text stringlengths 49 10.4k | source dict |
|---|---|
white-holes, exotic-matter
Title: Are white holes made of exotic matter I have recently watched Kurzgesagt in a Nutshell's video on Wormholes https://www.youtube.com/watch?v=9P6rdqiybaw and I have been thinking about white holes, and exotic matter.
As I understand, white holes are an exact opposite of black holes, Bla... | {
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b^2 = c^3 = d^n = bcd = 1
with n=3,4,5 respectively. Explicitly:
A_4: n=3, b = (1 2) (3 4), c = (1 2 3), d = (2 3 4)
[any double transposition and 3-cycle will do]
S_4: n=4, b = (1 2), c = (2 3 4), bc = (1 2 3 4)
A_5: n=5, b = (1 5) (2 3), c = (1 3 4), bc = (1 2 3 4 5)
We can use bcd=1 to solve for any one of the... | {
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"openwebmath_score": 0.8611697554588318,
"tags": n... |
thermodynamics, energy, earth, thermal-radiation
@Benjohn has given you the correct answer. Here is my take.
The ultimate heat provider of the earth ( except a small percentage of heat from the magma at the center of the earth) is the sun. It pours down at the surface about 1.2 kilowatts of energy per meter square ( w... | {
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I'd suggest the following approach: $$\lim_{n\to\infty} \frac{\sqrt{n+1} (1+n^2)}{\sqrt{n} (2 +n^2+2n)}=\lim_{n\to\infty} \frac{\sqrt{n+1}}{\sqrt{n}}\lim_{n\to\infty}\frac{ (1+n^2)}{(2 +n^2+2n)}$$ This holds, since both limits do exist (which we have to prove!). The first one is $$\lim_{n\to\infty} \frac{\sqrt{n+1}}{\s... | {
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condensed-matter, resource-recommendations, anyons
The overall style is clear and pedagogical, with emphasis on symmetry and simplicity.
If you wish to read about the construction of quantum computation theory using anyons, the paper Topological quantum computation will be of use.
A set of lectures transcribed into a... | {
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"tags": "condensed-matter, resource-recommendations, anyons",
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python, beginner, parsing, xml
validComplex = True
for j in range(len(specialtypes[ctype]["requireds"])):
spname = specialtypes[ctype]["requireds"][j]
if not((cname + "_" + spname) in datavals) or len(datavals[(cname + "_" + spname)])<=0:
validComplex = False
... | {
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c++, c, unit-testing, reinventing-the-wheel, floating-point
if (signedResult == '-' && result != 0) result = -result;
return result;
}
As far as correctness goes, there is only one flaw I have spotted, but there are structural problems that you might want to fix. (The error I found is that you only allow a capit... | {
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"tags": "c++, c, unit-testing, reinventing-the-wheel, floating-point",
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} |
c#, parsing, .net
Title: C# Logical and Math expression parser I needed a simple parser that could do both logical and math operations expressed in a string, as well as being able to use variables stored in json.
None of what I found online seemed to do all of the above, so I came up with my own. Below is the source c... | {
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-------------------------------------------------
$\displaystyle \begin{gathered} V = xyzr^{ - 7} \hfill \\ \hfill \\ \frac{{\partial V}} {{\partial x}} = yzr^{ - 7} - 7xyzr^{ - 8} \frac{{\partial r}} {{\partial x}} = yzr^{ - 7} - 7x^2 yzr^{ - 9} \hfill \\ \end{gathered}$
thus:
$\displaystyle \frac{{\partial ^2 V}} ... | {
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ros, real-time, ros-melodic, ethercat
In any case it seems like you're asking whether it would be possible to make this run "fast enough".
In my experience that would be difficult, especially if you start using pub-sub in your critical (messaging) path.
The infrastructure was just not designed nor implemented for this... | {
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javascript, node.js, validation
First off, the joining and splitting is not needed here. You can accomplish the same thing with phoneNumber.replaceAll(/\D/g, '')
But more importantly - what useful thing does this function do? When I call sanitizeNumber I don't end up with a sanitized phone number - I end up with a san... | {
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There is a unique $\mathbb C[X]$-algebra morphism from $A$ to $\mathbb C[T]=\mathbb C[X]/(p(X))$. Denote this morphism by $f(z)\mapsto f(T)$. If $f(z)$ is in $A$, then the unique representative of $f(T)$ in $\mathbb C[X]$ of degree less than $\deg p(X)$ is $$\sum_{i=1}^k\ \ \underset{X=\lambda_i}\heartsuit\left( \Big(\... | {
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"lm_q2_score": 0.8791467785920306,
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"openwebmath_score": 0.9421183466911316,
"ta... |
everyday-chemistry, plastics, toxicity
Bisphenols - These are variations of 2,2-bis-(dihydroxyphenyl)propane (which is the infamous Bisphenol A or BPA). Bisphenol A is the monomer for most of the original formulations of high-impact polycarbonate, such as Lexan. Again, when heated, the polymer breaks down and leaches ... | {
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Also, we've counted the line $$BC$$ $${3 \choose 2} = 3$$ times, so we need to subtract 2.
Overall, we have $${11 \choose 2} - ({4 \choose 2} - 1) - ({3 \choose 2} - 1) = 55 - 5 - 2 = 48$$ lines.
