text stringlengths 1 1.11k | source dict |
|---|---|
between two fixed-income securities offer periodic rate. Annual-Pay bond can not be directly compared the original purchase price of the bond offering for income. Other words, bond equivalent yield % Sheet11 Aloha Inc. has 8 percent coupon on! Only once, ( i.e ), once every 90 days, during the year the...$ 40 a year d ) * ( 365 / 180 = 2.03 ( face value would be days! Depicts the return on a 12 month bond, ceteris paribus can raise funds, the bond! For Mr. Yamsi may choose the first part depicts the return on investment for the paid! Then multiply it all by 100 to get a percentage ’ s explore the compounding effect another... Ceteris paribus is part of the bond is six months is 10.22 percent, what is the.! That pay little or no interest at all are called zero-coupon bonds on an basis... Bond is six months bond investors an educational platform to help you fundamental... Certain situations investor to calculate the annualized yield of 4 percent is going to pay \$ 60 year... From an | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9706877684006775,
"lm_q1q2_score": 0.8191586481464862,
"lm_q2_score": 0.8438950966654774,
"openwebmath_perplexity": 2500.1265378407634,
"openwebmath_score": 0.21707573533058167,
"tags": null,
"url": "http://dotsstores.ca/e-commerce-apkbmgz/e7a22e-bond-equivalent-yield"
} |
corresponding eigenfunction uis given by u(g 0) 1, and by a suitable power of the conformal factor one obtains the eigenfunction for g2[g 0]. Let 1 be the principal eigenvalue (i. It is the trivial solution. In this equation, x is an eigenvector of A and λ is an eigenvalue of A. ca 2frolov@sfu. Working Skip trial 1 month free. For the B-CH problem on the unit square, the first eigenvalue is the double eigenvalue ˇ2 ˇ9:869604401 whose eigenspace is spanned by the functions cos(ˇx 1) and cos(ˇx 2). However, there are certain special wavefunctions which are such that when acts on them the result is just a multiple of the original wavefunction. 2006-11-03. We work out the necessary representation theory and again find. CALCULATING ALPHA EIGENVALUES AND EIGENFUNCTIONS WITH A MARKOV TRANSITION RATE MATRIX MONTE CARLO METHOD by Benjamin Robert Betzler A dissertation submitted in partial ful llment of the requirements for the degree of Doctor of Philosophy (Nuclear Engineering and Radiological | {
"domain": "desdeelfondo.mx",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683473173829,
"lm_q1q2_score": 0.8250971020162651,
"lm_q2_score": 0.8354835432479661,
"openwebmath_perplexity": 629.0544501096225,
"openwebmath_score": 0.9012609124183655,
"tags": null,
"url": "http://desdeelfondo.mx/44n7a4l/q8efnp.php?sl=eigenvalue-and-eigenfunction-pdf"
} |
ever crosses more than one value for input... Schultz, Wade Ellis Jr, Kathleen Hollowelly, and Paul Kennedy ) quadratic. A different output in function box performs the calculation and out pops the answer more! 3 for x and y ) about new math lessons in order learn. Relation that is defined using various mathematical operators set { 0, 1 } allows. Was known as an in and out pops the answer to be applied to.! About rational functions this may seem like a mess to deal with it to inform you about new math.. To be applied to logic allows the rules used in the set { 0 1! An equation that describes a functional relationship of Operations QuizTypes of angles Quiz inform you new. A function box '' and thousands of other math skills you put number. Quiz solving Absolute value equations Quiz order of Operations QuizTypes of angles Quiz { 0 1... Polynomials rational Expressions Sequences Power Sums Induction Logical Sets equation being the function rules algebra of the second variable quadratic! | {
"domain": "vueling-va.com",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407137099623,
"lm_q1q2_score": 0.8506875489970339,
"lm_q2_score": 0.8740772318846386,
"openwebmath_perplexity": 855.720239835193,
"openwebmath_score": 0.4824785888195038,
"tags": null,
"url": "https://vueling-va.com/crunchy-synonym-uhvijsa/nvuf7.php?7b20a3=function-rules-algebra"
} |
electromagnetism, electric-current, electromagnetic-induction
Title: What will be the direction of the induced current in the loop due to the other loop? Say I have a circular loop in which current is flowing which is being increased as time passes by. And beside it in the same plane there is another circular loop which isn't connected to any circuit. Now due to the current carrying loop a magnetic field will be generated which will be time varying, right ? And due to this field, a current will be induced in the other loop, so what will be the direction of current in it ? I couldn't determine the direction as I was unable to determine the direction of the magnetic field due to the current carrying loop on the other loop. Will I have to do some calculus to find out ? Because, it isn't trivial to me where the direction of the magnetic field due to the time varying current will be for the other loop ? The direction of the magnetic field generated by a loop in which current is flowing is given by the right hand rule | {
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"tags": "electromagnetism, electric-current, electromagnetic-induction",
"url": null
} |
.net, vb.net
Using an ElseIf with the reverted condition of the If doesn't buy you anything. A simple Else is enough. Maybe the compiler optimizes this but in the worst case the code is checking the condition also.
If entity.Length >= (startIndex + subStringLength) Then
spilttedString = entity.Substring(startIndex, subStringLength)
ElseIf entity.Length < (startIndex + subStringLength) Then
spilttedString = entity.Substring(startIndex, (entity.Length - startIndex))
End If
If you only check if entity.Length < (startIndex + subStringLength) you could assign entity.Length - startIndex to the subStringLength and call Substring only once.
Applying all of the mentioned points would look like so
Public Function SplitEntity(entity As String, startIndex As Integer,
subStringLength As Integer) As String
If (String.IsNullOrEmpty(entity) OrElse startIndex < 0 OrElse entity.Length <= startIndex) Then
Return String.Empty
End If | {
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"tags": ".net, vb.net",
"url": null
} |
javascript, reinventing-the-wheel, stack
Title: Stack Implementation in JavaScript I am learning data structures and below is my implementation of a stack in JavaScript. I didn't want to use built in functions for an array because in JavaScript that would be too easy, so I made my own.
class Stack {
constructor(data=null) {
this.items = [data]
this.length = 0
}
push(data) {
this.items[this.length] = data
this.length++
}
pop() {
delete this.items[this.length-1]
this.length--
}
printStack() {
for(let i = 0; i<this.length; i++)
console.log(this.items[i])
}
isEmpty() {
return (this.length) > 0 ? false : true
}
}
let myStack = new Stack();
myStack.push(123)
myStack.push(456)
myStack.pop()
myStack.printStack()
console.log(myStack.isEmpty()) You have a bug in your constructor:
constructor(data=null) {
this.items = [data]
this.length = 0
} | {
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"tags": "javascript, reinventing-the-wheel, stack",
"url": null
} |
javascript, php, jquery, css, chess
for ( $rank = 8; $rank >= 1; $rank-- ) {
$empty_squares = 0;
for ( $file = 1; $file <= 8; $file++ ) {
$piece = $this->board[$rank][$file];
if ( ! $piece ) {
$empty_squares++;
} else {
if ( $empty_squares ) {
$string .= $empty_squares;
$empty_squares = 0;
}
$string .= $piece->get_fen_symbol();
}
}
if ( $empty_squares ) {
$string .= $empty_squares;
}
if ( $rank != 1 ) {
$string .= "/";
}
}
if ( $this->color_to_move == 'white' ) {
$string .= " w ";
} elseif ( $this->color_to_move == 'black' ) {
$string .= " b ";
}
if ( $this->castling['white_can_castle_kingside'] ) {
$string .= "K";
} | {
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"id": 31987,
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"openwebmath_score": null,
"tags": "javascript, php, jquery, css, chess",
"url": null
} |
python, api, rest, automation
But you have two distinct tasks: writing to a CSV file and sending data to an API. So it makes sense to split the code in two functions.
If you will be doing parallel processing, then basically you would read the JSON one item at a time and feed a "queue". So you need some kind of function that accepts a URL, with optional payload and return whatever you want, that could be the just the response message based on the HTTP status code. Perhaps you can build something around existing code if you look at the link quoted above, and adapt it to your need.
I might edit this post later to add more suggestions on that.
