right after xx in memory is not necessarily true. I modified your code a bit so that it prints the addresses:
<pre><code>#include <iostream>
int main() {
char xx[20];
char yy[20];
std::cin >> yy;
... | <blockquote>
Could you tell me why this is happening?
</blockquote>
When Visual Studio compiles this code on my machine, it puts the buffer "xx" at the memory location 0x012ff894. It puts "yy" at memory location 0x012ff878.
So, yy is at a lower address than xx.
Therefore you can not overflow xx into yy by writin... | https://security.stackexchange.com |
1,438 | [
"https://mathoverflow.net/questions/1438",
"https://mathoverflow.net",
"https://mathoverflow.net/users/788/"
] | This is in the same vein as my previous question on the representability of the cohomology ring. Why are the homology groups not corepresentable in the homotopy category of spaces?
| Corepresentable functors preserve products; homology does not.
One replacement is the following. Let X be a CW-complex with basepoint. Then the spaces {K(Z,n)} represent reduced integral homology in the sense that for sufficiently large n, the reduced homology H<sub>k</sub>(X) coincides with the homotopy groups of t... | While it's true that there are lots of internal things that a corepresentable homology functor wouldn't support, I think it's also enlightening to see that you wouldn't get the nice sorts of dualities that homology and cohomology theories have. After all, we've already agreed that cohomology theories ought to be someh... | https://mathoverflow.net |
69,563 | [
"https://mathoverflow.net/questions/69563",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9947/"
] | Assume that $\beta:\tilde{X}\to X$ is the blow-up of a nonsinular $\Bbbk$-variety $X$ along a sheaf of ideals $\mathcal{I}$. Let $Y:=Z(\mathcal{I})$. Given nonsingular, closed subvarieties $Z_1,\ldots,Z_r\subseteq X$ such that $\bigcap_i Z_i \subseteq Y$, is it true that $\bigcap_i \tilde{Z}_i=\emptyset$, where $\tilde... | As Sasha and Ramsey point out, this isn't true in the generality requested. However, the following is true, see Hartshorne, Chapter II, Exercise 7.12.
<strong>Statement:</strong> Suppose that $X$ is a Noetherian scheme and let $Y, Z$ be closed subschemes, neither one containing the other. Let $\widetilde{X}$ be the... | In general the answer is no. For example if $X$ is a plane, $Y$ is a point and $Z_1,Z_2$ are curves tangent in $Y$, then the strict transforms intersect. If however $Y$ is smooth and normal bundles $N_{Z_i/Y}$ do not intersect in $N_{X/Y}$ then the intersection is empty. Note that transverslity is another condition, th... | https://mathoverflow.net |
284,120 | [
"https://mathoverflow.net/questions/284120",
"https://mathoverflow.net",
"https://mathoverflow.net/users/78705/"
] | Consider a full-period LSFR with a feedback polynomial of degree n. In the cyclic sequence generated by the LSFR, each n-bit sequence appears exactly once. Given two n-bit sequences, one can define the distance as the number of application of the recursion rule that are needed to move from the first to the second seque... | Similar to the linked variants on this problem, the optimal strategy takes the form of a function $v(t)$, which corresponds to the strategy in which you travel at velocity $v(t)$ until the light turns green, then you slam on the accelerator and accelerate at $a$ until you reach the speed limit $L$.
If $T$ is the time ... | This is just the first step in obtaining a possible answer: formalization. For simplicity, let us ignore the possibility that the light will change more than once before it is reached by the vehicle.
Let $V$ and $D$ denote, respectively, the speed when you pass the light and the distance to cover after the light. Then... | https://mathoverflow.net |
10,423 | [
"https://cs.stackexchange.com/questions/10423",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7216/"
] | So I have been given the task of creating an PDA that recognises the language
$\{a^{2n} b^{3n} \mid n = 0,1,2,\dots\}$.
Am I right in thinking that it needs to have at least 3 times number of $b$'s than $a$'s?
So for example:
$aabbb$ would be accepted
$aaabb$ would NOT be accepted
However, how do I show that using... | The following pushdown automaton should do the trick. I publish this only because the existing answer can be improved upon. (Note, I am using $e$ to denote $\epsilon$- (or $\lambda$-) transitions.
<img src="https://i.stack.imgur.com/CgbuO.png" alt="enter image description here">
The idea is that the left-hand part co... | Yes the number of b's is at least 3 times the number of a's except when n=0 in which case you get the empty string. Your language is equivalent to $\{(aa)^n(bbb)^n:n=0,1,\dots\}$. So if you can find a PDA for $\{a^nb^n\}$, then you can find one for your language. Here is the transition function $\delta$ (the stack init... | https://cs.stackexchange.com |
105,591 | [
"https://softwareengineering.stackexchange.com/questions/105591",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29032/"
] | You know them, those errors that make NO sense. Where it seems like a gremlin just jumped deep inside your chips and messed up something. Do you take a walk, write stuff, call an uncle?
| For those really horrible problems my strategy usually goes as follows.
<ul>
<li>Experiment and google. Keep trying to solve the problem. Most of the time this solves the problem in an hour or less.</li>
<li>So that hasn't worked. Take a break. Have a coffee, talk about something unrelated to a colleague. Push the pro... | Quit. No, not your job! Just get up and go home. You're done for the day or the weekend. 19 times out of 20 when you come back to the problem next, the solution will present itself within an hour.
| https://softwareengineering.stackexchange.com |
61,657 | [
"https://stats.stackexchange.com/questions/61657",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/26846/"
] | Many econometrics textbooks (e.g. Wooldridge, "Econometric analysis...") simply write something similar to: "If the population model is <span class="math-container">$y = xB + u$</span> and (1) <span class="math-container">$\text{Cov}(X,U) = 0$</span>; (2) <span class="math-container">$X'X$</span> is full rank, then OLS... | An estimator is consistent if $\hat{\beta} \rightarrow_{p} \beta$
Or $\lim_{n \rightarrow \infty} \mbox{Pr}(|\hat{\beta} - \beta| < \epsilon) = 1 $ for all positive real $\epsilon$.
Consistency in the literal sense means that sampling the world will get us what we want. There <em>are</em> inconsistent minimum vari... | When we talk about consistent estimation, we mean consistency of estimating the parameters $\beta$ from a regression like
$$y = \alpha + \beta x + u$$ $\newcommand{\plim}{{\rm plim}}\newcommand{\Cov}{{\rm Cov}}\newcommand{\Var}{{\rm Var}}$
We don't know the true value of the slope of $x$ in this linear model, i.e. we d... | https://stats.stackexchange.com |
52,256 | [
"https://stats.stackexchange.com/questions/52256",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20131/"
] | I'm working with some data and I used R to the a linear regression model <code>Y = aX + b</code>.
The code I used was
<code>summary(lm(Y~X))</code>
What I got was
<pre><code> Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.3884045 0.0260232 -14.93 <2e-16 ***
X 0.0062095 0.00... | No.
The output when you print the summary of the original model contains (in this case), the column <code>Pr(>|t|)</code> gives you the p-value associated with the hypothesis test you want
<pre><code> Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.3884045 0.0260232 -14.93 <2e-16 **... | If I understand correctly, you're overthinking it. You're interested in a linear model mapping X, and an intercept, to Y. You're interested in the slope a mapping X to Y. The linear regression that you run (without that offset) finds a coefficient of 0.0062095. That coefficinet is very much significantly different ... | https://stats.stackexchange.com |
10,793 | [
"https://softwareengineering.stackexchange.com/questions/10793",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66/"
] | I've heard in several places "Don't make large commits" but I've never actually understood whats a "large" commit. Is it large if you work on a bunch of files even if there related? How many parts of a project should you be working on at once?
To me, I have trouble trying to make "small commits" since I forget or crea... | <blockquote>
To me, I have trouble trying to make "small commits" since I forget or create something that creates something else that creates something else.
</blockquote>
That is a problem. It sounds like you need to <em>learn</em> to break down your work into smaller, more manageable chunks.
The problem with lar... | Imagine that the client asked to have a particular change made - for example to add a rule that something or another can't be done within two days of the "whatever" date. Then, after you've made the change, they change their minds. You will want to roll back your commit. If it's all mushed in with some things about cha... | https://softwareengineering.stackexchange.com |
3,716,910 | [
"https://math.stackexchange.com/questions/3716910",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/732469/"
] | Suppose we have a right triangle with an opposite edge of constant length <span class="math-container">$y$</span> and an adjacent edge whose length varies continuously between <span class="math-container">$x_1$</span> and <span class="math-container">$x_2$</span>. Is there a way to find the average angle this triangle ... | You have to specify the probability distribution of the adjacent edge, but then, yes there is. If <span class="math-container">$x$</span> is the length of the adjacent edge, the angle is <span class="math-container">$\arctan \left(\frac yx \right)$</span>. The average angle is then <span class="math-container">$\in... | Let <span class="math-container">$\triangle ABC$</span> be right angled at <span class="math-container">$B$</span> and let <span class="math-container">$BC=\ell$</span> (fixed length) and <span class="math-container">$AB=x$</span> (variable), where <span class="math-container">$a \leq x \leq b$</span> and let <span cla... | https://math.stackexchange.com |
81,041 | [
"https://dba.stackexchange.com/questions/81041",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/35850/"
] | I try this, but the SwitchCase can not return more than one value.
<pre><code>WHERE CP.NumIntAut IN (
CASE WHEN @NumIntAut IS NOT NULL
THEN (@NumIntAut)
ELSE (SELECT NumIntAut FROM @TAB_NumIntAut) END)
</code></pre>
How can I do?
| <pre><code>DECLARE @NumIntAut INT = 123 --filter by only one NumIntAut...
DECLARE @CodUsu INT = 789 --or more than one NumIntAut from User
DECLARE @TAB_NumIntAut TABLE (NumIntAut INT)
INSERT @TAB_NumIntAut SELECT [...]
INSERT @TAB_NumIntAut SELECT @NumIntAut
[...]