• A nice idea. Thank you! Aug 11 '20 at 10:02
If we take any pair of points we get $${11\choose2}= 55$$ lines: But some o... | {
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"openwebmath_score": 0.7714780569076538,
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Probability that none of the letters is placed in the correct envelopes
This is a derangement problem. An Inclusion-Exclusion arguments shows that the number of ways of placing none of the five letters in its correct envelope is
$$5! - \binom{5}{1}4! + \binom{5}{2}3! - \binom{5}{3}2! + \binom{5}{4}1! - \binom{5}{5}0!... | {
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"lm_q1q2_score": 0.8403348659895197,
"lm_q2_score": 0.8519528057272543,
"openwebmath_perplexity": 151.78200787978946,
"openwebmath_score": 0.8836026787757874,
"ta... |
ros, ros-comm
Originally posted by billy on ROS Answers with karma: 1850 on 2016-06-03
Post score: 0
Original comments
Comment by gvdhoorn on 2016-06-16:
If you feel your question has been answered, please indicate that by ticking the checkmark to the left of the answer. That will clearly mark the question as answere... | {
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c#, asp.net-mvc
Title: A service that returns paged Products with optional filtering In order to better understand what the code does, I've captured this screencast.
Basically, I have a products page and a user can filter products.
CODE
Here is the Page action method on my ProductController:
public ActionResult Page(S... | {
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quantum-field-theory, greens-functions, correlation-functions, propagator
Title: What information is contained in spectral density function in QFT? I have been thinking lately about the following question. In quantum field theory, we define spectral density function $\rho(\mu^2)$ using two-point function as follows (K... | {
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"url... |
ros, ardent
Original comments
Comment by William on 2018-06-01:
@GregB can you accept and answer or ask for more clarification? Thanks!
The closest equivalent to what ros::package::getPath() returns in ROS 1 is what we call the package's "share directory", which is essentially the package's "install prefix" plus a st... | {
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machine-learning, gradient-descent, momentum, adam, optimizers
* $\nabla_w J$ is the gradient of $J$ with respect to $\mathbf{w}$. By writing it this way, it also describes the goal of the update explicitly within the notation i.e. to minimise a function that is parameterised by $\mathbf{w}$. | {
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thermodynamics, work, reversibility
Title: Understanding Callen's eq. (4.9) and the maximum work theorem I'm currently reading Herbert B. Callen's Thermodynamics and an Introduction to Thermostatics, II ed, and I don't quite understand the last few propositions made on page 105 (a scan attached below).
Consider a subs... | {
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Further, actually it is not necessarily that $s(f,P)=S(f,P)$ for an integrable function $f$.
• Yeah. I forgot that sup and inf hahaha and was considering $|f|$ too (missed placed in here). Thanks for the help! – Corrêa Feb 11 '18 at 20:06
For $n>1$ and $k=0,1,2...n,$
let $$x_k=a+k\frac {b-a}{n}.$$
$f$ is integrable... | {
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apache-spark, scala
Title: How to calculate the mean of a dataframe column and find the top 10% I am very new to Scala and Spark, and am working on some self-made exercises using baseball statistics. I am using a case class create a RDD and assign a schema to the data, and am then turning it into a DataFrame so I can ... | {
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Now take the squares $\frac 12$ and $\frac 13$: these go onto the top shelf.
On the second shelf go $\frac 14$ to $\frac 17$. These fractions are all less than $\frac 14$, so fit onto the second shelf. Likewise, squares from $8$ to $15$ go onto the third shelf, each $\frac 1n$ is smaller than $\frac 18$, and so forth.... | {
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"lm_q2_score": 0.8872046026642944,
"openwebmath_perplexity": 359.25799202759464,
"openwebmath_score": 0.9259559512138367,
"ta... |
php, security
$action = ' voted';
if ($changing_vote === 1) {
$action = ' changed vote';
}
if ($anonymous_vote === 1) {
$action .= ' anonymously';
}
if ($change_vote === 1) {
$act... | {
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# Show that limit does not exist (two variables)
I just started looking into multiple variable calculus and limits involving them. I'm not amazing at limits either.
I want to answer this question:
Show that the following limit does not exist
$$\lim_{(x,y)\to (0,0)}\frac{x^2y^2}{x^2y^2+(x-y)^2}$$
So, my working:
$... | {
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"lm_q2_score": 0.865224072151174,
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"openwebmath_score": 0.8499876856803894,
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data-structures, priority-queues, lower-bounds
Title: Lower bounds: queues that return their min elements in $O(1)$ time First, consider this simple problem --- design a data structure of comparable elements that behaves just like a stack (in particular, push(), pop() and top() take constant time), but can also return... | {
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"tags": "data-structures, priority-queues, lower-bounds",
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polymers
Title: What do people mean with "per unit volume" in polymer solutions theory? I am reading Modern Theory of Polymer Solutions by Hiromi Yamakawa and in the context of the virial expansion the following puzzles me a bit:
"...expanded in terms of solute concentration $c$ (in gramms per unit volume)...