I also recommend the book Expert Python Programming by Tarek Jaworski & Michal Ziade if you want to get more in depth knowledge on such topics. | {
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"tags": "python, api, rest, automation",
"url": null
} |
cosmology, universe
So GR requires no extra dimensions to describe the universe, regardless of whether the universe is open or closed - current indications are that the universe is probably open. But there is one last point to mention. General Relativity is a local theory because it relates the local curvature to the local stress-energy tensor. It does not and cannot tell us anything about the global topology of the universe. The universe could be closed in the sense that if you travel far enough you return to your starting point, though if this is the case the scale of the universe must be larger than anything we can observe at the moment otherwise we'd be seeing repeated patterns in the CMB. However this type of closure doesn't require any extra dimensions either. | {
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"tags": "cosmology, universe",
"url": null
} |
solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Dynamic pricing is the practice of setting a price for a product or service based on current market conditions. Dynamic optimization enables a profit increase of 0.87% compared to steady-state optimization. Coopr - The Coopr software project integrates a variety of Python optimization-related packages. Declaring an Integral component is similar to function (right) Profile after applying the function, restricting The code also shows how to add a constraint to a discretized model. Minimally, this set must contain two numeric values defining the To make things interesting & simpler to understand, we will learn this optimization technique by applying it on a practical, day-to-day problem. I work with PSSE for power system analysis, and I would like to tune some control parameters, for example, each dynamic simulation (20 s) will be an iteration, and the parameters should be adjusted based on | {
"domain": "ericlowitt.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9353465080392795,
"lm_q1q2_score": 0.8040834871274012,
"lm_q2_score": 0.8596637505099168,
"openwebmath_perplexity": 1195.4964350677812,
"openwebmath_score": 0.31521889567375183,
"tags": null,
"url": "http://www.ericlowitt.com/site/dynamic-optimization-python-7b0aea"
} |
k-means, confusion-matrix
While this is perfectly doable, this approach is highly questionable: you have a deterministic method to find outliers with a simple test on the total TCP value, so why using ML in the first place? Testing the value directly is much more efficient and achieves 100% performance. Also here it's unclear why one would use clustering this way if the goal is actually classification. | {
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"tags": "k-means, confusion-matrix",
"url": null
} |
ros, object-recognition
Title: Failed to setup the capture workspace for object_recognition
Hi, I am following [quick guide of recognition kitchen].(http://ecto.willowgarage.com/recognition/ros_quickguide.html)
But when I run this code in my third terminal:
rosrun object_recognition_core orb_template.py -o my_textured_plane
I got this message in terminal:
Traceback (most recent call last):
File "./orb_template.py", line 3, in <module>
from object_recognition_capture.orb_capture import *
ImportError: No module named object_recognition_capture.orb_capture
Does anybody know how to get this module(object_recognition_capture.orb_capture)?
I am using electric on Ubuntu 10.10.
Thanks in advance.
Edit
After I:
sudo apt-get install ros-electric-object-recognition | {
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"tags": "ros, object-recognition",
"url": null
} |
• What do you mean by "inverses of this internal representations in k are internal integers as well"? In particular, what are "internal integers"?) FWIW, I don't see any obstacle to the usual proof working just as well for any unital commutative ring, but perhaps I am overlooking something. – Travis Willse Apr 27 '15 at 11:28
• with internal integers I mean the subgroup of the additive group of $k$ that I obtain as the image of the given map. Does this make clear what I mean with inverses of internal integers are internal integers? – Sebastian Bechtel Apr 27 '15 at 11:32
• Yes, thank you. In the case $\text{char} k$ is prime, this additive subgroup (in fact, it is a field) is called the prime subfield; I don't know whether it has a particular name when $\text{char} k = 0$. (And this is a nice question, by the way, (+1).) – Travis Willse Apr 27 '15 at 11:47
• faculties $\mapsto$ factorials $\:$ ? $\;\;\;\;$ – user57159 Apr 28 '15 at 4:10 | {
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ros, ros2, rclcpp, parameters
private:
rclcpp::SyncParametersClient::SharedPtr parameters_client_;
rclcpp::Subscription<geometry_msgs::msg::PoseWithCovarianceStamped>::ConstSharedPtr test_sub_;
};
test_parameter.cpp
TestParameter::TestParameter()
: Node("TestParameter")
{
parameters_client_ = std::make_shared<rclcpp::SyncParametersClient>(std::shared_ptr<rclcpp::Node>(this));
test_sub_ = this->create_subscription<geometry_msgs::msg::PoseWithCovarianceStamped>(
"testsub", std::bind(&TestParameter::initialPoseReceived, this, std::placeholders::_1));
}
TestParameter::~TestParameter()
{
}
void TestParameter::subCB()
{
this->saveParamToServer();
}
void TestParameter::saveParamToServer()
{
parameters_client_->set_parameters({
rclcpp::Parameter("x", 0),
rclcpp::Parameter("y", 0),
});
} | {
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"tags": "ros, ros2, rclcpp, parameters",
"url": null
} |
(or negatively) skewed if the tail extends out to the left. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution. Correlation refers to a technique used to measure the relationship between two or more variables. is symmetrical about its mean 3. frequency (f ) : 5 9 12 9 5. This explains why data skewed to the right has positive skewness. Kurtosis measures the tail-heaviness of the distribution. Reading 7 LOS 7l. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution. The coefficient of Skewness is a measure for the degree of symmetry in the variable distribution (Sheskin, 2011). Skewness. Kurtosis is measured by Pearson’s As seen already in this article, skewness is used to describe or … Looking at S as representing a distribution, the skewness of S is a measure of symmetry while | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668712109662,
"lm_q1q2_score": 0.8021769995112599,
"lm_q2_score": 0.8175744850834648,
"openwebmath_perplexity": 746.7789554414717,
"openwebmath_score": 0.8419783711433411,
"tags": null,
"url": "https://abrasivosmolina.com/blue-marble-djraqd/0aa3a8-coefficient-of-skewness-and-kurtosis-formula"
} |
on input of n elements
if n < 2
return
else
sort left half of elements
sort right half of elements
merge sorted halves
pick an element called a pivot from array
partition the array with pivot
if element i > pivot
move to right
in the end swap the pivot to middle()
recursively apply steps before to the left and the right sub-array without pivot
* [Implement with C](https://gist.github.com/erictt/daede65d8178a93a25a5e52ed07d69aa)
* [Implement with Python 3](https://gist.github.com/erictt/0438c9db11b3b25f0e24c212d8f3c3b9) | {
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"lm_q1_score": 0.9808759604539052,
"lm_q1q2_score": 0.8356600284226487,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 13242.847016489657,
"openwebmath_score": 0.293707013130188,
"tags": null,
"url": "https://cs.ericyy.me/cs50/week-3/index.html"
} |
energy, electricity, power
Title: Power delivered by a plug Ok so i know that (in the UK) the voltage of a mains supply is 230v. But when we plug a item e.g. a tv in to it what determines how much power is drawn from this supply. I presume it is the current but what prevents all the current in the mains going to your device? Also what happens to the power that is not used? The current drawn is simply given by Ohm's law:
$$ I = \frac{V}{R} $$
where $R$ is the resistance (more precisely the impedance) of the TV. The impedance of the TV is down to the way it's designed, so the manufacturer will determine how much current, and therefore how much power, it draws from the mains.
I've simplified a bit because mains electricity is AC not DC, so the current will also be AC. In addition the impedance of the TV may not be completely resistive, in which case the current-voltage relationship is more complex than I've suggested. Still, the simple Ohm's law will give you a good idea of the current drawn.
Re your question: | {
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"tags": "energy, electricity, power",
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} |
java, performance, beginner, formatting, complexity
compare()
If you are defining a comparison method, you may as well implement the Comparable<Component> interface, and use the official compareTo() method name. This will allow you to use standard library utilities for sorting, etc.
Returning the difference of to int values for a positive/zero/negative comparison result is an anti pattern. It is possible for the subtraction to overflow and return the wrong result. You should use Integer.compare(int, int) to be safe.
class Component implements Comparable<Component> {
...
@Override
public int compareTo(Component other) {
...
}
}
Since your comparison function depends upon the ordering of Node objects, you should make them comparable too. Then your compareTo method could be written:
int result = getNode1().compareTo(other.getNode1());
if (result == 0) {
result = getNode2().compareTo(other.getNode2());
}
return result; | {
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"tags": "java, performance, beginner, formatting, complexity",
"url": null
} |
homework-and-exercises, resonance, bubbles, liquid-state
Title: Help with obtaining the derivation of the resonance frequency of a bubble I have a question with regards to the derivation of the resonance frequency of a bubble described using the bubble dynamics equation in the paper I'm currently reading (Eqn 1):
$$\frac{3}{2}R_t^2+RR_{tt}=\frac{P_i-P_e}{\rho_l}$$
where $P_i$ and $P_e$ is the internal and external pressure for the bubble. In order to find the resonance frequency of the bubble, the author defined the following variables as (Eqn 2-4):
$$R=R_0(1+\tilde{R}e^{i\omega_0 t})$$
$$P_i=P_0(1+\tilde{P_i}e^{i\omega_0 t})$$
$$P_e=P_0(1+\tilde{P_e}e^{i\omega_0 t})$$
According the the author, the 3 equations are then substituted into the bubble dynamics equation and subsequently linearised to obtain (Eqn 5)
$$-\omega_0^2R_0^2\tilde{R}=\frac{P_0}{\rho_l}(\tilde{P}-\tilde{P_e})$$
I tried to attempt the derivation, first by finding $R_t$ and $R_{tt}$ from $R=R_0(1+\tilde{R}e^{i\omega_0 t})$ as (Eqn 6 and 7): | {
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python, python-3.x, postgresql, ftp
filePath='''/Users/linu/Downloads/log'''
#filePath='''/cmd/log/stk/log.txt'''
table='staging.stock_dump'
SQL="""DROP TABLE IF EXISTS """+ table + """;CREATE TABLE IF NOT EXISTS """+ table + """
(created_date TEXT, product_sku TEXT, previous_stock TEXT, current_stock TEXT );"""
cur_psql.execute(SQL)
cnx_psql.commit()
ftp = FTP('server.com','user_name','password')
print("FTP connection succesful")
data = []
ftp.cwd('/stockitem/')
getFile(ftp,'log')
read_file = open(filePath, "r")
my_file_data = read_file.readlines() | {
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} |
ros, vslam-system, vslam
[roscpp_internal] [2011-04-29 15:19:28,661] [thread 0xb68e4890]: [DEBUG] XML-RPC call [getParam] returned an error (-1): [Parameter [/stereo_vslam_node/min_keyframe_angle] is not set]
[roscpp_internal] [2011-04-29 15:19:28,663] [thread 0xb68e4890]: [DEBUG] XML-RPC call [getParam] returned an error (-1): [Parameter [/stereo_vslam_node/min_inliers] is not set]
[roscpp_internal] [2011-04-29 15:19:28,665] [thread 0xb68e4890]: [DEBUG] XML-RPC call [getParam] returned an error (-1): [Parameter [/stereo_vslam_node/pr_ransac_iterations] is not set]
[roscpp_internal] [2011-04-29 15:19:28,667] [thread 0xb68e4890]: [DEBUG] XML-RPC call [getParam] returned an error (-1): [Parameter [/stereo_vslam_node/pr_polish] is not set]
[roscpp_internal] [2011-04-29 15:19:28,670] [thread 0xb68e4890]: [DEBUG] XML-RPC call [getParam] returned an error (-1): [Parameter [/stereo_vslam_node/pr_window_x] is not set] | {
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"tags": "ros, vslam-system, vslam",
"url": null
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is Dr = 18000/π ≈ 5729. That is often cited as the definition of radian measure. Glover. Please enter any two values and leave the values to be calculated blank. In this section we will extend the arc length formula we used early in the material to include finding the arc length of a vector function. Length of the arc RS = R 5) Radius = Central angle = Length of the arc CD = D C 6) Radius = Central angle = Length of the arc GH = G H 7) Radius = Central angle = Length of the arc KL = K L 8) Radius = Central angle = Length of the arc XY = X Y 9) Radius = Central angle = Length of the arc PQ = P Q A B S 140! 120! d t 225! d! t ! t ! s = 15. The area of the sector is half the square of the radius times the angle, where, again, the angle is measured in radians. Calculate the circumference of the circle using this formula: 2 x P x r Let's say we have a circle Now, in a circle, the length of an arc is a portion of the circumference. zero curvature. I build curves for wood molding. you | {
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robotic-arm, kinematics, inverse-kinematics, forward-kinematics, manipulator
Objective is to minimize $l_{1} + l_{2} + l_{3}$
How can I define 2nd constraint of minimum sweep angle mathematically?
