url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://www.mathworks.com/matlabcentral/cody/problems/262-swap-the-input-arguments/solutions/182449 | 1,505,880,947,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818686169.5/warc/CC-MAIN-20170920033426-20170920053426-00425.warc.gz | 832,937,984 | 11,505 | Cody
# Problem 262. Swap the input arguments
Solution 182449
Submitted on 28 Dec 2012 by Brandon Nipper
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
%% [q,r] = swapInputs(5,10); assert(isequal(q,10)); assert(isequal(r,5));
``` ```
2 Pass
%% [q,r] = swapInputs(magic(3), 'hello, world'); assert(isequal(q,'hello, world')); assert(isequal(r,magic(3)));
``` ```
3 Pass
%% [q,r] = swapInputs({}, NaN); assert(isnan(q)); assert(iscell(r) && isempty(r));
``` ``` | 180 | 591 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-39 | latest | en | 0.524549 |
https://celebrat.net/calendar/how-many-working-weeks-are-there-in-a-year-uk/ | 1,713,172,286,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816954.20/warc/CC-MAIN-20240415080257-20240415110257-00307.warc.gz | 141,184,459 | 25,849 | # How many working weeks are there in a year UK?
Other reforms have included the 28 holiday minimum per year, 20 minute breaks for each six hours worked, and a maximum average of 8 hours work in a 24-hour period for night-workers (the average is usually calculated over 17 weeks, but it can be over a longer period of up to 52 weeks if the workers and the employer ….
## How many weeks per year is full time?
Crunching the Numbers
Let’s start with the basics — 2080 hours in a person year is equivalent to one person, working 40 hours a week for 52 weeks in a year. To be even more accurate, perhaps even to an annoying degree, 2087 hours would take into account leap years.
### How do you calculate working days in a year?
The number of work days in 2021 is calculated by adding up all the weekdays (Mon-Fri) in 2021 and subtracting the 11 public federal holidays that fall on a weekday in 2021. The number of work days in a given year varies depending on what day of the week the year starts on.
### How often are there 53 weeks in a year?
This occurs approximately every five to six years, though this is not always the case. 2006, 2012, 2017 and 2023 are all 53-week years.
### What is a standard work year?
Standard Work Year means 2080 hours per calendar year. Sample 1. Standard Work Year for a Salaried Participant means 2080 hours per calendar year.
## Is there a week 53 in 2022 payroll?
If you pay your employees weekly, two weekly or four weekly on Monday 4 April 2022, you’ll have an extra pay run at the end of the 2021-22 tax year. If you pay your employees monthly, you won’t have a week 53.
### Are there 52 or 53 weeks in a year?
The weeks of the year in a Gregorian calendar are numbered from week 1 to week 52 or 53, depending on several varying factors. Most years have 52 weeks, but if the year starts on a Thursday or is a leap year that starts on a Wednesday, that particular year will have 53 numbered weeks.
### How many days are in a work year 2020?
So for 2020, we had 262 work days.
How do I calculate my work hours in a year? To figure out how many hours are in a “work year,” multiply the number of work hours in a week by the number of weeks in a year. In other words, multiply a typical 40 hour work week by 52 weeks. That makes 2,080 hours in a typical work year.
## How many working days are there in a year 2020 UK?
In 2020 in the UK there are: 366 days. 256 working days.
### How many working days are in a year?
Online calculator to find the number of work days in a year. There are 250 work days in 2021.
### How many working days are in 12 months?
260 Days: That’s the total number of working days in the year 2022.
### How many working days are in a year without holidays?
As a rule, a common year consists of 52 weeks and 260 work days. A leap year may contain an extra work day, so there will be 261 work days. While counting working days, it’s also important to remember that there are a number of federal holidays that can be paid days off.
How many working days are there in a year 2020? 255 working days. 104 week-end days.
How many 5 day weeks are there in a year? There are 52 weeks in a year and 5 working days in each which comes to 260.
## What is the standard working week in the UK?
You can’t work more than 48 hours a week on average – normally averaged over 17 weeks. This law is sometimes called the ‘working time directive’ or ‘working time regulations’. You can choose to work more by opting out of the 48-hour week. If you’re under 18, you can’t work more than 8 hours a day or 40 hours a week.
### How many weeks are there in a year without holidays?
Subtracting down after federal holidays means 50 weeks minus another 2 work weeks (or 10-11 work days), and you get to that number of 48 working weeks in the year.
### Does 37.5 hours include lunch?
Usually works out as 8.30-5 or 9-5.30 which is 7.5 hours plus an hour for lunch. Depends whether lunch breaks are counted in the hours. 37.5 sounds pretty standard.
### What is a standard working week?
You have a standard working week of 40 hours (eight hours a day).
## Does a 40 hour week include lunch UK?
What doesn’t count as work. A working week doesn’t include: time you spend on call away from the workplace. breaks when no work is done, eg lunch breaks.
### How many work days are in a year excluding holidays?
As a rule, a common year consists of 52 weeks and 260 work days. A leap year may contain an extra work day, so there will be 261 work days. While counting working days, it’s also important to remember that there are a number of federal holidays that can be paid days off.
### How do you calculate working days in a year Excel?
Working days in year
1. DATE(D5,1,1) // first day of year DATE(D5,12,31) // last day of year.
2. =NETWORKDAYS(DATE(D6,1,1),DATE(D6,12,31))
3. =NETWORKDAYS(TODAY(),DATE(D5,12,31),holidays)
Is there a week 53 in 2021 payroll? Week 53 takes place when a company pay date falls on 5th April in 2021. Each year is made up of 365 days or 52 weeks and 1 day and when the extra day falls on your company payday, Week 53 comes into effect. | 1,312 | 5,131 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2024-18 | latest | en | 0.956765 |
https://math.stackexchange.com/questions/1564887/find-matrix-of-linear-operator-mathcala-mathcalp-5-rightarrow-mathcal | 1,575,765,741,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540503656.42/warc/CC-MAIN-20191207233943-20191208021943-00331.warc.gz | 453,783,344 | 30,015 | Find matrix of linear operator $\mathcal{A} : \mathcal{P_5}\rightarrow \mathcal{P_5},\mathcal{A}(p)=-2p+(3x-1)p^{'}$
Find matrix of linear operator $\mathcal{A} : \mathcal{P_5}\rightarrow \mathcal{P_5},\mathcal{A}(p)=-2p+(3x-1)p^{'}$
$\mathcal{P_5}$ is the space of polynomials with degree not greater than $5$.
$\mathcal{A}(p)=(-2p-p^{'})+3p^{'}x+0x^2+0x^3+0x^4+0x^5$
$$\mathcal{A} \begin{bmatrix} p_1 \\ p_2 \\ p_3 \\ p_4 \\ p_5 \\ \end{bmatrix}= \begin{bmatrix} -2p_1-p_1^{'} \\ 3p_2^{'} \\ 0 \\ 0 \\ 0 \\ 0 \\ \end{bmatrix}$$
How to get matrix of $\mathcal{A}$?
• You’re not going to get very far with only five components in the vector on the lhs. – amd Dec 7 '15 at 23:33
• $\mathcal{P}_5$ is has dimension 6 and i guess $p'$ denotes the derivative of $p$. – testman Dec 7 '15 at 23:35
Let $p(x) = ax^5+bx^4+cx^3+dx^2+ex+f$ be an arbitrary polynomial in $\mathcal{P}_5$. Then \begin{align} (\mathcal{A}p)(x)&= -2p(x)+(3x-1)p'(x) \\ &= -2p(x)+(3x-1)(5ax^4+4bx^3+3cx^2+2dx+e) \\ &=13ax^5+(10b-5a)x^4+(7c-4b)x^3\\ &\quad +(4d-3c)x^2+(e-2d)x-2f-e. \end{align}
Using the canonical transformation $T:\mathbb{R}^6 \to \mathcal{P}_5, (a,b,c,d,e,f)^T\mapsto p$ you can write $\mathcal{A}p = TBT^{-1}p$ where $$B = \begin{bmatrix} 13 & 0 & 0 & 0 & 0 & 0 \\ -5 & 10 & 0 & 0 & 0 & 0 \\ 0 & -4 & 7 & 0 & 0 & 0 \\ 0 & 0 & -3 & 4 & 0 & 0 \\ 0 & 0 & 0 & -2 & 1 & 0 \\ 0 & 0 & 0 & 0 & -1 & -2 \\ \end{bmatrix}.$$ | 670 | 1,408 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2019-51 | latest | en | 0.412805 |
https://foodfuck.net/simple-pendulum-experiment-lab-report-trust-the-answer/ | 1,680,075,794,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948951.4/warc/CC-MAIN-20230329054547-20230329084547-00388.warc.gz | 311,984,175 | 23,717 | # Simple Pendulum Experiment Lab Report? Trust The Answer
Are you looking for an answer to the topic “simple pendulum experiment lab report“? We answer all your questions at the website https://foodfuck.net in category: https://foodfuck.net/blog. You will find the answer right below.