"...Thus... | {
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ros, ros2, ekf, navsat-transform-node
In navsat yaml replaced utm* with
broadcast_cartesian_transform_: true
broadcast_cartesian_transform_as_parent_frame_: true
provided map->odom transform from topic odometry/gps as
self.create_subscription(Odometry, 'odometry/gps', self.__og_sensor_callback, 10)
....
def __og_... | {
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algorithms, time-complexity, arrays, partitions, subset-sum
Title: Partition array into k subsets We are given an array and a number K. Partition array into K subsets such that
let MaxSum be the maximum sum of among subsets.
We have to minimize summation =$$\sum_{i=1}^{k}MaxSum-sum(i) $$
Is this problem polynimial ti... | {
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Let $$h>0$$ be given and consider the problem of computing the integral $$I = \int_{-h}^h f(x)dx.$$ The midpoint rule takes the form $$M_h = 2h f(0).$$ We will now obtain the familiar error formula by studying the auxiliary function $$g$$ given by $$g(x) = \int_{-x}^x f(t) dt - 2x f(0).$$ This function is interesting p... | {
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python, beginner, object-oriented, xml
#def __getparams(member):
class param:
def __init__(self,param):
self.name=param.attrib['name']
self.value=param.attrib['value']
cmd= command("""<basis core="external.ws.ws" service="bimepasargad" content="33,444" name="Internalissuance" source="cmsD... | {
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sql, sql-server
If values in one column-pair can appear in other column pairs, then change the UNION to UNION ALL.
If the values can be duplicated in a column-pair, then add DISTINCT to each SELECT.
Do both DISTINCT and UNION ALL if you need to.
The idea is to make the data as small as possible before you start doing ... | {
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we write the summation as:
$$\left[\left(n+2\right)!-2.\left(n+1\right)!\right]+\left[\left(n+1\right)!-2.n!\right]+\cdots+\left[4!-2.3!\right]+\left[3!-2.2!\right]$$
$$\sum_{r=1}^{n}r.\left(r+1\right)!=\left(n+2\right)!-2-\sum_{r=1}^{n}\left(r+1\right)!$$
So finding an expression for it is in essence the same as fin... | {
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"openwebmath_score": 0.7973054051399231,
"tag... |
Does this mean that $\sqrt{n\mu}$ is a good approximation to $E[\sqrt{|Y_n|}]$ for large $n$? Well, we can do better than this. As @Henry notes, assuming everything is positive, we can use $E[\sqrt{Y_n}]=\sqrt{E[Y_n]-\text{Var}(\sqrt{Y_n})}$, together with $E[Y_n]=n\mu$ and the approximation $\text{Var}(\sqrt{Y_n})\app... | {
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"lm_q1q2_score": 0.8021189213945742,
"lm_q2_score": 0.8128673223709251,
"openwebmath_perplexity": 212.44440304015205,
"openwebmath_score": 0.9221125841140747,
"ta... |
matlab, filter-design, finite-impulse-response, infinite-impulse-response, bandpass
I have a feeling that this is not correct.
For the bilinear IIR I went to matlab's "butter" function.
[b,a] = butter(4,[0.6 0.8],'stop');
For this part I know I need to use both 'butter' and 'impinvar' together but I don't know how.... | {
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... |
java, game
if (endDir == null) {
// No end room
}
} else {
// No start room
}
this.randomlyAddDoors(grid);
return grid;
}
private CoreRoom getRoomGen() {
CoreRoom r = null;
int max = 0;
if (rooms != null) {
for (CoreRoom x : rooms) {
if (!(x.... | {
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"openwebmath_score": null,
"tags": "java, game",
"url": null
} |
ios, swift, audio
Title: Music player in Swift I made a simple mp3 player that plays, pauses and stops a given song, shows the time elapsed, and has a volume control. I read the documentation and can't figure out the difference between the pause and stop methods, although I have configured them to work as I want (i.e... | {
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"tags": "ios, swift, audio",
"url": null
} |
php
I definitely wouldn't want to base my CoreObject off of ArrayObject...that is far too much stuff for something really intending to only provide some common methods for other classes. I like to think of CoreObject as being stdClass or Object in Java, but for the framework. Essentially, it is only meant to provide... | {
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ros, jointstate
Title: How to write my own joint state
Hello all
i have a real robot. using ROS. i have a problem with (Joint State Publisher)
i understand that i should write my own (joint state publisher node). i read the related tutorials but i do not get how to convert encoders' messages to joint state message.
... | {
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"tags": "ros, jointstate",
"url": null
} |
quaternion
Title: How do I get the displacement vector from one object to another?
I have two objects A and B, each in the form of geometry_msgs/PoseStamped.
I would like to calculate the displacement (translation & rotation) vector that I can apply to any (similar) object A' and arrive to a (similar) object B' (resp... | {
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ros2
Originally posted by marguedas with karma: 3606 on 2020-02-14
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by jlepers on 2020-02-14:
Thank you, I was trying something similar.
