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https://documen.tv/question/28-out-of-50-8th-graders-said-they-prefer-snow-to-rain-42-out-of-58-10th-graders-said-they-prefe-23239336-97/
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# 28 out of 50 8th graders said they prefer snow to rain. 42 out of 58 10th graders said they prefer snow. did a larger percentage of 8th grad
Question
28 out of 50 8th graders said they prefer snow to rain. 42 out of 58 10th graders said they prefer snow. did a larger percentage of 8th graders or 10th graders prefer snow?
in progress 0
1 year 2021-09-04T11:16:05+00:00 2 Answers 4 views 0
Step-by-step explanation:
Hey I hope I will be able to help!
To find out the percentage we need to divide the fractions-
28 divided by 50 = 0.56 and in percentage form its 56%
42 divided by 58 = approximately 0.72 which is 72%
56% < 72%
72% is obviously greater so 10th graders prefer snow more than 8th graders do.
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http://riot.ieor.berkeley.edu/Applications/WeightedMinCut/
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RIOT -- The Minimum and Maximum Cut Problems
The Minimum/Maximum Cut Problem
### Introduction
Many optimization problems can be formulated in terms of finding that minimum (or maximum) cut in a network or graph. A cut is formed by partitioning the nodes of a graph into two mutually exclusive sets. An edge between a node in one set and a node in the other is said to be in the cut. The weight, or the capacity, of the cut is the sum of the weights of the edges that have exactly one endpoint in each of the two sets.
### Minimum Cut
The problem of finding the minimum weight cut in a graph plays an important role in the design of communication networks. If a few of the links are cut or otherwise fail, the network may still be able to transmit messages between any pair of its nodes. If enough links fail, however, there will be at least one pair of nodes that cannot communicate with each other. Thus an important measure of the reliability of a network is the minimum number of links that must fail in order for this to happen. This number is referred to as the edge connectivity of the network and can be found by assigning a weight of 1 to each link and finding a minimum weight cut. In other applications, such as the open pit mining problem, we seek a minimum weight cut such that a specific pair of nodes, say node s and node t, are not in the same set. Solving this type of problem, known as a minimum s-t cut problem, is a fundamental part of the calculations used to find the baseball elimination and clinch numbers. Ahuja, Magnanti and Orlin [AMO93], present many other applications of cut problems.
### Maximum Cut
This problem is the same as the minimum cut except that the capacity of the cut is maximized. Thus, we want to partition the nodes of the graph into two subsets so that the sum of the weights of the edges going from one subset to the other is maximized.
The problem of cluster analysis, partitioning a set of data points into groups of "closely related" observations, can be modeled as a maximum cut problem. The points in a particular group, or cluster, should be more "similar" or "close" to each other than they are to points in other clusters. Cluster analysis can be formulated as a maximum cut problem by creating a graph that contains a node for each data point and an edge between each pair of points. The weight of the edge is determined by the relative "closeness" of the points represented by the nodes it connects. For numerical data, for example, the relative closeness may be defined as the Euclidean distance. The clusters that are formed by finding maximum weight cuts in this graph have the property that points in one cluster are more dissimilar from points in other clusters. Barahona, Grötschel, Jünger and Reinelt [BGJR88] describe how the maximum cut problems also arises in the design of VLSI circuits and the analysis of spin-glass models.
### Solving Cut Problems
Any graph has a finite number of cuts, so one could find the minimum or maximum weight cut in a graph by enumerating and comparing the size of all the cuts. This is not a practical approach for large graphs which arise in real-world applications since the number of cuts in a graph grows exponentially with the number of nodes. Fortunately, we can solve minimum cut problems without exhaustive enumeration using network flow algorithms. No such luck with the maximum weight cut: there is no known way to solve the problem optimally other than enumeration.
Rather than using enumeration to find the maximum weight cut, RIOT uses a "greedy" approximation algorithm due to Sahni and Gonzales [SG76] which is very fast and always finds a cut that has at least half the weight of the true maximum cut. For example, if you use the application to create a graph which has a maximum cut of weight 150, then RIOT will find a cut with weight 75 or higher. This type of procedure is known as an approximation algorithm since it does not always find the optimal solution, but it gives a guarantee about the quality of the solutions that it does find. In the future, RIOT will also provide an implementation of a maximum cut algorithm due to Goemans and Williamson [GW94] which finds a cut with weight at least 88% of optimal. A comprehensive treatment of approximation algorithms for a wide variety of problems can be found in "Approximation Algorithms for NP-Hard Problems", [H96] edited by Dorit S. Hochbaum.
### RIOT Interactive Minimum/Maximum Cut Problem
RIOT provides an interactive problem with which you may experiment. Using a simple interface, you may construct a graph, and then let RIOT find a minimum weight or approximately maximum weight cut. To construct a network, select the number of nodes you would like, then use the mouse button to draw them on the page. Once you've laid down your nodes, draw the connections between them. The weight of the edges is set by dragging the "weight" (small black circle with a number next to it) along the edge until the desired value appears next to the weight. When you are finished defining your network, click the Submit button and wait for RIOT to solve the problem. The solution will consist of a set of GREEN nodes and a set of BLUE nodes. The minimum/maximum cut edges between the two sets will be highlighted in RED. You can submit the same graph to both the minimum and maximum cut solvers.
Note that for the maximum cut, RIOT may not give you an optimal solution. See if you can find a better solution than the cut produced by the "greedy" algorithm.
### References
[AMO93] R. Ahuja, T. Magnanti and J. Orlin, "Network Flows: theory, algorithms and applications," Prentice-Hall, Inc. Englewood Cliffs, New Jersey. 1993
[BGJR88] F. Barahona, M. Grötschel, M. Jünger and G. Reinelt, "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, 3:493-513 (1988)
[GW94] M. Goemans and P. Williamson, "Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming," J. Assoc. Comput. Mach., (1994).
[H96] Dorit S. Hochbaum, editor. "Approximation Algorithms for NP-Hard Problems," PWS Publishing Company, Boston, MA. 1996
[SG76] S. Sahni and T. Gonzales, "P-complete approximation problems," Journal of the ACM 23:555-565. 1976
[ Maximum/Minimum Cut | Demonstration | Try It! | Instructions ]
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# Rapidity
Rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates.
Rapidity equals the arctargent of the ratio between the velocity and the speed of light.
## Formula
symbol description physical quantity
θ rapidity "Rapidity"
v velocity "Speed"
## Examples
Get the resource:
In[1]:=
Out[1]=
Get the formula:
In[2]:=
Out[2]=
Use some values:
In[3]:=
Out[3]=
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Switch to:
Garmin Ltd (NAS:GRMN) Net Cash per Share: \$-0.83 (As of Jun. 2017)
Net cash per share is calculated as Cash And Cash Equivalents minus Total Liabilities and then divided by Shares Outstanding (Diluted Average). Garmin Ltd's net cash per share for the quarter that ended in Jun. 2017 was \$-0.83.
Historical Data
* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.
Garmin Ltd Annual Data
Dec07 Dec08 Dec09 Dec10 Dec11 Dec12 Dec13 Dec14 Dec15 Dec16 Net Cash per Share 0.50 0.56 0.39 -0.56 0.04
Garmin Ltd Quarterly Data
Sep12 Dec12 Mar13 Jun13 Sep13 Dec13 Mar14 Jun14 Sep14 Dec14 Mar15 Jun15 Sep15 Dec15 Mar16 Jun16 Sep16 Dec16 Mar17 Jun17 Net Cash per Share -1.35 -0.61 0.04 1.03 -0.83
Competitive Comparison
* Competitive companies are chosen from companies within the same industry, with headquarter located in same country, with closest market capitalization; x-axis shows the market cap, and y-axis shows the term value; the bigger the dot, the larger the market cap.
Calculation
In the calculation of a company's net cash, assets other than cash and short term investments are considered to be worth nothing. But the company has to pay its debt and other liabilities in full. This is an extremely conservative way of valuation. Most companies have negative net cash. But sometimes a company's price may be lower than its net-cash.
Garmin Ltd's Net Cash Per Share for the fiscal year that ended in Dec. 2016 is calculated as
Net Cash Per Share (A: Dec. 2016 ) = (Cash And Cash Equivalents - Total Liabilities) / Shares Outstanding (Diluted Average) = (1113.835 - 1107.13) / 188.57 = 0.04
Garmin Ltd's Net Cash Per Share for the quarter that ended in Jun. 2017 is calculated as
Net Cash Per Share (Q: Jun. 2017 ) = (Cash And Cash Equivalents - Total Liabilities) / Shares Outstanding (Diluted Average) = (1108.464 - 1264.325) / 188.16 = -0.83
* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.
Explanation
Ben Graham invested in situations where the company's stock price was lower than its net-cash. He assigned some value to the company's other current asset. The value is called Net Current Asset Value (NCAV). One research study, covering the years 1970 through 1983 showed that portfolios picked at the beginning of each year, and held for one year, returned 29.4 percent, on average, over the 13-year period, compared to 11.5 percent for the S&P 500 Index. Other studies of Graham's strategy produced similar results.
You can find companies that are traded below their Net Current Asset Value (NCAV) with our Net-Net screener. GuruFocus also publishes a monthly Net-Net newsletter.
Related Terms
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EE131A TA Recitation 6
# EE131A TA Recitation 6 - EE131A Probability TA Recitation 6...
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EE131A Probability TA Recitation 6 Chihkai Chen [email protected] Office hours: Monday, 9:15-10:15pm Tuesday, 9:15-10:15pm Saturday, 2:30-3:30pm (email by Friday)
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Moment generating function Moment generating function Obtain moments tX tn n n=0 (t) =E{e } e p . φ = n 1n n t=0 t=0 dd (t) = m ; (t) = m , n = 1, 2, . .. dt dt φφ
Characterisitic function Characteristic function Obtain moments n n n ω =0 1d ( ω ) = m , n = 1, 2, . .. d ω n i φ i ω Xi ω
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EE131A TA Recitation 6 - EE131A Probability TA Recitation 6...
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Ask a homework question - tutors are online
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### D - Bracket sequence
##### Languages: C, C++, Java, Python, ... (details)
Given two sequences of brackets $a$ and $b$ of length $n$, such that $a$ is not greater than $b$, you must count the number of balanced bracket sequences of length $n$ not less than $a$ and not greater than $b$. We assume comparisons are made in a lexicographical sense.
We define balanced bracket sequences as follows:
• The empty sequence is a balanced bracket sequence.
• If $s$ is a balanced bracket sequence, then so is $(s)$.
• If $s$ and $t$ are balanced bracket sequences, then so is $st$.
Given two sequences of brackets $x$, $y$ of length $n$, we say $x$ is lexicographically smaller than $y$ if they share a prefix of size $t \in [0, n-1]$ and $x[t+1] < y[t+1]$. You may assume character '(' is smaller than character ')'.
#### Input
The first line of input contains the integer $n$ $(1 \leq n \leq 10^3)$, the size of the sequences. Next two lines contain respectively sequences $a$ and $b$, composed only by characters '(' and ')'. It is guaranteed that sequence $b$ is not lexicographically smaller than $a$.
#### Output
Print a line with the answer. Since this number may be very large you should output the answer modulo $10^9+7$.
#### Sample test(s)
Input
4 (((( ()))
Output
2
Input
3 ()) )()
Output
0
Input
12 ((()))(()()) ((()))(()())
Output
1
Input
38 (((((((((((((((((((((((((((((((((((((( ))))))))))))))))))))))))))))))))))))))
Output
767263183
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https://www.casinocitytimes.com/frank-scoblete/article/are-my-7-outs-unusual-37200
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Stay informed with the
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# Are my 7 outs unusual?
16 September 2007
Dear Frank:
Why don't you address the following:
1. Majority of my "7 Outs" are 6/1 or 5/2 combinations with a rare 4/3. I've noticed these outcomes over several years of playing craps. I've become highly sensitive to these unusual results.
2. Finally, on my last visit to the Borgata of Atlantic City I kept track of the numbers. After 210 rolls ending in a "7 Out," 175 were a 5-2 combination, 26 were a 6-1 combination, and only 9 were a 4-3 combination.
3. What is also unusual is that often times just before a 7 Out, you will see a heavy incidence of craps with 1-1, 1-2, 6-6 combinations - - - all not involving the 4 & 3.
Any thoughts?
Mr. N
Dear Mr. N:
If you are not a controlled shooter using the Hardway set (all hardways around the faces of the dice with the six-spot and one-spot on the sides), there is no way for me to tell if what you are experiencing is some kind of pattern based on your skill at a given table or just a random fluctuation.
Believe it or not a run of 210 rolls of seven-outs is not that significant when it comes to a random game, nor is your noticing such craps numbers appearing before most of these seven-outs significant - randomness can be quite pattern-filled yet not predictable. Maybe the next 210 seven-outs will be different.
However, if you are a controlled shooter using the Hardway set then every time you see a 1:1 or a 6:6, your dice have flipped over to one side or the other. Every time you see a 6:1 or 1:6, both dice have probably flipped in opposite directions. Those 5:2 and 4:3 or 2:5 and 3:4 seven-outs, while disheartening, mean that you dice are on axis but that you are double-pitching - meaning one die is turning twice in relation to the other die bringing up the 7. Your double-pitch is resulting in a 5:2 or 2:5 respectively.
If you are a controlled shooter, the first thing to look at is the placement of your fingers on the grip - chances are they are not even across but one is slightly lower than the rest. That means either your ring finger (most likely) or your pointer. You can fix your double pitching by getting those fingers straight. Although many dice adviocates would have you mesing around with changing your set the real culprit in most on axis seven outs is usually the grip.
There is a wonderful device called the "Gripper" that can be bought at http://www.goldentouchcraps.com/dice.shtml. This ingenius device teaches you how to have a perfect grip and is recommended for some who is constantly double pitching.
I am giving you a free month on my private web site at www.goldentouchcraps.com for your question. There are over 5,000 members and I think you will enjoy the lively conversations.
All the best in and out of the casinos!
Frank Scoblete
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Frank Scoblete
Frank Scoblete is the #1 best selling gaming author in America. His newest books are Slots Conquest: How to Beat the Slot Machines; Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo and Pai Gow Poker!; Beat Blackjack Now: The Easiest Way to Get the Edge; Casino Craps: Shoot to Win!; Cutting Edge Craps: Advanced Strategies for Serious Players; Casino Conquest: Beat the Casinos at Their Own Games! and The Virgin Kiss.
Frank and Casino City Times columnist Jerry "Stickman" teach private lessons in dice control. Frank's books are available at Amazon.com, in bookstores or by mail order. Call 1-800-944-0406 or write to Frank Scoblete Enterprises, PO Box 446, Malverne, NY 11565. Frank can also be reached by email at fscobe@optonline.net.
#### Frank Scoblete Websites:
www.goldentouchcraps.com
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#### Books by Frank Scoblete:
Frank Scoblete
Frank Scoblete is the #1 best selling gaming author in America. His newest books are Slots Conquest: How to Beat the Slot Machines; Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo and Pai Gow Poker!; Beat Blackjack Now: The Easiest Way to Get the Edge; Casino Craps: Shoot to Win!; Cutting Edge Craps: Advanced Strategies for Serious Players; Casino Conquest: Beat the Casinos at Their Own Games! and The Virgin Kiss.
Frank and Casino City Times columnist Jerry "Stickman" teach private lessons in dice control. Frank's books are available at Amazon.com, in bookstores or by mail order. Call 1-800-944-0406 or write to Frank Scoblete Enterprises, PO Box 446, Malverne, NY 11565. Frank can also be reached by email at fscobe@optonline.net.
#### Frank Scoblete Websites:
www.goldentouchcraps.com
www.goldentouchblackjack.com
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My Math Forum π(x)
Number Theory Number Theory Math Forum
February 14th, 2017, 04:51 PM #1 Newbie Joined: Jul 2014 From: Taiwan Posts: 8 Thanks: 0 π(x) Sorry, my math and English are poor, but I still want to ask a question about π(x). If we let x/ln(x) be substituted into x, and so that becomes to be [x/ln(x)]/ln[x/ln(x)], then repeat this step over and over again; thus, is it correct that finally equals π(x)? Would someone like to explain to me if that is correct?
February 14th, 2017, 07:00 PM #2 Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,493 Thanks: 752 repeated iteration of $\dfrac{x}{\ln(x)}$ results in $e,~\forall x > 1$ $\dfrac{x}{\ln(x)}=x$ $1 = \ln(x)$ $x = e$ $e \neq \pi(x)$
Tags hypothesis, πx, number theory, prime, prime number
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Number 1050436
Number 1,050,436 spell 🔊, write in words: one million, fifty thousand, four hundred and thirty-six, approximately 1.1 million. Ordinal number 1050436th is said 🔊 and write: one million, fifty thousand, four hundred and thirty-sixth. The meaning of the number 1050436 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 1050436. What is 1050436 in computer science, numerology, codes and images, writing and naming in other languages
What is 1,050,436 in other units
The decimal (Arabic) number 1050436 converted to a Roman number is (M)(L)CDXXXVI. Roman and decimal number conversions.
Weight conversion
1050436 kilograms (kg) = 2315791.2 pounds (lbs)
1050436 pounds (lbs) = 476474.6 kilograms (kg)
Length conversion
1050436 kilometers (km) equals to 652711 miles (mi).
1050436 miles (mi) equals to 1690514 kilometers (km).
1050436 meters (m) equals to 3446271 feet (ft).
1050436 feet (ft) equals 320177 meters (m).
1050436 centimeters (cm) equals to 413557.5 inches (in).
1050436 inches (in) equals to 2668107.4 centimeters (cm).
Temperature conversion
1050436° Fahrenheit (°F) equals to 583557.8° Celsius (°C)
1050436° Celsius (°C) equals to 1890816.8° Fahrenheit (°F)
Time conversion
(hours, minutes, seconds, days, weeks)
1050436 seconds equals to 1 week, 5 days, 3 hours, 47 minutes, 16 seconds
1050436 minutes equals to 2 years, 2 months, 1 day, 11 hours, 16 minutes
Codes and images of the number 1050436
Number 1050436 morse code: .---- ----- ..... ----- ....- ...-- -....
Sign language for number 1050436:
Number 1050436 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
Mathematics of no. 1050436
Multiplications
Multiplication table of 1050436
1050436 multiplied by two equals 2100872 (1050436 x 2 = 2100872).
1050436 multiplied by three equals 3151308 (1050436 x 3 = 3151308).
1050436 multiplied by four equals 4201744 (1050436 x 4 = 4201744).
1050436 multiplied by five equals 5252180 (1050436 x 5 = 5252180).
1050436 multiplied by six equals 6302616 (1050436 x 6 = 6302616).
1050436 multiplied by seven equals 7353052 (1050436 x 7 = 7353052).
1050436 multiplied by eight equals 8403488 (1050436 x 8 = 8403488).
1050436 multiplied by nine equals 9453924 (1050436 x 9 = 9453924).
show multiplications by 6, 7, 8, 9 ...
Fractions: decimal fraction and common fraction
Fraction table of 1050436
Half of 1050436 is 525218 (1050436 / 2 = 525218).
One third of 1050436 is 350145,3333 (1050436 / 3 = 350145,3333 = 350145 1/3).
One quarter of 1050436 is 262609 (1050436 / 4 = 262609).
One fifth of 1050436 is 210087,2 (1050436 / 5 = 210087,2 = 210087 1/5).
One sixth of 1050436 is 175072,6667 (1050436 / 6 = 175072,6667 = 175072 2/3).
One seventh of 1050436 is 150062,2857 (1050436 / 7 = 150062,2857 = 150062 2/7).
One eighth of 1050436 is 131304,5 (1050436 / 8 = 131304,5 = 131304 1/2).
One ninth of 1050436 is 116715,1111 (1050436 / 9 = 116715,1111 = 116715 1/9).
show fractions by 6, 7, 8, 9 ...
Calculator
1050436
Is Prime?
The number 1050436 is not a prime number. The closest prime numbers are 1050431, 1050437.
Factorization and factors (dividers)
The prime factors of 1050436 are 2 * 2 * 59 * 4451
The factors of 1050436 are 1, 2, 4, 59, 118, 236, 4451, 8902, 17804, 262609, 525218, 1050436.
Total factors 12.
Sum of factors 1869840 (819404).
Powers
The second power of 10504362 is 1.103.415.790.096.
The third power of 10504363 is 1.159.067.668.885.281.792.
Roots
The square root √1050436 is 1024,907801.
The cube root of 31050436 is 101,653702.
Logarithms
The natural logarithm of No. ln 1050436 = loge 1050436 = 13,864716.
The logarithm to base 10 of No. log10 1050436 = 6,02137.
The Napierian logarithm of No. log1/e 1050436 = -13,864716.
Trigonometric functions
The cosine of 1050436 is 0,870797.
The sine of 1050436 is 0,491643.
The tangent of 1050436 is 0,564589.
Properties of the number 1050436
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
Number 1050436 in Computer Science
Code typeCode value
1050436 Number of bytes1.0MB
Unix timeUnix time 1050436 is equal to Tuesday Jan. 13, 1970, 3:47:16 a.m. GMT
IPv4, IPv6Number 1050436 internet address in dotted format v4 0.16.7.68, v6 ::10:744
1050436 Decimal = 100000000011101000100 Binary
1050436 Decimal = 1222100221001 Ternary
1050436 Decimal = 4003504 Octal
1050436 Decimal = 100744 Hexadecimal (0x100744 hex)
1050436 BASE64MTA1MDQzNg==
1050436 MD5d22cf18299318d63c37d145c026a13b6
1050436 SHA1294e9a1cbd6b3538c28c58efcec03e81c69c121a
1050436 SHA256713505cf1593d69b2095004edc7f6ce3ff7c77fc8c59c63e26342e8c38f769a6
1050436 SHA384124fb878b3586a3c1078b179470c485beaf5ceacb8db3ba1cf4845424127ed37ff801fc3dd19ef0f2975621d8e20369a
More SHA codes related to the number 1050436 ...
If you know something interesting about the 1050436 number that you did not find on this page, do not hesitate to write us here.
Numerology 1050436
Character frequency in the number 1050436
Character (importance) frequency for numerology.
Character: Frequency: 1 1 0 2 5 1 4 1 3 1 6 1
Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 1050436, the numbers 1+0+5+0+4+3+6 = 1+9 = 1+0 = 1 are added and the meaning of the number 1 is sought.
№ 1,050,436 in other languages
How to say or write the number one million, fifty thousand, four hundred and thirty-six in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 1.050.436) un millón cincuenta mil cuatrocientos treinta y seis German: 🔊 (Nummer 1.050.436) eine Million fünfzigtausendvierhundertsechsunddreißig French: 🔊 (nombre 1 050 436) un million cinquante mille quatre cent trente-six Portuguese: 🔊 (número 1 050 436) um milhão e cinquenta mil, quatrocentos e trinta e seis Hindi: 🔊 (संख्या 1 050 436) दस लाख, पचास हज़ार, चार सौ, छत्तीस Chinese: 🔊 (数 1 050 436) 一百零五万零四百三十六 Arabian: 🔊 (عدد 1,050,436) واحد مليون و خمسون ألفاً و أربعمائة و ستة و ثلاثون Czech: 🔊 (číslo 1 050 436) milion padesát tisíc čtyřista třicet šest Korean: 🔊 (번호 1,050,436) 백오만 사백삼십육 Dutch: 🔊 (nummer 1 050 436) een miljoen vijftigduizendvierhonderdzesendertig Japanese: 🔊 (数 1,050,436) 百五万四百三十六 Indonesian: 🔊 (jumlah 1.050.436) satu juta lima puluh ribu empat ratus tiga puluh enam Italian: 🔊 (numero 1 050 436) un milione e cinquantamilaquattrocentotrentasei Norwegian: 🔊 (nummer 1 050 436) en million, femti tusen, fire hundre og tretti-seks Polish: 🔊 (liczba 1 050 436) milion pięćdziesiąt tysięcy czterysta trzydzieści sześć Russian: 🔊 (номер 1 050 436) один миллион пятьдесят тысяч четыреста тридцать шесть Turkish: 🔊 (numara 1,050,436) birmilyonellibindörtyüzotuzaltı Thai: 🔊 (จำนวน 1 050 436) หนึ่งล้านห้าหมื่นสี่ร้อยสามสิบหก Ukrainian: 🔊 (номер 1 050 436) один мільйон п'ятдесят тисяч чотириста тридцять шість Vietnamese: 🔊 (con số 1.050.436) một triệu năm mươi nghìn bốn trăm ba mươi sáu Other languages ...
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Frequently asked questions about the number 1050436
• How do you write the number 1050436 in words?
1050436 can be written as "one million, fifty thousand, four hundred and thirty-six".
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臺灣博碩士論文加值系統
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本文利用Naïve模型、OLS模型及VECM模型對台灣30天期利率期貨與台灣30、90與180三種天期的商業本票進行最適避險比率的計算，並比較其避險績效，實證結果發現：一、經由單根檢定後發現，原始資料的價格時間數列具有單根的現象，而經過一階差分後成為穩定數列。二、在共整合的檢定中，發現期貨與現貨間具有長期均衡的關係，因此可在實證中加入誤差修正項進行避險。三、樣本內與樣本外的實證中都得到相同的結論，在避險績效的衡量上，投資組合之避險績效由大到小依序是：OLS＞VECM＞Naïve，即利用OLS模型進行避險可得到最好的效果，另外在避險模型中加入誤差修正項，並無法有效的改善其績效；在投資組合的選取上，可發現以台灣30天期利率期貨和台灣90天期商業本票所組合成的投資避險組合，具有最佳之避險績效。
The purpose of this research is to estimate optimal hedge ratio and compare hedge performance by using Naive model , OLS model and VECM model . The data include Taiwan 30-Day Commercial Paper Futures and Taiwan 10-Day , 90-Day , 180-Day Commercial Paper . The major results are as follows：1. By using unit roots testing of all data , we find that the significance of unit roots and the nonstationarity of the price series . Hence , price series should be differenced to induce stationary .2. The result of cointegration test has shown that there is a long-run equilibrium relationships between spot and futures prices . Consequently , a cointegration measure can be taken into account in the hedge model .3. We find the same result in detecting the effects of in-of sample periods and out-of sample periods . The OLS model performs more well than all other hedge models for Taiwan 30-Day Commercial Paper Futures , and the VECM model is the second best . The results also has indicated that the VECM model can not improve the hedge performance . The portfolio including Taiwan 30-Day Commercial Paper Futures and Taiean 90-Day Commercial Paper can make the best hedge performance.
謝誌…………………………………………………………………………………I中文摘要……………………………………………………………………………II英文摘要……………………………………………………………………………III目錄…………………………………………………………………………………IV圖目次………………………………………………………………………………VI表目次………………………………………………………………………………VII第一章 緒論…………………………………………………………………………1第一節 研究背景與動機…………………………………………………1第二節 研究目的與限制……………………………………………………3第三節 研究架構……………………………………………………………4第二章 文獻探討與理論基礎………………………………………………………6第一節 台灣貨幣市場…………………………………………………………6第二節 我國票券利率期貨市場……………………………………………13第三節 期貨相關避險理論…………………………………………………19第四節 期貨相關避險文獻…………………………………………………22第三章 研究方法…………………………………………………………………33第一節 單根檢定……………………………………………………………33第二節 共整合檢定…………………………………………………………36第三節 誤差修正模型………………………………………………………39第四節 避險模型與績效衡量…………………………………………………40第四章 實證結果…………………………………………………………………44第一節 資料來源……………………………………………………………44第二節 基本統計分析………………………………………………………45第三節 單根檢定……………………………………………………………51第四節 共整合檢定…………………………………………………………53第五節 避險績效評估…………………………………………………………54第五章 結論與建議……………………………………………………………59第一節 結論……………………………………………………………………59第二節 建議……………………………………………………………………60參考文獻 ……………………………………………………………………………61附錄一 ………………………………………………………………………………64
一、中文1.李彥賢（2003）。股價指數期貨在國內與跨國市場避險效益的比較。私立真理大學管理科學研究所碩士論文。2.林鳳珍（2001）。美國國庫券與歐洲美元期貨間動態關係之探討-根據美國股市崩盤前後資料。國立成功大學碩士論文。3.林靖文（2000）。最適公債期貨避險策略之實證研究。高雄第一科技大學財務管理學系研究所碩士學位論文。4.施能仁（2003）。期貨與選擇權學理與實務。台北市：華立書局。5.陳碧瑤（1995）。利率期貨避險之實證與問卷分析。國立成功大學企業管理學系研究所碩士學位論文。6.陳順宇（2000）。多變量分析。台北市：華泰書局。7.張哲宇（1996）。股價指數期貨避險比率之研究。國立台灣工業技術學院管理技術研究所企業管理學程碩士論文。8.游淑華（1994）。貨幣市場間整合性與效率性之探討-根據三個月期美國國庫券與歐洲美元期貨價格。國立成功大學會計學系研究所碩士論文。9.楊亦農（2006）。時間序列分析。台北市：雙葉書局。10.廖源龍（2001）。我國票券利率期貨之研究。國立台灣大學財務金融研究所碩士論文。11.劉志霂（1999）。美國國庫券與歐洲美元期貨在價格變動率暨波動性之動態研究-根據EGARCH模型探討。國立成功大學會計學研究所碩士論文。12.魏志良（2001）。國際股價指數期貨與現貨直接避險策略之研究，私立淡江大學財務金融研究所碩士論文。13.鍾翠芬（1993）。國外利率期貨交叉避險之研究。國立台灣大學國際貿易學系研究所碩士學位論文。14.叢宏文（1995）。日經股價指數期貨避險效果之實證研究-GARCH模型之應用。國立政治大學企業管理研究所碩士學位論文。15.蘇雅芬（2003）。台灣商業本票及美國國庫券利率期貨之動態避險分析。國立中正大學企業管理研究所碩士學位論文。二、英文1.Benet, B. A（1992）.Hedge Period Length and Ex-Ante Futures HedgingEffectiveness: The Case of Foreign-Exchange Risk Cross Hedges.Journal of Futures Markets, Vol.12, pp.163-175.2.Cecchetti, S. G, Cumby, R. E. ,and Figlewski, S.（1988）.Estimation of Optimal Futures Hedge.Review of Economics and Statistics.Vol.70, pp.623-6303.Choudhry, T.（2003）.Short-Run Deviations and Optiomal Hedge Ratio:Evidence from Stock Futures.Journal of multinational financial managerment.Vol.13,pp.171-192.4.Engle, R. F. and Granger, C. W. J.（1987）.Co-integration and Error Correction: Representation Estimation and Testing.Econometrica, Vol. 55, No.2, pp.251-2765.Frankle, C. T.（1980）.The Hedging Performance of the new Futures Market: Comment. Journal of Finance, Vol.35, No.5, pp.1273-1279.6.Ghosh, A.（1993）.Hedging with Stock Index Futures:Estimation and Forecasting with Error Correction Mode.Journal of Futures Markets, Vol.13, No.7, pp.743-752.7.Hill, J. and Schneeweis, T.（1981）.A Note on the Hedging Effectiveness of Foreign currency Futures.Journal of Future Markets, Vol.1, No.4, pp.659-664.8.Johansen and Juselius,（1990）.Maximum Likelihood Estimation and Inference onCointegration:with Application to the Demand for Money.Oxford Bulletin of Economics and Statistics, Vol.52,pp.169-210.9.Koutmos, G. and Pericli, A.（1999）.Hedging GNMA Mortage-Backed Securities with T-Note Futures: Dynamic versus Static Hedging.Real Estate Economics,Vol.27, No.2, pp.335-363.10.Kroner, K. F. and Sultan, J.（1993）.Time Varying Distribution and Dynamic Hedging with Foreign Currency Futures. Journal of Financial and Quantitative Analysis, Vol.28, pp.535-551.11.Myers, R. J.（1991）.Estimating Time Varying Optimal Hedge Ratios on Futures Markets. Journal of Futures Markets, Vol.11 No.1, pp.39-53.12.Tong, W. H. S.（1996）.An examination of dynamic hedging.Journal of International Money and Finance.Vol.15, No.1, pp.19-3513.Witt, H. J, Schroeder. T. C.,and Hayenga, M. L.（1987）.Comparison of Analytical Approaches for Estimating Hedge Ratios for Agricultural Commodities, Journal of Futures Markets, Vol.7, No.2, pp.135-146.
國圖紙本論文
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1 日經股價指數期貨避險效果之實證研究：GARCH模型之應用 2 國際股價指數期貨與現貨直接避險策略之研究 3 股價指數期貨避險比率之研究 4 台灣商業本票及美國國庫券利率期貨之動態避險分析 5 最適公債期貨避險策略之實證研究 6 國外利率期貨交叉避險之研究 7 美國國庫券與歐洲美元期貨間動態關係之探討-根據美國股市崩盤前後資料 8 股價指數期貨在國內與跨國市場避險效益的比較 9 利率期貨避險之實證與問卷分析 10 貨幣市場間整合性與效率性之探討-根據三個月期美國國庫券與歐洲美元期貨價格 11 我國票券利率期貨之研究 12 美國國庫券與歐洲美元期貨在價格變動率暨波動性之動態研究-根據EGARCH模型探討 13 資訊不對稱對期貨市場贏家效用之研究 14 台股指數期貨避險績效之研究 15 期貨契約最適避險策略之研究：以股價指數期貨為例
1 余朝權、楊碧雲，1996，強制性財務預測準確度之影響因素分析，輔仁管理評論，第3卷第1期，頁1-28。 2 吳安妮，1991，經理人員自願性揭露盈餘預測資訊給外界之決定因素-實證研究，會計評論，第25期，頁1-24。 3 金成隆、林修葳與林美鳳，2002，新上市公司股價異常漲跌與財務預測關係之研究，會計評論，第34期，頁31-56。 4 金成隆、林修葳與黃書楣，2000，國內現金增資企業盈餘管理之實證研究，中山管理評論，第8卷4期，頁709-744。
1 都會型連鎖藥局品牌知名度之個案研究 2 股價指數期貨與現貨價格關聯性之研究 3 禽流感預防認知態度行為研究–以中部某大學為例 4 復健科病房病患需求探討 5 高級中等學校軍訓主管領導模式與部屬工作滿意度關聯之研究 6 健康運動器材公司顧客市場區隔之個案研究 7 台灣50ETF與台股股價指數期貨套利性之研究 8 骨質疏鬆症的影響因素之探討 9 中等學校跆拳道社團學員參與動機之研究-以南投縣為例 10 以自適應共振理論進行中草藥作用的自動化推論 11 初感風寒適用的中藥方劑分析 12 遠匯契約與外匯期貨投資組合避險策略之研究 13 股價指數期貨上市對台股現貨影響之研究 14 應用人工智慧技術於台灣股價指數期貨套利之研究 15 對鏡：皮膚醫學美容病患身體意象及其相關影響因素
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##### Discrete Math Proofs
label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5
We are doing proofs by contrapositive in my discrete math class. The original statement is "Suppose x is a real number. If (x^3-x)>0, then x>-1."
Oct 15th, 2015
(x^3-x) > 0
x( x^2 -1) > 0
therefore
x>0 and x^2-1
if x^2-1 >1
there will be two solution
x > -1 or x >1
Oct 15th, 2015
...
Oct 15th, 2015
...
Oct 15th, 2015
Oct 19th, 2017
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# Co-orbital configuration
(Redirected from Trojan planet)
In astronomy, a co-orbital configuration is a configuration of two or more astronomical objects (such as asteroids, moons, or planets) orbiting at the same, or very similar, distance from their primary, i.e. they are in a 1:1 mean-motion resonance. (or 1:−1 if orbiting in opposite directions[1])
There are several classes of co-orbital objects, depending on their point of libration. The most common and best-known class is the trojan, which librates around one of the two stable Lagrangian points (Trojan points), L4 and L5, 60° ahead of and behind the larger body respectively. Another class is the horseshoe orbit, in which objects librate around 180° from the larger body. Objects librating around 0° are called quasi-satellites.[2]
An exchange orbit occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchange semi-major axes or eccentricities when they approach each other.
## Parameters
Orbital parameters that are used to describe the relation of co-orbital objects are the longitude of the periapsis difference and the mean longitude difference. The longitude of the periapsis is the sum of the mean longitude and the mean anomaly ${\displaystyle ({\lambda }=\varpi +M)}$ and the mean longitude is the sum of the longitude of the ascending node and the argument of periapsis ${\displaystyle (\varpi =\Omega +\omega )}$.
## Trojans
Trojan points are the points labelled L4 and L5, highlighted in red, on the orbital path of the secondary object (blue), around the primary object (yellow).
Main article: Trojan (astronomy)
Trojan objects orbit 60° ahead of (L4) or behind (L5) a more massive object, both in orbit around an even more massive central object. The best known example are the asteroids that orbit ahead of or behind Jupiter around the Sun. Trojan objects do not orbit exactly at one of either Lagrangian points, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around ${\displaystyle ({\Delta }{\lambda },{\Delta }\varpi )}$ = (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity.[2]
### Trojan minor planets
There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near Jupiter's Lagrangian points, the traditional Jupiter trojans. As of 2015 there are also 13 Neptune trojans, 7 Mars trojans, 1 Uranus trojan (2011 QF99) and 1 Earth trojan (2010 TK7) known to exist.
### Trojan moons
The Saturnian system contains two sets of trojan moons. Both Tethys and Dione have two trojan moons, Telesto and Calypso in Tethys's L4 and L5 respectively, and Helene and Polydeuces in Dione's L4 and L5 respectively.
Polydeuces is noticeable for its wide libration: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along a tadpole orbit in 790 days (288 times its orbital period around Saturn, the same as Dione's).
### Trojan planets
A pair of co-orbital exoplanets was proposed to be orbiting the star Kepler-223, but this was later retracted.[3]
The possibility of a trojan planet to Kepler-91b was studied but the conclusion was that the transit-signal was a false-positive.[4]
One possibility for the habitable zone is a trojan planet of a giant planet close to its star.[5]
#### Formation of the Earth–Moon system
According to the giant impact hypothesis, the Moon formed after a collision between two co-orbital objects—Theia, thought to have had about 10% of the mass of Earth (about as massive as Mars), and the proto-Earth—whose orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.
## Horseshoe orbits
Rotating-frame depiction of the horseshoe exchange orbits of Janus and Epimetheus
Main article: Horseshoe orbit
Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. L4 and L5.[2]
### Co-orbital moons
The Saturnian moons Janus and Epimetheus share their orbits, the difference in semi-major axes being less than either's mean diameter. This means the moon with the smaller semi-major axis will slowly catch up with the other. As it does this, the moons gravitationally tug at each other, increasing the semi-major axis of the moon that has caught up and decreasing that of the other. This reverses their relative positions proportionally to their masses and causes this process to begin anew with the moons' roles reversed. In other words, they effectively swap orbits, ultimately oscillating both about their mass-weighted mean orbit.
### Earth co-orbital asteroids
A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid 3753 Cruithne, orbits the Sun with a period slightly less than one Earth year, resulting in an orbit that (from the point of view of Earth) appears as a bean-shaped orbit centered on a position ahead of the position of Earth. This orbit slowly moves further ahead of Earth's orbital position. When Cruithne's orbit moves to a position where it trails Earth's position, rather than leading it, the gravitational effect of Earth increases the orbital period, and hence the orbit then begins to lag, returning to the original location. The full cycle from leading to trailing Earth takes 770 years, leading to a horseshoe-shaped movement with respect to Earth.[6]
More resonant near-Earth objects (NEOs) have since been discovered. These include 54509 YORP, (85770) 1998 UP1, 2002 AA29, 2010 SO16, 2009 BD, and 2015 SO2 which exist in resonant orbits similar to Cruithne's. 2010 TK7 is the first and so far only identified Earth trojan.
## Quasi-satellite
Main article: Quasi-satellite
Quasi-satellites are co-orbital objects that librate around 0° from the primary. Low-eccentricity quasi-satellite orbits are highly unstable, but for moderate to high eccentricities such orbits can be stable.[2] From a co-rotating perspective the quasi-satellite appears to orbit the primary like a retrograde satellite, although at distances so large that it is not gravitationally bound to it.[2]
## Exchange orbits
In addition to swapping semi-major axes like Saturn's moons Epimetheus and Janus, another possibility is to share the same axis, but swap eccentricities instead.[7]
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Vocab Quiz- Work And Machinery: Question Preview (ID: 18561)
Below is a preview of the questions contained within the game titled VOCAB QUIZ- WORK AND MACHINERY: Work And Machinery .To play games using this data set, follow the directions below. Good luck and have fun. Enjoy! [print these questions]
Calculate the mass and velocity and you can determine this
a) momentum
b) law of conservation
c) collision
d) mechanical energy
Unless something hits the ball, it will just keep on rolling
a) momentum
b) law of conservation of Momentum
c) collision
d) mechanical energy
An object's motion is often interrupted when it is run into by something else
a) momentum
b) law of conservation of momentum
c) colliision
d) mechanical energy
The ball already had the potential to move, but now it is moving.
a) momentum
b) law of conservation of momentum
c) collision
d) mechanical
We don't pay you to sit there and do nothing in the warehouse. Get up and use your might to set those boxes in motion on the truck.
a) work
b) joule
c) power
d) machine
Let's see how much you have done today!
a) work
b) joule
c) power
d) machine
You only put two boxes on the truck in the last thirty minutes. Are you lazy or just plain weak?
a) work
b) joule
c) power
d) machine
I know there are some heavy boxes on that pallet. I don't expect you to be able to lift them yourself silly. That's what forklifts are for!
a) work
b) joule
c) power
d) machine
The forklift doesn't turn itself on you knucklehead. You have to put the keys in the ignition to get it started.
a) input force
b) output force
d) efficiency
Once you get it started, and press the buttons on the forklift, you can just sit back relax and watch it lift the boxes all by itself.
a) input force
b) output force
d) efficiency
Once you crank the lawn mower. All you have to do is push it and it will multiply your efforts by 5.
a) input force
b) output force
d) efficiency
How awesome! The forklift is doing 1200% of the work I am. That's amazing!
a) input force
b) output force
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https://scicomp.stackexchange.com/questions/20951/what-are-the-numerical-methods-for-testing-for-dissimiliarity-between-image-base/21368
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# What are the numerical methods for testing for dissimiliarity between image based probability histograms?
I have several probability distribution histograms of images that I am comparing to test for dissimilarity. Each histogram has 256 bins, the bins are common for all histograms.
The images are taken in very low light conditions, using narrow bandpass filters and illuminated by the same light source (with any other light source excluded). Each image is to be compared to the 'dark noise' histograms to determine (if any) dissimilarities exist between the low light image and dark noise distributions.
What is an effective numerical method to determine for testing for dissimiliarity between image based probability histograms?
## 2 Answers
Sounds like a job for the Earth Mover's Distance (or Wasserstein metric).
In computer science, the earth mover's distance (EMD) is a measure of the distance between two probability distributions.
Informally, if the distributions are interpreted as two different ways of piling up a certain amount of dirt over the region $$D$$, the EMD is the minimum cost of turning one pile into the other; where the cost is assumed to be amount of dirt moved times the distance by which it is moved.
Here's a link to a Python+C implementation (strictly speaking a Python wrapper).
And here's the original implentation by Yossi Rubner: http://ai.stanford.edu/~rubner/emd/default.htm
• Better known as the "Wasserstein metric"; computing such a transport plan is known as "optimal transport". If the cost is proportional to the distance, there's a very efficient algorithm based on the Sinkhorn-Knopp algorithm. @dirk has a nice write-up on his blog. Oct 7 '15 at 17:27
• @ChristianClason yep, removed that from the Wiki quotation (not sure why I did...), thanks though!! Oct 7 '15 at 17:31
You can also use the Bhattachariyya distance, which is very easy to compute.
https://en.m.wikipedia.org/wiki/Bhattacharyya_distance
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# Optimization Problems with Items and Categories in Oracle – Intro
I recently posted a series of eight articles on my GitHub Pages blog.
## [Here is the general introduction to the articles…]
The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
• Knapsack problem
• The knapsack problem and many other problems in combinatorial optimization require the selection of a subset of items to maximize an objective function subject to constraints. A common approach to solving these problems algorithmically involves recursively generating sequences of items of increasing length in a search for the best subset that meets the constraints.
I applied this kind of approach using SQL for a number of problems, starting in January 2013 with A Simple SQL Solution for the Knapsack Problem (SKP-1), and I wrote a summary article, Knapsacks and Networks in SQL
, in December 2017 when I put the code onto GitHub, sql_demos – Brendan’s repo for interesting SQL.
Here is a series of eight articles that aim to provide a more formal treatment of algorithms for item sequence generation and optimization, together with practical implementations, examples and verification techniques in SQL and PL/SQL.
### GitHub
• Optimization Problems with Items and Categories in Oracle
• ## [Here is the conclusion to the articles…]
We can list here some of the features and concepts considered in the whole series.
### Sequence Generation
• 4 types of sequence defined
• sequence generation explained via recursion…
• …implemented by recursion and by iteration
### Optimization Problems
• sequence truncation using simple maths
• value filtering techniques with approximation and bounding
• two-level iterative refinement methods
### SQL
• recursive SQL
• materializing subqueries via hints or use of temporary tables
• cycles and some anomalies
• storing sequences of items in SQL by concatenation, nested tables, and linking tables
• index organised tables
• partitioned outer joins
• splitting concatenated lists into items via row-generation
• combining lists of items into concatenated strings by aggregation
• passing bind variables into views via system contexts
• automated generation of execution plans
### PL/SQL
• PL/SQL with embedded SQL as alternative solution methods to recursive SQL…
• …with sequence generation by both recursion and iteration, with performance comparisons
• use of arrays and temporary tables for intermediate storage, with performance comparisons
• methods for compact storage of sequences of items
• use of PL/SQL functions in SQL and performance effects of context switching
• automated code timing
### Automation
• installation
• running the solution methods
• code instrumentation
• unit testing
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What is inertia? How does inertia act and how is inertia overcome? What is centrifugal force and teh relationship between inertia.
Energy is used in overcoming three different kinds of resistance: (1) the resistance of gravity, (2) the resistance of friction, and (3) the resistance of molecular attraction. Work must also be done when another kind of resistance is overcome.
When you get on a bicycle, you must exert a force to make it move. After it starts to move, much less force is needed. In fact, once the bicycle is moving along fairly fast, it will coast for some distance without needing any force at all. But to slow it down or stop it, a force must be exerted. Scientists know that all objects act like this because of a certain property that matter has. This property is called inertia.
EXPERIMENT:
1. Tie a cord at least 6 feet long around a brick and hang the brick where it can swing freely. Pull the brick slowly toward you. Does it take much force to start it moving?
2. Stop the brick from swinging. Does it take much force to do this?
3. Now start the brick with a quick jerk. Is more force needed this time?
4. As the brick is swinging rapidly back and forth, stop its motion. Be careful not to injure your hand when you do this. Is more force needed than before?
5. If you have a spring balance, you can measure the force needed to overcome the resistance of inertia. Fasten the spring balance to the brick with a cord and then repeat each part of the experiment.
All objects have inertia. They will stay in the same place unless a force starts them moving. And they will keep on moving in the same direction unless a force stops them or turns them aside. So we can say that inertia is the tendency of all objects to stay still if still or, if moving, to go on moving in the same direction unless acted on by a force. If an object is standing still, we say that it has the inertia of rest. But if it is moving, we say it has the inertia of motion.
You have noticed these two forms of inertia many times. If you lay a book on a table, it stays where you put it because of the inertia of rest. When you throw a ball, it leaves your hand and keeps on going because of the inertia of motion. Did you ever bump into a chair in the dark or stub your toe on a stone when you were barefooted? You had the inertia of motion, while the chair or the stone had the inertia of rest.
Probably you have been in a car that started up suddenly. As it jumped forward, you felt your body pushed backward against the seat. Actually, because of the inertia of rest, you stood still for an instant after the car started. The seat really moved forward and pushed against you. If the car stopped quickly, you kept on going forward because of the inertia of motion. Perhaps you even slid off the seat. Do you remember what happened when the car turned a corner or went around a sharp curve? If it was moving fairly fast, you felt as though you were being thrown outward against the side of the car. The car changed its direction as it turned, but you were moving straight ahead. The outward force that you felt was caused by the inertia of motion. This outward force has a special name. It is called centrifugal force.
centrifugal force
When a ball tied to a string is whirled around in a circle, the ball pulls outward on the string. The faster the ball whirls, the harder it pulls. If it is whirled fast enough, it may even break the string and go flying away. Centrifugal force makes the ball pull away from the center around which it is whirling. The ball tends to move in a straight line because of inertia, but the string pulls inward and makes the ball move in a circle.
Centrifugal force is caused by the inertia of objects that are made to move in a curve instead of a straight line. This force is well named. Centrifugal means fleeing, or flying away, from the center. Ali whirling objects have centrifugal force, because their direction is constantly being changed. Centrifugal force throws your arms out from your sides when you spin around on skates. It throws water and mud off the wheels of bicycles and cars. And sometimes centrifugal force even bursts grinding wheels that are turned too fast.
Stationary objects resist being moved, and moving objects resist being stopped or having their direction changed. No object starts, stops, or changes direction by itself. A force is always needed to overcome the resistance of inertia. Without energy to exert forces, we could not move stationary objects. Nor could we stop or change the direction of moving objects. So, by using energy to exert a force greater than the inertia, we can overcome the resistance of inertia. inertia of rest is overcome when a piano is moved, while inertia of motion is overcome when a bicycle is stopped or when it has its direction changed.
| 1,037
| 4,841
|
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| 4.34375
| 4
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CC-MAIN-2024-10
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longest
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https://la.mathworks.com/matlabcentral/cody/problems/94-target-sorting/solutions/2160794
| 1,591,262,594,000,000,000
|
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crawl-data/CC-MAIN-2020-24/segments/1590347439213.69/warc/CC-MAIN-20200604063532-20200604093532-00504.warc.gz
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|
Cody
# Problem 94. Target sorting
Solution 2160794
Submitted on 15 Mar 2020 by Jan Olsen
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
a = [1 2 3 4]; t = 0; b_correct = [4 3 2 1]; assert(isequal(targetSort(a,t),b_correct))
b = 4 3 2 1
2 Pass
a = -4:10; t = 3.6; b_correct = [-4 -3 10 -2 9 -1 8 0 7 1 6 2 5 3 4]; assert(isequal(targetSort(a,t),b_correct))
b = -4 -3 10 -2 9 -1 8 0 7 1 6 2 5 3 4
3 Pass
a = 12; t = pi; b_correct = 12; assert(isequal(targetSort(a,t),b_correct))
b = 12
4 Pass
a = -100:-95; t = 100; b_correct = [-100 -99 -98 -97 -96 -95]; assert(isequal(targetSort(a,t),b_correct))
b = -100 -99 -98 -97 -96 -95
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|
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| 2.953125
| 3
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CC-MAIN-2020-24
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latest
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| 0.614801
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https://www.cardinalpath.com/blog/data-science-month-blog-post-uplift-modeling-measuring-true-campaign-impact
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crawl-data/CC-MAIN-2020-50/segments/1606141748276.94/warc/CC-MAIN-20201205165649-20201205195649-00033.warc.gz
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| 226,222
|
Cardinal Path’s response to COVID-19 Cardinal Path is sharing all we know to help marketers during COVID-19. Learn more.
### Data Science Series- Uplift Modeling: measuring true campaign impact
Reading Time: 3 minutes
You’ve just finished running a new advertising campaign. Now you want to know the answer to your obvious and most pressing question: did it work? That is, did the campaign create uplift, causing more customers to purchase your product than would have without the campaign?
Naïve and incorrect approach
The conversion rate after receiving the offer was 7%, and so you conclude that 7% of customers bought your product because they saw the ad.
This is incorrect. What if those same customers were going to purchase your product anyways? Without comparing the conversion rate of those who saw the ad to those that didn’t, you aren’t getting a true measure of how much ‘lift’ your campaign actually caused.
In other words, you should not use the approach outlined above.
Basic solution: controlled testing
It is always a good idea to send your campaign to some potential customers (your ‘test’ group) and not send it to others (your ‘control’ group). These two groups should be as comparable as possible in all other ways.
For example, you should not send your campaign to women only and not to men and then try to compare the conversion rate between these groups; you won’t be able to separate out whether the impact was due to gender or to the campaign.
Once you have run your test on comparable results, you can analyze the results and measure the uplift that the campaign created. As an extremely basic example, if the audience segment that was sent the campaign had a conversion rate of 7%, but the segment who were not sent the offer in the same time period had a conversion rate of 5%, then the true uplift of your campaign is 2%. Although this may paint a bleaker picture than using the naïve and incorrect approach, it is the true measure of lift for your campaign rather than assuming causality and not comparing what would have happened without your campaign.
That being said, it is always a good idea to check your results for statistical significance, to ensure you have found true uplift and that the difference between the groups is likely not due to chance.