## PHYS 170L Pendulum: Lab Report
• Views: 33920
• Date: 33 minute ago
• Likes: 9395
• Dislikes: 5
## What is a pendulum experiment?
• Views: 2484 times
• Likes: 4979
• Dislikes: 7
The purpose of this pdf is to educate physics beginners about the pendulum theory and its principle in a practical way. Most universities and colleges will have a Pendulum experiment in their syllabus for Practicals. This experiment is also known as the Simple Harmonic motion experiment
The Pendulum Experiment is an experiment about gravity. Pendulums (or pendula if we are being exact!) are a fascinating scientific phenomenon. For many years they have been used for keeping time.
## What is the time period of a simple pendulum?
• Views: 3145 times
• Likes: 2592
• Dislikes: 6
The time period, t, of a simple pendulum is time it takes for one full oscillation. An oscillation is a to and fro movement of the pendulum. There are two laws of a simple pendulum studied in this lab. The first one is the law of length.
The time period of a simple pendulum is 0.2 sec. What is its frequency of oscillation?
How do you find the time period of simple pendulum?
A mass ‘m’ hung by a string of length ‘L’ is a simple pendulum and undergoes simple harmonic motion for amplitudes approximately below 15º. The time period of simple pendulum derivation is T = 2π√Lg T = 2 π L g, where ‘g’ = the acceleration owing to gravity (9.8 m/s² on Earth).
What is the use of a pendulum in music?
The pendulum is also used for identifying the beats. It is interesting to note that the time period of the pendulum remains constant even if the amplitude is changed but if the acceleration due to gravity changes the time period of the simple pendulum also changes.
Is the energy of a pendulum constant over time?
However, the total energy is constant as the function of time. In a simple pendulum, the mechanical energy of the simple pendulum is conserved. If the temperature of a system changes then the time period of the simple pendulum changes due to a change in length of the pendulum.
Which of the following is a property of simple pendulum?
This property is known as the law of length. Law of Iscochronism: The time period of the simple pendulum is independent of the amplitude, provided the amplitude is sufficiently small. This property is known as the law of isochronism. The oscillation of the simple pendulum is isochronous.
## What are the laws of a simple pendulum?
• Views: 7378 times
• Likes: 4184
• Dislikes: 5
There are two laws of a simple pendulum studied in this lab. The first one is the law of length. This law states that the time period of the simple pendulum is directly proportional to the square root of its effective length. This means that as the string gets longer, the pendulum takes more time to complete one oscillation.
Law of Length: The time period of the simple pendulum is directly proportional to the square root of its length. This property is known as the law of length. Law of Iscochronism: The time period of the simple pendulum is independent of the amplitude, provided the amplitude is sufficiently small. This property is known as the law of isochronism.
## What is the simple pendulum setup used for?
• Views: 948 times
• Likes: 3358
• Dislikes: 9
The simple pendulum setup can be used for the determination of acceleration of gravity value (g) (Cutnell, & Kenneth, 2013). The mass of the pendulum should be kept constant while the length of the string is varied. The length is the manipulated variable, period (T) a responding variable while the mass of the pendulum a fixed variable.
Simple pendulums are used in clocks as the pendulum has a fixed time period they can be used to keep a track of time. Following are example of a simple pendulum: Pendulums can be used as metronome. Pendulums are used to calculate acceleration due to gravity.
References:
Lab Report 1 The Simple Pendulum | PDF | Pendulum
Physics Report – Simple Pendulum | PDF | Pendulum
Simple Pendulum Lab Report Introduction Free Essay …
## Information related to the topic simple pendulum experiment lab report
Here are the search results of the thread simple pendulum experiment lab report from Bing. You can read more if you want.
How do you find the time period of simple pendulum?
What is the use of a pendulum in music?
Is the energy of a pendulum constant over time?
Which of the following is a property of simple pendulum?
What is the time period of a simple pendulum?
What is the simple pendulum setup used for?
What is a pendulum experiment?
What are the laws of a simple pendulum?
simple pendulum experiment lab report
You have just come across an article on the topic simple pendulum experiment lab report. If you found this article useful, please share it. Thank you very much. | 1,182 | 5,097 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2023-14 | latest | en | 0.896025 |
https://www.unitsconverters.com/en/A/M-To-Ka/M/Utu-4059-4061 | 1,679,982,904,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00689.warc.gz | 1,191,528,227 | 30,915 | Formula Used
1 Ampere per Meter = 0.001 Kiloampere per Meter
1 Ampere per Meter = 0.001 Kiloampere per Meter
## A/m to kA/m Conversion
The abbreviation for A/m and kA/m is ampere per meter and kiloampere per meter respectively. 1 A/m is 1000 times smaller than a kA/m. To measure, units of measurement are needed and converting such units is an important task as well. unitsconverters.com is an online conversion tool to convert all types of measurement units including A/m to kA/m conversion.
## Ampere per Meter to kA/m
Check our Ampere per Meter to kA/m converter and click on formula to get the conversion factor. When you are converting magnetic field strength from Ampere per Meter to kA/m, you need a converter that is elaborate and still easy to use. All you have to do is select the unit for which you want the conversion and enter the value and finally hit Convert.
## A/m to Kiloampere per Meter
The formula used to convert A/m to Kiloampere per Meter is 1 Ampere per Meter = 0.001 Kiloampere per Meter. Measurement is one of the most fundamental concepts. Note that we have Kiloampere per Meter as the biggest unit for length while Ampere per Meter is the smallest one.
## Convert A/m to kA/m
How to convert A/m to kA/m? Now you can do A/m to kA/m conversion with the help of this tool. In the length measurement, first choose A/m from the left dropdown and kA/m from the right dropdown, enter the value you want to convert and click on 'convert'. Want a reverse calculation from kA/m to A/m? You can check our kA/m to A/m converter.
## A/m to kA/m Converter
Units of measurement use the International System of Units, better known as SI units, which provide a standard for measuring the physical properties of matter. Measurement like magnetic field strength finds its use in a number of places right from education to industrial usage. Be it buying grocery or cooking, units play a vital role in our daily life; and hence their conversions. unitsconverters.com helps in the conversion of different units of measurement like A/m to kA/m through multiplicative conversion factors. When you are converting magnetic field strength, you need a Ampere per Meter to Kiloampere per Meter converter that is elaborate and still easy to use. Converting A/m to Kiloampere per Meter is easy, for you only have to select the units first and the value you want to convert. If you encounter any issues to convert Ampere per Meter to kA/m, this tool is the answer that gives you the exact conversion of units. You can also get the formula used in A/m to kA/m conversion along with a table representing the entire conversion.
Let Others Know | 615 | 2,648 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2023-14 | latest | en | 0.840581 |
http://www.education.com/reference/article/sound-vibrations1/ | 1,369,146,497,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368700107557/warc/CC-MAIN-20130516102827-00006-ip-10-60-113-184.ec2.internal.warc.gz | 440,466,218 | 26,881 | Education.com
# Sound Vibrations: Rubber Band Music
By Pam Walker| Elaine Wood
John Wiley & Sons, Inc.
Sound is a form of energy that travels in waves. Sound is produced by the vibration of matter. A stringed instrument such as a guitar or violin produces sound when the strings vibrate. The pitch of the sound varies from high to low, depending on how fast the string vibrates. Pitch is dependent on factors such as the diameter, tension, and length of the string. In this activity you will find out how the diameter of a string affects its pitch.
### Materials
Very thick rubber band
Medium-thick rubber band
Thin rubber band
### Activity
1. Put the thin rubber band over your five fingers and stretch your fingers so the rubber band is only lightly stretched.