WHERE CP.NumIntAut IN (SELECT NumIntAut FROM @TAB_Nu... | I think you are looking to do something like this
<pre><code>WHERE CP.NumIntAut IN (
SELECT CASE WHEN @NumIntAut IS NOT NULL
THEN @NumIntAut
ELSE NumIntAut END
FROM @TAB_NumIntAut )
</co... | https://dba.stackexchange.com |
103,035 | [
"https://electronics.stackexchange.com/questions/103035",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4940/"
] | I was browsing through the example code that MikroE provides for PIC programming using MikroC, and they always set PORTx before setting TRISx. What is the reason for this?
Since TRIS just selects whether the port or pin is output/input mode, why does it matter what the pin is set to before we set the mode?
Example co... | The PORTx bits are adjusted before the TRISx bits so you know what the output will be before you make the pin an output. If you are setting the TRISx bits to inputs, it doesn't matter. However, if you are clearing the TRISx bits and making them outputs, it is safer to determine what the output will be before it switche... | For this specific bit of code the answer is that the programmer wants to set the pins to a known state/voltage before setting them as outputs. But in general, the TRIS bits do more than just set a pin to input or output mode.
The TRIS mnemonic stands for tri-state. When a pin is tristated the resistance of that pin go... | https://electronics.stackexchange.com |
30,019 | [
"https://security.stackexchange.com/questions/30019",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/20239/"
] | I'm a web developer, but I occasionally step over into doing some mobile app development here and there. A client recently asked me to help them develop a very simple app. The app is essentially just an HTML / jQuery form that the user fills out to reserve my clients service. Having heard a lot about phonegap, I decide... | Sending credit card info via e-mail is very bad and likely a violation of their merchant service agreement. Credit card details must be protected in transit and e-mail leaves it flapping in the breeze.
The SSL connection to the server or not for transmitting form data is irrelevant unless the server is somehow encr... | If that form is not embedded in the app and is delivered over an unencrypted channel then it is possible for an attacker to change it in transit to <code>action=https://evil-site.com/carding.php</code>.
Ensure that all communication is encrypted and user data is being validated thoroughly on the server.
To make sure ... | https://security.stackexchange.com |
197,515 | [
"https://physics.stackexchange.com/questions/197515",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/86889/"
] | In the box $x = 0$ to $x = L$, $V = 0$, and for $x < 0$ and $x > L$, $V = \infty$ (infinite potential well).
The eigenvalues of the Hamiltonian are:
$$E_n = \frac{n^2 h^2}{8L^2} \, .$$
Since as $V = 0$ in the box, this is kinetic energy only, so:
\begin{align}
\frac{p^2}{2m} &= \frac{n^2 h^2}{8L^2} \\
p^2... | Consider a molecule of oxygen in a balloon.
You know that at nonzero temperature all those molecules are bouncing around in all directions.
Of course, the mass of air doesn't have any net motion in any direction.
Indeed, the average velocity of each molecule is zero:
$$\langle v \rangle = 0 \, .$$
Of course, the averag... | In the free-electron model of metals, the electrons are treated as particles in a 3-dimensional box. States are filled from the bottom up. The highest energy electrons have the Fermi energi, with a Fermi wave vector and yes - a Fermi velocity.
This velocity is then related the mean free path by $\lambda_{\it free} = ... | https://physics.stackexchange.com |
2,146 | [
"https://scicomp.stackexchange.com/questions/2146",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/34/"
] | An Amazon EC2 compute cluster costs about \$800-\$1000 (depending on duty cycle) per physical CPU core over the course of 3 years. In our last round of hardware acquisition, my lab picked up 48 cores worth of hardware very similar to that of Amazon's clusters for about ~$300 a core.
Am I missing something here? Are th... | The main advantage, in my opinion, of using Cloud-based resources is flexibility, i.e. if you have a fluctuating workload, you only pay for what you need.
If this is not the case in your application, i.e. you know you will have a quantifiable and constant workload, then you're probably better-off building your own clu... | There are some things to worry about when doing cloud computing with MD simulations. For instance, you need to worry about the physical layout of the processors in the server farm where these jobs will be running. The reason is that, depending upon the size of your simulations, and the kinds of calculations you're runn... | https://scicomp.stackexchange.com |
3,371,332 | [
"https://math.stackexchange.com/questions/3371332",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/368425/"
] | Good night, I'm trying to prove this theorem:
<blockquote>
Let <span class="math-container">$B = \{-n +(1/n) \mid n = 2,3,4,\ldots \}$</span>. Prove that <span class="math-container">$B$</span> is closed in <span class="math-container">$\mathbb R$</span>.
</blockquote>
<strong>My attempt:</strong>
Let <span class=... | Apparently, the author defines <span class="math-container">$x\cdot y=x^Ty$</span>, even when <span class="math-container">$x$</span> or <span class="math-container">$y$</span> are complex vectors. This is a bit different from the definition of the usual inner product <span class="math-container">$\langle x,y\rangle=\o... | The dot product can be indicated by
<span class="math-container">$$\vec w \cdot \vec v$$</span>
or equivalently
<span class="math-container">$$\vec w^T\vec v$$</span>
or also
<span class="math-container">$$\langle \vec w,\vec v\rangle$$</span>
and we can move the scalar factor <span class="math-container">$\lambd... | https://math.stackexchange.com |
104,422 | [
"https://mathoverflow.net/questions/104422",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4542/"
] | I have a projective variety $X$ and an open immersion $j : U \to X$.
Say I have a sheaf, locally free in my case of interest, $\mathcal{S}$ on $U$. Is there any reasonable relationship between $H^i(X,j_! \mathcal{S})$ and $H^i(U,\mathcal{S})$? What if I add that I know that $H^i(U,\mathcal{S}) = 0$ for $i>0$. I'm h... | Consider $X = \mathbb{P}^{1}$, $U =\mathbb{A}^{1}$ and j the inclusion of a affine chart in the projective line. The complement of the affine chart is a point P, let i be the inclusion of this point in the projective line.
Consider the sheaf $\mathcal{F} = \mathcal{O}(-2)$ on the projective line. One has $dim H^{1}( \m... | If $X$ is smooth and we consider sheaves of $k$-modules, $k$ a commutative ring, then $H^*(X, j_!\mathcal{S})\cong H^*_c(U,\mathcal{S})$; the latter is equipped with a non-degenerate pairing $$H^*_c(U,\mathcal{S})\otimes H^{2d-*}(U,\mathcal{S}^{\vee})\to k,$$
where $\mathcal{S}^\vee$ is the Verdier dual local system ... | https://mathoverflow.net |
65,169 | [
"https://mechanics.stackexchange.com/questions/65169",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/45133/"
] | 2012 Ford Focus SE
My windshield wipers have been going crazy. The other day, after parking my car and taking the key out my windshield wipers turned on. Eventually they stopped after a few minutes.
Normally, with the car off I can't turn them on (for example if I turn the car off before they return all the way down ... | Just to give an update - I didn't do anything and the problem just went away. The wipers and wiper controls work fine now.
| Maybe an automatic control has a faulty sensor ? My 2011 Murano has auto wipers that turn on and off and adjust speed according to any rain : Such a system would cause your condition with a bad sensor. I expect it would need to be evaluated by the dealer.
| https://mechanics.stackexchange.com |
46,471 | [
"https://security.stackexchange.com/questions/46471",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/35072/"
] | Someone with the same name as my sister seems to have inadvertently created a Facebook account with her email address. The funny thing is that this person doesn't seem to have ever accessed my sister's Gmail account. My sister tipped me off that emails from Facebook were appearing in her inbox. I took a look, and saw t... | In Facebook its possible to create account with another person email, but your account still unverified until you use one of the verification methods (phone, another email).
The account can even be activated/verified if the real owner of the email address accidentally confirms by clicking on the link.
Just go to the ... | Besides the fact the facebook account could have been created there is also the posibility that the emails are phising attempts that only look like they are coming from facebook.
So do not follow links in the emails, it may not be facebook they go to.
The idea in another answer to reset the password to prevent the ac... | https://security.stackexchange.com |
125,644 | [
"https://softwareengineering.stackexchange.com/questions/125644",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22991/"
] | I am trying to solve an issue with reusing components. I have some UI components (a mix of JS, CSS, and HTML) that are not specific to any application. These UI components need to be able to be used in multiple applications. One is a RoR application, the other is an ASP.NET MVC application. How can I maintain these co... | I think you can look at any number of publicly available client-side frameworks like jQuery and YUI and see how they are deployed. Any particular project may be dependent on a specific version of the UI lib. It can either copy the relevant version to it's own repo or grab as part of the deployment process. Another opti... | One option would be to host the packages (JS, CSS, Static Images, etc) on a publicly accessible URL and just reference them where needed by the url. This is how jQuery and all the big libraries do it.
| https://softwareengineering.stackexchange.com |
35,346 | [
"https://stats.stackexchange.com/questions/35346",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10354/"
] | This question contains a relatively long prelude, since I want to explain as clearly as possible the motivation for the question. It may well be the case that I am asking the wrong question (i.e. there is a better way of solving the problem than what I am attempting) and I would welcome any good answers along those lin... | You can "fit" the model to different data and then simulate:
<pre><code>m2 <- Arima(z,model=m1)
simulate.Arima(m2,future=TRUE,bootstrap=TRUE)
</code></pre>
<code>m2</code> will have the same parameters as <code>m1</code> (they are not re-estimated), but the residuals, etc., are computed on the new data.
However, ... | On a related note, you can accomplish the same objective if your ARIMA model has external regressors. This has been helpful for me on occasion.
For instance, say your first model was created as follows:
<pre><code>fit.arimax <- Arima(response, order=c(1, 0, 1), xreg=xreg)
</code></pre>
Then suppose that after cre... | https://stats.stackexchange.com |
478,216 | [
"https://math.stackexchange.com/questions/478216",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/42631/"
] | Is it true that if the fundamental groups of two spaces are isomorphic, then their first homology groups are isomorphic? I think the answer is yes;
Let $f:\pi_1(X)\to\pi_1(Y)$ be an isomorphism and $p:\pi_1(X)\to \pi_1(X)^*, q:\pi_1(Y)\to \pi_1(Y)^*$ be the quotient maps, where $\pi_1(X)^*, \pi_1(Y)^*$ are the abelian... | $p\circ f^{-1}$ (this is the correct composition) is a homomorphism from $\pi_1(Y)$ to $\pi_1(X)^*$; it is not this map which is an isomorphism.