Advanced solution: customized model for efficient targeting
Once you have measured the uplift of your campaign, you might be curious to keep going and dig even deeper. Who did the campaign have the greatest impact on? Did it increase conversion for certain demographics more so than others? Were there any customers who didn’t convert because of the campaign? Is there any way to use the results of this campaign to decide who on your customer list should be targeted in the future?
If you possess user level data for both customers who were targeted by an ad campaign, and for those who were not, a customized uplift model is a great way to get user-level insights from your data. As with controlled testing, you will want the customers who were sent the ad and those who not to be as comparable as possible in all other ways. Then, a model can be built using machine learning and statistical techniques to predict how likely it was that someone would have purchased with and without having seen the ad.
You will gain two types of insights from this model:
1. The uplift the campaign caused for each customer within your customer list. With this data also comes the cutoffs for which customers were in the top 25% of uplift, or those who saw more than 10% uplift as a result of the campaign.
2. Profile of demographics and traits associated with higher or lower uplift. This is based on the variables that were input into the model, so if you knew the gender, region, and urban vs. suburban status of your customers, this would predict which combinations of these resulted in the highest uplift.
Once you have obtained this information, you will be able to spend your campaign budget more efficiently. For example, you could increase ROI by targeting customers with high uplift, and decrease costs by no longer displaying ads to customers with low or negative uplift. You will even be able to acquire new customers by seeking demographic groups that match your demographic profiling.
This may also bring up more questions for you: Why didn’t a certain demographic respond well to your campaign? Can we more effectively reach that demographic through different forms of advertising? This is where market research questions will come in, and you you will have to do further research in order to get the answers to those questions.
Conclusion
Uplift modelling can help decrease unnecessary and potentially harmful costs, increase ROI through efficient targeting, and grow your user base through demographic profiling of those most responsive to advertising.
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| 2.6875
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https://stonespounds.com/228-9-stones-in-stones-and-pounds
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|
# 228.9 stones in stones and pounds
## Result
228.9 stones equals 228 stones and 12.6 pounds
You can also convert 228.9 stones to pounds.
## Converter
Two hundred twenty-eight point nine stones is equal to two hundred twenty-eight stones and twelve point six pounds (228.9st = 228st 12.6lb).
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| 3.125
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CC-MAIN-2021-17
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latest
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https://www.hite-research.com/understanding-the-satta-matka-guidelines-and-basics-a-beginners-guide-2.html
| 1,701,404,385,000,000,000
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crawl-data/CC-MAIN-2023-50/segments/1700679100264.9/warc/CC-MAIN-20231201021234-20231201051234-00703.warc.gz
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# Understanding the Satta Matka Guidelines and Basics: A Beginner’s Guide
On the earth of playing and betting, there are countless games and activities that folks take pleasure in to strive their luck and win big. One such game that has gained immense popularity in India over the years is Satta Matka. It’s a traditional form of playing that has evolved into a full-fledged lottery-style game. Should you’re a newbie looking to explore the world of Satta Matka, it’s crucial to understand the principles and fundamentals of the game to maximize your chances of winning while minimizing risks.
What’s Satta Matka?
Satta Matka is a type of playing that originated in India in the course of the 1960s. Initially, it concerned betting on the opening and closing rates of cotton transmitted from the New York Cotton Exchange to the Bombay Cotton Exchange. Over time, the game advanced to include betting on random numbers, and it gained immense widespreadity, particularly in Mumbai.
The game involves choosing a set of numbers from a pool and inserting bets on these numbers. The winning numbers are then declared, and participants are rewarded based mostly on the accuracy of their predictions. While Satta Matka is illegal in India, it continues to be a thriving underground activity, attracting players from all walks of life.
Understanding the Fundamentals:
1. Choice of Numbers:
In Satta Matka, you must choose a set of three numbers ranging from 0 to 9. For example, you may select the numbers 2, 5, and 7. These numbers are then added collectively to give you the first set of numbers. In this case, the sum is 2 + 5 + 7, which equals 14. You utilize the last digit of this sum, which is 4, as your first set of numbers.
2. Repeat the Process:
The process is repeated to choose the second set of numbers. Let’s say you select the numbers three, 6, and 8. Adding them collectively provides you three + 6 + eight, which equals 17. Once once more, you utilize the last digit, which is 7, as your second set of numbers.
3. Final Numbers:
Now that you’ve got your first two sets of numbers, you could have 4 and 7. These numbers are then mixed to provde the final result. In this case, you’ll have the numbers 4 and seven as your closing Satta Matka numbers.
4. Betting:
After selecting your ultimate numbers, you can place your bets with a Satta Matka bookie. You possibly can wager on a variety of options, such as the open consequence, close end result, Jodi (mixture of numbers), Patti (three-digit number), and more. Each type of guess has totally different odds and payouts, so it’s essential to understand them before inserting your wager.
5. Outcomes:
The outcomes for Satta Matka are typically introduced twice a day, once within the morning and once in the evening. The winning numbers are drawn by way of a random process, and participants are rewarded based on their bets. In case your chosen numbers match the declared results, you win a prize according to the percentages related with your bet.
Suggestions for Freshmen:
Start Small: In the event you’re new to Satta Matka, it’s sensible to start with small bets and gradually improve your stake as you gain more expertise and confidence in the game.
Learn the Odds: Different bets have completely different odds and payouts. Take the time to understand these odds to make informed betting decisions.
Manage Your Bankroll: Set a budget for your Satta Matka activities and stick to it. Keep away from chasing losses and gambling with money you may’t afford to lose.
Stay Informed: Keep an eye on the latest Satta Matka results and trends to make more educated bets.
Play Responsibly: Keep in mind that Satta Matka is an illegal activity in India and might lead to legal consequences. Play responsibly and within the bounds of the law.
In conclusion, Satta Matka is a traditional gambling game that has evolved right into a lottery-type activity with a faithful following in India. As a newbie, it’s essential to grasp the fundamental guidelines and strategies to participate wisely. Bear in mind to gamble responsibly, and never wager more than you possibly can afford to lose. With endurance and observe, you possibly can explore the world of Satta Matka and probably expertise the thrill of winning big.
## Les Meilleurs Casinos en Ligne Luxembourg en 2023
Tous les casinos mettent en ligne les conditions liées aux bonus. Pour satisfaire sa clientèle, un casino doit tenir compte de cet élément et permettre à tous les abonnés de faire leur dépôt et retrait suivant les canaux les plus populaires : carte bancaire, carte prépayée, portefeuille électronique, crypto monnaie, […]
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| 3.703125
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CC-MAIN-2023-50
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http://www.comfsm.fm/~dleeling/statistics/sa1/q05-51ripstik-learning-curve.xhtml
| 1,550,766,701,000,000,000
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application/xhtml+xml
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crawl-data/CC-MAIN-2019-09/segments/1550247505838.65/warc/CC-MAIN-20190221152543-20190221174543-00573.warc.gz
| 330,969,155
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# q05 5.1 RipStik Learning Curve • Name:
My youngest daughter wanted to learn to ride a RipStik. She had made a couple of attempts on two prior days without any success, she would fall off almost as soon as she started moving. On Wednesday evening I took her out to the movie theater parking lot and worked with her on learning to ride the RipStik. The data in the table indicates her attempt number and the number of seconds (s) she remained up, rolling, and successfully riding the RipStik [rolling time (s)]. With each attempt she was generally, but not always able to ride longer. No children were hurt in the production of this data.
AttemptRolling time (s)
10.0
20.5
30.9
42.6
58.5
63.6
75.8
84.8
912.3
107.9
118.3
1210.4
139.3
1410.6
1510.1
1616.6
1712.0
186.3
1. __________ Find the sample size n for the data.
2. __________ Find the rolling time (s) mode.
3. __________ Find the rolling time (s) median.
4. __________ Find the rolling time (s) sample mean x.
5. sx = 4.57 Freebie: This is the standard deviation sx for the rolling time (s). If you obtain a different value, then you typed in the wrong data!
6. __________ Calculate the slope of the linear trend line for the data.
7. __________ Calculate the y-intercept of the linear regression for the data.
8. __________ Use the slope and intercept to predict the rolling time (s) for a 20th attempt.
9. __________ Use the slope and intercept to predict the attempt at which she will have a rolling time of 30 seconds.
10. __________ Does the relationship appear to be linear, non-linear, or random?
11. __________ Is the correlation positive, negative, or neutral?
12. __________ Determine the correlation coefficient r.
13. __________ What is the strength of the correlation: strong, moderate, weak, or none?
14. __________ Determine the coefficient of determination r².
15. __________ What percent of the variation in the attempt number explains the variation in the rolling time data?
16. p(3) = ______________ What is the probability of rolling a three on a six-sided die numbered from one to six?
17. p(odd) = ______________ What is the probability of rolling an odd number on an nine sided die numbered one to nine?
18. Can a die be one-sided? What shape would a one-sided die be?
| 575
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| 3.671875
| 4
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CC-MAIN-2019-09
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latest
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en
| 0.876413
|
https://mathspace.co/textbooks/syllabuses/Syllabus-98/topics/Topic-4523/subtopics/Subtopic-17511/
| 1,723,722,877,000,000,000
|
text/html
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crawl-data/CC-MAIN-2024-33/segments/1722641291968.96/warc/CC-MAIN-20240815110654-20240815140654-00080.warc.gz
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|
Hong Kong
Stage 1 - Stage 3
Expanding Difference of two Squares
Lesson
We've already looked at how to expand brackets when we were multiplying a binomial by a single number, as well as how to expand binomial products. Now we are going to look at a special case of expanding binomial products, called the difference of two squares
When we have a difference of two squares in a factorised form, it looks something like this:
$\left(a+b\right)\left(a-b\right)$(a+b)(ab)
To expand this binomial product, will still use the distributive law, making sure we multiply both terms in the first set of brackets by both terms in the second set of brackets, as shown in the picture below.
By doing this we get the expanded expression:
$a^2-ab+ab-b^2$a2ab+abb2
If we then collect any like terms and simplify the expression we are left with the difference of two squares:
$a^2-b^2$a2b2
Difference of Two Squares
$\left(x+y\right)\left(x-y\right)=x^2-y^2$(x+y)(xy)=x2y2
So in general, if we see something of the form $\left(x+y\right)\left(x-y\right)$(x+y)(xy) (or equivalently $\left(x-y\right)\left(x+y\right)$(xy)(x+y)) we know it's expansion will be $x^2-y^2$x2y2. Lets confirm this result by expanding using our rectangle method.
Set up the rectangle with the binomial expressions on each side
Multiply each term and write the answers in the relevant boxes.
When collecting like terms we can see the ab will cancel out with the $ba$ba. leaving us just with $a^2-b^2$a2b2. A difference of two squares.
More examples
Question 1
Expand the following:
$\left(m+3\right)\left(m-3\right)$(m+3)(m3)
Question 2
Expand the following:
$\left(3x-8\right)\left(3x+8\right)$(3x8)(3x+8)
Question 3
Expand the following:
$6\left(8x-9y\right)\left(8x+9y\right)$6(8x9y)(8x+9y)
| 531
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| 4.875
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CC-MAIN-2024-33
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latest
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en
| 0.820791
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https://2021.help.altair.com/2021.1/hwsolvers/ms/topics/solvers/ms/gcosub.htm
| 1,685,597,198,000,000,000
|
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# GCOSUB
ModelingCalculates a constraint defined using a Constraint_General element. Such constraints are typically used in conjunction with defining a broad range of holonomic and non-holonomic constraints. A typical example is the so called "curve of pursuit" constraint, where one particle is chasing another particle.
## Use
A Constraint_General element calling a GCOSUB for the calculation of a user-defined general constraint:
<Constraint_General
id = "1"
usrsub_param_string = "USER(5000000,1,30101020,30102020)"
usrsub_dll_name = "NULL"
usrsub_fnc_name = "GCOSUB"
/>
## Format
Fortran Calling Syntax
SUBROUTINE GCOSUB (ID, TIME, PAR, NPAR, DFLAG,IFLAG, RESULT)
C/C++ Calling Syntax
void STDCALL GCOSUB (int *id, double *time, double *par, int *npar, int *dflag, int *iflag, double *result)
Python Calling Syntax
def GCOSUB(id, time, par, npar, dflag, iflag):
return result
MATLAB Calling Syntax
function result = GCOSUB(id, time, par, npar, dflag, iflag)
## Attributes
ID
[integer]
The Constraint_General element identifier.
TIME
[double precision]
The current simulation time.
PAR
[double precision]
An array that contains the constant arguments from the list provided in the user- defined statement
NPAR
[integer]
The number of entries in the PAR array.
DFLAG
[integer]
An array of control value integers that define the type of outputs. The first value controls the ARRAY output, the second value controls the SCALAR output, and the third value controls the MATRIX output.
IFLAG
[logical]
The initialization flag.
## Output
RESULT
[double precision]
The value of the constraint.
## Example
def GCOSUB(id, time, par, npar, dflag, iflag):
[u1, errflg] = py_sysary("TDISP", [par[1],par[0]])
[v1, errflg] = py_sysary("TDISP", [par[5],par[3]])
[u2, errflg] = py_sysary("TDISP", [par[2],par[0]])
[v2, errflg] = py_sysary("TDISP", [par[4],par[3]])
result = u1[0]*v1[0]+u1[1]*v1[1]+u1[2]*v1[2]+u2[0]*v2[0]+u2[1]*v2[1]+u2[2]*v2[2]
return result
| 586
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|
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| 2.59375
| 3
|
CC-MAIN-2023-23
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latest
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en
| 0.608291
|
https://metanumbers.com/2777777777777777776
| 1,721,446,415,000,000,000
|
text/html
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crawl-data/CC-MAIN-2024-30/segments/1720763514981.25/warc/CC-MAIN-20240720021925-20240720051925-00230.warc.gz
| 338,537,362
| 8,277
|
# 2777777777777777776 (number)
2777777777777777776 is an even nineteen-digits composite number following 2777777777777777775 and preceding 2777777777777777777. In scientific notation, it is written as 2.777777777777777776 × 1018. The sum of its digits is 127. It has a total of 8 prime factors and 80 positive divisors. There are 1,375,590,638,956,259,800 positive integers (up to 2777777777777777776) that are relatively prime to 2777777777777777776.
## Basic properties
• Is Prime? no
• Number parity even
• Number length 19
• Sum of Digits 127
• Digital Root 1
## Name
Name two quintillion seven hundred seventy-seven quadrillion seven hundred seventy-seven trillion seven hundred seventy-seven billion seven hundred seventy-seven million seven hundred seventy-seven thousand seven hundred seventy-six
## Notation
Scientific notation 2.777777777777777776 × 1018 2.777777777777777776 × 1018
## Prime Factorization of 2777777777777777776
Prime Factorization 24 × 107 × 4409 × 283511 × 1298027
Composite number
Distinct Factors Total Factors Radical ω 5 Total number of distinct prime factors Ω 8 Total number of prime factors rad 347222222222222222 Product of the distinct prime numbers λ 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 2777777777777777776 is 24 × 107 × 4409 × 283511 × 1298027. Since it has a total of 8 prime factors, 2777777777777777776 is a composite number.
## Divisors of 2777777777777777776
80 divisors
Even divisors 64 16 8 8
Total Divisors Sum of Divisors Aliquot Sum τ 80 Total number of the positive divisors of n σ 5.4335e+18 Sum of all the positive divisors of n s 2.65572e+18 Sum of the proper positive divisors of n A 6.79187e+16 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G 1.66667e+09 Returns the nth root of the product of n divisors H 40.8986 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 2777777777777777776 can be divided by 80 positive divisors (out of which 64 are even, and 16 are odd). The sum of these divisors (counting 2777777777777777776) is 5433498422086452480, the average is 67918730276080656.
## Other Arithmetic Functions (n = 2777777777777777776)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ 1375590638956259840 Total number of positive integers not greater than n that are coprime to n λ 21493603733691560 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π ≈ 67030809302028004 Total number of primes less than or equal to n r2 0 The number of ways n can be represented as the sum of 2 squares
There are 1,375,590,638,956,259,800 positive integers (less than 2777777777777777776) that are coprime with 2777777777777777776. And there are approximately 67,030,809,302,028,000 prime numbers less than or equal to 2777777777777777776.
## Divisibility of 2777777777777777776
m n mod m
2 0
3 1
4 0
5 1
6 4
7 1
8 0
9 1
The number 2777777777777777776 is divisible by 2, 4 and 8.
• Arithmetic
• Deficient
• Polite
## Base conversion 2777777777777777776
Base System Value
2 Binary 10011010001100101001100010101111101101011010110001110001110000
3 Ternary 200111200111011220002222111020001111201
4 Quaternary 2122030221202233231122301301300
5 Quinary 141300202342102342102342101
6 Senary 330343040130234400420544
8 Octal 232145142575532616160
10 Decimal 2777777777777777776
12 Duodecimal 13036231ab71617754
20 Vigesimal 1di37748hfb248g
36 Base36 l3r41ifs0q5s
## Basic calculations (n = 2777777777777777776)
### Multiplication
n×y
n×2 5555555555555555552 8333333333333333328 11111111111111111104 13888888888888888880
### Division
n÷y
n÷2 1.38889e+18 9.25926e+17 6.94444e+17 5.55556e+17
### Exponentiation
ny
n2 7716049382716049372839506172839506176 21433470507544581577503429355281207159396433470507544576 59537418076512726566072245084590763749428440786465477761073007163542142976 165381716879202018133245270876729496519839455367576080448441125167233992246981320598147301376
### Nth Root
y√n
2√n 1.66667e+09 1.40572e+06 40824.8 4883.59
## 2777777777777777776 as geometric shapes
### Circle
Diameter 5.55556e+18 1.74533e+19 2.42407e+37
### Sphere
Volume 8.97803e+55 9.69627e+37 1.74533e+19
### Square
Length = n
Perimeter 1.11111e+19 7.71605e+36 3.92837e+18
### Cube
Length = n
Surface area 4.62963e+37 2.14335e+55 4.81125e+18
### Equilateral Triangle
Length = n
Perimeter 8.33333e+18 3.34115e+36 2.40563e+18
### Triangular Pyramid
Length = n
Surface area 1.33646e+37 2.52596e+54 2.26805e+18
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# QuTiP example: Phonon-assisted initialization using the time-dependent Bloch-Redfield master equation solver¶
K.A. Fischer, Stanford University
This Jupyter notebook demonstrates how to use the time-dependent Bloch-Redfield master equation solver to simulate the phonon-assited initialization of a quantum dot, using QuTiP: The Quantum Toolbox in Python. The purpose is to show how environmentally-driven dissipative interactions can be leveraged to initialize a quantum dot into its excited state. This notebook closely follows the work, Dissipative preparation of the exciton and biexciton in self-assembled quantum dots on picosecond time scales, Phys. Rev. B 90, 241404(R) (2014).
In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'retina'
In [2]:
import matplotlib.pyplot as plt
import numpy as np
import itertools
In [3]:
from qutip import *
from numpy import *
## Introduction¶
The quantum two-level system (TLS) is the simplest possible model to describe the quantum light-matter interaction between light and an artificial atom (quantum dot). While the version in the paper (both experiment and simulation) used a three-level system model, I decided to show only a TLS model here to minimize the notebook's runtime.
In the version we simulate here, the system is driven by a continuous-mode coherent state, whose dipolar interaction with the system is represented by the following Hamiltonain
$$H =\hbar \omega_0 \sigma^\dagger \sigma + \frac{\hbar\Omega(t)}{2}\left( \sigma\textrm{e}^{-i\omega_dt} + \sigma^\dagger \textrm{e}^{i\omega_dt}\right),$$
where $\omega_0$ is the system's transition frequency, $\sigma$ is the system's atomic lowering operator, $\omega_d$ is the coherent state's center frequency, and $\Omega(t)$ is the coherent state's driving strength.
The time-dependence can be removed to simplify the simulation by a rotating frame transformation. Then,
$$H_r =\hbar \left(\omega_0-\omega_d\right) \sigma^\dagger \sigma + \frac{\hbar\Omega(t)}{2}\left( \sigma+ \sigma^\dagger \right).$$
Additionally, the quantum dot exists in a solid-state matrix, where environmental interactions are extremely important. In particular, the coupling between acoustic phonons and the artifical atom leads to important dephasing effects. While the collapse operators of the quantum-optical master equation can be used to phenomenologically model these effects, they do not necessarily provide any direct connection to the underlying physics of the system-environmental interaction.
Instead, the Bloch-Redfield master equation allows for a direct connection between the quantum dynamics and the underlying physical interaction mechanism. Furthermore, the interaction strengths can be derived from first principles and can include complex power-dependences, such as those that exist in the quantum-dot-phonon interaction. Though we note that there are important non-Markovian effects which are now being investigated, e.g. in the paper Limits to coherent scattering and photon coalescence from solid-state quantum emitters, Phys. Rev. B 95, 201305(R) (2017).
### Problem parameters¶
Note, we use units where $\hbar=1$.
In [4]:
n_Pi = 13 # 8 pi pulse area
Om_list = np.linspace(0.001, n_Pi, 80) # driving strengths
wd_list_e = np.array([-1, 0, 1]) # laser offsets in meV
wd_list = wd_list_e*1.5 # in angular frequency
tlist = np.linspace(0, 50, 40) # tmax ~ 2x FWHM
# normalized Gaussian pulse shape, ~10ps long in energy
t0 = 17 / (2 * np.sqrt(2 * np.log(2)))
#pulse_shape = np.exp(-(tlist - 24) ** 2 / (2 * t0 ** 2))
pulse_shape = '0.0867 * exp(-(t - 24) ** 2 / (2 * {0} ** 2))'.format(t0)
### Setup the operators, Hamiltonian, and initial state¶
In [5]:
# initial state
psi0 = fock(2, 1) # ground state
# system's atomic lowering operator
sm = sigmam()
# Hamiltonian components
H_S = -sm.dag() * sm # self-energy, varies with drive frequency
H_I = sm + sm.dag()
# we ignore spontaneous emission since the pulse is much faster than
# the decay time
c_ops = []
Below, we define the terms specific to the Bloch-Redfield solver's system-environmental coupling. The quantum dot couples to acoustic phonons in its solid-state environment through a dispersive electron-phonon interaction of the form
$$H_\textrm{phonon}=\hbar J(\omega)\sigma^\dagger \sigma,$$
where $J(\omega)$ is the spectra density of the coupling.
In [6]:
# operator that couples the quantum dot to acoustic phonons
a_op = sm.dag()*sm
# This spectrum is a displaced gaussian multiplied by w^3, which
# models coupling to LA phonons. The electron and hole
# interactions contribute constructively.
"""
# fitting parameters ae/ah
ah = 1.9e-9 # m
ae = 3.5e-9 # m
# GaAs material parameters
De = 7
Dh = -3.5
v = 5110 # m/s
rho_m = 5370 # kg/m^3
hbar = 1.05457173e-34 # Js
T = 4.2 # Kelvin, temperature
# results in ~3THz angular frequency width, w in THz
# zero T spectrum, for w>0
J = 1.6*1e-13*w**3/(4*numpy.pi**2*rho_m*hbar*v**5) * \
(De*numpy.exp(-(w*1e12*ae/(2*v))**2) -
Dh*numpy.exp(-(w*1e12*ah/(2*v))**2))**2
# for temperature dependence, the 'negative' frequency
# components correspond to absorption vs emission
# w > 0:
JT_p = J*(1 + numpy.exp(-w*0.6582119/(T*0.086173)) / \
(1-numpy.exp(-w*0.6582119/(T*0.086173))))
# w < 0:
JT_m = -J*numpy.exp(w*0.6582119/(T*0.086173)) / \
(1-numpy.exp(w*0.6582119/(T*0.086173)))
"""
# the Bloch-Redfield solver requires the spectra to be
# formatted as a string
spectra_cb =' 1.6*1e-13*w**3/(4*pi**2*5370*1.05457173e-34*5110**5) * ' + \
'(7*exp(-(w*1e12*3.5e-9/(2*5110))**2) +' + \
'3.5*exp(-(w*1e12*1.9e-9 /(2*5110))**2))**2 *' + \
'((1 + exp(-w*0.6582119/(4.2*0.086173)) /' + \
'(1+1e-9-exp(-w*0.6582119/(4.2*0.086173))))*(w>=0)' + \
'-exp(w*0.6582119/(4.2*0.086173)) /' + \
'(1+1e-9-exp(w*0.6582119/(4.2*0.086173)))*(w<0))'
## Visualize the dot-phonon interaction spectrum¶
$J(\omega)$ has two components that give rise to its shape: a rising component due to the increasing acoustic phonon density of states and a roll-off that occurs due to the physical size of the quantum dot.
In [7]:
spec_list = np.linspace(-5, 10, 200)
plt.figure(figsize=(8, 5))
plt.plot(spec_list, [eval(spectra_cb.replace('w', str(_))) for _ in spec_list])
plt.xlim(-5, 10)
plt.xlabel('$\omega$ [THz]')
plt.ylabel('$J(\omega)$ [THz]')
plt.title('Quantum-dot-phonon interaction spectrum');
## Calculate the pulse-system interaction dynamics¶
The Bloch-Redfield master equation solver takes the Hamiltonian time-dependence in list-string format. We calculate the final population at the end of the interaction of the pulse with the system, which represents the population initialized into the excited state.
In [8]:
# we will calculate the dot population expectation value
e_ops = [sm.dag()*sm]
# define callback for parallelization
def brme_step(args):
wd = args[0]
Om = args[1]
H = [wd * H_S, [Om * H_I, pulse_shape]]
# calculate the population after the pulse interaction has
# finished using the Bloch-Redfield time-dependent solver
return qutip.brmesolve(H, psi0, tlist, [[a_op, spectra_cb]],
e_ops,options=Options(rhs_reuse=True)).expect[0][-1]
# use QuTiP's builtin parallelized for loop, parfor
results = parfor(brme_step, itertools.product(wd_list, Om_list))
# unwrap the results into a 2d array
inv_mat_X = np.array(results).reshape((len(wd_list), len(Om_list)))
### Visualize the quantum dot's initialization fidelity¶
Below, consider the trace of excited state occupation for increasing pulse area at a detuning of $\omega_d-\omega_L=0$. Here, the oscillations represent the standard Rabi oscillations of a driven two-level system, damped for increasing pulse area by a Markovian-like dephasing. This damping could be represented with a power-dependent collapse operator in the normal quantum-optical master equation. However, for nonzero pulse detunings, the results are quite nontrivial and difficult to model with a collapse operator. Herein lies the power of the Bloch-Redfield approach: it captures the dephasing in a more natural basis, the dressed atom basis, from first principles.
In this basis, the dispersive phonon-induced dephasing drives a population difference between the dressed states. This amounts to driving the system towards a dissipative quasi-steady state that initializes the population into the excited state with almost unity fidelity. The initialization effect is very insensitive to precise pulse area or laser detuning, as discussed in our paper, and hence is a powerfully robust way to pump a quantum dot into its excited state. Below is an example trace showing this dissipative initialization for a +1meV laser detuning. The high fidelity of the initialization relies on a low temperature bath that prefers phonon emission over absorption. As a complement, for a laser detuning of -1meV, the excited state is barely populated.
In [9]:
plt.figure(figsize=(8, 5))
plt.plot(Om_list, inv_mat_X[0])
plt.plot(Om_list, inv_mat_X[1])
plt.plot(Om_list, inv_mat_X[2])
plt.legend(['laser detuning, -1 meV',
'laser detuning, 0 meV',
'laser detuning, +1 meV'], loc=4)
plt.xlim(0, 13)
plt.xlabel('Pulse area [$\pi$]')
plt.ylabel('Excited state population')
plt.title('Effects of phonon dephasing for different pulse detunings');
## Versions¶
In [10]:
from qutip.ipynbtools import version_table
version_table()
Out[10]:
SoftwareVersion
QuTiP4.3.0.dev0+aca609e9
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.26
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.2 |Anaconda custom (x86_64)| (default, Jul 20 2017, 13:14:59) [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Wed Aug 23 22:40:21 2017 MDT
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CC-MAIN-2022-27
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https://www.airmilescalculator.com/distance/rdm-to-anc/
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Distance between Redmond, OR (RDM) and Anchorage, AK (ANC)
Flight distance from Redmond to Anchorage (Roberts Field – Ted Stevens Anchorage International Airport) is 1658 miles / 2669 kilometers / 1441 nautical miles. Estimated flight time is 3 hours 38 minutes.
Driving distance from Redmond (RDM) to Anchorage (ANC) is 2679 miles / 4311 kilometers and travel time by car is about 51 hours 35 minutes.
Map of flight path and driving directions from Redmond to Anchorage.
Shortest flight path between Roberts Field (RDM) and Ted Stevens Anchorage International Airport (ANC).
How far is Anchorage from Redmond?
There are several ways to calculate distances between Redmond and Anchorage. Here are two common methods:
Vincenty's formula (applied above)
• 1658.453 miles
• 2669.022 kilometers
• 1441.156 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth.
Haversine formula
• 1655.169 miles
• 2663.736 kilometers
• 1438.302 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
Airport information
A Roberts Field
City: Redmond, OR
Country: United States
IATA Code: RDM
ICAO Code: KRDM
Coordinates: 44°15′14″N, 121°9′0″W
B Ted Stevens Anchorage International Airport
City: Anchorage, AK
Country: United States
IATA Code: ANC
ICAO Code: PANC
Coordinates: 61°10′27″N, 149°59′45″W
Time difference and current local times
The time difference between Redmond and Anchorage is 1 hour. Anchorage is 1 hour behind Redmond.
PDT
AKDT
Carbon dioxide emissions
Estimated CO2 emissions per passenger is 190 kg (418 pounds).
Frequent Flyer Miles Calculator
Redmond (RDM) → Anchorage (ANC).
Distance:
1658
Elite level bonus:
0
Booking class bonus:
0
In total
Total frequent flyer miles:
1658
Round trip?
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https://testbook.com/question-answer/ifrmvec-u-hat-i-times-vec-a-time--61124bbd4b028dd0b71a347b
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# If $$\rm\vec u = \hat i \times ( \vec a \times \hat i) + \hat j \times ( \vec a \times \hat j) + \hat k \times ( \vec a \times \hat k)$$ then $$\rm \vec u$$ is equal to
This question was previously asked in
UP TGT Mathematics 2021 Official Paper
View all UP TGT Papers >
1. $$\vec 0$$
2. $$\vec a$$
3. $$2 \vec a$$
4. $$3 \vec a$$
Option 3 : $$2 \vec a$$
Free
UP TGT Biology Mock Test
11.1 K Users
10 Questions 40 Marks 10 Mins
## Detailed Solution
Given:
$$\rm\vec u = \hat i \times ( \vec a \times \hat i) + \hat j \times ( \vec a \times \hat j) + \hat k \times ( \vec a \times \hat k)$$
Concept:
î × î = ĵ × ĵ = k̂ × k̂ = 0
î × ĵ = k̂ , ĵ × k̂ = î , k̂ × î = ĵ
Calculation:
Let a = mî + nĵ +lk̂
According to the Question
$$\rm\vec u = \hat i \times ( \vec a \times \hat i) + \hat j \times ( \vec a \times \hat j) + \hat k \times ( \vec a \times \hat k)$$
$$\vec u$$ = î × (mî + nĵ +lk̂ × î) + ĵ × (mî + nĵ +lk̂ × ĵ) + k̂ × (mî + nĵ +lk̂ × k̂)
$$\vec u$$ = î × (-nk̂ + lĵ) + ĵ × (mk̂ -lî ) + k̂ × (-mĵ + nî)
$$\vec u$$ = nĵ + lk̂ + mî + lk̂ + mî + nĵ
$$\vec u$$ = 2(mî + nĵ +lk̂ ) = 2$$\vec a$$
∴ The correct option is 3
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https://www.wikidoc.org/index.php?title=Classical_test_theory&printable=yes
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Classical test theory
Classical test theory is a body of related psychometric theory that predict outcomes of psychological testing such as the difficulty of items or the ability of test-takers. Generally speaking, the aim of classical test theory is to understand and improve the reliability of psychological tests.
Classical test theory may be regarded as roughly synonymous with true score theory. The term "classical" refers not only to the chronology of these models but also contrasts with the more recent psychometric theories, generally referred to collectively as item response theory, which sometimes bear the appellation "modern" as in "modern latent trait theory".
True and error scores
Classical test theory is based on the decomposition of observed scores into true and error scores. The theory views the observed score ${\displaystyle x}$ of person ${\displaystyle i}$, denoted as ${\displaystyle x_{i}}$, as a realization of a random variable ${\displaystyle X}$. The person is characterized by a probability distribution over the possible realizations of this random variable. This distribution is called a "propensity distribution". Person ${\displaystyle i}$'s true score, ${\displaystyle t_{i}}$, is axiomatically defined as the expectation of this propensity distribution. This definition is formally stated as
(Eq. 1) ${\displaystyle {\varepsilon }(X_{i})=t_{i}.}$
Secondly, the so-called error score for person ${\displaystyle i}$, ${\displaystyle E_{i}}$, is defined as the difference between ${\displaystyle i}$'s observed score and his true score:
(Eq. 2) ${\displaystyle E_{i}=X_{i}-t_{i}.}$
Note that ${\displaystyle X_{i}}$ and ${\displaystyle E_{i}}$ are random variables, but ${\displaystyle t_{i}}$ is a constant. Also note that it directly follows from these definitions that the error score has expectation zero:
(Eq. 3) ${\displaystyle {\varepsilon }(E_{i})={\varepsilon }(X_{i}-t_{i})={\varepsilon }(X_{i})-{\varepsilon }(t_{i})=t_{i}-t_{i}=0.}$
Relation to population
The above equations represent the assumptions that classical test theory makes at the level of the individual person. However, the theory is never used to analyze individual test scores; rather, the focus of the theory is on properties of test scores relative to populations of persons. Hence, the next step is to introduce a population-sampling scheme into the structure of classical test theory. When we assume that people are randomly sampled from a population, the true score becomes a random variable too, so that we get the (in)famous equation
(Eq. 4) ${\displaystyle X=T+E}$
Classical test theory is concerned with the relations between the three variables ${\displaystyle X}$, ${\displaystyle T}$, and ${\displaystyle E}$ in the population. These relations are used to say something about the quality of test scores. In this regard, the most important concept is that of reliability. The reliability of the observed test scores ${\displaystyle X}$, which is denoted as ${\displaystyle {\rho _{XT}^{2}}}$, is defined as the ratio of true score variance ${\displaystyle {\sigma _{T}^{2}}}$ to the observed score variance ${\displaystyle {\sigma _{X}^{2}}}$:
(Eq. 5) ${\displaystyle {\rho _{XT}^{2}}={\frac {\sigma _{T}^{2}}{\sigma _{X}^{2}}}.}$
Because the variance of the observed scores can be shown to equal the sum of the variance of true scores and the variance of error scores, this is equivalent to
(Eq. 6) ${\displaystyle {\rho _{XT}^{2}}={\frac {\sigma _{T}^{2}}{\sigma _{X}^{2}}}={\frac {\sigma _{T}^{2}}{{\sigma _{T}^{2}}+{\sigma _{E}^{2}}}}.}$
This equation, which formulates a signal-to-noise ratio, has intuitive appeal: The reliability of test scores becomes higher as the proportion of error variance in the test scores becomes lower and vice versa. The reliability is equal to the proportion of the variance in the test scores that we could explain if we knew the true scores. The square root of the reliability is the correlation between true and observed scores.
Reliability
Note that reliability is not, as is often suggested in textbooks, a fixed property of tests, but a property of test scores that is relative to a particular population. This is because test scores will not be equally reliable in every population. For instance, as is the case for any correlation, the reliability of test scores will be lowered by restriction of range. Thus, IQ-test scores that are highly reliable in the general population will be less reliable in a population of college students. Also note that test scores are perfectly unreliable for any given individual ${\displaystyle i}$, because, as has been noted above, the true score is a constant at the level of the individual, which implies it has zero variance, so that the ratio of true score variance to observed score variance, and hence reliability, is zero. The reason for this is that, in the classical test theory model, all observed variability in ${\displaystyle i}$'s scores is random error by definition (see Eq. 2). Classical test theory is relevant only at the level of populations, not at the level of individuals.
Reliability cannot be estimated directly since that would require one to observe the true scores, which according to classical test theory is impossible. However, estimates of reliability can be obtained by various means. One way of estimating reliability is by constructing a so-called parallel test. A parallel test is a test that has the property that, for every individual, it yields the same true score and the same observed score variance as the original test. If we have parallel tests x and x', then this means that
(Eq. 7) ${\displaystyle {\varepsilon }(X_{i})={\varepsilon }(X'_{i})}$
and
(Eq. 8) ${\displaystyle {\sigma }_{E_{i}}^{2}={\sigma }_{E'_{i}}^{2}}$.
Under these assumptions, it follows that the correlation between parallel test scores equals reliability (see Lord & Novick, 1968, Ch. 2, for a proof).
(Eq. 9) ${\displaystyle {\rho }_{XX'}={\frac {{\sigma }_{XX'}}{{\sigma }_{X}{\sigma }_{X'}}}={\frac {{\sigma }_{T}^{2}}{{\sigma }_{X}^{2}}}={\rho }_{XT}^{2}.}$
The estimation of reliability by the use of parallel tests is cumbersome, because parallel tests are very hard to come by. In practice the method is rarely used. Instead, researchers use a measure of internal consistency known as Cronbach's ${\displaystyle {\alpha }}$. Consider a test consisting of ${\displaystyle k}$ items ${\displaystyle u_{j}}$, ${\displaystyle j=1,\ldots ,j,\ldots ,k}$. The total test score is defined as the sum of the individual item scores, so that for individual ${\displaystyle i}$
(Eq. 10) ${\displaystyle X_{i}=\sum _{j=1}^{k}{U_{ij}}}$.
Then Cronbach's alpha equals
(Eq. 11) ${\displaystyle \alpha ={\frac {k}{k-1}}{\frac {\sum _{j=1}^{k}{\sigma _{U_{i}}^{2}}}{\sigma _{X}^{2}}}}$.
Cronbach's ${\displaystyle {\alpha }}$ can be shown to provide a lower bound for reliability under rather mild assumptions. Thus, the reliability of test scores in a population is always higher than the value of Cronbach's ${\displaystyle {\alpha }}$ in that population. Thus, this method is empirically feasible and, as a result, it is very popular among researchers.
As has been noted above, the entire exercise of classical test theory is done to arrive at a suitable definition of reliability. Reliability is supposed to say something about the general quality of the test scores in question. The general idea is that, the higher reliability is, the better. Classical test theory does not say how high reliability is supposed to be. In the literature a value over .80 appears to be deemed 'acceptable'; a value over .90 is 'good'. Values between .70 and .80 are seen as mediocre but still defensible; values below .70 are bad.[citation needed] It must be noted that these 'criteria' are not based on reasonable arguments but the result of convention. Whether they make any sense or not is unclear.
Alternatives
Classical test theory is by far the most influential theory of test scores in the social sciences. In psychometrics, the theory has been superseded by the more sophisticated models in Item Response Theory (IRT). IRT models, however, are catching on very slowly in mainstream research. One of the main problems causing this is the lack of widely available, user-friendly software; also, IRT is not included in standard statistical packages like SPSS, whereas these packages routinely provide estimates of Cronbach's ${\displaystyle {\alpha }}$. As long as this problem is not solved, classical test theory will probably remain the theory of choice for many researchers.
References
• Allen, M.J., & Yen, W. M. (2002). Introduction to Measurement Theory. Long Grove, IL: Waveland Press.
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When it’s time to tackle a roofing project, one of the crucial questions you’ll face is, “How many bundles of shingles do I need for 100 square feet?” Roofing can seem like a complex task, but with the right information, it becomes much simpler.
In this blog, we’ll break it down into easy-to-understand steps, provide real-world examples, and help you determine the right amount of shingles for your project.
1. The Basics: Shingles and Roofing
Before we get into the calculations, let’s cover the basics. Shingles are like the protective skin of your roof, shielding your home from the elements. Whether you’re repairing a section or re-roofing your entire house, you need to know how many shingles to buy.
2. Standard Shingle Size:
Shingles come in standard sizes, with the most common being 3-tab shingles measuring 3 feet by 1 foot (3 ft x 1 ft). These shingles are like the building blocks of your roof.
3. The Formula: Shingles per Square Foot
To calculate how many bundles of shingles you need for 100 square feet, you’ll need to determine the number of shingles required per square foot. Here’s the formula:
• Shingles per Square Foot = 100 / (Shingle Length x Shingle Width)
4. Example Calculation:
Let’s use the standard 3-tab shingles (3 ft x 1 ft) as an example:
• Shingles per Square Foot = 100 / (3 ft x 1 ft) = 100 / 3 sq ft = 33.33 shingles per square foot
Now that we know you need approximately 33.33 shingles per square foot, we can calculate how many bundles you’ll need. Typically, a bundle contains about 33 shingles, but this can vary depending on the manufacturer and shingle type.
5. Calculating Bundles:
• Bundles Required = (Shingles per Square Foot x Roof Area in Square Feet) / Shingles per Bundle
6. Example Calculation for 100 Square Feet:
Let’s assume your roof area is 100 square feet, and a bundle contains 33 shingles:
• Bundles Required = (33.33 shingles/sq ft x 100 sq ft) / 33 shingles/bundle = 100 bundles
Verdict:
To answer the question, for a 100 square foot roof, you’ll need approximately 100 bundles of shingles, assuming a bundle contains around 33 shingles.
Understanding how many bundles of shingles you need is like having the blueprint for your roofing project. It ensures you have the right amount of materials, minimizing waste and saving you time and money.
Roofing calculations might seem daunting, but with a simple formula and a bit of math, you can confidently plan your roofing project and achieve a job well done.
As a civil engineer and roofer, I love to share the experience that I have gained through the last couple of years. In the roofing industry, practical experience is a very crucial fact that can help you a lot. Hence, I want to help you with my blog.
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# Projective Space in Synthetic Algebraic Geometry
Felix Cherubini ββ Thierry Coquand ββ Matthias Hutzler and David WΓ€rn
## Introduction
Grothendieck advocated for a functor of points approach to schemes early in his project of foundation of algebraic geometry (see the introduction of [EGAI]). In this approach, a scheme is defined as a special kind of (covariant) set valued functor on the category of commutative rings. This functor should in particular be a sheaf w.r.t.Β the Zariski topology. As a typical example, the projective space $\bP^{n}$ is the functor, which to a ring $A$, associates the set of finitely presented sub-modules of $A^{n+1}$, which are direct factors [Demazure, Eisenbud, Jantzen].
In the 70s, Anders Kock suggested to use the language of higher-order logic [Church40] to describe the Zariski topos, the collection of sheaves for the Zariski topology [Kock74, kockreyes]. This allows for a more suggestive and geometrical description of schemes, that can now be seen as a special kind of types satisfying some properties and morphisms of schemes in this setting are just general maps. There is in particular a βgeneric local ringβ $R$, which associates to $A$ its underlying set. As described in [kockreyes] the projective space $\bP^{n}$ is then the set of lines in $R^{n+1}$.
A natural question is if we can show in this setting that the automorphism group of $\bP^{n}$ is $\PGL_{n+1}(R)$. More generally, can we show that any map $\bP^{n}\rightarrow\bP^{m}$ is given by $m+1$ homogeneous polynomials of same degree in $n+1$ variables? From this, it is possible to deduce the corresponding result about $\bP^{n}$ defined as a functor of points (but the maps are now natural transformations) or about $\bP^{n}$ defined as a scheme (but the maps are now maps of schemes). (This result, though fundamental, is surprisingly not in [Hartshorne].) One goal of this paper is to present such a proof.
In [draft], we presented an axiomatisation of the Zariski higher topos [lurie-htt], using instead of the language of higher-order logic the language of dependent type theory with univalence [hott]. The first axiom is that we have a local ring $R$. We then define an affine scheme to be a type of the form $\Sp(A)=\Hom_{\Alg{R}}(A,R)$ for some finitely presented $R$-algebra $A$. The second axiom, inspired from the work of Ingo Blechschmidt [ingo-thesis], states that the evaluation map $A\rightarrow R^{\Sp(A)}$ is a bijection. The last axiom states that each $\Sp(A)$ satisfies some form of local choice [draft]. We can then define a notion of open proposition, with the corresponding notion of open subset, and define a scheme as a type covered by a finite number of open subsets that are affine schemes. In particular, we define $\bP^{n}$ as in [kockreyes] and show that it is a scheme. In this setting, dependent type theory with univalence extended with these 3 axioms, we show the above result about maps between $\bP^{n}$ and $\bP^{m}$ and the result about automorphisms of $\bP^{n}$.
Interestingly, though these results are about the Zariski $1$-topos, the proof makes use of types that are not (homotopy) sets (in the sense of [hott]), since it proceeds in characterizing $\bP^{n}\rightarrow\KR$, where $\KR$ is the delooping (thus a type which is not a set) of the multiplicative group of units of $R$. More technically, we also use such higher types as an alternative to the technique of Quillen patching [Quillen, lombardi-quitte, Lam].
## 1 Definition of $\bP^{n}$ and some linear algebra
We follow the notations and setting for Synthetic Algebraic Geometry [draft]. In particular, $R$ denotes the generic local ring and $R^{\times}$ is the multiplicative group of units of $R$.
In Synthetic Algebraic Geometry, a scheme is defined as a set satisfying some property [draft]. In particular the projective space $\bP^{n}$ can be defined to be the quotient of $R^{n+1}\setminus\{0\}$ by the equivalence relation $a\sim b$ which expresses that $a$ and $b$ are proportional, which is equal to $\Sigma_{r:R^{\times}}ar=b$. We can then prove [draft] that this set is a scheme. This definition goes back to [Kock74].
In this setting, a map of schemes is simply an arbitrary set theoretic map. An application of this work is to show that the maps $\bP^{n}\rightarrow\bP^{m}$ are given by $m+1$ homogeneous polynomials of the same degree in $n+1$ variables.
There is another definition of $\bP^{n}$ which uses βhigherβ notions. Let $\KR$ be the delooping of $R^{\times}$. It can be defined as the type of lines $\Sigma_{M:\Mod{R}}\|{M=R^{1}}\|$. Over $\KR$ we have the family of sets
$T_{n}(l)=l^{n+1}\setminus\{0\}$
Note that we use the same notation for an element $l:\KR$, its underlying $R$-module and its underlying set. An equivalent definition of $\bP^{n}$ is then
$\bP^{n}=\sum_{l:\KR}T_{n}(l)$
That is, we replaced the quotient, here a set of orbits for a free group action, by a sum type over the delooping of this group [Sym]. More explicitly, we will use the following identifications:
###### Remark 1.1.
Projective $n$-space $\bP^{n}$ is given by the following equivalent constructions of which we prefer the first in this article:
1. [(i)]
2. 1.
$\sum_{l:\KR}T_{n}(l)$
3. 2.
The set-quotient $R^{n+1}\setminus\{0\}/R^{\times}$, where $R^{\times}$ acts on non-zero vectors in $R^{n+1}$ by multiplication.
4. 3.
For any $k$ and $R$-module $V$ we define the Grassmannian
$\Gr(k,V)\colonequiv\{U\subseteq V\mid\text{UisanR-submoduleand\|U=R^{k}\|}\}% \hbox to0.0pt{.\hss}$
Projective $n$-space is then $\Gr(1,R^{n+1})$.
We use the following, well-defined identifications:
1. (i)$\to$(iii): Map $(l,s)$ to $R\cdot(us_{0},\dots,us_{n})$ where $u:l=R^{1}$
2. (iii)$\to$(i): Map $L\subseteq R^{n+1}$ to $(R^{1},x)$ for a non-zero $x\in L$
3. (ii)$\leftrightarrow$ (iii): A line through a non-zero $x:R^{n+1}$ is identified with $[x]:R^{n+1}\setminus\{0\}/R^{\times}$
We construct the standard line bundles $\OO(d)$ for all $d\in\Z$, which are classically known as Serreβs twisting sheaves on $\bP^{n}$ as follows:
###### Definition 1.2.
For $d:\Z$, the line bundle $\OO(d):\bP^{n}\to\KR$ is given by $\OO(d)(l,s)=l^{\otimes d}$ and the following definition of $l^{\otimes d}$ by cases:
1. [(i)]
2. 1.
$d\geqslant 0$: $l^{\otimes d}$ using the tensor product of $R$-modules
3. 2.
$d<0$: $(l^{\vee})^{-d}$, where $l^{\vee}\colonequiv\Hom_{\Mod{R}}(l,R^{1})$ is the dual of $l$.
This definition of $\OO(d)$ agrees with [draft][Definition 6.3.2] where $\OO(-1)$ is given on $\Gr(1,R^{n+1})$ by mapping submodules of $R^{n+1}$ to $\KR$. Using the identification of $\bP^{n}$ from \Crefidentification-Pn we can give the following explicit equality:
###### Remark 1.3.
We have a commutative triangle:
{tikzcd}
β_l:\KR T_n(l)\ar[rr]\ar[dr,swap,β\OO(1)β] & R^n+1β{0}/R^Γ\ar[ld,β\OO(1)β]
\KR
by the isomorphism given for $(l,s)$ by mapping $x:l$ to $r(us_{0},\dots,us_{n})\mapsto r(ux)$ for some isomorphism $u:l\cong R^{1}$.
Connected to this definition of $\bP^{n}$, we will prove some equalities in the following. To prove these equalities, we will make use of the following lemma, which holds in synthetic algebraic geometry:
###### Lemma 1.4.
Let $n,d:\N$ and $\alpha:R^{n}\to R$ be a map such that
$\alpha(\lambda x)=\lambda^{d}\alpha(x)$
then $\alpha$ is a homogenous polynomial of degree $d$.
###### Proof 1.5.
By duality, any map $\alpha:R^{n}\to R$ is a polynomial. To see it is homogenous of degree $d$, let us first note that any $P:R[\lambda]$ with $P(\lambda)=\lambda^{d}P(1)$ for all $\lambda:R^{\times}$ also satisfies this equation for all $\lambda:R$ and is therefore homogenous of degree $d$. Then for $\alpha^{\prime}_{x}:R[\lambda]$ given by $\alpha^{\prime}_{x}(\lambda)\colonequiv\alpha(\lambda\cdot x)$ we have $\alpha^{\prime}_{x}(\lambda)=\lambda^{d}\alpha^{\prime}_{x}(1)$. This means any coeffiecent of $\alpha^{\prime}_{x}$ of degree different from $d$ is 0. Since this means every monomial appearing in $\alpha$, which is not of degree $d$, is zero for all $x$ and therefore 0.
###### Proposition 1.6.
$\prod_{l:\KR}l^{n}\rightarrow l\;\;\;=\;\;\;\Hom(R^{n},R)$
###### Proof 1.7.
We rewrite $\Hom(R^{n},R)$, the set of $R$-module morphism, as
$\sum_{\alpha:R^{n}\rightarrow R}\prod_{\lambda:R^{\times}}\prod_{x:R^{n}}% \alpha(\lambda x)=\lambda\alpha(x)$
using \Crefinvariant-implies-homogenous with $d=1$.
It is then a general fact that if we have a pointed connected groupoid $(A,a)$ and a family of sets $T(x)$ for $x:A$, then $\prod_{x:A}T(x)$ is the set of fixedpoints of $T(a)$ for the $(a=a)$ action [Sym].
We will use the following remark, proved in [draft][Remark 6.2.5].
###### Lemma 1.8.
Any map $R^{n+1}\setminus\{0\}\rightarrow R$ can be uniquely extended to a map $R^{n+1}\rightarrow R$ for $n>0$.
We will also use the following proposition, already noticed in [draft].
###### Proposition 1.9.
Any map from $\bP^{n}$ to $R$ is constant.
###### Proof 1.10.
Since $\bP^{n}$ is a quotient of $R^{n+1}\setminus\{0\}$, the set $\bP^{n}\rightarrow R$ is the set of maps $\alpha:R^{n+1}\setminus\{0\}\rightarrow R$ such that $\alpha(\lambda x)=\alpha(x)$ for all $\lambda$ in $R^{\times}$. These are exactly the constant maps using \Crefext and \Crefinvariant-implies-homogenous with $d=0$.
###### Proposition 1.11.
For all $n:\N$ we have:
$\prod_{l:\KR}T_{n}(l)\rightarrow T_{n}(l)\;\;=\;\;\GL_{n+1}$
###### Proof 1.12.
For $n=0$, this is the direct computation that a Laurent-polynomial $\alpha:(R[X,1/X])^{\times}$ which satisfies $\alpha(\lambda x)=\lambda\alpha(x)$ is $\lambda\alpha(1)$ where $\alpha(1):R^{\times}=\GL_{1}$.
For $n>0$, the proposition follows from two remarks.