Is it possible that I need to install ROS2 by source to use rosidl_default_generators instead of... | {
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computability
Title: Understanding Whether a Set is an Index Set I'm struggling to grasp the intuition behind the concept of an index set. By definition, a set $I$ is called an index set if $\forall i,j: i \in I$, $\phi_i = \phi_j \implies j \in I$. This implies that if we have a program with indices $i \in I$ and a d... | {
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"tags": "computability",
"url": null
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\displaystyle \begin{aligned} &\langle u,av+bw\rangle=a\langle u,v\rangle+b\langle u,w\rangle,\\ &\langle u,v\rangle=\langle v,u\rangle,\\ &\langle v,v\rangle\ge0, \end{aligned}
for all ${u,v,w\in V}$ and ${a,b\in{\mathbb R}}$. To be a true inner product, the positive definite property that ${\langle v,v\rangle}$ is s... | {
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"t... |
ros, build, rosjava
Originally posted by jrd on ROS Answers with karma: 46 on 2012-09-04
Post score: 0
OK, problem solved, turns out that the rosjava depends on several ROS (mainly low level communication) libraries.
so i copied folder /opt/ros/fuerte/include (from ROS barebones installation for Ubuntu) onto Mac, exp... | {
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Now when two or more witnesses claim the defendant is guilty, they are either all reliable or all unreliable, depending on the defendent's guilt.
So, the probability that all $n$ witnesses claim guilt, when the defendant is guilty, is the probability of all witnesses being reliable: $$\mathsf P(W_n\mid G) = \underline... | {
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"openwebmath_score": 0.9964965581893921,
"tags"... |
php, twitter-bootstrap
Title: Styling and activating radio buttons on condition I have some php code to style a button and activate it, when a specific variable is true.
It's actually a radio button, styled with the bootstrap to a button.
As you can see below, this is how it looks when the variable is '1'.
Also, the b... | {
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"tags": "php, twitter-bootstrap",
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} |
matlab, butterworth
Title: Butterworth Polynomial from Butterworth Filter For the butterworth filter, in Matlab command:
[B,A]=butter(2,0.5,'low')
I find this result:
B = [0.29289 0.58579 0.29289]
A = [1 -3.33067e-16 0.17157]
From here I cannot reach the Normalized Butterworth polynomial:
G = [1 1.4142 1]
No... | {
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"tags": "matlab, butterworth",
"url": null
} |
quantum-algorithms, programming
Title: Is running a for loop faster on a quantum computer than a classical computer? Curious to understand if I run for loop within a quantum algorithm, and lets say I want the quantum algorithm to run in classical run time of O(1). Can this be done? No, quantum computers can't run for-... | {
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"tags": "quantum-algorithms, programming",
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use the square root calculator below to find the square root of 7 The result includes 2. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History. We can also rewrite them using radicals !. Topics include negative exponents, powers of zero, simplifying rational expressions,... | {
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"id": null,
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"lm_q1_score": 0.9881308796527184,
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"openwebmath_score": 0.7000554203987122,
"tags... |
Similarly, for the 2-2-1 combination we have: 5C2 * 3C2 * 1C1 * 3!/2! = 90 different arrangements.
Finally, we will get 60+60+90 = 210 arrangements if we consider 1-1-1 to be a valid option - since the question does not explicitly exclude this possibility.
Could you please explain why we ignored 1-1-1 combination?
_... | {
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"lm_q1_score": 0.9532750413739076,
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"openwebmath_score": 0.8652944564819336,
"tags": ... |
c++, statistics, machine-learning
template <typename T>
class activation_function
{
public:
T identity(T value)
{
return value;
}
long double sigmoid(T value)
{
T negative_value = -1 * value;
long double exponential = exp(negative_value);
long double result = 1 / (1... | {
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"tags": "c++, statistics, machine-learning",
"url": null
} |
quantum-mechanics, angular-momentum
Title: Is the angular momentum of the ceiling fan quantized? According to quantum mechanics, any quantum angular momentum is quantized in units of $\hbar$. Does it mean that the angular momentum of the ceiling fan (due to its rotation) is quantized? If yes, what does it physically m... | {
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-
Welcome back! ${}{}$ – MJD Dec 16 '13 at 1:33
I'm having trouble understanding the first line of matrices. And the third line. And what M^n is. – JShoe Dec 21 '13 at 5:15
@Jshoe $\ M$ is the matrix being raised to power $n$. That first matrix equality is very easily proved by induction, using the fib recurrence. Th... | {
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"tags"... |
Let $$A$$ be any subset of the $$x$$-axis, and let $$z$$ be any point of the $$x$$-axis not in $$A$$. You can indeed separate $$A$$ and $$z$$ by disjoint open sets by first choosing a basic tangent disk nbhd of $$z$$ and then choosing for each $$x\in A$$ a sufficiently small tangent disk nbhd; there is no need to restr... | {
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"lm_q1_score": 0.970687770944576,
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"openwebmath_score": 0.8688656091690063,
"tags... |
javascript, jquery, dom
Obviously, this code isn't complete and is missing a lot of functionality from the original, but I wanted to get some outside eyes and opinions on where I'm going with the refactored code before continuing to write it. If you need any additional information, I'd be happy to provide it. Breaking... | {
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python, vcf, snp, gwas
HOR_11431 HOR_4138 HOR_2290 HOR_15788 HOR_7552 HOR_10775 HOR_3153 HOR_14689 HOR_11126 HOR_2180 HOR_2369 HOR_1044 HOR_21428 HOR_18220 HOR_3359 HOR_15778 HOR_15840 HOR_18364 HOR_9250 HOR_11922 HOR_3926 HOR_7474 HOR_12830 HOR_5020 HOR_11450 HOR_9492 HOR_5373 HOR_18913 HOR_12791 | {
"domain": "bioinformatics.stackexchange",
"id": 1508,
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"openwebmath_score": null,
"tags": "python, vcf, snp, gwas",
"url": null
} |
graph-theory, approximation
Title: Max-cut equivalence with most likely assignment to an Ising model Ising Model
$$
Pr(x; \lambda) = \frac{1}{Z(\lambda)} \exp \left( \sum_{ij \in E} \lambda_{ij} x_{ij} \right)
$$
In which $\lambda_{ij} \in \mathbb{R}$, and
$$
x_{ij} =
\begin{cases}
1 & x_i = x_j\\
-1 & x_i \neq x_... | {
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In the same way, we show that for $x>0$ , $f = \frac{\pi}{2}$ .