2. Pluck the rubber band and listen for the pitch of the sound.
3. Stretch the rubber band farther by spreading your fingers. Repeat step 2.
4. Stretch the rubber band using both hands so it is very taut. Repeat step 2.
5. Repeat steps 1 through 4 with the medium-thick rubber band and then with the very thick rubber band.
### Follow-Up Questions
1. When you increased the stretch of each rubber band by spreading your fingers, did the pitch of the sound increase or decrease?
2. Which of the three rubber bands had the highest pitch when it was held in its tautest position?
1. Increase.
2. The thinnest rubber band had the highest pitch.
### Extension
Position a wooden ruler on a desk or table so the majority of it extends off the edge. Gently push down and let go of the free end of the ruler so it vibrates up and down. Shorten the length of the ruler extended over the desk's edge and repeat this process. How is the loudness of sound affected by the length of the ruler?
150 Characters allowed
### Related Questions
#### Q:
See More Questions
### Today on Education.com
#### WORKBOOKS
May Workbooks are Here!
#### WE'VE GOT A GREAT ROUND-UP OF ACTIVITIES PERFECT FOR LONG WEEKENDS, STAYCATIONS, VACATIONS ... OR JUST SOME GOOD OLD-FASHIONED FUN!
Get Outside! 10 Playful Activities | 474 | 2,075 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2013-20 | longest | en | 0.906698 |
https://uwaterloo.ca/pure-mathematics/events/computability-learning-seminar-106 | 1,656,343,363,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103334753.21/warc/CC-MAIN-20220627134424-20220627164424-00674.warc.gz | 668,675,410 | 15,326 | # Computability Learning Seminar
Tuesday, September 17, 2019 — 2:00 PM EDT
Dino Rossegger, Department of Pure Mathematics, University of Waterloo
"The complexity of Scott sentences of scattered linear orders"
Scott showed that for every countable structure $\mathcal A$ there is a sentence $\phi$ in the infinitary logic $L_{\omega_1\omega}$ such that for all countable structures $\mathcal B$, $\mathcal B\cong \mathcal A$ if and only if $\mathcal B \models \phi$. This sentence is commonly known as the Scott sentence of $\mathcal A$. Similarly to first order logic we can measure the complexity of sentences in $L_{\omega_1\omega}$ and obtain natural complexity classes $\Sigma_\alpha$, $\Pi_\alpha$ and $d\text{-}\Sigma_\alpha$ for all countable ordinals $\alpha$. The complexity of a structures least complex Scott sentence is strongly connected to its Scott rank and thus provides a good measure of complexity of a structure.
We investigate the complexity of Scott sentences of \emph{scattered} linear orders -- linear orders which do not have dense suborders. Hausdorff gave an inductive definition of the countable scattered linear orders. This allows us to assign an ordinal to every countable scattered linear order, its \emph{Hausdorff rank}. We obtain tight bounds on the complexity of the Scott sentences of countable scattered linear orders.
Theorem 1. Let $L$ be a linear order with countable Hausdorff rank $\alpha$. Then it has a $d\text{-}\Sigma_{2\alpha+1}$ Scott sentence.
Our result is optimal in the sense that for every countable $\alpha$ there is a linear order of Hausdorff rank $\alpha$ which does not have a Scott sentence of less complexity. This is a drastic improvement of bounds obtained by Nadel and extends work of Ash who calculated the Scott rank of countable well orders.
We furthermore show that for all countable $\alpha$, the set of presentations of linear orders of Hausdorff rank $\alpha$ is $\pmb \Sigma_{2\alpha+2}$ complete and that for $\alpha<\omega_1^{\mathrm CK}$, the index set of linear orders of Hausdorff rank $\alpha$ is $\Sigma_{2\alpha+2}$ complete.
This is joint work with Rachael Alvir, University of Notre Dame.
MC 5413
### June 2022
S M T W T F S
29
30
31
3
4
5
6
7
9
10
11
12
13
17
18
19
20
21
24
25
26
27
30
1
2
1. 2022 (75)
1. June (14)
2. May (13)
3. April (14)
4. March (15)
5. February (12)
6. January (7)
2. 2021 (135)
1. December (11)
2. November (22)
3. October (15)
4. September (5)
5. August (15)
6. July (17)
7. June (15)
8. May (1)
9. April (4)
10. March (11)
11. February (9)
12. January (10)
3. 2020 (103)
4. 2019 (199)
5. 2018 (212)
6. 2017 (281)
7. 2016 (335)
8. 2015 (211)
9. 2014 (235)
10. 2013 (251)
11. 2012 (135) | 790 | 2,706 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2022-27 | latest | en | 0.898771 |
https://www.sawaal.com/data-sufficiency-questions-and-answers/gaurav-ranks-eighteenth-in-a-class-what-is-his-rank-from-the-last-nbsp--i-there-are-47-students-in_2588 | 1,708,906,592,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474649.44/warc/CC-MAIN-20240225234904-20240226024904-00703.warc.gz | 986,644,406 | 15,356 | 4
Q:
# Gaurav ranks eighteenth in a class. What is his rank from the last ? I. There are 47 students in the class. II. Jatin who ranks 10th in the same class, ranks 38th from the last.
A) If the data in statement I alone are sufficient to answer the question B) If the data in statement II alone are sufficient answer the question C) If the data either in I or II alone are sufficient to answer the question; D) If the data even in both the statements together are not sufficient to answer the question
Answer: C) If the data either in I or II alone are sufficient to answer the question;
Explanation:
To find the rank from other end, we need to know the total number of students in the class. So. I is sufficient. Also: from II, we can conclude that there are (10 + 38- 1 = 47) students in the class.
So. II alone is also sufficient.
Q:
Pradeep correctly remembers that his mother's is before twenty third February but after ninteenth February, whereas his brother correctly remembers that their mother's birthday is not on or after twentysecond February. On which day in February is definitely their mother's birthday ?
A) 20 or 21 B) 20 C) 21 D) None
Explanation:
According to Pradeep : 20,21 or 22...(1)
According to his brother : not 22....(2)
From (1)&(2), the birthday falls on February 20 or 21.
6 4379
Q:
Rakesh scored more than Raju
Ravi scored less than Rakesh
Raju scored more than Ravi
Ranga score more than Raju but less than Rakesh
Then who is the top scorrer among them ?
A) Ranga B) Raju C) Rakesh D) Ravi
Explanation:
1. Rakesh
2. Ranga
3. Raju
4. Ravi
8 7615
Q:
First day of the month is Tuesday and Last day of the same month is Monday. Then which one will be that month ?
A) January B) February C) March D) August
Explanation:
We know that the day repeats after every seven days.
Given that first day of the month is Tuesday
i.e 1st - Tuesday
1+7 = 8 - Tuesday
8+7 =15- Tuesday
15+7=22-Tuesday
22+7=29-Tuesday
But given that last day of the same month is Monday
It is possible only in he month of Febuary with 28 days.
14 8415
Q:
Each boy contribute rupees equal to the number of girls and each girl contribute rupees equal to the number of boys in a class of 60 students. If the total contribution collected is Rs.1600,how many girls are there in the class ?
A) 30 B) 25 C) 15 D) 40
Explanation:
13 5380
Q:
Vipin's and Javed's salaries are in the proportion of 4 : 3 respectively. What is Vipin's salary ?
I. Javed's salary is 75% that of Vipin's salary.
II. Javed's salary is Rs 4500.
A) If the data in statement I alone are sufficient to answer the question B) If the data in statement II alone are sufficient answer the question C) If the data either in I or II alone are sufficient to answer the question; D) If the data even in both the statements together are not sufficient to answer the question
Answer & Explanation Answer: B) If the data in statement II alone are sufficient answer the question
Explanation:
Statement I is merely an interpretation of the information contained in the question
However, Vipin's salary can be determined from statement II as follows
Let Vipin's and Javed's salaries be 4x and ax respectively.
Then, 3x = 4500 or x = 1500 Vipin's salary = 4x = Rs 6000.
Thus, II alone is sufficient.
15 13636
Q:
How is B related to A ?