The first remark is that maps $T_{n}(R)\to T_{n}(R)$, which are invariant under the induced $\KR$ action, are linear. To prove this remark, we first map from $T_{n}(l)\to T_{n}(l)$ to $T_{n}(l)\to l^{n+1}$ by composing with the inclusion. Maps of the latter kind can be uniquely extended to maps $l^{n+1}\to l^{n+1}$, since by \Crefext the restriction map
$(l^{n+1}\rightarrow l)\rightarrow((l^{n+1}\setminus\{0\})\rightarrow l)$
is a bijection for $n>0$ and all $l:\KR$.
The second remark is that a linear map $u:R^{m}\rightarrow R^{m}$ such that
$x\neq 0~{}\rightarrow~{}u(x)\neq 0$
is exactly an element of $\GL_{m}$.
We show this by induction on $m$. For $m=1$ we have $u(1)\neq 0$ iff $u(1)$ invertible.
For $m>1$, we look at $u(e_{1})=\Sigma\alpha_{i}e_{i}$ with $e_{1},\dots,e_{m}$ basis of $R^{m}$. We have that some $\alpha_{j}$ is invertible. By composing $u$ with an element in $\GL_{m}$, we can then assume that $u(e_{1})=e_{1}+v_{1}$ and $u(e_{i})=v_{i}$, for $i>1$, with $v_{1},\dots,v_{m}$ in $Re_{2}+\dots+Re_{m}$. We can then conclude by induction.
We can generalize \Crefend and get a result related to \Crefaut as follows.
###### Lemma 1.13.
1. [(i)]
2. 1.
$\prod_{l:\KR}l^{n}\rightarrow l^{\otimes d}\;\;=\;\;(R[X_{1},\dots,X_{n}])_{d}$
That is, every element of the left-hand side is given by a unique homogeneous polynomial of degree $d$ in $n$ variables.
3. 2.
An element in
$\prod_{l:\KR}T_{n}(l)\rightarrow T_{m}(l^{\otimes d})$
is given by $m+1$ homogeneous polynomials $p=(p_{0},\dots,p_{m})$ of degree $d$ such that $x\neq 0$ implies $p(x)\neq 0$.
###### Proof 1.14.
We show the first item. Following [Sym] again, this product is the set of maps $\alpha:R^{n}\rightarrow R^{\otimes d}$ which are invariant by the $R^{\times}$-action which in this case acts by mapping $\alpha$ to $r^{d}\alpha(r^{-1}x)$ for each $r:R^{\times}$. So by \Crefinvariant-implies-homogenous these are exactly the maps given by homogeneous polynomials of degree $d$.
## 2 Line bundles on affine schemes
A line bundle on a type $X$ is a map $X\rightarrow\KR$.
A line bundle $L$ on $\Spec(A)$ will define a f.p. $A$-module $\prod_{x:\Spec(A)}L(x)$ [draft]. It is presented by a matrix $P$. Since this f.p. module is locally free, we can find $Q$ such that $PQP=P$ and $QPQ=Q$ [lombardi-quitte]. We then have $Im(P)=Im(PQ)$ and this is a projective module of rank $1$. We can then assume $P$ square matrix and $P^{2}=P$ and the matrix $I-P$ can be seen as listing the generators of this module.
If $M$ is a matrix we write $\Delta_{l}(M)$ for the ideal generated by the $l\times l$ minors of $M$. We have $\Delta_{1}(I-P)=1$ and $\Delta_{2}(I-P)=0$, since this projective module is of rank $1$.
The module is free exactly if we can find a column vector $X$ and a line vector $Y$ such that $XY=I-P$. We then have $YX=1$, since if $r=YX$ we have $I-P=XYXY=rXY=r(I-P)$ and hence $r=1$ since $\Delta_{1}(I-P)=1$.
The line bundle on $\Spec(A)$ is trivial on $D(f)$ if, and only if, the module $M\otimes A[1/f][X]$ is free, which is equivalent to the fact that we can find $X$ and $Y$ such that $YX=(f^{N})$ and $XY=f^{N}(I-P)$ for some $N$.
In Appendix 1, we prove the following special case of Horrocksβ Theorem.
###### Lemma 2.1.
If $A$ is a commutative ring then any ideal of $A[X]$ divides a principal ideal $(f)$, with $f$ monic, is itself a principal ideal.
We can then apply this result in Synthetic Algebraic Geometry for the ring $R$.
###### Proposition 2.2.
If we have $L:\A^{1}\rightarrow\KR$ which is trivial on some $D(f)$ where $f$ in $R[X]$ is monic then $L$ is trivial on $\A^{1}$.
###### Corollary 2.3.
If we have $L:\bP^{1}\rightarrow\KR$ then we have
$\|{\prod_{r:R}L([1:r])=L([1:0])}\|\,\,\,\,\,\,\,\,\,\,\,\,\,\|{\prod_{r:R}L([r% :1])=L([0:1])}\|$
###### Proof 2.4.
By Zariski local choice [draft], the line bundle $L$ is locally trivial. On one chart of $\bP^{1}$, $L$ is trivial on a neighborhood $U$ of $0$, so we get $g:R[X]$ such that $g(0)\neq 0$ and $L$ is trivial on $D(g)$. Passing to the other chart, there is some $N$ such that $f\colonequiv f(0)^{-1}\cdot g(1/X)\cdot X^{N}$ is a monic polynomial and $L$ is trivial on $D(f)$, since $D(f)\subseteq U$.
## 3 Picard group of $\bP^{1}$
###### Lemma 3.1.
Let $A$ be a connected111If $e(1-e)=0$ then $e=0$ or $e=1$. ring, then an invertible element of $A[X,1/X]$ can be written $X^{N}\Sigma a_{n}X^{n}$ with $N$ in $\Z$ and $a_{0}$ unit and $a_{n}$ nilpotent if $n\neq 0$.
###### Proof 3.2.
Let $P=\sum_{i}a_{i}X^{i}:A[X,1/X]$ be invertible. The result is clear if $A$ is an integral domain. Let $B(A)$ is the constructible spectrum of $A$ with the two generating maps $D(a)$ and $V(a)$ for $a$ in $A$ [LQ]. The argument for an integral domain, looking at $D(a)$ as $a\neq 0$ and $V(a)$ as $a=0$, shows that we have $\sup_{i}D(a_{i})=1$ and $D(a_{i}a_{j})=0$ for $i\neq j$. Since $A$ is connected, this implies that exactly one $a_{i}$ is a unit, and all the other coefficient are nilpotent.
Using this Lemma we deduce the following.
###### Lemma 3.3.
Any invertible element of $A[X,1/X]$ can be written uniquely as a product $uX^{l}(1+a)(1+b)$ with $l$ in $\Z$, $u$ in $A^{\times}$ and $a$ (resp. $b$) polynomial in $A[X]$ (resp. $1/XA[1/X]$) with only nilpotent coefficients.
###### Proof 3.4.
Write $\Sigma v_{n}X^{n}$ the invertible element of $A[X,1/X]$. W.l.o.g. we can assume that the polynomial is of the form $1+\Sigma v_{n}X^{n}$ with all $v_{n},~{}n\in\Z$ nilpotent. We let $J$ be the ideal generated by these nilpotent elements. We have some $N$ such that $J^{N}=0$.
We first multiply by the inverse of $1+\Sigma_{n<0}v_{n}X^{n}$, making all coefficients of $X^{n},~{}n<0$ in $J^{2}$. We keep doing this until all these elements are $0$. We have then written the invertible polynomials on the form $(1+a)(1+b)$.
Such a decomposition is unique: if we have $(1+a)(1+b)$ in $A^{\times}$ with $a=\Sigma_{n\geqslant 0}a_{n}X^{n}$ and $b=\Sigma_{n<0}b_{n}X^{n}$ then we have $a_{n}=0$ for $n>0$ and $b_{n}=0$ for $n<0$.
###### Corollary 3.5.
We have $\prod_{L:\bP^{1}\rightarrow\KR}\Sigma_{p:\Z}\|L=\OO(p)\|$
###### Proof 3.6.
A line bundle $L([x_{0},x_{1}])$ on $\bP^{1}$ is trivial on each of the affine charts $x_{0}\neq 0$ and $x_{1}\neq 0$ by Corollary 2.3, so it is characterised by an invertible Laurent polynomial on $R$, and the result follows from Lemma 3.3.
We can then state the following strengthening.
###### Proposition 3.7.
The map $\KR\times\Z\rightarrow(\bP^{1}\rightarrow\KR)$ which associates to $(l_{0},d)$ the map $x\mapsto l_{0}\otimes\OO(d)(x)$ is an equivalence.
###### Proof 3.8.
Corollary 3.5 shows that this map is surjective. So we can conclude by showing that the map is also an embedding. For $(l,d),(l^{\prime},d^{\prime}):\KR\times\Z$ let us first consider the case $d=d^{\prime}$. Then we merely have $(l,d)=(\ast,d)$ and $(l^{\prime},d^{\prime})=(\ast,d)$, so it is enough to note that the induced map on loop spaces based at $(\ast,d)$ is an equivalence by \Crefconst. Now let $d\neq d^{\prime}$. To conclude we have to show $\OO(k)$ is different from $\OO(0)$ for $k\neq 0$. It is enough to show that for $k>0$ the bundle $\OO(k)$ has at least two linear independent sections, since we know $\OO(0)$ only has constant sections by \Crefconst. This follows from the fact that $\OO(k)(x)$ is $\Hom_{\Mod{R}}(Rx^{\otimes k},R)$ and has all projections as sections.
It is a curious remark that $\KR\rightarrow\KR$ is also equivalent to $\KR\times\Hom_{\mathrm{Group}}(R^{\times},R^{\times})=\KR\times\Z$.
###### Corollary 3.9.
We have $\prod_{L:\bP^{1}\rightarrow\KR}\prod_{x:R}L([1:x])=L([0:1])$.
###### Proof 3.10.
By the equivalence in \CrefMatthias, we have
$\prod_{L:\bP^{1}\to\KR}\,\prod_{x:\bP^{1}}L(x)=l_{0}\otimes\OO(d)(x)$
for some $(l_{0},d)$ corresponding to $L$. $\OO(d)([0:1])$ can be identified with $R^{1}$ and $\OO(d)$ is trivial on $R$, so we have $L([1:x])=l_{0}=L([0:1])$ for all $x:R$.
## 4 Line bundles on $\bP^{n}$
We will prove $\Pic(\bP^{n})=\Z$ and a strengthening thereof in this section by mostly algebraic means. In \Crefgeometric-proof we will give a shorter geometric proof.
We can now reformulate Quillenβs argument for Theorem 2β [Quillen] in our setting.
###### Proposition 4.1.
For all $V:\bP^{n}\rightarrow\KR$ we have ${\prod_{s:R^{n}}V([1:s])=V([0:1:0:\cdots:0])}$.
###### Proof 4.2.
We define $L:R^{n-1}\rightarrow(\bP^{1}\to\KR)$ by $L~{}t~{}[x_{0}:x_{1}]=V([x_{0}:x_{1}:x_{0}t])$. Let $s=(s_{1},\dots,s_{n}):R^{n}$. We apply Corollary 3.9 and we get
$V([1:s])=L~{}(s_{2},\dots,s_{n})~{}[1:s_{1}]=L~{}(s_{2},\dots,s_{n})~{}[0:1]=V% ([0:1:0:\cdots:0])\hbox to0.0pt{.\hss}$
Note that the use of Corollary 3.9 replaces the use of the βQuillen patchingβ [lombardi-quitte] introduced in [Quillen].
Let $T$ be the ring of polynomials $u=\Sigma_{p}u(p)X^{p}$ with $X^{p}=X_{0}^{p_{0}}\dots X_{n}^{p_{n}}$ with $\Sigma p_{i}=0$. We write $T_{l}$ for the subring of $T$ which contains only monomials $X^{p}$ with $p_{i}\geqslant 0$ if $i\neq l$ and $T_{lm}$ the subring of $T$ which contains only monomials $X^{p}$ with $p_{i}\geqslant 0$ if $i\neq l$ and $i\neq m$.
Note that $T_{l}$ is the polynomial ring $T_{l}=R[X_{0}/X_{l},\dots,X_{n}/X_{l}]$.
A line bundle on $\bP^{n}$ is given by compatible line bundles on each $\Spec(T_{l})$.
By \Creftrivial, a line bundle on $\bP^{n}$ is trivial on each $\Spec(T_{l})$. So it is determined by $t_{ij}$ invertible in $T_{i}[X_{i}/X_{j}]=T_{j}[X_{j}/X_{i}]=T_{ij}$ such that $t_{ik}=t_{ij}t_{jk}$ and $t_{ii}=1$. Using \Crefstand we can assume without loss of generality, that $t_{ij}=(X_{i}/X_{j})^{N_{ij}}u_{ij}$, for some $N_{ij}$ in $\Z$, where $u_{ij}(p)$ is invertible for $p=0$ and all other coefficients $u_{ij}(p)$ for $p\neq 0$ are nilpotent. By looking at the relation $t_{ik}=t_{ij}t_{jk}$ when we quotient by nilpotent elements, we see that $N_{ij}=N$ does not depend on $i,j$. The result $\Pic(\bP^{n})=\Z$ will then follow from the following result.
###### Proposition 4.3.
There exists $s_{i}$ invertible in $T_{i}$ such that $u_{ij}=s_{i}/s_{j}$
###### Proof 4.4.
Each $u_{ij}$ is such that $u_{ij}(p)$ unit for $p=0$ and all $u_{ij}(p)$ nilpotent for $p\neq 0$.
Like in the proof of \Crefnilpotent, we can change $u_{01}$ so that we have $u_{01}(p)=0$ if $p\neq 0$ and $p_{0}\geqslant 0$ or $p_{1}\geqslant 0$ by multiplying $u_{01}$ by a unit in $T_{0}$ and a unit in $T_{1}$. Let us show for instance how to force $u_{01}(p)=0$ if $p\neq 0$ and $p_{1}\geqslant 0$ by multiplying $u_{01}$ by a unit in $T_{0}$. Let $M$ be the ideal generated by $u_{01}(p)$ for $p\neq 0$, which is a nilpotent ideal. If we multiply $u_{01}$ by $u_{01}(0)-\Sigma_{p_{1}\geqslant 0}u_{01}(p)$ we change $u_{01}$ to $u^{\prime}_{01}$ where all $u_{01}^{\prime}(p)$, for $p_{1}\geqslant 0$ and $p\neq 0$, are in $M^{2}$. We iterate this process and since $M$ is nilpotent, we force $u_{01}(p)=0$ or $p\neq 0$ and $p_{1}\geqslant 0$.
We can thus assume that $u_{01}(p)=0$ if $p\neq 0$ and $p_{0}\geqslant 0$ or $p_{1}\geqslant 0$.
We claim then that, in this case, $u_{01}$ has to be a unit. For this we show that $u_{01}(p)=0$ if $p_{l}>0$ for each $l\neq 0,1$. This is obtained by looking at the relation $u_{01}=u_{0l}u_{l1}$. Let $L$ be the ideal generated by coefficients $u_{0l}(p)$ and $u_{1l}(p)$ with $p_{l}>0$ and $I$ the ideal generated by all nilpotent coefficients of $u_{0l}$ and $u_{l1}$. Thanks to the form of $u_{01}$ we must have $L\subseteq LI$ and so $L=0$ by Nakayama. Indeed we have
$u_{01}(p)=u_{0l}(p)u_{l1}(0)+u_{0l}(0)u_{l1}(p)+\Sigma_{q+r=p,q\neq 0,r\neq 0}% u_{0l}(q)u_{l1}(r)$
and we use this to show that $u_{0l}(p)$ is in $LI$. Since $p_{l}>0$, we have $u_{0l}(p)=0$ if $p_{0}\geqslant 0$, hence we can assume $p_{0}<0$. We also have $u_{0l}(p)$ if $p_{1}<0$ and we can assume $p_{1}\geqslant 0$. This implies $u_{l1}(p)=0$ (since $p_{0}<0$) and $u_{01}(p)=0$ (since $p_{0}<0$ and $0\leqslant p_{1}$). We get thus
$u_{0l}(p)u_{l1}(0)=-\Sigma_{q+r=p,q\neq 0,r\neq 0}u_{0l}(q)u_{l1}(r)$
and each member in the sum $u_{0l}(q)u_{l1}(r)$ is in $IL$ since $q_{l}+r_{l}=p_{l}>0$ and hence $q_{l}>0$ or $r_{l}>0$.
We thus deduce $L=0$ by Nakayama. We get, for $p_{l}>0$
$u_{01}(p)=u_{0l}(p)u_{l1}(0)+u_{0l}(0)u_{l1}(p)$
and if $p_{0}<0$ and $p_{1}<0$ we have $u_{0l}(p)=u_{l1}(p)=0$.
This implies that all coefficients $u_{01}(p)$ such that $p_{l}>0$ are $0$.
Since this holds for each $l>1$ we have that $u_{01}$ is a unit in $R$.
W.l.o.g. we can assume $u_{01}=1$. We then have $u_{0l}=u_{1l}$ in $T_{0l}\cap T_{1l}=T_{l}$
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# The Chicken Quiz:A Fun Way To Learn And Test Your Knowledge On Chicken
Discussion in 'Games, Jokes, and Fun!' started by Louieandthecrew, Dec 30, 2010.
1. ### LouieandthecrewI am actually a female!
Ready to test your knowledge? Heres your chance! This is a quiz solely about chickens. Answer the questions on a seperate post and let everyone see how you did. Once you know if you were right or not, go back and write TRUE or FALSE next to each correct or incorrect answer so that all of those chicken newbies can learn while they play! Ready?
1. How many days is the normal chick in its egg before it hatches?
2. How hot should the incubator be?
3. Without a heat lamp, how many chicks cuddled together using their own body heat for warpth would it take to keep them alive?
4. At what age can you take:
A. A meat bird
B. A dual-purpose bird
C. A average laying bird
out from under the heat lamp and into the coop?
5. How old does a pullet have to be to be considered a Hen?
6. How old does a cockerel have to be to be considered a Rooster?
7. How old is the average laying pullet when she starts to lay?
8. How old is the average meat bird before they are ready for slaughter?
9. How long does the average laying hen cease in laying?
10. How long can chickens live?
BONUS: ``~The Bonus Section Is The Part Of This Quiz Where You Have A Chance To Ask Your Own Question!~``
Now, just answer the questions as best you can!
2. ### 44WolvesHere is Your New Title
Jun 28, 2009
1. How many days is the normal chick in its egg before it hatches? 21 Days?
2. How hot should the incubator be?99 Degrees F
3. Without a heat lamp, how many chicks cuddled together using their own body heat for warpth would it take to keep them alive?3
4. At what age can you take:
A. A meat bird2 Months?
B. A dual-purpose bird3 Months
C. A average laying bird2 Months?
out from under the heat lamp and into the coop?
5. How old does a pullet have to be to be considered a Hen?60 Days
6. How old does a cockerel have to be to be considered a Rooster?80 Days?
7. How old is the average laying pullet when she starts to lay?16 Months?
8. How old is the average meat bird before they are ready for slaughter?
9. How long does the average laying hen cease in laying?2 1/2 yrs?
10. How long can chickens live?up to 15 yrs
3. ### ChickLover98The Chicken Princess
Apr 24, 2010
Pennsylvania
1. How many days is the normal chick in its egg before it hatches? 21 days
2. How hot should the incubator be? 99.5 degrees F
3. Without a heat lamp, how many chicks cuddled together using their own body heat for warpth would it take to keep them alive? 25
4. At what age can you take:
A. A meat bird When fully feathered
B. A dual-purpose bird When fully feathered
C. A average laying bird When fully feathered
out from under a heat lamp? ALL DEPENDING ON TEMP OUTSIDE^^^^
5. How old does a pullet have to be to be considered a Hen? At least one year
6. How old does a cockerel have to be to be considered a Rooster? At least one year
7. How old is the average laying pullet when she starts to lay? 3-4 months
8. How old is the average meat bird before they are ready for slaughter? a few months to a year
9. How long does the average laying hen cease in laying? During molt and when she gets old
10. How long can chickens live? 4-6 years
Last edited: Dec 30, 2010
4. ### LouieandthecrewI am actually a female!
Everyone is doing pretty good so far! I'll wait to have more people try before we start discussing right and wrong answers!
5. ### Cats CrittersCompletely Indecisive
1. How many days is the normal chick in its egg before it hatches? 21 days
2. How hot should the incubator be? 99.5 degrees F
3. Without a heat lamp, how many chicks cuddled together using their own body heat for warmth would it take to keep them alive? 30?
4. At what age can you take:
A. A meat bird
B. A dual-purpose bird
C. A average laying bird
out from under the heat lamp and into the coop? Depends on your outside temps. You should be starting at about 95 degrees and decreasing 5 degrees per week. Or when they are fully feathered
5. How old does a pullet have to be to be considered a Hen? One year
6. How old does a cockerel have to be to be considered a Rooster? One year
7. How old is the average laying pullet when she starts to lay? 20wks
8. How old is the average meat bird before they are ready for slaughter? 8wks
9. How long does the average laying hen cease in laying? 2 years for regular laying
10. How long can chickens live?15-20 years
6. ### LouieandthecrewI am actually a female!
Quote:I love how detailed those answers are! Thank you!
7. ### iluvsedwardOverrun With Chickens
5,683
18
251
Jan 19, 2010
Calvert county MD
1. How many days is the normal chick in its egg before it hatches?21
2. How hot should the incubator be?100*
3. Without a heat lamp, how many chicks cuddled together using their own body heat for warpth would it take to keep them alive?25?
4. At what age can you take:
A. A meat bird
B. A dual-purpose bird
C. A average laying bird
out from under the heat lamp and into the coop?I wait till they are fully featherd if its not winter
5. How old does a pullet have to be to be considered a Hen? 6 months?
6. How old does a cockerel have to be to be considered a Rooster? 4 mnths?
7. How old is the average laying pullet when she starts to lay? 6 months
8. How old is the average meat bird before they are ready for slaughter? 8 weeks
9. How long does the average laying hen cease in laying?any amount of time?
10. How long can chickens live? 10 yrs.?
8. ### LouieandthecrewI am actually a female!
Gooooooood job Thank you very much!
9. ### Cat WaterThat Person
Jul 4, 2010
Mid Coast Maine
Quote:I didn't look at other people's posts before I answered the questions
1. 21 days
2. 97.5* F
3. 50?
4. a. 3 weeks
b. 6 weeks
c. 6 weeks
5+6. 1 year
7. 17 weeks
8. 6 weeks
9. 1 month
10. 25 years
10. ### LouieandthecrewI am actually a female!
Quote:I didn't look at other people's posts before I answered the questions
1. 21 days
2. 97.5* F
3. 50?
4. a. 3 weeks
b. 6 weeks
c. 6 weeks
5+6. 1 year
7. 17 weeks
8. 6 weeks
9. 1 month
10. 25 years
Keep 'em comin'!
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# How Much Did It Weigh Before Percent Weight Loss Math What Is A Body Fat Calculator?
You are searching about How Much Did It Weigh Before Percent Weight Loss Math, today we will share with you article about How Much Did It Weigh Before Percent Weight Loss Math was compiled and edited by our team from many sources on the internet. Hope this article on the topic How Much Did It Weigh Before Percent Weight Loss Math is useful to you.
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## What Is A Body Fat Calculator?
People don’t usually know that there is actually more to how much you weigh on a scale.
Many consider the scale to be the best tool for measuring the amount of weight gained or lost. But being overweight and “excess fat” are definitely not the same thing. Being “overweight” usually refers to excess total body weight compared to your height and body structure. Being “overfat”, however, is completely different and is defined as excess fat, regardless of the person’s weight.
Did you know that “thin” people can still have a high body fat percentage?
So what is a body fat calculator and how do you use it?
Your body fat percentage is an average of the total percentage of fat your body carries.
For example, if your total body weight is 200 pounds and you have 20 pounds of body fat, your body fat percentage would be around 10 percent.
There are many methods you can use to measure body fat. Some of these would include using skinfold calipers and home body fat scales. Skinfold clamps are devices that look like giant clamps and are used to attach to the skin at different specific points on the body. They are designed to measure the thickness of skin folds at these strategic points. After writing down your measurements, you can use a standard chart usually provided when you buy the skinfold clamps to figure out what your body fat percentage is.
*Note: Body fat in the rest of this article will be referred to as BF.
Home BF scales can quickly measure your BF percentage. These scales work by passing a low level current through the body and the impedance is measured. These are not always very accurate, so always use them with caution.
And of course there’s also the BF calculator. Definitely useful for those math geeks out there!
You can use this “elegant” method:
For women:
%BF = 495/(1.29579-0.35004(log(waist+hip-neck))+0.22100(log(height)))-450
For men:
%BF = 495/(1.0324-0.19077(log(waist-neck))+0.15456(log(height)))-450
Otherwise, you can use your body mass index (BMI) to estimate if you fall into a healthy range.
Here’s a mathematical way to calculate your BMI:
Write how much you weigh (in pounds). Then simply multiply your weight by 703.
Then write your height (in inches) and multiply by 703. Then divide your weight number by your height number. This will be your BMI.
Based on the end product you measured, you now have your BMI.
It is estimated that for both men and women, a healthy BMI range should be between 18.6 and 24.8.
This is just a method that will give you a rough idea of where you stand.
BMI is not the best indicator of overall health and does not give you your BF percentage. In fact, many professional bodybuilders with very low body fat percentages still rank high in BMI just because their muscle weighs so much.
Also keep in mind that there is no perfect body fat percentage. Your gender and age greatly affect your BF percentage.
Some people may do well with a lower BF percentage, while others may do better with slightly higher percentages.
It is highly recommended that you visit your doctor to best find what the ideal BF percentage is for you.
## Question about How Much Did It Weigh Before Percent Weight Loss Math
If you have any questions about How Much Did It Weigh Before Percent Weight Loss Math, please let us know, all your questions or suggestions will help us improve in the following articles!
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## How To Be A Creative Math Teacher In Secondary Education How to Compose a Welcome Letter to Prospective Students & Parents
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Top-Rated Free Essay
# Forced Convection (in a cross flow heat exchanger)
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Forced Convection (in a cross flow heat exchanger)
3rd Year Thermodynamics Lab Report
Mechanical Engineering Science 10
Forced Convection (in a cross flow heat exchanger)
Summary
The aim of this lab is to determine the average convective heat transfer coefficient for forced convection of a fluid (air) past a copper tube, which is used as a heat transfer model.
Introduction
The general definition for convection may be summarized to this definition "energy transfer between the surface and fluid due to temperature difference" and this energy transfer by either forced (external, internal flow) or natural convection.
Heat transfer by forced convection generally makes use of a fan, blower, or pump to provide high velocity fluid (gas or liquid). The high-velocity fluid results in a decreased thermal resistance across the boundary layer from the fluid to the heated surface. This, in turn, increases the amount of heat that is carried away by the fluid. [1]
Theory Background [2]
Considering the heat lost by forced convection form the test rod. The amount of heat transferred is given by (1)
Where = rate of heat transfer, unknown value.
= film heat transfer coefficient, this is what we need to found out.
A = area for heat transfer, this is the area of the cross section area of test section.
T = temperature of the copper rod, the temperature after heating. Ta = temperature of air, surrounding temperature.
So, in any period of time, dt, then the fall in temperature, dT, will be given as:
(2) Where m = mass of copper rod, cp = specific heat of the copper rod, J/kgK
Eliminating Q from (1) and (2) then
Since Ta is constant, dT=d(T-Ta)
Integrating gives:
At t = 0, T=To, hence C1 = ln(T-To), hence:
Or
Therefore a plot of ln((T-Ta)/(Tmax-Ta))) against t should give a straight line of gradient from which the heat transfer coefficient, , can be found.
To find the velocity of air passing the rod, first the velocity upstream must be found.
From basic fluid flow theory in the air stream And in the measuring manometer
Therefore (3) Where a = density of air w = density of fluid in manometer v = mean velocity of air h = head in manometer
Therefore measuring the air temperature and air pressure the density can be found,
Where R=289 J/kg K. if w is taken as 1000 kg/m3 and h is measured in m, then
however the velocity, u, used in heat transfer calculations is normally based on the minimum flow area.
Therefore with the single rod , since the inclusion of the rod reduces the cross section and increases velocity.
Practical forced convection heat transfer relationships are often expressed in the dimensionless form
Nu = C.Ren.Prm
However for gases, Pr is virtually constant, therefore
Nu = K.Ren
Typical K and n values are (for Pr 0.7)
Re
K
n
3 - 35
0.795
0.384
35 - 5000
0.583
0.471
5000 – 50 000
0.148
0.633
50 000 – 230 000
0.0208
0.814
Apparatus
Figure 1 shows the test section which contains 18 removable Perspex rods. Any slot can be inserting with a test rod which made of copper and connect with computer. This test section are sealed in an enclosed box made from isolating material which make sure that no heat will escape to the surrounding. The heat flow rate from the test rod is found by heating the cylinder in an electrical heater.
The cooling is provided by a cooling fan, the cooling rate can be change by controlling the inlet area of the fan.
Procedure
1. Insert the test rod in electrical heater leave it until the temperature reading does not rise anymore.
2. Switch on cooling fan and change the inlet area to 20%.
3. Take the reference temperature using the thermometer by the test section.
4. Replace any Perspex rod with test rod and start recording the temperature change against time.
5. Switch off the cooling fan pull out test rod and insert it back to heater, keeping heating until reached maximum temperature again.
6. Switch on cooling fan and change the inlet area to 40%.
7. Repeat step 3 and change adjusting cooling fan inlet area to 60%, 80% and 100%.
8. Organize the results and put them in table then plot diagram.
Results
Plot the time against temperature change in the tube due to different inlet velocities.
From theroy background we know that the gradient of this diagram should equal to the gradient of - .
, this should equal to since the mass and specific heat of the copper rod does not change, we can found α.
From above results we can conclude that heat transfer coefficient can be changed by: (1) Change the area of cross section (2) Plug in more tubes
Discussion
1. Perform the necessary calculations to find the influence of free stream velocity, V, on the heat transfer coefficient, , over the entire range of velocities measured.
2. Convert the above experimental data to a dimensionless form, and plot the Nusselt Number as a function of the Reynolds number, Re , on a linearlized plot, where: and d is the diameter of the disk.
3. Estimate the uncertainty of the experimental data and plot appropriate uncertainty bands on the above plot.
4. What is the main error in this lab and how can we minimize it?
5. Due to the resistance-temperature characteristics of the thermistor, it is very easy to overheat the thermistor and destroy it. The thermistor overheat protective circuit used in this experiment guards the thermistor, against overheating, by switching off the system when a certain temperature is exceeded. Explain how it determines this temperature. Also, is it possible to adjust this temperature? If yes, explain, how? [3]
Conclusions
The flow of fluids and heat transfer in tube banks represents an idealization of many industrially important processes. Typical examples include filtration, flow in biological systems, tubular heat exchangers, flow and heat transfer in fibrous media as encountered in polymer processing and in insulation materials, etc. Additional examples where this flow configuration is of relevance include flow in the fluidized bed drying of fibrous materials (such as coconut shell, rice husk) and paper pulp suspensions and in food processing applications (Kiljanski & Dziubinski, 1996; Mauret & Renaud, 1997). Notwithstanding the importance of the detailed kinematics of the flow and temperature fields, it is readily agreed that the variables of central interest in all these applications are the frictional pressure gradient and the convective heat transfer coefficient (or the rate of heat transfer) as functions of the pertinent system variables. Consequently, over the years, considerable research effort has been expended in developing satisfactory methods for the prediction of pressure drop for the flow of incompressible Newtonian fluids in cross-flow configuration over a collection of circular cylinders, as can be gauged from the number of books and survey articles in this field (e.g., [Zukauskas 1987a] and [Zukauskas 1987b], Chap. 6; Drummond & Tahir, 1984; Nishimura, 1986; Satheesh, Chhabra, & Eswaran, 1999; Shibu, Chhabra, & Eswaran, 2001). Perhaps it is fair to point out here that a bulk of the literature relates to momentum transfer or the estimation of frictional pressure drop incurred during the cross flow of fluids over tube banks in the low Reynolds number region. This work addresses the question of the prediction of the Nusselt number as a function of the Reynolds and Prandtl numbers for a range of voidages of tube banks. It is, however, instructive and useful to briefly summarize the pertinent studies available in the literature. [5]
References
[1]: http://mizisystem.blogspot.co.uk/2011/10/force-convection.html
[2]: Laboratory Handbook
[3]: Experiment 8 Forced Convection on a Flat Disk
[4]: http://dspace.mit.edu/bitstream/handle/1721.1/61456/HTL_TR_1969_064.pdf?sequence=1
[5]: FLUENT - Forced Convection by Yong Sheng Khoo, last edited by Rajesh Bhaskaran
Fig.1 Laboratory Handbook
References: [1]: http://mizisystem.blogspot.co.uk/2011/10/force-convection.html [2]: Laboratory Handbook [3]: Experiment 8 Forced Convection on a Flat Disk [4]: http://dspace.mit.edu/bitstream/handle/1721.1/61456/HTL_TR_1969_064.pdf?sequence=1 [5]: FLUENT - Forced Convection by Yong Sheng Khoo, last edited by Rajesh Bhaskaran Fig.1 Laboratory Handbook
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Cody
# Problem 7. Column Removal
Solution 328863
Submitted on 4 Oct 2013 by Awadhesh Srivastava
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% A = [1 2 3; 4 5 6]; n = 2; B_correct = [1 3; 4 6]; assert(isequal(column_removal(A,n),B_correct))
2 Pass
%% A = magic(4); n = 3; B = [16 2 13; 5 11 8; 9 7 12; 4 14 1]; B_correct = B; assert(isequal(column_removal(A,n),B_correct))
3 Pass
%% A = 1:10; n = 7; B_correct = [1 2 3 4 5 6 8 9 10]; assert(isequal(column_removal(A,n),B_correct))
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# Multiplying Multiple Fractions Worksheet
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## Excel as a different programming paradigm
(via Gamasutra via /.) Reminds me of the Subtexts of the world: a 3D graphics system in Excel, with programming rant. Pretty fun.
## Comment viewing options
### Also reminiscent of
Also reminiscent of Mathematica 6's dynamic interactivity feature.
This paradigm is called "nonmonotonic dataflow programming" in this paradigm taxonomy. It is very similar to concurrent logic programming. There is one problem with this paradigm: it introduces "glitches": extra nondeterminism that is not part of the problem specification. An improved version of this paradigm that removes the extra nondeterminism is called Functional Reactive Programming (FRP). It would be nice if Excel could implement FRP (hint to the Excel developers!).
### I'm assuming you refer to
the ability to create cyclic references in Excel spreadsheets, and how Excel attempts to resolve them (by repeatedly evaluating terms until something converges).
In many cases where Excel is used, this is a reasonable approach.
### Excel's execution model
Actually, I was referring to the incremental stream calculation: changing the value of a cell triggers a recalculation. That's exactly like adding a value to a stream in a nonmonotonic dataflow program.
Converging on cyclic references is an optimization: when a stream calculates values that are identical (or within a small epsilon), the calculation stops.
The problem of nondeterminism still exists in Excel. For example, consider b=a+1, c=b*a. Changing cell a causes b and c to change. But if c is calculated before b then there is a glitch: c changes twice. Usually you don't see it because you're changing one cell at a time and at a human time scale the glitch is invisible. But if Excel would be used as a programming environment (e.g., a server) that communicates with other programs through streams of cell values, then you would see the glitches. FRP gets rid of these glitches and restores determinism.
### How is changing the value of a cell...
any different than changing a manifest constant in a program and re-executing? Excel, of course, blurs the distinction between code and data, any cell can contain either.
I do see your point about cells "changing twice". As Excel does permit cyclic references, a topological sort of the cells is probably out of the question, so my understanding is Excel evaluates cells in some trivial order (tables, rows, columns or something like that). OTOH, it would seem to me that sanity can also be restored by adding some transactional notion on top--until a computation stabilizes (or convergence is decided to be impossible due to too many iterations occurring), the intermediate results (which can contain cells in an inconsistent state) are not visible outside.
### bias
Using a "trivial order" and iteration to convergence (or indefinitely) is known to lead to biased results in simulations. Some implementers choose to eliminate the bias with pseudo-random ordering, e.g., Swarm. Others use systolic "frame based" data synchronization, e.g., PST Parallel Inference Machine.
### Excel's cells are streams
How is changing the value of a cell any different than changing a manifest constant in a program and re-executing?
It's not really different, but the spreadsheet can do a lot more (e.g., remember old values, modify itself). A cell corresponds exactly to a stream of values (in the same way that "state" in CTM is defined as a "sequence of values"). Changing the cell's value corresponds to adding the new value to the stream. The stream viewpoint is nice because it fits with how Excel works: the Excel run-time system "waits" for changes in cell values. So cells are just input streams and Excel runs as a dataflow language!
adding some transactional notion on top--until a computation stabilizes
You've hit on the issue. Keeping changes invisible until everything stabilizes is a possible fix. That's exactly the technique used in the FRP in Oz example. FRP researchers have come up with more clever fixes, including topological sorts extended to handle cyclic references.
### I dealt with this issue in
I dealt with this issue in SuperGlue by having changes propagate where the notified then re-compute their values using new information. In this model, there is no buffering, which would otherwise create a few glitches while the change propagations stabilize. In the loose world of UI, this isn't such a big deal, but the FRP community takes this much more seriously.
Buffering in general is more trouble than its worth. The only exception are multi-valued data, which have to handled specially (add/remove notifications don't fit into the "change" notification category).
### top
My experiences with writing apps in Flapjax made me realize they are indeed a big deal for RIAs, but maybe you think that is sufficiently different from the loose world of UIs :) I'm still on the fence with graph reconstruction semantics for things like conditionals. You probably want synchrony per time-step that preserves event clock ticks and a notion of atomicity to prevent glitches within those ticks. Topological eval order is probably the most efficient way to achieve it for single processors (I haven't found it to be a terrible hit, and if you're serious about the implementation, adding JIT support to dynamic graphs for safe parallelism would probably take you far).
It's interesting to consider transactions for expressions within time steps as the implementation strategy, or even over multiple time steps. I've been thinking about this wrt optimistic concurrency for multi/manycore SMPs and even allowing imperative coding fragments. A lot of the target applications (and indeed original motivations) for this style of code are visual, so I've been a bit stuck on what fairness guarantees you want between different visual components. Synchronizing rendering between them seems like an odd task for developers as ideally rendering should be expressed just as a form of sampling a (temporally) continuous data structure. Instead of explicit synchronization, I've been thinking of nested constraint based prioritization, which means explicit resource scheduling can be done underneath.
### I guess its how you define
I guess its how you define RIAs, which I'm not really happy with, as even gmail seems way too slow for me. Given my experience with UI (more animation-based), invalidate/refresh is a much better strategy than sending accurate deltas. With invalidate/refresh, we just need to track possible dependencies, we can be conservative, we don't have to do a lot of bookkeeping, and we especially don't have to deal with an explicit dependency graph.
Agreed buffering opens a big can of worms, but...can you provide some specific non-toyish examples of where glitch-free buffering is actually needed in a RIA (assuming the database isn't a part of the FRP code)?
### But does it? Depends on how
But does it? Depends on how Excel is implemented. A topological sort of the cell dependencies solves this problem. Kenny Tilton's "Cells" system will always compute b before c. So the cells are not like asynchronous channels since they have a deterministic ordering.
### What of cycles?
How are cycles handled? Are they banned, handled with iteration-until-convergence, etc?
### Check out QCalc
Some here might find Albert Graef's QCalc written in the functional programming language Q, interesting. Although not really 3D, you can stick GUI elements, gnuplots, mplayer files, or any function you can create in Q (the entire language is available) in cells in an interactive way. Since Q has threading libraries, I'm pretty sure it would be possible to network individual cells in one spreadsheet to various cells in other spreadsheets over a network. Unfortunately, only *n*x or MAC users can run QCalc right now.
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# If x is an integer is x |x| < 2^x? 1. x > 0 2. x = 10
Author Message
Senior Manager
Joined: 10 Mar 2008
Posts: 331
If x is an integer is x |x| < 2^x? 1. x > 0 2. x = 10 [#permalink]
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18 Aug 2008, 13:16
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If x is an integer is x |x| 0
2. x = 10
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Director
Joined: 12 Jul 2008
Posts: 511
Schools: Wharton
### Show Tags
18 Aug 2008, 13:19
vksunder wrote:
If x is an integer is x |x| < 2^x?
1. x > 0
2. x = 10
(1) Insufficient
If x = 1:
x|x| = 1
2^x = 2
If x = 2:
2|2| = 4
2^2 = 4
(2) Sufficient
Current Student
Joined: 28 Dec 2004
Posts: 3288
Location: New York City
Schools: Wharton'11 HBS'12
### Show Tags
18 Aug 2008, 13:20
i think B is correct..
1) x=1 is less than 2..but if x=3 then 9>8...
2) x=10 is suff
Intern
Joined: 15 Jul 2008
Posts: 5
### Show Tags
18 Aug 2008, 19:42
xIXIo
x**2<2**x
so many values possible for x...........valid for all x <2........try 1, sqrt(2)....
2. x=10
10*I10I=100<2**10
B suff
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Re: DS: Inequalities [#permalink] 18 Aug 2008, 19:42
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| 3.75
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CC-MAIN-2018-30
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latest
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en
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https://www.daniweb.com/programming/software-development/threads/283409/issue-with-passing-values
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crawl-data/CC-MAIN-2018-43/segments/1539583513508.42/warc/CC-MAIN-20181020225938-20181021011438-00181.warc.gz
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|
## Lygris
Alright...
So I created a strange little query that takes an abbreviated currency amount and converts it into raw numbers. It you were to enter \$2.5k, it would give you "2500" in return.
Unfortunately, I'm having an issue passing values into the function. Previously, I was just having an InputBox let me test the values that went in and out, but I need it to accept the value from another function that loops through columns in a table.
How do I get my code to pass by reference or value? Whenever I run the following code, all I get back is the value I entered. So if I entered "\$2.5k", I get back "\$2.5k"
``````Private Sub Code_Test_Click()
Code_Click
End Sub
Function Code_Click()
Dim Amount As String
Amount = InputBox("#", "#")
Convert_NumAbbreviations_to_Numbers (Amount)
MsgBox (Amount)
End Function
Function Convert_NumAbbreviations_to_Numbers(ByRef Amount As String) 'Prototype
'Dim Amount As String
Dim CheckVar As Integer
Dim LoopValue As Integer
Dim MorK As String
Dim DecimalPlace As Integer
'Amount = InputBox("What value?", "Value")
DecimalPlace = 0
CheckVar = InStr(1, Amount, "M")
If Not IsNull(CheckVar) And CheckVar <> 0 Then
MorK = "M"
Amount = Replace(Amount, "M", "")
Else
CheckVar = InStr(1, Amount, "K")
If Not IsNull(CheckVar) And CheckVar <> 0 Then
MorK = "K"
Amount = Replace(Amount, "K", "")
Else
MorK = "None"
End If
End If
CheckVar = InStr(1, Amount, "\$")
If Not IsNull(CheckVar) Then
Amount = Replace(Amount, "\$", "")
End If
LoopValue = Len(Amount)
Do While (LoopValue <> 0)
CheckVar = InStr(1, Amount, ",")
If Not IsNull(CheckVar) Then
Amount = Replace(Amount, ",", "")
End If
LoopValue = LoopValue - 1
Loop
CheckVar = InStr(1, Amount, ".")
If Not IsNull(CheckVar) And CheckVar <> 0 Then
DecimalPlace = Int(Len(Amount)) - CheckVar
Amount = Replace(Amount, ".", "")
End If
If MorK = "M" Then
DecimalPlace = Abs(DecimalPlace - 6)
Else
If MorK = "K" Then
DecimalPlace = Abs(DecimalPlace - 3)
End If
End If
Do While DecimalPlace <> 0
Amount = Amount + "0"
DecimalPlace = DecimalPlace - 1
Loop
End Function``````
Thanks.
## vb5prgrmr 143
Ah yes... One of the funny (or not so) undocumented things about VB... Your call to the procedure with the parens wrapped around the variable forces the value to be passed byvalue instead of byref...
``````Convert_NumAbbreviations_to_Numbers (Amount) 'forced byval
Convert_NumAbbreviations_to_Numbers Amount 'normal byref``````
Good Luck
## WaltP 2,905
When you create a Function, set the return value to the function name to return it:
``````Function GetValue(aVal as Integer, bVal as Integer) as Integer
...
Use: `newValue = GetValue(a,b)`
| 749
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| 2.546875
| 3
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CC-MAIN-2018-43
|
latest
|
en
| 0.615933
|
http://www.vias.org/matsch_capmag/matsch_toroid_coil.html
| 1,411,235,865,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-41/segments/1410657133485.50/warc/CC-MAIN-20140914011213-00296-ip-10-196-40-205.us-west-1.compute.internal.warc.gz
| 907,414,826
| 4,081
|
Capacitors, Magnetic Circuits, and Transformers is a free introductory textbook on the physics of capacitors, coils, and transformers. See the editorial for more information....
The Toroidal Coil
Figure 3-9(a) shows a toroidal coil with a uniformly distributed winding of N turns carrying a practically constant current of i amp. A toroid may be shaped like a doughnut or it may be in the form of a hollow cylinder such as is shown in Fig. 3-9(a). If the number of turns N is large, the current will produce magnetic lines of flux that are concentric circles confined to the toroid. This is evident from the direction of the flux lines through the plane of a rectangular loop carrying current as illustrated in Fig. 3-9(b). The magnetic flux is in a direction normal to that plane.
Figure 3-9. (a) Toroid with winding carrying current; (b) magnetic flux lines of a rectangular loop of current
Each turn in the winding of Fig. 3-9(a) is such a loop, and if the number of turns or loops is large the flux will be normal to the radius everywhere in the toroid. This means that the flux lines will be concentric circles.
Consider the elemental flux path of thickness dx and radius x in the toroid. The width of this elemental path is the width of the toroid, namely w. Since this path closed upon itself, being a circle, Ampere's circuital law can be applied to express the magnetic field intensity in terms of the radius x. All the turns in the winding link the flux path, hence the total current that links the elemental path is the product of the current / and the number of turns N. Therefore, according to Eq. 3-34, we have
[3-35]
From Fig. 3-9(a) it is apparent that in the scalar product Hdl = H cosΘ dl, the product cosΘ dl is the projection of dl on the circle of radius x and is expressed by
[3-36]
Since the flux lines are concentric circles and if the material in the toroid has constant magnetic permeability, as is the case for free space, air and most nonferrous materials, H is constant everywhere in the circular path of radius x. Under these conditions the magnetic field intensity H in the line integral of Eq. 3-35 is a constant multiplier when coupled with the relationship expressed in Eq. 3-36. As a result Eq. 3-35 can be reduced as follows for this simple circular path
[3-37]
where F the magnetomotive force or mmf expressed in ampere turns. Then from Eq. 3-37 we get
[3-38]
Substitution of Eq. 3-15 in Eq. 3-38 yields the expression for the magnetic flux density in the circular path of radius x as follows
[3-39]
The magnetic flux crossing the incremental area dA = w dx in Fig. 3-9(a) is expressed by
[3-40]
where Θ is the angle between the flux density vector B and the normal to the vector dA. Since the vector associated with areas is perpendicular to the surface of the area being represented, the angle Θ in this case is zero. The vector B is tangent to the circle and the surface of the area w dx is radial. Then from Eqs. 3-39 and 3-40 we get
The total flux within the toroid is found by integrating as follows
[3-41]
Materials known as magnetic materials are ferrous materials and certain alloys of metals. They have a magnetic permeability that is much greater than that of free space. In the rationalized MKS system of units the permeability μ is taken as the product μrμ0 where μ0 = 4μ x 10-7 h per m, the magnetic permeability of free space and μr = the relative permeability of the toroid.
The relative permeability of ferromagnetic materials varies not only with the kind of material but also varies with the flux density in a given material. For example 24 gauge U.S.S. Electrical Sheet Steel has a relative permeability of about 1,300 at a value of H of about 24 amp turns per m, rising to a maximum of 5,800 at a value of H of about 120 amp turns, then decreasing to 1,300 at 960 amp turns per m.
If the toroid consists of a magnetic material that has a uniform relative permeability μr the total flux in the toroid is expressed by
[3-42]
In many applications it is sufficient to take H as the total ampere turns divided by the mean length of flux path. The value of B, resulting therefrom, multiplied by the area normal to the mean path is assumed to give the total flux. Thus for the toroid of Fig. 3-9(a) this approximation yields
and A = (r2 - r1)w, hence
[3-42a]
In general, if the magnetic circuit has a uniform cross-sectional area A normal to the direction of the magnetic flux and if the mean length of the flux path is l, the steady flux or slowly varying flux can be expressed approximately as follows
[3-43]
Last Update: 2011-08-01
| 1,118
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| 3.171875
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CC-MAIN-2014-41
|
longest
|
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| 0.915179
|
https://www.tensorflow.org/addons/api_docs/python/tfa/metrics/CohenKappa
| 1,721,503,184,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763517515.18/warc/CC-MAIN-20240720174732-20240720204732-00471.warc.gz
| 850,160,646
| 27,470
|
# tfa.metrics.CohenKappa
Computes Kappa score between two raters.
The score lies in the range `[-1, 1]`. A score of -1 represents complete disagreement between two raters whereas a score of 1 represents complete agreement between the two raters. A score of 0 means agreement by chance.
`num_classes` Number of unique classes in your dataset.
`weightage` (optional) Weighting to be considered for calculating kappa statistics. A valid value is one of [None, 'linear', 'quadratic']. Defaults to `None`
`sparse_labels` (bool) Valid only for multi-class scenario. If True, ground truth labels are expected to be integers and not one-hot encoded.
`regression` (bool) If set, that means the problem is being treated as a regression problem where you are regressing the predictions. Note: If you are regressing for the values, the the output layer should contain a single unit.
`name` (optional) String name of the metric instance
`dtype` (optional) Data type of the metric result. Defaults to `None`.
`ValueError` If the value passed for `weightage` is invalid i.e. not any one of [None, 'linear', 'quadratic'].
#### Usage:
````y_true = np.array([4, 4, 3, 4, 2, 4, 1, 1], dtype=np.int32)`
`y_pred = np.array([4, 4, 3, 4, 4, 2, 1, 1], dtype=np.int32)`
`weights = np.array([1, 1, 2, 5, 10, 2, 3, 3], dtype=np.int32)`
`metric = tfa.metrics.CohenKappa(num_classes=5, sparse_labels=True)`
`metric.update_state(y_true , y_pred)`
`<tf.Tensor: shape=(5, 5), dtype=float32, numpy=`
` array([[0., 0., 0., 0., 0.],`
` [0., 2., 0., 0., 0.],`
` [0., 0., 0., 0., 1.],`
` [0., 0., 0., 1., 0.],`
` [0., 0., 1., 0., 3.]], dtype=float32)>`
`result = metric.result()`
`result.numpy()`
`0.61904764`
`# To use this with weights, sample_weight argument can be used.`
`metric = tfa.metrics.CohenKappa(num_classes=5, sparse_labels=True)`
`metric.update_state(y_true , y_pred , sample_weight=weights)`
`<tf.Tensor: shape=(5, 5), dtype=float32, numpy=`
` array([[ 0., 0., 0., 0., 0.],`
` [ 0., 6., 0., 0., 0.],`
` [ 0., 0., 0., 0., 10.],`
` [ 0., 0., 0., 2., 0.],`
` [ 0., 0., 2., 0., 7.]], dtype=float32)>`
`result = metric.result()`
`result.numpy()`
` 0.37209308`
```
Usage with `tf.keras` API:
````inputs = tf.keras.Input(shape=(10,))`
`x = tf.keras.layers.Dense(10)(inputs)`
`outputs = tf.keras.layers.Dense(1)(x)`
`model = tf.keras.models.Model(inputs=inputs, outputs=outputs)`
`model.compile('sgd', loss='mse', metrics=[tfa.metrics.CohenKappa(num_classes=3, sparse_labels=True)])`
```
`activity_regularizer` Optional regularizer function for the output of this layer.
`compute_dtype` The dtype of the layer's computations.
This is equivalent to `Layer.dtype_policy.compute_dtype`. Unless mixed precision is used, this is the same as `Layer.dtype`, the dtype of the weights.
Layers automatically cast their inputs to the compute dtype, which causes computations and the output to be in the compute dtype as well. This is done by the base Layer class in `Layer.call`, so you do not have to insert these casts if implementing your own layer.
Layers often perform certain internal computations in higher precision when `compute_dtype` is float16 or bfloat16 for numeric stability. The output will still typically be float16 or bfloat16 in such cases.
`dtype` The dtype of the layer weights.
This is equivalent to `Layer.dtype_policy.variable_dtype`. Unless mixed precision is used, this is the same as `Layer.compute_dtype`, the dtype of the layer's computations.