I will sketch the correct idea for you, avoiding the more sophisticated concepts from user87690's answer. Elements of $\pi_1(X)^*$ are equivalence classes of elements of $\p... | Since $H_1(X)$ is isomorphic to abelianization of $π_1(X)$ for $X$ path-connected and isomorphic groups have isomorphic abelinizations, positive answer to your question follows.
Abelinization is a functor from groups to abelian groups. Let $Ab(G)$ mean the abelinization of $G$ and let $π_G: G \to Ab(G)$ be the canonic... | https://math.stackexchange.com |
573,286 | [
"https://physics.stackexchange.com/questions/573286",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/272324/"
] | I'm currently going a little more in depth with thermodynamics and I'm trying to familiarise myself with Mollier's diagram. What I don't understand is how to read precise values given the initial conditions. For example, I am given <span class="math-container">$p=0.6MPa, T=473,15K$</span> and I want precise values for ... | As material falls to a horizon, emitting light as it goes, there are three effects to consider: the worldline of the emitter, the redshift of the light, and the intensity of the light (headlight effect).
As the emitter sends out light signals, they get more and more red-shifted and more and more dim and more and more i... | You are not wrong. If we could live forever, and if we could observe indefinitely small light energies, we would observe the light from material falling into to a forming black hole forever. Because time appears to stop at the Schwarzschild radius, an issue is raised as to whether a singularity can actually form. In 19... | https://physics.stackexchange.com |
31,052 | [
"https://electronics.stackexchange.com/questions/31052",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9542/"
] | What is the disadvantage of oversampling a signal?
For example, if I sample a signal at twice the Nyquist sampling rate, what will the disadvantages?
| First thing: the Nyquist rate is not sufficient to obtain a correct sampling of a signal, it's just the theoretical minimum. Reasonable sampling rates go from twice the Nyquist rate (four-five times the maximum frequency) up.
Several ADC architectures use oversampling with averaging to obtain higher precision than the... | You'll need more processing power: you'll have to execute your filters twice as fast. This may come with higher power consumption and/or a higher price tag.
| https://electronics.stackexchange.com |
92,375 | [
"https://mathoverflow.net/questions/92375",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19783/"
] | If you have a number of large matrices, and you wish to determine whether each matrix has determinant zero or not, what is the most efficient way to do this in MAGMA
(it appears that calculating the rank is slightly more efficient than calculating the determinant).
**EDIT: **In case it helps, the matrix entries are r... | I don't know about Magma specifically, but in general, computing the determinant modulo a bunch of primes is the way to go (bunch = enough small primes so that their product exceeds the Hadamard bound, but of course, once the determinant is nonzero modulo some prime, you can safely halt).
<strong>EDIT</strong> Just a ... | I can guess that both the rank and the determinant are computed through some kind of (pivoted) LU factorization.
If so, in order to compute the determinant, after computing the LU factorization, you have to take the product of the factors on the diagonal of U, so it is not surprising that it takes more time than compu... | https://mathoverflow.net |
27,810 | [
"https://physics.stackexchange.com/questions/27810",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2740/"
] | Consider a spinning wheel, which is held up by one end of it's axis like this: <img src="https://i.stack.imgur.com/bGYsu.gif" alt="Spinning wheel from hyperphysics">
To explain why the change of angular momentum is directed as shown in the figure above, one usually says that there is an applied torque $\vec{\tau} = \v... | You are correct to observe that there is an often unstated assumption in the standard setup of this problem. When given this problem you are supposed to assume that the off-major-axis components of angular velocity make a contribution to L which is negligible compared to the on-axis angular velocity. Obviously this i... | What I see here on the picture is that the formula
$$\tau = I \alpha$$
is probably not applicable for this situation. This is because $\omega$ is constant, i.e. $\alpha = 0$!
This situation is analogous to <em>circular rotation with constant velocity</em>. There you have velocity $\vec{v}$, whose <em>magnitude</em... | https://physics.stackexchange.com |
118,131 | [
"https://electronics.stackexchange.com/questions/118131",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11636/"
] | Let's say I'm using a software like EagleCAD to create a panel with a few copies of a design (or even different designs).
There is a "Dimension" layer (mapped to an Outline layer, e.g., GKO), but this is for the overall outline of the panel.
Which layer is traditionally used to communicate where the individual cut-ou... | I've always used the dimension layer for marking out anywhere there should not be PCB, whether that's the outer edge or a cutout. I believe it is traditionally used for that (with 100 mil wide lines).
However, if you're marking out boards that should actually be separate pieces you should use the 'Vscore' layer. This... | There are not standardized layer names for Gerber files, so usually you will want to include a readme file that maps the file names to layer in the stackup.
Normally for outline, you will create a separate Gerber layer for the PCB (or panel) that has the V-groove score line centers and/or milling outlines shown. You ... | https://electronics.stackexchange.com |
2,386,683 | [
"https://math.stackexchange.com/questions/2386683",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/557708/"
] | Let $A=(0,1)$ and $B= (2,0)$ in the plane. Let $O$ be the origin and $C=(2,1)$. Let $P$ move on the segment $OB$ and let $Q$ move on the segment $AC$. Find the coordinates of $P$ and $Q$ for which the length of the path consiting of the segmet $AP$,$PQ$ and $QB$ is the least.
I was trying to solve this question ... | NO. If two statements are logically equivalent, then their columns in the combined truth-table will be exactly the same. Truth-tables are a way of showing the truth-conditions of statements, and two statements are equivalent if and only if they have the same truth-conditions ... i.e. have the same truth-table!
By 'com... | No. In fact, what is true is that two claims have equivalent truth-tables if and only if they are equivalent. And two statements are not logically equivalent if and only if they do not have equivalent truth-tables.
You claim that $P\to Q \equiv \lnot P \lor Q$ is an example in which the two statements are logically ... | https://math.stackexchange.com |
71,654 | [
"https://softwareengineering.stackexchange.com/questions/71654",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23334/"
] | In my team, we don't do formal code reviews. We tend to think that it's enough with pair programming and rotating pairs often.
Should we consider doing formal code reviews?
What would be the advantages?
| We do code reviews a bit different (maybe).
We come up all programmers together (every Friday) and look what we have done in a weeks period. Then we chose what projects we want to review so that every done/in progress project would have at least one or few people. Then in hour or so we look at the changes that was m... | I don't have a lot of experience in reviewing in your environment. We don't do a lot of pair programming here we do code reviews to spread knowledge of the software in the team, have another pair of eyes to pick out the mistakes and have a formal point to check if the software sticks to our coding guidelines.
The fir... | https://softwareengineering.stackexchange.com |
337,091 | [
"https://mathoverflow.net/questions/337091",
"https://mathoverflow.net",
"https://mathoverflow.net/users/121674/"
] | Let <span class="math-container">$W_t$</span> be a standard Brownian motion. Let <span class="math-container">$T$</span> be the terminal date, <span class="math-container">$X_T=x$</span>, and
<span class="math-container">$$
dX_t=f_tdt+B_tdW_t
$$</span>
where <span class="math-container">$f_t$</span> and <span class="ma... | The are surely many ways to do this. One classical example of this kind of process is the Brownian Bridge from <span class="math-container">$0$</span> to <span class="math-container">$x$</span>, given by the SDE
<span class="math-container">$$
dX_t = \frac{x - X_t}{1-t}dt + dW_t.
$$</span>
This is solved by <span cla... | (Cross-listed on Math Stackexchange) So I think I figured out an answer to my question. Here is an example where <span class="math-container">$f$</span> and <span class="math-container">$B$</span> are not necessarily zero.
Let <span class="math-container">$Y_t$</span> be some Ito process with <span class="math-contai... | https://mathoverflow.net |
7,256 | [
"https://electronics.stackexchange.com/questions/7256",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2099/"
] | I want to remove the Vcc pin from a USB cable and connect my computer to a device. My goal is to allow the device to communicate with the computer while not charging the device.
Does some section of the USB spec permit this?
Is my plan flawed in some way?
<ol>
<li>Will communication fail to happen?</li>
<li>Is the de... | Yes, communication should fail - the reason is, devices are not allowed to feed any current into D+ or D- (which is how they communicate) until they observe Vbus (the 5V) high. This is actually guaranteed by the cable in many cases, because the device will 1) only have power from Vbus, and 2) not be connected to D+/D- ... | The spec allows a device to expect to have 100mA available.
<ol>
<li>Communication should not fail.</li>
<li>No, no device should pull power from D+.</li>
<li>I often design devices to use the USB power to power whichever chip I use as an interface. This means that without 5V power my communication chip does not power... | https://electronics.stackexchange.com |
1,185,656 | [
"https://math.stackexchange.com/questions/1185656",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/180222/"
] | I understand that the eigenvalues of a positive definite matrix must be positive, but if the matrix isn't diagonalizable, does this still hold?
Also, it doesn't seem like the reverse would be true but I can't think of a counterexample, so that would also be helpful.
Thank you!
| There are lots of ways to solve this problem. Here is a relatively straightforward srategy.
We are given that $T:\Bbb R^3\to\Bbb R^3$ is the linear map satisfying
\begin{align*}
T(0,1,1)&=(2,-1,1) & T(2,-1,0) &=(1,1,0) & T(-1,0,0)&=(1,-1,1)
\end{align*}
We wish to find a formula for $T(\vec x)$. To... | <strong>Hint:</strong> Notice that $(0,1,1)$, $(2,-1,0)$, and $(-1,0,0)$ form a linearly independent set. On top of that, $(2,-1,1)$, $(1,1,0)$, and $(1,-1,1)$ form a linearly independent set. That means you already know $T$ with respect to the first basis (first set of vectors I wrote), and you know that it maps to an... | https://math.stackexchange.com |
35,845 | [
"https://mechanics.stackexchange.com/questions/35845",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1530/"
] | I am using Volkswagen Vento. Its one of abs sensor damaged. Is it possible to repair the sensor. One sensor worth 4k.