I. A is B's sister.
II. is the father of A and B.
A) If the data in statement I alone are sufficient to answer the question B) If the data in statement II alone are sufficient answer the question C) If the data either in I or II alone are sufficient to answer the question; D) If the data even in both the statements together are not sufficient to answer the question
Answer & Explanation Answer: D) If the data even in both the statements together are not sufficient to answer the question
Explanation:
From statements I and II together, we can conclude only that either B is the sister or brother of A.
So, even from both the statements, the exact relation cannot be known.
6 8070
Q:
In a certain code language, '297' means 'tie clip button'. Which number means 'button' ?
I. In that language '926' means 'clip your tie'.
II. In that language '175' means 'hole and button'.
A) If the data in statement I alone are sufficient to answer the question B) If the data in statement II alone are sufficient answer the question C) If the data either in I or II alone are sufficient to answer the question; D) If the data even in both the statements together are not sufficient to answer the question
Answer & Explanation Answer: C) If the data either in I or II alone are sufficient to answer the question;
Explanation:
Comparing the information in the question with statement 1. we find that '2' and '9' are the codes for 'tie' and 'dip'. So, '7' represents 'button'.
Thus, I alone iS sufficient.
Again, comparing the information in the question with II, WO find that the common code number '7' stands for the common word 'button'.
Thus, II alone also is sufficient.
7 11272
Q:
In a code, 'lee pee tin' means 'Always keep smiling'. What is the code for ?
I. 'tin lut lee' means 'Always keep left'.
II. 'dee pee' means 'Rose smiling.
A) If the data in statement I alone are sufficient to answer the question B) If the data in statement II alone are sufficient answer the question C) If the data either in I or II alone are sufficient to answer the question; D) If the data even in both the statements together are not sufficient to answer the question
Answer & Explanation Answer: C) If the data either in I or II alone are sufficient to answer the question;
Explanation:
Comparing the information in the question with I. we find that 'tin' and 'lee' are the codes for 'always' and 'keep'.
So. 'pee' represents 'smiling' Thus, I alone is sufficient Am.
comparing the information in the question with II, we find that the common code word 'pee' stands for the common word 'smiling'.
Thus, II alone is also sufficient | 1,510 | 5,987 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-10 | latest | en | 0.9419 |
https://python-forum.io/Thread-How-matplotlib-automatically-set-x-axis-and-y-axis-limits-for-bar-graph?pid=85207 | 1,620,795,919,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00522.warc.gz | 488,877,566 | 21,820 | ##### How matplotlib automatically set x-axis and y-axis limits for bar graph ?
How matplotlib automatically set x-axis and y-axis limits for bar graph ? ift38375 Silly Frenchman Posts: 29 Threads: 18 Joined: Apr 2019 Reputation: Jul-03-2019, 11:08 AM Hi, I am confused in math/logic behind automatically by-default setting of x-axis and y-axis limits in bar graph ? Here i am sharing some examples 1. ```import matplotlib.pyplot as plt x = [1,2,3,4,5] y = [1000, 1002, 1001, 1003, 1005] plt.bar(x,y) plt.show()```In this bar graph, X axis limits are 0,1,2,3,4,5 and Y axis limits are 0,200,400,600,800,1000. How is happened?? 2. ```import matplotlib.pyplot as plt x=[20,30,90,70, 50, 60, 80, 70] y=[3,2,5,10, 3, 9, 7, 6] plt.bar(x,y) plt.show()```In this bar graph, X axis limits are 0,20,30,40,50,60,70,80,90 and Y axis limits are 0,2,4,6,8,10. How is happened?? Reply Posts: 818 Threads: 1 Joined: Mar 2018 Reputation: Jul-03-2019, 11:37 AM If you look at `plt.bar` function docs, you find keyword `bottom`; its default value 0, that means all bars will start at 0 and have height as defined in the second argument passed to `bar` (`y`). By default, matplotlib chooses axes limits to cover provided range of values. Note, bar function plots filled rectangles of specified heights, so, by default matplotlib chooses axes to cover range from 0 (bottom value) to (bottom + y). Ticks and tick labels are placed in regular manner. Check out `axes.set_xticks`, `axes.set_xticklabels`, `axes.set_xlim` (you can get current axes instance using `plt.gca()`) to change this behavior. Reply ift38375 Silly Frenchman Posts: 29 Threads: 18 Joined: Apr 2019 Reputation: Jul-03-2019, 02:26 PM (This post was last modified: Jul-03-2019, 02:26 PM by ift38375.) (Jul-03-2019, 11:37 AM)scidam Wrote: If you look at `plt.bar` function docs, you find keyword `bottom`; its default value 0, that means all bars will start at 0 and have height as defined in the second argument passed to `bar` (`y`). By default, matplotlib chooses axes limits to cover provided range of values. Note, bar function plots filled rectangles of specified heights, so, by default matplotlib chooses axes to cover range from 0 (bottom value) to (bottom + y). Ticks and tick labels are placed in regular manner. Check out `axes.set_xticks`, `axes.set_xticklabels`, `axes.set_xlim` (you can get current axes instance using `plt.gca()`) to change this behavior. please explain first example where Y axis limits are 0,200,400,600,800,1000. How these limit/range comes in graph ? Reply Posts: 818 Threads: 1 Joined: Mar 2018 Reputation: Jul-04-2019, 08:23 AM I didn't explore source code of matplotlib in detail, but in general, computation of values where ytick labels will be shown is performed by a `matplotlib.ticker` instance. By default, it is `ticker.AutoLocator`: ```from matplotlib.ticker import AutoLocator aul = AutoLocator() aul.tick_values(1, 3)`````Output:array([1. , 1.25, 1.5 , 1.75, 2. , 2.25, 2.5 , 2.75, 3. ])`````from pylab import * plt.plot([1,2,3]) plt.show() # yields a graph with ticks placed in above positions```This default behavior is made for convenience, and it could be easily overridden using `axes.set_yticks` etc. Note, there are minor and major ticks (we are talking about major one here), so underlying machinery is quite tricky. Reply
Possibly Related Threads… Thread Author Replies Views Last Post IndexError: index 0 is out of bounds for axis 0 with size 0 atomxkai 2 847 Mar-03-2021, 08:26 AM Last Post: atomxkai Bar Chart axis Blyzz 0 301 Dec-01-2020, 02:36 AM Last Post: Blyzz IndexError: index 0 is out of bounds for axis 0 with size 0 tmhsa 0 2,000 Apr-24-2020, 10:00 AM Last Post: tmhsa how to get x values based on y-axis values from curvefit function python_newbie09 1 1,144 Sep-19-2019, 02:09 AM Last Post: scidam Automatically plot each variable on the same graph for each "ID" AdWill97 0 898 Apr-15-2019, 09:29 AM Last Post: AdWill97 How to prevent tick labels overlapping with axis SriRajesh 2 17,842 May-12-2018, 06:13 PM Last Post: SriRajesh Current time on x axis in matplolib Stumpy_L 2 2,310 Feb-07-2018, 02:07 PM Last Post: Stumpy_L Automatically updated graph in jupyter notebook using qt5 capponero 0 2,485 May-16-2017, 03:08 PM Last Post: capponero
Forum Jump:
### User Panel Messages
##### Announcements
Announcement #1 8/1/2020
Announcement #2 8/2/2020
Announcement #3 8/6/2020 | 1,328 | 4,398 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2021-21 | latest | en | 0.770898 |
https://inprogrammer.com/complexity-notations/ | 1,723,749,269,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641311225.98/warc/CC-MAIN-20240815173031-20240815203031-00764.warc.gz | 252,056,970 | 33,280 | # Complexity Notations
Contents
## Introduction
In this article, let’s have a look at complexity notations like Big Theta, Big Omega, and Big O notation.
Complexity notations are mathematical notations used to describe the performance of algorithms in terms of their time and space requirements. These notations allow us to compare the efficiency of different algorithms for solving the same problem, and to choose the most efficient algorithm for a given application.
## Types of Notations:
The most common complexity notation is Big O notation, which gives an upper bound on the time or space required by an algorithm as a function of the size of the input. For example, an algorithm with a time complexity of O(n) means that its running time grows linearly with the size of the input.
Other common complexity notations include Big Theta notation, which gives both an upper and lower bound on the time or space required by an algorithm, and Big Omega notation, which gives a lower bound on the time or space required by an algorithm.