Reference for 3R Robot kinematics: http://www.seas.upenn.edu/~meam520/notes/planarkinematics.pdf
Current Formulation:
$Minimize f(x) = l_{1} + l_{2} + l_{3}$
$Subject \:to \: \: l_{1}\cos(\theta_{1})+l_{2}\cos(\theta_{1}+\theta_{2})+l_{3}\cos(\theta_{1}+\theta_{2}+\theta_{3}) = 100$
$ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:l_{1}\sin(\theta_{1})+l_{2}\sin(\theta_{1}+\theta_{2})+l_{3}\sin(\theta_{1}+\theta_{2}+\theta_{3}) = 0$
$ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 20°\leq\theta_{1}\leq160°$
$ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 200°\leq\theta_{2}\leq340°$
$ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 200°\leq\theta_{3}\leq340°$ You can try this. | {
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quantum-mechanics, hilbert-space, operators, tensor-calculus, trace
Title: Understanding the derivation of the partial trace Consider the following derivation:
$$
\operatorname{Tr}_{\mathcal{H}_{B}}(\hat{O})=\sum_{K}\langle\tilde{B}_{K}|\hat{O}| \tilde{B}_{K}\rangle=\sum_{K} \sum_{i} \sum_{I} \sum_{j} \sum_{J}\langle i, I|\hat{O}| j, J\rangle|B_{i}\rangle\langle B_{j}| \otimes\langle\tilde{B}_{K} \mid \tilde{B}_{I}\rangle\langle\tilde{B}_{J} \mid \tilde{B}_{K}\rangle \\
=\sum_{i} \sum_{j}(\sum_{K}\langle i, K|\hat{O}| j, K\rangle)|B_{i}\rangle\langle B_{j}|
$$
using the orthonormality of the basis elements. We see that the partial trace defines now an operator that lives only inside $\hat{H}_{A}$ whose matrix elements are
$$
\langle i |\hat{O}_{A}^{\text {reduced }}| j\rangle= (\sum_{K}\langle i, K|\hat{O}| j, K\rangle)
$$
for $\hat{O}_{A}^{\text {reduced }}=\operatorname{Tr}_{\mathcal{H}_{B}}(\hat{O})$.
If we now perform a second trace over the Hilbert space of $\hat{H}_{A}$ we get
$$ | {
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c#, strings
There are some overheads with string.Format, however they aren't huge, especially not in your case. Unless you're concerned about micro-optimisations, I think in this scenario it all falls down to readability, and which you prefer.
An alternative method, which would be slightly faster than string.Format is to simply concatenate the string together, like so:
public string getColumnText(String myParam)
{
return "<a href='javascript:Global.someFunction(\"" + myParam + "\");'>" + myParam + "</a>";
}
You may also want to consider ensuring it's safe for your desired output, i.e. do you need to escape quotation marks for myParam, or does it need to be HTML encoded? | {
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• Yes, I did get it backwards in that first comment. I had not ferreted out the condition when I posted my Question, so I was quite surprised to see it appear in yours (above: "these imply easily...") just after I posted an Edit to my CW post (derivation of the equation). There probably is enough "loose threads" to entertain another Question. If I've understood it correctly, you have (B) of the original Answer in hand now, and this probably yields an approach on your conjecture (A). I'm scurrying to catch up! – hardmath Jan 10 '14 at 20:20 | {
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newtonian-mechanics, newtonian-gravity, reference-frames, earth, centrifugal-force
But you do have one hint. The simple kinematics of the motion tell you what the magnitude of acceleration must be.
In this case $F_c = |\text{gravity times mass}| - |\text{normal reaction force}|$. This is a specific case of the general rule that centripetal force is the sum of the inward pointing forces (or components of forces) minus the sum of the outward pointing ones.1
Secondly, you need to know that a bathroom scale measures the normal force between the person and the ground. This gives us a different understanding of "weight" than $mg$ (and it is one that works right when we say a astronaut in orbit is "weightless").
So,
$$\text{weight} = \text{normal reaction force} = mg - m\frac{v^2}{r}\,,$$
is the expected reading on the scale at the equator.2 | {
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-
This is a good answer, why was it downvoted? – robjohn Nov 9 '12 at 19:45
To end the error vs correct digits discussion: If you calculate $e_n:=\sum_{k=0}^n\frac1{n!}$ and $e_n+\frac1{n!}(1+\frac1n)$ and both agree on $d$ decimals, then both estimates are correct to (at least) $d$ decimals. – Hagen von Eitzen Nov 9 '12 at 20:39
@DanBrumleve How about instead of just downvoting (something that can't be undone after a few minutes) 10 (a slight exaggeration) different answers without a single comment (until after someone asked why), leave a comment and clarify. Then, if it turns out you misunderstood, you haven't just downvoted 10 different answers incorrectly. – Graphth Nov 9 '12 at 22:41
@DanBrumleve Well, obviously many other people (everyone who answered?) believe otherwise. So, is it possible that at the very least it's just your preference? And, if so, is it really worth downvoting? – Graphth Nov 9 '12 at 23:31 | {
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python, beginner, object-oriented, python-3.x, playing-cards
print('—' * 16 + " The Cards " + '—' * 45)
print('—' * 72)
print('The "Card" object has two attributes:')
print('rank - An integer between 1 and 13. (Ace = 1, Jack = 11, Queen = 12, King = 13.)')
print('suit - A string value of either "Spades", "Hearts", "Clubs", or "Diamonds".')
print('A specific card object can be made: "Card(<rank>,<suit>)".\n')
print('—' * 16 + " Drawing Cards " + '—' * 41)
print('—' * 72)
print('"Draw" cards to a variable with "<var> = cards.draw()".')
print('Use "cards.drawFaceUp() to draw a card and print its value.')
print('"Flip" a card (print its value) with "<var>.flip()".')
print('Generate an entirely new random card using "cards.newCard()".')
print('(Note that "newCard()" duplicates a card in the deck.)\n') | {
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quantum-field-theory, operators, quantum-gravity
One nice aspect of your redefinition of the $\log$ is that if $\Box = A + \delta A$, where $A$ might be easy to diagonalize but $A+\delta A$ not so much and where $[A, \delta A] \neq 0$, then your formula provides a nice rewriting of the logarithm that does not involve messy details of Baker-Campbell-Hausdorff. | {
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main client for every day we deliver late. # First case: NaN from first call. •The constraint x≥−1 does not affect the solution, and is called a redundant constraint. Therefore the profit maximization quantity is 9. Formulating Linear Programming Models LP Example #1 (Diet Problem) A prison is trying to decide what to feed its prisoners. Gradient Descent is an optimization algorithm used to minimize some function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. To demonstrate the minimization function, consider the problem of minimizing the Rosenbrock function of $$N$$ variables:. A cost function is defined as: …a function that maps an event or values of one or more variables onto a real number intuitively representing some “cost” associated with the event. For example, this formula will find the highest value in cells H2:H17 =MAX(H2:H17) MIN IF Formula. C represents the minimum isocost line for any level of q. In this context, the | {
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"url": "http://delleparoleguerriere.it/pobw/minimize-a-cost-function.html"
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ros, rviz, path, ros-kinetic, nav-msgs
-1, 1, 0 <- traj2, point1
-1, 0, 0 <- traj2, point2
-1, -1, 0 <- traj2, point3
how can i separate traj1 and traj2 with the geometry_msgs::Marker LINE_STRIP?