During the first time the abs warning lights were disappear after pump the break pedal 10 times. Now the warning light is on.
Model : 2013
Location : India
Sensor Location : Right Back
| If the sensor itself is damaged it would be a challenging task (if not impossible) to repair it.
There could be also other causes. I would suggest you to check the following things:
<ol>
<li>Most of times just the abs ring needs to get cleaned. The ring is on the backside of the wheel hub. Remove the brake disc, then... | Hi Even me too faced the same problem with front right sensor. Sensor life is good however, it can go faulty. But most of the time cleaning the ring in the hub may clear the problem. Sensor cannot repair. You can get one from Skoda Rapid since both are similar vehicle. Check the model.
| https://mechanics.stackexchange.com |
47,413 | [
"https://stats.stackexchange.com/questions/47413",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/16545/"
] | Is it possible to extract fixed effects in the fixed effects model in Stata?
I know that in R I can do something like this with <code>fixef</code> command:
<pre><code>withinmodel <- plm(formula=y~x,data=Data, model="within")
summary(fixef(withinmodel))
</code></pre>
But is it possible in Stata?
| As an alternative you can also use the <code>areg</code> command which will give you the same estimated fixed effects as <code>xtreg</code>. Taking up the previous example:
<pre><code>webuse nlswork
areg ln_w grade age c.age#c.age ttl_exp c.ttl_exp#c.ttl_exp tenure c.tenure#c.tenure 2.race not_smsa south, a(idcode)
pr... | The previous answer seems to be confusing fixed effects meta-analysis with a fixed effects panel data regression, which is what is being done in R.
In Stata you can obtain estimates of the fixed effects using the -predict- command
<pre><code>webuse nlswork
xtset idcode
xtreg ln_w grade age c.age#c.age ttl_exp c.ttl_e... | https://stats.stackexchange.com |
2,583,551 | [
"https://math.stackexchange.com/questions/2583551",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/409319/"
] | The question is to find set of all positive values of a for which the series $$\displaystyle\sum_{n=1}^{\infty}\left[\frac{1}{n}-\tan^{-1}\left(\frac{1}{n}\right)\right]^{a}$$ converges. Looking at $a_n $ I am just confused how to proceed.Which test I should try?
| Note that:
$$tan^{-1}\left(\frac{1}{n}\right)=\frac{1}{n}-\frac{1}{3n^3}+o\left(\frac{1}{n^3}\right)$$
thus
$$\frac{1}{n}-tan^{-1}\left(\frac{1}{n}\right)=\frac{1}{3n^3}+o\left(\frac{1}{n^3}\right)$$
therefore the series converges for $$a>\frac13$$
| We have
$${1\over n}-\arctan\left(1\over n\right)=\int_0^{1/n}\left(1-{1\over1+x^2}\right)dx=\int_0^{1/n}{x^2\over1+x^2}dx$$
and, for $n\ge1$, we have
$${1\over6n^3}=\int_0^{1/n}{x^2\over2}dx\le\int_0^{1/n}{x^2\over1+x^2}dx\le\int_0^{1/n}x^2dx={1\over3n^3}$$
so
$${1\over6}\sum_{n=1}^\infty{1\over n^{3a}}\le\sum_{n... | https://math.stackexchange.com |
522,878 | [
"https://physics.stackexchange.com/questions/522878",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167281/"
] | So far in my thermodynamics lecture course, my understanding of the laws of thermodynamics is that the first law is about the conservation of energy, the second law says entropy must always increase or stay the same which apparently results in the fact you can never achieve 100% efficiency of heat engines, unless at <s... | The fact that a heat engine cannot be 100% efficient is a consequence of the Kelvin-Plank statement of the second law, which can be summarized as
<strong>Kelvin-Plank Statement of Second Law</strong>
"No heat engine can operate in a <em>cycle</em> while transferring heat with a single heat reservoir" (my emphasis on <... | If you can convert all of the heat to work, you're reducing entropy by definition (<span class="math-container">$\Delta S = \frac{Q}{T}$</span> , If <span class="math-container">$Q<0$</span> then <span class="math-container">$\Delta S < 0$</span>).
If you allow yourself to let some heat flow into somewhere cold... | https://physics.stackexchange.com |
21,107 | [
"https://dba.stackexchange.com/questions/21107",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2502/"
] | I want to shutdown one node in RAC. I did the following steps:
<ol>
<li>Shutdown database instance
<code>export ORACLE_SID=mydb1<br>
sqlplus / as sysdba<br>
shutdown immediate;</code></li>
<li>shutdown ASM instance
<code>. oraenv<br>
+ASM1<br>
sqlplus / as sysasm<br>
shutdown immediate;</code></li>
</ol>
But shows... | I found the solution.
--------------------------------------To shutdown
----------shutdown database instance first
<pre><code>$. oraenv
>mydb1
>/u01/app/oracle/product/11.2.0/db_1
$sqlplus / as sysdba
SQL> shutdown immediate;
</code></pre>
---------stopping Oracle Clusterware, It will shutdown ASM instance... | DISCLAIMER : Not an Oracle DBA
Use <code>srvctl</code>, the grid control program that allows you to manipulate parts of the RAC Cluster
<pre><code>Usage: srvctl <command> <object> [<options>]
commands: enable|disable|start|stop|relocate|status|add|remove|modify|getenv|setenv|unsetenv|config
... | https://dba.stackexchange.com |
204,557 | [
"https://softwareengineering.stackexchange.com/questions/204557",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/58153/"
] | A common operation in JavaScript is to replace an object method with a new one while still calling the original method. This is often done like this:
<pre><code>var originalMethod = obj.method;
obj.method = function(arg) {
// call original method
originalMethod.call(this, arg);
// do my stuff new stuff
}
<... | <strong>In layman's words:</strong>
<ul>
<li>Not all users use all of a company's apps</li>
<li>Different users have different needs</li>
<li>Why force an user to buy a full package when he/she needs only a part ? (Ok, Google apps are free, but other software maker's aren't.)</li>
<li>Having those apps separate makes ... | Users expect a mobile app to perform a single task, or a small set of very related tasks.
The mobile platforms that you mention started particularly as phone OS's. Typically users performs many short tasks on their smartphone throughout the day. This is totally different from desktop computers. This short bursted usag... | https://softwareengineering.stackexchange.com |
291,644 | [
"https://mathoverflow.net/questions/291644",
"https://mathoverflow.net",
"https://mathoverflow.net/users/120136/"
] | "Let <span class="math-container">$G$</span> be a transitive group of permutations on a given set of letters. Let a new fixed letter be adjoined to every permutation of <span class="math-container">$G$</span>. Then a transitive group <span class="math-container">$H$</span> of permutations on the combined set of le... | Updated: In the finite case (as in the reference), the only examples are $\mathrm{AGL}(1,q)$ for $q$ a prime power.
This follows, for example, by "Lucchini, Mainardis, Stellmacher, Transitive permutation groups with cyclic point stabilizers of maximum order. Geom. Dedicata 100 (2003), 117–121."
| Let the cyclic group on question have order $k-1.$ In the event that $k$ is a prime power, the multiplicative group $F_k^*$ of the field of order $k$ is cyclic on the non-zero elements and is the stabilizer of $0$ in the affine group of all non-constant transformations $f(x)=mx+b$ which acts transitively on the $k$ e... | https://mathoverflow.net |
7,828 | [
"https://electronics.stackexchange.com/questions/7828",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1841/"
] | I need to solder some headers onto an Arduino shield - what's the recommended wattage for working on that scale? I ask because the shield is already populated with ICs and I don't want to burn them out.
| Selecting an iron that is too low in wattage requires the user to apply heat for a longer amount of time. This actually makes the surrounding area heat up more than if a more powerful iron were used to heat the component. Although a <strong>25W iron</strong> will likely do this job without any trouble, and <strong>80W ... | The correct choice is a sufficiently powerful temperature-controlled iron (50W, say) set to the right temperature for the solder used, with an appropriate size tip. I use Metcal equipment and they recommend a tip roughly the same size as the item being soldered, for optimum heat transfer.
| https://electronics.stackexchange.com |
229,499 | [
"https://stats.stackexchange.com/questions/229499",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/127465/"
] | Let <strong>a, b</strong> be real numbers randomly selected independently and uniformly from the range of (0,1).
What is <strong>P(a < b)</strong>?
The problem here is that <strong>a</strong> can be equal to <strong>b</strong>, so is
<strong>P(a < b) ≈ 0.5</strong> or
<strong>P(a < b) → 0.5</strong> ... | If $a$ and $b$ are independent and identically distributed as $U[0,1]$, then $P(a \lt b) = 0.5$. It is also true that $P(a \le b) = 0.5$, because $P(a = b) = 0.$
In fact, if $a$ and $b$ are independent and identically distributed from any continuous distribution on the real numbers, then $P(a \lt b) = 0.5$, $P(a \le b... | For independent continuous $U(0,1)$ random variables we have (taking into account that their density is constant and equal to $1$)
$$P(a<b) =P(a\leq b)= \int_0^1 \int_0^b da\,db = \int_0^1(b-0)\, db $$
$$=\int_0^1b\, db = \frac 12 b^2 \big|^1_0 = \frac 12\cdot1^2 - \frac 12\cdot 0^2 = \frac 12$$
| https://stats.stackexchange.com |
528,340 | [
"https://electronics.stackexchange.com/questions/528340",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/264969/"
] | I've just bought a 12V 260mA electromagnet and I have some questions about it
<ol>
<li>I don't know why, but when I connect electromagnet, my 12V power source (9V and 2 1.5V AA batteries in series) drops to 8V. I suspect that this is because of the protection of the 9V battery, because the 9V battery drops to 5V wherea... | Your plan of using 9v "transistor radio" batteries is not workable for this purpose.
Probably the minimum suitable would be a series collection of some number of AA cells. It's better that you use conventional flashlight batteries and not lithium for such a learning process.