`dtype_policy` The dtype policy associated with this layer.
This is an instance of a `tf.keras.mixed_precision.Policy`.
`dynamic` Whether the layer is dynamic (eager-only); set in the constructor.
`input` Retrieves the input tensor(s) of a layer.
Only applicable if the layer has exactly one input, i.e. if it is connected to one incoming layer.
`input_spec` `InputSpec` instance(s) describing the input format for this layer.
When you create a layer subclass, you can set `self.input_spec` to enable the layer to run input compatibility checks when it is called. Consider a `Conv2D` layer: it can only be called on a single input tensor of rank 4. As such, you can set, in `__init__()`:
``````self.input_spec = tf.keras.layers.InputSpec(ndim=4)
``````
Now, if you try to call the layer on an input that isn't rank 4 (for instance, an input of shape `(2,)`, it will raise a nicely-formatted error:
``````ValueError: Input 0 of layer conv2d is incompatible with the layer:
expected ndim=4, found ndim=1. Full shape received: [2]
``````
Input checks that can be specified via `input_spec` include:
• Structure (e.g. a single input, a list of 2 inputs, etc)
• Shape
• Rank (ndim)
• Dtype
For more information, see `tf.keras.layers.InputSpec`.
`losses` List of losses added using the `add_loss()` API.
Variable regularization tensors are created when this property is accessed, so it is eager safe: accessing `losses` under a `tf.GradientTape` will propagate gradients back to the corresponding variables.
````class MyLayer(tf.keras.layers.Layer):`
` def call(self, inputs):`
` self.add_loss(tf.abs(tf.reduce_mean(inputs)))`
` return inputs`
`l = MyLayer()`
`l(np.ones((10, 1)))`
`l.losses`
`[1.0]`
```
````inputs = tf.keras.Input(shape=(10,))`
`x = tf.keras.layers.Dense(10)(inputs)`
`outputs = tf.keras.layers.Dense(1)(x)`
`model = tf.keras.Model(inputs, outputs)`
`# Activity regularization.`
`len(model.losses)`
`0`
`model.add_loss(tf.abs(tf.reduce_mean(x)))`
`len(model.losses)`
`1`
```
````inputs = tf.keras.Input(shape=(10,))`
`d = tf.keras.layers.Dense(10, kernel_initializer='ones')`
`x = d(inputs)`
`outputs = tf.keras.layers.Dense(1)(x)`
`model = tf.keras.Model(inputs, outputs)`
`# Weight regularization.`
`model.add_loss(lambda: tf.reduce_mean(d.kernel))`
`model.losses`
`[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>]`
```
`metrics` List of metrics added using the `add_metric()` API.
````input = tf.keras.layers.Input(shape=(3,))`
`d = tf.keras.layers.Dense(2)`
`output = d(input)`
`d.add_metric(tf.reduce_max(output), name='max')`
`d.add_metric(tf.reduce_min(output), name='min')`
`[m.name for m in d.metrics]`
`['max', 'min']`
```
`name` Name of the layer (string), set in the constructor.
`name_scope` Returns a `tf.name_scope` instance for this class.
`non_trainable_weights` List of all non-trainable weights tracked by this layer.
Non-trainable weights are not updated during training. They are expected to be updated manually in `call()`.
`output` Retrieves the output tensor(s) of a layer.
Only applicable if the layer has exactly one output, i.e. if it is connected to one incoming layer.
`submodules` Sequence of all sub-modules.
Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).
````a = tf.Module()`
`b = tf.Module()`
`c = tf.Module()`
`a.b = b`
`b.c = c`
`list(a.submodules) == [b, c]`
`True`
`list(b.submodules) == [c]`
`True`
`list(c.submodules) == []`
`True`
```
`supports_masking` Whether this layer supports computing a mask using `compute_mask`.
`trainable`
`trainable_weights` List of all trainable weights tracked by this layer.
Trainable weights are updated via gradient descent during training.
`variable_dtype` Alias of `Layer.dtype`, the dtype of the weights.
`weights` Returns the list of all layer variables/weights.
## Methods
### `add_loss`
Add loss tensor(s), potentially dependent on layer inputs.
Some losses (for instance, activity regularization losses) may be dependent on the inputs passed when calling a layer. Hence, when reusing the same layer on different inputs `a` and `b`, some entries in `layer.losses` may be dependent on `a` and some on `b`. This method automatically keeps track of dependencies.
This method can be used inside a subclassed layer or model's `call` function, in which case `losses` should be a Tensor or list of Tensors.
#### Example:
``````class MyLayer(tf.keras.layers.Layer):
def call(self, inputs):
return inputs
``````
The same code works in distributed training: the input to `add_loss()` is treated like a regularization loss and averaged across replicas by the training loop (both built-in `Model.fit()` and compliant custom training loops).
The `add_loss` method can also be called directly on a Functional Model during construction. In this case, any loss Tensors passed to this Model must be symbolic and be able to be traced back to the model's `Input`s. These losses become part of the model's topology and are tracked in `get_config`.
#### Example:
``````inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Activity regularization.
``````
If this is not the case for your loss (if, for example, your loss references a `Variable` of one of the model's layers), you can wrap your loss in a zero-argument lambda. These losses are not tracked as part of the model's topology since they can't be serialized.
#### Example:
``````inputs = tf.keras.Input(shape=(10,))
d = tf.keras.layers.Dense(10)
x = d(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Weight regularization.
``````
Args
`losses` Loss tensor, or list/tuple of tensors. Rather than tensors, losses may also be zero-argument callables which create a loss tensor.
`**kwargs` Used for backwards compatibility only.
### `add_metric`
Adds metric tensor to the layer.
This method can be used inside the `call()` method of a subclassed layer or model.
``````class MyMetricLayer(tf.keras.layers.Layer):
def __init__(self):
super(MyMetricLayer, self).__init__(name='my_metric_layer')
self.mean = tf.keras.metrics.Mean(name='metric_1')
def call(self, inputs):
return inputs
``````
This method can also be called directly on a Functional Model during construction. In this case, any tensor passed to this Model must be symbolic and be able to be traced back to the model's `Input`s. These metrics become part of the model's topology and are tracked when you save the model via `save()`.
``````inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
``````
``````inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
``````
Args
`value` Metric tensor.
`name` String metric name.
`**kwargs` Additional keyword arguments for backward compatibility. Accepted values: `aggregation` - When the `value` tensor provided is not the result of calling a `keras.Metric` instance, it will be aggregated by default using a `keras.Metric.Mean`.
### `build`
Creates the variables of the layer (for subclass implementers).
This is a method that implementers of subclasses of `Layer` or `Model` can override if they need a state-creation step in-between layer instantiation and layer call. It is invoked automatically before the first execution of `call()`.
This is typically used to create the weights of `Layer` subclasses (at the discretion of the subclass implementer).
Args
`input_shape` Instance of `TensorShape`, or list of instances of `TensorShape` if the layer expects a list of inputs (one instance per input).
### `compute_mask`
Args
`inputs` Tensor or list of tensors.
`mask` Tensor or list of tensors.
Returns
None or a tensor (or list of tensors, one per output tensor of the layer).
### `compute_output_shape`
Computes the output shape of the layer.
This method will cause the layer's state to be built, if that has not happened before. This requires that the layer will later be used with inputs that match the input shape provided here.
Args
`input_shape` Shape tuple (tuple of integers) or `tf.TensorShape`, or structure of shape tuples / `tf.TensorShape` instances (one per output tensor of the layer). Shape tuples can include None for free dimensions, instead of an integer.
Returns
A `tf.TensorShape` instance or structure of `tf.TensorShape` instances.
### `count_params`
Count the total number of scalars composing the weights.
Returns
An integer count.
Raises
`ValueError` if the layer isn't yet built (in which case its weights aren't yet defined).
### `from_config`
Creates a layer from its config.
This method is the reverse of `get_config`, capable of instantiating the same layer from the config dictionary. It does not handle layer connectivity (handled by Network), nor weights (handled by `set_weights`).
Args
`config` A Python dictionary, typically the output of get_config.
Returns
A layer instance.
### `get_config`
View source
Returns the serializable config of the metric.
### `get_weights`
Returns the current weights of the layer, as NumPy arrays.
The weights of a layer represent the state of the layer. This function returns both trainable and non-trainable weight values associated with this layer as a list of NumPy arrays, which can in turn be used to load state into similarly parameterized layers.
For example, a `Dense` layer returns a list of two values: the kernel matrix and the bias vector. These can be used to set the weights of another `Dense` layer:
````layer_a = tf.keras.layers.Dense(1,`
` kernel_initializer=tf.constant_initializer(1.))`
`a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))`
`layer_a.get_weights()`
`[array([[1.],`
` [1.],`
` [1.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b = tf.keras.layers.Dense(1,`
` kernel_initializer=tf.constant_initializer(2.))`
`b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))`
`layer_b.get_weights()`
`[array([[2.],`
` [2.],`
` [2.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b.set_weights(layer_a.get_weights())`
`layer_b.get_weights()`
`[array([[1.],`
` [1.],`
` [1.]], dtype=float32), array([0.], dtype=float32)]`
```
Returns
Weights values as a list of NumPy arrays.
### `merge_state`
Merges the state from one or more metrics.
This method can be used by distributed systems to merge the state computed by different metric instances. Typically the state will be stored in the form of the metric's weights. For example, a tf.keras.metrics.Mean metric contains a list of two weight values: a total and a count. If there were two instances of a tf.keras.metrics.Accuracy that each independently aggregated partial state for an overall accuracy calculation, these two metric's states could be combined as follows:
````m1 = tf.keras.metrics.Accuracy()`
`_ = m1.update_state([[1], [2]], [[0], [2]])`
```
````m2 = tf.keras.metrics.Accuracy()`
`_ = m2.update_state([[3], [4]], [[3], [4]])`
```
````m2.merge_state([m1])`
`m2.result().numpy()`
`0.75`
```
Args
`metrics` an iterable of metrics. The metrics must have compatible state.
Raises
`ValueError` If the provided iterable does not contain metrics matching the metric's required specifications.
### `reset_state`
View source
Resets all of the metric state variables.
View source
### `result`
View source
Computes and returns the scalar metric value tensor or a dict of scalars.
Result computation is an idempotent operation that simply calculates the metric value using the state variables.
Returns
A scalar tensor, or a dictionary of scalar tensors.
### `set_weights`
Sets the weights of the layer, from NumPy arrays.
The weights of a layer represent the state of the layer. This function sets the weight values from numpy arrays. The weight values should be passed in the order they are created by the layer. Note that the layer's weights must be instantiated before calling this function, by calling the layer.
For example, a `Dense` layer returns a list of two values: the kernel matrix and the bias vector. These can be used to set the weights of another `Dense` layer:
````layer_a = tf.keras.layers.Dense(1,`
` kernel_initializer=tf.constant_initializer(1.))`
`a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))`
`layer_a.get_weights()`
`[array([[1.],`
` [1.],`
` [1.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b = tf.keras.layers.Dense(1,`
` kernel_initializer=tf.constant_initializer(2.))`
`b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))`
`layer_b.get_weights()`
`[array([[2.],`
` [2.],`
` [2.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b.set_weights(layer_a.get_weights())`
`layer_b.get_weights()`
`[array([[1.],`
` [1.],`
` [1.]], dtype=float32), array([0.], dtype=float32)]`
```
Args
`weights` a list of NumPy arrays. The number of arrays and their shape must match number of the dimensions of the weights of the layer (i.e. it should match the output of `get_weights`).
Raises
`ValueError` If the provided weights list does not match the layer's specifications.
### `update_state`
View source
Accumulates the confusion matrix condition statistics.
Args
`y_true` Labels assigned by the first annotator with shape `[num_samples,]`.
`y_pred` Labels assigned by the second annotator with shape `[num_samples,]`. The kappa statistic is symmetric, so swapping `y_true` and `y_pred` doesn't change the value.
`sample_weight` `optional`
for weighting labels in confusion matrix Defaults to `None`. The dtype for weights should be the same as the dtype for confusion matrix. For more details, please check `tf.math.confusion_matrix`.
Returns
Update op.
### `with_name_scope`
Decorator to automatically enter the module name scope.
````class MyModule(tf.Module):`
` @tf.Module.with_name_scope`
` def __call__(self, x):`
` if not hasattr(self, 'w'):`
` self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))`
` return tf.matmul(x, self.w)`
```
Using the above module would produce `tf.Variable`s and `tf.Tensor`s whose names included the module name:
````mod = MyModule()`
`mod(tf.ones([1, 2]))`
`<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>`
`mod.w`
`<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,`
`numpy=..., dtype=float32)>`
```
Args
`method` The method to wrap.
Returns
The original method wrapped such that it enters the module's name scope.
### `__call__`
Accumulates statistics and then computes metric result value.
Args
`*args`
`**kwargs` A mini-batch of inputs to the Metric, passed on to `update_state()`.
Returns
The metric value tensor.
[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]
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http://worldfullofquestions.com/tag/sjf/
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## Numerical Solved by Shortest Job First Scheduling Algorithm
Q8. Consider the following:
Arrive Time Process Burst Time
0 P1 10
1 P2 4
2 P3 3
3 P4 1
Draw Gantt Chart and calculate average turnaround and waiting time using Shortest Job First Scheduling Algorithm.
Grant Chart:
P1 P2 P4 P2 P3 P1
0 1 3 4 6 9 18
Turnaround Time
P1=18-0=18
P2=6-1=5
P3=9-2=7
P4=4-3=1
Average Turnaround Time
=(18+5+7+1)/4
=31/4
=7.77 ms
Waiting Time
P1’s waiting time=9-1=8
P2’s waiting time=4-3=1
P3’s waiting time=6-2=4
P4’s waiting time=3-3=0
Average Waiting Time
=(8+1+4+0)/4
=13/4
=3.25 ms
## Numerical Solved by SJF
Q5. Consider the set of process P1,P2,P3,P4 and P5 having burst time as 10,1,2,1 and 5 ms and priority 5,1,3,4 and 2. The processes are assumed to have arrived at time 0, then draw Gantt Chart and calculate average turnaround and waiting time using Shortest Job First Scheduling Algorithm.
Ans. Solving by SJF
Process Burst Time Priority Time
P1 10 5
P2 1 1
P3 2 3
P4 1 4
P5 5 2
Gantt Chart
P2 P4 P3 P5 P1
0 1 2 4 9 19
Turnaround Time
P1=19
P2=1
P3=4
P4=2
P5=9
Average Turnaround Time
=(19+1+4+2+9)/5
=35/5
=7 milliseconds
Waiting Time
P1’s waiting time=9
P2’ waiting time=0
P3’s waiting time=2
P4’swaiting time=1
P5’s waiting time=4
Average Waiting Time
=(9+0+2+1+4)/5
=16/5
=3.2 ms
## Non-preemptive Shortest Job First Scheduling Algorithm
Q3. Explain Non-preemptive Shortest Job First Scheduling with example.
Ans. Once CPU is given to the process it cannot be preempted until completes its CPU burst.
Let’s take four processes that arrive at the same time in this order:
Process CPU Time Needed (ms)
P1 6
P2 8
P3 7
P4 3
Gantt Chart:
P4 P1 P3 P2
0 3 9 16 24
P1’ waiting time=3
P2’s waiting time=16
P3’s waiting time=9
P4’s waiting time=0
Average Waiting Time
=(3+16+9+0)/4
=28/4
=7 milliseconds
Turnaround Time
Turnaround Time = Burst Time + Waiting Time
Process Turnaround Time
P1 6+3=9
P2 8+16=24
P3 7+9=16
P4 3+0=3
Average Turnaround Time
=(9+24+16+3)/4
=13 milliseconds
## Classification of Shortest Job First Scheduling Algorithm
Q2. What is the classification of Shortest Job First Scheduling Algorithm?
Ans. SJF scheduling can be classified into two schemes, they are as follow:
1. Non-Preemptive Shortest Job First Scheduling
2. Preemptive Shortest Job First Scheduling
## Explain Shortest Job First (SJF).
Q1. Explain Shortest Job First (SJF).
Ans. Clearly, the average waiting time under a purely first-in first-out system is going to often be poor if one task is significantly longer than the others.
So, the first idea that comes about after seeing this is the idea of having the shortest task go first, or shortest job first scheduling. This, obviously, would be similar to the idea above, except that as each job comes in, it is sorted into the queue based on size.
In shortest job first (SJF), waiting job (or process) with the smallest estimated run time to completion is run next. In other words, when CPU is available, it is assigned to the process that has smallest next CPU burst.
The SJF scheduling is especially appropriate for batch jobs for which the run times are known in advance.
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## What is the Cash Conversion Cycle Formula?
The cash conversion cycle is a formula used to assess and assess the liquidity of a company, which measures how long it takes a business to convert inventory and other resources into cash. To calculate it, you must consider investment in inventory, accounts receivable, and accounts payable. The formula for the cash conversion cycle is calculated as follows:
• Cash Conversion Cycle = Days Inventory Outstanding + Days Sales Outstanding - Days Payable Outstanding
The cash conversion cycle takes into account all the elements that affect the time a company takes to collect money from its customers, pay its suppliers and renew its stock, represented by days of inventory outstanding, days of sales outstanding and days of accounts payable. This cycle is usually measured monthly, quarterly and annually. For example, let’s consider a company with the following activity pattern:
• Inventory turnover in weeks: 8
• Sales outstanding in weeks: 12
• Accounts payable in weeks: 8
To calculate the cash conversion cycle of this company:
• Days Inventory Outstanding = 8 x 7 = 56 days
• Days Sales Outstanding = 12 x 7 = 84 days
• Days Payable Outstanding = 8 x 7 = 56 days
• Cash Conversion Cycle = 56 + 84 - 56 = 84 days
The lower the cash conversion cycle value, the better, since it implies that the company is able to manage more efficiently its working capital and have cash more quickly. To reduce the cash conversion cycle, businesses should keep a close eye on the elements that affect it and make efforts to reduce the time necessary for each process, for example by collecting payments from customers in a timely manner, paying vendors early to qualify for discounts, or investing in automation solutions.Key Takeaways:
• The Cash Conversion Cycle (CCC) measures how effective a company is at converting raw materials into cash.
• The components of the CCC are the inventory days, accounts receivable period, and accounts payable period.
• Companies can reduce their CCC by reviewing credit policies, exploring early payment discounts, and negotiating longer payment terms with suppliers.
• Understanding and utilizing the Cash Conversion Cycle can improve operations, finances, and revenues.
## How can I calculate the Cash Conversion Cycle?
The Cash Conversion Cycle (CCC) is a metric used to evaluate and measure the effectiveness of a company’s management of its cash flow. It measures the amount of time that a company’s inventory is held until it is converted into revenue. Calculating the CCC is essential to gain insight into a company’s cash flow while providing an indication of the company’s liquidity and health. Here are some tips and examples on how to calculate Cash Conversion Cycle:
• Calculate Inventory Turnover Ratio: The first step you need to take when calculating the CCC is to calculate the inventory turnover ratio. This number is calculated by dividing the cost of goods sold by average inventory. This ratio is used to measure how quickly a company is selling its goods. It can also be used to identify potential weaknesses in the business.
• Calculate Collection Period: Once the inventory turnover ratio is calculated, the collection period can be determined. This number is calculated by taking the number of days in the period and dividing it by the sales outstanding. This will give you the number of days it takes for a company to receive payment from customers.
• Calculate Payment Period: To calculate the payment period, take the number of days in the period and divide it by the amount of accounts payable outstanding. This will give you the number of days it takes for the company to pay its bills to its suppliers.
• Calculate the CCC: Once you have all of the above information, you’re ready to calculate the CCC. To do so, subtract the payment period from the collection period and then subtract this number from the inventory turnover ratio. This will give you the CCC.
For example, if a company had an inventory turnover ratio of 10 days and a collection period of 15 days and a payment period of 8 days, the CCC would be calculated as follows: 10 – (15 – 8) = 7 days.
Using the Cash Conversion Cycle will enable a company to have a better understanding of their cash flow and identify areas where improvements can be made. Implementing the tips and examples stated above can assist a company in accurately calculating and evaluating the CCC.
## What Cash Conversion Cycle Formula Should I Use?
The Cash Conversion Cycle (CCC) is a formula that measures how long it takes a company to convert its investments in inventory and other resources into cash sales. The formula looks like this: CCC = Days Inventory Outstanding (DIO) + Days Sales Outstanding (DSO) - Days Payables Outstanding (DPO)
To accurately calculate the Cash Conversion Cycle, you need to understand what each part of the equation measures:
• Days Inventory Outstanding (DIO): This metric measures the average time it takes for a company to sell its inventory. DIO is calculated by dividing the average inventory for the period by cost of goods sold and then multiplying that number by the number of days in the period.
• Days Sales Outstanding (DSO): This metric tracks the average number of days a company takes to collect cash from its customers. To calculate DSO, take the total amount of accounts receivable, divide it by total sales, and multiply it by the number of days in the period.
• Days Payables Outstanding (DPO): This metric measures the average amount of time a company takes to pay its suppliers. You can calculate DPO by taking the total amount of accounts payable, dividing it by total purchases, and multiplying it by the number of days in the period.
Using the above formula, you can calculate the length of time it takes for a company to turn its investments in inventory and other resources into cash. By closely monitoring the Cash Conversion Cycle, you can gain valuable insight into a company's financial performance and make more informed business decisions.
## Why is the Cash Conversion Cycle Important?
The cash conversion cycle (CCC) is the measure of the time it takes a company to convert raw materials into available cash. This metric is important not only because it indicates the company's efficiency in managing its resources but also because it reveals how effective the firm is in making money. The shorter the cash conversion cycle, the more effective the firm is in its operations. The key components of the CCC are the inventory days, accounts receivable period, and accounts payable period.
Inventory Days refer to the length of time it takes for a company to convert its inventory into sales. It consists of the time taken to purchase inventory, which can range from days to weeks depending on the industry, the length of time it takes for the inventory to be shipped and arrive at the company, and the time it takes to be sold and converted into cash. A shorter inventory period indicates the company is able to market and sell its inventory quickly and efficiently. On the other hand, a longer inventory period might indicate the company has difficulty moving its inventory.
Accounts receivable period refers to the length of time it takes for the customer to pay for their purchase. It consists of the time taken for customers to purchase the goods or services, how quickly the customer pays the invoice, and the time it takes for the company to receive the payment. A shorter accounts receivable period indicates that customers are paying quickly and efficiently, which is beneficial for the company’s ability to generate cash. A longer accounts receivable period might indicate that the company is facing difficulty getting customers to pay in a timely manner.
Accounts payable period refers to the length of time it takes the company to pay its suppliers once it has received the goods. This period consists of the length of time it takes to receive approval for payments and when the payment will be sent to the supplier. A shorter accounts payable period indicates that the company is able to keep track of its payments efficiently and quickly, which can result in better relationships with suppliers. A longer accounts payable period might indicate that the company is facing difficulty in making timely payments.
By understanding its cash conversion cycle, a company can identify areas of improvement and develop strategies to boost efficiency in operations and increase revenues. Here are some tips on how to improve a company’s cash conversion cycle:
• Review credit policies and consider tightening credit terms to reduce the accounts receivable period.
• Explore early payment discounts and other payment incentives to encourage customers to pay their invoices quickly.
• Negotiate longer payment terms with suppliers to reduce the accounts payable period.
• Maintain accurate inventory records and reorder goods in a timely manner to reduce the inventory days.
• Implement processes to speed up shipment times to reduce the time it takes for inventory to arrive.
Overall, the cash conversion cycle gives companies a much-needed insight into their operations, finances, and potential areas of improvement. By understanding and utilizing the CCC, companies can ensure that their operations are efficient and that the firm is profitable and generating revenue.
## How do I interpret the results of the cash conversion cycle formula?
The cash conversion cycle (CCC) formula is used to assess the efficiency of a business’ cash flow. The formula measures the cash invested in operating activities compared to the cash generated. The general formula for the CCC is (Inventory Days + Receivable Days - Payable Days).
Interpreting the results of the CCC formula is relatively straightforward. A low number means that there is a lower amount of money invested in inventory and accounts receivable, and there is a faster turnaround of that cash into cash generated. Alternatively, a higher number signifies higher amounts of production and/or sales, and a slower turnaround of cash into cash generated.
Here are some examples and tips to consider when interpreting the results of the CCC formula:
• If the CCC value is negative or zero, then the company is generating cash quickly and effectively.
• If the CCC result is greater than zero, then the company is generating cash comparatively slowly.
• To reduce the CCC value, a business may consider offering discounts to customers for early payment or using more efficient forms of inventory management.
• It is important to be aware of changes in the CCC result over time, as that can signify an issue with cash flow management.
By understanding and interpreting the results of the cash conversion cycle formula, businesses can gain a better understanding of their cash flow management and identify areas for further improvement.
## Is the Cash Conversion Cycle the Same for All Businesses?
The Cash Conversion Cycle (CCC) is an effective tool used to measure a company’s liquidity, efficiency and profitability. It is a calculation of the number of days between making an inventory purchase and collecting cash on the sale of the inventory. In theory, all businesses should have the same CCC since the same equation is used to calculate it but this may not always be the case. Depending on the type of business and the systems in place, the cycle may differ. For instance, a brick and mortar store will have a longer cycle than an online retailer since the products need to be physically shipped and collected from the customers. Businesses also have the ability to reduce their CCC by changing certain components within the cycle. Here are a few tips on how to do this:
• Negotiate better terms with suppliers.
• Offer discounts for early payment from customers.
• Optimize inventory levels so that stock is neither too low nor too high.
• Implement centralised purchase systems.
• Use upgraded inventory management software.
By maximizing their efficiency through careful planning, businesses have the potential to increase profits and reduce costs within their CCC.
## How does inventory impact the cash conversion cycle formula?
Inventory can have a significant impact on the Cash Conversion Cycle (CCC) formula, while goods in transit and goods in process can also play a role. Inventory is the main factor that affects the number of days it takes a company to convert cash used in production (raw materials, manufacturing, and labor costs) into goods and services it can sell.
Inventory, goods in transit, and goods in process significantly affect the two main components of the Cash Conversion Cycle, Accounts Receivable and Inventory. When a company has a large amount of inventory or goods in transit or goods in process, the company must wait longer before cash is collected. This results in a longer CCC and less liquidity for the company.
The following are some tips for managing inventory to reduce the overall cash conversion cycle:
• Optimize the production process to reduce the time required to produce goods from raw materials.
• Reduce lead times by developing better processes for coordinating production and purchasing.
• Implement a Just-in-Time (JIT) inventory system to reduce inventory levels.
• Utilize Enterprise Resource Planning (ERP) software to track, schedule, and manage inventory.
• Strengthen customer relationships by providing on-time deliveries.
By managing inventory, companies can improve their cash conversion cycle and reduce their working capital needs. Ultimately, this will lead to increased profitability, improved liquidity, and increased shareholder value.Conclusion: The Cash Conversion Cycle is an important tool for evaluating and optimizing the cash flow of a business. By understanding the components and impact of the CCC, companies can identify areas for improvement and develop strategies to maximize profits and efficiency. With the right strategies in place, firms can not only increase their revenues but also have better relationships with suppliers, customers, and other stakeholders.
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Help protect the Great Barrier Reef with TensorFlow on Kaggle
# tf.compat.v1.metrics.precision_at_k
Computes precision@k of the predictions with respect to sparse labels.
If class_id is specified, we calculate precision by considering only the entries in the batch for which class_id is in the top-k highest predictions, and computing the fraction of them for which class_id is indeed a correct label. If class_id is not specified, we'll calculate precision as how often on average a class among the top-k classes with the highest predicted values of a batch entry is correct and can be found in the label for that entry.
precision_at_k creates two local variables, true_positive_at_<k> and false_positive_at_<k>, that are used to compute the precision@k frequency. This frequency is ultimately returned as precision_at_<k>: an idempotent operation that simply divides true_positive_at_<k> by total (true_positive_at_<k> + false_positive_at_<k>).
For estimation of the metric over a stream of data, the function creates an update_op operation that updates these variables and returns the precision_at_<k>. Internally, a top_k operation computes a Tensor indicating the top k predictions. Set operations applied to top_k and labels calculate the true positives and false positives weighted by weights. Then update_op increments true_positive_at_<k> and false_positive_at_<k> using these values.
If weights is None, weights default to 1. Use weights of 0 to mask values.
labels int64 Tensor or SparseTensor with shape [D1, ... DN, num_labels] or [D1, ... DN], where the latter implies num_labels=1. N >= 1 and num_labels is the number of target classes for the associated prediction. Commonly, N=1 and labels has shape [batch_size, num_labels]. [D1, ... DN] must match predictions. Values should be in range [0, num_classes), where num_classes is the last dimension of predictions. Values outside this range are ignored.
predictions Float Tensor with shape [D1, ... DN, num_classes] where N >= 1. Commonly, N=1 and predictions has shape [batch size, num_classes]. The final dimension contains the logit values for each class. [D1, ... DN] must match labels.
k Integer, k for @k metric.
class_id Integer class ID for which we want binary metrics. This should be in range [0, num_classes], where num_classes is the last dimension of predictions. If class_id is outside this range, the method returns NAN.
weights Tensor whose rank is either 0, or n-1, where n is the rank of labels. If the latter, it must be broadcastable to labels (i.e., all dimensions must be either 1, or the same as the corresponding labels dimension).
metrics_collections An optional list of collections that values should be added to.
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The OEIS is supported by the many generous donors to the OEIS Foundation.
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A178032 Numbers n such that n, n+1, n+2 are all of the form p*q^2 for distinct primes p,q. 4
603, 2523, 4203, 4923, 7442, 10467, 18027, 20402, 54475, 58923, 79011, 97675, 104211, 118323, 120787, 122571, 124891, 132723, 134307, 148075, 200491, 229707, 243602, 246571, 249307, 258507, 303651, 324331, 331387, 370827, 385675 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 (first 500 terms from Harvey P. Dale) EXAMPLE 603=3*3*67, 604=2*2*151, 605=5*11*11 2523=3*29*29, 2524=2*2*631, 2525=5*5*101 MATHEMATICA SequencePosition[Table[If[Sort[FactorInteger[n][[All, 2]]]=={1, 2}, 1, 0], {n, 400000}], {1, 1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 30 2019 *) PROG (Sage) is_A178032 = lambda n: all(sorted(m for p, m in factor(k)) == [1, 2] for k in (n, n+1, n+2)) # D. S. McNeil, Dec 17 2010 CROSSREFS Cf. A054753, A074172, A308683, A141621. Sequence in context: A252957 A348077 A066785 * A107256 A177685 A250907 Adjacent sequences: A178029 A178030 A178031 * A178033 A178034 A178035 KEYWORD nonn AUTHOR John L. Drost, Dec 16 2010 EXTENSIONS Corrected and extended by D. S. McNeil, Dec 16 2010 STATUS approved
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# What are two lines that don't go over each other more than once?
Updated: 9/17/2023
Wiki User
14y ago
those two lines are perpendicular lines
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14y ago
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### How are perpendicular lines like intersecting lines?
perpendicular lines are similar to intersecting lines because that's what they are. Intersecting lines are two lines that cross each other. Perpendicular lines are the same, two lines crossing each other, just with a more specific rule to have right angles.
### Will inuyasha beat sesshomaru?
No, InuYasha does not beat sesshomaru and netheir does Sesshomaru beat InuYasha. In the end they dont really like each other more,but I dont think they hate each other more either.
### What the definition of parallel lines?
Parallel lines are two or more lines that run perfectly straight, into infinite, next to each other so that none of the lines will ever touch.
### What is an intersecting line?
An intersection is the point at which two or more lines touch or cross, therefore, lines are intersecting when they cross each-other.
### Do James Stewart and Chad Reed like each other?
it depends on what condition there in cause they like each other more when they dont get in each others way
### Does each line of sonnet rhyme with the others?
No, it does not, though usually there is a pattern of two or more lines rhyming with each other. But usually not all 14 lines have the same rhyme sound.
### What does the lines outside yin yang mean?
The lines represent yin and yang as the grow and fall from each other. The full lines represent yang (white) and the broken lines represent yin (black). The more full lines in the tetragram, the more yang influence. Thus, the more broken lines in the tetragram, the more yin influence.
### Can a given point be in more than one line?
Yes. The lines would cross each other
### What is the locus of point equidistant from two intersecting lines?
The locus in a plane is two more intersecting lines, perpendicular to each other (and of course half-way between the given lines.
### What two lines meet at a point?
I think you're talking about an intersection. An intersection is where two or more separate lines meet each other in one point.
### Can a pair of lines be both parallel and skew?
No. Parallel has a specific meaning. For lines to be parallel, they have to lie in a common plane, but not touch each other. If they are skew, they still don't touch each other, but they now do not lie in a common plane. More specifically, skew lines, by definition, are not co-planar.
### How does parallels meet?
Parallel lines cannot meet each other at all.Read the questions below to know and understand more.Q2. It is look like this -> it can also be like this -> \\ but they must be same and they don't meet each other it can also be like this too -> = and more but cannot meet each other. Q3. You just cannot meet each other that's all, all you need to remember is they just cannot meet each other not like perpendicular lines they can meet each other but parallel lines don't meet each other.Q4. It is easy to remember parallel lines because when you see ll in the word parallel lines means it is parallel lines.Parallel lines has two ll just like this \\,,= that i just showed you just now at question number two.Q5.So remember parallel lines cannot meet each other and when you see two ll it means that is parallel lines.It is so easy to remember parallel lines.
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# How many tablespoons in 30ml?
How many tablespoons in 30ml? 30 ml is equivalent to 1.0 US fl oz, which is 1.06375 US tbsp, which is equivalent to 3.71535 grams, which is equivalent to 0.1042 US oz, which is 1.6 US tbsp, which is equivalent to 0.000316 US cup, which is 1.95910 milliliters, which is equivalent to 0.001042 US pint, which is 0.00116 US quart, which is 0.00321 US pint, which is 0.000276 US quarts, which is 0.000029 US gallons, which is 0.00118 US pints, which is 0.00450 US liters, which is equivalent to 28.412 US fl oz, which is 15.875498 US cups, which is equivalent to 0.119 US gallons.
#### How many ml does a 1 tablespoon hold?
If you’re measuring a tablespoon of water, it will hold 3.75 ml. The same tablespoon of oil, however, will hold 14.25 ml. This can be confusing, so it’s best to measure using a separate measuring spoon for water and another for oil. Keep in mind that a teaspoon holds 5 ml and other cooking measurements may differ from a tablespoon.
#### What measuring spoon is 30ml?
Your measuring spoons should not be the same as your cooking spoons because they are different in size. The most commonly used measuring spoon is a U.S. standard which is 1/8th of a cup. The actual measurement of it is a little above 30 ml. It is possible that your measuring spoon may not be the U.S. standard. If that’s the case, you can ignore this answer.
#### How much is 30ml of medicine?
30 ml is equal to 1 fluid ounce. 30 ml is used to measure 30 ccs (cubic centimeters) of liquids. While we think that ml is used to measure liquids, it is actually used to measure medicines. Commonly used medicines are measured in the following common ml’s.
#### How many teaspoons is 30 ml of Nyquil?
30 ml of Nyquil is equivalent to 90 Nyquil No Drip Liquid Capsules, as both contain the same active ingredient, doxylamine succinate, at ten milligrams per capsule.
#### How many tablespoons is 30mL of DayQuil?
One tablespoon is 15 mL while a teaspoon is 5 mL. So we can have 30 mL (1/2 cup) of DayQuil. It is equivalent to 7 teaspoons or 15 tablespoons.
#### How much alcohol is in 30 mL of NyQuil?
The active ingredients of NyQuil are doxylamine succinate and dextromethorphan hydrobromide. Both drugs are sedative-hypnotics. Dextromethorphan hydrobromide is the active ingredient in the most common over-the-counter cough suppressants. 99% of the dose of this ingredient is dextrorphan, a metabolite of dextromethorphan that has dissociative and hallucinogenic effects. The lethal dose of doxylamine is mg/kg in humans. A cup of NyQuil contains _ mL. Therefore, the lethal dosage is _ mL of NyQuil.
#### How many tablespoons is 30ml UK?
There are 2 tablespoons in 30ml. A tablespoon is a commonly used unit of volume. The symbol for tablespoon is “tbsp”. The symbol for millilitre is “ml”. One UK tablespoon is equal to 1.2 US tablespoons. US tablespoon is 1.5 times bigger than UK tablespoon. US tablespoon is used in most of the US (e.g. USA, Canada, and others).
#### How many teaspoons is 30 milligrams?
Well, at least about 2 or 3 teaspoons. It depends on the size of the teaspoon, though. I’ll tell you the same thing I told a co-worker earlier today: The teaspoon you’re using is not the official dosage of a teaspoon. You can’t go around measuring medicine that way.
#### What is 30ml in teaspoons UK?
30ml is a unit of volume, commonly used in the UK. There is no fixed definition for the volume of a teaspoon. However, a US tablespoon is 15ml which is about half the size of a UK tablespoon which is 20ml. So 30ml is slightly less than 1 US tbsp.
#### How many tablespoons is 300ml UK?
According to nutritionist, 300ml UK measurement contains around 30 tablespoons. The common weight and volume measuring systems used are: Metric system: 0.3 kilogram = 1 liter UK: 1 gram = 1 cubic centimeter US: 1 ounce = 28.35 grams
#### Is a teaspoon 5ml?
Yes, a teaspoon is 5ml in volume. The teaspoon is one of the measures used to measure the amount of liquid. The word teaspoon is also known as a dessert spoon. In order to determine the amount of tablespoon, we should measure the diameter of the spoon. For instance, if your tablespoon is 2.5 inches in diameter, then you can say that the teaspoon is 5ml in volume. The teaspoon is sometimes referred to as the dessert spoon. Hence one dessert spoon is 5ml. A tablespoon is 15ml. The ratio is normally 1 teaspoon to 2 tablespoons.
#### What is a tablespoon UK?
A tablespoon (UK) is officially measured as 0.21006907 ml. The tablespoon, Teaspoon, and Tablespoon are three different units of measurement each defined as a standard volume of a particular foodstuff. A tablespoon is defined as one three-hundredth of a gallon. A teaspoon is defined as one three-hundredth of a fluid ounce. A tablespoon is defined as one-sixteenth of a fluid ounce. As a general rule, a fluid ounce is equivalent to an actual ounce of liquid.
#### How many ml is a spoon full?
The usual spoon used by people are spoons that hold approximately 5 ml to 8 ml each. The exact amount of ml that a spoon holds will depend on the size of the spoon. Another way to measure the amount of liquid that is scooped up is in teaspoons. A tablespoon is equal to 3 teaspoons.
#### How many milliliters is 3 tablespoons of liquid?
Three tablespoons are equal to roughly 20 ml. It all depends on the type of liquid though. For example, water and cream are measured differently. The same is true for measurements that are in cups, such as milk and juice. If you’re looking for the answer to a different question, feel free to submit your own Quora question and one of our experts will get back to you with an answer.
#### Is a table spoon 5ml?
Yes. Usually, measurement units like a tablespoon, ounce, or liter are used for liquids, while weights are measured in grams and kilograms. However, there is no universal measurement system, so depending on the country you are in, you might use different measurements. In the United States, a tablespoon is 15ml, while in the United Kingdom it is 10ml.
#### How much is a tablespoon?
A tablespoon is a common cooking measurement. It’s always the same amount no matter which recipe you use. It’s often used for wet ingredients that you pour and not solid ones that you measure. For example, you can use it to measure water, oil, and other liquids that you pour. You can also use it to measure loose ingredients that you scoop, such as flour or sugar. What’s a Teaspoon? A teaspoon is a very small amount of liquid, about half a tablespoon. If you’re used to cooking in the US, you probably already know what a teaspoon means. But if you don’t, here’s how it works. In the US, there are teaspoons in a tablespoon and tablespoons in a cup. So, 1/2 tablespoon is one teaspoon in the U.S.
#### How much is a teaspoon?
1 teaspoon is the same size as 1 tablespoon. So 1 tablespoon is 3 teaspoons. But a teaspoon can be of different sizes depending on where you are. In some countries, 1 teaspoon is less than in others, and the tradition of eating with spoons varies too. 1 tablespoon however is the same size all around the world, as it is equal to 3 teaspoons.
#### What does tbsp mean in cooking?
A tablespoon is a very common cooking measurement unit. One tablespoon is equal to 1/2 ounce, or 15 ml. One teaspoon equals 1/3 ounce or 5 ml. Some recipes also take a teaspoon as a measurement unit. But teaspoon is not a standard kitchen measurement unit. As for cooking, it is better to use a tablespoon. For example, if you want to make a cup of coffee, you should use 1/2 cup of water. If you use a tablespoon as the measurement unit, you have to use 1 tablespoon of water. To avoid confusion, restaurant cooks usually use fluid ounces as the unit of measurement in food preparation.
#### How much acetaminophen is in 30 mg of DayQuil?
That’s a tough question! You see, there’s no real easy way to answer it without knowing a few other things. For example, you didn’t tell me how much DayQuil you used. Did you use the entire single bottle, or did you use part of it? Did you use it for a fever, or for pain? Did you take it as recommended, or did you take more than the recommended dose? Did you take anything else along with the DayQuil? (How many tablespoons in 30ml?)
#### How much cough suppressant is in DayQuil?
DayQuil contains 8mg of Dextromethorphan Hydrobromide (DM) and 10mg of Diphenhydramine HCL (D). It is true that Dextromethorphan is a cough suppressant, but it also causes hallucinations and euphoria. Although diphenhydramine is also a cough suppressant, it is also an antihistamine that causes drowsiness. Both of the active ingredients in DayQuil — Dextromethorphan and Diphenhydramine — are common ingredients in other over-the-counter drug products. They are also found in many prescription drugs. (How many tablespoons in 30ml?)
#### What is the difference between DayQuil and NyQuil?
DayQuil and NyQuil are the leading brand names of two separate, yet very similar over-the-counter medications which are both used to treat colds and flu. Although they are similar, there are some differences between the two that pharmacists and doctors might not always pick up. In this answer, we will compare the two popular medications and tell you what they are used to treat, how they are similar and how they differ from one another. (How many tablespoons in 30ml?)
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https://pennylane.readthedocs.io/en/latest/code/api/pennylane.qaoa.layers.cost_layer.html
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# qml.qaoa.layers.cost_layer¶
cost_layer(gamma, hamiltonian)[source]
Applies the QAOA cost layer corresponding to a cost Hamiltonian.
For the cost Hamiltonian $$H_C$$, this is defined as the following unitary:
$U_C \ = \ e^{-i \gamma H_C}$
where $$\gamma$$ is a variational parameter.
Parameters
• gamma (int or float) – The variational parameter passed into the cost layer
• hamiltonian (Hamiltonian) – The cost Hamiltonian
Raises
ValueError – if the terms of the supplied cost Hamiltonian are not exclusively products of diagonal Pauli gates
We first define a cost Hamiltonian:
from pennylane import qaoa
import pennylane as qml
cost_h = qml.Hamiltonian([1, 1], [qml.PauliZ(0), qml.PauliZ(0) @ qml.PauliZ(1)])
We can then pass it into qaoa.cost_layer, within a quantum circuit:
dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(gamma):
for i in range(2):
cost_layer(gamma, cost_h)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(2)]
which gives us a circuit of the form:
>>> print(qml.draw(circuit)(0.5))
0: ──H─╭ApproxTimeEvolution(1.00,1.00,0.50)─┤ <Z>
1: ──H─╰ApproxTimeEvolution(1.00,1.00,0.50)─┤ <Z>
>>> print(qml.draw(circuit, expansion_strategy="device")(0.5))
0: ──H──MultiRZ(1.00)─╭MultiRZ(1.00)─┤ <Z>
1: ──H────────────────╰MultiRZ(1.00)─┤ <Z>
Using PennyLane
Development
API
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http://www.evi.com/q/convert_%C2%A3_25.00_to_us_dollars
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# convert £ 25.00 to us dollars
• £25 is \$39.12.
• tk10npubl tk10ncanl
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Address Sikeston, MO 63801 (573) 388-1268
# complex error function asymptotic Catron, Missouri
It is defined as:[1][2] erf ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0 x e − t Cook© All rights reserved. Similarly, (8) (OEIS A103979 and A103980). Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.
The system returned: (22) Invalid argument The remote host or network may be down. New York: Chelsea, 1999. Keywords: Fresnel integrals, auxiliary functions for Fresnel integrals Permalink: http://dlmf.nist.gov/7.12.ii See also: info for 7.12 The asymptotic expansions of C(z) and S(z) are given by (7.5.3), (7.5.4), and 7.12.2 f(z)∼1πz∑m=0∞(-1)m(12)2m(πz2/2)2m, Symbols: Required fields are marked *Comment Notify me of followup comments via e-mailName * Email * Website Search for: Subscribe to my newsletter Latest Posts GOTO Copenhagen Mathematical modeling for medical devices
Related functions The error function is essentially identical to the standard normal cumulative distribution function, denoted Φ, also named norm(x) by software languages, as they differ only by scaling and translation. For |z| < 1, we have erf ( erf − 1 ( z ) ) = z {\displaystyle \operatorname ζ 8 \left(\operatorname ζ 7 ^{-1}(z)\right)=z} . Generated Wed, 05 Oct 2016 11:36:22 GMT by s_hv977 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection comm., May 9, 2004).
Despite the name "imaginary error function", erfi ( x ) {\displaystyle \operatorname 4 (x)} is real when x is real. For , (11) (12) Using integration by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079). The error bounds are obtained by setting t=τ in (7.12.6) and (7.12.7), rotating the integration path in the τ-plane through an angle -4phz, and then replacing |τ+1| by its minimum value R. (March 1, 2007), "On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand", Monthly Notices of the Royal Astronomical Society, 375 (3): 1043–1048,
The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf ( x 2 ) = 1 2 New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels. Continued Fractions. Integrals and Series, Vol.2: Special Functions.
Assoc. Weisstein ^ Bergsma, Wicher. "On a new correlation coefficient, its orthogonal decomposition and associated tests of independence" (PDF). ^ Cuyt, Annie A. New York: Gordon and Breach, 1990. p.297.
Referenced on Wolfram|Alpha: Erf CITE THIS AS: Weisstein, Eric W. "Erf." From MathWorld--A Wolfram Web Resource. Your cache administrator is webmaster. Cook John Smith 5 January 2015 at 08:37 Although these series are esthetically beautiful, they are, unfortunately, inefficient in numerical programming. Amer., p.16, 1990.
After division by n!, all the En for odd n look similar (but not identical) to each other. comm., Dec.15, 2005). Definite integrals involving include Definite integrals involving include (34) (35) (36) (37) (38) The first two of these appear in Prudnikov et al. (1990, p.123, eqns. 2.8.19.8 and 2.8.19.11), with , For previous versions or for complex arguments, SciPy includes implementations of erf, erfc, erfi, and related functions for complex arguments in scipy.special.[21] A complex-argument erf is also in the arbitrary-precision arithmetic
Both functions are overloaded to accept arguments of type float, double, and long double. And as before, the series is valid for complex z but the error is simpler when z is real. A printed companion is available. 7.11 Relations to Other Functions7.13 Zeros John D. Whittaker, E.T.
For exponentially-improved expansions use (7.5.7), (7.5.10), and §7.12(i). §7.12(iii) Goodwin–Staton Integral Keywords: Goodwin–Staton integral Permalink: http://dlmf.nist.gov/7.12.iii See also: info for 7.12 See Olver (1997b, p. 115) for an expansion of G(z) with New York: Dover, pp.179-182, 1967. Please try the request again. Weisstein. "Bürmann's Theorem" from Wolfram MathWorld—A Wolfram Web Resource./ E.
For , (5) where is the incomplete gamma function. Soc. 3, 282-289, 1928. Also, sometimes numerical difficulties require separate software for evaluating erf and erfc as explained here.)If you're unfamiliar with the n!! Your cache administrator is webmaster.
Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Computerbasedmath.org» Join the initiative for modernizing math education. We have rewritten the sum more concisely using Pochhammer’s symbol. The bounds on the remainder term are described in section 7.1.24.
Springer-Verlag. Erf has the values (21) (22) It is an odd function (23) and satisfies (24) Erf may be expressed in terms of a confluent hypergeometric function of the first kind as is the double factorial: the product of all odd numbers up to (2n–1). notation, see this explanation of double factorial.Note that the series has a squiggle ~ instead of an equal sign.
Taylor series The error function is an entire function; it has no singularities (except that at infinity) and its Taylor expansion always converges. Numerical approximations Over the complete range of values, there is an approximation with a maximal error of 1.2 × 10 − 7 {\displaystyle 1.2\times 10^{-7}} , as follows:[15] erf ( Please try the request again. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.
For complex double arguments, the function names cerf and cerfc are "reserved for future use"; the missing implementation is provided by the open-source project libcerf, which is based on the Faddeeva This directly results from the fact that the integrand e − t 2 {\displaystyle e^{-t^ 8}} is an even function. It's often easier to work with the logarithm of the gamma function than to work with the gamma function directly, so one of the asymptotic series we'll look at is the
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Square number
Encyclopedia
In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a square number, sometimes also called a perfect square, is an integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3.
The usual notation for the formula for the square of a number n is not the product n × n, but the equivalent exponentiation
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...
n2, usually pronounced as "n squared". The name square number comes from the name of the shape. This is because a square with side length n has area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
n2.
Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number, is that its square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
is again an integer. For example, √9 = 3, so 9 is a square number.
A positive integer that has no perfect square divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s except 1 is called square-free
Square-free integer
In mathematics, a square-free, or quadratfrei, integer is one divisible by no perfect square, except 1. For example, 10 is square-free but 18 is not, as it is divisible by 9 = 32...
.
For a non-negative integer n, the nth square number is n2, with 02 = 0 being the zeroth
Zeroth
Zero-based numbering is numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday circumstances. Under zero-based numbering, the initial element is sometimes termed the zeroth element, rather than the first element; zeroth is a...
square. The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square (e.g., 4/9 = (2/3)2).
Starting with 1, there are square numbers up to and including m, where the expression represents the floor
Floor function
In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively...
of the number x.
## Examples
The squares below 602 are:
The difference between any perfect square and its predecessor is given by the identity . Equivalently, it is possible to count up square numbers by adding together the last square, the last square's root, and the current root, that is, .
## Properties
The number m is a square number if and only if one can arrange m points in a square:
m = 12 = 1 m = 22 = 4 m = 32 = 9 m = 42 = 16 m = 52 = 25
The expression for the nth square number is n2. This is also equal to the sum of the first n odd numbers as can be seen in the above pictures, where a square results from the previous one by adding an odd number of points (shown in magenta). The formula follows:
So for example, 52 = 25 = 1 + 3 + 5 + 7 + 9.
There are several recursive
Recursive
Recursive may refer to:*Recursion, the technique of functions calling themselves*Recursive function, a total computable function*Recursive language, a language which is decidable...
methods for computing square numbers. For example, the nth square number can be computed from the previous square by . Alternatively, the nth square number can be calculated from the previous two by doubling the (n − 1)-th square, subtracting the (n − 2)-th square number, and adding 2, because n2 = 2(n − 1)2 − (n − 2)2 + 2. For example, 2 × 52 − 42 + 2 = 2 × 25 − 16 + 2 = 50 − 16 + 2 = 36 = 62.
A square number is also the sum of two consecutive triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
s. The sum of two consecutive square numbers is a centered square number
Centered square number
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a...
. Every odd square is also a centered octagonal number
Centered octagonal number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers...
.
Another property of a square number is that it has an odd number of divisors, while other numbers have an even number of divisors. An integer root is the only divisor that pairs up with itself to yield the square number, while other divisors come in pairs.
Lagrange's four-square theorem
Lagrange's four-square theorem
Lagrange's four-square theorem, also known as Bachet's conjecture, states that any natural number can be represented as the sum of four integer squaresp = a_0^2 + a_1^2 + a_2^2 + a_3^2\ where the four numbers are integers...
states that any positive integer can be written as the sum of four or fewer perfect squares. Three squares are not sufficient for numbers of the form 4k(8m + 7). A positive integer can be represented as a sum of two squares precisely if its prime factorization contains no odd powers of primes of the form 4k + 3. This is generalized by Waring's problem
Waring's problem
In number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers...
.
A square number can end only with digits 0,1,4,6,9, or 25 in base 10, as follows:
1. If the last digit of a number is 0, its square ends in an even number of 0s (so at least 00) and the digits
Numerical digit
A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...
digits preceding the ending 0s must also form a square.
2. If the last digit of a number is 1 or 9, its square ends in 1 and the number formed by its preceding digits must be divisible by four.
3. If the last digit of a number is 2 or 8, its square ends in 4 and the preceding digit must be even.
4. If the last digit of a number is 3 or 7, its square ends in 9 and the number formed by its preceding digits must be divisible by four.