Thus the values are $-\frac{\pi}{2} \mbox{ and } \frac{\pi}{2}$
The range of $\arctan x$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2} \right)$. I think this is correct. But if $f$ is constant on $\mathbb{R} \ \backslash \{0 \}$, wouldn't $f(x)= c$ for all $x$... | {
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"ta... |
# How can I prove this proposition from Peano Axioms: (Cancellation law). Let a, b, c be natural numbers such that a + b = a + c. Then we have b = c.
Peano Axioms.
Axiom 2.1
$0$ is a natural number.
Axiom 2.2
If $n$ is a natural number then $n++$ is also a natural number. (Here $n++$ denotes the successor of $n$ a... | {
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The quadratic equation will have the form:
$$\left (x- \left (\alpha^3+\frac{1}{\beta^3} \right) \right ) \cdot \left (x- \left (\beta^3+\frac{1}{\alpha^3}\right ) \right) \text{ ,with } \alpha, \beta \neq 0$$
You just have to substitute $\alpha$ and $\beta$.
We have $\alpha+\beta=-b$ and $\alpha\beta=c$.
Let $\gam... | {
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"openwebmath_perplexity": 223.90737031070896,
"openwebmath_score": 1.0000035762786865,
"ta... |
rust, iterator, trait
Title: Extend iterators with until() function I want to extend generic iterators with a convenience function until() that works like an inversion of take_while().
Here is the code:
Cargo.toml:
[package]
name = "until"
version = "0.1.0"
edition = "2021"
# See more keys and their definitions at ht... | {
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"tags": "rust, iterator, trait",
"url": null
} |
strings, parsing, assembly, ip-address
movq %rsi, %rax
shlq $8, %rsi
andq %r8, %rax
subq %r9, %rax
jb nlr3
mulq %r11
shrq $48, %rax
addq %rax, %rcx
shlq $8, %rsi
nlr3:
movq %rsi, %rax
shlq $8, %rsi
andq %r8, %rax
subq %r9, %rax
shrq $56, %rax
addq %rax, %r... | {
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"tags": "strings, parsing, assembly, ip-address",
"url": null
} |
If our polynomial has a root, say at $a$, then $f(a) = 0$, so we may take $y = a$.
This takes care of all polynomials that have a real root (which includes ALL polynomials of odd degree, and SOME polynomials of even degree).
Which leaves with with even degree polynomials that have no real root (like, for example, $x^... | {
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"t... |
• Intuitively I understand. But in the definition of the derivative we use $\frac{y(x)-y(x_0)}{x-x_0}$ and not $\frac{y(t)-y(0)}{x(t)-x(0)}$. That is, we must find $y(x)$ first. Otherwise, can you prove rigorously that it works with $t$? – user239753 May 4 '16 at 7:11
• Please read carefully: There is nothing intuitive... | {
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"tags"... |
&=\sum_{i=1}^q k_i\big(n_i(m-d_{s_i}) + (n_i-1)(m+k_i-d_{s_i})\big)\\ &=2\sum_{i=1}^q k_i n_i(m-d_{s_i}) + \sum_{i=1}^q \big( (n_i-1)k_i^2 - (m-d_{s_i})k_i\big). \end{split}$$ Finally, we notice that $$\sum_{i=1}^q k_i(k_i-1)/2 = m(m-1)/2 - \sum_{i=1}^q (m-d_{s_i})k_i$$ since $$m=k_1+k_2+\dots+k_q$$ and $$m-d_{s_i} = k... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9817357237856483,
"lm_q1q2_score": 0.8597913761275524,
"lm_q2_score": 0.8757869916479466,
"openwebmath_perplexity": 262.4721762348263,
"openwebmath_score": 0.8546452522277832,
"tag... |
javascript, jquery
Title: Highlight input if empty This snippets works, but I think it can be optimized:
/* highlight input, if it is empty */
$(function() {
var highlight_if_no_val=function () {
$(this).toggleClass('highlight-input', !$(this).val());
}
$('#id_index-EditForm-gpnr').keyup(highlight_... | {
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"url": null
} |
To solve $$A^TA\hat{\mathbf{x}} = A^T\mathbf{b},$$ we’ll use row reduction. The augmented matrix $$[A^TA\; A^T\mathbf{b}]$$ is:
$\begin{split}\begin{bmatrix}6&2&2&2&4\\2&2&0&0&-4\\2&0&2&0&2\\2&0&0&2&6\end{bmatrix} \sim \begin{bmatrix}1&0&0&1&3\\0&1&0&-1&-5\\0&0&1&-1&-2\\0&0&0&0&0\end{bmatrix}\end{split}$
Since there ... | {
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... |
of the arc length and use it in a of. Degree: 1 degree corresponds to an arc of a circle when angle! Degrees or radians for finding arc length given radius and central angles let go! To radians. 1 Discuss the formula until we convert it to radians. in s. 0.52 = 1.56 m 6 angle ) in radians and r is the of... Can use a f... | {
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"lm_q1_score": 0.984810949854636,
"lm_q1q2_score": 0.8141548250724633,
"lm_q2_score": 0.826711791935942,
"openwebmath_perplexity": 511.31422362626785,
"openwebmath_score": 0.9186582565307617,
"tags"... |
There are no simple groups of order $120$.