A voltage divider is not really s... | <ol>
<li>The 9V battery can't supply the current you need for the electromagnet, at least not for a long time; it is too small. The voltage will drop almost immediately, and the battery won't last long.
</li>
<li>The electromagnet has a coil, an inductance, and there will be a kickback when you disconnect it. You will ... | https://electronics.stackexchange.com |
130,740 | [
"https://mathoverflow.net/questions/130740",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29850/"
] | If $X$ is a compact oriented surface in a 4-dimensional oriented manifold $M$, then the self-intersection number $X^2$ of $X$ is given by the integral over $X$ of the Euler class of the normal bundle. In the case of $CP^1$ embedded in $CP^2$, the normal bundle is isomorphic to the Hopf bundle, therefore $X^2$ can be ob... | You can find $\mathbb CP^1$ in a wide variety of $4$-manifolds having any Euler class you like. One really simple way is to take the connect-sum of $k$ copies of $\mathbb CP^2$. The idea is to embed $\mathbb CP^1$ in the connect sum so that you are simultaneously breaking the $\mathbb CP^1$ up as a connect sum in all... | Take your favorite complex line bundle $L$ over $\newcommand{\bCP}{\mathbb{CP}}$ $\bCP^1$. Form the rank-two complex vector bundle $E\to\bCP^1$ defined as the direct sum of $L$ with the trivial line bundle $\newcommand{\uc}{\underline{\mathbb{C}}}$ $\uc\to\bCP^1$
$$ E=L\oplus \uc. $$
Now form the projectivization ... | https://mathoverflow.net |
68,788 | [
"https://electronics.stackexchange.com/questions/68788",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10456/"
] | Reading Hennessy's book "Computer Organization and Design" it is mentioned "Register.Rd" and "Register.Rs" but what does it mean? The .Rd, .Rt and .Rs parts I can't understand, on page 365:
<img src="https://i.stack.imgur.com/XEg7P.png" alt="enter image description here">
| They are just generic ways of referring to cpu registers:
<ul>
<li>Rd is usually denotes a destination register.</li>
<li>Rs, Rt usually denote source registers.</li>
</ul>
For example, a cpu instruction could be:
<code>add Rs,Rt,Rd</code>
Which would mean: <code>Rd = Rs+Rt</code>
The Rd,Rs,Rt are placeholders fo... | I'm not very familiar with this exact subject, but within instruction sets tables for microcontrollers these conventions are often used:
<ul>
<li>rd : destination register</li>
<li>rs : first source register</li>
<li>rt : second source register</li>
</ul>
This looks quite similar with your quote.
| https://electronics.stackexchange.com |
368,485 | [
"https://stats.stackexchange.com/questions/368485",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/140965/"
] | I've been researching Generative Models recently, and Probabilistic Graphical Models.
Every time I read about Generative Models, I see they're trying to predict <span class="math-container">$P(x,y)$</span> or equivalently <span class="math-container">$P(x|y)$</span> and <span class="math-container">$P(y)$</span>, and ... | Of course generative models work for continuous variables. Especially, you can extend any regression model with a prior distribution on x and a specific noise model on y to yield a generative model for that situation.
As an example for simple linear 1D regression x->y you could additionally assume that x comes from ... | I am also thinking about this problem. What kind of model would you get if you make the output of Gaussian discriminant model continuous, namely:
<span class="math-container">\begin{align*}
\boldsymbol y_{(i)} &\sim \mathcal N (\mu_1, \sigma^2) \\
[X_{(i)}, \boldsymbol y_{(i)}] &\sim \mathcal N(\boldsymbol\mu... | https://stats.stackexchange.com |
29,130 | [
"https://stats.stackexchange.com/questions/29130",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8401/"
] | In the context of neural networks, what is the difference between the learning rate and weight decay?
| The learning rate is a parameter that determines how much an updating step influences the current value of the weights. While weight decay is an additional term in the weight update rule that causes the weights to exponentially decay to zero, if no other update is scheduled.
So let's say that we have a cost or error f... | In addition to @mrig's answer (+1), for many practical application of neural networks it is better to use a more advanced optimisation algorithm, such as Levenberg-Marquardt (small-medium sized networks) or scaled conjugate gradient descent (medium-large networks), as these will be much faster, and there is no need to ... | https://stats.stackexchange.com |
78,118 | [
"https://physics.stackexchange.com/questions/78118",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/27898/"
] | As I understand it (from a lay physics perspective), quantum entanglement has been experimentally demonstrated - it is a reality. As I understand it, you can measure something like the spin of an electron and know that its entangled pair will, in that same instant, no matter where in the universe it is, have the opposi... | This 'spooky action at a distance' will not and can not lead to communications technologies. The point is that the correlation between the two states cannot be used for information transmission. The two observers can influence each others' observations, but they can never communicate their own observations to the other... | To rephrase Danu answer, you can not use the correlation of these entangled particles before you have exchanged some information with another (subluminal) device.
The main problem comes from the fact that the outcome of a measurement is random, so there is no way to agree beforehand on how to interpret a measurement do... | https://physics.stackexchange.com |
3,174,020 | [
"https://math.stackexchange.com/questions/3174020",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/356885/"
] | The first part is crystal: A, which is the subset of the real numbers set is bounded iff... but that's where I get lost.
As far as I'm aware, if <span class="math-container">$A$</span> is a set, then <span class="math-container">$|A|$</span> is the amount of elements it has. What exactly does the definition part mean?... | Here, <span class="math-container">$|A|$</span> no longer stands for the cardinality of <span class="math-container">$A$</span>. Instead, <span class="math-container">$A$</span> is the set obtained by taking the absolute value of all the elements in <span class="math-container">$A$</span>. So, as you've written,
<span... | The claim depends on a <em>new, different</em> meaning of the notation <span class="math-container">$|A|$</span>, namely the one it defines after "where".
Is it perhaps clearer for you if we use a different notation?
<blockquote>
Let <span class="math-container">$f : \mathcal P(\mathbb R)\to\mathcal P(\mathbb R)$</... | https://math.stackexchange.com |
125,981 | [
"https://chemistry.stackexchange.com/questions/125981",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/64580/"
] | My lecturer said that the increasing flexibility of an alicyclic ring is an inherent property. I'm not entirely sure what they mean by flexibility. Number of feasible conformations? How far the bond angles can be away from non-ideal?
Is there an actual explanation for the increasing flexibility?
| <strong>It's geometry and you can get a petty good intuition by building simple models of the molecules</strong>
Saturated carbon-carbon bonds have two key properties of relevance. The angle between a pair of bonds on a carbon prefer to point to the corners of a perfect tetrahedron (~109.5 ° between each bond) if ther... | The answer is simple. You have a potentially much larger number of rotatable bonds between any two atoms. Cyclopropane is very inflexible, simply because every atom is joined to every other by a single bond. Each extra atom added to its ring gives you an extra pivot point about which the bonds can rotate.
So large ... | https://chemistry.stackexchange.com |
82,657 | [
"https://dba.stackexchange.com/questions/82657",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/27870/"
] | I have in production a MySQL table <code>pageviews</code> with 4M rows that records page views of users on posts. I need to know which posts a specific user have read, but this request takes up to 15 seconds to execute:
<pre><code>SELECT post_id
FROM pageviews
WHERE user_id = 981
GROUP BY post_id
</code></pre>
Here i... | In addition to @tombom's suggestions, <strong>creating an index on <code>(user_id, post_id)</code></strong> instead of (or in addition, but the less indexes the better) separate indexes on user_id and post_id will simplify the query, probably <strong>getting rid of the filesort and temporary table</strong>, plus giving... | Why have an <code>id</code> at all? Why not have <code>PRIMARY KEY (user_id, post_id)</code>?
Why have <code>user_id</code> and <code>post_id</code> nullable? Shouldn't they be <code>NOT NULL</code>?
@jynus is right about a covering index, but if you change the PK as I suggest, that separate index won't be necessar... | https://dba.stackexchange.com |
18,463 | [
"https://quantumcomputing.stackexchange.com/questions/18463",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/14802/"
] | This might be a straightforward problem for you guys; it would be helpful if you can explain it in simple language.
I have <span class="math-container">$n$</span>-qubits given as
<span class="math-container">$$\frac{1}{\sqrt{2}} \left(|0\rangle+ e^{\iota\theta_{1}}|1\rangle \right) \otimes \frac{1}{\sqrt{2}} \left(|0\r... | The idea is that you want to use the adiabatic theorem. This states (roughly) that if your Hamiltonian <span class="math-container">$H(s)$</span> has an energy gap <span class="math-container">$\Delta(s)$</span> between the ground and excited states, then provided
<span class="math-container">$$
\frac{d\Delta}{ds}\ll\e... | <strong>What is <code>τ(s)</code> and <code>s</code> in Schrödingers equation</strong>
Let me break it down for you:
We know <code>s(t)</code> is the "way" in time to change from state 1 to 0.
That of course happens for different cases faster or less fast. So you get different "long" ways to achieve... | https://quantumcomputing.stackexchange.com |
54,147 | [
"https://mechanics.stackexchange.com/questions/54147",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3138/"
] | Does it require expensive machinery and/or a lot of space? I've considered doing it in the past for mine and my friends vehicles but never seriously investigated it.
| To do it manually you need a bead breaker, a manual tire changing tool, and a manual wheel balancer, plus some basic tools. The tire changing tool uses a lot of leverage, so you'll need to fix it to concrete or similar. They're not expensive tools, but it mounts up, and you're never going to be up to the speed of the p... | Depends on the vehicles, sizes/profiles of tyres etc. Once a wheel is secured some tyres can be changed relatively easily with just levers etc. However most would be a struggle and others near impossible.