5. If the last digit of a number is 4 or 6, its square ends in 6 and the preceding digit must be odd.
6. If the last digit of a number is 5, its square ends in 25 and the preceding digits must be 0, 2, 06, or 56.
In base 16, a square number can end only with 0,1,4 or 9 and
- in case 0, only 0,1,4,9 can precede it,
- in case 4, only even numbers can precede it.
In general, if a prime
Prime
A prime is a natural number that has exactly two distinct natural number divisors: 1 and itself.Prime or PRIME may also refer to:In mathematics:*Prime , the ′ mark, typically used as a suffix...
p divides a square number m then the square of p must also divide m; if p fails to divide , then m is definitely not square. Repeating the divisions of the previous sentence, one concludes that every prime must divide a given perfect square an even number of times (including possibly 0 times). Thus, the number m is a square number if and only if, in its canonical representation, all exponents are even.
Squarity testing can be used as alternative way in factorization
Factorization
In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...
of large numbers. Instead of testing for divisibility, test for squarity: for given m and some number k, if k² − m is the square of an integer n then k − n divides m. (This is an application of the factorization of a difference of two squares
Difference of two squares
In mathematics, the difference of two squares, or the difference of perfect squares, is when a number is squared, or multiplied by itself, and is then subtracted from another squared number...
.) For example, 100² − 9991 is the square of 3, so consequently 100 − 3 divides 9991. This test is deterministic for odd divisors in the range from k − n to k + n where k covers some range of natural numbers k ≥ √m.
A square number cannot be a perfect number
Perfect number
In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself . Equivalently, a perfect number is a number that is half the sum of all of its positive divisors i.e...
.
The sum of the series of power numbers
can also be represented by the formula
The first terms of this series (the square pyramidal number
Square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...
s) are:
0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201... .
All fourth powers, sixth powers, eighth powers and so on are perfect squares.
## Special cases
• If the number is of the form m5 where m represents the preceding digits, its square is n25 where n = m × (m + 1) and represents digits before 25. For example the square of 65 can be calculated by n = 6 × (6 + 1) = 42 which makes the square equal to 4225.
• If the number is of the form m0 where m represents the preceding digits, its square is n00 where n = m2. For example the square of 70 is 4900.
• If the number has two digits and is of the form 5m where m represents the units digit, its square is AABB where AA = 25 + m and BB = m2. Example: To calculate the square of 57, 25 + 7 = 32 and 72 = 49, which means 572 = 3249.
## Odd and even square numbers
Squares of even numbers are even (and in fact divisible by 4), since (2n)2 = 4n2.
Squares of odd numbers are odd, since (2n + 1)2 = 4(n2 + n) + 1.
It follows that square roots of even square numbers are even, and square roots of odd square numbers are odd.
## Uses
Since the product of real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
negative numbers is positive, and the product of two real positive numbers is also positive, it follows that no square number is negative. It follows that no square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
can be taken of a negative number within the system of real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s. This leaves a gap in the real number system that mathematicians fill by postulating complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s, beginning with the imaginary unit
Imaginary unit
In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which in turn provides at least one root for every polynomial . The imaginary unit is denoted by , , or the Greek...
i, which by convention is one of the square roots of −1.
Squaring is used in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
in determining the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
of a set of values. The deviation of each value from the mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
of the set is defined as the difference . These deviations are squared, then a mean is taken of the new set of numbers (each of which is positive). This mean is the variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
, and its square root is the standard deviation. In finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, the volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
of a financial instrument is the standard deviation of its values.
• Square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
• Methods of computing square roots
Methods of computing square roots
There are several methods for calculating the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below.- Rough estimation :...
• Polygonal number
Polygonal number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...
• Euler's four-square identity
Euler's four-square identity
In mathematics, Euler's four-square identity says that the product of two numbers, each of which being a sum of four squares, is itself a sum of four squares. Specifically:=\,...
• Cube (algebra)
• Fermat's theorem on sums of two squares
• Pythagorean theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
• Parallelogram law
Parallelogram law
In mathematics, the simplest form of the parallelogram law belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals...
• Brahmagupta–Fibonacci identity
• The Book of Squares
The Book of Squares
The Book of Squares, in the original Latin is a book on algebra by Leonardo Fibonacci, published in 1225. Fibonacci's identity, establishing that the set of all sums of two squares is closed under multiplication, appears in it. The book anticipated the works of later mathematicians like Fermat and...
• Integer square root
Integer square root
In number theory, the integer square root of a positive integer n is the positive integer m which is the greatest integer less than or equal to the square root of n,...
• Square triangular number
Square triangular number
In mathematics, a square triangular number is a number which is both a triangular number and a perfect square....
• Automorphic number
Automorphic number
In mathematics an automorphic number is a number whose square "ends" in the same digits as number itself. For example, 52 = 25, 762 = 5776, and 8906252 = 793212890625, so 5, 76 and 890625 are all automorphic numbers.The sequence of automorphic numbers begins 1, 5, 6, 25, 76, 376, 625, 9376, .....
• Exponentiation
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...
• Power of two
Power of two
In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....
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# I need a rough guess on what 10gh bandwidth amounts to in terms of visits
#### ggames
##### New Member
how many visits is 10gb worth? suppose we're talking about a small site with html files, and some images. no videos or big files hosted here.
get back to me fast.
Millions.
#### ggames
##### New Member
seriously over a million? a decent image would take about say 14k to 17k.
#### aliasneo
##### New Member
Well 10GB would allow you to sesrve up 631612837.65 images at that (17kb) size. Divide it by 100 for example, say your page is 170KB, that's still 6316128.38.
(10GB == 10240MB == 10737418240KB)
#### masshuu
Community Support
Enemy of the State
(10GB == 10240MB == 10737418240KB)
wrong.
its
10BG == 10240MB == 10485760KB == 10737418240 Bytes
My site is about 140KB bytes total, with all the JavaScript and images
http://wordpress.org/ = 78KB
http://en.blog.wordpress.com/ = 192KB
http://www.fox.com/ = 1170KB
now these are all rough, and don't represent well, but i'm gonna use them to average anyways. Average webpage is 750KB
now heres a difference
10gb or 10GB
10gb = 1.25 GB = 1310720 KB / 750 = 1747 pagehits
10GB = 10485760 KB / 750 = 13976 pagehits
This assumes the client redownloads everything every time it loads a page, which usually isn't the case. So lets say each page is 25kb in size, and there are 40kb worth of new images on each page.
1310720 / 65 = 20165
10485760 / 65 = 161319
Now assuming there are no new images(like a blog)
1310720 / 25 = 52428
10485760 / 25 = 419430
So anywhere between 1,700 hits and 400,000 hits.
every kb counts
Last edited:
#### Zubair
Community Support
***Moved to Off Topic***
#### techairlines
##### x10 Flyer
Community Support
Last edited:
#### Gouri
##### Community Paragon
Community Support
wrong.
its
10BG == 10240MB == 10485760KB == 10737418240 Bytes
My site is about 140KB bytes total, with all the JavaScript and images
http://wordpress.org/ = 78KB
http://en.blog.wordpress.com/ = 192KB
http://www.fox.com/ = 1170KB
now these are all rough, and don't represent well, but i'm gonna use them to average anyways. Average webpage is 750KB
now heres a difference
10gb or 10GB
10gb = 1.25 GB = 1310720 KB / 750 = 1747 pagehits
10GB = 10485760 KB / 750 = 13976 pagehits
This assumes the client redownloads everything every time it loads a page, which usually isn't the case. So lets say each page is 25kb in size, and there are 40kb worth of new images on each page.
1310720 / 65 = 20165
10485760 / 65 = 161319
Now assuming there are no new images(like a blog)
1310720 / 25 = 52428
10485760 / 25 = 419430
So anywhere between 1,700 hits and 400,000 hits.
every kb counts
Nice Calculation masshuu.
that's a lot
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How To Grow Periwinkle Plant, Elca Racial Justice Ministries, Have And Had Difference, What Is L-tyrosine, Solidworks Combine Multiple Drawings Into One, Watercolor Flower Brushes Photoshop, Ak Rear Sight Block, Jonathan Creek Maggie Valley Fishing, " /> How To Grow Periwinkle Plant, Elca Racial Justice Ministries, Have And Had Difference, What Is L-tyrosine, Solidworks Combine Multiple Drawings Into One, Watercolor Flower Brushes Photoshop, Ak Rear Sight Block, Jonathan Creek Maggie Valley Fishing, " />
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December 29, 2020
Who is the longest reigning WWE Champion of all time? ANDY. How long will the footprints on the moon last? You're going somewhere and you know two things: You know the distance (miles) and you know the speed (mph) your car is driving. 30 miles in 10 minutes is 3 miles per minute, or 180 miles per h our. 45 minutes = 3/4 of an hour. How many miles an hour was it traveling? So it takes 1/60 of an hour to travel one mile by car on the highway, and since there are 60 minutes in an hour, it takes 1 minute. Then click the Convert Me button. You do not need to know how long it takes to drive one mile to answer the primary question. 2 Miles per hour = 0.000556 Miles per second: 20 Miles per hour = 0.0056 Miles per second: 5000 Miles per hour = 1.3889 Miles per second: 3 Miles per hour = 0.000833 Miles per second: 30 Miles per hour = 0.0083 Miles per second: 10000 Miles per hour = 2.7778 Miles per second: How many sides does a 2520 angled polygon have? How many right angels can be in an obtuse triangle? Averaging 60 MPH it would take 10 minutes. 90mph, 2 minutes 30 seconds. as we know s= vt where s means the distance v means the velocity t means the time so t = s/v hence t = 14/60 = 7/30 hour or 14 mins There are several costs related to a car, not only gas and insurance. All Rights Reserved. All Rights Reserved. Now, you want to know how long it will take to drive to your destination. Example. To switch the unit simply find the one you want on the page and click it. Assuming a really simple case of a car travelling at 60 Miles per hour, without deviation in speed. 60 miles/60 - 1 hour/60. How many minutes is 10 miles by car answers. How many right angels can be in an obtuse angle? ( 1 mile a minute ) So at 30 mph it would take 8 minutes. For what value or values of x will the triangles be similar? At 60mph, 5 minutes. Distance in miles . Is this statement true or falseTo prove triangles similar using the Side-Side-Side Similarity Theorem, you must first prove that corresponding angles are congruent? 2: Enter the value you want to convert (minutes per mile). 6 years ago. 1 mile is equal to 1.609344 kilometers: 1 mi = 1.609344 km. What is the solutions to y plus 3 squared minus 81? Then at 45 mph it would take 6 minutes. Lv 7. Calculate how much time you save by increasing the speed. Copyright © 2020 Multiply Media, LLC. How long would it take to travel 2.2 miles in minutes on car? How far will it travel in 46 m… How many minutes will it t… That would depend on the speed of the car. Enter your distance in miles and your time, then click the compute button and your pace will appear in the Minutes/Mile field. Hi.Running 2.25 is actually quite good.I know for myself at least it takes 30 minutes for me to run 3 miles. When did organ music become associated with baseball? Miles per minute to Kilometers per hour formula Kilometers per hour. The total distance between the two locations is 70 miles. The distance d in kilometers (km) is equal to the distance d in miles (mi) times 1.609344:. When the car is traveling at 60 km per hour, it is traveling at 60 / 60 = 1 km per minute. I run 10 minutes a mile. Convert 20 miles to kilometers: What is the perimeter of a heptagon with a side length of 14cm? Road speed limits are given in kilometers per hour which is abbreviated as kph or km/h. It is 144.75 miles and 2 hours and 36 minutes of estimated driving according to MapQuest. At 60mph, about 5 miles. Which proportion can be used to determine the value of x? How long would it take to travel 2.2 miles in minutes on car. How many right angels can be in an obtuse triangle? 2) Say a car is travelling on a highway at 60 miles per hour. You are faster which is great. Copyright © 2020 Multiply Media, LLC. Our Miles Per Hour Calculator can tell you how many miles you drive in a single stretch. Miles Per Hour Definition. This cannot be answered properly without knowing how fast you what- An artist is cutting sheet metal in the shape of triangles to create a sculpture. If a car is traveling at 5 miles per hour then it will travel 5 miles in one hour. This is a measurement of speed typically used in countries using the metric system for transport. Is this statement true or falseMOP is an example of the Reflexive Property of Similarity? how many minutes is 10 miles by driving a car? what- An artist is cutting sheet metal in the shape of triangles to create a sculpture. 25 miles/3 minutes x 60 minutes/hour = 1500 miles/3 hours = 500 miles per hour How many miles will a car travel in 3 minutes if its speed is constant at 60 mph? At 90mph, about 7.5 miles By car, less than 2 minutes on the highway. It travels 3 1/2 miles in 5 1/4 minutes. How many sides does a 2520 angled polygon have? If yu are curious, however, you need to divide 60 by 65 and that shows you that it takes .92 minutes. 60 miles - 1 hour. Top Answer. That would depend on the speed of the car. per hour, without deviation in speed. Click here to get an answer to your question ️ A car is traveling at a steady speed. You can also go to the universal conversion page. It depends how fast you're driving. Which proportion can be used to determine the value of x? Minutes/mile For your convenience: 5K = 3.106856M 7K = 4.3495984M 8K = 4.9709696M 10K = 6.213712M. 30mph, 10 minutes. At 60 mph, it would take exactly 4 minutes. If for 60 minutes we can trven 45 miles, then for 1 minute we can travel = (45/60)mpminute. If you're driving on the highway, it takes about 2.5 minutes. How many right angels can be in an obtuse angle? You can convert between miles per hour, meters per second and kilomoters per hour. 1 hour = 60 minutes. In 1 hour 30 miles = 60 minutes 3 miles = 6 minutes 1 mile = 2 minutes 11 miles = 22 minutes How many hours is it from Fort Hood to San Antonio Texas driving? The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. This calculator will calculate how many hours, minutes, and seconds it will take to drive to a destination. How to convert miles to kilometers. Probably less than 5 mins. So in 45 minutes it will travel 45 * 1 = 45 km. what- Two triangular windows are shown.Which statement is correct? Seconds . Click here to get an answer to your question ️ A car is traveling at a constant speed. Why don't libraries smell like bookstores? are moving. Is this statement true or falseTo prove triangles similar using the Side-Side-Side Similarity Theorem, you must first prove that corresponding angles are congruent? You need to divide 310 by 65 and the answer will be 4.77 hours. what- Two triangular windows are shown.Which statement is correct? With these nice numbers it’s even easy to calculate in your head. 15 16 17. Log On 2010-03-20 11:58:02. depends on the speed. For what value or values of x will the triangles be similar? Answer Save. H how long is the journey? Calculate how many days you have lived and find out if you are close to your 10 000th birthday perhaps! Assuming a really simple case of a car travelling at 60 Miles per hour, without deviation in speed. It travels 2 1/2 miles in 3 1/3 minutes. Andy C. 1 … Hours . d (km) = d (mi) × 1.609344 . The speed you can travel at. Riding a bike, 15 minutes. Algebra -> Customizable Word Problem Solvers -> Travel -> SOLUTION: A mans car traveled 18.5 miles in 30 minutes. Asked by Wiki User. But for a few of us, this trip of 2 miles takes less than a minute with no car and no engine at all… Just ask anyone that has stepped clear of a plane from over two miles high and experienced the true meaning of flight. How long will the footprints on the moon last? Hello. Is this statement true or falseMOP is an example of the Reflexive Property of Similarity? 60 mph = 1 mile per minute so in 3 minutes it will travel 3 miles. Relevance. That depends on what you have not told us. 5 miles … How long is 2.7 miles in minutes by car? A car travels 200 miles in 2 hours and 30 minutes. At 30mph, about 2.5 miles. Plus, unlike other you can put this solution on your website! If you ran 2.5 miles and you ran for 20 minutes: 2.5 mi ÷ 20 min = 0.125 miles per minute You can use this calculator to find your ideal pace to run an event like a marathon or half marathon. Wiki User Answered . When did organ music become associated with baseball? It would take 2 minutes 12 seconds Averaging 30 MPH it would take 20 minutes. This is a conversion chart for minutes per mile (Pace (Various Sports)). What is it's average speed? How many miles is there in a 5 minutes worth of driving? Why don't libraries smell like bookstores? What is the perimeter of a heptagon with a side length of 14cm? On long road trips, knowing how many miles you are averaging per hour can give you an idea of how long it will take to get to your destination.It is also a good indicator if you are taking too many breaks or if traffic has caused delays in your journey. To calculate in your head Champion of all time 30 mph it would take 6 minutes universal page! We can travel = ( 45/60 ) mpminute miles is there in a single stretch depends on you!, less than 2 minutes 12 seconds how long it takes to drive to your 10 000th birthday!... ( 1 mile is equal to 1.609344 kilometers: you can convert between miles per hour, per! 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# deriv.fd: Compute a Derivative of a Functional Data Object In fda: Functional Data Analysis
deriv.fd R Documentation
## Compute a Derivative of a Functional Data Object
### Description
A derivative of a functional data object, or the result of applying a linear differential operator to a functional data object, is then converted to a functional data object. This is intended for situations where a derivative is to be manipulated as a functional data object rather than simply evaluated.
### Usage
```## S3 method for class 'fd'
deriv(expr, Lfdobj=int2Lfd(1), ...)
```
### Arguments
`expr` a functional data object. It is assumed that the basis for representing the object can support the order of derivative to be computed. For B-spline bases, this means that the order of the spline must be at least one larger than the order of the derivative to be computed. `Lfdobj` either a positive integer or a linear differential operator object. `...` Other arguments to match generic for 'deriv'
### Details
Typically, a derivative has more high frequency variation or detail than the function itself. The basis defining the function is used, and therefore this must have enough basis functions to represent the variation in the derivative satisfactorily.
### Value
a functional data object for the derivative
`getbasismatrix`, `eval.basis` `deriv`
### Examples
```
# Estimate the acceleration functions for growth curves
# See the analyses of the growth data.
# Set up the ages of height measurements for Berkeley data
age <- c( seq(1, 2, 0.25), seq(3, 8, 1), seq(8.5, 18, 0.5))
# Range of observations
rng <- c(1,18)
# Set up a B-spline basis of order 6 with knots at ages
knots <- age
norder <- 6
nbasis <- length(knots) + norder - 2
hgtbasis <- create.bspline.basis(rng, nbasis, norder, knots)
# Set up a functional parameter object for estimating
# growth curves. The 4th derivative is penalyzed to
# ensure a smooth 2nd derivative or acceleration.
Lfdobj <- 4
lambda <- 10^(-0.5) # This value known in advance.
growfdPar <- fdPar(hgtbasis, Lfdobj, lambda)
# Smooth the data. The data for the boys and girls
# are in matrices hgtm and hgtf, respectively.
hgtmfd <- smooth.basis(age, growth\$hgtm, growfdPar)\$fd
hgtffd <- smooth.basis(age, growth\$hgtf, growfdPar)\$fd
# Compute the acceleration functions
accmfd <- deriv.fd(hgtmfd, 2)
accffd <- deriv.fd(hgtffd, 2)
# Plot the two sets of curves
par(mfrow=c(2,1))
plot(accmfd)
plot(accffd)
```
fda documentation built on April 27, 2022, 1:07 a.m.
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# Puzzle..find out the fallacy...(interesting)
Ranch Hand
Posts: 628
Consider the equattion X+X+X...(X TIMES)..
2+2=2^2
3+3+3=3^2
similarly x+x+x+x...(x times)=x^2
Now Differentiate on both side with respect to x
1+1+1...x times = 2x
=x=2x
=>1 =2
What is the mistake here??any idea?
[ March 13, 2006: Message edited by: Rambo Prasad ]
Ulf Dittmer
Rancher
Posts: 42968
73
The equality is not true (or rather, is not defined) for numbers that are not integers. And since differentiation is defined only for continuous functions -which the one on the LHS is not- it can't be applied here.
Stefan Wagner
Ranch Hand
Posts: 1923
Another explanation:
x^2 might be a notation for a function x^2.
But you use it as a value (x^2=x | x=1).
Then you mix both notations, but you may not differentiate a value.
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Lesson With
Daring Double Division
The lesson for Daring Double Division will tell you how to do the different things you will need to know to take the double division tests.
When you divide by a two digit number, you continue to follow the four steps: divide, multiply, subtract, and bring down. When you divide by two digit numbers, the “divide” step takes a little more thought, because we have not memorized the two digit multiplication facts.
Example: Divide 150 ÷ 12
Solution:
Begin by breaking the division into a smaller division problem. Starting from the first digit in 150, we try to find a number that 12 will divide into at least once. Our first smaller division is 15 ÷ 12. We see that there is one 12 in 15, so we write “1” above the 5 of 15. Then we multiply, subtract, and bring down.
Now we begin a new division. Our next smaller division is 30 ÷ 12. If you are not sure of the division answer, you may need to try more than once to find the number of 12s in 30. We find that there are two 12s in 30. We write “2” above the 0 of 150 and then multiply and subtract.
Since there is no digit to bring down, you are finished. The remainder is 6 (12 r 6).
To check the answer, multiply 12 ×12, and then add the remainder, which is 6;
12 × 12 = 144 144 + 6 = 150 (to check)
Now, that you know how to do double division, you can go on and take the Daring Double Division tests.
Have Fun!!!
Home
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# BPFactor2Factor3
#### class BPFactor2Factor3 extends BPFactor2 with DiscreteMarginal2Factor3[DiscreteVar, DiscreteVar, VectorVar]
Linear Supertypes
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. BPFactor2Factor3
2. DiscreteMarginal2Factor3
3. BPFactor2
4. BPFactor
5. FactorMarginal
6. DiscreteMarginal2
7. Marginal2
8. DiscreteMarginal
9. Marginal
10. AnyRef
11. Any
1. Hide All
2. Show all
Visibility
1. Public
2. All
### Value Members
1. #### final def !=(arg0: AnyRef): Boolean
Definition Classes
AnyRef
2. #### final def !=(arg0: Any): Boolean
Definition Classes
Any
3. #### final def ##(): Int
Definition Classes
AnyRef → Any
4. #### final def ==(arg0: AnyRef): Boolean
Definition Classes
AnyRef
5. #### final def ==(arg0: Any): Boolean
Definition Classes
Any
6. #### val _1: DiscreteVar
Definition Classes
DiscreteMarginal2Marginal2
7. #### val _2: DiscreteVar
Definition Classes
DiscreteMarginal2Marginal2
8. #### var _proportions: Proportions2
Attributes
protected
Definition Classes
DiscreteMarginal2
9. #### final def asInstanceOf[T0]: T0
Definition Classes
Any
10. #### def betheObjective: Double
Normalized probabilities over values of only the varying neighbors, in the form of a Proportions
Normalized probabilities over values of only the varying neighbors, in the form of a Proportions
Definition Classes
BPFactor
11. #### def calculateBeliefsTensor: la.Tensor2
Unnormalized log scores over values of varying neighbors
Unnormalized log scores over values of varying neighbors
Definition Classes
BPFactor2BPFactor
12. #### def calculateLogZ: Double
The logSum of all entries in the beliefs tensor
The logSum of all entries in the beliefs tensor
Definition Classes
BPFactor
13. #### def calculateMarginalTensor: Tensor
Normalized probabilities over values of varying neighbors
Normalized probabilities over values of varying neighbors
Definition Classes
BPFactor
14. #### def calculateOutgoing1: Tensor
Definition Classes
BPFactor2
15. #### def calculateOutgoing2: Tensor
Definition Classes
BPFactor2
16. #### def clone(): AnyRef
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
17. #### val edge1: BPEdge
Definition Classes
BPFactor2
18. #### lazy val edge1Max2: Array[Int]
Definition Classes
BPFactor2
19. #### val edge2: BPEdge
Definition Classes
BPFactor2
20. #### lazy val edge2Max1: Array[Int]
Definition Classes
BPFactor2
21. #### final def eq(arg0: AnyRef): Boolean
Definition Classes
AnyRef
22. #### def equals(arg0: Any): Boolean
Definition Classes
AnyRef → Any
24. #### def finalize(): Unit
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
25. #### final def getClass(): Class[_]
Definition Classes
AnyRef → Any
26. #### val hasLimitedDiscreteValues12: Boolean
Definition Classes
BPFactor2Factor3BPFactor2
27. #### def hashCode(): Int
Definition Classes
AnyRef → Any
28. #### def incrementCurrentValue(w: Double): Unit
Definition Classes
DiscreteMarginal2
29. #### final def isInstanceOf[T0]: Boolean
Definition Classes
Any
30. #### def limitedDiscreteValues12: SparseBinaryTensor2
Definition Classes
BPFactor2Factor3BPFactor2
31. #### final def ne(arg0: AnyRef): Boolean
Definition Classes
AnyRef
32. #### final def notify(): Unit
Definition Classes
AnyRef
33. #### final def notifyAll(): Unit
Definition Classes
AnyRef
34. #### def proportions: Proportions2
Definition Classes
BPFactor2DiscreteMarginal2DiscreteMarginal
35. #### val scores: la.Tensor2
Definition Classes
BPFactor2Factor3BPFactor2BPFactor
36. #### def setToMaximize(implicit d: variable.DiffList): Unit
Definition Classes
DiscreteMarginal2Marginal
37. #### val summary: BPSummary
Definition Classes
BPFactor2BPFactor
38. #### final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
40. #### def toString(): String
Definition Classes
AnyRef → Any
41. #### def updateOutgoing(e: BPEdge): Unit
Re-calculate the message from this factor to edge "e" and set e.
Re-calculate the message from this factor to edge "e" and set e.messageFromFactor to the result.
Definition Classes
BPFactor2BPFactor
42. #### def updateOutgoing(): Unit
Definition Classes
BPFactor2BPFactor
43. #### def updateOutgoing1(): Unit
Definition Classes
BPFactor2
44. #### def updateOutgoing2(): Unit
Definition Classes
BPFactor2
45. #### def variables: Seq[VectorVar]
Definition Classes
DiscreteMarginal2Marginal2DiscreteMarginalMarginal
46. #### final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
47. #### final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
48. #### final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
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http://openturns.github.io/openturns/master/user_manual/probabilistic_modelling.html
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# Probabilistic modelling¶
## Continuous parametric distributions¶
Distribution(*args) Base class for probability distributions. DistributionCollection(*args) Collection. PythonDistribution([dim]) Allow to override Distribution from Python. ChaospyDistribution(dist) Allow to override Distribution from a chaospy distribution. SciPyDistribution(dist) Allow to override Distribution from a scipy distribution.
Arcsine(*args) Arcsine distribution. Beta(*args) Beta distribution. Burr(*args) Burr distribution. Chi(*args) distribution. ChiSquare(*args) distribution. Dirichlet(*args) Dirichlet distribution. Epanechnikov(*args) Epanechnikov distribution. Exponential(*args) Exponential distribution. FisherSnedecor(*args) Fisher-Snedecor distribution. Frechet(*args) Frechet distribution. Gamma(*args) Gamma distribution. GeneralizedExtremeValue(*args) Generalized ExtremeValue distribution. GeneralizedPareto(*args) Generalized Pareto distribution. Gumbel(*args) Gumbel distribution. Histogram(*args) Histogram distribution. InverseChiSquare(*args) InverseChiSquare distribution. InverseGamma(*args) InverseGamma distribution. InverseNormal(*args) Inverse normal distribution. InverseWishart(*args) Inverse-Wishart distribution. KPermutationsDistribution(*args) KPermutations distribution. Laplace(*args) Laplace distribution. Logistic(*args) Logistic distribution. LogNormal(*args) Lognormal distribution. LogUniform(*args) LogUniform distribution. MeixnerDistribution(*args) Meixner distribution. NonCentralChiSquare(*args) NonCentralChiSquare distribution. NonCentralStudent(*args) NonCentralStudent distribution. Normal(*args) Normal distribution. NormalGamma(*args) NormalGamma distribution. Pareto(*args) Pareto distribution. Rayleigh(*args) Rayleigh distribution. Rice(*args) Rice distribution. SmoothedUniform(*args) SmoothedUniform distribution. SquaredNormal(*args) Squared Normal distribution. Student(*args) Student distribution. Trapezoidal(*args) Trapezoidal distribution. Triangular(*args) Triangular distribution. TruncatedNormal(*args) TruncatedNormal distribution. Uniform(*args) Uniform distribution. VonMises(*args) von Mises distribution. WeibullMin(*args) WeibullMin distribution. WeibullMax(*args) WeibullMax distribution. Wishart(*args) Wishart distribution.
## Discrete parametric distributions¶
Bernoulli(*args) Bernoulli distribution. Binomial(*args) Binomial distribution. Dirac(*args) Dirac distribution. Geometric(*args) Geometric distribution. Hypergeometric(*args) Hypergeometric distribution. Multinomial(*args) Multinomial distribution. NegativeBinomial(*args) NegativeBinomial distribution. Poisson(*args) Poisson distribution. Skellam(*args) Skellam distribution. UserDefined(*args) UserDefined distribution. ZipfMandelbrot(*args) ZipfMandelbrot distribution.
## Parametrized distributions¶
ParametrizedDistribution(*args) Parametrized distribution. DistributionParameters(*args) Define a distribution with particular parameters. ArcsineMuSigma(*args) Arcsine distribution parameters. BetaMuSigma(*args) Beta distribution parameters. GammaMuSigma(*args) Gamma distribution parameters. GumbelLambdaGamma(*args) Gumbel rate/location parametrization. GumbelMuSigma(*args) Gumbel distribution parameters. LogNormalMuSigma(*args) LogNormal distribution parameters. LogNormalMuSigmaOverMu(*args) LogNormal distribution parameters. WeibullMaxMuSigma(*args) WeibullMax distribution parameters. WeibullMinMuSigma(*args) WeibullMin distribution parameters.
## Pseudo-random numbers generator¶
RandomGenerator(*args, **kwargs) Uniform random generator. RandomGeneratorState(*args) Random generator state.
## Combining and transforming distributions¶
BayesDistribution(*args) Bayes distribution. BlockIndependentDistribution(*args) Merge of a collection of independent distributions. ComposedDistribution(*args) Composed distribution. CompositeDistribution(*args) Composite distribution. ConditionalDistribution(*args) Conditional distribution. Composed distribution. DiscreteCompoundDistribution(*args) Discrete compound distribution. MaximumDistribution(*args) Maximum distribution. MaximumEntropyOrderStatistics distribution.
MixedHistogramUserDefined(*args) Mixed Histogram/UserDefined distribution. Compatibility tests of marginals with respect to the order statistics constraint. PosteriorDistribution(*args) Distribution conditioned by observations.
ProductDistribution(*args) Product distribution. RandomMixture(*args) RandomMixture distribution.
TruncatedDistribution(*args) Truncated distribution. KernelMixture(*args) Build a particular linear combination of probability density functions. Mixture(*args) Build a linear combination of probability density functions.
## Copulas¶
Refer to Copulas.
ArchimedeanCopula(*args) Base class for bivariate Archimedean copulas.
AliMikhailHaqCopula(*args) AliMikhailHaq copula. ClaytonCopula(*args) Clayton copula. FarlieGumbelMorgenstern copula. FrankCopula(*args) Frank copula. GumbelCopula(*args) Gumbel copula. IndependentCopula(*args) Independent copula. PlackettCopula(*args) Plackett copula. EmpiricalBernsteinCopula(*args) EmpiricalBernstein copula. ExtremeValueCopula(*args) ExtremeValue copula. JoeCopula(*args) Joe copula. MarshallOlkinCopula(*args) MarshallOlkin copula. MaximumEntropyOrderStatisticsCopula copula. MinCopula(*args) MinCopula. NormalCopula(*args) Normal copula.
## Combining and transforming copulas¶
ComposedCopula(*args) Merge of a collection of independent copulas. SklarCopula(*args) Sklar copula. OrdinalSumCopula(*args) Copula built as an ordinal sum of copulas.
## Random vectors¶
RandomVector(*args) Random vectors. PythonRandomVector([dim]) Allow to overload RandomVector from Python. CompositeRandomVector(*args) Random Vector obtained by applying a function. ConditionalRandomVector(*args) Conditional random vector. ConstantRandomVector(*args) Constant Random Vector. UsualRandomVector(*args) Random Vector from a distribution.
## Low-level distribution functions¶
DistFunc_dBinomial(n, p, k) Probability function of a binomial distribution. DistFunc_dHypergeometric(n, k, m, x) The probability function of an hypergeometric distribution. Probability function of a NonCentralChiSquare distribution. DistFunc_dNonCentralStudent(nu, delta, x) Probability function of a NonCentralStudent distribution. DistFunc_dPoisson(_lambda, k) Probability function of a Poisson distribution. DistFunc_eZ1(n) Expectation of the min of n independent standard normal random variables. DistFunc_kFactor(n, p, alpha) Exact margin factor for bilateral covering interval of a Normal population. DistFunc_kFactorPooled(n, m, p, alpha) Exact margin factor for bilateral covering interval of pooled Normal populations. DistFunc_logdBinomial(n, p, k) Logarithm of the probability function of a binomial distribution. DistFunc_logdHypergeometric(n, k, m, x) Logarithm of the probability function of an hypergeometric distribution. DistFunc_logdPoisson(_lambda, k) Logarithm of the probability function of a Poisson distribution. DistFunc_pHypergeometric(n, k, m, x[, tail]) The cumulative probability function of an hypergeometric distribution. DistFunc_pPearsonCorrelation(size, rho[, tail]) Asymptotic probability function for the Pearson correlation. DistFunc_pNormal(*args) CDF of an unit-variance centered Normal distribution. DistFunc_qNormal(*args) Quantile of an unit-variance centered Normal distribution. DistFunc_rBinomial(*args) Realization of a binomial distribution. DistFunc_rDiscrete(*args) Realization of a bounded integral discrete distribution. DistFunc_rHypergeometric(*args) Realization of an hypergeometric distribution. DistFunc_rNormal(*args) Realization of an unit-variance centered Normal distribution. DistFunc_rPoisson(*args) Realization of a Poisson distribution.
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http://www.chegg.com/homework-help/questions-and-answers/x-component-b-y-component-c-z-component-29-45-46-56-35-72-52-50-79-d-calculate-angle-posit-q642234
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What are (a) the x component,(b) the y component, and(c) the z component of = - + if = 2.9 + 4.5 - 4.6, = -5.6 + 3.5 + 7.2, and = 5.2 + 5.0 + 7.9. (d) Calculate the angle between and the positive z axis. (e) Whatis the component of along the direction of ? (f) What is the magnitude of thecomponent of perpendicular to the direction of but in the plane of and ?
Will rate life saver for best answer, thanks.
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https://www.gamedev.net/forums/topic/271601-scaled-bitmap-buffer/
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# Scaled Bitmap Buffer
This topic is 5415 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Ok how to explain this... What I am trying to do is apply a heightmap that is scaled 1:256...(1 pixel = 256 units) and applying it to a mesh for terrain rendering. I already use perlin noise to give me a bit of variance. but sadly it isnt enough. The scaled heightmap will obviously produce mesas 256x256 units in my terrain even when I apply the perlin noise to the returned color variables of my heightmap. The abrupt edge between 2 colors needs to be smoothed somehow this much I know. Now how would I go about smoothing the pixel color variations? If I have pixel one as 255 and pixel 2 as 0 what about pixel 1.5? Obviosly 128 right...Now the problem I am having is coming up with a fast way of producing this. I could use a ton of assignments and if statements but that slows the render down to a crawl... So basically what I want to do is a sort of nearest neighbor color calculation with a resolution of 256 units between each pixel. So far I have this basic code that half-asses the process.
double Terrain::landHeight(double x, double y, SCALE_P s) {
int red,green,blue;
int where;
double image_color;
//double perlin = (PerlinNoise2D(x*s.s1,y*s.s2,s.s3,s.s4,1)+1)/2;
int X = abs((int)x/256);
int Y = abs((int)y/256);
double iX = (absd(x)/256) - X;
double iY = (absd(y)/256) - Y;
//print(iX);
if(X > 1024) X = 1024;
if(Y > 512) Y = 512;
if(X < 0) X = 0;
if(Y < 0) Y = 0;
where = (((int)X+0)*3) * (((int)Y+0)+1024); // center point
red = planet_texRGB[planet[nearest_obj].landTexID].imageData[where];
green = planet_texRGB[planet[nearest_obj].landTexID].imageData[where+1];
blue = planet_texRGB[planet[nearest_obj].landTexID].imageData[where+2];
image_color = ((double)(red + green + blue) * 0.3333) * iX;
//if(where+2 > 1572864) where = 1572864-where;
return image_color/256;
}
To turn this: ___ | | -- -- into this: /--/ \-- Any suggestions? Thanks! [Edited by - keyofrassilon on September 20, 2004 8:27:54 PM]
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https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Buckingham_%CF%80_theorem.html
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# Buckingham π theorem
related topics {math, number, function} {math, energy, light} {ship, engine, design} {album, band, music} {mi², represent, 1st} {film, series, show}
The Vaschy-Buckingham π theorem is a key theorem in dimensional analysis. The theorem loosely states that if we have a physically meaningful equation involving a certain number, n, of physical variables, and these variables are expressible in terms of k independent fundamental physical quantities, then the original expression is equivalent to an equation involving a set of p = nk dimensionless parameters constructed from the original variables: it is a scheme for nondimensionalization. This provides a method for computing sets of dimensionless parameters from the given variables, even if the form of the equation is still unknown. However, the choice of dimensionless parameters is not unique: Vaschy-Buckingham's theorem only provides a way of generating sets of dimensionless parameters, and will not choose the most 'physically meaningful'.
## Contents
### Statement
More formally, the number of dimensionless terms that can be formed, p, is equal to the nullity of the dimensional matrix, and k is the rank. For the purposes of the experimenter, different systems which share the same description in terms of these dimensionless numbers are equivalent.
In mathematical terms, if we have a physically meaningful equation such as
where the qi are the n physical variables, and they are expressed in terms of k independent physical units, then the above equation can be restated as
where the πi are dimensionless parameters constructed from the qi by p = nk equations of the form
where the exponents mi are rational numbers (they can always be taken to be integers: just raise it to a power to clear denominators).
The use of the πi as the dimensionless parameters was introduced by Edgar Buckingham in his original 1914 paper on the subject from which the theorem draws its name.
Full article ▸
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http://pirate.shu.edu/~wachsmut/complex/numbers/proofs/complex_field.html
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### Theorem 1.1.8: Complex Numbers are a Field
The set of complex numbers C with addition and multiplication as defined above is a field with additive and multiplicative identities (0,0) and (1,0). It extends the real numbers R via the isomorphism (x,0) = x. We define the complex number i = (0,1). With that definition we can write every complex number interchangebly as z = (x,y) = x + i*y = x + i y Back
We need to prove the field axioms for our definition of addition and multiplication:
• z + w = (x,y) + (u,v) = (x+u, y+v)
• z * w = (x,y) * (u,v) = (x*u - y*v, x*v + y*u)
1. Both + and * are associative, which is obvious for addition. For multiplication we nned to show that a*(b*c)=(a*b)*c. Let a=(x1,y1), b=(x2,y2), and c=(x3,y3). Then:
2. Both + and * are commutative, i.e. a+b=b+a and a*b=b*a
Exercise
3. The distributive law holds, i.e. a*(b+c)=(a*b)+(a*c)
Exercise
4. The additive identity is (0,0), and the multiplicative identity is (1,0), which you can easily confirm.
5. The additive inverse to (x,y) is (-x,-y). The multiplicative inverse to (x,y) is (x/(x2+y2), -y/(x2+y2).
That shows that C is a field.
We now identify the real number x with the complex number (x,0). Thus, the (real) numbers 0 and 1 are the same as the complex numbers (0,0) and (1,0), respectively. Technically, the map
f: R {(x,y) C: y = 0}
defined via f(x)=(x,0) is an isomorphism (a bijection such that it and its inverse are homomorphisms) that identifies the real numbers with a subset of the complex numbers.
The complex number (0,1) has the property that (0,1)*(0,1)=(-1,0), which is the same property as our symbol i.
Interactive Complex Analysis, ver. 1.0.0
(c) 2006-2007, Bert G. Wachsmuth
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https://www.topperlearning.com/answer/2-x-5/4uwta6uu
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Request a call back
2-x=5
Asked by mangalrane71 | 01 Feb, 2019, 05:24: PM
2-x=5
Subtracting 5 from both sides, we get
2-x-5 = 5-5
-3-x=0
Now, Add 3 on both sides, we get
-3+3-x=0+3
-x=3
Multiply both sides by (-1),
we get,
x=-3
Answered by | 01 Feb, 2019, 05:49: PM
## Concept Videos
ICSE 6 - Maths
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# Discussion Board using Derivatives
posted in: Research Paper | 0
Discuss a real-world application of the use of calculus-based derivatives for maximizing profits.
In your initial post, clearly describe the profit function (mathematical expression, e.g., P(x) = -7x^3 + 11x^2 + x – 23) and how the first derivative of this function will help you identify the maximum profit.
Clearly define the function, its variable, domain, and range. Note that there are two ways of maximizing profit:
(1) maximizing the profit function, (2) either maximizing revenue or minimizing cost. Thus, if you do not have a profit function, you could work with the revenue or cost functions instead.
Last Updated on December 19, 2019 by EssayPro
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Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
## #26 2014-06-13 11:22:41
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
I think the way it should be is if we have a number a, we can't say it is a coefficient. 2 is not a coefficient. However, I think we can say that 2 is a coefficient of 2x^0.
Offline
## #27 2014-06-13 11:25:16
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
2 can be a coefficient based on the context.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #28 2014-06-13 11:25:53
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
2
Is that a coefficient? I think most people would say 2 on it's own is not one (that's just my thinking).
Offline
## #29 2014-06-13 11:27:11
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
Hm, then how would you say that 2 is a coefficient when you write 2x+1?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #30 2014-06-13 11:27:40
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
I would say that 2 is a coefficient of x in that expression.
Offline
## #31 2014-06-13 11:29:17
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
Then I could say that 1 is the coefficient f x^0 in that polynomial.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #32 2014-06-13 11:30:52
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
Me too. But I wouldn't say 1 on it's on is a coefficient.
According to Wikipedia
Wikipedia wrote:
For instance in 7x^2-3xy+1.5+y the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant.
Offline
## #33 2014-06-13 11:34:27
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
Well, then you couodn't say 2 is a coefficient when talking about the same expression.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #34 2014-06-13 11:36:37
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
This is what I mean
in 2x + 1, 2 is a coefficient of x
However, 1 is not a coefficient - it is a constant.
In 2x + 1x^2 though, both 2 and 1 are coefficients.
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## #35 2014-06-13 11:44:23
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
MathsIsFun wrote:
What does everyone think about that?
To be honest, it isn't too big of an issue. Such terminology discrepancies occur all the time and it is just a matter of convention (e.g. in the UK they use R^d instead of R^n like here in the US in real analysis).
Offline
## #36 2014-06-13 11:58:18
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
That's true. There's no exact notation for the Stirling numbers, for example.
The R^whatever does not seem like too much a problem either, considering it's the R that matters.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #37 2014-06-13 12:00:05
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
And I don't think a student will get a mark off on a test for saying 2 is a coefficient or isn't.
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## #38 2014-06-13 12:08:08
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
True. It's very dependant on the content. And it's a very narrow concept, seeing hiw I haven't noticed it being used anywhere besides in polynomials and binomial expansions.
Last edited by anonimnystefy (2014-06-13 12:08:38)
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #39 2014-06-13 13:10:56
Chris2
Member
From: Gallifrey
Registered: 2014-04-23
Posts: 2,290
Website
### Re: Coefficient vs Constant
Hmm.. From what I know is : If we have 3xy and the question ask what is the coefficient of y then my answer is 3x.
And another example, if we have 34abc and the question ask find the coefficient of 34 then it's abc.
God oppose the proud, but give grace to the humble.
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## #40 2014-06-13 13:12:18
ShivamS
Member
Registered: 2011-02-07
Posts: 3,640
### Re: Coefficient vs Constant
Here, we have two different names. The numerical coefficient of 34 in 34abc is abc and the literal coefficient of 34 in 34abc is abc.
Offline
## #41 2014-06-13 13:52:34
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,918
### Re: Coefficient vs Constant
Hi;
MIF wrote:
What does everyone think about that?
Write the definition you like and whomever disagrees, kill them.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Online
## #42 2014-06-13 13:54:39
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
Yay, constructive crticism!
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #43 2014-06-13 13:58:21
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,918
### Re: Coefficient vs Constant
No dissent allowed, like in the Middle Ages. What a great time to be alive that must have been.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Online
## #44 2014-06-13 14:47:56
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
It depends on perspective.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
## #45 2014-06-13 23:28:11
MathsIsFun
Registered: 2005-01-21
Posts: 7,559
### Re: Coefficient vs Constant
I have updated the definition to this:
I wrote:
Coefficient
A number used to multiply a variable.
Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.
Sometimes a letter stands in for the number.
Example: In ax² + bx + c, "x" is a variable, and "a" and "b" are coefficients.
Let me know if you feel it can be improved.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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## #46 2014-06-13 23:54:28
Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,939
Website
### Re: Coefficient vs Constant
A number used to multiply a variable
Use instead: Something used to multiply the concerned variable
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym
Offline
## #47 2014-06-14 00:00:43
anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889
### Re: Coefficient vs Constant
Yes, that way, the definition encompasses stuff like (k^2+1)x+2.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Online
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## deGPTed
Posted in Books, Kids, Statistics, University life with tags , , , , , on December 20, 2022 by xi'an
As shown above, automated chatbots are becoming a nuisance on fori such as Stack Exchange. To illustrate the nuisance capacity, here is a question / answer I produced there:
It sounds completely correct except for the core issue of not explaining why the Uniform density is not expressible as an exponential… And the answer is exactly the same when substituting Gamma for Uniform!
## Bayesian sampling without tears
Posted in Books, Kids, R, Statistics with tags , , , , , , , , , , , , on May 24, 2022 by xi'an
Following a question on Stack Overflow trying to replicate a figure from the paper written by Alan Gelfand and Adrian Smith (1990) for The American Statistician, Bayesian sampling without tears, which precedes their historical MCMC papers, I looked at the R code produced by the OP and could not spot an issue as to why their simulation did not fit the posterior produced in the paper. Which proposes acceptance-rejection and sampling-importance-resampling as two solutions to approximately simulate from the posterior. The later being illustrated by simulations from the prior being weighted by the likelihood… The illustration is made of 3 observations from the sum of two Binomials with different success probabilities, θ¹ and θ². With a Uniform prior on both.
```for (i in 1:N)
for (k in 1:3){
llh<-0
for (j in max(0,n2[k]-y[k]):min(y[k],n1[k]))
llh<-llh+choose(n1[k],j)*choose(n2[k],y[k]-j)*
theta[i,1]^j*(1-theta[i,1])^(n1[k]-j)*theta[i,2]^(y[k]-j)*
(1-theta[i,2])^(n2[k]-y[k]+j)
l[i]=l[i]*llh}
```
To double-check, I also wrote a Gibbs version:
```theta=matrix(runif(2),nrow=T,ncol=2)
x1=rep(NA,3)
for(t in 1:(T-1)){
for(j in 1:3){
a<-max(0,n2[j]-y[j]):min(y[j],n1[j])
x1[j]=sample(a,1,
prob=choose(n1[j],a)*choose(n2[j],y[j]-a)*
theta[t,1]^a*(1-theta[t,1])^(n1[j]-a)*
theta[t,2]^(y[j]-a)*(1-theta[t,2])^(n2[j]-y[j]+a)
)}
theta[t+1,1]=rbeta(1,sum(x1)+1,sum(n1)-sum(x1)+1)
theta[t+1,2]=rbeta(1,sum(y)-sum(x1)+1,sum(n2)-sum(y)+sum(x1)+1)}
```
which did not show any difference with the above. Nor with the likelihood surface.
## stack exchange will not restrict access from Russia
Posted in Statistics with tags , , , , , on March 18, 2022 by xi'an
## triple ruin
Posted in Books, Kids, pictures, R, Statistics, Wines with tags , , , , , , , , , , on December 28, 2021 by xi'an
An almost straightforward riddle from The Riddler involving a triple gambler’s ruin: Dawn competes against three players Alessandra, Berenike, and Chinue, with probabilities of winning one round ¾, ½, and ¼, respectively, until the cumulated score reaches ±15, ±30, and ±45, for the first, second, and third games. What is Dawn’s optimal sequence of adversaries?
First, a brute force R simulation shows that the optimal ordering is to play the three adversaries first weakest, third strongest and middle fair:
```ord=function(p){
z=2*(runif(1)<p[1])-1
while(abs(z)<15)z=z+2*(runif(1)<p[1])-1
y=2*(runif(1)<p[2])-1
while(abs(z+y)<30)y=y+2*(runif(1)<p[2])-1
x=2*(runif(1)<p[3])-1
while(abs(z+y+x)<45)x=x+2*(runif(1)<p[3])-1
return(x+y+z>0)}
mcord=function(p,T=1e2){
for(t in 1:T)F=F+ord(p)
return(F/T)}
comp=function(T=1e2){
return(c(mcord(c(.5,.55,.45),t),
#mcord(c(.5,.45,.55),t),#1-above
mcord(c(.55,.5,.45),t),
#mcord(c(.45,.5,.55),t),#1-above
mcord(c(.55,.45,.5),t)
#mcord(c(.45,.55,.5),t)))#1-above
))}
```
where I used probabilities closer to ½ to avoid estimated probabilities equal to one.
```> comp(1e3)
[1] 0.051 0.038 0.183
```
(and I eliminated the three other probabilities by sheer symmetry). Second, checking in Feller’s bible (Vol. 1, XIV.3) for the gambler’s ruin probability, a simple comparison of the six orderings confirms this simulation.
## inf R ! [book review]
Posted in Books, R, Travel with tags , , , , , , , , , , , on June 10, 2021 by xi'an
Thanks to my answering a (basic) question on X validated involving an R code, R mistakes and some misunderstanding about Bayesian hierarchical modelling, I got pointed out to Patrick Burns’ The R inferno. This is not a recent book as the second edition is of 2012, with a 2011 version still available on-line. Which is the version I read. As hinted by the cover, the book plays on Dante’s Inferno and each chapter is associated with a circle of Hell… Including drawings by Botticelli. The style is thus most enjoyable and sometimes hilarious. Like hell!
The first circle (reserved for virtuous pagans) is about treating integral reals as if they were integers, the second circle (attributed to gluttons, although Dante’s is for the lustful) is about allocating more space along the way, as in the question I answered and in most of my students’ codes! The third circle (allocated here to blasphemous sinners, destined for Dante’s seven circle, when Dante’s third circle is to the gluttons) points out the consequences of not vectorising, with for instance the impressive capacities of the ifelse() function [exploited to the max in R codecolfing!]. And the fourth circle (made for the lustfuls rather than Dante’s avaricious and prodigals) is a short warning about the opposite over-vectorising. Circle five (destined for the treasoners, and not Dante’s wrathfuls) pushes for and advises about writing R functions. Circle six recovers Dante’s classification, welcoming (!) heretics, and prohibiting global assignments, in another short chapter. Circle seven (alloted to the simoniacs—who should be sharing the eight circle with many other sinners—rather than the violents as in Dante’s seventh) discusses object attributes, with the distinction between S3 and S4 methods somewhat lost on me. Circle eight (targeting the fraudulents, as in Dante’s original) is massive as it covers “a large number of ghosts, chimeras and devils”, a collection of difficulties and dangers and freak occurences, with the initial warning that “It is a sin to assume that code does what is intended”. A lot of these came as surprises to me and I was rarely able to spot the difficulty without the guidance of the book. Plenty to learn from these examples and counter-examples. Reaching Circle nine (where live (!) the thieves, rather than Dante’s traitors). A “special place for those who feel compelled to drag the rest of us into hell.” Discussing the proper ways to get help on fori. Like Stack Exchange. Concluding with the tongue-in-cheek comment that “there seems to be positive correlation between a person’s level of annoyance at [being asked several times the same question] and ability to answer questions.” This being a hidden test, right?!, as the correlation should be negative.
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# Library Coq.QArith.Qfield
Require Export Field.
Require Export QArith_base.
Require Import NArithRing.
# field and ring tactics for rational numbers
Definition Qsrt : ring_theory 0 1 Qplus Qmult Qminus Qopp Qeq.
Definition Qsft : field_theory 0 1 Qplus Qmult Qminus Qopp Qdiv Qinv Qeq.
Lemma Qpower_theory : power_theory 1 Qmult Qeq Z.of_N Qpower.
Ltac isQcst t :=
match t with
| inject_Z ?z => isZcst z
| Qmake ?n ?d =>
match isZcst n with
true => isPcst d
| _ => false
end
| _ => false
end.
Ltac Qcst t :=
match isQcst t with
true => t
| _ => NotConstant
end.