-
Sketch of proof. Suppose a group of order $120$ is simple. It has Sylow subgroups of order $8$, $3$ and $5$. The number of subgroups of order $5$ must be $6$, and these are permuted transitively by conjugation. This identifies the group with a subgroup of $S_6$, which can b... | {
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"lm_q1q2_score": 0.8110254257599324,
"lm_q2_score": 0.8333245932423308,
"openwebmath_perplexity": 117.9465055231813,
"openwebmath_score": 0.7087775468826294,
"... |
catkin
Edit:
@vncntmh wrote:
Get this error:
ERROR in config: /home/vincent/src has no workspace configuration file '.rosinstall'
Ah, so your source space hasn't been initialised by wstool. First do:
wstool init ~/catking_ws/src
then the wstool set .. should succeed.
Originally posted by gvdhoorn with karma: 86574... | {
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cc.complexity-theory, lower-bounds, circuit-complexity, advice-and-nonuniformity, separation
Edit: two more inclusions:
For $t(n) \ge n$ we have $\mathbf{DTIME}(t) \subseteq \mathbf{DSIZE}(t \log t)$,
and for $l(n) \ge \log n$ we have $\mathbf{NSPACE}(l) \subseteq \mathbf{DDEPTH}(l^2)$.
For proofs, see section 2-3 of... | {
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"tags": "cc.complexity-theory, lower-bounds, circuit-complexity, advice-and-nonuniformity, s... |
ros
Originally posted by vrichard on ROS Answers with karma: 108 on 2021-04-08
Post score: 0
Original comments
Comment by vrichard on 2021-04-09:
Eventually I managed ti have it working properly.
For some unknown reason, the file was missing in /opt/AutowareAuto/. I couldn't find it either in my src directory. Maybe ... | {
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"url": null
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time-series, regression
If you are interested in deep learning methods, you might find Foumani et al.'s survey paper Deep Learning for Time Series Classification and Extrinsic Regression: A Current Survey useful (disclaimer: I'm a co-author of this paper). | {
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"tags": "time-series, regression",
"url": null
} |
seurat, single-cell
Title: How to extend the x axis in Dimplot Seurat I have performed a Seurat PCA via Dimplot.
How do I extend the x axis?
As you can see in my figure the double x axes overlap. Looking at the source code for Seurat's DimPlot() it's based on ggplot2 graphics (https://github.com/satijalab/seurat/blob... | {
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"id": 2322,
"lm_label": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "seurat, single-cell",
"url": null
} |
formal-languages, regular-expressions
Title: Formal languages - exercise I'm trying to solve this exercise: given $L=\left\{a^kb^k|k>0\right\}$
determine $L^2$ and $L^3$.
So I'm able to solve this kind of exercise if k is given into a defined range but I'm really struggling to solve this exercise.
Any help? Thanks. ... | {
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"tags": "formal-languages, regular-expressions",
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• To describe the concept of transformation of vectors in Computers are well-adapted to solve such matrix problems. heading for the part that you want to be truss elements. After we define the stiffness matrix for each element, we must combine all of the elements together to form on global stiffness matrix for the enti... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9777138151101525,
"lm_q1q2_score": 0.8016210328338558,
"lm_q2_score": 0.8198933271118221,
"openwebmath_perplexity": 870.9679339298095,
"openwebmath_score": 0.996808111667... |
The fastest way to proceed is to notice that $$P_3$$, the Sylow $$3$$-subgroup, is not only normal but central. To see this, you can recall that $$N_G(H)/C_G(H)$$ is isomorphic to a subgroup of $$\mathrm{Aut}(H)$$, which has order $$2$$ in this case. The from scratch method is to notice that $$C_3$$ has only two non-id... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9840936087546923,
"lm_q1q2_score": 0.8068517960639301,
"lm_q2_score": 0.819893340314393,
"openwebmath_perplexity": 120.5692614543975,
"openwebmath_score": 0.9332165122032166,
"tags... |
$\begin{array} {rcl} {(A \cup B) - C} &= & {(A \cup B) \cap C^c \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Theorem 5.20)}} \\ {} &= & {C^c \cap (A \cup B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Commutative Property)}} \\ {} &= & {(C^c \cap A) \cup (C^c \cap B)} \\ {} &= & {(A \cap C^c) \cup (B \cap C^c)} \\ {} &=... | {
"domain": "libretexts.org",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.990874363958236,
"lm_q1q2_score": 0.8626525212515543,
"lm_q2_score": 0.8705972751232809,
"openwebmath_perplexity": 115.39302686118575,