Pneumatic car tyre replacement machinery doesn't really take up much room, but it is expensive. With a little tra... | https://mechanics.stackexchange.com |
17,041 | [
"https://datascience.stackexchange.com/questions/17041",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/426/"
] | I recently had a phone interview with a consumer tech company for a quant position. The question was basically, "imagine a facebook style social network site. Six months ago a new feature called 'mentions' was added which allows you to tag your friends with an @ sign. How would determine whether this feature was a succ... | This question (something I've asked variants of several times in interviews) has absolutely nothing to do with statistical or other quantitative procedures. What is being asked here is for an understanding of the overall data mining process itself. The first thing to determine is what the definition of success. So you... | Personally, I don't think this question is reasonable. The first thing you need to do is determine from the stakeholders what "success" is. This could be increase traffic, increase revenue, etc. Without knowing how the stakeholders view success you can find all kind of interesting things in whatever data you have and ... | https://datascience.stackexchange.com |
18,309 | [
"https://electronics.stackexchange.com/questions/18309",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4067/"
] | So I think this is going to be some kind of sensor... :P
I'm looking for ideas on the best way to measure a dispensed volume of .1uL from the tip of a pipette
This is for a open source medical liquid handler =] ...<br>
- Fluid will be mostly transparent<br>
- Pipette tips can be clear or black<br>
- Will be measuring... | I suspect that the best solution is likely in the physical design of the pipette mechanism rather than in active electronic control based on feedback from the fluid itself.
Another possibility would be to use a stepper motor on your peristaltic pump.
In general though, precise metering of fluids is something that the... | I think a <strong>digital caliper's sensor</strong> may be the right tool to measure the micropipette's <strong>piston displacement</strong>. Resolution is in the order of 1/100th mm, so that should agree with 10\$^{-1}\mu\$l.
| https://electronics.stackexchange.com |
5,289 | [
"https://biology.stackexchange.com/questions/5289",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/1677/"
] | That is to say, are there cells that, between infancy and adulthood, get larger? Or is all growth done entirely via cell division? I'm wondering if it is safe to assume that the approximate number of cells per unit mass in a mammal will remain fairly constant throughout its lifespan.
| <blockquote>
I'm wondering if it is safe to assume that the approximate number of cells per unit mass in a mammal will remain fairly constant throughout its lifespan.
</blockquote>
<em>Not exactly.</em> When a tissue is put under stress, it can respond in four main ways:
<ol>
<li><strong>Hypertrophy</strong> - ind... | This is not my field so I am sure there are other examples, but certain neurons will definitely be larger in adulthood than in infancy. There are motor neurons that connect the spine to, for example, the toes. These will grow in length as an animal grows. So, in a human infant they will be a few centimeters long and ca... | https://biology.stackexchange.com |
173,379 | [
"https://security.stackexchange.com/questions/173379",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/161637/"
] | Is it possible to use an exported OpenPGP private key to sign a file via OpenSSL?
I've tried this:
<pre><code>$ gpg2 --export-secret-keys --no-armor 84E2C2E5 > secret.key
$ openssl rsautl -sign -in testfile -inkey secret.key -out test.sign
</code></pre>
But that gives me this error:
<blockquote>
unable to load... | While OpenPGP and X.509 mostly share the same cryptographic algorithms, they have completely different representations of the key material. GnuPG (or to be more specific, <code>gpg</code>; <code>gpgsm</code> implements S/MIME and X.509 but not OpenPGP and is also part of GnuPG) does not "speak" X.509, OpenSSL does not ... | You need to convert the key to the correct format -
<pre><code>gpg2 --export-secret-keys
--export-options export-reset-subkey-passwd,export-minimal,no-export-attributes
--no-armor 84E2C2E5 | openpgp2ssh 84E2C2E5 > id_rsa
</code></pre>
Why are you trying to do this? Why not just sign the document with g... | https://security.stackexchange.com |
436,184 | [
"https://softwareengineering.stackexchange.com/questions/436184",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/234727/"
] | I am filled with questions pertaining to the situations where a desktop-application hangs, possibly for minutes.
I've got this complicated game-engine written in c++. Several times during development, I've accidentally found an infinite loop during testing and the program causes the entire system to hang, usually for a... | Theoretically, it is the responsibility of the OS to stop any single application from impacting the rest of the system through resource starvation. However, this is a complicated problem and as you have discovered, there are numerous failure cases. The OS should at least be able to minimize the chance of any permanent ... | Perhaps a list of possible ways a program can hang itself and/or the system would help:
<ul>
<li>CPU overload -- but usually the OS gives other things time slices too, unless you have grabbed real time priority</li>
<li>memory overload -- swap can make this better or worse (usually worse); mitigation is to tune your OO... | https://softwareengineering.stackexchange.com |
132,699 | [
"https://mathoverflow.net/questions/132699",
"https://mathoverflow.net",
"https://mathoverflow.net/users/32796/"
] | Suppose we have a Brownian motion(or transition density) on a Lie group G and a Riemmanian manifold H on which G acts transitively and isometrically. Can we construct a Brownian motion( or transition density) on H?
Any help will be useful.
| This question is not as trivial as some people think.
One point is that a quotient of a Markov chain is not Markov in general; there is a certain condition that has to be satisfied. More precisely, if $\pi_x$ are the transition probabilities of a Markov chain on a space $X$, and $X\to \overline X,\; x\mapsto \overlin... | Fix $x \in M$. Since $G$ acts transitively and isometrically on $M$, there exists a left-invariant metric on $G$, that makes the map $\pi: g \in G \to gx \in M$ a Riemannian submersion. If you project the left invariant Brownian motion on $G$ by $\pi$, you get a Brownian motion on $M$ started at $x$.
In this construc... | https://mathoverflow.net |
13,091 | [
"https://electronics.stackexchange.com/questions/13091",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | Quick question: is using a capacitor rated for high voltage (let's say 35 V) in a system that, let's say, supplies 5 V (like for LEDs or what have you) dangerous?
Since it can store up to 35 V, will it like somehow store a bunch and then release it at once, damaging the system, or it is OK to use a higher-rated capacit... | While not a perfect analogy, think of the voltage on the capacitor similar to the liter capacity of a tank. It will hold "35 V" but you needn't fill it completely. But like @JustJeff said, you'd be wise to ensure the container can hold more than necessary to prevent spills (and in an electrolytic capacitor's case, the ... | No, having a higher rated cap will not somehow store up more voltage than is available in the circuit. You actually want a cap with a slightly higher voltage rating than the highest voltage you expect to put across it. In fact, if you put more voltage on a cap than it is rated for, it is apt to catastrophically fail, i... | https://electronics.stackexchange.com |
36,114 | [
"https://scicomp.stackexchange.com/questions/36114",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/35806/"
] | In particular, I want to focus on finding the volume <span class="math-container">$V$</span> because I will need it to start working on solving the centre of mass
This <span class="math-container">$3D$</span> homogenous body (Torus section) is defined by
<span class="math-container">$$x^2 + \left(\sqrt{y^2+z^2}-5\right... | Here is a corrected and slightly improved code, set up here for calculation of the full torus volume to verify the result.
<pre><code>import numpy as np
from scipy import random
def func(x,y,z):
return x**2 + (np.sqrt(y**2 + z**2)-5)**2
def MCvolume(N=1000):
#Limits of Integration
x_min = -2
x_max = ... | You are missing an integral part of what makes up a Monte Carlo integration.
The steps to integrate the area (in your case volume) are, to generate random samples, across the whole domain which includes the wanted volume, (which you did). Now, you want to sum up all the dots that are <em>within</em> the region you want... | https://scicomp.stackexchange.com |
234,108 | [
"https://dba.stackexchange.com/questions/234108",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/176562/"
] | I understand that you use foreign keys to relate rows from one table to the other and if this foreign key also becomes a primary key of that table then it is a primary foreign key.
But, for example, if a hotel <strong>records the date and time of check-ins for each customer</strong>, and each customer has a customer ... | <blockquote>
should I include the customer ID as a primary foreign key or just a foreign key?
</blockquote>
It can't be a "primary foreign key" because a <code>PRIMARY KEY</code> is always <code>UNIQUE</code> (and <code>NOT NULL</code>) and presumably a customer can check in again, perhaps at a different day or time... | There is already an accepted answer. This answer may shed new light on the topic.
Look up "shared primary key". This is a design technique that is often used when there is a relationship that is one-to-one, and mandatory in one direction but optional in the other. IS-A type relationships fit this pattern. For exam... | https://dba.stackexchange.com |
2,406,516 | [
"https://math.stackexchange.com/questions/2406516",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/309566/"
] | The identity $\frac{1}{2^n}\binom{n}{n}+\frac{1}{2^{n+1}}\binom{n+1}{n}+...+\frac{1}{2^{2n}}\binom{2n}{n}=1$ arises from a question on probability in my textbook. A proof by induction on $n$, which exploits the fact that $\binom{a}{b}+\binom{a}{b+1}=\binom{a+1}{b+1}$, is straightforward but not enlightening.
Is it pos... | Suppose you are flipping a coin until you get $n+1$ heads or $n+1$ tails. For $k=0,\dots,n$, what is the probability that you are done after exactly $n+1+k$ flips?