By using complexity notations, we can compare the performance of different algorithms and choose the most efficient one for a given application. This can help us write efficient and scalable programs that can handle large inputs without running out of time or space. Try again.
## Big oh notation (O):
Big O notation is a mathematical notation used to describe the performance of an algorithm in terms of its time or space complexity. It gives an upper bound on the number of steps or the amount of space required by the algorithm to solve a problem of size n.
For example, an algorithm with a time complexity of O(n) means that its running time grows linearly with the size of the input. This means that if the input size is doubled, the running time of the algorithm will also be roughly doubled. On the other hand, an algorithm with a time complexity of O(log n) means that its running time grows logarithmically with the size of the input. This means that if the input size is doubled, the running time of the algorithm will only increase by a constant amount.
Big O notation is commonly used to compare the efficiency of different algorithms for solving the same problem. By choosing algorithms with lower time or space complexity, we can ensure that our programs will run quickly and efficiently, even on large inputs.
## Big Theta notation (Θ) :
Big Theta notation is a mathematical notation used to describe the performance of an algorithm in terms of its time or space complexity. It gives both an upper and lower bound on the number of steps or the amount of space required by the algorithm to solve a problem of size n.
For example, an algorithm with a time complexity of Θ(n) means that its running time grows linearly with the size of the input. This means that if the input size is doubled, the running time of the algorithm will also be roughly doubled. On the other hand, an algorithm with a time complexity of Θ(log n) means that its running time grows logarithmically with the size of the input. This means that if the input size is doubled, the running time of the algorithm will only increase by a constant amount.
See also General Data Protection Regulation (GDPR)
Big Theta notation is commonly used to compare the efficiency of different algorithms for solving the same problem. By choosing algorithms with lower time or space complexity, we can ensure that our programs will run quickly and efficiently, even on large inputs. Unlike Big O notation, which only gives an upper bound on the time or space required by an algorithm, Big Theta notation provides a more precise analysis of an algorithm’s performance.
## Big Omega notation (Ω) :
Big Omega notation is a mathematical notation used to describe the performance of an algorithm in terms of its time or space complexity. It gives a lower bound on the number of steps or the amount of space required by the algorithm to solve a problem of size n.
For example, an algorithm with a time complexity of Ω(n) means that its running time grows linearly with the size of the input. This means that if the input size is doubled, the running time of the algorithm will also be roughly doubled. On the other hand, an algorithm with a time complexity of Ω(log n) means that its running time grows logarithmically with the size of the input. This means that if the input size is doubled, the running time of the algorithm will only increase by a constant amount.
Big Omega notation is commonly used to compare the efficiency of different algorithms for solving the same problem. By choosing algorithms with lower time or space complexity, we can ensure that our programs will run quickly and efficiently, even on large inputs. Unlike Big O notation, which only gives an upper bound on the time or space required by an algorithm, Big Omega notation provides a more precise analysis of an algorithm’s performance by providing a lower bound on its time or space complexity.
See also SUM OF THE NATURAL NUMBERS USING RECURSION and FACTORIAL USING RECURSION
## Conclusion
That’s it for this article. In the next article, we will learn the differences between stack and heap memory.
#### Ads Blocker Detected!!!
we provide projects, courses, and other stuff for free. in order for running we use Google ads to make revenue. please disable adblocker to support us. | 1,074 | 5,388 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2024-33 | latest | en | 0.914934 |
https://sandialabs.github.io/Prove-It/packages/proveit/numbers/multiplication/__pv_it/theorems/1395f2bb46871a94fb8b4f3f0c15f2f0cc1858d40/expr.html | 1,716,242,119,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058313.71/warc/CC-MAIN-20240520204005-20240520234005-00211.warc.gz | 450,660,014 | 4,514 | from the theory of proveit.numbers.multiplication¶
In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, Function, Lambda, Q, f
from proveit.core_expr_types import b_1_to_j
from proveit.logic import InSet
from proveit.numbers import Complex
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Lambda(sub_expr1, Conditional(InSet(Function(f, sub_expr1), Complex), Function(Q, sub_expr1)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in \mathbb{C} \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0Lambdaparameters: 10
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 10
4Literal
5ExprTuple7, 8
6Variable
7Operationoperator: 9
operands: 10
8Literal
9Variable
10ExprTuple11
11ExprRangelambda_map: 12
start_index: 13
end_index: 14
12Lambdaparameter: 18
body: 15
13Literal
14Variable
15IndexedVarvariable: 16
index: 18
16Variable
17ExprTuple18
18Variable | 528 | 1,796 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-22 | latest | en | 0.389663 |
https://cboard.cprogramming.com/c-programming/45613-displaying-float-digits.html | 1,508,648,273,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825141.95/warc/CC-MAIN-20171022041437-20171022061437-00242.warc.gz | 642,576,578 | 12,147 | # Thread: displaying float digits
1. ## displaying float digits
Hey there, i'm curious on how to display the first and rightmost digit of the integral portion of a floating point integer. I'm not quite sure how to do this.
whould I create a two variables like so:
float floatintPointInt;
float result;
....
result = floatingPointInt % floatingPointInt / 10;
....
Thanks
2. Code:
`int result = (int)floatingPointInt % 10;`
3. Thanks a lot man.
4. Hi, i'm sorry.. I'm not quite sure what is wrong with my code.
It's supposed to print the first and the second rightmost digit of the integral portion of the float.
Code:
```int main()
{
float decimal = 0.0;
int result = (int)decimal % 10;
printf("Floating point Int: ");
scanf("%f", result);
printf("\n\n%f", result);
return 0;
}```
I'm not sure if i should assign the "decimal" to 0.0.. when i don't the compiler give an error.
thank you.
5. >I'm not sure if i should assign the "decimal" to 0.0.. when i don't the compiler give an error.
An error? Or a warning that you are using the value of 'decimal' before it has been initialized?
>scanf("%f", result);
Here scanf expects a pointer to a float -- give it one.
Code:
`scanf("%f", &decimal);`
Convert the float 'decimal' to the int 'result' after you've gotten 'decimal'.
>It's supposed to print the first and the second rightmost digit of the integral portion of the float.
You may want to use % 100.
>printf("\n\n%f", result);
Use %d with an int.
Code:
`printf("\n%d\n", result);`
6. Oh geeeezzz.. man.. thank you so much.
I can't believe i missed that scanf("%d", &result);........... bahhh
Thank you
Popular pages Recent additions | 442 | 1,659 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2017-43 | latest | en | 0.763667 |
http://en.academic.ru/dic.nsf/cide/112910/Modulus | 1,501,189,512,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549429485.0/warc/CC-MAIN-20170727202516-20170727222516-00607.warc.gz | 95,576,933 | 12,159 | Modulus of a machine
Modulus Mod"u*lus, n.; pl. {Moduli}. [L., a small measure. See {Module}, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength, efficiency, etc.; a parameter. [1913 Webster]
{Modulus of a machine}, a formula expressing the work which a given machine can perform under the conditions involved in its construction; the relation between the work done upon a machine by the moving power, and that yielded at the working points, either constantly, if its motion be uniform, or in the interval of time which it occupies in passing from any given velocity to the same velocity again, if its motion be variable; -- called also the efficiency of the machine. --Mosley. --Rankine.
{Modulus of a system of logarithms} (Math.), a number by which all the Napierian logarithms must be multiplied to obtain the logarithms in another system.
{Modulus of elasticity}. (a) The measure of the elastic force of any substance, expressed by the ratio of a stress on a given unit of the substance to the accompanying distortion, or strain. (b) An expression of the force (usually in terms of the height in feet or weight in pounds of a column of the same body) which would be necessary to elongate a prismatic body of a transverse section equal to a given unit, as a square inch or foot, to double, or to compress it to half, its original length, were that degree of elongation or compression possible, or within the limits of elasticity; -- called also {Young's modulus}.
{Modulus of rupture}, the measure of the force necessary to break a given substance across, as a beam, expressed by eighteen times the load which is required to break a bar of one inch square, supported flatwise at two points one foot apart, and loaded in the middle between the points of support. --Rankine. [1913 Webster]
The Collaborative International Dictionary of English. 2000.