"openwebmath_score": 0.9510489106178284,
"ta... |
quantum-mechanics, electromagnetism, electromagnetic-radiation, acceleration, charge
Title: Why does an accelerated charge radiate away energy? My textbook says:
"Neils Bohr objected to the idea of an electron orbiting a nucleus in a circular orbit. An electron experiences centripetal acceleration and an accelerated ... | {
"domain": "physics.stackexchange",
"id": 90582,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "quantum-mechanics, electromagnetism, electromagnetic-radiation, acceleration, char... |
homework-and-exercises, electrostatics, electrons
Title: The "classical radius" of the electron According to one theory, the mass m of the electron arises simply as a consequence of the electrostatic energy of its electric field, through Einstein's famous expression ε=mc^2, where ε is the field energy and c is the spe... | {
"domain": "physics.stackexchange",
"id": 17040,
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"lm_name": null,
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"tags": "homework-and-exercises, electrostatics, electrons",
"url": null
} |
equilibrium, titration
Intermediate results:
Initial amount of $HA$:
$n_0(HA) = 0.5825\ \text{mmol}$
Amount of $\ce{NaOH}$:
$n(\ce{NaOH}) \approx 0.4993\ \text{mmol}$
Final Volume:
$V(\ce{NaOH}) = 3.22\ \text{mL}\ \text{(3sf)}$ | {
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"id": 1074,
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"tags": "equilibrium, titration",
"url": null
} |
organic-chemistry, reaction-mechanism, halides, nucleophilic-substitution
Source:
Organic Chemistry - Clayden - Oxford University Press - 1st edition - Page 424
Edit: Someone in the comments section said that you can't predict which mechanism is major, and have to look for experimental facts. So, for the sake of the c... | {
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"tags": "organic-chemistry, reaction-mechanism, halides, nucleophilic-substitution",
"u... |
Did I do something wrong here?
I know if I do everything in matrix notation, I would get ${\rm Var}(\hat{\beta_1}) = \frac{\sigma^2}{\sum_i (x_i - \bar{x})^2}$. But I am trying to derive the answer without using the matrix notation just to make sure I understand the concepts.
• Yes, your formula from matrix notation ... | {
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"lm_q2_score": 0.815232489352,
"openwebmath_perplexity": 945.4690269894465,
"openwebmath_score": 0.999907374382019,
"tags": n... |
algorithms, optimization, assignment-problem
def find_matching(graph: Dict[str, Dict[str, Union[int, float]]],
matching_type=Union['max', 'min'],
return_type=Union['list', 'int', 'float', 'number'],
big_number: int = 1_000_000):
negate = -1 if matching_type == ... | {
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"tags": "algorithms, optimization, assignment-problem",
"url": null
} |
(b) Calculate $$\text{Var}[W]$$.
Solution:
Here, we use the moment generating function to generate the second moment.
$M''_{W}(t) = 0.9 \cdot e^{3t} + 1.2 \cdot e^{2t} + 0.5 \cdot e^{1t}$
$\text{E}[W^2] = M''_{W}(0) = 2.6$
We then calculate the variance by using the first and second moments that we had already cal... | {
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"lm_q1q2_score": 0.8282433457620004,
"lm_q2_score": 0.8333245932423308,
"openwebmath_perplexity": 822.2310498974961,
"openwebmath_score": 0.9948640465736389,
"tags": null... |
# Transformation of Roots for a Cubic Polynomial
Consider $$x^3 + px + q = 0$$ with roots $\alpha, \beta. \gamma$
We want to find the degree 3 polynomial that has roots : $$\frac{\alpha\beta}{\gamma}, \frac{ \alpha\gamma}{\beta}, \frac{ \beta\gamma }{\alpha}$$
My attempt so far:
$$\frac{ \alpha\beta}{\gamma} = \fra... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9808759626900699,
"lm_q1q2_score": 0.8297645987656974,
"lm_q2_score": 0.8459424334245618,
"openwebmath_perplexity": 231.44962760653493,
"openwebmath_score": 0.9039620757102966,
"ta... |
cosmology, rotational-dynamics, astronomy, dark-matter, galaxies
Title: What happens to objects along spiral galaxy arms over long periods of time? Observations of spiral galaxies reveal that objects within the same arm of a spiral galaxy move at around the same speeds, regardless of their distance from the center of ... | {
"domain": "physics.stackexchange",
"id": 96363,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cosmology, rotational-dynamics, astronomy, dark-matter, galaxies",
"url": null
} |
# If function is differentiable at a point, is it continuous in a neighborhood?
I was reading a proof for the multi-variable chain rule and in the proof the mean-value theorem was used. The use of the theorem requires that a function is continuous between two points.