If the last flip was a tails, this means that in the former $n+k$ flips there were exactly $n$ tails, and this happens with probability $\frac{1}{2}\cdot\f... | <strong>Updated Solution</strong>
Here's a neater solution!
$$\begin{align}
\sum_{k=0}^n \frac 1{2^{n+k}}\binom {n+k}n
&=\frac 1{2^{2n}}\sum_{k=0}^n \binom {k+n}k 2^{n-k}\\
&=\frac 1{2^{2n}}\sum_{k=0}^n \binom {k+n}k \sum_{j=0}^{n-k}\binom {n-k}j\\
&=\frac 1{2^{2n}}\sum_{l=0}^n \binom {2n-l}{n-l}\sum_{j=0... | https://math.stackexchange.com |
160,387 | [
"https://mathoverflow.net/questions/160387",
"https://mathoverflow.net",
"https://mathoverflow.net/users/48273/"
] | Would anyone be able to recommend text books that give an introduction to Geometric Representation Theory and survey papers that give an outline of the work that has been done in the field? I'm looking for references that would be suitable as a follow up to James Humphrey's "Linear Algebraic Groups" and a first year gr... | I would encourage you to consider "Representation Theory and Complex Geometry" by Chriss and Ginzburg. In particular, I think you might enjoy the realization of irreducible representations of the Weyl group of a complex semisimple group $G$ on the Borel-Moore homology of the fibres of the Springer resolution of the nil... | Additionally to Peter Crooks answer I would recommend to study the book of Hotta and others :
D-Modules, Perverse Sheaves, and Representation Theory
Here you can learn about derived categories and perverse sheaves/d-modules (which are essential tools to study geometric representation theory) and how they are connected... | https://mathoverflow.net |
64,102 | [
"https://security.stackexchange.com/questions/64102",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/52774/"
] | Considering <strong>OpenVZ</strong>, <strong>KVM</strong> and <strong>Xen</strong>:
<em>Which VM technology is the most difficult for the host's administrators to access given an <strong>encrypted</strong> root partition?</em>
Can I have a reasonable expectation that rogue administrators cannot become root inside my ... | With KVM and Xen, the rogue administrator can take a snapshot of your live machine, then explore at his leisure what is in the RAM of your VM. In particular, he will easily obtain the encryption keys for the encrypted filesystem, and then proceed to read all your files. By the very nature of the snapshot system, you wi... | Regardless of what virtualization technology you use. Once the attacker has access to the hardware, it's game over. In case of a VPS, even when encrypting the root partition, if the key is stored in memory and you have no control of the hypervisor, then you cannot protect your system's confidentiality with encryption.
... | https://security.stackexchange.com |
283,209 | [
"https://physics.stackexchange.com/questions/283209",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/131639/"
] | We're learning about normal forces and I came up with the following scenario. Its conclusion doesn't make sense, and I was wondering where I went wrong in my assumptions?
If you put a book on a table, the table exerts a normal force on the book, the book in turn exerts a normal force on the table (Newton's Third Law).... | If you draw a free body diagram for the book, the forces acting on the book are its weight (downward gravitational force) $W_B$ and the upward force exerted on the book by the table $N_B$. So the force balance on the book is $$W_B-N_B=0$$
If you draw a free body diagram for the table, the forces acting on the table... | No, the force exerted downwards is just the weight of the table and book together. What you called N_B is W_B.
| https://physics.stackexchange.com |
528,519 | [
"https://physics.stackexchange.com/questions/528519",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/252025/"
] | After spending quite a lot at understanding ,I could still not help myself in clearing this doubt-In free electron sea model used in electrodynamics the actual motion of electrons causes current to flow but as we move to band theory how the simple jump causes current to flow?Simply put, why an electron jump from valenc... | From <span class="math-container">$\vec F= m\vec a$</span>, we know that direction of <span class="math-container">$\vec F$</span> and <span class="math-container">$\vec a$</span> are same.
Let's define a unit vector such that <span class="math-container">$$\vec u = \frac{\vec F}{|\vec F|} = \frac{\vec a}{|\vec a|}$$... | Since <span class="math-container">$\vec F= m\vec a$</span> this would imply <span class="math-container">$| \vec F|= m|\vec a|$</span>. And since magnitude of a vector is scalar, we can say <span class="math-container">$$m=\frac{|\vec F|}{|\vec a|}$$</span>
| https://physics.stackexchange.com |
328,740 | [
"https://softwareengineering.stackexchange.com/questions/328740",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/101923/"
] | I'm lead on a team with a half-dozen senior engineers. I very much believe it would benefit us greatly to do code reviews for all the standard reasons. Not necessarily every change but at least a steady stream of background reviews. So people at least see other's changes and start talking about them.
Is there a good w... | This is not a problem of tooling or process. It's about culture. You describe a team that is comprised of people who are sensitive of criticism and protective of their own work. It's very, <em>very</em> common. But it is not professional.
My advice is to start leading by example. Offer your commits for review. Be open... | The first step would be to walk up to someone and say "hey, would you review my code?". Be the change you want to see in your organization. If you can't find a single individual willing to do it, you won't be able to convince the whole team. If the two of you have some success, report back to the team.
Once you've fo... | https://softwareengineering.stackexchange.com |
489,857 | [
"https://physics.stackexchange.com/questions/489857",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236156/"
] | The legs of the world's fastest man (Usain Bolt) can develop up to 5 times the force compared to those of normal people. What stops him from being faster? A normal healthy high-school student can complete the 100 metres in 11-13 seconds while Usain Bolt takes 9.58 seconds. If Usain Bolt's legs can exert so much more f... | Human legs carry their actuation muscles along their length, which establishes their rotary inertia about the knee and hip joint. this inertia limits the speed with which the runner can swing his or her legs back and forth, which limits the speed at which they can run.
Adding muscle mass for more strength adds inerti... | Force at a point in time is all very well, but most of the time a running man's feet (even Usain's) are not touching anything and exerting no force at all. You need to calculate what the average force is over the total time he is running.
I would expect that the 1 or two second slower high schooler's are exerting a lo... | https://physics.stackexchange.com |
108,722 | [
"https://physics.stackexchange.com/questions/108722",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28958/"
] | Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. It is then often said that the Goldstone boson's live in the coset. In what sense is this statement true? The Lagrangian ... | I understand the statement in the following way:
Pions, which are pseudo-goldstone bosons of chiral symmetry breaking, are described by the introduction of a unitary matrix $U(x)$, defined as
$$U(x)=\text{exp}\left(2i\pi^a(x)T^af_\pi^{-1}\right),$$
where $\pi^a$ is the pion field, $f_\pi$ is the pion decay constant... | It is in fact a very simple matter if you use a different parametrization of the fields. Since we care about the Goldstone bosons only, just send $\lambda\rightarrow \infty$ so that the Higgslike state decouples. Moving to the following parametrization<br>
$$
\phi_i(x)=U(x)\langle \phi_i\rangle \,,\qquad U(x)=e^{i \ha... | https://physics.stackexchange.com |
138,081 | [
"https://mathoverflow.net/questions/138081",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4149/"
] | Consider the real algebraic group $SO(p,q)$, this is the automorphism group of the vector space $\mathbb{R}^n$ of dimension $n=p+q$ over $\mathbb{R}$, endowed with the diagonal quadratic form with $p$ pluses and $q$ minuses on the diagonal and with a nonzero skew symmetric $n$-form.
Now consider the corresponding sp... | To expand on my comment to the question, we have the following algebraic construction (I think originally due to Robert Brown, 'A characterization of spin representations'):
Let $V$ be a quadratic space over a field $k$ of characteristic $\neq 2$. Attached to this is the Clifford algebra $C=C(V)$: it is equipped wit... | It seems that you are asking for descriptions of the groups $\mathrm{Spin}(p,q)$ as algebraic groups. This can certainly be done explicitly for low values of $p$ and $q$, but I don't know a general process that works well when $p$ or $q$ is large.
For low values, the exceptional isomorphisms turn out to provide good ... | https://mathoverflow.net |
2,935,387 | [
"https://math.stackexchange.com/questions/2935387",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/448441/"
] | In my exam preparation I'm currently stuck at this task:
Let <span class="math-container">$X_1,..,X_5$</span> be i.i.d random variables each having uniform distributions in the interval (0, 1)
Find the probability that <span class="math-container">$X_1$</span> is the minimum and <span class="math-container">$X_5$</span... | Let us consider the general case of <span class="math-container">$n$</span> independent random variables (instead of 5), and let <span class="math-container">$x_1=a$</span> and <span class="math-container">$x_n=b$</span>. Then the probability that all <span class="math-container">$n-2$</span> variables <span class="mat... | Your method fails because the events <span class="math-container">$X_1<X_2$</span> and <span class="math-container">$X_1<X_3$</span> are not independent.
Per the given distribution and independence, the probability that any two of the random vars are equal is <span class="math-container">$0$</span>. Hence one o... | https://math.stackexchange.com |
1,547,904 | [
"https://math.stackexchange.com/questions/1547904",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/291763/"
] | Question:
<blockquote>
Marks obtained by certain number of students are assumed to be
normally distributed with mean 65 and variance 25. If three students
are taken at random, what is the probability that exactly two of them
will have marks over 70?
</blockquote>
The textbook way to solve it is:
Finding the p... | This is correct and the proof is straightforward:
$\implies$: $A \cap B \subseteq A$ is trivial. If $x \in A$, then $x \in B$, by hypothesis. So $x \in A \cap B$ and $A \subseteq A \cap B$.
$\impliedby$: We have $A = A \cap B \subseteq B$.
| Assume $A\subseteq B$ and let $x\in A\cap B$, then $x\in A$, therefore $A\cap B\subseteq A$. Conversely, let $x\in A$, since $A\subseteq B$, $x\in B$ and $x\in A\cap B$, therefore $A\subseteq A\cap B$. Finally, one has: $A\cap B=A$.
Assume $A\cap B=A$, let $x\in A$, then $x\in A\cap B$ and $x\in B$. Therefore, $A\subs... | https://math.stackexchange.com |
514,474 | [
"https://electronics.stackexchange.com/questions/514474",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/161323/"
] | I have a negative voltage which I want to measure using an ADS1115, but it can t measure negative voltages.
Can anyone recommend a simple schematic / device etc which is capable to just invert the polarity and not affect the voltage? E.G. If input is -(minus)1.5V I want to transform it into +1.5V
Thank you in advance
| The actual connector part will fit without problems - a 4mm banana connector always fits the same across all vendors.
Unfortunately the plastic protection is not standardized - I experience problems every now and then. Either the plastic is too long or the thicker part of the connector starts too early or the tiny plas... | They're all the same 4mm diameter banana hole same diameter shroud and a compatible springy pin.
For a phase sequence meter choosing plugs with a shroud that's deep enough to fully protect the pin is probably important.
| https://electronics.stackexchange.com |
256,806 | [
"https://security.stackexchange.com/questions/256806",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/269651/"
] | I got a mesh router downstairs. Aoes a switch protect your network if connected to the mesh router?
| Depends on the capabilities of the switch, Arisa for example have ACL support and some firewall capabilities on it, so depends on the product basically.
| Switch just connects network parts. It is not a firewall. If you mean "can switch provide protection like firewall", then the answer is NO.
| https://security.stackexchange.com |
99,602 | [
"https://security.stackexchange.com/questions/99602",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/86100/"
] | I see a lot of people say to hash for the token on email verification when dealing with member registration.