Ltac Qpow_tac t :=
match t with
| Z0 => N0
| Zpos ?n => Ncst (Npos n)
| Z.of_N ?n => Ncst n
| NtoZ ?n => Ncst n
| _ => NotConstant
end.
(decidable Qeq_bool_eq,
completeness Qeq_eq_bool,
constants [Qcst],
power_tac Qpower_theory [Qpow_tac]).
Exemple of use:
Section Examples.
Let ex1 : forall x y z : Q, (x+y)*z == (x*z)+(y*z).
Qed.
Let ex2 : forall x y : Q, x+y == y+x.
Qed.
Let ex3 : forall x y z : Q, (x+y)+z == x+(y+z).
Qed.
Let ex4 : (inject_Z 1)+(inject_Z 1)==(inject_Z 2).
Qed.
Let ex5 : 1+1 == 2#1.
Qed.
Let ex6 : (1#1)+(1#1) == 2#1.
Qed.
Let ex7 : forall x : Q, x-x== 0.
Qed.
Let ex8 : forall x : Q, x^1 == x.
Qed.
Let ex9 : forall x : Q, x^0 == 1.
Qed.
Let ex10 : forall x y : Q, ~(y==0) -> (x/y)*y == x.
Qed.
End Examples.
Lemma Qopp_plus : forall a b, -(a+b) == -a + -b.
Lemma Qopp_opp : forall q, - -q==q.
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https://sheffield.pressbooks.pub/introducingmathematicalbiology/chapter/introducing-models-of-cancer-dynamics/
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# Introducing cancer models
More than one in three people will develop some form of cancer during their lifetime. Given this, it is no surprise that cancer research is a highly active field, and, relevant to this course, that there are a great many researchers interested in modelling the dynamics of cancer growth and its treatments. It can also mean it is a difficult subject for some to think about – I have personally lost much-loved family to cancer, and it is only recently I have felt able to start teaching content in this area – but the more research we can do, the sooner better treatments and even cures will come.
In this chapter we will examine a number of different model forms for thinking about how cancer tumours – which we essentially treat as localised populations of cells – grow or proliferate over time (see chapter references). For the most part we will not do any in-depth analysis of the models here, but we will look at one specific model in more detail in the next chapter.
# Single variable models
From a mathematical viewpoint we can essentially think about the growth of a population of cancer cells in much the same way as we would the growth of any population. We have seen some of these model structures already in this textbook, but will cover them again here for completeness.
## Linear growth (with or without mortality)
The most basic model for growth of a population of cancer cells, $c$ – even more basic model than we have examined before – would be for linear growth, given by,
$$$\frac{dc}{dt} = r.$$$
While you may spot a few flaws in such a model (for example we have positive proliferation even with zero cancer cells), it has been used to describe the dynamics of certain cancers. There is also no mortality of cells here, or shrinkage of the tumour. Such a term is readily added to give,
$$$\frac{dc}{dt} = r-kc.$$$
We can solve this model either by separation of variables or an integrating factor to give,
$$$c(t) =\frac{r}{k}+\left(c(0)-\frac{r}{k}\right)e^{-kt}.$$$
This suggests the tumour will tend towards an intermediate size of $c=r/k$ (which we can also see by just looking for the equilibrium from the ODE).
## Exponential growth (with or without mortality)
The more classic example of population growth we saw at the very start of this resource was that of exponential growth, where the population growth depends on the current density, that is,
$$$\frac{dc}{dt} = rc.$$$
There might then be a question of whether $r$ is purely the proliferation rate or, as we assumed earlier, the difference between proliferation and shrinkage. Let’s say that we do include a separate shrinkage term, the equation can still be solved using separation of variables,
\begin{align*} \frac{dc}{dt} &= rc-kc,\\ \implies c(t)&=c(0)e^{(r-k)t}, \end{align*}
giving either exponential growth or decay of the tumour depending on whether proliferation or shrinkage is greater.
## Logistic growth
Again, as we saw back in chapter 1, there is a realism problem with exponential growth in that it predicts growth to infinite numbers of cells. We introduced one approach to deal with this which is to assume a linear decline in the growth rate, $r$, as the population density increases, leading to a carrying capacity at size $K$ after which the population declines. This is given by the ODE,
$$$\frac{dc}{dt} = r_0c\left(1-\frac{c}{K}\right).$$$
We solved the non-dimensionalised version of this earlier, with the full solution here being given by,
$$$c(t) = \frac{Kc(0)}{c(0)+(K-c(0))e^{-r_0t}}.$$$
## Gompertz growth
The logistic equation assumes the growth rate decreases linearly with the population density, but experimental studies have indicated that the decrease in cell proliferation is often closer to exponential. We can readily make our density-dependent growth rate take a different functional form to represent different scenarios. One classic example that has been used to good effect in cancer modelling is the Gompertz model, with the ODE given as,
$$$\frac{dc}{dt} = r_0c\ln\left(\frac{K}{c}\right).$$$
Now the individual-level growth rate (I’d like to say per-capita, but it has been pointed out to me that cells do not have heads) is $r_0\ln(K/c)$. This equals 0 when $c=K$, retaining the meaning of $K$ as a carrying capacity. Note we do have an issue that we cannot let $c=0$. What is the solution to this?
Exercises
Using the substitution $u=\ln\left(\frac{K}{c}\right)$, show that the solution to the Gompertz model is,
$$$c(t)=K\left(\frac{c(0)}{K}\right)^{e^{-rt}}.$$$
Click for solution
If we’re given a substitution we can assume we want to replace all instances of $c$ with some function of $u$. If $u=\ln(K/c)$, we can find that $du/dc=-1/c$. Putting this all together we can rewrite the ODE as follows,
\begin{align*} \frac{1}{c\ln(K/c)}\frac{dc}{dt}&=r\\ \implies -\frac{1}{u}\frac{du}{dc}\frac{dc}{dt}&=r\\ \implies \frac{1}{u}\frac{du}{dt}&=-r. \end{align*}
At this point we can now use separation of variables to find the solution for $u$,
\begin{align*} \ln(u)&=-rt+A\\ \implies u&=A_1e^{-rt}\\ \implies \ln\left(\frac{K}{c}\right)&=A_1e^{-rt} \end{align*}
where $A$ is the constant of integration and $A_1=e^A$. If we have density $c(0)$ at $t=0$ we can find that $A_1=\ln(K/c(0))$. Then if we remember that $\ln(A/B)=\ln(A)-\ln(B)$, this means that $-\ln(A/B)=\ln(B/A)$. Using this fact we can then say,
\begin{align*} \ln\left(\frac{K}{c}\right)&=\ln\left(\frac{K}{c(0)}\right)e^{-rt}\\ \implies \ln\left(\frac{c}{K}\right)&=\ln\left(\frac{c(0)}{K}\right)e^{-rt}\\ \implies \frac{c}{K}&=e^\left[\ln\left(\frac{c(0)}{K}\right)e^{-rt}\right]\\ \implies \frac{c}{K}&=\left(\frac{c(0)}{K}\right)^{e^{-rt}}. \end{align*}
We then just multiply the $K$ to the other side to reach the required solution.
This results in a rather more complex solution that we saw for logistic growth, but at the benefit of a curve that often fits real data much better.
## Volume-based growth
Let’s return to the exponential growth model for a moment. A more general form for this is given by,
$$$\frac{dc}{dt}=rc^b.$$$
It has been suggested that the best choice for the power is not $b=1$ (as we implicitly assumed in our approach to the exponential model) but $b=2/3$. Why might that be? Unlike an ecological population, a cancer tumour forms as a roughly spherical object. If it has volume $V$, then its surface area scales with $V^{2/3}$. If we assume that all resources that the tumour needs must enter through the outer edge of the tumour, then its growth rate will be dependent on its surface area rather than its volume. Note that this need not be limited to the exponential growth model, and may equally well form the growth rate in more complex models.
# Two variable models
All of the model forms we have looked at so far assume that there is only one variable of interest – the density (or maybe volume) of a cancer tumour. However, there are many reasons why we may wish to explore models with two or more variables. We will explore some of these here.
## Proliferating and quiescent cells
Not all cancer cells in a tumour are growing all the time, and this may have impacts on the overall dynamics. We might therefore choose to separate out the cells into those that are proliferating and those that are not, which we call quiescent. A simple model structure for this case would be,
\begin{align} \frac{dP}{dt}&=f(P)-m_1P+m_2Q\\ \frac{dQ}{dt}&=m_1P-m_2Q. \end{align}
The function $f(P)$ describes the growth dynamics of the tumour, likely using one of the model forms we saw earlier. There is then a simple linear transfer of cells between the proliferative and quiescent states. The ability to solve this system will depend on the nature of $f(P)$. If it is linear we will be able to solve the system explicitly. Otherwise we would use our qualitative approaches to find the long-term behaviour. Let’s look at a quick example here.
Exercises
Find the possible equilibria for $P$ and $Q$ for the system,
\begin{align*} \frac{dP}{dt}&=f(P)-m_1P+m_2Q\\ \frac{dQ}{dt}&=m_1P-m_2Q. \end{align*}
when there is logistic growth of proliferating cells with basic growth rate $r_0$ and the carrying capacity for all cells is $K$.
Click for solution
If we have logistic growth with the carrying capacity determined for all cells we can write our system as,
\begin{align*} \frac{dP}{dt}&=r_0P\left(1-\frac{P+Q}{K}\right)-m_1P+m_2Q\\ \frac{dQ}{dt}&=m_1P-m_2Q. \end{align*}
Since this is non-linear it looks like we will not be able to solve it explicitly. Instead, let us determine the equilibria and their stability. If we set the second ODE to 0 we find $Q=Pm_1/m_2$. If we substitute this into the first ODE and set it to 0 we obtain,
$\begin{equation*} r_0P\left(1-\frac{P(1+m_1/m_2)}{K}\right)=0. \end{equation*}$
The long-term equilibria are therefore either,
• $P^*=0$, meaning $Q^*=0$;
• $P^*=\frac{Km_2}{m_1+m_2}$, meaning $Q^*=\frac{Km_1}{m_1+m_2}$.
In the first case the tumour is absent, while at the second the tumour is present, and its total size is at its carrying capacity, but only a proportion of those cells are proliferating.
We can check the stability of these equilibria by writing out the Jacobian,
\begin{align*} J=&\left( \begin{array}{cc} r_0-2\frac{r_0P^*}{K}-\frac{r_0Q^*}{K}-m_1 & -\frac{r_0P^*}{K}+m_2 \\ m_1 & -m_2 \end{array} \right). \end{align*}
At the no tumour equilibrium this reduces to,
\begin{align*} J=&\left( \begin{array}{cc} r_0-m_1 & m_2 \\ m_1 & -m_2 \end{array} \right), \end{align*}
which gives $tr=r_0-m_1-m_2$ and $\det=-r_0m_2$. Since the determinant is negative, this equilibrium is always a saddle. For the equilibrium where the tumour is present, if we substitute in the equilibria and then do some cancelling we have,
\begin{align*} J=&\left( \begin{array}{cc} -\frac{r_0m_2}{m_1+m_2}-m_1 & -\frac{r_0m_2}{m_1+m_2}+m_2 \\ m_1 & -m_2 \end{array} \right). \end{align*}
Here we have $tr=-\frac{r_0m_2}{m_1+m_2}-m_1-m_20$ and $\det=r_0m_2>0$, so it is definitely stable. Substituting in some values, it is quite easy to find examples where $tr^2-4\det\lt 0$, meaning we can have a stable spiral into the equilibrium. Note that this is different to if we just had proliferating cells with logistic growth, where no such damped oscillations would be possible.
## Drug-resistant and drug-sensitive cells
An important question when thinking about treatment strategies for tumours is whether they can develop drug resistance. If so, we might divide our population into two compartments: sensitive and resistant. We would assume drug-sensitive cells have their proliferation rate reduced through treatment but drug-resistant cells do not. Different assumptions might then be made over whether resistance is a pre-existing trait or if it can be acquired. Similarly, we might explore whether cells can switch back and forth between being sensitive and resistant. Such a model might be represented as,
\begin{align} \frac{dS}{dt}&=f_S(S)-m_1S+m_2R\\ \frac{dR}{dt}&=f_R(R)+m_1S-m_2R. \end{align}
This looks similar to our previous model for proliferating and quiescent cells, except here both types of cell can proliferate, just at different rates. We might also think about whether the transition rates, $m_1$ and $m_2$, depend on the level of treatment.
# Summary
We have seen just a few examples of model structures here, and there are many more we haven’t covered, for example directly including the effects of treatment or the immune system. In the next chapter we will see another specific example where we think about how a tumour both grows and impacts its own carrying capacity through angiogenesis.
It is worth stressing that these different model forms are not necessarily limited to cancer modelling, and you may find that some of these different scenarios are more or less suited to the system you are interested in.
Key Takeaways
• We can model growth of tumours in many different ways.
• Single variable models can often be solved explicitly, and include examples such as logistic growth and Gompertz growth.
• Two variable models allow us to explore cell dynamics in more biological detail.
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Enter the initial power output of the solar panel, the annual degradation rate, and the number of years the panel has been in use into the calculator to determine the annual power loss. This calculator can also evaluate any of the variables given the others are known.
## Solar Panel Loss Formula
The following formula is used to calculate the annual solar panel power loss.
PL = P * r * n
Variables:
• PL is the annual power loss (kWh)P is the initial power output of the solar panel (kWh) r is the annual degradation rate (decimal) n is the number of years the panel has been in use
To calculate the annual solar panel power loss, multiply the initial power output of the solar panel by the annual degradation rate, then multiply the result by the number of years the panel has been in use. This will give the total power loss over that period.
## What is a Solar Panel Loss?
Solar panel loss refers to the decrease in the efficiency and power output of a solar panel over time. This can be caused by various factors such as degradation of materials, dust and dirt accumulation, shading, temperature changes, and improper installation. The standard performance loss for solar panels is about 0.5-1% per year. This means that after 25 years, a solar panel may operate at around 80-90% of its original capacity.
## How to Calculate Solar Panel Loss?
The following steps outline how to calculate the Solar Panel Loss.
1. First, determine the initial power output of the solar panel (P) in kWh.
2. Next, determine the annual degradation rate (r) as a decimal.
3. Next, determine the number of years the panel has been in use (n).
4. Next, gather the formula from above = PL = P * r * n.
5. Finally, calculate the Solar Panel Loss (PL) in kWh.
6. After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
initial power output of the solar panel (P) = 500 kWh
annual degradation rate (r) = 0.05
number of years the panel has been in use (n) = 10
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https://www.studyxapp.com/homework-help/the-claim-is-that-the-percentage-is-not-570-confidence-level-is-95-write-formal-q411677358
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# Question I need help finding the answer. Please and Thank you! The claim is that the percentage is NOT 57.0. Confidence level is 95%. Write formally Steps 1, 2, and 3 as discussed in class. Step 1 Ho: p=o Po = Or 57 HA²P +0.57 klaim) Step 2 X= : = 0.05 step 3 Two-Tailes test.
7CAHIF The Asker · Probability and Statistics
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http://www.chegg.com/homework-help/questions-and-answers/3-consider-function-ln-x-1-following--find-maclaurin-series-expansion-n-4-b-plot-ln-x-1-se-q3275838
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3. Consider the function ln(x + 1) and do the following. a. Find the MacLaurin series expansion for n = 4 b. Plot ln(x + 1) and its series expansion using your graphing calculator with a window of [0, 3] X [0, 1] with Yscl = .1. c. We use series to approximate values of functions. Therefore it is important that we know for which values of x the series will provide good approximations of the given function. Based on the graph can we use the MacLaurin series expansion to approximate ln(x + 1) for any value of x or is there a limit to the values of x? If there is a limit then what interval provides the x � values for which the MacLaurin series expansion will provide a good estimate of the value of ln(x + 1)? Explain. d. What effect does increasing the number of terms in the series expansion have on the way it approximates the given function? Why?
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# Practice problems by wuyunyi
VIEWS: 2 PAGES: 5
• pg 1
``` Practice problems 2 - answers
1. Answer: PPP states that the exchange rate between two countries’ currencies equals
the ratio of the countries’ price levels.
A fall in a currency’s domestic purchasing power (i.e. an increase in the domestic
price level) will be associated with a proportional currency depreciation in the foreign
exchange market and vice versa.
E\$/E = PUS/PE where P is the price of a reference commodity basket.
Rearrange: PUS = (E\$/E) x (PE)
Thus, PPP asserts that all countries’ price levels are equal when measured in
terms of the same currency.
2. Answer: PPP theory is a monetary approach to the exchange rate. It is a long-run
theory because it does not allow for price rigidities. It assumes that prices can adjust
right away to maintain full employment as well as PPP.
3.
Answer: All else equal, a rise in a country’s expected inflation rate will eventually cause
an equal rise in the interest rate that deposits of its currency offer. Similarly, a fall in the
expected inflation rate will eventually cause a fall in the interest rate.
Ex: If the expected U.S. inflation were to rise permanently from Π to (Π + ΔΠ),
current dollar interest rates R\$ would eventually catch up to the higher inflation, rising by
a value ΔR\$ = ΔΠ in accordance with the Monetary Approach that in the long run purely
monetary developments should have no effect on an economy’s relative prices since the
real rate of return on dollar assets would remain unchanged.
4. Answer: The real exchange rate between two countries is a broad summary measure of
the prices of one country’s goods and services relative to the other’s. PPP predicts that
the real exchange rate never permanently changes, which is different from nominal
exchange rates that deal with the relative price of two currencies.
The spot exchange rate is equal to the real exchange rate times the ratio of U.S. to
European price levels.
Increase in U.S. money supply: The price level in the U.S. rises in proportion to the
money supply; the real exchange rate remains the same. All dollar prices will rise
(including the dollar price of the euro).
Increase in growth rate of U.S. money supply: The inflation rate, dollar interest rate,
price level in the U.S., and spot exchange rate rise in proportion to the increase in the
price level in the U.S.
Increase in world relative demand for U.S. products: E falls, and q does as well.
Increase in relative U.S. output supply: The dollar depreciates, lowering the relative
price of U.S. output. The real exchange rate rises; the effect on E is not clear since the
real exchange rate and the price level in the U.S. work in opposite directions.
6.
a) Nigeria suffers a depreciation of its real exchange rate as the price of non-traded
goods in Nigeria falls with its fall in income.
b) There will be no effect, at least in the long run, of this purely monetary change.
In the short run, we would see a nominal and real depreciation. As prices adjust,
the real exchange rate returns to its original level.
7. A rise in the expected future rate of the real dollar/euro depreciation causes the
long-run exchange rate to depreciate. An increase in the expected rate of
depreciation of the real exchange rate increases the domestic nominal interest
rates, all else equal, as shown by the relationship between interest rate differences,
expected inflation differences and the expected change in the real exchange rate.
An increase in the domestic nominal interest rate causes excess money supply.
The money market is brought back into equilibrium through an erosion of real
balances due to an increase in the price level. By PPP, an increase in the price
level causes a depreciation of the currency.
8. Answer: The figure below shows the phenomenon of overshooting. A permanent
increase in the money supply starting from full employment equilibrium will shift the AA
curve to the right from AA1 to AA2. Now, a steadily increasing price level shifts the AA
and the DD schedules to the left until a new long-run equilibrium is reached. Note that
point 3 is above point 1, because Ee is permanently higher after a permanent increase in
the money supply. The expected exchange rate, Ee , has risen by the same percentage as
Ms. Notice that along the adjustment path between the initial short-run equilibrium (point
2) and the long-run equilibrium (point 3) the domestic currency actually appreciates
(from E2 to E3) following its initial sharp depreciation (from E1 to E2). This exchange
rate behavior is an example of overshooting, in which the exchange rate’s initial response
to some change is greater than its long-run response.
a) In this case the AA schedule is vertical and the DD schedule retains its former
positive slope.
b) A temporary increase in the money supply has a larger effect on the exchange rate
and on output when we assume that the exchange rate always equals its long-run level.
c) A temporary increase in the government spending has no effect on output, and a
larger effect on the exchange rate when we assume that the future exchange rate always
equal its long run level.
10. a) By interest parity logic, raising the interest rate should bring money back into
country causing the exchange rate to appreciate, or at least counterbalance the attack.
b) The act of raising the interest rate may make some investors feel the cost of policies
necessary to maintain a fixed exchange rate are too high and that the government will be
unable to maintain them. These costs could be due to high government debt that becomes
more expensive when rates go up, or due to high unemployment which may get worse
due to monetary tightening. These costs may lead some domestic constituencies to call
for a devaluation, further raising investors’ concerns.
c) Yes. Even if the fixed rate was originally sensible, if the costs of defending the attack
weakens the government to the point that it no longer looks able to maintain the current
exchange rate, then investors who originally thought the rate was sensible may now feel
that a change in the exchange rate is necessary. For example, the costs of high interest
payments during the time of the attack may take the government more likely to raise the
money supply growth rate and thus make more investors inclined to attack the currency
even if they would not have done so before the initial attack.
11. A contraction of the German money supply shifts the interest parity curve out. British
monetary authorities would be forced to contract their money supply in response to
maintain the fixed Pound/DM exchange rate.
12. For example, we may find the following (only the direction of change, not the actual
amounts, can be inferred from the question). The Fed decreases its holdings of dollar
assets and increases its euro holdings thus increasing the public’s supply of dollar assets
and decreasing its holdings of euro assets.
Balance Sheet of the ECB Balance Sheet of the ECB
Before intervention After intervention
Assets Liabilities Assets Liabilities
Domestic 2000 bill. 2800 bill. Domestic 2300 bill. 2800 bill.
Foreign 800 bill. Foreign 500 bill.
•Sterilized foreign exchange intervention – policy by which central banks carry out
equal foreign and domestic asset transactions in opposite directions to nullify the impact
of foreign exchange operations on domestic money supply.
•Example: Bank of Pecunia sells \$100 in foreign assets, receives \$100 check from
PecuniaCorp. Central foreign assets and liabilities decline simultaneously by \$100; fall in
money supply.
•To negate effect on money supply, central bank buys \$100 of domestic assets. This
increases its domestic assets and its liabilities by \$100, offsetting the money supply effect
of sale of foreign assets.
14. Answer: Under floating, by purchasing domestic assets the central bank causes an
initial excess supply of domestic money that simultaneously pushed the domestic interest
rate downward and weakens the currency. However, under fixed exchange rate the
central bank will resist any tendency of the currency to depreciate by selling foreign
assets for domestic money and so removing the initial excess supply of money its policy
move has caused.
15.
Answer: 1. Allow the government to fight domestic unemployment despite the
lack of effective monetary policy.
2. Improve the current account.
3. Increase foreign reserves held by the central bank.
16. Answer: The fixed exchange rate DD – AA model requires the assumption that
E = E0 . This shows that the economy’s short-run equilibrium is at point 1 when the
central bank fixes the exchange rate at the level C. Output equals Y1 at point 1 and the
money supply is at the level where a domestic interest rate equal to the foreign rate (R*)
clears the domestic market.
To Increase Output: Hoping to increase output to Y2, the central bank increases the
money supply through the purchase of domestic assets and shifting AA1 to AA2. Because
the exchange rate is fixed, the central bank must maintain E0, it has to sell foreign assets
for domestic currency, thereby decreasing the money supply immediately and returning
AA2 back to AA1. Output is unchanged as the initial equilibrium is maintained.
17. Answer: An expansionary fiscal policy shifts the DD curve to the right. Under
flexible exchange rate, point 2 in the figure is the equilibrium, e decreases (appreciates)
and Y goes up. The picture is more complicated under fixed exchange rate, however,
since E cannot change. Output is going up as a result of the fiscal expansion, and thus the
demand for domestic money increases. To prevent the increased money demand from
increase domestic interest rate above R*, and with the appreciation of the currency, the
central bank must buy foreign assets with domestic money and thereby increase the
money supply. The AA shifts to the right until E is restored to the initial fixed exchange
rate, E0, at point 3 in the figure. So under fixed exchanger rate, Y will increase by more
than under a flexible exchange rate regime. Unlike monetary policy, fiscal policy can be
used to affect output under a fixed exchange rate. A central bank is forced to expand the
money supply through foreign exchange purchases.
```
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# Search by Topic
#### Resources tagged with Mathematical reasoning & proof similar to Permute It:
Filter by: Content type:
Stage:
Challenge level:
### There are 176 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
### Tri-colour
##### Stage: 3 Challenge Level:
Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?
### Cycle It
##### Stage: 3 Challenge Level:
Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.
### Tis Unique
##### Stage: 3 Challenge Level:
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
### Shuffle Shriek
##### Stage: 3 Challenge Level:
Can you find all the 4-ball shuffles?
### Even So
##### Stage: 3 Challenge Level:
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
### Number Rules - OK
##### Stage: 4 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
### Greetings
##### Stage: 3 Challenge Level:
From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How. . . .
### How Many Dice?
##### Stage: 3 Challenge Level:
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
### Aba
##### Stage: 3 Challenge Level:
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
### What Numbers Can We Make Now?
##### Stage: 3 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
### What Numbers Can We Make?
##### Stage: 3 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
### N000ughty Thoughts
##### Stage: 4 Challenge Level:
How many noughts are at the end of these giant numbers?
##### Stage: 3 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
##### Stage: 3 Challenge Level:
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
### Master Minding
##### Stage: 3 Challenge Level:
Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?
##### Stage: 2 and 3
A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.
### Composite Notions
##### Stage: 4 Challenge Level:
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
### Pattern of Islands
##### Stage: 3 Challenge Level:
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
### One O Five
##### Stage: 3 Challenge Level:
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
### More Mathematical Mysteries
##### Stage: 3 Challenge Level:
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
### Mod 3
##### Stage: 4 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
### Eleven
##### Stage: 3 Challenge Level:
Replace each letter with a digit to make this addition correct.
### Cross-country Race
##### Stage: 3 Challenge Level:
Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?
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##### Stage: 4 Challenge Level:
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Theater Critic: The play La Finestrina, now at Central : GMAT Critical Reasoning (CR)
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# Theater Critic: The play La Finestrina, now at Central
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Theater Critic: The play La Finestrina, now at Central [#permalink]
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25 Dec 2009, 07:27
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Theater Critic: The play La Finestrina, now at Central Theater, was written in Italy in the eighteenth century. The
director claims that this production is as similar to the original production as is possible in a modern theater.
Although the actor who plays Harlequin the clown gives a performance very reminiscent of the twentieth-century
American comedian Groucho Marx, Marx's comic style was very much within the comic acting tradition that had
begun in sixteenth-century Italy.
The considerations given best serve as part of an argument that
(A) modern audiences would find it hard to tolerate certain characteristics of a historically accurate
performance of an eighteenth-century play
(8) Groucho Marx once performed the part of the character Harlequin in La Finestrina
(C) in the United States the training of actors in the twentieth century is based on principles that do not differ
radically from those that underlay the training of actors in eighteenth-century Italy
(D) the performance of the actor who plays Harlequin in La Finestrina does not serve as evidence against the
director's claim
(E) the director of La Finestrina must have advised the actor who plays Harlequin to model his performance on
comic performances of Groucho Marx
Not satisfied with the explanation of OG pls someone can help on this?
If you have any questions
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28 Dec 2009, 07:40
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sagarsabnis wrote:
Theater Critic: The play La Finestrina, now at Central Theater, was written in Italy in the eighteenth century. The
director claims that this production is as similar to the original production as is possible in a modern theater.
Although the actor who plays Harlequin the clown gives a performance very reminiscent of the twentieth-century
American comedian Groucho Marx, Marx's comic style was very much within the comic acting tradition that had
begun in sixteenth-century Italy.
The considerations given best serve as part of an argument that
(A) modern audiences would find it hard to tolerate certain characteristics of a historically accurate
performance of an eighteenth-century play
(8) Groucho Marx once performed the part of the character Harlequin in La Finestrina
(C) in the United States the training of actors in the twentieth century is based on principles that do not differ
radically from those that underlay the training of actors in eighteenth-century Italy
(D) the performance of the actor who plays Harlequin in La Finestrina does not serve as evidence against the
director's claim
(E) the director of La Finestrina must have advised the actor who plays Harlequin to model his performance on
comic performances of Groucho Marx
Not satisfied with the explanation of OG pls someone can help on this?
I'll give it a try...
premise 1: The play La Finestrina was written and performed ('director claims that this production is as similar to the original production') in Italy in the 18th century.
premise 2: "Although the actor who plays............sixteenth-century Italy." this statement implies that the performance of the actor who played harlenquin was within the comic acting tradition that had begun in the 16th century.
conclusion: the director claims that the production is quite similar to the original production in modern theater.
now closely look at the premise 2.... premise 2, in no way does it support (since no one knows how the actors during the 18th century performed the show) or, as a matter of fact, oppose (since the actor who plays harlequin now represents the style of the 16th century Italians, his act might have been similar to the act performed in the 18th century) the director's claim...
A. characteristics of the historically accurate performance in not known.
B. this is definitely not known to us, it is not mentioned in the argument.
C. this is a sweeping generalization, not necessarily true.
D. yeah.. this statement is true. as we have seen above, the performance of the actor does not serve as evidence against the director's claim.
E. this cannot be said. it need not be the director who advised the actor, the producer or any other member of the crew could have advised him to model marx's performance. having said that, the actor imitating marx could have been intentional, but not necessarily on the director's advise.
i hope my explanation is clear...
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25 Oct 2011, 11:33
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I picked D...if you negate option D the argument falls apart...it took me 3:08 mins.
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25 Dec 2009, 10:18
is it D
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25 Dec 2009, 11:47
sHOULD BE D,NOT EXTREME AND OGICAL
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25 Dec 2009, 12:39
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25 Dec 2009, 16:59
my choice is C
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28 Dec 2009, 10:17
Agreed good explanation...
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15 May 2010, 05:30
I have never seen such a Brain Thugh. It took me more than 5 min to decide b/w C and D.
I fell for C as the stimulus is on some Traditions...16/18/20th century....
God help me .
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25 Oct 2011, 20:35
+1 for D
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Re: Theater Critic: The play La Finestrina, now at Central [#permalink]
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10 Jul 2014, 12:45
the 12th edition GMAT book answers D to be the correct choice.
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Re: Theater Critic: The play La Finestrina, now at Central [#permalink]
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11 Apr 2016, 00:50
Hello from the GMAT Club VerbalBot!
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Re: Theater Critic: The play La Finestrina, now at Central [#permalink]
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30 Jul 2016, 09:00
Please update the OA and difficulty
Re: Theater Critic: The play La Finestrina, now at Central [#permalink] 30 Jul 2016, 09:00
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# Evaluate each function for the given value of x, and write the input x and output f(x) as an ordered pair. f(x) = 2/9x - 9/2 for x = 9
#1
Evaluate each function for the given value of x, and write the input x and output f(x) as an ordered pair.
f(x) = 2/9x - 9/2 for x = 9
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# Excited state
"Excited" redirects here. For other uses, see Excited (disambiguation).
After absorbing energy, an electron may jump from the ground state to a higher energy excited state.
Excitations of copper 3d orbitals on the CuO2-plane of a high Tc superconductor; The ground state (blue) is x2-y2 orbitals; the excited orbitals are in green; the arrows illustrate inelastic x-ray spectroscopy
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being raised to an excited state.
In quantum mechanics an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). The temperature of a group of particles is indicative of the level of excitation (with the notable exception of systems that exhibit Negative temperature).
The lifetime of a system in an excited state is usually short: spontaneous or induced emission of a quantum of energy (such as a photon or a phonon) usually occurs shortly after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state). This return to a lower energy level is often loosely described as decay and is the inverse of excitation.
Long-lived excited states are often called metastable. Long-lived nuclear isomers and singlet oxygen are two examples of this.
## Atomic excitation
A simple example of this concept comes by considering the hydrogen atom.
The ground state of the hydrogen atom corresponds to having the atom's single electron in the lowest possible orbit (that is, the spherically symmetric "1s" wavefunction, which has the lowest possible quantum numbers). By giving the atom additional energy (for example, by the absorption of a photon of an appropriate energy), the electron is able to move into an excited state (one with one or more quantum numbers greater than the minimum possible). If the photon has too much energy, the electron will cease to be bound to the atom, and the atom will become ionised.
After excitation the atom may return to the ground state or a lower excited state, by emitting a photon with a characteristic energy. Emission of photons from atoms in various excited states leads to an electromagnetic spectrum showing a series of characteristic emission lines (including, in the case of the hydrogen atom, the Lyman, Balmer, Paschen and Brackett series.)
An atom in a high excited state is termed Rydberg atom. A system of highly excited atoms can form a long-lived condensed excited state e.g. a condensed phase made completely of excited atoms: Rydberg matter. Hydrogen can also be excited by heat or electricity.
## Perturbed gas excitation
A collection of molecules forming a gas can be considered in an excited state if one or more molecules are elevated to kinetic energy levels such that the resulting velocity distribution departs from the equilibrium Boltzmann distribution. This phenomenon has been studied in the case of a two-dimensional gas in some detail, analyzing the time taken to relax to equilibrium.
## Calculation of excited states
Excited states are often calculated using Coupled cluster, Møller–Plesset perturbation theory, Multi-configurational self-consistent field, Configuration interaction,[1] and Time-dependent density functional theory. These calculations are more difficult than non-excited state calculations.[2][3][4][5][6]
## Reaction
A further consequence is reaction of the atom in the excited state, as in photochemistry. Excited states give rise to chemical reaction.
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# Resolve the cartesian unit vectors into their cylindrical components
JasonPhysicist
## Homework Statement
The problem is :''Resolve the cartesian unit vectors into their cylindrical components(using scale factors)
## The Attempt at a Solution
It's simple to do the inverse(resolving cylindricl unit vectors into cartesian components),but I'm having some ''trouble'' with the above problem.
$$x=\rho\cos\varphi - \varphi\sin\varphi$$
$$y=\varphi\sin\varphi + \varphi\cos\varphi$$
$$z=z$$
Could someone shed some light?Thank you.
[
I think you're forgeting the vectors in the answer that you know. If you're converting the i,j,k (or x,y,z) unit vectors into their equivalent vectors in cylinderical coordinates, your answer will be in terms of 3 vectors, $$\vec{e_{r}},\vec{e_{\theta}},\vec{e_{z}}$$ (they might be presented differently in different texts though.)
The way to get to these base vectors is to look at the normals to the surfaces that are created when theta, r, and z are fixed constant. For example if you wish to find $$\vec{e_{r}}$$
$$x^{2}+y^{2} = r^{2}$$
$$\vec{e_{r}} = cos(\theta)\vec{i}+sin(\theta)\vec{j}$$
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# AI: Neural Network for Beginners (Part 3 of 3)
, 29 Jan 2007
Rate this:
AI: An introduction into neural networks (multi-layer networks / trained by Microbial GA).
## Introduction
1. Part 1: This one will be an introduction into Perceptron networks (single layer neural networks)
2. Part 2: Will be about multi-layer neural networks, and the back propagation training method to solve a non-linear classification problem such as the logic of an XOR logic gate. This is something that a Perceptron can't do. This is explained further within this article.
3. Part 3: This one is about how to use a genetic algorithm (GA) to train a multi-layer neural network to solve some logic problem, ;f you have never come across genetic algorithms, perhaps my other article located here may be a good place to start to learn the basics.
## Summary
This article will show how to use a Microbial Genetic Algorithm to train a multi-layer neural network to solve the XOR logic problem.
## A Brief Recap (From Parts 1 and 2)
Before we commence with the nitty griity of this new article which deals with multi-layer neural networks, let's just revisit a few key concepts. If you haven't read Part 1 or Part 2, perhaps you should start there.
### Part 1: Perceptron Configuration (Single Layer Network)
The inputs (x1,x2,x3..xm) and connection weights (w1,w2,w3..wm) in figure 4 are typically real values, both positive (+) and negative (-). If the feature of some xi tends to cause the perceptron to fire, the weight wi will be positive; if the feature xi inhibits the perceptron, the weight wi will be negative.
The perceptron itself consists of weights, the summation processor, and an activation function, and an adjustable threshold processor (called bias hereafter).
For convenience, the normal practice is to treat the bias as just another input. The following diagram illustrates the revised configuration:
The bias can be thought of as the propensity (a tendency towards a particular way of behaving) of the perceptron to fire irrespective of its inputs. The perceptron configuration network shown in Figure 5 fires if the weighted sum > 0, or if you are into math type explanations.
## Part 2: Multi-Layer Configuration
The multi-layer network that will solve the XOR problem will look similar to a single layer network. We are still dealing with inputs / weights / outputs. What is new is the addition of the hidden layer.
As already explained above, there is one input layer, one hidden layer, and one output layer.
It is by using the inputs and weights that we are able to work out the activation for a given node. This is easily achieved for the hidden layer as it has direct links to the actual input layer.
The output layer, however, knows nothing about the input layer as it is not directly connected to it. So to work out the activation for an output node, we need to make use of the output from the hidden layer nodes, which are used as inputs to the output layer nodes.
This entire process described above can be thought of as a pass forward from one layer to the next.
This still works like it did with a single layer network; the activation for any given node is still worked out as follows:
where wi is the weight(i), and Ii is the input(i) value. You see it the same old stuff, no demons, smoke, or magic here. It's stuff we've already covered.
So that's how the network looks. Now I guess you want to know how to go about training it.
## Learning
There are essentially two types of learning that may be applied to a neural network, which are "Reinforcement" and "Supervised".
### Reinforcement
In Reinforcement learning, during training, a set of inputs is presented to the neural network. The output is 0.75 when the target was expecting 1.0. The error (1.0 - 0.75) is used for training ("wrong by 0.25"). What if there are two outputs? Then the total error is summed to give a single number (typically sum of squared errors). E.g., "your total error on all outputs is 1.76". Note that this just tells you how wrong you were, not in which direction you were wrong. Using this method, we may never get a result, or could be hunt the needle.
Using a generic algorithm to train a multi-layer neural network offers a Reinforcement type training arrangement, where the mutation is responsible for "jiggling the weights a bit". This is what this article is all about.
### Supervised
In Supervised learning, the neural network is given more information. Not just "how wrong" it was, but "in what direction it was wrong", like "Hunt the needle", but where you are told "North a bit" "West a bit". So you get, and use, far more information in Supervised learning, and this is the normal form of neural network learning algorithm.
This training method is normally conducted using a Back Propagation training method, which I covered in Part 2, so if this is your first article of these three parts, and the back propagation method is of particular interest, then you should look there.
## So Now the New Stuff
From this point on, anything that is being discussed relates directly to this article's code.
What is the problem we are trying to solve? Well, it's the same as it was for Part 2, it's the simple XOR logic problem. In fact, this articles content is really just an incremental build, on knowledge that was covered in Part 1 and Part 2, so let's march on.
For the benefit of those that may have only read this one article, the XOR logic problem looks like the following truth table:
Remember with a single layer (perceptron), we can't actually achieve the XOR functionality as it's not linearly separable. But with a multi-layer network, this is achievable.
So with this in mind, how are we going to achieve this? Well, we are going to use a Genetic Algorithm (GA from this point on) to breed a population of neural networks that will hopefully evolve to provide a solution to the XOR logic problem; that's the basic idea anyway.
So what does this all look like?
As can be seen from the figure above, what we are going to do is have a GA which will actually contain a population of neural networks. The idea being that the GA will jiggle the weights of the neural networks, within the population, in the hope that the jiggling of the weights will push the neural network population towards a solution to the XOR problem.
### So How Does This Translate Into an Algorithm
The basic operation of the Microbial GA training is as follows:
• Pick two genotypes at random
• Compare scores (fitness) to come up with a winner and loser
• Go along genotype, at each locus (point)
So only the loser gets changed, which gives a version of Elitism for free; this ensures the best in breed remains in the population.
• With some probability, copy from winner to loser (overwrite)
• With some probability, mutate that locus of the loser
That's it. That is the complete algorithm.
But there are some essential issues to be aware of when playing with GAs:
1. The genotype will be different for a different problem domain
2. The fitness function will be different for a different problem domain
These two items must be developed again whenever a new problem is specified. For example, if we wanted to find a person's favourite pizza toppings, the genotype and fitness would be different from that which is used for this article's problem domain.
These two essential elements of a GA (for this article problem domain) are specified below.
### 1. The Geneotype
For this article, the problem domain states that we had a population of neural networks. So I created a single dimension array of `NeuralNetwork` objects. This can be seen from the constructor code within the `GA_Trainer_XOR` object:
```//ANN's
private NeuralNetwork[] networks;
public GA_Trainer_XOR()
{
networks = new NeuralNetwork[POPULATION];
//create new ANN objects, random weights applied at start
for (int i = 0; i <= networks.GetUpperBound(0); i++)
{
networks[i] = new NeuralNetwork(2, 2, 1);
networks[i].Change +=
new NeuralNetwork.ChangeHandler(GA_Trainer_NN_Change);
}
}```
### 2. The Fitness Function
Remembering the problem domain description stated, the following truth table is what we are trying to achieve:
So how can we tell how fit (how close) the neural network is to this ? It is fairly simply really. What we do is present the entire set of inputs to the Neural Network one at a time and keep an accumulated error value, which is worked out as follows:
Within the `NeuralNetwork` class, there is a `getError(..)` method like this:
```public double getError(double[] targets)
{
//storage for error
double error = 0.0;
//this calculation is based on something I read about weight space in
//Artificial Intellegence - A Modern Approach, 2nd edition.Prentice Hall
//2003. Stuart Rusell, Peter Norvig. Pg 741
error = Math.Sqrt(Math.Pow((targets[0] - outputs[0]), 2));
return error;
}```
Then in the `NN_Trainer_XOR` class, there is an `Evaluate` method that accepts an `int` value which represents the member of the population to fetch and evaluate (get fitness for). This overall fitness is then returned to the GA training method to see which neural network should be the winner and which neural network should be the loser.
```private double evaluate(int popMember)
{
double error = 0.0;
//loop through the entire training set
for (int i = 0; i <= train_set.GetUpperBound(0); i++)
{
//forward these new values through network
//forward weights through ANN
forwardWeights(popMember, getTrainSet(i));
double[] targetValues = getTargetValues(getTrainSet(i));
error += networks[popMember].getError(targetValues);
}
//if the Error term is < acceptableNNError value we have found
//a good configuration of weights for teh NeuralNetwork, so tell
//GA to stop looking
if (error < acceptableNNError)
{
bestConfiguration = popMember;
foundGoodANN = true;
}
//return error
return error;
}```
So how do we know when we have a trained neural network? In this article's code, what I have done is provide a fixed limit value within the `NN_Trainer_XOR` class that, when reached, indicates that the training has yielded a best configured neural network.
If, however, the entire training loop is done and there is still no well-configured neural network, I simply return the value of the winner (of the last training epoch) as the overall best configured neural network.
This is shown in the code snippet below; this should be read in conjunction with the `evaluate(..)` method shown above:
```//check to see if there was a best configuration found, may not have done
//enough training to find a good NeuralNetwork configuration, so will simply
//have to return the WINNER
if (bestConfiguration == -1)
{
bestConfiguration = WINNER;
}
//return the best Neural network
return networks[bestConfiguration];```
## So Finally the Code
Well, the code for this article looks like the following class diagram (it's Visual Studio 2005, C#, .NET v2.0):
The main classes that people should take the time to look at would be:
• `GA_Trainer_XOR`: Trains a neural network to solve the XOR problem using a Microbial GA.
• `TrainerEventArgs`: Training event args, for use with a GUI.
• `NeuralNetwork`: A configurable neural network.
• `NeuralNetworkEventArgs`: Training event args, for use with a GUI.
• `SigmoidActivationFunction`: A static method to provide the sigmoid activation function.
The rest are the GUI I constructed simply to show how it all fits together.
Note: The demo project contains all code, so I won't list it here. Also note that most of these classes are quite similar to those included with the Part 2 article code. I wanted to keep the code similar so people who have already looked at Part 2 would recognize the common pattern.
## Code Demos
The demo application attached has three main areas which are described below:
#### Live Results Tab
It can be seen that this has very nearly solved the XOR problem; it did however take nearly 45000 iterations (epoch) of a training loop. Remembering that we have to also present the entire training set to the network, and also do this twice, once to find a winner and once to find a loser. That is quite a lot of work; I am sure you would all agree. This is why neural networks are not normally trained by GAs; this article is really about how to apply a GA to a problem domain. Because the GA training took 45000 epochs to yield an acceptable result does not mean that GAs are useless. Far from it, GAs have their place, and can be used for many problems, such as:
• Sudoko solver (the popular game)
• Backpack problem (trying to optimize the use of a backpack of limited size, to get as many items in as will fit)
• Favourite pizza toppings problem (try and find out what someone's favourite pizza is)
To name but a few, basically, if you can come up with the genotype and a Fitness function, you should be able to get a GA to work out a solution. GAs have also been used to grow entire syntax trees of grammar, in order to predict which grammar is more optimal. There is more research being done in this area as I write this article; in fact, there is a nice article on this topic (Gene Expression Programming) by Andrew Krillov, right here at the CodeProject, if anyone wants to read further.
#### Training Results Tab
Viewing the target/outputs together:
Viewing the errors:
#### Trained Results Tab
Viewing the target/outputs together:
It is also possible to view the neural network's final configuration using the "View Neural Network Config" button.
## What Do You Think?
That is it; I would just like to ask, if you liked the article, please vote for it.
## Points of Interest
I think AI is fairly interesting, that's why I am taking the time to publish these articles. So I hope someone else finds it interesting, and that it might help further someone's knowledge, as it has my own.
Anyone that wants to look further into AI type stuff, that finds the content of this article a bit basic, should check out Andrew Krillov's articles at Andrew Krillov CP articles as his are more advanced, and very good.
## History
• v1.1: 27/12/06: Modified the `GA_Trainer_XOR` class to have a random number seed of 5.
• v1.0: 11/12/06: Initial article.
## Bibliography
• Artificial Intelligence 2nd edition, Elaine Rich / Kevin Knight. McGraw Hill Inc.
• Artificial Intelligence, A Modern Approach, Stuart Russell / Peter Norvig. Prentice Hall.
## Share
Software Developer (Senior) United Kingdom
I currently hold the following qualifications (amongst others, I also studied Music Technology and Electronics, for my sins)
- MSc (Passed with distinctions), in Information Technology for E-Commerce
- BSc Hons (1st class) in Computer Science & Artificial Intelligence
Both of these at Sussex University UK.
Award(s)
I am lucky enough to have won a few awards for Zany Crazy code articles over the years
• Microsoft C# MVP 2016
• Codeproject MVP 2016
• Microsoft C# MVP 2015
• Codeproject MVP 2015
• Microsoft C# MVP 2014
• Codeproject MVP 2014
• Microsoft C# MVP 2013
• Codeproject MVP 2013
• Microsoft C# MVP 2012
• Codeproject MVP 2012
• Microsoft C# MVP 2011
• Codeproject MVP 2011
• Microsoft C# MVP 2010
• Codeproject MVP 2010
• Microsoft C# MVP 2009
• Codeproject MVP 2009
• Microsoft C# MVP 2008
• Codeproject MVP 2008
• And numerous codeproject awards which you can see over at my blog
## You may also be interested in...
ask GA hybrid GMDH Member 996288221-Jul-13 20:10 Member 9962882 21-Jul-13 20:10
General Question Re using AI just william16-Feb-07 20:43 just william 16-Feb-07 20:43
Re: General Question Re using AI Sacha Barber16-Feb-07 23:20 Sacha Barber 16-Feb-07 23:20
Re: General Question Re using AI just william17-Feb-07 11:24 just william 17-Feb-07 11:24
Re: General Question Re using AI Sacha Barber18-Feb-07 21:46 Sacha Barber 18-Feb-07 21:46
Now it should be your time - congratulation Andrew Kirillov10-Jan-07 7:54 Andrew Kirillov 10-Jan-07 7:54
Re: Now it should be your time - congratulation Sacha Barber10-Jan-07 8:31 Sacha Barber 10-Jan-07 8:31
Re: Now it should be your time - congratulation Sacha Barber18-Jan-07 2:23 Sacha Barber 18-Jan-07 2:23
Sadly Andrew it looks like I will not get this. Though the voting has been very strange, up until 1 day ago myself and Peter (the very very very crazy russian Phd dude) were clearly in front. All of a sudden one of the another articles has gained some 30 odds votes or there abouts in a single day. With the rest of the competitors not moving by much at all. Ho hum, I guess thats how it is. I think I am not going to worry about the competition from now on, just write articles that I am interested in. although I would have liked the KwikClick stuff, that looked cool. Perhaps ill buy that. sacha barber
Re: Now it should be your time - congratulation Andrew Kirillov18-Jan-07 8:58 Andrew Kirillov 18-Jan-07 8:58
Re: Now it should be your time - congratulation Sacha Barber18-Jan-07 21:37 Sacha Barber 18-Jan-07 21:37
Re: Now it should be your time - congratulation Sacha Barber23-Jan-07 9:46 Sacha Barber 23-Jan-07 9:46
Quick Question BlitzPackage29-Dec-06 18:51 BlitzPackage 29-Dec-06 18:51
Re: Quick Question Sacha Barber2-Jan-07 8:35 Sacha Barber 2-Jan-07 8:35
1 XOR 1 erratic behavior Jay Gatsby23-Dec-06 19:29 Jay Gatsby 23-Dec-06 19:29
Re: 1 XOR 1 erratic behavior Sacha Barber24-Dec-06 8:25 Sacha Barber 24-Dec-06 8:25
Re: 1 XOR 1 erratic behavior Jay Gatsby24-Dec-06 9:36 Jay Gatsby 24-Dec-06 9:36
Re: 1 XOR 1 erratic behavior Sacha Barber27-Dec-06 0:18 Sacha Barber 27-Dec-06 0:18
Re: 1 XOR 1 erratic behavior Jay Gatsby27-Dec-06 18:04 Jay Gatsby 27-Dec-06 18:04
Re: 1 XOR 1 erratic behavior Sacha Barber27-Dec-06 23:45 Sacha Barber 27-Dec-06 23:45
Re: 1 XOR 1 erratic behavior Sacha Barber9-Jan-07 9:19 Sacha Barber 9-Jan-07 9:19
Industrial controller PID kamarchand11-Dec-06 14:07 kamarchand 11-Dec-06 14:07
Re: Industrial controller PID Sacha Barber11-Dec-06 20:58 Sacha Barber 11-Dec-06 20:58
Re: Industrial controller PID kamarchand17-Dec-06 5:01 kamarchand 17-Dec-06 5:01
Re: Industrial controller PID Sacha Barber17-Dec-06 10:19 Sacha Barber 17-Dec-06 10:19
Thanks giongquyqua11-Dec-06 3:45 giongquyqua 11-Dec-06 3:45
Last Visit: 31-Dec-99 18:00 Last Update: 23-Jul-17 10:50 Refresh « Prev123 Next »
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# Superficial Fluid Velocity.
Register Blogs Members List Search Today's Posts Mark Forums Read
October 17, 2010, 22:45 Superficial Fluid Velocity. #1 New Member Join Date: Aug 2010 Posts: 6 Rep Power: 9 Hi All. I am a beginner so I hope u will not mind the questions. I am working of liquid fluidized beds. I am tryng to simulate two dimensional fluid-solid flow. I want fluent to calculate the superficial fluid velocity at the end. How do I get that? Can I get them from surface/volume integrals? Thanx. BZ.
October 24, 2010, 13:22 #2 Senior Member karine Join Date: Nov 2009 Posts: 158 Rep Power: 10 Hi for the superficial velocity, just divide ure flow rate by ure outlet section.... To get the flow rate, go to report--->Fluxes
October 24, 2010, 19:33 Thanks. #3 New Member Join Date: Aug 2010 Posts: 6 Rep Power: 9 Hi. I have already posted the following lines in my earlier post. Can u plz have alook at my situation and advise me accordingly. I have a 2D (x,y) domain of size (0,0)(xmax,ymax) divided into a 50x50 grid. I want to find properties (e.g. y-velocity) of all points at any given instant in the following manner. for (y=0,y=ymax,y++) { for(x=0,x=xmax,x++) { location[x][y]= ........ ? y_velocity[x][y]=........ ? } } It means that I fix y, then loop over all available x-cells to store values. Then increase y and repeat the process for x-cells. I need to store the values in arrays for further analysis or written to files. How do I add it to my UDF ? Thanx.
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All times are GMT -4. The time now is 08:14.
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# Calculating shortest path between two points along a rail network
I would like to calculate the shortest path from mines to ports, along the rail network. Since the mines and ports are not directly on the network, I first worked out the nearest rail point for each mine and port.
However, I am now struggling to convert the rail network into a NetworkX graph and from there, calculating the shortest distance between each mine and port. When I ran my code, it is unable to work out the nearest path since all of the distances are zero. Please see below for the code I have written thus far. The rail network can be downloaded from here. I would kindly appreciate any assistance that can be provided. Thank you.