Hence the motivation for the question, if a functi... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812318188365,
"lm_q1q2_score": 0.8048633285026991,
"lm_q2_score": 0.8311430478583169,
"openwebmath_perplexity": 218.04719188098375,
"openwebmath_score": 0.9104799032211304,
"ta... |
quantum-mechanics
Title: Is a bra-ket always a scalar? I am reading a derivation of the representation of the position operator $\hat{\mathbf{r}}$ in momentum space that goes like this:
$$
\langle\mathbf{p}|\hat{\mathbf{r}}|\psi\rangle =\int d^{3}x\langle\mathbf{p}|\mathbf{r}\rangle\langle\mathbf{r}|\hat{\mathbf{r}}|\... | {
"domain": "physics.stackexchange",
"id": 55950,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-mechanics",
"url": null
} |
kinetic-theory, viscosity
Title: Derivation of viscosity using basic kinetic theory? This question has been asked in part before in the question Kinetic theory derivation of viscosity of a gas although the given accepted answer does not give the required detail for the part of the question I am most interested in.
I w... | {
"domain": "physics.stackexchange",
"id": 27078,
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"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "kinetic-theory, viscosity",
"url": null
} |
1. This shadow is a two-dimensional region, and we turn the triple integral over $\dlv$ into a double integral over the shadow. I Triple integrals in arbitrary domains. Integral calculator This is a calculator which computes the definite and indefinite integrals (antiderivative) of a function with respect to a variable... | {
"domain": "slowscape.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877038891779,
"lm_q1q2_score": 0.8076262646235371,
"lm_q2_score": 0.822189121808099,
"openwebmath_perplexity": 479.3420013305369,
"openwebmath_score": 0.8485875129699707,
"tags"... |
string-theory, path-integral, topological-field-theory, brst
Title: About Vanishing of BRST commutator in path integral In Witten's paper Topological Quantum Field Theory, about formula (3.2), the property $\langle\{Q,\mathcal{O}\}\rangle=0$ depends on the assertion that,
$$Z_{\varepsilon}(\mathcal{O})= \int \mathcal{... | {
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"openwebmath_score": null,
"tags": "string-theory, path-integral, topological-field-theory, brst",
"url": null
} |
c#, performance, programming-challenge, array
// Sort the array in ascending order.
Array.Sort(cpus);
// Get the initial min/max values.
var min = cpus[0];
var max = cpus[cpus.Length - 1];
// Distribute the jobs over the CPUs until all jobs are allocated or all CPUs have an equal number o... | {
"domain": "codereview.stackexchange",
"id": 43137,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, performance, programming-challenge, array",
"url": null
} |
design-patterns, swift
var apprenticeMechanics = MechanicSkillGroup(skill: .Apprentice, mechanics: [tyson, tina, bryan, lin], nextLevel: masterMechanics)
var ken = Mechanic(skill: .Junior, name: "Ken Hudson")
var matt = Mechanic(skill: .Junior, name: "Matt Lowes")
var sandeep = Mechanic(skill: .Junior, name: "Sandeep... | {
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"id": 19510,
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"openwebmath_score": null,
"tags": "design-patterns, swift",
"url": null
} |
observational-astronomy, spectroscopy, space-telescope, james-webb-space-telescope
Title: How will microshutter arrays be used in the James Webb and future space telescopes? Question: How will microshutter arrays be used in the James Webb and future space telescopes? Are they acting as a sort of moving pinhole or slit... | {
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"id": 4022,
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"lm_q2_score": null,
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"tags": "observational-astronomy, spectroscopy, space-telescope, james-webb-space-telescop... |
vcf, genomics
2 --adaptive-pruning-initial-error-rate 0.001 --pruning-lod-threshold 2.302585092994046 --pruning-seeding-lod-threshold 9.210340371976184 --max-unpruned-variants 100 --linked-de-bruijn-graph false --disable-artificial-haplotype-recovery false --enable-legacy-graph-cycle-detection false --debug-assembly f... | {
"domain": "bioinformatics.stackexchange",
"id": 2669,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "vcf, genomics",
"url": null
} |
forces, mass, water, weight
Title: Is it possible to create weighing machine with water indicator I want to create a weighing machine that works with water.
After researching on Google I got this. $1$ $\text{cm}^3$ of water weights $1$ g.
So, with that equation I'm planned to create this below type of weighing machine... | {
"domain": "physics.stackexchange",
"id": 51734,
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"openwebmath_score": null,
"tags": "forces, mass, water, weight",
"url": null
} |
moveit, ros-kinetic, ur5
[WARN] [1575393061.915051]: No calibration offset for joint "shoulder_lift_joint"
[WARN] [1575393061.915374]: No calibration offset for joint "elbow_joint"
[WARN] [1575393061.915642]: No calibration offset for joint "wrist_1_joint"
[WARN] [1575393061.915880]: No calibration offset for joint "w... | {
"domain": "robotics.stackexchange",
"id": 34082,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "moveit, ros-kinetic, ur5",
"url": null
} |
Another way of looking at this, where you are naturally led to the result: Since $f(x)$ is even, what you need to show is that $$\int_{-a}^a {f(x) \over 1 + e^x}\,dx = {1 \over 2}\int_{-a}^a f(x)\,dx$$ The difference between the left hand side and the right hand side is $$\int_{-a}^a f(x)\left({1 \over 1 + e^x} - {1 \o... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9877587268703082,
"lm_q1q2_score": 0.8075663237266926,
"lm_q2_score": 0.8175744761936437,
"openwebmath_perplexity": 381.21532558890095,
"openwebmath_score": 0.9508289694786072,
"ta... |
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