<em>I am wondering, if the email token is only to activate the account and nothing else, would the email token still need to be hashed ? Or do I need to hash the email token?</em>
<strong>My thought</strong>:... | The discussion you are linking actually says that you should <strong>not</strong> hash your token, you must only ensure that it is long and random enough, quoting Tom Leek:
<blockquote>
Don't compromise, use a good PRNG. Don't try to make something
yourself by throwing in hash function and the like; only sorrow l... | Generate a cryptographically secure random string (e.g. 128 bits) and use this for the token.
On the server side, you can hash this using SHA-256 and store it. That way, if anyone performs a successful SQL injection attack or the like, they will not be able to use any of the tokens retrieved. Again, the token supplied... | https://security.stackexchange.com |
101,620 | [
"https://electronics.stackexchange.com/questions/101620",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/32556/"
] | Is my thinking correct.
Below is a simple diagram of the concept I want to check.
<img src="https://i.stack.imgur.com/JYItk.jpg" alt="enter image description here">
Is this:
1: Possible
2: Feasible? I.E are there any concerns or foreseen issues with this design?
Edit:
<img src="https://i.stack.imgur.com/2d5zA.jpg" ... | It will work fine as long as gray and brown wires are not present at the same time.
The diodes are redundant, they don't fix anything - they will prevent a short-circuit present when both green and brown wires are attached, but the output won't be 12V.
I don't see why you simply won't keep the 12V parallel connectio... | On the second diagram why don't you add the fifth diode between battery A and B so that the power supplied from D4 & D2 doesn't short the 12V output/motor output due to the grey wire that connects the two wires D2&D4. I think the fifth diode can separate the and allow the flow of series to flow from negative to... | https://electronics.stackexchange.com |
643,698 | [
"https://electronics.stackexchange.com/questions/643698",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/326846/"
] | I'm trying to decide on pin mapping (forgive me if this is the wrong term) for a PIC32MZ1024EFF100, but this isn't something I've ever done before.
There are 32 GPIOs and 8 Analog inputs that need to be connected. I want to ensure they are connected to the optimal pins of the MCU, but I don't know how to tell what is ... | In case there are no critical EMC or high speed signal issues, then normally the software engineer is allowed to dictate which pins to use and group them as per how the GPIO peripheral port registers are defined in the MCU. That is, your option "Connect them to pins that share the same register inside the PIC"... | <strong>Where</strong> you have options, you can give some thought to physical connections if you expect layout to be gnarly, or you can give some thought to logical arrangement if you expect to need to wring the last bit of speed out of the MCU, but often these days it's not so important - we often have luxurious amou... | https://electronics.stackexchange.com |
394,828 | [
"https://softwareengineering.stackexchange.com/questions/394828",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/308741/"
] | Currently, whenever I am developing a feature, I write the behaviour tests for it using mocks for our downstream services. These mocks are dumb always serve the same output. I faced something grave today. My BDDs were passing in my local and build environment. Therefore, I went ahead and merged my changes into the 'mas... | Testing with stubs/mocks/fakes is good, but it can never fully replace system and integration tests where the real thing gets used.
If you don't have enough control over the external service to reliably use it in an automated integration test, then you should perform a manual integration test <em>before</em> you merge... | Not having separate QA is a very bad thing. At the most basic level, the software developer wants the software to work to demonstrate they did a good job, and the QA person wants the software to <em>not</em> work to demonstrate they did a good job. You can't do both at the same time.
| https://softwareengineering.stackexchange.com |
89,802 | [
"https://mathoverflow.net/questions/89802",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21785/"
] | I've been trying to find, without much success, 4 triangles whose corresponding sides are congruent that cannot be folded into a tetrahedron.
Anyone has any clue how to approach this problem?
| What do you mean by "corresponding sides"? If what you mean that you have a gluing diagram which is consistent, just take your triangles $ABC, ABD, ACD, BCD$ in such a way that the angles at $A$ in all three triangles sharing that vertex is $5\pi/6,$ and otherwise the three triangles with vertex at $A$ are isosceles (s... | A tetrahedron with congruent faces will have all acute face angles. No obtuse or right angles.
| https://mathoverflow.net |
99,975 | [
"https://softwareengineering.stackexchange.com/questions/99975",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6559/"
] | In C and C++ (and I guess other languages that allow taking a "reference" to an array element or something similar), when you have an array like type, accessing individual elements of such an array can be done "directly" or via a temporary reference or pointer.
Example:
<pre><code>// Like this:
for(int i=0; i<n; +... | Each approach has advantages.
The temporary reference approach has the advantage that you get to name the reference. This can provide additional information to help make the code more self-explanatory. It also eliminates having multiple instances of the same expression to access the variable.
The no-reference approac... | There is nothing wrong with taking those temporary references - in fact it may be preferable in some cases because you can name the reference. If that particular reference has a particular role that may not be immediately obvious from the array index then the name will add clarity.
If the discussion centers around "p... | https://softwareengineering.stackexchange.com |
241,239 | [
"https://softwareengineering.stackexchange.com/questions/241239",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/125088/"
] | So we use hexadecimal which has the advantage of going up to 15 in single digits A-F, but why is it an issue that it takes 2 digits to represent the number 10 in decimal?
I was reading up about hexadecimal and I came across these 2 lines:
<blockquote>
Base 16 suggests the digits 0 to 15, but the problem we face i... | Because 15 was the maximum value of a "word" at one point in time. A "word" refers to (among many other things over the years) the number of bits that a CPU is designed to operate on as a single thing. 4 bits toggled 1111 makes the binary value of 15.
Hexadecimal was created with the explicit purpose of being able to ... | It's an awkward way to phrase it, but it's only a "problem" when you're trying to write hexadecimal numbers. It's not a problem in decimal. If you used <code>10</code> instead of <code>A</code> in hexadecimal, then <code>100</code> could be parsed as <code>1 0 0</code> or <code>10 0</code>, which are two very differe... | https://softwareengineering.stackexchange.com |
1,811,303 | [
"https://math.stackexchange.com/questions/1811303",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/262797/"
] | F-test statistic is the ratio of two variance and if the value of F-test statistic equals to 1 that means that those two variance are equal and we accept the null hypothesis.But when we want to check the equality of several mean we perform F-test.Here F-test statistic is the ratio of between mean sum square and within ... | You already know that $[Z,Z]_t = \int_0^t \sigma^2(s) \,ds$ for any Itô process $$dZ_t = b(t) \, dt + \sigma(t) \, dW_t.$$ Moreover, the quadratic covariation is defined via the polariation formula, i.e.
$$[X,Y]_t = \frac{1}{2} [X+Y,X+Y]_t - [X,X]_t-[Y,Y]_t. \tag{1}$$
Since both $(X_t)_{t \geq 0}$ and $(Y_t)_{t \geq ... | It looks like there is a missing Brownian term in your expression for $X(t)$
If so then the only term that will appear in the quadratic variation is the product of the two random terms as these are effectively order $dt$, with all order terms in the product now higher order Hence the resulting quadratic variation wil... | https://math.stackexchange.com |
435,451 | [
"https://stats.stackexchange.com/questions/435451",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/39829/"
] | At a certain men's college, the probability that a student selected at random on a given day will require a hospital bed is <span class="math-container">$\dfrac {1}{5000}.$</span> If there are <span class="math-container">$8000$</span> students, how many beds should the hospital have so that the probability that a stud... | <span class="math-container">$X$</span> is binomial and we try to find the minimum <span class="math-container">$n$</span> that satisfy the following: <span class="math-container">$P(X>n)\leq 0.01$</span>, i.e. number of ill students is larger than number of beds in the hospital. This is equivalent to <span class="... | <em>Comment continued:</em> In case the 'search' implied by the brackets <code>[ ]</code> in R is not clear, and in order to show how well the Poisson approximation to the binomial distribution works in this example, here is a table of relevant Poisson and binomial CDFs.
<pre><code>x = 1:10; p.pr = ppois(x, 8/5); b.pr... | https://stats.stackexchange.com |
1,363,882 | [
"https://math.stackexchange.com/questions/1363882",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/255027/"
] | I am aware that the area under the curve of $\frac{1}{x}$ is infinite yet the area under the curve of $\frac{1}{x^2}$ is finite.
Calculus and series wise, I understand what is going on, but I can't seem to get a good geometric intuition of the problem.
Both curves can be shown to converge to $0$ (the curves themselve... | I do not think there is any geometric intuition behind the convergence you mentioned. As much as there is no geometric intuition which can help solving Zeno's paradox of the Tortoise and Achilles.
Indeed, the convergence is due to how the integral is defined - in terms of Riemann sums (here I assume you are talking a... | I made drawings of both functions.
With respect to 1/x^2 I was very strict: I calculated the area under the straight line connecting ( 1,1) and (2,1/4) and so on. This gives two series that are both convergent by comparison with the series 1, 1/2, 1/4 ....The area of this series is larger than the area we are interest... | https://math.stackexchange.com |
267,683 | [
"https://softwareengineering.stackexchange.com/questions/267683",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12402/"
] | It's drilled into the newbie Java programmers that Java (<em>pre-Java 8</em>) has no multiple class inheritance, and only multiple interface inheritance, because otherwise you run into diamond inheritance problem (<em>Class A inherits from classes B and C, both of which implement method X. So which of those classes' im... | The fundamental difference is that Java defines conversions from a type to any of its supertype as being identity-preserving. This is a useful property to have, but it is incompatible with multiple inheritance. If <code>d1</code> and <code>d2</code> both derive from <code>b</code>, and <code>thing</code> is of a type... | There's nothing fundamental in the internal design which causes this. The lack of multiple inheritance is a deliberate design decision in Java, not an external manifestation of a shortcoming in the internal design.
(I'm deliberately avoiding getting into the flame war as to whether multiple inheritance is a good idea ... | https://softwareengineering.stackexchange.com |
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