``````# Ports
ports =
[{'port_name': 'Geraldton', 'geometry': POINT (114.59786 -28.77688)},
{'port_name': 'Bunbury', 'geometry': POINT(115.673447 -33.318797)},
{'port_name': 'Albany', 'geometry': POINT(117.895025 -35.032831)},
{'port_name': 'Esperance', 'geometry': POINT(121.897114 -33.871834)}]
# Mine sites
mines =
[{'mine_name': 'Gold', 'geometry': POINT (117.94568 -34.93467),
{'mine_name': 'Silver', 'geometry': POINT (115.16923 -29.65613)},
{'mine_name': 'Bronze', 'geometry': POINT (115.11039 -29.51287)},
{'mine_name': 'Platinum', 'geometry': POINT (115.11130 -29.42621)}]
# Convert to GeoDataFrame
crs = 'EPSG:4326'
ports = gpd.GeoDataFrame(ports, crs=crs, geometry = 'geometry')
mine_sites = gpd.GeoDataFrame(ports, crs=crs, geometry = 'geometry')
# Column for nearest rail point
ports['nearest_rail_point'] = None
mine_sites['nearest_rail_point'] = None
# Nearest rail point
for index, row in ports.iterrows():
port_point = row['geometry']
nearest_point = nearest_points(port_point, rail_network.unary_union)[1]
ports.at[index, 'nearest_rail_point'] = nearest_point
for index, row in mine_sites.iterrows():
mine_site_point = row['geometry']
nearest_point = nearest_points(mine_site_point, rail_network.unary_union)[1]
mine_sites.at[index, 'nearest_rail_point'] = nearest_point
G = momepy.gdf_to_nx(rail_network)
shortest_distances = {}
# Calculate shortest path
for mine_index, mine_row in mines.iterrows():
mine_name = mine_row['mine_name']
mine_point = mine_row['geometry']
shortest_distances[mine_name] = {}
for port_index, port_row in ports.iterrows():
port_name = port_row['port_name']
port_point = port_row['geometry']
try:
shortest_distance = nx.shortest_path_length(G,
source=(mine_point.x, mine_point.y),
target=(port_point.x, port_point.y),
weight='length')
shortest_distances[mine_name][port_name] = shortest_distance
except nx.NetworkXNoPath:
shortest_distances[mine_name][port_name] = float('inf') # No path found
``````
• "I'm strugglung" is not a valid question. How to Ask and minimal reproducible example Commented Jul 11 at 0:55
• What additional information do you need to be able to assist? Commented Jul 11 at 3:18
It's unclear if you need the shortest path between each mine and its corresponding port (at the same index) or among all ports. Either way, one option would be to use a primal approach (with `momempy`) to create the graph and compute the `shortest_path_length` (or `shortest_path`, depending on your expected output). However, before that, you need to snap the mines to the nearest rail boundary :
``````spots = (pd.concat([
ports.rename(columns={"port_name": "spot_name"}),
mine_sites.rename(columns={"mine_name": "spot_name"})])
.to_crs("EPSG:3857"))
import momepy
G = (momepy.gdf_to_nx(
rail_network[["name", "geometry"]].explode(),
approach="primal", multigraph=False, length="dis"))
def nearest_bnd(p, ls, shp=False):
sp, *_, ep = ls.coords
nb = min(map(Point, [sp, ep]), key=p.distance)
return nb if shp else (nb.x, nb.y)
coos = (spots.rename_geometry("geom_sp")
.sjoin_nearest(rail_network.assign(geom_rn=rail_network["geometry"]))
.set_geometry("geom_rn").assign(coo=lambda x: [nearest_bnd(p, ls)
for p, ls in x[["geom_sp", "geom_rn"]].to_numpy()])
.set_index("spot_name")["coo"])
all_spl = {}
for mn in mine_sites["mine_name"]:
for pn in ports["port_name"]:
try:
uv = map(coos.get, [mn, pn])
spl = nx.shortest_path_length(G, *uv, weight="dis")
spl = round(spl / 1000, 2)
except nx.NetworkXNoPath:
spl = float("inf")
all_spl.setdefault(mn, []).append({pn: spl})
``````
``````{mn: min(d, key=lambda x: list(x.values())[0]) for mn, d in all_spl.items()}
# {
# "Gold": {"Albany": 0.0},
# "Silver": {"Geraldton": 117.85},
# "Bronze": {"Geraldton": 117.85},
# "Platinum": {"Geraldton": 117.85},
# }
``````
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# “Objects” Creation— One Pattern of Evolution of Programming Language
Tianyi Cheng
This week, I tried to savor the process of using programming language and noted the difference between Python language and my thinking pattern, and between the ways computers and human solve problems. I want to use solving the problem of rounding numbers as an example. We do rounding in everyday life. It is one of the simplest information processing in our brain. However, I found myself stuck when teaching computer to do rounding in Python language. Basically, I think the way I solve this problem is similar to this pattern:
What is the first number after the “.”? If it is one of “5,6,7,8,9”, then round up. Add 1 to the number before “.”; If it is one of “0,1,2,3,4”, then round down. Only remain the number before “.”. Maybe I can create a loop section to let computer compare the number after “.” with “0~9”, then let it go through a “if…. else…”section to decide round up/down. However, it is not similar to my thinking patterns. I don’t use a loop section to solve this problem. I can easily combine the look of a string with the number it symbolizes. For me, number and string are just like two properties of one thing. However, for computers, properties of single things are processed separately.
The most direct way that computer takes is different than mine. In this algorithm, it adds every input “x” with 0.5 and takes the integer part of the result. I think this process reflects the original intention of doing rounding. “0.5” means half way of the “distance” between two integers. What computer does is moving “x” forward 0.5 unit to test whether it reaches the first integer larger than “x”.
Interestingly, It seems that I just ignores the very series of logical processes and always generate the output directly. I noticed that I tend to follow certain rules that directly link two objects and simplify the relationship between them. So the hardest part of using python language is not obtaining the very grammar, but creating a mode which matches computer’s “thinking pattern”. By doing this, I need to move away my eyes from “objects” and unfold the interrelationships among them.
“The Stack” shows different layers between users and the physical materials of network. The interface simulates the way human view the world. However, when the layers go deeper, things are presented in a way that more distant from natural language.
Before the Von Neumann architecture was created, program was not stored inside. Engineers had to rearrange hardware to run a new program. At this level, relationships in blackbox are exposed. But after that, it was still a period that engineers had to shoulder arduous work by dealing with endless “1” and “0”, which recorded slight different of changes in the machines. Then programming language was developed. On a slightly higher level is assembly language, which supply step-by-step instructions for the processor to carry out (White & Downs, 2007). On the higher end, languages such as C and Java allow programmers to write more closely parallel English (White & Downs, 2007). Complicated relationships are closured into various functions. And those functions can be called to other systems without clarifying how it works inside. The grouping of several individual sub-steps into a larger step is an example of abstraction (Conery, 2010). To me, the principle of functional abstraction (Hillis, 2013) lead computer to imitate human thinking pattern.
Creating new functions and term them with English words is just one aspect. At the same time, programmers symbolize series of relationships can create more “objects”. The creation of Wolfram Language also followed the law of the evolution of programming language. I think this new language is revolutionary, because we need no longer to teach computer the difference of “string”, “number” or other data types. Different features of one symbol are combined together.
The “names” of capital cities can work as text, number, locations of map, diagram and datas storing other information. They can be called in functions without clarifying the data type.
I think our brain has similar pattern of “Closure”. We perceive the world by letting subtle information passing through our eyes, ears, hands and other sensory organ. Special processes that wrote in our brain integrate the information and create a mode of the world by mapping objects. Some questions are generated by this reflection: Is it an evolutionary advantage of brain’s function of “information hiding” to closure relationships into objects? Can this function be connected to the definition of intelligence? Or is “ignoring relationship” merely a phenomenon caused by our using of language?
Works Cited
Conery, J. S. (2010). Ubiquity symposium’What is computation?’: Computation is symbol manipulation. Ubiquity2010(November), 4.
Hillis, D. (2013). The pattern on the stone. Hachette UK. P IX
White, R., & Downs, T. (2007). How computers work. Que Corp. P95-96
# Computers and Everyday Life
After watching the amusing example of the study lamps at Harvard University CS50 Introduction Computer Science Lectures, you rapidly understand the importance of the mathematical binary code structure of computers and also the intrinsic relationship between binary math and binary logic as the interface form between code and electronics (Irvine 3). However, as Daniel Hillis affirms, one of the most important things about a computers essential nature is that it transcends technology (8).
As Peter J. Denning states, the computational model of representation and transformation refocuses computation from computers to information processes (9). Therefore, as Denning defends, for a long time the approach of representing algorithms as the heart of computing and computational thinking has left aside other information processes also relevant in the computational field where no algorithms are used (9). The importance of computation is that it is not about math or machines, but rather it is a form of symbolic implementation and representation that can be implemented and repeated in other processes (Irvine). Moreover, Andrew Hodges argues that with the appearance of the universal Turing machine he was modeling the action of human minds (3). It is this change in how humans conceive computers that will enable our current integration of technological devices such as Apple technology as important tools of our everyday life.
As a user of Apple gadgets, I have become accustomed to direct and fast access to all my data on the ICloud. ICloud gives you access to this enormous database just by owning one Apple. Once you open an account and have entry to this storage database, all Apple devices synchronize at the same time allowing you to listen to any music, view photos, or use data that you have recently purchased either on your IPad, iPhone, or Macbook. Similarly, Google docs or Dropbox work in a comparable way. They allow customers to access and use their stored documents at any time from any device with an internet connection. Denning asserts that the subject of computation also embraces other areas whose definitions are not clear yet such as cloud computing which will have to continue to be analyzed and studied (10).
In the present time when technology has been incorporated into most of our everyday lives, computation is no longer about machines but about how these machines contribute to our lives in forms of social communication, working tools, and cultural representations of our society, community, families, and friends in a more globalized and interconnected world. Another great way to use artificial intelligence / robotics is for teaching purposes (the new TA´s) as seen in the attached news. This is just the beginning.
http://rt.com/news/iran-praying-robot-children-888/
Works Cited
Denning, Peter. “What is Computation.” Ubiquity. Nov. 2010. Web. 4 March 2014.
Harvard University CS50 Introduction Computer Science Lectures. Web. 3 March 2014.
Hillis, Daniel W. “Preface: Magic in the Stone.” The Pattern on the Stone: The Simple Ideas that Make Computers Work. NY: Basic Books, 1999.
Hodges, Andrew. “Turing: A natural philosopher” Alan Turing: one of The Great Philosophers. 1997. Web. 4 March 2014.
Irvine, Martin. “Computation: A very Basic Introduction to Foundational Concepts.” Media Theory Communication, Culture, and Technology Department, Georgetown U, Feb. 2014. Web. 4 March 2014.
# To code or not to code, that is the question
Computers are now part of our everyday life. Most households around the world have a personal computer in their homes used for their daily routines. Computers are such an integral part of our lives that all pieces of gadgetry are based on computing technology or in the interface design computers use to interact with their end-users.
Academics like Alan Turing have been intrigued by computers and their thought process. He dared to ask whether a machine could think. (Hodges, 1) Turing went as far as comparing the human spirit and the human thought process with computers, in one of his essays he claims: “when the body dies the “mechanism” of the body, holding the spirit is gone and the spirit finds a new body sooner or later perhaps immediatley”. (Hodges, 1)
To understand Turing´s line of thought and fully understand how computers work, we first have to establish a clear definition of what computation is. “Computation is a logical and mathematical process, typically modeled in an algorithm...” (Irvine, 1)
Algorithms give the right basis for understanding mathematics and physics. (Hodges, Turing Scrapbook, 6) Algorithms have helped society to accomplish great and daunting feats, they can be applied in all kinds of disciplines from bioengineering to music production. Algorithms have proven that computation has indeed become a process that people from around the world need to get used to and understand completely.
Computation is a process; a process that cannot come into fruition without learning some programming or “coding”. Coding is the language of computers, and with the proper code; computers can create any kind of application or program we can come up with. With some coding knowledge we can create revolutionary apps like Facebook or Google, we can build something that changes the world completely.
Nowadays, communication professionals and entrepreneurs that want to have a competitive advantage venture into the process of learning how to code.
While going through the courses in the Code Academy and Udacity websites, I was able to learn the coding language “Python” a simple coding language than can be used to build a lot of different things like applications, and even a search engine.
I think it’s a great learning to experience to get your hands on material of this quality. Learning some programming not only gives you the opportunity to learn more about the language of computers, but it also develops your ability to think “outside the box”.
If we had to compare the academical approach in both websites, i would certainly give Udacity the both of confidence. They use small Youtube videos in a very simple, and clear way to explain “Python” and the process to write this programming language.
Even though Udacity has in its Introduction to Computer Science material worth 7 weeks of learning, i was captivated by a statement they lead early on about natural languages are ambiguous.
The guys in the Udacity website are on to something. Without noticing they have open a debate about the meaning of words, how we encode information to a receiver and how are messages are built all around the world. This all happens with the hopes that by communicating, we cannot only change our thought process or how we speak but the world itself.
WORKS CITED
Martin Irvine, An Introduction to Computational Concepts Media Theory Communication, Culture, and Technology Department, Georgetown U, Feb. 2014. Web. 4 March 2014.
Andrew Hodges, Turing (Great Philosopher’s Series). London: Phoenix, 1997; New York: Routledge, 1999.
Andrew Hodges, Turing’s Online Scrapbook http://www.turing.org.uk/scrapbook/index.html
Why I Learned to Code and How you Can in 3 Months, Entrepreneur, http://www.entrepreneur.com/article/230241
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Oct 27 comment Sum of a set normalize by total items in set It's ok, I guess they are doing this for my good too. They want me to learn by myself through the hard way so that I will remember it by heart. Oct 27 comment Sum of a set normalize by total items in set I did say that "I have a set of weighted terms, $w_1, w_2$... but I included more information now. Oct 27 comment Sum of a set normalize by total items in set @BISHD I am more that happy to edit and learn and improve the answer so that it benefits everyone else too. But NO information provided to advise how/what should I improve? Oct 27 comment Sum of a set normalize by total items in set Thanks very much. Oct 27 comment Sum of a set normalize by total items in set For the guys who downvoted, that's very helpful. Thanks very much. Oct 27 comment Sum of a set normalize by total items in set I understand that, and $w$ is the individual item in $W$, what I want is to avoid using $W$ just because I want to show $\left | W \right |$ if it's possible Oct 27 comment Sum of a set normalize by total items in set I am cool to get a downvote like I said this is a simple question and I am clarifying it. But for the nice guy who downvoted would you be nice again and explain why do I get a downvote? Oct 27 comment Sum of a set normalize by total items in set $w$ is a set of weighted terms. Count of $w$ is total number of terms, i.e. $n$ Oct 16 comment Symbol for “if any” Thanks for your useful comment, it is more for an algorithm writing than mathematical writing. What I really want to mean is, if there exist $p_i$, where $length(p_i) = length(p) + 1$ and $p$ is a strict subset of $p_i$ Oct 16 comment Symbol for “if any” if $∃pi : length(pi) = length(p) + 1 ∧ p ⊏ pi ∧ support(p) = support(pi)$ ? Dec 20 comment Help on mathematical notation and formalisation for the following description Thanks a lot :) Dec 20 comment Help on mathematical notation and formalisation for the following description Thanks Hauke, I think I know the problem. It should be $\sum_{t \in p}$, if the sum is greater, means it is more important, does that make sense to you now? Dec 20 comment Help on mathematical notation and formalisation for the following description It is an unordered tuple, I found some papers that describe this if it is an ordered tuple, e.g. Wu et al. "Deploying approaches for pattern refinement in text mining" Dec 5 comment Set notation “element-of” multiple sets Yes that sounds good, I will begin with some discrete maths reading and move on from there, thanks! Dec 5 comment Set notation “element-of” multiple sets @PatrickDaSilva: No, I am particularly interested in mathematical notation and formalisation of algorithm (please let me know if it's still too vague) Dec 5 comment Set notation “element-of” multiple sets DylanMoreland: agree, @PatrickDaSilva:thanks. A bit newbie to mathematical notation and formalisation from a coder background. I was wondering is there any books on such topics or good material to learn? Dec 5 comment Set notation “element-of” multiple sets so there is no such thing as {$e \in X,Y$} I supposed?
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# cone geometric shape
Jul 11, 2016 · A cone is a tridimensional geometric shape formed by rotating a right-angled triangle around one of its sides. The circle formed by the other side is called the base of the cone, while the upper extremity is called the vertex. In this oneHOWTO article we'll show you, step by step, how to make a cone with paper.You will find it useful to explain geometry, to use as a container for candy or
• ### cone geometry simplified for the elementary student
Cone geometry at Elementary math level, only requires that your child can calculate the volume and the surface area of a cone. In general establishing the formula for these is not required. Your child simply needs to know the formula and how to use it to calculate area and volume. To do this, they MUST be comfortable identifying the different parts of the circl e, digits of Pi and calculating the area and …
• ### cone | math wiki | fandom
Template:This. A right circular cone and an oblique circular cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat, round base to a point called the apex or vertex.More precisely, it is the solid figure bounded by a plane base and the surface (called the lateral surface) formed by the locus of all straight line segments joining the apex to the perimeter of the base
• ### geometric shapes | definition, types, list and examples
Q.3. Is a cone a two-dimensional shape or a three-dimensional shape? Answer: A cone is a three-dimensional solid shape with a circular base and a single vertex. The surface of the cone is narrowed from the base to the vertex. Download BYJU’S- The Learning App and watch interactive videos. Also, take free tests to practise for exams
• ### spinning cone - math
An object shaped like a cone is said to be conical. A Cone is a Rotated Triangle. A cone can be made by rotating a triangle! The triangle is a right-angled triangle, and it gets rotated around one of its two short sides. The side it rotates around is the axis of the cone
• ### geometry: cylinders and cones - infoplease
A cone is named based on the shape of its base. Figure 21.5 shows a circular cone. Circular cones fall into one of two categories: right circular cones and oblique circular cones. A right circular cone is a circular cone where the line segment connecting the apex of the cone to the center of the circular base is perpendicular to the plane of
• ### geometric shapes and their symbolic meanings
Jul 08, 2019 · Geometric shapes—triangles, circles, squares, stars—have been part of human religious symbolism for thousands of years, long before they became part of scientific endeavors and construction projects by the Egyptians and Greeks.The simplest shapes are found in nature and are used by many different cultures around the world to represent a wide variety of meanings
• ### geometricalshapes| types ofshapes| examples
The Geometrical Shapes or figures that have three dimensions i.e., width, length, and thickness is called 3D Shapes or Solid Shapes. Some of the examples for the solid shapes are Cylinder, Cone, Sphere, Cube, Cuboid, etc. Types of 2D Shapes, Names & their Definition Types of 3D Shapes, Names & their Definition
• ### cone geometric vector images(over 3,400)
The best selection of Royalty Free Cone Geometric Vector Art, Graphics and Stock Illustrations. Download 3,400+ Royalty Free Cone Geometric Vector Images
• ### volume ofcone- formula, derivation and examples
A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all the points on a base that is in …
• ### cone geometrysimplified for the elementary student
Cone geometry at Elementary math level, only requires that your child can calculate the volume and the surface area of a cone. In general establishing the formula for these is not required. Your child simply needs to know the formula and how to use it to calculate …
• ### 11real life examples of cone– studiousguy
A number of cone-shaped pieces of equipment and instruments are present in our homes, place we work, laboratories, etc. Let’s understand more about cones and its examples in real life. Cone is a three-dimensional geometrical structure that tapers smoothly from flat base to a point called apex or vertex
• ### list of different types ofgeometric shapeswith pictures
It is a cone-shaped structure, but instead of an apex, a circle is present at one end. A comprehensive knowledge of geometric shapes and figures is very important, especially if one has an inclination towards this sub-field of mathematics. Also, one must learn to follow the different mathematical rules that are needed while drawing geometrical
• ### geometricalshapes| types ofshapes| examples
3D Shapes (Three Dimensional Shapes) or Solid Shapes; The Geometrical Shapes or figures that have three dimensions i.e., width, length, and thickness is called 3D Shapes or Solid Shapes. Some of the examples for the solid shapes are Cylinder, Cone, Sphere, Cube, Cuboid, etc
• ### listof geometric shapes and their names| science trends
Oct 09, 2018 · The geometric shapes and their names below give you a general sense of what you will find in any given geometry classroom. Intuitively, one can think of shape as a set of lines that enclose a space. According to this intuitive understanding, the shape of an object is the external form or appearance of an object in space that can be represented
• ### geometric shape- crossword answers, clues, definition
Synonyms, crossword answers and other related words for GEOMETRIC SHAPE [cone] We hope that the following list of synonyms for the word cone will help you to finish your crossword today. We've arranged the synonyms in length order so that they are easier to find. 3 letter words COP 4 letter words CASE - CONE - CYME - FILE - HEAD - HORN 5 letter
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Believe it or not, most of our writers didn't enter the world sporting an @baseballprospectus.com address; with a few exceptions, they started out somewhere else. In an effort to up your reading pleasure while tipping our caps to some of the most illuminating work being done elsewhere on the internet, we'll be yielding the stage once a week to the best and brightest baseball writers, researchers and thinkers from outside of the BP umbrella. If you'd like to nominate a guest contributor (including yourself), please drop us a line.
Andrew Gelman is a professor of statistics and political science at Columbia University. He occasionally blogs on baseball, including here, here, here, and here.
I read my first Bill James book in 1984, took my first statistics class in 1985, and began graduate study in statistics the next year. Besides giving me the opportunity to study with the best applied statistician of the late 20th century (Don Rubin) and the best theoretical statistician of the early 21st (Xiao-Li Meng), going to graduate school at Harvard in 1986 gave me the opportunity to sit in a basement room one evening that October with about 20 other students, screaming at the TV, "Put Stapleton in!" Unfortunately, John McNamara didn't hear us, and the rest was history.
I'm much less of a sports fan than I used to be, but the lessons I've learned from reading the Baseball Abstracts have done much to form me as a statistician. James doesn't write much about statistical methods in any general sense—he comes up with what he needs to solve any particular problem—but from his practice one can extract some general principles:
• Methodological pluralism: Rather than try to come up with a single number or a single approach to summarizing player abilities, team strategies, or any other topic, he tried out a bunch of different ideas. In statistics, I like to say that each substantive hypothesis deserves its own analysis: it's generally hopeless to expect that you can run a single regression and pull off the answers to each of your research questions, one coefficient at a time.
• Controlled comparisons: Instead of comparing simple aggregates, be more careful and make comparisons on pairs or groups of similar players or teams. As economists Rajeev Dehejia and Sadek Wahba demonstrated in a pair of influential articles (they have been cited over 2400 times since their publication a decade ago), these comparisons work only when you are controlling for appropriate characteristics. In the case of Bill James's analysis, player age is typically a key comparison variable. From the standpoint of applied statistics, controlled comparisons combine the averaging that you get from having a moderate or large sample size with the insight that comes from understanding individual cases.
• Conceptual models used as guides to comparisons: James has written many times that he does not study statistical questions, he studies baseball questions. Each analysis is grounded in some goal. A conceptual model such as the defensive spectrum, or the narrowing of abilities, or the contribution of speed to both offense and defense, drives the direction of the study and motivates many of the details of the analysis. I have tried to follow these principles in my own work.
One central method of statistics that Bill James does not draw upon very often (if at all) is fitting parametric models. For example, James found that the power two in the Pythagorean prediction for wins worked pretty well. He didn't try to estimate the power from data, nor did he, for example, try to come up with a conclusion such as, "each additional run is worth 0.093 wins." On the rare occasions that he did estimate a parameter (for example, the relative values of stolen bases and times caught stealing), he buried his methodology and had no interest in making a big deal about the estimation.
Fitting models is something that statisticians are trained to do and in fact do all the time. Why didn't Bill James follow the example of Pete Palmer and others and try to estimate the relative values of walks, singles, doubles, and other outcomes? I can't really say, but perhaps he felt that the formulas he used, such as runs created, which generally relied on few (if any) estimated parameters, worked well enough.
James's most famous number may be 27—his estimate of the age at which the typical player (including the typical superstar) reaches his peak. James has explained, illustrated, and justified this number in various places, but I've never seen him set it up as a statistical estimation problem: "find the value where the average curve hits its peak." He just doesn't seem to think that way. A statistician would naturally want to estimate the form of the curve (possibly using a nonparametric method such as a spline), estimate the peak, and then see how this peak varies over time, position on the field, player ability, and other measurable factors.
There is a mathematical reason, perhaps, for a Jamesian reticence about estimating parameters. It goes like this. Consider some curve (for example, the rising and then falling curve of ability for a single or average player, plotted vs. age). It will have some peak. At the peak, the curve will be flat (mathematically, it has zero derivative) and, as a result, the precise location of the peak in time will be difficult to specify. If a player is expected to have maximum ability around age 27, his actual best season might occur at 25 or 28, or even 35, perhaps. Even with averages it can be difficult to spot the exact peak. So perhaps it is better to come up with a reasonable number such as 27, check that it works with the data, and then use it as a baseline to think about the occasional shooting stars who peak early and the drug-assisted sluggers who have their statistically best years in their late thirties.
Another thing that I do all the time, but that James almost never seems to do, is make graphs. He loves looking at numbers but seems to avoid any and all chances to make scatter plots, line plots, and the rest. This may be simply a matter of taste. Two exercises in which I often use graphs are (1) checking and cleaning data, and (2) exploratory analysis—finding patterns in data beyond what is explained by my existing models. It's possible that James is so in touch with his data that he can do all the checking and cleaning just by looking at the numbers—he thinks of each data point as its own unique person or event rather than merely as one point in a distribution. If so, it may be that the Bill Jameses of the world can do their exploratory data analysis by looking at numbers, but the rest of us may benefit from graphical displays.
My two favorite Bill James lines:
• When someone wrote asking him to look into some idea or another, James replied, "I'm not a public utility. If you care so much about this, do the analysis yourself."
• Responding to a comment by some humanist type who was yammering on about how there are all sorts of truths that aren't in the numbers, James pointed out that the alternative to good statistics is not "no statistics," it's bad statistics. People who argue against statistical reasoning often end up backing up their arguments with whatever numbers they have at their command, over- or under-adjusting in their eagerness to avoid anything systematic.
I also love how he sprinkles his writing with commonsensical but non-obvious points. For example, when talking about a player being replacement level, he points out that this is not an insult—if you're "replacement-level," you're good enough to play for one of the best baseball teams in the world. Finally, I appreciate James's focus on defining players based on what they can do rather than what they can't. These are insights that don't sound like much in isolation but pack a punch when coming at the end of a statistical analysis.
Let me conclude this appreciation by listing a few things that Bill James has written that baffle me. One of the lessons of statistics, as with science in general, is that we can learn from anomalies. What are some of James's anomalies—those items he has written (or not written) that surprise me?
Quantitative analysis of baseball can take many directions. James has always focused on the decisions of a team's management: which players to hire or let go, what positions to play them at, when to platoon a hitter or rest a pitcher, when to yank a starter and put in a reliever, whether to save your best reliever for "save" situations. Related are other recurrent themes such as rating players or teams, adjusting for park effects, and estimating the offensive value of stolen bases.
But there are other quantitative aspects to the game. I think it's just as well that James has not tried to estimate what factors predict player compensation—I couldn't care less about this one, and I get bored when I open the newspaper and find that the entertainment page or the sports page has become the financial page—but it's notable that he hasn't written much about the topic, especially given his extensive experience in arbitration meetings.
Another much-studied topic in baseball is game strategy. James has occasionally written about when it's advisable to bunt and when a team should use a pinch-hitter, but I haven't seen him spend much time on calculations such as, "If you have a man on second with one out, you can expect to get 1.2 runs," those Markov chain analyses that are a natural part of the sabermetrician's trade. I wonder why James has not written more about these analyses—is it just because others have done it well, so he feels no need to duplicate the effort?
Similarly, I've never seen James write much about strategies within a plate appearance. If a pitcher has a few different pitches, should he just throw them at random? Or does it makes sense to be more likely to throw a fastball (say) on the first pitch? Which sorts of pitches are more likely to be fouled off, and by how much? I realize that I'm demonstrating my ignorance by even asking these questions in this way; my point here is that I'm surely not the only person whose knowledge of sabermetrics is bounded by the Baseball Abstracts at one end and Moneyball at the other, and I'm surprised that James never seemed interested in tackling these questions systematically. I'm not demanding or even asking that he do so (see the "public utility" quote above), just curious that he hasn't done so already.
A similar line of study concerns a batter's choices. In one of his books, James remarked that if you swing at more pitches, you're likely to end up with fewer walks but a higher batting average. This makes sense, but I'd be interested in seeing a more systematic analysis, along with related issues such as when it makes sense to let a first pitch go by, and how effective is the strategy of having a batter who can exhaust the pitcher by fouling off pitch after pitch after pitch. (That last strategy has always seemed a bit unsportsmanlike to me, but that's another story.) Again, I'm not saying that James should do this or that analysis, just wondering about his choices of what to focus on. He seems more comfortable reimagining the decisions of a team's general manager than thinking about the microdecisions of individual players.
Bill James is now one of the biggest names in baseball, but he used to be an outsider. The very first article in his 1984 Baseball Abstract is called "Inside-Out Perspective," and it expresses his opinion that when studying baseball it is better not to be too close to the individual players and outcomes: "There will be in this book no new tales about the things that happen on a team flight, no sudden revelations about the way that drugs and sex and money can ruin a championship team. I can't tell you what a locker room smells like, praise the Lord. But perspective can be gained only when details are lost…"
Things have changed, though. By the time the updated edition of his Historical Abstract came out, in 2001, James was writing, "Are athletes special people? In general, no, but occasionally, yes. Johnny Pesky at 75 was trim, youthful, optimistic, and practically exploding with energy. You rarely meet anybody like that who isn't an ex-athlete—and that makes athletes seem special." I've met 75-year-olds like that, and none of them was an ex-athlete. That's probably because I don't know a lot of ex-athletes. But Bill James…he knows a lot of athletes. He went to the bathroom with Tim Raines once! The most I can say is that I saw Rickey Henderson steal a couple bases in a game against against the Orioles.
Cognitive psychologists talk about the base-rate fallacy, which is the mistake of estimating probabilities without accounting for underlying frequencies. Bill James knows a lot of ex-athletes, so it's no surprise that the youthful, optimistic, 75-year-olds he meets are likely to be ex-athletes. The rest of us don't know many ex-athletes, so it's no surprise that most of the youthful, optimistic, 75-year-olds we meet are not ex-athletes. The mistake James made in the above quote was to write "You" when he really meant "I." I'm not disputing his claim that athletes are disproportionately likely to become lively 75-year-olds; what I'm disagreeing with is his statement that almost all such people are ex-athletes. Yeah, I know, I'm being picky. But the point is important, I think, because of the window it offers into the larger issue of people being trapped in their own environments (the "availability heuristic," in the jargon of cognitive psychology). Athletes loom large in Bill James's world—I wouldn't want it any other way—and sometimes he forgets that the rest of us live in a different world.
Just last month, James concluded an article in Slate on racism and society by writing, "this situation is not a failing of the sporting world. Rather, it is that the rest of society has been too proud to follow our lead." The ultimate outsider is now in the clubhouse.
I noted above that I like BIll James's methodological pluralism, his willingness to try out lots of ideas and get different insights using different methods. Sometimes, though, the results confuse me. For example, he's argued for decades that on-base percentage and slugging average are more informative than batting average and RBI—but then he provides the following four statistics for every player in his historical abstract: games played, home runs, RBI, and batting average. At the very least, why not give on-base percentage and runs scored? Similarly, James was really into the concept of "secondary average" for a few years before it seemed to disappear. I can't tell whether he decided it was a bad idea or simply became interested in other things.
My biggest Bill James puzzle involves batting order. Over and over he talks about bad leadoff men and great leadoff men and criticizes managers who lead off with a speedy "contact hitter" with a .280 OBP. Where to start? The 1985 Abstract features a long discussion of the San Diego Padres' lead-off problem and then continues a few pages later with a lengthy explication of James's frustration with managers who don't know how to set up a lineup.
But then, in his 1997 book on baseball managers, James looked at the subject one more time: "There is probably no subject within the province of managing which draws more comment than batting order…Let's start with the broadest question: How much difference would it make?" He ran a simulation (on the 1930 Cubs) and reported his results: "How much difference was there between the 'correct' batting order, and the same players in an obviously irrational order? Surprisingly enough, very little…50 runs per season [i.e., about 5 games, using the standard 10:1 conversion factor]…if the difference between a reasonable batting order and an unreasonable batting order is only 5%, what do you suppose would be the difference between two reasonable batting orders? That's right: it's nothing." James concludes his discussion in his usual pugnacious style: "Our model is far from perfect…But for now, this discussion has two groups. On the one hand, you have the barroom experts, the traditional sportswriters, the couch potatoes, and the call-show regulars, all of whom believe that batting orders are important. And then, on the other hand, you have a few of us who have actually studied the issue, and who have been forced to draw the conclusion that it doesn't make much difference what order you put the hitters in, they're going to score just as many runs one way as another. You can believe whoever you want to; it's up to you."
My question is, where does the Bill James of the Baseball Abstracts fit in to this scheme? It's perfectly fine—admirable, even—for him to change his mind on the importance of batting order, but it's odd that he doesn't acknowledge the shift. Was it actually okay all those years for those managers to be leading off with .250 hitters who never drew walks?
I don't want to conclude on a down note, though. It is only because Bill James's ideas, methods, and principles have influenced me so much and have burned themselves into my brain that I am aware of the places where he's changed. In statistics we like to say that God is in every leaf of every tree: whenever we work on any serious problem in a serious way, we find ourselves quickly thrust to the boundaries of what existing statistical methods can achieve.
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# Are electromagnetic waves in phase?
Contents
Electromagnetic waves consist of both electric and magnetic field waves. These waves oscillate in perpendicular planes with respect to each other, and are in phase.
## Are electric and magnetic fields in phase?
The magnetic field oscillates in phase with the electric field. In other words, a wave maximum of the magnetic field always coincides with a wave maximum of the electric field in both time and space. . Electromagnetic waves are clearly a type of transverse wave.
## Can we produce electromagnetic waves?
An electromagnetic wave can be created by accelerating charges; moving charges back and forth will produce oscillating electric and magnetic fields, and these travel at the speed of light.
## What are electromagnetic waves made of?
Definition of ‘Electromagnetic Waves’ Definition: Electromagnetic waves or EM waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric fields.
## How do you find the phase of a wave?
The Phase:
The phase of the wave is the quantity inside the brackets of the sin-function, and it is an angle measured either in degrees or radians. The important result here is that the two waves can be: (1) In phase if x2−x1=nλ, i.e the wave is doing exactly the same thing at such points along the x-axis.
## Can you have a magnetic field without an electric field?
No you can have a magnetic field without an electric field. Consider a rod with an equal number of positive and negative charges (such that they are equally spaced). Let the positive move to the left with speed v and the negative to the right with speed v. This will result in a magnetic field but no electric field.
## Is magnetic field a wave?
Electromagnetic waves consist of both electric and magnetic field waves. These waves oscillate in perpendicular planes with respect to each other, and are in phase. The creation of all electromagnetic waves begins with an oscillating charged particle, which creates oscillating electric and magnetic fields.
## Why electromagnetic wave can travel in vacuum?
An EM wave can travel without a material medium—that is, in a vacuum or space empty of matter—and does not lose energy as it moves. In theory, an EM wave can travel forever. Because they do not need a medium, EM waves can pass through outer space, which is a near vacuum.
## Can electromagnetic waves travel in a vacuum?
These changing fields form electromagnetic waves. Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.
IT IS INTERESTING: What is meant by electromagnetic damping?
## How fast electromagnetic waves travel?
Electromagnetic radiation is a type of energy that is commonly known as light. Generally speaking, we say that light travels in waves, and all electromagnetic radiation travels at the same speed which is about 3.0 * 108 meters per second through a vacuum.
## What are the 7 electromagnetic waves in order?
This range is known as the electromagnetic spectrum. The EM spectrum is generally divided into seven regions, in order of decreasing wavelength and increasing energy and frequency. The common designations are: radio waves, microwaves, infrared (IR), visible light, ultraviolet (UV), X-rays and gamma rays.
## What are the uses of the 7 electromagnetic waves?
Behaviour and uses of electromagnetic waves
• Microwaves. Microwaves are used for cooking food and for satellite communications. …
• Infrared. …
• Visible light. …
## Are electromagnetic waves harmful?
There is no doubt that short-term exposure to very high levels of electromagnetic fields can be harmful to health. … Despite extensive research, to date there is no evidence to conclude that exposure to low level electromagnetic fields is harmful to human health.
## What is the phase difference between two waves?
The phase difference between two sound waves of the same frequency moving past a fixed location is given by the time difference between the same positions within the wave cycles of the two sounds (the peaks or positive-going zero crossings, for example), expressed as a fraction of one wave cycle.
## What is the formula for calculating phase difference?
ΔΦ is the phase difference between two waves.
Phase Difference And Path Difference Equation.FormulaUnitPhase DifferenceDelta phi=frac{2piDelta x}{lambda }Radian or degreeЕщё 2 строки
IT IS INTERESTING: Do electromagnetic waves need matter to travel?
## What is the formula for calculating phase shift?
Now you can see that the phase shift will be π/2 units, not π units. So the phase shift, as a formula, is found by dividing C by B. For F(t) = A f(Bt – C) + D, where f(t) is one of the basic trig functions, we have: the amplitude is |A|
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304 North Cardinal St.
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# Iterables and Iterators Hacker Rank Solution – Queslers
## Problem: Iterables and Iterators Hacker Rank Solution
The itertools module standardizes a core set of fast, memory efficient tools that are useful by themselves or in combination. Together, they form an iterator algebra making it possible to construct specialized tools succinctly and efficiently in pure Python.
To read more about the functions in this module, check out their documentation here.
You are given a list of N lowercase English letters. For a given integer K, you can select any K indices (assume 1-based indexing) with a uniform probability from the list.
Find the probability that at least one of the K indices selected will contain the letter: ‘a’.
#### Input Format :
The input consists of three lines. The first line contains the integer N, denoting the length of the list. The next line consists of N space-separated lowercase English letters, denoting the elements of the list.
The third and the last line of input contains the integer K, denoting the number of indices to be selected.
#### Output Format :
Output a single line consisting of the probability that at least one of the K indices selected contains the letter:’a’.Note: The answer must be correct up to 3 decimal places.
#### Constraints :
• 1 <= N <= 10
• 1 <= K < = N
All the letters in the list are lowercase English letters.
4
a a c d
2
0.8333
#### Explanation :
All possible unordered tuples of length 2 comprising of indices from 1 to 4 are:(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)
Out of these 6 combinations, 5 of them contain either index 1 or index 2 which are the indices that contain the letter ‘a’.
### Iterables and Iterators Hacker Rank Solution in python 2
import math
def nCr(n,r):
f = math.factorial
return f(n) / f(r) / f(n-r)
N = input()
letters = raw_input().strip().split()
K = input()
N_a = letters.count('a')
if N_a == 0:
print '0'
elif N - N_a < K:
print '1'
else:
num = nCr(N - N_a, K)
denum = nCr(N, K)
print (denum - num) * 1.0 / denum
### Iterables and Iterators Hacker Rank Solution in python 3
# Enter your code here. Read input from STDIN. Print output to STDOUT
from itertools import combinations
N = int(input())
L = input().split()
K = int(input())
C = list(combinations(L, K))
F = filter(lambda c: 'a' in c, C)
print("{0:.3}".format(len(list(F))/len(C)))
### Iterables and Iterators Hacker Rank Solution in pypy
from __future__ import division
import itertools
n = int(raw_input())
alphas = raw_input().split()
k = int(raw_input())
checkSymbol = 'a'
combinations = list(itertools.combinations(alphas,k))
filtered = [cb for cb in combinations if checkSymbol in cb]
print len(filtered)/ len(combinations)
### Iterables and Iterators Hacker Rank Solution in pypy 3
from itertools import combinations
# Enter your code here. Read input from STDIN. Print output to STDOUT
n = int(input())
lst = [i for i in input().split()]
k = int(input())
a_indxs = {i for i in range(1, n + 1) if lst[i - 1] == 'a'}
a_num = 0
comb_len = 0
for comb in combinations(range(1, n + 1), k):
comb_len += 1
if set(comb) & a_indxs:
a_num += 1
print(a_num / comb_len)
##### Iterables and Iterators Hacker Rank Solution Review:
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http://data.allenai.org/tqa/determining_relative_ages_L_0124/
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# determining relative ages
## determining the relative ages of rocks
Stenos and Smiths principles are essential for determining the relative ages of rocks and rock layers. In the process of relative dating, scientists do not determine the exact age of a fossil or rock but look at a sequence of rocks to try to decipher the times that an event occurred relative to the other events represented in that sequence. The relative age of a rock then is its age in comparison with other rocks. If you know the relative ages of two rock layers, (1) Do you know which is older and which is younger? (2) Do you know how old the layers are in years? In some cases, it is very tricky to determine the sequence of events that leads to a certain formation. Can you figure out what happened in what order in (Figure 1.1)? Write it down and then check the following paragraphs. The principle of cross-cutting relationships states that a fault or intrusion is younger than the rocks that it cuts through. The fault cuts through all three sedimentary rock layers (A, B, and C) and also the intrusion (D). So the fault must be the youngest feature. The intrusion (D) cuts through the three sedimentary rock layers, so it must be younger than those layers. By the law of superposition, C is the oldest sedimentary rock, B is younger and A is still younger. The full sequence of events is: 1. Layer C formed. 2. Layer B formed. A geologic cross section: Sedimentary rocks (A-C), igneous intrusion (D), fault (E). 3. Layer A formed. 4. After layers A-B-C were present, intrusion D cut across all three. 5. Fault E formed, shifting rocks A through C and intrusion D. 6. Weathering and erosion created a layer of soil on top of layer A. Click image to the left or use the URL below. URL:
## instructional diagrams
No diagram descriptions associated with this lesson
## questions
the relative age of a rock is
``````a) the age of the rock in years.
--> b) the age of the rock relative to other rocks and geologic structures.
c) the age of the rock as determined by radiometric dating.
d) all of these.
``````
the _ rock unit lies beneath the __ rock units above it.
``````a) sedimentary; igneous
b) igneous; sedimentary
--> c) older; younger
d) younger; older
``````
if a fault cuts a rock sequence that fault is
``````--> a) younger than the rock sequence.
b) older than the rock sequence.
c) the same age as the rock sequence.
d) of an unknown age relative to the rock sequence.
``````
older rocks lie above the younger rocks.
``````a) true
--> b) false
``````
in the geologic cross section in the concept, intrusion d cuts across rock layers c and b. rock layer b and intrusion d are offset by fault e. what are the relative ages of these features from older to younger?
``````a) fault e, intrusion d, rock layer b, rock layer c
b) rock layer c, rock layer b, fault e, intrusion d
c) intrusion d, fault e, rock layer b, rock layer c
--> d) rock layer c, rock layer b, intrusion d, fault e
``````
a fault can cut through three or more sedimentary rock layers.
``````--> a) true
b) false
``````
in the geologic cross section in the concept, the last thing to happen in the sequence was
``````a) the laying down of sedimentary rock layer c.
b) the igneous intrusion d.
c) the fault e.
--> d) the erosion of the surface.
``````
a fault offsets three older sedimentary rock layers. this displays the principle of
``````a) horizontality.
--> b) cross-cutting relationships.
c) lateral continuity.
d) faunal succession.
``````
a fault can shift rocks so that the layers no longer match up.
``````--> a) true
b) false
``````
if we learn the succession of geological events in a region, it only tells us about that region and does not apply to other locations.
``````a) true
--> b) false sources figure 1: ck-12: http://www.ck12.org/earth-science/determining-relative- ages/lesson/determining-relative-ages/
``````
## diagram questions
No diagram questions associated with this lesson
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http://math.stackexchange.com/questions/6616/metric-and-topological-structures-induced-by-a-norm
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Metric and Topological structures induced by a norm
While proving that some normed spaces were complete, two questions came to my mind. They relate the topological and the metric structures induced by a norm.
1) Is it possible to find two equivalent norms $\|\cdot\|_1$ and $\|\cdot\|_2$ on a vector space $V \$ such that $(V \ ,\|\cdot\|_1)$ is complete and $(V \ ,\|\cdot\|_2)$ is not?
2) Is there a vector space $V \$ and two non-equivalent norms such that $V \$ is complete relative to both?
Here I'm assuming $V \$ a vector space over a subfield of $\mathbb{C}$. Also I know that the answer is no if we only consider finite-dimensional vector spaces.
[Edit: I'm considering two norms equivalent if they define the same topology. I think it's the usual notion Jonas referred in his comment.]
-
Regarding completeness, this notion actually only depends on $V$ as a topogolical vector space. (We can say that $v_n$ is a Cauchy sequence if for any neighbourhood $U$ of $0$, there is a natural number $N$ such that $v_n \in U$ if $n \geq N$.) This explains why the notion of Cauchy sequence, and hence the notion of completeness, is independent of any particular norm defining the given topology on $V$. – Matt E Oct 12 '10 at 19:59
V has no chance of being complete unless it's a vector space over a complete subfield of C (so C or R), assuming the usual norm on C. – Qiaochu Yuan Oct 12 '10 at 20:21
Dear Nuno, There is an intermediate notion between topological spaces and metric spaces, namely uniform spaces. These are spaces in which it makes sense to make uniform statements such as "for sufficiently large $m$ and $n$ the elements $x_m$ and $x_n$ are arbitrarily close", they key point being that we have a notion of what "close means" for any pair of points. (In a metric space we can do this, by asking that $d(x,y) < \epsilon$. In a general topological space, we can't do this: if we fix $x$ then we can use neighbourhoods of $x$ to say that $y$ is close to $x$, but we can't ... – Matt E Oct 13 '10 at 0:02
... compare the sizes of neighbourhoods of different points, and so we can't have a notion of closeness which applies to a pair $x,y$ when both $x$ and $y$ are allowed to vary.) If $G$ is a topological group (e.g. a topological vector space) then it automatically becomes a uniform space, because we can measure closeness by choosing a neighbourhood $U$ of the identity, and then say that $x$ and $y$ are close if $x y^{-1}$ lies in $U$. (Here I am using multiplicative notation for the operation in $G$.) Another way to think of this is that we can use translation by group elements ... – Matt E Oct 13 '10 at 0:05
... to move the neighbourhood $U$ around: e.g. $Uy$ is a neighbourhood of $y$, and $x$ and $y$ are "$U$-close" if $x \in Uy.$ In other words, in the presence of the group operation, which allows us to move points around, we can compare the size of neighbourhoods of different points. – Matt E Oct 13 '10 at 0:06
1) No. It is straightforward to show that equivalent norms yield both the same convergent sequences and the same Cauchy sequences. (Written before Rasmus's answer was posted, but posted afterward.)
2) Yes. One way to see this is to note that isomorphism classes of vector spaces depend only on linear dimension, so the question amounts to finding 2 nonisomorphic Banach spaces of the same linear dimension. There are lots of examples of these. Every infinite dimensional separable Banach space has linear dimension $2^{\aleph_0}$. However, for example, $\ell^1$ and $c_0$ are separable Banach spaces that are not isomorphic (as Banach spaces).
Actually, "amounts to" wasn't quite accurate. It is certainly sufficient that the 2 Banach spaces are not isomorphic, but it is not necessary because you are only asking that one particular map (the identity in the original formulation) is not an isomorphism. So what I gave above is actually stronger. To just answer 2), you could just take any infinite dimensional Banach space and induce a new norm via an unbounded linear isomorphism with itself.
The answer above was assuming that equivalent norms are defined as in this PlanetMath article. If instead you meant only that the spaces are homeomorphic in the norm topologies, as Jyotirmoy Bhattacharya suspected, then the examples alluded to above won't work. However, there are also examples of pairs of Banach spaces that have the same linear dimension but are not homeomorphic, and this will work in either case. For example, $\ell^\infty$ and $c_0$ are not homeomorphic because $\ell^\infty$ is nonseparable. Both spaces have linear dimension $2^{\aleph_0}$. This was already mentioned for $c_0$, and for $\ell^\infty$ it follows because $c_0$ embeds in $l^\infty$ (which gives the lower bound on dimension) and because the cardinality of $\ell^\infty$ is $2^{\aleph_0}$ (which gives the upper bound).
(I'm now pretty sure this isn't what you want, based on your edit, but this still gives another example for the actual question as well as an answer to Jyotirmoy's comment.)
Incidentally, another way to see that $2^{\aleph_0}$ is a lower bound for the linear dimensions of $\ell^1$ and friends is to consider the linearly independent set $\{(1,t,t^2,t^3,\ldots):0\lt t\lt 1\}$. Cardinality of the spaces gives an upper bound.