### Look at other dictionaries:
• Modulus of a system of logarithms — Modulus Mod u*lus, n.; pl. {Moduli}. [L., a small measure. See {Module}, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength,… … The Collaborative International Dictionary of English
• Modulus of elasticity — Modulus Mod u*lus, n.; pl. {Moduli}. [L., a small measure. See {Module}, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength,… … The Collaborative International Dictionary of English
• Modulus of rupture — Modulus Mod u*lus, n.; pl. {Moduli}. [L., a small measure. See {Module}, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength,… … The Collaborative International Dictionary of English
• Modulus — Mod u*lus, n.; pl. {Moduli}. [L., a small measure. See {Module}, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength,… … The Collaborative International Dictionary of English
• Young's modulus — Modulus Mod u*lus, n.; pl. {Moduli}. [L., a small measure. See {Module}, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength,… … The Collaborative International Dictionary of English
• Strength of materials — Internal force lines are denser near the hole, a common stress concentration In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear … Wikipedia
• Comparison of Java and C++ — Programming language comparisons General comparison Basic syntax Basic instructions Arrays Associative arrays String operations … Wikipedia
• List of engineering topics — This page aims to list all topics related to the broad field of engineering. A more compact list can be found at list of basic engineering topics. See the bottom of the page for links to lists for specific engineering disciplines or for… … Wikipedia
• List of structural engineering topics — This page aims to list all articles related to the specific discipline of structural engineering. For a broad overview of engineering, please see List of engineering topics. For biographies please see List of engineers.compactTOC NOTOC AA frame… … Wikipedia
• Glossary of fuel cell terms — The Glossary of fuel cell terms lists the definitions of many terms used within the fuel cell industry. The terms in this glossary may be used by fuel cell industry associations, in education material and fuel cell codes and standards to name but … Wikipedia | 1,103 | 4,994 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2017-30 | latest | en | 0.905383 |
https://help.scilab.org/docs/5.3.0/fr_FR/pencan.html | 1,721,839,341,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518304.14/warc/CC-MAIN-20240724140819-20240724170819-00443.warc.gz | 254,404,039 | 3,962 | Change language to:
English - 日本語 - Português
See the recommended documentation of this function
Manuel Scilab >> Algèbre Lineaire > pencan
pencan
canonical form of matrix pencil
Calling Sequence
```[Q,M,i1]=pencan(Fs)
[Q,M,i1]=pencan(E,A)```
Arguments
Fs
a regular pencil `s*E-A`
E,A
two real square matrices
Q,M
two non-singular real matrices
i1
integer
Description
Given the regular pencil `Fs=s*E-A`, `pencan` returns matrices `Q` and `M` such than `M*(s*E-A)*Q` is in "canonical" form.
`M*E*Q` is a block matrix
```[I,0;
0,N]```
with `N` nilpotent and `i1` = size of the `I` matrix above.
`M*A*Q` is a block matrix:
```[Ar,0;
0,I]```
Examples
```F=randpencil([],[1,2],[1,2,3],[]);
F=rand(6,6)*F*rand(6,6);
[Q,M,i1]=pencan(F);
W=clean(M*F*Q)
roots(det(W(1:i1,1:i1)))
det(W(\$-2:\$,\$-2:\$))``` | 308 | 821 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-30 | latest | en | 0.600264 |
http://mathfraction.com/fraction-simplify/scientific-notation/formula-of-square-root-in.html | 1,519,028,351,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812556.20/warc/CC-MAIN-20180219072328-20180219092328-00367.warc.gz | 225,335,131 | 10,593 | Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
Ineq. #4:
Ineq. #5:
Ineq. #6:
Ineq. #7:
Ineq. #8:
Ineq. #9:
Solve for:
Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:
formula of square root in visual basic
Related topics:
math grade 8 tests +pdf ontario | polynomial inequality sketch graph | graphing linear and quadratic functions and interpreting graphs; solving systems of linear equations and inequalities; and applications. | Adding Variable Exponents | square root of difference of squares | maths grades ks2 adding | a. solve the equation w=cr^-2 for r. hint: use the rules of exponents to remove the negative exponent. | integrated algebra practice 9th grade | worksheets for slopes | approximate quadratic equation using slopes
Author Message
Salbavos
Registered: 03.03.2005
From:
Posted: Friday 29th of Dec 21:22 Hi gals and guys I’m really stuck on formula of square root in visual basic and would sure appreciate help to get me started with converting fractions, like denominators and side-angle-side similarity. My homework is due soon. I have even thought of hiring a tutor, but they are dear . So any help would be very much treasured.
oc_rana
Registered: 08.03.2007
From: egypt,alexandria
Posted: Saturday 30th of Dec 18:15 You seem to be more horrified than confused. First you need to control your self. Do not panic. Sit back, relax and look at the books with a clear mind. They will seem tough if you think they are hard . formula of square root in visual basic can be easily understood and you can solve almost every problem with the help of Algebrator. So chill .
malhus_pitruh
Registered: 23.04.2003
From: Girona, Catalunya (Spain)
Posted: Monday 01st of Jan 12:05 Algebrator truly is a must-have for us algebra students. As already said in the post above , not only does it solve questions but it also explains all the intermediary steps involved in reaching that final solution . That way you don’t just get to know the final answer but also learn how to go about solving questions from the scratch , and it helps a lot in preparing for exams .
Momepi
Registered: 22.07.2004
From: Ireland
Posted: Tuesday 02nd of Jan 09:31 I am a regular user of Algebrator. It not only helps me get my homework faster, the detailed explanations given makes understanding the concepts easier. I strongly advise using it to help improve problem solving skills. | 693 | 2,757 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2018-09 | latest | en | 0.900034 |
https://wikimili.com/en/Method_of_Fluxions | 1,627,976,171,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154432.2/warc/CC-MAIN-20210803061431-20210803091431-00625.warc.gz | 602,025,620 | 15,833 | # Method of Fluxions
Last updated
Author Cover of book published in 1736 Isaac Newton English Mathematics Henry Woodfall 1736 339
Method of Fluxions (latin De Methodis Serierum et Fluxionum) [1] is a book by Isaac Newton. The book was completed in 1671, and published in 1736. Fluxion is Newton's term for a derivative. He originally developed the method at Woolsthorpe Manor during the closing of Cambridge during the Great Plague of London from 1665 to 1667, but did not choose to make his findings known (similarly, his findings which eventually became the Philosophiae Naturalis Principia Mathematica were developed at this time and hidden from the world in Newton's notes for many years). Gottfried Leibniz developed his form of calculus independently around 1673, 7 years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and fluents..." from 1666. Leibniz however published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion notation form of calculus in part during 1693. [2] The calculus notation in use today is mostly that of Leibniz, although Newton's dot notation for differentiation ${\displaystyle {\dot {x}}}$ for denoting derivatives with respect to time is still in current use throughout mechanics and circuit analysis.
## Contents
Newton's Method of Fluxions was formally published posthumously, but following Leibniz's publication of the calculus a bitter rivalry erupted between the two mathematicians over who had developed the calculus first, provoking Newton to reveal his work on fluxions.
## Newton's development of analysis
For a period of time encompassing Newton's working life, the discipline of analysis was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry. Instead, analysts were often forced to invoke infinitesimal, or "infinitely small", quantities to justify their algebraic manipulations. Some of Newton's mathematical contemporaries, such as Isaac Barrow, were highly skeptical of such techniques, which had no clear geometric interpretation. Although in his early work Newton also used infinitesimals in his derivations without justifying them, he later developed something akin to the modern definition of limits in order to justify his work. [3] | 530 | 2,569 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-31 | latest | en | 0.969779 |
https://www.khanacademy.org/math/cc-1st-grade-math/cc-1st-add-subtract/cc-1st-sub-20/v/subtracting-within-20 | 1,716,763,353,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058973.42/warc/CC-MAIN-20240526200821-20240526230821-00075.warc.gz | 729,815,579 | 60,594 | If you're seeing this message, it means we're having trouble loading external resources on our website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
Lesson 3: Subtraction within 20
# Subtracting 14 - 6
Sal subtracts 14 - 6 by first thinking about subtracting 2 and 4. Created by Sal Khan.
## Want to join the conversation?
• I am struggling to find a video on Subtracting within 20 with regrouping. I dont want to use blocks, I don't want to use visualizations. I want to know how to know how to write subtract 9 from 16 with regrouping.