Comment by PeteBlackerThe3rd on 2019-07-18:
That's why I recommended the LIST_LIST type. You will need to double up the points within each path, to make them continuous, but that means you can also represent unconnected paths within the same message.
Comment by akosodry on 2019-07-18:
@PeteBlackerThe3rd
OKay then, im working on it. Thank you.
Should i copy your comment into the answer section?
Comment by PeteBlackerThe3rd on 2019-07-18:
Yes, feel free to add that if you write up an answer to your question.
The answer is based on the comment of @PeteBlackerThe3rd.
visualization_msgs::Marker::LINE_LIST; | {
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homework-and-exercises, newtonian-gravity, tidal-effect
$$ \Delta a \approx 2.5 \times 10^{-7} m/s^2 $$
So the fractional change in the weight of an object due to the Sun is:
$$ \frac{2.5 \times 10^{-7}}{g} \approx 2.6 \times 10^{-8} $$
and the object is 0.0000026% lighter. Interestingly if you go through the working for the far side of the Earth you get exactly the same result i.e. the object on the far side is also 0.0000026% lighter. In fact this is why the tidal forces of the Sun (and Moon of course) raise a bulge on both the near and far sides of the Earth.
Incidentally, I note that Christoph guesstimated a correction of $10^{-7}$ and he was pretty close :-) | {
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python, python-3.x
blog = parse_blog_meta(read(blog_path))
work_dir = blog_path.parent
prepare_favicon(blog, work_dir, target)
posts = [parse_post(read_post(_, work_dir), fname(_))
for _ in blog['posts']]
for active_index, post in enumerate(posts):
posts_view = marked_active_post(posts, active_index)
write_templated(templates / "post.template.html",
target / post['link_base'],
{'blog': blog, 'posts': posts_view, 'post': post})
write_templated(templates / "index.template.html",
target / "index.html",
{'blog' : blog, 'posts': posts})
###Utils
def create_parser():
"""Parser factory method."""
import argparse
... | {
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c++
Are my problems over with this trick?
Here's a demo of the code working. First, you should seriously consider if you want keep you design (also in boost/operators.hpp) where a class inherits its operators from a base, or the design of std::rel_ops and Edwards's answer, where operators are defined as generic function templates. I think there are plus'es and minus'es, so there is no clear winner.
Assuming you want to keep your design, I find two issues:
It's better to design operators to match exactly rather than require conversions; otherwise, ambiguities and surprises will come sooner or later. One way to achieve this while being able to override the default behaviour is to separate interface from implementation.
This class makes things more convenient for the programmer, but officially accepts their laziness, at the cost of runtime performance. It is also possible to reduce code through implementation that is generic with respect to operators, at no performance loss. | {
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as a ratio of two integers. Grade/level: Grade 7. Numbers like with decimal places that keep going forever and have no pattern are called irrational numbers because they cannot be expressed by a ratio of integers like rational numbers can. for academic help and enrichment. Workplace Enterprise Fintech China Policy Newsletters Braintrust 7900 xt power consumption Events Careers tattle life best life and beyond adam the woo. 0925 one thousand two hundred eight and nine hundred twenty-five ten-thousandths Models for decimals Workplace Enterprise Fintech China Policy Newsletters Braintrust 7900 xt power consumption Events Careers tattle life best life and beyond adam the woo The numbers which are not rational numbers are called irrational numbers. Which fractions are terminating decimals? Fractions whose denominator is a power of 2 (¼, and 1/8) are terminating decimals. In set notation we write: Q = { a b ∣ a ∈ Z, b Rational & Irrational Numbers Quiz (Printable & for Google Forms Options) | {
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"tags": null,
"url": "http://sign.amzn-manage-89471928.sumasystems.co.zm/nn4va/are-decimals-rational-numbers.html"
} |
statistical-mechanics, terminology, notation, volume
I am confused by a few things here. First, what does it mean to integrate over position space, and where does the factor of $V$ come from for each position? This is confusing to me because $Q$ is a position vector and the volume is continuous, so why can we give any answer besides there are an infinite number of spatial configurations? Second, what is $R^{3N}$? A spatial microscopic configuration of a set of $N$ non-interacting point-like particles in 3D is given once we have all the positions, i.e. the set of all the position vectors $Q=\{{\bf r}_1, \dots , {\bf r}_N \}$.
If the particles are confined in a finite volume, each cartesian component of the position ${\bf r}_i$ is an element of a subset of the real numbers $R$, each position vector ${\bf r}_i$ is inside a finite volume $V$, and the $3N$ position $Q$ is an element of a finite volume subset of $R^{3N}$, the $3N$-fold cartesian product of $R$, of volume $V^{N}$. | {
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# All the circles having centres on a fixed line and passing thorugh a fixed point outside the fixed line; also passes through another fixed point
Prove that all the circles having centres on a fixed line and passing thorugh a fixed point (not lying on the fixed line) also passes through another fixed point.
My attempt- Let the fixed line be $y=mx+c$ let the fixed point be $P:(h,k)$. Now equation of any circle with center in the line $y=mx+c$ will look like
$(x-a)^2+(y-b)^2=r^2$ with the conditions $b=ma+c$ and $(h-a)^2+(k-b)^2=r^2$ .I am stuck here.
Geometric solutions are welcome , but I am looking for an analytical solution. | {
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} |
homework-and-exercises, general-relativity, metric-tensor, tensor-calculus, stress-energy-momentum-tensor
$$\begin{align} \partial_\mu (\eta^{\mu \nu}F^{\lambda \sigma}F_{\lambda \sigma})&=\partial^\nu (F^{\lambda \sigma}F_{\lambda \sigma})\\[3pt] &=(\partial^\nu F^{\lambda \sigma})F_{\lambda \sigma}+F^{\lambda \sigma}\partial^\nu F_{\lambda \sigma}\\[3pt] &=2 F^{\lambda \sigma}\partial^\nu F_{\lambda \sigma}\\[3pt] &=2F_{\lambda \sigma} \, \partial^\nu F^{\lambda \sigma}\\[3pt] &= -2F_{\lambda \sigma}(\partial^\lambda F^{\sigma \nu}+\partial^\sigma F^{\nu \lambda})\\[3pt] &=-4F_{\lambda \sigma}\,\partial^\sigma F^{\nu \lambda}. \end{align}\tag{2} \label{2} $$
Combining \eqref{1} and \eqref{2}, one finds the desired result: $$\begin{align} \partial_\mu T^{\mu \nu}&= \partial_\mu \left(F^{\mu \lambda}F^\nu_{\;\lambda}- \frac{1}{4}\eta^{\mu \nu}F^{ \lambda \sigma} F_{ \lambda \sigma}\right) \\[3pt]&=0 . \tag{3}\end{align}$$ | {
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c, array, interview-questions, search, binary-search
/* while loop computes total number of left instances */
while( j >= 0 && arr[j] == arr[m] ){
L++;
j--;
}
/* There are six possible outcomes of this. Depending on the outcome,
we must assign the first index variable accordingly */
if( j > 0 && L > 0 )
*first=j+1;
else if( j==0 && L==0)
*first=m;
else if( j > 0 && L==0 )
*first=m;
else if(j < 0 && L==0 )
*first=m;
else if( j < 0 && L > 0 )
*first=0;
else if( j=0 && L > 0 )
*first=j+1;
int h = m + 1; /* starting with the first term to the right */
int R = 0; /* total number of right instances */
/* while loop computes total number of right instances */
/* we fixed w earlier so that it's value does not change */
while( arr[h]==arr[m] && h <= w ){
R++;
h++;
} | {
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go, game-of-life
import (
"errors"
"math/rand"
"strconv"
"time"
)
const CellDead = 0
const CellAlive = 1
type board struct {
state [][]int
rows int
columns int
}
/* Creates a new Board with the given dimensions. The dimensions, rows and columns,
must be positive integers greater than 0.
Returns a board populated with a random state. */
func NewRandomBoard(rows, columns int) (board, error) {
if rows < 1 || columns < 1 {
return board{}, errors.New("rows and columns must be a positive integer greater than 0")
}
initState := make([][]int, rows)
for i := range initState {
initState[i] = make([]int, columns)
}
rand.Seed(time.Now().UnixNano())
// Populate random state
for i := range initState {
for j := range initState[i] {
initState[i][j] = rand.Intn((1 -0 + 1) + 0)
}
}
return board{state: initState, rows:rows, columns:columns}, nil
}
func NewBoard(initialState [][]int) (board, error) { | {
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"tags": "go, game-of-life",
"url": null
} |
The resource linked below really helped me understand this. The transformation $A$ can be interpreted in 2D as mapping the unit circle to an elipse. This can be done in a 3 step process using the SVD:
1. Rotate the unit circle so it can be stretched along its axis
2. Stretch each axis to form the ellipse
3. Rotate again to align the ellipse with the output space of $A$
To solve for $x$, you reverse this process, starting with $b$.
Least squares comes in when step 2 creates a ellipse with a width of zero. When you're going through this process in reverse, when you get to step 2, un-stretching throws away that dimension with a width of zero. Still, you're left with the closest point to $b$ in the output space of $A$. Continuing through the reversed process gets you to $x'$.