-
That was the easy part anyway. =) – Rasmus Oct 12 '10 at 17:29
In (2), shouldn't we be looking at homeomorphisms since the OP is interested in topological equivalence? And isn't it then the case that all separable Banach spaces are homeomorphic to $l_2$ and hence to each other and therefore at least for separable spaces the answer to (2) is "No"? – Jyotirmoy Bhattacharya Oct 12 '10 at 18:55
Good question. I assumed the usual notion of equivalent norms, and I don't think it is clear in the question. I'd ask for clarification, but I'll be away from computer for several hours starting now. – Jonas Meyer Oct 12 '10 at 18:57
Thanks for this nice answer! About the first one, it was a lapse of memory. I forgot that property with constants characterizes equivalent norms. The other one I was expecting some counterexamples and I liked your approach. – Nuno Oct 12 '10 at 19:35
@Jyotirmoy: Sorry I didn't fully understand your question, so would you mind reformulating it assuming that I'm not well-versed in functional analysis? – Nuno Oct 12 '10 at 19:54
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# 0.17 tonne per metric teaspoon [t/metric tsp] in long tons per liter
## tonnes/metric teaspoon to long ton/liter unit converter of density
0.17 tonne per metric teaspoon [t/metric tsp] = 33.46 long tons per liter [long tn/l]
### tonnes per metric teaspoon to long tons per liter density conversion cards
• 0.17
through
24.17
tonnes per metric teaspoon
• 0.17 t/metric tsp to long tn/l = 33.46 long tn/l
• 1.17 t/metric tsp to long tn/l = 230.3 long tn/l
• 2.17 t/metric tsp to long tn/l = 427.15 long tn/l
• 3.17 t/metric tsp to long tn/l = 623.99 long tn/l
• 4.17 t/metric tsp to long tn/l = 820.83 long tn/l
• 5.17 t/metric tsp to long tn/l = 1 017.67 long tn/l
• 6.17 t/metric tsp to long tn/l = 1 214.51 long tn/l
• 7.17 t/metric tsp to long tn/l = 1 411.35 long tn/l
• 8.17 t/metric tsp to long tn/l = 1 608.19 long tn/l
• 9.17 t/metric tsp to long tn/l = 1 805.03 long tn/l
• 10.17 t/metric tsp to long tn/l = 2 001.88 long tn/l
• 11.17 t/metric tsp to long tn/l = 2 198.72 long tn/l
• 12.17 t/metric tsp to long tn/l = 2 395.56 long tn/l
• 13.17 t/metric tsp to long tn/l = 2 592.4 long tn/l
• 14.17 t/metric tsp to long tn/l = 2 789.24 long tn/l
• 15.17 t/metric tsp to long tn/l = 2 986.08 long tn/l
• 16.17 t/metric tsp to long tn/l = 3 182.92 long tn/l
• 17.17 t/metric tsp to long tn/l = 3 379.77 long tn/l
• 18.17 t/metric tsp to long tn/l = 3 576.61 long tn/l
• 19.17 t/metric tsp to long tn/l = 3 773.45 long tn/l
• 20.17 t/metric tsp to long tn/l = 3 970.29 long tn/l
• 21.17 t/metric tsp to long tn/l = 4 167.13 long tn/l
• 22.17 t/metric tsp to long tn/l = 4 363.97 long tn/l
• 23.17 t/metric tsp to long tn/l = 4 560.81 long tn/l
• 24.17 t/metric tsp to long tn/l = 4 757.65 long tn/l
• 25.17
through
49.17
tonnes per metric teaspoon
• 25.17 t/metric tsp to long tn/l = 4 954.5 long tn/l
• 26.17 t/metric tsp to long tn/l = 5 151.34 long tn/l
• 27.17 t/metric tsp to long tn/l = 5 348.18 long tn/l
• 28.17 t/metric tsp to long tn/l = 5 545.02 long tn/l
• 29.17 t/metric tsp to long tn/l = 5 741.86 long tn/l
• 30.17 t/metric tsp to long tn/l = 5 938.7 long tn/l
• 31.17 t/metric tsp to long tn/l = 6 135.54 long tn/l
• 32.17 t/metric tsp to long tn/l = 6 332.38 long tn/l
• 33.17 t/metric tsp to long tn/l = 6 529.23 long tn/l
• 34.17 t/metric tsp to long tn/l = 6 726.07 long tn/l
• 35.17 t/metric tsp to long tn/l = 6 922.91 long tn/l
• 36.17 t/metric tsp to long tn/l = 7 119.75 long tn/l
• 37.17 t/metric tsp to long tn/l = 7 316.59 long tn/l
• 38.17 t/metric tsp to long tn/l = 7 513.43 long tn/l
• 39.17 t/metric tsp to long tn/l = 7 710.27 long tn/l
• 40.17 t/metric tsp to long tn/l = 7 907.12 long tn/l
• 41.17 t/metric tsp to long tn/l = 8 103.96 long tn/l
• 42.17 t/metric tsp to long tn/l = 8 300.8 long tn/l
• 43.17 t/metric tsp to long tn/l = 8 497.64 long tn/l
• 44.17 t/metric tsp to long tn/l = 8 694.48 long tn/l
• 45.17 t/metric tsp to long tn/l = 8 891.32 long tn/l
• 46.17 t/metric tsp to long tn/l = 9 088.16 long tn/l
• 47.17 t/metric tsp to long tn/l = 9 285 long tn/l
• 48.17 t/metric tsp to long tn/l = 9 481.85 long tn/l
• 49.17 t/metric tsp to long tn/l = 9 678.69 long tn/l
• 50.17
through
74.17
tonnes per metric teaspoon
• 50.17 t/metric tsp to long tn/l = 9 875.53 long tn/l
• 51.17 t/metric tsp to long tn/l = 10 072.37 long tn/l
• 52.17 t/metric tsp to long tn/l = 10 269.21 long tn/l
• 53.17 t/metric tsp to long tn/l = 10 466.05 long tn/l
• 54.17 t/metric tsp to long tn/l = 10 662.89 long tn/l
• 55.17 t/metric tsp to long tn/l = 10 859.73 long tn/l
• 56.17 t/metric tsp to long tn/l = 11 056.58 long tn/l
• 57.17 t/metric tsp to long tn/l = 11 253.42 long tn/l
• 58.17 t/metric tsp to long tn/l = 11 450.26 long tn/l
• 59.17 t/metric tsp to long tn/l = 11 647.1 long tn/l
• 60.17 t/metric tsp to long tn/l = 11 843.94 long tn/l
• 61.17 t/metric tsp to long tn/l = 12 040.78 long tn/l
• 62.17 t/metric tsp to long tn/l = 12 237.62 long tn/l
• 63.17 t/metric tsp to long tn/l = 12 434.47 long tn/l
• 64.17 t/metric tsp to long tn/l = 12 631.31 long tn/l
• 65.17 t/metric tsp to long tn/l = 12 828.15 long tn/l
• 66.17 t/metric tsp to long tn/l = 13 024.99 long tn/l
• 67.17 t/metric tsp to long tn/l = 13 221.83 long tn/l
• 68.17 t/metric tsp to long tn/l = 13 418.67 long tn/l
• 69.17 t/metric tsp to long tn/l = 13 615.51 long tn/l
• 70.17 t/metric tsp to long tn/l = 13 812.35 long tn/l
• 71.17 t/metric tsp to long tn/l = 14 009.2 long tn/l
• 72.17 t/metric tsp to long tn/l = 14 206.04 long tn/l
• 73.17 t/metric tsp to long tn/l = 14 402.88 long tn/l
• 74.17 t/metric tsp to long tn/l = 14 599.72 long tn/l
• 75.17
through
99.17
tonnes per metric teaspoon
• 75.17 t/metric tsp to long tn/l = 14 796.56 long tn/l
• 76.17 t/metric tsp to long tn/l = 14 993.4 long tn/l
• 77.17 t/metric tsp to long tn/l = 15 190.24 long tn/l
• 78.17 t/metric tsp to long tn/l = 15 387.08 long tn/l
• 79.17 t/metric tsp to long tn/l = 15 583.93 long tn/l
• 80.17 t/metric tsp to long tn/l = 15 780.77 long tn/l
• 81.17 t/metric tsp to long tn/l = 15 977.61 long tn/l
• 82.17 t/metric tsp to long tn/l = 16 174.45 long tn/l
• 83.17 t/metric tsp to long tn/l = 16 371.29 long tn/l
• 84.17 t/metric tsp to long tn/l = 16 568.13 long tn/l
• 85.17 t/metric tsp to long tn/l = 16 764.97 long tn/l
• 86.17 t/metric tsp to long tn/l = 16 961.82 long tn/l
• 87.17 t/metric tsp to long tn/l = 17 158.66 long tn/l
• 88.17 t/metric tsp to long tn/l = 17 355.5 long tn/l
• 89.17 t/metric tsp to long tn/l = 17 552.34 long tn/l
• 90.17 t/metric tsp to long tn/l = 17 749.18 long tn/l
• 91.17 t/metric tsp to long tn/l = 17 946.02 long tn/l
• 92.17 t/metric tsp to long tn/l = 18 142.86 long tn/l
• 93.17 t/metric tsp to long tn/l = 18 339.7 long tn/l
• 94.17 t/metric tsp to long tn/l = 18 536.55 long tn/l
• 95.17 t/metric tsp to long tn/l = 18 733.39 long tn/l
• 96.17 t/metric tsp to long tn/l = 18 930.23 long tn/l
• 97.17 t/metric tsp to long tn/l = 19 127.07 long tn/l
• 98.17 t/metric tsp to long tn/l = 19 323.91 long tn/l
• 99.17 t/metric tsp to long tn/l = 19 520.75 long tn/l
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SWEETENED CORN PUFF CEREAL WITH REAL PEANUT BUTTER, PEANUT BUTTER, UPC: 042400221029 weigh(s) 42.27 gram per (metric cup) or 1.41 ounce per (US cup), and contain(s) 433 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
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CaribSea, Freshwater, Instant Aquarium, Torpedo Beach weighs 1 505.74 kg/m³ (94.00028 lb/ft³) with specific gravity of 1.50574 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
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#### Weights and Measurements
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#### Calculators
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# ELEVATOR PHYSICS
ELEVATOR PHYSICS.
Télécharger la présentation
## ELEVATOR PHYSICS
E N D
### Presentation Transcript
1. ELEVATOR PHYSICS
2. A passenger of mass m= 72.2 kg stands on a bathroom scale in an elevator. What are the scale readings when the cab is stationary, when it is moving up and moving down?(a) Find the general equation for the scale reading, whatever the vertical motion of the cab.(b) What does the scale read if the cab is stationary or moving upward at a constant 0.50 m/s?(c) What does the scale read if the cab accelerates upward at 3.20 m/s2 and downward at 3.20 m/s2 ?
3. (a) To determine the apparent weight (Fapp), first we find all of the forces in the y direction: Ʃ Fy = Fapp + FW Then we use Newton's Second Law. may = Fapp + mg Then solve for F Fapp = may – mg = m (ay-g) This works no matter what the acceleration is for the cab. (b) When the acceleration is zero, Fapp = (72.2 kg) (0 - -9.8m/s2) = 708 N This is just the weight of the passenger when the elevator is at rest or moving with a constant velocity. (c) When the acceleration is directed upward, Fapp = (72.2 kg) (3.2m/s2 - -9.8m/s2) = 939 N When the acceleration is directed downward, Fapp = (72.2 kg) (-3.2m/s2 - -9.8m/s2) = 477 N
4. DESIGNATION OF FORCES IN A FREE BODY DIAGRAM FA = applied force FN = normal force; Force which is perpendicular to the surfaces in contact FW = weight of the object; this is always directed downward FT = force as it is acting on a rope or a wire
5. Neglecting friction, determine the normal force and horizontal force needed to accelerate a 25 kg grocery cart from rest to a velocity of 0.45 m/s in 1.35 s. Given: m= 25 kg Vix = 0 Vfx = 0.45 m/s t = 1.35 s Find FN and FA The cart has no vertical motion since there is no unbalanced force along the y-axis. FW + FN = 0 FN = - FW FN = -(25kg)(-9.8 m/s2) FN = 245 N FN FA 25 kg FW
6. To solve for the acceleration: a = Vfx-Vix = 0.45 m/s – 0 m/s = 0.33 m/s2 t 1.35 s To solve for the applied force, FA: FA= m a = (25 kg) (0.33 m/s2 ) = 8.25 N
7. A 20-kg bag is being pulled along the floor by a tourist with a force of 50 N. The force is applied on the handle that forms an angle of 30o with the horizontal. What is the acceleration of the bag? How much force is exerted by the floor on the bag if friction is neglected?
8. Given: m = 20 kg FA = 50 N at 30 o from horizontal Find a and FN FA FN FAy 20 kg 30 o Solve for the FAx and FAy FAx = FA cos θ = (50 N) (cos 30 o) = 43.3 N FAy = FA sin θ = (50 N) (sin 30 o) = 25 N FAx FW
9. FA FN a = FAx= 43.3 N = 2.17 m/s 2 m 20 kg FAy 20 kg 30 o FAx FW All forces along the y-axis: FN + FAy + FW= 0 FN = - FW – FAy = - (20kg)(-9.8 m/s2) – 25 N = 196 N – 25 N = 171 N
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# Question Video: Using Polynomial Division to Solve Problems Mathematics • 10th Grade
Use polynomial division to simplify (6𝑥³ + 5𝑥² − 20𝑥 − 21)/(2𝑥 + 3).
03:53
### Video Transcript
Use polynomial division to simplify six 𝑥 cubed plus five 𝑥 squared minus 20𝑥 minus 21 over two 𝑥 plus three.
One method we do have for simplifying algebraic fractions is to factor where necessary. It’s not particularly straightforward to factor this cubic on our numerator. So instead, we’re going to recall that this line in a fraction actually just means divide. And we’re going to use polynomial long division. Our dividend, that’s the numerator of our fraction, goes inside the bus stop. The divisor, that’s the denominator, goes on the outside.
And then, we remember the first thing that we do is we take the first term in our dividend, that’s six 𝑥 cubed, and we divide it by the first term in our divisor, that’s two 𝑥. Six divided by two is three. Then, if we consider 𝑥 as being 𝑥 to the power of one, we know that we can subtract these exponents. And 𝑥 cubed divided by 𝑥 to the power of one is 𝑥 squared. This means that six 𝑥 cubed divided by two 𝑥 must be three 𝑥 squared.
Our next step is to multiply three 𝑥 squared by each term in our divisor. Three 𝑥 squared times two 𝑥 is six 𝑥 cubed. Notice that this is the same as the first term in our dividend, so we know we’ve probably started this correctly. We then calculate three times three 𝑥 squared. Well, that’s nine 𝑥 squared. Our next step is to subtract six 𝑥 cubed plus nine 𝑥 squared from six 𝑥 cubed plus five 𝑥 squared. Six 𝑥 cubed minus six 𝑥 cubed is zero. We don’t really need to write this zero. And then, five 𝑥 squared minus nine 𝑥 squared is negative four 𝑥 squared. We bring down the next term. Some people bring down all of the terms, but I prefer to keep things a little bit simpler.
And we’re now going to divide negative four 𝑥 squared by two 𝑥. Negative four divided by two is negative two. 𝑥 squared divided by 𝑥 to the power of one is 𝑥. So, negative four 𝑥 squared divided by two 𝑥 is negative two 𝑥. And we add negative two 𝑥 above five 𝑥 squared in our problem. Now, we multiply negative two 𝑥 by each term in our divisor. Two 𝑥 multiplied by negative two 𝑥 is negative four 𝑥 squared, and negative two 𝑥 times three is negative six 𝑥.
We then subtract each of these terms from negative four 𝑥 squared minus 20𝑥. Negative four 𝑥 squared minus negative four 𝑥 squared is negative four 𝑥 plus four 𝑥 squared. So that’s zero, and we don’t really need to write that. We then do negative 20𝑥 minus negative six 𝑥. That’s negative 20𝑥 plus six 𝑥, which is negative 14𝑥. We bring down negative 21. And we’re now going to divide negative 14𝑥 by two 𝑥. 𝑥 divided by 𝑥 is just one. So, we get negative 14 divided by two, which is negative seven. So, we add negative seven here. And once again, we divide this number by each term in our divisor. Negative seven times two 𝑥 is negative 14𝑥, and negative seven times three is negative 21.
We do one final subtraction, and this is a really important step to do because it tells us whether there’s a remainder or not. In fact, negative 14𝑥 minus 21 minus itself is just zero. And so, we’ve completed the division. When we simplify our algebraic fraction, we’re left with three 𝑥 squared minus two 𝑥 minus seven.
Now, at this stage, it’s really useful just to discuss briefly how we might check our solution. We perform an inverse operation. We take our quotient, here that’s the solution to the division, and multiply that by the divisor, remembering, of course, that the divisor is the algebraic expression here that we’re dividing by. We multiply three 𝑥 squared minus two 𝑥 minus seven by two 𝑥 plus three. And when we do, we should get the numerator, or the dividend.
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# Random field, homogeneous
A random field $X ( s)$ defined on a homogeneous space $S = \{ s \}$ of points $s$ equipped with a transitive transformation group $G = \{ g \}$ of mappings of $S$ into itself, and having the property that the values of the statistical characteristics of this field do not change when elements of $G$ are applied to their arguments. One distinguishes two different classes of homogeneous random fields: $X ( s)$ is called a homogeneous random field in the strict sense if for all $n = 1 , 2 \dots$ and $g \in G$, the finite-dimensional probability distribution of its values at any $n$ points $s _ {1} \dots s _ {n}$ coincides with that of its values at $g s _ {1} \dots g s _ {n}$. If ${\mathsf E} | X ( s) | ^ {2} < \infty$ and ${\mathsf E} X ( s) = {\mathsf E} X ( g s )$, ${\mathsf E} X ( s) \overline{ {X ( s _ {1} ) }}\; = {\mathsf E} X ( g s ) \overline{ {X ( g s _ {1} ) }}\;$ for all $s , s _ {1} \in S$ and $g \in G$, then $X ( s)$ is called a homogeneous random field in the wide sense.
An important special case is that of a homogeneous random field on a $k$- dimensional Euclidean space $\mathbf R ^ {k}$( or on the lattice $\mathbf Z ^ {k}$ of points of $\mathbf R ^ {k}$ with integral coordinates), where $G$ is the group of all parallel translations. Sometimes the term "homogeneous random field" is reserved for a field of this type. A homogeneous random field on $\mathbf R ^ {k}$, with $G$ the group of all isometric transformations of $\mathbf R ^ {k}$( generated by parallel translations, rotations and reflections) is often called an isotropic homogeneous random field.
The concept of a homogeneous random field is a natural generalization of that of a stationary stochastic process: in both cases, the field and the covariance function admit a spectral decomposition (cf. Spectral decomposition of a random function) of special kind (see, for example, [1][5]). Homogeneous random fields and some of their generalizations often arise in questions of an applied nature. In particular, in the statistical theory of turbulence, an important role is played by isotropic homogeneous (scalar and vector) random fields on $\mathbf R ^ {k}$, as well as by so-called simultaneously locally homogeneous and locally isotropic random fields (that is, fields with homogeneous and isotropic increments), which are simple generalizations of isotropic homogeneous fields (see [4], for example). Moreover, in the modern theory of physical quantum fields and in statistical physics there are applications of the theory of generalized homogeneous random fields, which include homogeneous random fields as a special case (see Random field, generalized).
#### References
[1] A.M. Yaglom, "Second-order homogeneous random fields" , Proc. 4-th Berkeley Symp. Math. Stat. Probab. , 2 , Univ. California Press (1961) pp. 593–622 [2] E.J. Hannan, "Group representations and applied probability" , Methuen (1965) [3] M.I. Yadrenko, "Spectral theory of random fields" , Optim. Software (1983) (Translated from Russian) [4] A.S. Monin, A.M. Yaglom, "Statistical fluid mechanics" , 2 , M.I.T. (1975) (Translated from Russian) [5] A.M. Yaglom, "Correlation theory of stationary and related random functions" , 1–2 , Springer (1987) (Translated from Russian)
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p38_033
# p38_033 - 33. (a) Using K = me c2 ( 1) (Eq. 38-49) and me...
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33. (a) Using K = m e c 2 ( γ 1) (Eq. 38-49) and m e c 2 = 511 keV = 0 . 511 MeV (Table 38-3), we obtain γ = K m e c 2 +1= 1 . 00 keV 511 keV +1=1 . 00196 . Therefore, the speed parameter is β = r 1 1 γ 2 = r 1 1 1 . 00196 2 =0 . 0625 . (b) We could Frst Fnd β and then Fnd γ , as illustrated here: With K =1 . 00 MeV, we Fnd β = s 1 µ 1 . 00 MeV 0 . 511 MeV +1 2 =0 . 941 and γ =1 / p 1 β 2 =2 . 96. (c) ±inally, K = 1000 MeV, so
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## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
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# Kolmogorov-Smirnov test
(Redirected from Kolmogorov–Smirnov test)
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2010 Mathematics Subject Classification: Primary: 62G10 [MathSciNet]
A non-parametric test used for testing a hypothesis , according to which independent random variables have a given continuous distribution function , against the one-sided alternative : , where is the mathematical expectation of the empirical distribution function . The Kolmogorov–Smirnov test is constructed from the statistic
where is the variational series (or set of order statistics) obtained from the sample . Thus, the Kolmogorov–Smirnov test is a variant of the Kolmogorov test for testing the hypothesis against a one-sided alternative . By studying the distribution of the statistic , N.V. Smirnov [1] showed that
(1)
where and is the integer part of the number . Smirnov obtained in addition to the exact distribution (1) of its limit distribution, namely: If and , then
where is any positive number. By means of the technique of asymptotic Pearson transformation it has been proved [2] that if and , then
(2)
According to the Kolmogorov–Smirnov test, the hypothesis must be rejected with significance level whenever
where, by virtue of (2),
The testing of against the alternative : is dealt with similarly. In this case the statistic of the Kolmogorov–Smirnov test is the random variable
whose distribution is the same as that of the statistic when is true.
#### References
[1] N.V. Smirnov, "Approximate distribution laws for random variables, constructed from empirical data" Uspekhi Mat. Nauk , 10 (1944) pp. 179–206 (In Russian) [2] L.N. Bol'shev, "Asymptotically Pearson transformations" Theor. Probab. Appl. , 8 (1963) pp. 121–146 Teor. Veroyatnost. i Primenen. , 8 : 2 (1963) pp. 129–155 [3] L.N. Bol'shev, N.V. Smirnov, "Tables of mathematical statistics" , Libr. math. tables , 46 , Nauka (1983) (In Russian) (Processed by L.S. Bark and E.S. Kedrova) [4] B.L. van der Waerden, "Mathematische Statistik" , Springer (1957)
#### Comments
There is also a two-sample Kolmogorov–Smirnov test, cf. the editorial comments to Kolmogorov test and, for details, [a1], [a2].
#### References
[a1] G.E. Noether, "A brief survey of nonparametric statistics" R.V. Hogg (ed.) , Studies in statistics , Math. Assoc. Amer. (1978) pp. 39–65 [a2] M. Hollander, D.A. Wolfe, "Nonparametric statistical methods" , Wiley (1973)
How to Cite This Entry:
Kolmogorov–Smirnov test. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Kolmogorov%E2%80%93Smirnov_test&oldid=22659
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# Hydrostatic Pressure in a cube
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November 25, 2012, 08:20 Hydrostatic Pressure in a cube #1 New Member Join Date: Oct 2012 Posts: 14 Rep Power: 7 Dear Foamers, I would like to understand how to implement hydrostatic pressure on a wall. I am a beginner with OF. For that, I created a simple cube mesh: Code: ```convertToMeters 1; vertices ( (0 0 0) (0 0 1) (0 1 1) (0 1 0) (1 0 0) (1 0 1) (1 1 1) (1 1 0) ); blocks ( hex (0 1 2 3 4 5 6 7) (40 40 40) simpleGrading (1 1 1) ); edges ( ); boundary ( walls { type wall; faces ( (0 1 2 3) (4 5 6 7) (4 0 1 5) (5 6 2 1) (7 6 2 3) (4 7 3 0) ); } );``` I want the hydrostatic pressure, so I used buoyantPressure for p: Code: ```dimensions [0 2 -2 0 0 0 0]; internalField uniform 0; boundaryField { walls { type buoyantPressure; value uniform 0; } }``` The velocity type is pressureInletVelocity and the value is uniform(0 0 0). I also created a g folder in "constant": Code: ```FoamFile { version 2.0; format ascii; class uniformDimensionedVectorField; location "constant"; object g; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // dimensions [0 1 -2 0 0 0 0]; value ( 0 0 -9.81 );``` The fluid is not supposed to move since it is a closed cube. I don't know exactly what solver should I use but it seems that pisoFoam is ok. So here is the fvSolution: Code: ```solvers { p { solver PCG; preconditioner DIC; tolerance 1e-06; relTol 0; } U { solver PBiCG; preconditioner DILU; tolerance 1e-05; relTol 0; } } PISO { nCorrectors 2; nNonOrthogonalCorrectors 0; pRefCell 0; pRefValue 0; }``` And for the fvSchemes, I used an existing one: Code: ```ddtSchemes { default Euler; } gradSchemes { default Gauss linear; grad(p) Gauss linear; } divSchemes { default none; div(phi,U) Gauss linear; } laplacianSchemes { default none; laplacian(nu,U) Gauss linear corrected; laplacian((1|A(U)),p) Gauss linear corrected; } interpolationSchemes { default linear; interpolate(HbyA) linear; } snGradSchemes { default corrected; } fluxRequired { default no; p ; }``` Here are the TransportProperties: Code: ```nu nu [ 0 2 -1 0 0 0 0 ] 0.01; transportModel Newtonian;``` Here is the terminal response: Code: ```--> FOAM FATAL IO ERROR: keyword div((nuEff*dev(T(grad(U))))) is undefined in dictionary "/home/ubuntu/openfoam/simu/cube/system/fvSchemes::divSchemes"``` I don't know what model should I use for div((nuEff*dev(T(grad(U))))? Or maybe it is a wrong solver for a simple case like that? Thank you for your help!
November 25, 2012, 16:53 #2 Member Florian Join Date: Nov 2009 Posts: 59 Rep Power: 10 I don't know if pisoFoam is right solver for this kind of problem. For the error message you posted, simple add this expression to the divSchemes dictionary or set a default entry, e.g. Code: ```divSchemes { default Gauss linear; div(phi,U) Gauss linear; div((nuEff*dev(T(grad(U))))) Gauss linear; }```
November 26, 2012, 04:42 #3 New Member Join Date: Oct 2012 Posts: 14 Rep Power: 7 Thank you for your answer! I added that line in the fvSchemes, as well as the Code: `laplacian(nuEff,U) Gauss linear corrected;` in the laplacianSchemes. Still, the terminal doesn't find the "g" folder: Code: ```--> FOAM FATAL ERROR: request for uniformDimensionedVectorField g from objectRegistry region0 failed available objects of type uniformDimensionedVectorField are 0 ( )``` Where is the objectRegistry region0? I tried to copy/paste the g in all the folders (0,constant,system) still doesn't work. Thanks for your help!
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# Reproductive isolation in artificial panspermia model
Simulation of artificial panspermia, in inter-galactic travel, as a model for the study of reproductive isolation.
# Case 1:
If we send a mass of proto cells(kept alive by some mechanism like cryogenic freezing powered by some perpetual engine) to another far galaxy's habitable planet, such that the cells are subject constant variations in its surroundings( the cryogenic system is made up of a material that transmits 99.9% of the incoming radiation like the the radiation of stars, and the cells are subject to gravitational wave radiations, relativistic speeds and so on), and set up early-earth-like conditions in a constructed area in the the new planet where the cells can grow into another human, (just like they did during the early evolution on Earth); would there exist a reproductive isolation between a human on Earth and the new Homo sapiens( say their new name to be- Homo galaxiants) if they tried to sexually reproduce?
Assumption: Our species survive during the travel of the cells. We, on Earth remain unevolved from the time the cells leave the Earth till the time a Homo galaxiant matures.The pollution levels, the climatic conditions, the species richness, rate of consumption, radiation of the Sun, etc., all remain the same on Earth so that the DNA can be subject to the same conditions both for an organism on Earth and for the travelling mass of cells( although this is subject to additional changes en route).
• How long does it take to travel to this far-away galaxy? Dec 1, 2016 at 7:18
• Please ask only one question per question. Also, how do you imagine cell colony to grow into a human? Our cells can't do it. We need mothers. Dec 1, 2016 at 7:20
• @kingledion assuming the Andromeda galaxy, and moving with relativistic speeds of 99.9% the speed of light, it would take: $\approx{25.4}$ centuries. Dec 1, 2016 at 12:06
• @NaveenBalaji so you want to send some proto cells, which will evolve step by step into other forms and then possibly into human? Your question states it in a style like you would send human cells directly. You probably might consider editing it, so it is clearly stated. Dec 1, 2016 at 12:10
• Evolution does not work that way! Elephant's nose is one way to grab things, human arm is another and which one, if any, is dependent on many things, including random. Dec 1, 2016 at 15:09
# There can only be so much change before the DNA becomes non-viable
2500 years of mutating space radiation would be bad for cells. If humans were living and reproducing for 2500 years, then that would be a 100 generations. In each generation, some mutations would be viable and be passed on, and others would not be viable and die off. If the radiation level were high, then genetic drift could conceivably happen quickly.
However, if you are sending the people as a pile of cells, then all those mutations will happen at the same time to the sperm/egg cells of a new human. Each new human would have 100x as many changes to their DNA. Will all those changes be viable? Seems unlikely. Even if you get 99 good changes for better sight, hearing, stamina, whatever, it only takes one cystic fibrosis or spina bifida to ruin the new person.
Therefore, if you sent cells across the galaxy, either they would need to be shielded from radiation, or the resulting humans would probably not be viable.
In conclusion, the only way to make your humans valid in a far off galaxy is to ensure they are only one generation of changes away from the humans who sent them on earth. Thus the only changes will be the genetic drift of 2500 years for those who remained on Earth. And that just isn't that much.
Evolution is not repeatable. If they make it to the destination alive the cells will evolve, but the chance of their evolution resulting in animals resembling us is vanishingly small.
But in fact, without going into details, a strong argument can be made that the reduction of 100 initial possibilities to ten or so was the analogue of a bingo game, a grand-scale lottery. In fact any ten of the 100 could have made it. If you could rewind the tape of life, erasing what actually happened and let it run again, you'd get a different set of ten each time. There are 17 trillion different combinations of 10 that you can take from a group of 100. (Stephen Jay Gould, famous paleontologist, in an interview for the American Academy of Achievement)
Yes they would be reproductively isolated.
Why do I think so? Well, bats and birds can't interbreed, and neither can dolphins and sharks, and each pair have evolved in worlds with exactly the same early-earth conditions, to fulfill roles which are exceedingly similar to their other half (two animals evolved for flying, two evolved for swimming, of similar size and shape and similar sorts of "successes" I guess would be my term, and yet totally different). Even better, they share the same historical conditions with exacting precision, and a fair chunk of familial resemblance from their very-base level processes from their shared ancestors, which is above and beyond what your question requires :)
And so, if bipedal hairless monkeys evolve again from this simulation, to fit the niche of thinking predators who adapt the environment to them rather than the reverse and then tinker with the world... they would probably have less in common with human-people than a bird and a bat have in common. Evolving flight (and evolving into all the niches) is probably not more of an overlapping niche, or indeed more of a specialization, than what human-people have done.
Evolution on earth was driven by a lot, a lot of factors - including geography, local conditions, and each other. Some of which are factors we don't know. some of which are factors we can't recreate or influence, and some of which are factors tightly correlated with adapting to changing circumstances (again, including each other). we can't even run a stimulation of earth's historical conditions without running into patches where we're not exactly sure what was going on or which factors led to which results, and you would as a preliminary starter need to be able to perfectly reproduce them.
If you sent an exact replica of (early) earth, accurately programmed to change for every variable earth underwent - including cosmic radiation, precise light and gravity fluctuations, minutiae of geography including volcanic eruptions and tetonic movement, extinction events (and who/what survived and didn't), meteors and such, the moon - you still could not guarantee humans, because you can't monitor interactions of the evolving creatures with each other enough to insure evolution stayed "on course", and if you could any intervention would be "taken advantage of" or, hm, adapted around, to change the actual results.
The godling of the simulation favors primates, so now you have a thousand and a half extra primate species that survived thanks to its intervention - oops. Or else it knows dinosaurs are supposed to evolve and then go extinct, except it was juust a leeetle bit too good, and the predecessors to alligators, or some other lizards, or birds, now didn't survive, either - oops. Ah, wait, it knows that horses are gonna be really important, better make sure they don't get lost - and horses can now afford to be a little slower, a touch more arrogant, taking advantage of this invisible protection instead of getting better, and we end up with non-domesticable unicorns or thirteen extra species of zebra, instead of the horses we could breed for work and travel.
And in all those altered initial conditions and interactive shenanigans, the precursors to humans never get off the ground, or become something slightly different, and whatever ends up taking the human-people's niche (if, indeed, anything ever does) need not be any more closely related to us than a dolphin is to a shark just because they both swim and eat fish and can't stay still underwater too long or without drowning.
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# How To Calculate Discount
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### How to calculate Dividend Discount models (DDM)
(Last saved: \$2.00) Jun 11, 2021 · The formula to calculate: Dividend discount formula. represent the Intrinsic value. E ( ) represent Expected Future Value. D & P denotes dividends and Stock Price respectively. Thus this means. the expected dividends payout for year 5 of your holding period &means what your expectation for the stock to be valued at after 5 years has passed.
### How to Calculate a Discount and Sale Price | Math with Mr. J
(Last saved: \$5.00) Welcome to How to Calculate a Discount and Sale Price with Mr. J! Need help with calculating discounts and sale prices? You're in the right place!Whether you...
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### Discount Calculator: See Price Before Discount, After Discount
(Last saved: \$3.00) To calculate the discount percentage taken off your item, follow these steps: Find the original price of the item before the discount. Find the price of the item after the discount was applied. Subtract the after-discount price from the original price. Divide that by …
### How to Calculate Bond Premium or Discount? (Explained)
(Last saved: \$4.00) Bond premium or (Bond discount) = Issue price – Face value. If the above formula returns a positive value, the issuer issued the bond at a premium. In contrast, the bond discount will apply when the face value is higher than the issue price. However, bond premiums and discounts do not apply to this scenario often.
### Calculating Discounts - Percentage, Formula | How to Calculate?
(Last saved: \$5.00) Following are the listed formulas we use while calculating discounts. Discount = Listed Price - Selling Price Selling Price = Listed Price − Discount Listed Price = Selling Price + Discount If a discount is expressed as a percentage (rate) in that case, the discount formula is: Discount = Listed Price × Discount Rate
### Discount Calculator - Find Out the Sale Price
(Last saved: \$4.00) Mar 10, 2022 · To calculate the percentage discount between two prices, follow these steps: Subtract the post-discount price from the pre-discount price. Divide this new number by the pre-discount price. Multiply the resultant number by 100. Be proud of your mathematical abilities. What are fake discounts?
### Discount Factor (Meaning, Formula) | How to Calculate?
(Last saved: \$3.00) Discount Factor Calculator. Discount Rate. Number of Compounding Periods. Number of Years. Discount Factor Formula =. Discount Factor Formula =. 1 + ( Discount Rate / Number of Compounding Periods) −Number of Compounding Periods * Number of Years. 1 + ( 0 / 0) −0 * 0 =.
### Calculate the forward discount or premium for the following spot …
(Last saved: \$1.00) May 28, 2022 · 6. Calculate the forward discount or premium for the. following spot and three-month forward rates: (a) SR = SF2/¤1 and SF2.02/¤1 where SF is. the Swiss franc and ¤ is the euro (b) SR = ¥200/\$1 and FR = ¥190/\$1. 7. Assume that SR = \$2/£1 and the three-month FR = \$1.96/£1. How can an importer who will have. to pay £10,000 in three months ...
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### How to calculate discount with percentage | DISCOUNT AND …
(Last saved: \$4.00) how to calculate discount with percentage | DISCOUNT AND DISCOUNT PERCENTAGEhow to calculate discount pecentagehow to calculate discount with percentage
### Discount Calculator | margincalculator.net
(Last saved: \$3.00) It is available at a 20% discount on a sale. It means the following: The amount that is being withdrawn from the MRP is 20*500/100 = Rs.100. The amount that the purchaser pays after the discount = MRP – Discounted Amount = 500 – 100= Rs.400. Savings to the purchaser because of the discount = Rs. 100.
### Discount Factor: Formula and Excel Calculator
(Last saved: \$4.00) Discount Factor = (1 + Discount Rate) ^ (– Period Number) And the formula can be re-arranged as: Discount Factor = 1 / (1 + Discount Rate) ^ Period Number. Either formula could be used in Excel; however, we will be using the first formula in our example as it is a bit more convenient (i.e., Excel re-arranges the formula itself in the first ...
### How to calculate discount in Excel | Basic Excel Tutorial
(Last saved: \$6.00) Nov 28, 2021 · 1. The first thing you will have to do is subtract the percentage discount given from 1. This implies that you will be... 2. Take the 89% and multiply it …
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### Discount Formula- Explanation, Solved Examples and FAQs
(Last saved: \$1.00) In terms of Mathematics, the formula for discount is represented as below, Discount = Marked Price – Selling Price OR Discount Percentage Formula = Marked Price × Discount Rate Other basis Discount formula are as below:- Discount = List Price - Selling Price Therefore Selling Price = List Price - Discount List Price = Selling Price + Discount
### How To Calculate Percentage Discount (%)
(Last saved: \$1.00) Discount Amount = Original Price – New Price After Discount = 1000 – 800 = 200 Now that we have the discount amount and the Original price, we can just feed …
### How to Calculate Percentage Discounts - study.com
(Last saved: \$2.00) Sep 22, 2021 · To calculate the discount percentage, first, the discount price needs to be determined. The discount price is equal to the difference between …
### Percentage Discount Calculator. Find Discounted Price …
(Last saved: \$3.00) discount = 100 * (original_price - discounted_price) / original_price Subtract the final price from the original price. Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages. How …
### Discounting Formula | Steps to Calculate Discounted Value …
(Last saved: \$4.00) Steps to Calculate Discounted Values. To calculate discounted values, we need to follow the below steps. Calculate the cash flows for the asset and timeline that is in which year they will follow. Calculate the discount factors for the respective years using the formula. Multiply the result obtained in step 1 by step 2.
### Discount Rate Formula: Calculating Discount Rate [WACC/APV]
(Last saved: \$4.00) Aug 16, 2019 · There are two primary discount rate formulas - the weighted average cost of capital (WACC) and adjusted present value (APV). The WACC discount formula is: WACC = E/V x Ce + D/V x Cd x (1-T), and the APV discount formula …
### How Do I Calculate a Discount Rate Over Time Using Excel?
(Last saved: \$1.00) May 20, 2022 · The Excel formula for calculating the discount rate. It's often used to calculate the interest rate for a loan or to determine the rate of return required to …
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### Discount Yield - Overview, How To Calculate, Usage
(Last saved: \$3.00) The components of the discount yield formula are as follows: (Face Value – Purchase Price) is the total discount amount applied to the face value of the bond. (Face Value – Purchase Price) / Face Value is the percentage value of the total discount on the bond to its face value. 360 / No. of Days (or Months) to Maturity is the number of days ...
### Discount Calculator | Calculate a Discount | Discount Online
(Last saved: \$1.00) Formula to calculate a discount. If you wish to calculate a discount manually (in your head, using a calculator or on paper) then you can use the following equation for discounts: (discount percentage * total value) / 100. Will this formula you can work out discounts. If you want to know the final value, subtract this answer from the initial value.
### How to calculate the Discount? - GeeksforGeeks
(Last saved: \$6.00) May 12, 2022 · Discount = Listed Price – Selling Price Calculating Discount Percentage Discounts can be expressed as an amount or as a percentage. When the price of an item is reduced and sold for less than its list price, it indicates that a discount has been provided.
### How To Calculate Discount and Sale Price - Math Goodies
(Last saved: \$3.00) Procedure: To calculate the discount, multiply the rate by the original price. To calculate the sale price, subtract the discount from original price.
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### Discount Calculator - Calculate Discounts Faster
(Last saved: \$3.00) Our discount calculator helps you to know your savings you can enjoy because of discounts. You can easily calculate the price that you have to pay, especially when the marked discount percentages are numbers such as 33%, 22%, etc. Enter the original price or MRP before the discount and the percentage discount that is being offered to you.
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# Plane
• The equation of the plane passing through a point A(\vec{a}) whose normal vector is \vec{n} is \vec{r}\cdot \vec{n}=\vec{a}\cdot \vec{n}
• The equation of plane passing through a point A(x1, y1, z1) and a, b, c are the direction ratios of normal is a(x − x1) + b(y − y1) + c(z − z1) = 0
• The equation of the plane which is at a distance d units from origin and whose normal vector is \vec{n} is \vec{r}\cdot \hat{n}=d where \hat{n}=\frac{\vec{n}}{|\vec{n}|}
• The equation of the plane which is at a distance d units from origin and a, b, c are direction ratios of normal is lx + my + nz = d
where l=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}, m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}, n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}
• The equation of the plane passing through the points A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1}\\ x_{3}-x_{1} & y_{3}-y_{1} & z_{3}-z_{1} \end{vmatrix}=0
• The equation of the plane passing through the point (x1, y1, z1) and parallel to the lines whose directions are (a1, b1, c1) and (a2, b2, c2) is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ a_{1} & b_{1} & c_{1}\\ a_{2} & b_{2} & c_{2} \end{vmatrix}=0
• The equation of the plane passig through the point (x1, y1, z1) and perpendicular to the two plane a1x + b1y + c1z + d1 = 0, and a2x + b2y + c2z + d2 = 0 is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ a_{1} & b_{1} & c_{1}\\ a_{2} & b_{2} & c_{2} \end{vmatrix}=0
• The equation of the plane containing two lines \frac{x-x_{1}}{a_{1}}=\frac{y-y_{1}}{ b_{1}}=\frac{z-z_{1}}{c_{1}} and \frac{x-x_{2}}{a_{2}}=\frac{y-y_{2}}{ b_{2}}=\frac{z-z_{2}}{c_{2}} is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ a_{1} & b_{1} & c_{1}\\ a_{2} & b_{2} & c_{2} \end{vmatrix}=0
• The equation of the plane passing through the points (x1, y1, z1), (x2, y2, z2) and parallel to the line whose directions are (a1, b1, c1) is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\ a_{1} & b_{1} & c_{1} \end{vmatrix}=0
• The equation of the plane passing through the points (x1, y1, z1), (x2, y2, z2) and perpendicular to the plane a1x + b1y + c1z + d1 = 0 is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\ a_{1} & b_{1} & c_{1} \end{vmatrix}=0
• The equation of the plane containing two parallel lines \frac{x-x_{1}}{a_{1}}=\frac{y-y_{1}}{ b_{1}}=\frac{z-z_{1}}{c_{1}} and \frac{x-x_{2}}{a_{1}}=\frac{y-y_{2}}{ b_{1}}=\frac{z-z_{2}}{c_{1}} is\begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\ a_{1} & b_{1} & c_{1} \end{vmatrix}=0
• The equation of the plane making intercepts a, b, c on the x, y, z - axis respectively is \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1
• The equation of the plane passing through the intersection of the two planes a1x + b1y + c1z + d1 = 0, and a2x + b2y + c2z + d2 = 0 is (a1x + b1y + c1z + d1) + λ (a2x + b2y + c2z + d2) = 0
• The equation of the plane passing through the intersection of the two planes \vec{r}\cdot \vec{n}_{1}=d_{1} and \vec{r}\cdot \vec{n}_{2}=d_{2} is \vec{r}\cdot (\vec{n}_{1}+\lambda \vec{n}_{2})=d_{1}+\lambda d_{2}
• The area of the triangle formed by the plane \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 with x-axis, y-axis is \frac{1}{2}|ab|
The area of the triangle formed by the plane \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 with y-axis, z-axis is \frac{1}{2}|bc|
The area of the triangle formed by the plane \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 with z-axis, x-axis is \frac{1}{2}|ca|
• The equation of the plane passing through the point (x1, y1, z1) and parallel to the plane ax + by + cz + d = 0 is a(x − x1) + b(y − y1) + c(z − z1) = 0
• The equation of xy-plane z = 0
The equation of yz-plane x = 0
The equation of zx-plane y = 0
• The equation of the plane passing through (x1, y1, z1) and parallel xy-plane is z = z1
The equation of the plane passing through (x1, y1, z1) and parallel yz-plane is x = x1
The equation of the plane passing through (x1, y1, z1) and parallel zx-plane is y = y1
• The equation of the palne midway between the planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is ax + by+cz\left(\frac{d_{1}+d_{2}}{2}\right)=0
• Equation of the plane parallel to x-axis is \frac{y}{b}+\frac{z}{c}=1
Equation of the plane parallel to y-axis is \frac{x}{a}+\frac{z}{c}=1
Equation of the plane parallel to z-axis is \frac{x}{a}+\frac{y}{b}=1
• The vector equation of the plane passing through a given point A(\vec{a}) and parallel to the vectors \vec{b},\vec{c} is [\vec{r}-\vec{a} \ \ \ \vec{b} \ \ \ \vec{c}] = 0
• The vector equation of the plane passing through origin and points \vec{b},\vec{c} is [\vec{r} \ \ \ \vec{b} \ \ \ \vec{c}]=0
### Part2: View the Topic in this video From 01:30 To 47:42
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1. In the vector form, equation of a plane which is at a distance d from the origin, and \hat{n} is the unit vector normal to the plane through the origin is \vec{r}\cdot\hat{n}=d.
2. Equation of a plane which is at a distance of d from the origin and the direction cosines of the normal to the plane as l, m, n is lx + my + nz = d.
3. The equation of a plane through a point whose position vector is \vec{a} and perpendicular to the vector \vec{N} is (\vec{r}-\vec{a}).\vec{N}=0.
4. Equation of a plane perpendicular to a given line with direction ratios A, B, C and passing through a given point (x1, y1, z1) is A(x − x1) + B(y − y1) + C(z − z1) = 0
5. Equation of a plane passing through three non collinear points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is \begin{vmatrix}x-x_{1} & y-y_{1} & z-z_{1}\\x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\x_{3}-x_{1} & y_{3}-y_{1} & z_{3}-z_{1} \end{vmatrix}=0
6. Vector equation of a plane that contains three non collinear points having position vectors \vec{a},\vec{b} \ and \ \vec{c} is(\vec{r}-\vec{a}).[(\vec{b}-\vec{a})\times (\vec{c}-\vec{a})]=0
7. Equation of a plane that cuts the coordinates axes at (a, 0, 0), (0, b, 0) and (0, 0, c) is \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1
8. Vector equation of a plane that passes through the intersection of planes \vec{r}\cdot \vec{n}_{1}=d_{1} and \vec{r}\cdot \vec{n}_{2}=d_{2} is \vec{r}\cdot \left(\vec{n}_{1}+\lambda \vec{n}_{2}\right)=d_{1}+\lambda d_{2}, where λ is any nonzero constant.
9. Vector equation of a plane that passes through the intersection of two given planes A1x + B1y + C1z + D1 = 0 and A2x + B2y + C2z + D2 = 0 is (A1x + B1y + C1z + D1) + λ(A2x + B2y + C2z + D2) = 0.
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# Confusing wiring configuration
#1
02-16-06, 12:34 PM
bigbillya
Visiting Guest
Posts: n/a
Confusing wiring configuration
We have recently purchased a new house and are not familiar with the wiring. We have been tripping a 20A circuit breaker when the switch is turned on to our outside lights. We have unwired the switches and here is what is in the (2) switch box. (2) Black / white / ground wires going into the box (probably chained into the box from somewhere else. (1) Black / White / ground wire going to a ceiling light ( which is one separate switch) and one Black / White / Red / Ground wire which went to the other switch for the outside light.
The wires are connected in the basement into a connection box. In that box, the whites were all connected together, the blacks were connected together and the one red wire was connected to the single wire leading to the outside light.
What is the proper wiring in the switch box for the two switches and why was the red wire from the outside light switch connected to the black wire leading to the physical outdoor lighe??
#2
02-16-06, 01:17 PM
Member
Join Date: Sep 2003
Location: Central New York State
Posts: 13,973
It would help us if you told us ALL the wires in all the boxes.
The red wire is the switched hot wire for the light.
It's hard to tell what ALL the wires are for since you didn't tell us what ALL the wires are.
The most likely scenario for the switch box is that the whites should be tied together. The black for the ceiling light should be tied to one switch. The red wire should be ties to the other switch. The other black wires should be wire nutted together and then connected to the input sides of both switches.
If the outside lights trip the breaker, the most likely cause is a short in that wire. What type of outside light is this?
#3
02-17-06, 05:59 AM
bigbillya
Visiting Guest
Posts: n/a
I think you have helped with the red wire. If I understand what you are talking about: The black wires which would be nutted together would have the one black wire from the black / red / white / ground wire, two black wires from the two unidentified wires in the box and two jumpers, one going to the outside light switch and one going to the ceiling light switch.
Can a red nut hold the (5) black wires we are talking about???
#4
02-19-06, 01:58 AM
Member
Join Date: Jan 2006
Location: PA
Posts: 1,909
Can a red nut hold the (5) black wires we are talking about???
Color alone doesn't tell you. You need to see the listings from the manufacturer. It sounds like you are talking about five 12 AWG wires.
No. Get a big blue wirenut or divide into three groups of three.
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ScientificConstants - Maple Programming Help
Home : Support : Online Help : Science and Engineering : Scientific Constants : Functions : ScientificConstants/GetConstants
ScientificConstants
GetConstants
list the full names or symbols of all physical constants
Calling Sequence GetConstants( 'names', 'derivedfrom'=Const )
Parameters
'names' - (optional); specify that the full names be returned Const - (optional) symbol; return physical constants that are derived from Const
Description
• The GetConstants() command returns an expression sequence containing the symbols of the physical constants in the ScientificConstants package.
• The GetConstants( 'names' ) command returns an expression sequence containing the full names of the physical constants in the ScientificConstants package.
• The GetConstants( 'derivedfrom'=Const ) command returns an expression sequence containing the symbols of the physical constants that are directly derived from the constant of name or symbol Const.
• The GetConstants( 'names', 'derivedfrom'=Const ) command returns an expression sequence containing the full names of the physical constants that are directly derived from the constant of name or symbol Const.
• The sequence of names or symbols is sorted alphabetically.
Examples
> $\mathrm{with}\left(\mathrm{ScientificConstants}\right):$
> $\mathrm{GetConstants}\left(\right)$
${\mathrm{A\left[r\right]\left(alpha\right)}}{,}{\mathrm{A\left[r\right]\left(d\right)}}{,}{\mathrm{A\left[r\right]\left(e\right)}}{,}{\mathrm{A\left[r\right]\left(h\right)}}{,}{\mathrm{A\left[r\right]\left(n\right)}}{,}{\mathrm{A\left[r\right]\left(p\right)}}{,}{{E}}_{{h}}{,}{F}{,}{G}{,}{{G}}_{{0}}{,}{{K}}_{{J}}{,}{{M}}_{{\mathrm{Earth}}}{,}{{M}}_{{\mathrm{Sun}}}{,}{{M}}_{{u}}{,}{{N}}_{{A}}{,}{{\mathrm{Φ}}}_{{0}}{,}{R}{,}{{R}}_{{\mathrm{Earth}}}{,}{{R}}_{{K}}{,}{{R}}_{{\mathrm{∞}}}{,}{{V}}_{{m}}{,}{{Z}}_{{0}}{,}{{a}}_{{0}}{,}{{a}}_{{e}}{,}{{a}}_{{\mathrm{μ}}}{,}{\mathrm{α}}{,}{b}{,}{c}{,}{{c}}_{{1}{,}{L}}{,}{{c}}_{{1}}{,}{{c}}_{{2}}{,}{e}{,}{{\mathrm{ε}}}_{{0}}{,}{g}{,}{{g}}_{{e}}{,}{{g}}_{{\mathrm{μ}}}{,}{{g}}_{{n}}{,}{{g}}_{{p}}{,}{{\mathrm{γ}}}_{{e}}{,}{{\mathrm{γ}}}_{{n}}{,}{{\mathrm{γ}}}_{{p}}{,}{{\mathrm{gamma_prime}}}_{{h}}{,}{{\mathrm{gamma_prime}}}_{{p}}{,}{h}{,}{\mathrm{ℏ}}{,}{k}{,}{{l}}_{{P}}{,}{{\mathrm{λ}}}_{{C}{,}{\mathrm{μ}}}{,}{{\mathrm{λ}}}_{{C}{,}{n}}{,}{{\mathrm{λ}}}_{{C}{,}{p}}{,}{{\mathrm{λ}}}_{{C}{,}{\mathrm{τ}}}{,}{{\mathrm{λ}}}_{{C}}{,}{{m}}_{{P}}{,}{{m}}_{{\mathrm{α}}}{,}{{m}}_{{d}}{,}{{m}}_{{e}}{,}{\mathrm{m\left[e\right]/m\left[mu\right]}}{,}{{m}}_{{h}}{,}{{m}}_{{\mathrm{μ}}}{,}{{m}}_{{n}}{,}{{m}}_{{p}}{,}{{m}}_{{\mathrm{τ}}}{,}{\mathrm{m\left[tau\right]c^2}}{,}{{m}}_{{u}}{,}{{\mathrm{μ}}}_{{0}}{,}{{\mathrm{μ}}}_{{B}}{,}{{\mathrm{μ}}}_{{N}}{,}{{\mathrm{μ}}}_{{d}}{,}{\mathrm{mu\left[d\right]/mu\left[e\right]}}{,}{{\mathrm{μ}}}_{{e}}{,}{\mathrm{mu\left[e\right]/mu\left[p\right]}}{,}{\mathrm{mu\left[e\right]/mu_prime\left[p\right]}}{,}{{\mathrm{μ}}}_{{\mathrm{μ}}}{,}{{\mathrm{μ}}}_{{n}}{,}{\mathrm{mu\left[n\right]/mu_prime\left[p\right]}}{,}{{\mathrm{μ}}}_{{p}}{,}{{\mathrm{mu_prime}}}_{{h}}{,}{\mathrm{mu_prime\left[h\right]/mu_prime\left[p\right]}}{,}{{\mathrm{mu_prime}}}_{{p}}{,}{{n}}_{{0}}{,}{{r}}_{{e}}{,}{\mathrm{σ}}{,}{{\mathrm{σ}}}_{{e}}{,}{{\mathrm{sigma_prime}}}_{{p}}{,}{{t}}_{{P}}$ (1)
> $\mathrm{GetConstants}\left(\mathrm{names},\mathrm{derivedfrom}=G\right)$
${\mathrm{Planck_length}}{,}{\mathrm{Planck_mass}}{,}{\mathrm{Planck_time}}$ (2)
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Section01
# Section01 - Physics 204A Class Notes Section 1 An...
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Physics 204A Class Notes 1-1 Section 1 – An Introduction to Physics 204A Section Outline 1. A Preview of Physics 2. A Preview of Phys 204A 3. The Scientific Method a. Observation b. Theory c. Prediction d. Experiment 4. Coordinate Systems 1. A Preview of Physics Physics tries to answer the same question every human has asked since the dawn of mankind: Why are we here? Physicists break this question down into two parts: What is the universe made of? Here is what we know: How do the parts interact? This is the topic we’ll begin to investigate in this class. The Four Fundamental Interactions Interaction Strength Example Gravitational 1 Solar System Electromagnetic 10 36 Hydrogen Atom Weak Nuclear 10 25 Beta Decay Strong Nuclear 10 38 Nuclear Stability Quarks neutrons and protons are made of quarks Leptons the electron is one type of lepton Matter (5%) Nearly all the stuff in our corner of the universe Dark Matter Causes stars on the outer edge of galaxies to rotate faster Dark Energy Causes the universe to expand at an ever increasing rate Universre
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Physics 204A Class Notes 1-2 Classical Mechanics Translation The motion of objects as a whole Rotation The spinning motion of objects Energy Momentum Force Kinematics Energy Angular Momentum Torque Kinematics 2. A Preview of Physics 204A How do the parts interact? A better way to ask the question is: What do objects do and why do they do it? These are the central questions of the study of Classical Mechanics. Kinematics describes what objects do. That is to say, kinematics describes motion. Interactions explain why objects do what they do. Interactions are described in terms of forces, torques, energy, momentum and angular momentum. During our study this semester, we will discover seven and only seven fundamental laws of physics: Newton's Laws of Motion explain the concept of force.
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## This note was uploaded on 03/11/2012 for the course PHYSICS 204A taught by Professor Kagan during the Fall '09 term at CSU Chico.
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