• Try this,
We have the original number, but we can put it in expanded form*.
So, 16 = 10 + 6, and we can use this.
We know that 10 - 9 = 1, and then we can add the remaining 6 to get 7.
Expanded form is just taking the values of each number and adding them to create a number. For example, 17 = 10 + 7
You can also use this for bigger numbers
, like
1,234 = 1,000 + 200 + 30 + 4
• Hi there,
Could you please tell which video explains how to do 9-[]=5 and []-4=5.
Any help on this is much appreciated.
• Hello,
In these type of problems all you have to do is do the opposite of what it's asking. But, you would, in this case, still subtract since you are trying to find the number you subtract by and not the number you subtract from. So, 9-5=4 the missing value is 4.
For the second problem you add since you are trying to find the number you subtract from. So, 4+5=9 the missing value is 9.
Hope this helps!
• What is the commutative property? Is addition commutative?
• It is when you can change the order of an equation and get the same answer. For Ex: 4+3= 7 is the same as 3+4=7
(1 vote)
• If your subtracting by adding a negative number does that lead to borrowing to significant to basic subtraction?
• The basic concept of adding a negative number is exactly the same as subtracting that number. In higher math this may not always be the case but you will learn about those types of situations later. For now think about adding a negative number as the same process as subtraction. For example 10 + -3 = 7 and 10 - 3 = 7.
• so people can think of the four's cancelling each other out in the second problem and being left with only ten?
• Yes, but not all math problems are simple like that. But it is definitely not encouraged to think as such, as people might think that 14 - 4 = 1 if they cancel out the 4 and forget that there is a 0 behind the 1. | 653 | 2,480 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2024-22 | latest | en | 0.942124 |
https://edurev.in/test/13441/Olympiad-Test-Simple-Interest-2 | 1,723,076,419,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640713903.39/warc/CC-MAIN-20240808000606-20240808030606-00447.warc.gz | 169,493,288 | 47,825 | Olympiad Test: Simple Interest - 2 - Class 7 MCQ
# Olympiad Test: Simple Interest - 2 - Class 7 MCQ
Test Description
## 10 Questions MCQ Test - Olympiad Test: Simple Interest - 2
Olympiad Test: Simple Interest - 2 for Class 7 2024 is part of Class 7 preparation. The Olympiad Test: Simple Interest - 2 questions and answers have been prepared according to the Class 7 exam syllabus.The Olympiad Test: Simple Interest - 2 MCQs are made for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Simple Interest - 2 below.
Solutions of Olympiad Test: Simple Interest - 2 questions in English are available as part of our course for Class 7 & Olympiad Test: Simple Interest - 2 solutions in Hindi for Class 7 course. Download more important topics, notes, lectures and mock test series for Class 7 Exam by signing up for free. Attempt Olympiad Test: Simple Interest - 2 | 10 questions in 20 minutes | Mock test for Class 7 preparation | Free important questions MCQ to study for Class 7 Exam | Download free PDF with solutions
Olympiad Test: Simple Interest - 2 - Question 1
### What sum of the money will produce Rs 143 interest in years at 2.5% simple interest?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 1
Let the required sum be Rs P.
Then, Rs P = (100 Rs 143)/ 3.25 × 2.5 = Rs 1760
Olympiad Test: Simple Interest - 2 - Question 2
### A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 2
Let the sum be Rs 100
After 10 years it becomes Rs 200
Therefore Interest = Rs 200 – Rs 100 = Rs 100
Then, Rate = (100 × I)/ (P × T)
= (100 × 100)/ (100 × 10)
= 10%
1 Crore+ students have signed up on EduRev. Have you?
Olympiad Test: Simple Interest - 2 - Question 3
### A sum of money trebles itself in 20 years at SI. Find the rate of interest.
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 3
Rate = [100(3 – 1)]/20 = 10%
Olympiad Test: Simple Interest - 2 - Question 4
In what time does a sum of money become four times at the simple interest rate of 5% per annum?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 4
Time
= [100(Multiple number of principal – 1)] / Rate
= [100(4 – 1)]/5 =60 years
Olympiad Test: Simple Interest - 2 - Question 5
A sum was put at SI at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs 300 more. Find the sum.
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 5
Sum
= (More Interest × 100)/ (Time × More Rate)
= (300 × 100)/ (2 × 3) = 5000
Olympiad Test: Simple Interest - 2 - Question 6
A sum of money doubles itself in 7 years. In how many years will it become fourfold?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 6
Rate = [100(2 – 1)]/7 =100/7
Therefore Time = [100(4 – 1)]/ (100/7)
= 21 years
Olympiad Test: Simple Interest - 2 - Question 7
The simple interest on Rs 1650 will be less than the interest on Rs 1800 at 4% simple interest by Rs 30. Find the time.
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 7
We may consider that Rs (1800 – 1650) gives interest of Rs 30 at 4% per annum.
Therefore, Time = (30 × 100)/ (150 × 4) = 5 years
Olympiad Test: Simple Interest - 2 - Question 8
Bobby invested a certain sum of money at 8% p.a. simple interest for ‘n’ years. At the end of ‘n’ years, Bobby got back 4 times his original investment. What is the value of n?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 8
Let us say Bobby invested Rs 100.
Then, at the end of ‘n’ years he would have got back Rs 400.
Therefore, the Simple Interest earned
= 400 – 100 = Rs 300.
Simple Interest = PRT/100
Substituting the values in the above equation of we get
300 = (100 × n × 8)/100
⇒ 8n = 300
⇒ n = 37.5 years.
Olympiad Test: Simple Interest - 2 - Question 9
Anita invested a certain sum of money in a bank that paid simple interest. The amount grew to Rs 240 at the end of 2 years. She waited for another 3 years and got a final amount of Rs 300. What was the principal amount that she invested at the beginning?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 9
The sum grew to Rs 240 at the end of 2 years.
At the end of another 3 years, the sum grew to Rs 300
i.e. in 3 years, the sum grew by Rs 60
Therefore, each year, it grew by Rs 20
Sum at the end of 2 years = Rs 240
Sum grew by Rs 20 each year.