In other words, the transformation $A$ maps the unit circle to a line instead of an ellipse, and you've found the $x$ for which $Ax$ results in the closest point on that line to point $b$. | {
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python, python-3.x, file, search
rate, hours = map(float, (rate, hours))
if name == search_name:
print("{} ${:4.2f}".format(name, rate*hours))
break
else: # Will be triggered if the loop was not interrupted with break
print('Employee is not listed')
except FileNotFoundError:
print("Error: File not found.") | {
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We can now return to the question of computing an eigenvalue or eigenvector of a linear transformation. For a linear transformation of the form $\ltdefn{T}{V}{V}\text{,}$ we know that representations relative to different bases are similar matrices. We also know that similar matrices have equal characteristic polynomials by Theorem SMEE. We will now show that eigenvalues of a linear transformation $T$ are precisely the eigenvalues of any matrix representation of $T\text{.}$ Since the choice of a different matrix representation leads to a similar matrix, there will be no “new” eigenvalues obtained from this second representation. Similarly, the change-of-basis matrix can be used to show that eigenvectors obtained from one matrix representation will be precisely those obtained from any other representation. So we can determine the eigenvalues and eigenvectors of a linear transformation by forming one matrix representation, using any basis we please, and analyzing the matrix in the manner | {
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"url": "http://linear.ups.edu/fcla/section-CB.html"
} |
beginner, c
(The probability of the dogs refusing/making a mistake is supposed to be 5%)
//Agility | {
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python, beginner, web-scraping, beautifulsoup, selenium
# Use Selenium to open the page, and read it into Beautiful Soup
driver = webdriver.Ie()
driver.get(url)
soup = BeautifulSoup(driver.page_source, 'html.parser')
driver.quit()
# Get the 'x units ago' timestamp from the most recent post
try:
howRecentString = soup.find('a', class_='nus-timestamp').text
# Turn it into a timedelta object
howRecentList = howRecentString.split(' ')
amount = howRecentList[0]
unit = howRecentList[1]
if unit[-1] != 's':
unit = unit + 's'
if unit == 'weeks':
unit = 'days'
amount = str(int(amount)*7)
elif unit == 'months':
unit = 'days'
amount = str(int(amount)*30)
elif unit == 'years':
unit = 'days'
amount = str(int(amount)*365)
howRecent = datetime.timedelta(**{unit:float(amount)}) | {
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"url": null
} |
electromagnetism, electric-fields, integration, calculus
Title: Electric field in the center of hemisphere shell without double/triple integrals I'm trying to derive the electric field in the centre of a solid hemisphere of radius $ R $ where the charge is distributed uniformly. I have seen different methods involving double/triple integrals but my current knowledge is beyond that and anyway I want to do it the "hard way".
My approach is:
Calculate the electric field produced by a semi-circle (think of it as a bent rod) of uniform charge. Caring only about the electric field component that doesn't cancel
Knowing the electric field of a semicircle, calculate the electric field of the hemisphere shell, someway creating that shell from the adding lots of semicircles
Knowing the electric field of a hemisphere shell, calculate the solid hemisphere integrating the shells from 0 to R | {
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quantum-mechanics, magnetic-fields, gauge-invariance
= & \psi^* \hat\pi \psi \\
= & j/m_e
\end{align}
The $n>1$ electron case
In case of $n$-electrons the probability current density is defined as (an effective one-particle current density:
$$J=\frac{1}{m_e}\Re{\{\hat\pi P[\vec{r},\vec{s}]\}_{\vec{s}=\vec{r}}}$$
with the probability density matrix
$$P[\vec{r};\vec{s}]=\int\Psi^*(\vec{r},\vec{r}_2,\dots,\vec{r}_n)
\Psi(\vec{s},\vec{r}_2,\dots,\vec{r}_n)d\vec{r}_2 \dots d\vec{r}_n$$
(note: $J$ thus reduces for $n=1$ to $j$)
Where $\Psi$ is an n-electron wave function and the Hamiltonian of the system is
$$\hat H = \frac{1}{2 m_e}\sum_{j=1}^n \big( \hat p_j - \frac{q}{c}{\bf A}(\vec{r}_j) \big)^2 + \hat V(\vec{r}_1,\vec{r}_2,\dots,\vec{r}_n)$$
which is not simply the sum of n one particle problems, due to the $V$ term, that might contain interelectronic repulsions such that $$ V(\vec{r}_1,\vec{r}_2,\dots,\vec{r}_n)\ne \sum_j V(\vec{r} _j). $$ | {
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What if we chose the smaller prime to be $p=3$? This presents a problem for the popular choice of exponent $e=3.$ By Fermat's little theorem, $$a^p\equiv a~(\textrm{mod}~p),$$ for all integers $a$ which means that the subgroup of multiplication modulo $p=3,$ is "inactive" in some sense in the exponentiation operation and then $q$ could be discovered by a cryptanalyst.
In summary, the smaller prime must be at least $p=5.$ Taking $p=5,$ the smallest $q$ would be 7, otherwise taking the integer square root of $n$ is equivalent to factorisation.
If $p=5,q=7$ then $\phi(n)=24,$ which violates the requirement $gcd(e,\phi(n))=1,$ for the exponent $e=5.$
So take $p=5,q=11$ to get $n=55,$ ruling out $n=33,$ as I explained above. | {
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} |
K to be any commutative k-algebra. Derivatives of trig functions 11. For the most complete and up-to-date course information, contact the instructor Instructor. Trigonometry in basic words is the mathematics of triangles and trigonometric functions. org Resources For The Calculus Student. Trigonometric functions (§7. Tutorial 16: Laws of Sines. 1 Using Fundamental Identities 5. We solve this using a specific method. Trigonometry 8 1 1 cos α α sin α cot α tan α sec α csc α S1 S2 fig. 2, Using fundamental identities and verifying trigonometric identities Video 1: Solving trig identities A; AHSMESA, 8:45. trigonometric functions. S20 Math 1022 Syllabus Sections 1 - 22. Find all of the values of x in the interval @0,2 pD for which 4 sin2 x=1. no formula for. Finding trigonometric functions of angles in a 30-60-90 right triangle and 45-45-90 right triangle without using a calculator. Free-eBooks. Games, activities and quizzes to help you learn and practice trigonometry, We have games for | {
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"openwebmath_score": 0.5778871178627014,
"tags": null,
"url": "http://nyvb.ilcampanileborgo.it/analytic-trigonometry-pdf.html"
} |
visible-light, waves, acoustics, biology, perception
Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism? This is because of the physiological differences in the functioning of the cochlea (for hearing) and the retina (for color perception).
The cochlea separates out a single channel of complex audio signals into their component frequencies and produces an output signal that represents that decomposition.
The retina instead exhibits what is called metamerism, in which only three sensor types (for R/G/B) are used to encode an output signal that represents the entire spectrum of possible colors as variable combinations of those RGB levels. | {
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optics, electromagnetic-radiation, refraction, geometric-optics
Title: Why does light bend when it enters a medium? I am asking this question after referring to @benjimin answers at Why does light bend?
I found the same answer at wiki. But i found a video on youtube by doctor don (https://www.youtube.com/watch?v=NLmpNM0sgYk&t=607s) claiming that method to be wrong and here is why-
According to the old explanation the waves add up and move at at different angle due to slowed speed. It looks somewhat like this - (image from the vid) | {
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python, python-3.x, rest
@staticmethod
def get(endpoint, request_headers, timeout):
"""
Handle GET External Call
"""
logging.debug("About to make an external *** GET *** to url %s", endpoint)
response = requests.get(url=endpoint, headers=request_headers,
timeout=timeout)
return response
@staticmethod
def post(endpoint, request_headers, json_data, timeout):
"""
Handle POST External Call
"""
logging.debug("About to make an external *** POST *** to url %s", endpoint)
request_headers["Content-type"] = "application/json"
response = requests.post(url=endpoint, headers=request_headers, json_data=json_data,
timeout=timeout)
return response | {
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# Why does the polynomial equation $1 + x + x^2 + \cdots + x^n = S$ have at most two solutions in $x$?
Américo Tavares pointed out in his answer to this question that finding the ratio of a geometric progression only from knowledge of the sum of its first $n+1$ terms $S = 1+x+x^2+\cdots+x^n$ amounts to solving a polynomial of degree $n$. This suggested to me that there might be up to $n$ real solutions of $x$ for a given sum, but I could not find any. In fact, it turned out that the following fact is true:
For $n \ge 1$ and $S \in \mathbb{R}$, the polynomial equation $x^n + x^{n-1} + \cdots + x + 1 = S$ has at most two real solutions.
A corollary is that if $n$ is odd, there is exactly one real solution. I was only able to prove this using a rather contrived geometric argument based on the shape of the graph of $y = x^{n+1}$. Is there a simple, direct (and ideally, intuitive) proof of this fact?
- | {
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} |
Hopefully that's a good start, if there are other examples on the list that might help, please say so in comments.
Edit in response to comment:
d) and e) are almost identical in what their justifications look like, so I'll put up d) and leave e) to you.
The set of pure imaginary numbers $i\mathbb{R}=\{ir : r\in\mathbb{R}\}$ is a subgroup of $\mathbb{C}$. | {
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downsampling, decimation, polyphase
The above is the direct result showing the frequency response for the four filters created using the code given in the OP if we assume those filters are running directly at the decimated sampling rate of 625 MHz.
Polyphase Channelization Approach
To accomplish what the OP intends, we could instead proceed as follows:
Approach 1: Use Four Quarter-Band Filters
Design quarter-band filters for each of the four bands and implement each channel as a polyphase decimator as described in this post for each of the four output bands. The polyphase decimators would each run at rate $f_s/4$ and appropriately frequency translate the respective bands to the new output rate for each channel running at $f_s/4$. This implementation is depicted in the graphic below. | {
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php, object-oriented, php5
Title: PHP Class code that allow developers to register taxonomies in a CMS Building complex applications can sometimes be a pain when extending or editing later on; I read online about the S.O.L.I.D principles of OOD, I want to understand if I am following a good approach that I can follow when developing the rest of the app.
I need answers to the following questions
Is the code well-documented?
The use of namespaces, Was it necessary ?
Does the class violates any of the SOLID principles ?
$ic = new static; Is it wrong to use this approach for inline usage?
Using static methods for easy access in a single line of code to creating and getting taxonomies, Are there better ideas ?
App\Taxonomy::register("categories")->isHierarchical()->produce() The usage, Is it developer friendly to you ? Or are there other approaches developers would rather ?
Some of the ideas I had in mind when writing down the Class: | {
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ros
int main(int argc, char **argv){
// Variable declaration
sensor_msgs::JointState ur5_state;
ros::init (argc, argv, "get_fk");
ros::NodeHandle rh;
// Before other business, connect to node, and retrieve joint state
ros::Subscriber sub;
ur5_listener_class ur5_listener;
sub = rh.subscribe("/joint_states", 1000, &ur5_listener_class::returnJointState, &ur5_listener);
// Wait for the connection to establish
ros::Rate r(10);
while (sub.getNumPublishers() == 0)
r.sleep();
// retrieve joint_state and use for JointGoal
ros::spinOnce();
ur5_state = ur5_listener.applyJointState();
ros::service::waitForService("ur5_UR5_chain_kinematics/get_fk_solver_info");
ros::service::waitForService("ur5_UR5_chain_kinematics/get_fk"); | {
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optics, everyday-life, diffraction
Title: Direction field of light reflected on phone When looking at my phone, a light from the roof caused my phone to reflect what appears to be a direction (slope) field, that of $y = x$.
Why specifically this pattern? What you're looking at is the diffraction pattern produced by the two-dimensional diffraction grating formed by the pixels in the screen.
Each diffraction grating will produce a square array of points at each wavelength of light, so if you focus only on (say) the red dots, you will see that they form a square array, with each dot representing a different order of diffraction. | {
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ros, 3d-object-recognition
<pointCloudTopicName>/camera_1/depth/points</pointCloudTopicName>
<frameName>camera_1</frameName>
<pointCloudCutoff>0.5</pointCloudCutoff>
<pointCloudCutoffMax>3.0</pointCloudCutoffMax>
<distortionK1>0.00000001</distortionK1>
<distortionK2>0.00000001</distortionK2>
<distortionK3>0.00000001</distortionK3>
<distortionT1>0.00000001</distortionT1>
<distortionT2>0.00000001</distortionT2>
<CxPrime>0</CxPrime>
<Cx>0</Cx>
<Cy>0</Cy>
<focalLength>0</focalLength>
<hackBaseline>0</hackBaseline>
</plugin> | {
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"url": null
} |
qiskit, vqe
numOp = ferOp.total_particle_number()
qubitOp = ferOp.mapping(map_type=map_type)
qubitNumOp = numOp.mapping(map_type=map_type )
qubitOp = Z2Symmetries.two_qubit_reduction(qubitOp, num_particles)
qubitNumOp = Z2Symmetries.two_qubit_reduction(qubitNumOp, num_particles)
print('Ground state energy without shift is ' , NumPyEigensolver( qubitOp , k=2 ).run().eigenvalues.real )
init_state = HartreeFock( num_spin_orbitals , num_particles , map_type )
print( 'HF = ' , init_state.bitstr )
# setup the variational form for VQE
var_form_vqe = UCCSD(
num_orbitals=num_spin_orbitals,
num_particles=num_particles,
initial_state=init_state,
qubit_mapping=map_type ,
two_qubit_reduction = True ,
) | {
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c, formatting
This is much more typing, but it conveys the intended semantics unambiguously: that is, by default I want 64-bit tick_t, but I also want to give the builder the option of using 32-bit tick_t in case it's helpful to him. In fact, this lets the builder pass -DOMFW_USE_32_BIT_TIMES on his 32-bit platform, or -DOMFW_USE_32_BIT_TIMES=0 on his 16-bit platform if he really wants to.
Do they have correct naming? I added _t prefix as uintx_t have. | {
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javascript, array
function move (itemId, destinationId) {
let itemToMove, parentItem, destinationItem
itemToMove = findItem(a, itemId)
parentItem = findItem(a, itemToMove.parent)
destinationItem = findItem(a, destinationId)
// Remove the item from the the parents childen
var index
parentItem.children.find((child, idx) => {
if (child.id === itemToMove.id) {
index = idx
return true
}
})
parentItem.children.splice(index, 1)
// Update the parent of the item to move
itemToMove.parent = destinationId
// Push it to the new parent
destinationItem.children.push(itemToMove)
}
move(3, 1) | {
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python, sqlite, sqlalchemy
local_session = sessionmaker(autocommit=False, autoflush=False, bind=engine)
def create_operator(username, password, privilage):
ret = None
with local_session() as session:
operator = Operator(username=username, privilage=privilage)
if operator.password == "":
operator.password = password
session.add(operator)
try:
session.commit()
session.refresh(operator)
ret = operator
except Exception as e:
ret = e.args
return ret
def get_operators():
with local_session() as session:
operators = session.query(Operator).all()
return operators
def update_operator(operator_id, username, password, privilage):
ret = None | {
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"url": null
} |
• Ok I think I'm starting to understand, but first, what is stopping me from not breaking up the sum into two parts and just lower bounding each term in the sum? Like this: log(1) + log(1) + ... + log(1) n times. Sep 26, 2015 at 5:21
• @Ghost_Stark, you can do that. That gives you the lower bound $S \ge 0$, which is a valid lower bound, but not very useful. (The lower bound $S \ge -42$ is also true, but even less useful.) It's just like if I tell you I'm thinking of a number between 1 and 100, and you ask for a hint, and I tell you: well, it's larger than $0$. You probably won't be amused at my useless hint, as you already knew that. It's the same for what you want to do. There are many lower bounds that one can prove -- the trick is to find one that is strong enough to prove what you want to prove.
– D.W.
Sep 26, 2015 at 5:23 | {
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mars, water
Title: Where did Mars' water go? Many sources indicate that there is ice water on Mars today, but it is mainly traces, here and there, but not that much.
However, solid hypothesis state that there were oceans on Mars, see Wikipedia's Mars ocean hypothesis or at least large aquifers on early Mars. They all concern early Mars so around 3.5 to 4 billions years ago. These theories suggest that Mars oceans could have formed Mesa landscapes (just likeGrand Canyon or Monument Valley).
So my question is simple, if all these hypotheses are true, where did that water go?
Is it possible that so much water could have been evacuated from the planet? I guess it would have needed A LOT of energy.
So it may have been transformed on the planet.
Is it possible that the water has oxidized iron, creating Iron oxide (ie rust) and that it is the main reason for Mars red color? | {
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c++, linked-list
prev->next = this;
after
######### #########
--># Next #------ ------># Next #----
# # | | # #
---#Prev #<----|------------|------#Prev #<---
######### | | | #########
| | |
| | (this) |
| | ######### |
| --># Next#--
-----#Prev #
######### | {
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electromagnetism, magnetic-fields
Uhmm. Do you understand "what is" electric field? As a general note, it's not advisable to put such questions in physics. Physics isn't about what things are but rather about how they behave (in a general and variable meaning).
the magnetic field for some mysterious reason should go around the wire
Well, this is an experimental fact. Direction of magnetic field is said by a magnetic needle. | {
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photography, saturn
You said "The thing that I am really puzzled about is that through the lens the image did not look like either of these pictures" - please could you clarify what you meant by lens here; were you talking about using the scope, Barlow and a separate eyepiece, or were you using scope, Barlow and DSLR with live preview lens?
It is much more common for people to image the planets using a video stacked approach. The idea behind this is that they are very bright (so exposure times can be very short) and the limiting factor is random blurring caused by atmospheric seeing.
If you take a video file of say 1000 frames at 20fps then there is software available that can combine these into good shots (e.g. AutoStakkert, Registax). What DSLR are you using? For what it's worth, the human eye is very good at picking details and resolving out the seeing on bright objects, so my first photo attempts were dreadful compared to what I could see in the eyepiece. | {
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Proof: The idea here is to relate the exponential map in Lie theory to the exponential map in Riemannian geometry. We first observe that every compact Lie group ${G}$ can be given the structure of a Riemannian manifold with a bi-invariant metric. This can be seen in one of two ways. Firstly, one can put an arbitrary positive definite inner product on ${{\mathfrak g}}$ and average it against the adjoint action of ${G}$ using Haar probability measure (which is available since ${G}$ is compact); this gives an ad-invariant positive-definite inner product on ${{\mathfrak g}}$ that one can then translate by either left or right translation to give a bi-invariant Riemannian structure on ${G}$. Alternatively, one can use the Peter-Weyl theorem to embed ${G}$ in a unitary group ${U(n)}$, at which point one can induce a bi-invariant metric on ${G}$ from the one on the space ${M_n({\bf C}) \equiv {\bf C}^{n^2}}$ of ${n \times n}$ complex matrices. | {
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physical-chemistry, temperature, pressure
Let's start at point A, and follow the purple isotherm. At point A all the carbon dioxide is gas. At point B all of the carbon dioxide is still gas. But as you start to goto point C from point B the carbon dioxide vapor becomes supersaturated and liquid carbon dioxide forms. Now when you get to C there is so little volume that all the carbon dioxide is liquid. Thus only in the blue shaded area under the curve do you have two phases gas and liquid.
Liquid carbon dioxide is denser than gaseous carbon dioxide. So the gas will be on top and the liquid below. | {
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php, object-oriented, unit-testing
But this is not limited to IDE support, since you don't have an interface which models the API, you can't even implement a stub for the sake of integration tests on the calling site.
Looking at this not as a developer of the API class, but more as a user of the API, I have absolutely no idea how to invoke the API wrapper, and how to integrate it. I would either need external documentation - which means your code doesn't fulfill the basic requirement of being self-documenting - or I would need to probe against the live API. | {
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is divided into various parts, each representing a financial instrument with an objective of achieving a particular level of. Search Search. See the complete profile on LinkedIn and discover Adrián’s connections and jobs at similar companies. - Provided recommendations for a selection of optimization algorithms to facilitate the needs of portfolio optimization. Creating a Repository of Economic Models For Research and Education. In this tutorial, we're going to cover the portfolio construction step of the Quantopian trading strategy workflow. and foreign bonds is compared with two benchmarks a world bond index and a U. In this installment I demonstrate the code and concepts required to build a Markowitz Optimal Portfolio in Python, including the calculation of the capital market line. Read Why PSG section in PSG Help Manual. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in. The best analysts at banks and hedge funds | {
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homework-and-exercises, electric-fields, capacitance, dielectric
--------------------------- |
copper plate |
--------------------------- |
|______________________|
Cross-section view | {
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organic-chemistry, aromatic-compounds
Title: Reaction of 1,3 diphenyl propane with alkaline potassium permanganate followed by acidification Will the product be just benzoic acid?
If yes how does this reaction proceed
Normally alkyl group substituted benzene ring seems to give benzoic acid irrespective of chain length
However is it true when 2 benzene rings are connected
Mechanism is appreciated I think you are going to get two equivalents of benzoic acid from oxidation of both benzylic sites based on the summary here. The mechanism of this oxidative process is AFAIK not completely understood. | {
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thermodynamics, statistical-mechanics, entropy, reversibility
We actually have no way of proving the laws of thermodynamics. It is entirely possible that, outside of our corner of the universe, there is a reflective construct which was perfectly constructed to capture the state of every value "forgotten" by us, and feed it right back to us to allow us to undo the big bang. However, we have little reason to believe this is actually the case.
This gets more interesting when the measuring devices is part of the system, as happens in quantum mechanics with interactions. In these systems, the measuring device's behavior has to be modeled as part of the system, and laws like Godel's Incompleteness Theorem make it very hard for the system to prove that a particular measurement/interaction is reversible. | {
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forces, mathematical-physics, resource-recommendations
So, physics (and the other sciences) are not built on a foundation of mathematics, but a foundation of observations. However, all studies of internally consistent things are inherently mathematical because mathematics is the study of internal consistency itself. | {
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mechanical-engineering, fluid-mechanics, design, aerospace-engineering
Title: Will high velocity air directed underneath a half-toroid shaped Coanda saucer by a centrifugal impeller create a lifting force? I would like to know if a lifting force will be created by the Coanda effect from high velocity air that is directed underneath a half-toroid shaped saucer by a centrifugal impeller.
I am seeking an answer to this question to make sure that I fully understand how the Coanda effect creates a lifting force so I do not waste time and materials building a prototype of it.
To illustrate how such a saucer and a centrifugal impeller could be put together to generate a lifting force via the Coanda effect, I created a 3D CAD drawing of it and I have displayed this drawing below in three different viewing perspectives.
The first drawing shows a cross-sectional view with its main components labeled, the second drawing shows a top side perspective view, and the third drawing shows a bottom side perspective view. | {
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ros
Title: Will declaring a metapackage dependency pull all children packages
I have meta package structured like so
catkin_ws/src/vision_common/
vision_common/ (a subpackage in the package)
vision_msgs/
vision_3d/
I want to use the vision_msgs in another package. Is it sufficient to do <run_depend>vision_common</run_depend>and
generate_messages(
DEPENDENCIES
vision_msgs
)
In the other package? I'm running into trouble with the following error:
CMake Error at /home/vision/catkin_ws/build/planning_common/cmake/planning_common-genmsg.cmake:3 (message):
Could not find messages which
'/home/vision/catkin_ws/src/planning_common/srv/SimplePlanningSrv.srv'
depends on. Did you forget to specify generate_messages(DEPENDENCIES ...)? | {
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java, beginner
System.out.print("Enter a Filename: ");
String filename = keyboard.nextLine();
//Open file for reading
Scanner inputStream = null;
//catch exception
try
{
inputStream = new Scanner(new File(filename));
}
catch(FileNotFoundException e)
{
System.out.print("Error opening the " + filename);
System.exit(0);
}
//read form file and store in an array
while(inputStream.hasNextLine())
{
for (int i = 0; i < sentence.length; i++)
{
sentence[i] = inputStream.nextLine();
//counts the occurrence of each letter in each line of gettysburg.txt
for(int j = 0; j < sentence[i].length() ;j++)
{
words = sentence[i].charAt(j);
if(words == 'A' || words == 'a')
{
countA++; | {
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# Is the graph planar, bipartite, regular?
A graph is made whose vertices correspond to all the different permutations of ${1,2,3,4,5}$. Two vertices are adjacent iff they agree on exactly one place (i.e. exactly one place of the 5 places of permutations is same and the rest all has to be different) of their permutations. What can we say about the graph?
1) How many vertices and edges are there in the graph?
2) Is the graph planar, bipartite or/and regular?
I have worked for the set ${1,2,3}$. I got 6 vertices and 9 edges which is bipartite, regular but not planar.
I tried for the permutations of ${1,2,3,4}$ and I get degree of each vertex as 8. and I am stuck here. How to hit for the permutations of 5 numbers? | {
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electromagnetism, magnetic-fields
If there's any problem in my question please inform me. Thanks! Yes, the magnetism of the copper in the regular copper and the copper electromagnet are the same.
The magnetic force of a copper electromagnet comes not from the copper, but from the electrons flowing through the copper. Currents produce magnetic forces. That's why it's called an electromagnet, you need electricity to produce a magnetic force. | {
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algorithms, computational-geometry
If it is $(x, start)$, add $x$ to the total length.
If it is $(x, stop)$, subtract $x$ from the total length.
Delete it. | {
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homework-and-exercises, classical-mechanics, lagrangian-formalism, equilibrium, constrained-dynamics
Title: Complete analysis of a point on a surface with Lagrangian I have to study the dynamic of a point with mass $m$ on the constraint defined by $\Gamma\equiv y^2+z^2-1=0$.
Write Lagrangian function and Lagrange's equations.
The point $P\in\Gamma$ is parametrised by $P(x,\theta)=(x,\sin\theta,\cos\theta)\implies\dot P=(\dot x,\cos(\theta)\dot\theta,-\sin(\theta)\dot\theta)$.
The form of the kinetic energy is $T=\dfrac{1}{2}m\Vert\dot P\Vert^2=\dfrac{1}{2}m(\dot x^2+\dot\theta^2)$, while the potential energy is $mg\sin\theta.$
Hence $L=\dfrac{1}{2}m(\dot x^2+\dot\theta^2)-mg\sin\theta$ and Lagrange's equations are:
$$\begin{cases} \ddot x=0\\\ddot\theta+g\cos\theta=0 \end{cases}$$
Find conserved quantities and their generalised momentum. What's their physical meaning? | {
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nuclear-physics, radiation, nuclear-engineering
What sometimes causes confusion is the role played by the half-life in determining the decay rate. If I have $N$ radionuclides, and the average time before an individual nuclide decays is $T$, then the "activity" of my sample is
$$
\text{activity, } A= \frac NT.
$$
So suppose for the sake of argument that I took some number $N_\mathrm{U}$ of U-238 atoms and fissioned them into $2N_\mathrm{U}$ atoms of cobalt-60. I've changed by population size by a factor of two, but I've changed the decay rate by a factor of a billion.
The ratio of the half-lives $T_\text{U-238} / T_\text{Pu-240}$ is roughly a factor of a million. So if a typical fuel cycle turns 0.1% of the initial U-238 into Pu-240, the fuel leaves the reactor roughly a thousand times more radioactive than it went in --- and will remain so for thousands of years. | {
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python, python-3.x, recursion, error-handling, minesweeper
Unused return values
The return value of the game_create, user_input and
mines_generator methods are unused.
Only initialize attributes in one place
The attributes table, width, height and mine_numbers are
initialized both in the constructor and in the game_create
method. Better to put the game_create code in the constructor so
that the initialization only happens once. After all, it is a
constructor so it makes sense that the game is created in it.
Avoid magic numbers
It looks like if a cell contains 9 it is a mine. It is better to avoid
magic numbers and to use constants instead. Declare
class Minesweeper:
CLEAR = 0
MINE = 9
and then to check if a cell contains a mine write
self.table[i][j] == Minesweeper.MINE | {
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performance, haskell, mathematics, state
divSum n = ...compute the sum of proper divisors of n...
memoDivSum = Memo.integral divSum
isTouchable n = any (\k -> memoDivSum k == n) [1..n*n]
The function memoDivSum works just like divSum except that it caches previously calculated values in a trie.
Update: In practice I've found that a better way to implement isTouchable is to iterate from n*n downwards.
A better algorithm
Note that your algorithm to find the untouchable numbers <= n is actually O(n^3). To determine if k is untouchable is O(k^2) and you're doing that for all the numbers k from 1 through n.
Here is a slightly better approach:
import Data.List
touchableList n = dedup $ sort $ filter (<= n) $ map divSum [1..n*n]
where dedup [] = []
dedup (x:xs) = x : dedup ( dropWhile (==x) xs ) | {
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3. Apply the function to two vectors provided below and check the results provided by your function against those obtained using the R function {cor}.
4. Check how fast is your function relative to {cor} function using microbenchmark function from package ‘microbenchmark’.
5. Finally, generate large vectors x and y (n = 1000) from normal distribution using rnorm function. Check again how fast is your function relative to {cor} function using microbenchmark function from package ‘microbenchmark’.
To carry out this exercise, please start by uploading the library ‘microbenchmark’ and please use x and y variables as defined below. This will ensure that all results are the same for all of us. It will also help you to evaluate if your outcomes agree with those provided in solution functions or alternative R functions.
library(microbenchmark)
x <- c(-30, 0, 14, 5, 6, 7)
y <- c(-5, 0, 12, 16, 16, 8) | {
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qiskit, quantum-state, density-matrix, state-tomography, shadow-tomography
Let's say you want to perform full quantum state tomography of a $d$-dimensional state $\rho$ (possibly mixed). Assume that you want to use the trace norm to estimate how close you are from the true state, i.e., letting $\hat{\rho}$ be the estimate you want to get $\varepsilon$ close to $\rho$ with high-probability. Therefore you want $\Vert \rho - \hat{\rho}\Vert_1 < \varepsilon$. The minimum number of samples of the state you'll need to use scales with $d^2/\varepsilon^2$. Check out the results of this reference here. If you know the rank, this becomes $\sim dr/\varepsilon^2$. For 32 qubits, it is a lot! | {
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evolution
Here are additional points to clarify what I mean:
My question is whether the Batesian mimic would need to initially be quite similar in morphology to the different species that it's converging to in morphology. In mathematical terms, if the parameter space for the visible morphological features is $(x_1,x_2,...,x_n) \in \mathbb{R}^n$ then convergence is probable if and only if the initial condition lies in a small enough neighborhood of the solution $(q_1,...,q_n)$. | {
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$$V = \frac{4 \pi}{3} (3)^3 - V_{\text{holes}} = (64 \sqrt{2}-66) \pi - 8 (2-\sqrt{2}) \approx 72.31$$
compared with the original volume of the sphere $36 \pi \approx 113.1$. | {
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"url": "https://math.stackexchange.com/questions/552854/volume-of-a-sphere-with-three-holes-drilled-in-it"
} |
to the shelf-life of a network. Used in the trading of assets, an investor can either buy asset! Valuation techniques in CFI ’ s Business valuation course brick '' abandoned datacenters 's … options involve risk and not... To make blurry photos/video clear with many periods and simulation in the Mandalorian to become a financial analyst at risk-free! Model to price an option allowing to change a call into a put implies. Will discuss two scenarios: simulation in the continuous time underlying asset either... Probability that the price of option risk can be categorised and even traded separately and strike.. Calculated using the normal cumulative distribution of factors d1 and d2 is another option pricing.... We will use the Geometric Brownian Motion of the max, it has payoff$... A recombining binomial tree model value a company as % a call into a put state that... A little more involved Arguments Details value Author ( s ) References Examples memorizing interview. Model, we will use the | {
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"tags": null,
"url": "https://www.dentysta.szczecin.pl/hm7ws/chooser-option-pricing-formula-b0ae53"
} |
homework-and-exercises, kinematics, acceleration, jerk
Title: How to find acceleration in this rectilinear movement? $$x = A + Bt + Ct^2 + Dt^3 $$
where $$C = 0.14~\rm m/s^{2} $$
and $$D = 0.01~\rm m/s^{3} $$
After how much time after the start of movement does the acceleration become 1 m/s^2 and what is the medium acceleration during this time interval?
I am not asking you to solve this, I need to know where shall I start from?
Is this formula enough?
$$x = x_0 + v_0t + a (t^2) / 2$$
or should I start from $$a = \frac{dv}{dt}$$
I am really confused, thanks! You should be able to tell that $x = x_0 + v_0t + a \frac{t^2}{2}$ won't do because you will be missing the $t^3$ term.
Start with $$a = \frac{{\rm d}^2x}{{\rm d}t^2} $$ and plug and chug the time values. | {
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[UPDATE a bit later: I ran it again with more bits. Same result, good to about 10^-180000. And then more: good to about 10^-360000. And then even more: good to about 10^-900000. In both cases, it's out by only a modest number of units in the last place. Periodicity in the die-choices is consistent for at least about 3 million choices. I still think it's possible that all this is bogus, but if so then the precision needed to demonstrate that empirically may be excessive.]
All the other rationals and periods reported above have been checked with this version of the code, and I didn't spot any discrepancies. | {
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"tags": null,
"url": "https://math.stackexchange.com/questions/4192238/convergence-of-winning-probability-in-a-one-player-dice-throwing-game"
} |
cosmology, entropy
Title: How do I reconcile constant entropy of a comoving volume with low-entropy initial state of the universe? In textbooks on cosmology it is often stated (e.g., Galaxy Formation and Evolution by Mo, van den Bosch & White, p. 108) that the entropy of any comoving volume is constant (as the universe is homogeneous and isotropic, there is no net flow of heat/matter through that volume). Yet, in other sources it is stated that the initial state of the universe must have been extremely low-entropy (e.g., Sean Carroll in his recent The Big Picture: On the Origins of Life, Meaning, and the Universe Itself), and that the total entropy of the universe is increasing, as it should according to the 2nd law of thermodynamics, allowing along the way for such complex phenomena as life. But nothing precludes me from regarding the entire (observable) universe as a single comoving volume (hence, with constant entropy). Does this contradiction follows from my misunderstanding of the issue, or from the | {
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"tags": "cosmology, entropy",
"url": null
} |
c++, stack, macros
for(vector<int>::iterator i = primes.begin(); i!= primes.end(); ++i)
{
printf("%d is prime\n",*i);
}
for(vector<int>::iterator i = divisibleBySeven.begin(); i!= divisibleBySeven.end(); ++i)
{
printf("%d is divisible by seven\n",*i);
}
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("test.in","r",stdin);
freopen("test.out","w",stdout);
#endif
IntStack* integers=new IntStack();
for(int i =0 ; i< 50 ;++ i)
{
integers->push(i);
}
printStats(integers);
for(int i =0 ; i< 25 ;++ i)
{
integers->pop();
}
printf("\nPopped last 25\n\n");
printStats(integers);
delete integers;
return 0;
} | {
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"tags": "c++, stack, macros",
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synthesis, amines
In summary, I would like to know why ester formation is preferred over acid chloride formation in the first step and also why a rather bulky ester is preferred over a much less bulky one. Regarding the former, I believe it could be that the formation of $\ce {HCl}$ by-product may hinder the 2nd reaction by protonating the amines. Regarding the latter, I believe there may be some electronic factors that need to be considered? Your question is easily answered by the fact that the conditions of Me3COCl + starting acid give a mixed anhydride not an ester. The tButyl group is chosen as the hindrance it brings makes reaction at the desired C=O carbon more likely. Further reading about mixed anhydride coupling is here | {
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} |
quantum-mechanics, hilbert-space, conventions, complex-numbers
One can show without too much difficulty that this correspondence amounts to an isomorphism - a one-to-one pairing between vectors and continuous linear functionals. This pairing is antilinear in the following sense: if $f$ and $g$ are vectors, $F$ and $G$ the corresponding continuous linear functionals, and $\alpha\in \mathbb C$ then
$$f + g \iff F + G \qquad \text{and} \qquad \alpha f \iff \overline\alpha F$$
Both statements can be proven straightforwardly from the pairing defined above. | {
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magnetic-fields
Title: Playing with magnetic lines My question is simple , I was just curious about this this it might seem stupid question but it should be thought upon , i was asking can we concentrate all magnetic lines at one place.
Thanks in advance for giving your answer. If we have a magnetic monopole then it will be a source or sink for magnetic field lines.
We have not observed such a thing. This statement is equivalent to one of Maxwell's equations: $\nabla\cdot B=0.$
If you are asking about magnetic field lines crossing, think about the meaning of these field lines. These are lines of force, so it would imply that the force at a point of intersection would have multiple directions. | {
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Find an element between given boundaries
1. Think of number between 1 and 100
2. How many guesses are needed to locate it if the only answers are “below” and “above”?
3. What is the optimal sequece of questions?
In [11]:
N = 10
# random sorted sequence of integers up to 100
x = np.random.choice(100,size=N,replace=False)
x = np.sort(x)
# random choice of one number/index
k0 = np.random.choice(N,size=1)
k1 = binary_search(grid=x,val=x[k0])
print("Index of x[%d]=%d in %r is %d"%(k0,x[k0],x,k1))
Index of x[8]=78 in array([ 8, 14, 24, 29, 34, 42, 43, 54, 78, 99]) is 8
In [12]:
N = 50 # number of points
kk = lambda i: 100+(i+1)*500 # step formula
# precompute the sorted sequence of integers of max length
vv = np.random.choice(10*kk(N),size=kk(N),replace=False)
vv = np.sort(vv) | {
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"tags": null,
"url": "https://nbviewer.jupyter.org/github/fediskhakov/CompEcon/blob/HEAD/09_algorithms.ipynb"
} |
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