Hence, in the first 2 years, sum grew by 2 × 20 = Rs 40
Therefore, sum at the beginning of the period = Sum at the end of 2 years – Rs 40
= Rs 240 – Rs 40 = Rs 200
Olympiad Test: Simple Interest - 2 - Question 10
Pratap invested a certain sum of money in a simple interest bond whose value grew to Rs 300 at the end of 3 years and to Rs 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
Detailed Solution for Olympiad Test: Simple Interest - 2 - Question 10
Initial amount invested = Rs X
Therefore, the interest earned for the 5 years period between the 3rd year and 8th year = Rs 400 – Rs 300 = Rs 100
As the simple interest earned for a period of 5 years is Rs 100, interest earned per year = Rs 20
Therefore, interest earned for 3 years
= 3 × 20 = Rs 60
Hence, initial amount invested X
Amount after 3 years – interest for 3 years
= 300 – 60 = Rs 240
Rate of interest = (interest per year/ principal invested) × 100
= (20/240) × 100 = 8.33% | 1,616 | 5,560 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2024-33 | latest | en | 0.842044 |
https://studysoup.com/tsg/194937/introduction-to-algorithms-3-edition-chapter-15-problem-15-5 | 1,611,220,603,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703524270.28/warc/CC-MAIN-20210121070324-20210121100324-00219.warc.gz | 566,746,865 | 22,192 | ×
Get Full Access to Introduction To Algorithms - 3 Edition - Chapter 15 - Problem 15-5
Get Full Access to Introduction To Algorithms - 3 Edition - Chapter 15 - Problem 15-5
×
# Edit distance In order to transform one source string of
ISBN: 9780262033848 130
## Solution for problem 15-5 Chapter 15
Introduction to Algorithms | 3rd Edition
• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants
Introduction to Algorithms | 3rd Edition
4 5 1 244 Reviews
30
3
Problem 15-5
Edit distance In order to transform one source string of text x1 : : m to a target string y1 : : n, we can perform various transformation operations. Our goal is, given x and y, to produce a series of transformations that change x to y. We use an array assumed to be large enough to hold all the characters it will needto hold the intermediate results. Initially, is empty, and at termination, we should have j D yj for j D 1; 2; : : : ; n. We maintain current indices i into x and j into , and the operations are allowed to alter and these indices. Initially, i D j D 1. We are required to examine every character in x during the transformation, which means that at the end of the sequence of transformation operations, we must have i D m C 1. We may choose from among six transformation operations: Copy a character from x to by setting j D xi and then incrementing both i and j . This operation examines xi. Replace a character from x by another character c, by setting j D c, and then incrementing both i and j . This operation examines xi. Delete a character from x by incrementing i but leaving j alone. This operation examines xi. Insert the character c into by setting j D c and then incrementing j , but leaving i alone. This operation examines no characters of x. Twiddle (i.e., exchange) the next two characters by copying them from x to but in the opposite order; we do so by setting j D xi C 1 and j C 1 D xi and then setting i D i C 2 and j D j C 2. This operation examines xi and xi C 1. Kill the remainder of x by setting i D m C 1. This operation examines all characters in x that have not yet been examined. This operation, if performed, must be the final operation. for Chapter 15 407 As an example, one way to transform the source string algorithm to the target string altruistic is to use the following sequence of operations, where the underlined characters are xi and j after the operation: Operation x initial strings algorithm copy algorithm a copy algorithm al replace by t algorithm alt delete algorithm alt copy algorithm altr insert u algorithm altru insert i algorithm altrui insert s algorithm altruis twiddle algorithm altruisti insert c algorithm altruistic kill algorithm altruistic Note that there are several other sequences of transformation operations that transform algorithm to altruistic. Each of the transformation operations has an associated cost. The cost of an operation depends on the specific application, but we assume that each operations cost is a constant that is known to us. We also assume that the individual costs of the copy and replace operations are less than the combined costs of the delete and insert operations; otherwise, the copy and replace operations would not be used. The cost of a given sequence of transformation operations is the sum of the costs of the individual operations in the sequence. For the sequence above, the cost of transforming algorithm to altruistic is .3 cost.copy// C cost.replace/ C cost.delete/ C .4 cost.insert// C cost.twiddle/ C cost.kill/ : a. Given two sequences x1 : : m and y1 : : n and set of transformation-operation costs, the edit distance from x to y is the cost of the least expensive operation sequence that transforms x to y. Describe a dynamic-programming algorithm that finds the edit distance from x1 : : m to y1 : : n and prints an optimal operation sequence. Analyze the running time and space requirements of your algorithm. The edit-distance problem generalizes the problem of aligning two DNA sequences (see, for example, Setubal and Meidanis [310, Section 3.2]). There are several methods for measuring the similarity of two DNA sequences by aligning them. One such method to align two sequences x and y consists of inserting spaces at 408 Chapter 15 Dynamic Programming arbitrary locations in the two sequences (including at either end) so that the resulting sequences x0 and y0 have the same length but do not have a space in the same position (i.e., for no position j are both x0 j and y0 j a space). Then we assign a score to each position. Position j receives a score as follows: C1 if x0 j D y0 j and neither is a space, 1 if x0 j y0 j and neither is a space, 2 if either x0 j or y0 j is a space. The score for the alignment is the sum of the scores of the individual positions. For example, given the sequences x D GATCGGCAT and y D CAATGTGAATC, one alignment is G ATCG GCAT CAAT GTGAATC -*++*+*+-++* A + under a position indicates a score of C1 for that position, a - indicates a score of 1, and a * indicates a score of 2, so that this alignment has a total score of 6 1 2 1 4 2 D 4. b. Explain how to cast the problem of finding an optimal alignment as an edit distance problem using a subset of the transformation operations copy, replace, delete, insert, twiddle, and kill. 15-6 Plannin
Step-by-Step Solution:
Step 1 of 3
Step 2 of 3
Step 3 of 3
#### Related chapters
Unlock Textbook Solution | 1,290 | 5,502 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2021-04 | latest | en | 0.89768 |
https://www.pythoninformer.com/generative-art/generativepy-tutorial/ | 1,713,579,890,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817463.60/warc/CC-MAIN-20240419234422-20240420024422-00159.warc.gz | 867,079,057 | 6,315 | # generativepy tutorial
By Martin McBride, 2021-04-18
Categories: generativepy generativepy tutorial
This section is a basic tutorial for generativepy.
If you are new to generativepy, it is worth reading through the tutorials in order, to gain an understanding of how to use the library.
generativepy supports several different types of image creation:
• Vector images, which can be used to create all types of geometric art. It uses the Pycairo library, which provides a comprehensive set of vector drawing tools to produce very high-quality graphics.
• See the Getting started article to start leaning about creating vector graphics.
• Bitmap images, which can be used to create various types of pixel art. This uses two libraries:
• Pillow, an image processing library that provides a wide range of functions for manipulating images, similar to the sort of functions you might use in programs like GIMP or Photoshop.
• NumPy, which stores images as a data array. It is more suited to performing heavy-duty maths on image pixels, for example creating certain types of fractals.
• 3D images, using the ModernGL library, which supports modern OpenGL. This is still at quite an experimental stage.
Each of these modes supports a common interchange format, the frame, which is actually a NumPy array. This allows for the exchange of data between the different modes.
• Image sequences, which work by calling one of the above modes repeatedly to create a sequence of images. This can be stored as a set of PNG files (that can be converted to a movie using ffmpeg or similar), or an animated GIF file.
• Mathematical extensions for vector imaging, which can be used to create various graphs and geometric diagrams, that can also be stored as images or movies.
There are also some support modules:
• color, a module that provides common colour handling across the different modes, including support for named colours, HSL, and alpha. It also supports colour maps that can be used, for example, to colourise fractals.
• tween, a module that supports basic tweening of numerical values and vector quantities (such as positions and colours).** | 440 | 2,145 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-18 | latest | en | 0.912472 |
https://gmatclub.com/forum/a-ranch-has-horses-and-ponies-five-sixths-of-the-ponies-64570.html?fl=similar | 1,511,396,814,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806708.81/warc/CC-MAIN-20171122233044-20171123013044-00791.warc.gz | 631,447,398 | 43,329 | It is currently 22 Nov 2017, 17:26
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
Events & Promotions
Events & Promotions in June
Open Detailed Calendar
A ranch has horses and ponies. Five-sixths of the ponies
Author Message
Intern
Joined: 26 May 2008
Posts: 40
Kudos [?]: 5 [0], given: 0
A ranch has horses and ponies. Five-sixths of the ponies [#permalink]
Show Tags
27 May 2008, 23:23
00:00
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct 0% (00:00) wrong based on 3 sessions
HideShow timer Statistics
This topic is locked. If you want to discuss this question please re-post it in the respective forum.
A ranch has horses and ponies. Five-sixths of the ponies have horseshoes. Half of the ponies with horseshoes are Icelandic. If there are three more horses than ponies, what is the minimum number of horses and ponies on the ranch?
A) 12
B) 15
C) 27
D) 48
E) 54
I couldnot decipher the icelandic part..
Kudos [?]: 5 [0], given: 0
Director
Joined: 23 Sep 2007
Posts: 782
Kudos [?]: 247 [1], given: 0
Re: PS - horses and ponies [#permalink]
Show Tags
27 May 2008, 23:31
1
KUDOS
27 C
The icelandic phrase is the key to solving the problem.
if 5/6 of the ponies have shoes, and HALF of them are icelandic. Half of 5/6 is 2.5/6, but you can't have half of a pony, so you must double the 5/6 to 10/12.
12 is the minimum numbers of ponies
15 is the minimum numbers of horses
Kudos [?]: 247 [1], given: 0
Intern
Joined: 26 May 2008
Posts: 40
Kudos [?]: 5 [0], given: 0
Re: PS - horses and ponies [#permalink]
Show Tags
28 May 2008, 00:42
Thanks for the lucid explaination.
Kudos [?]: 5 [0], given: 0
CEO
Joined: 29 Mar 2007
Posts: 2553
Kudos [?]: 528 [0], given: 0
Re: PS - horses and ponies [#permalink]
Show Tags
28 May 2008, 08:38
kapilnegi wrote:
A ranch has horses and ponies. Five-sixths of the ponies have horseshoes. Half of the ponies with horseshoes are Icelandic. If there are three more horses than ponies, what is the minimum number of horses and ponies on the ranch?
A) 12
B) 15
C) 27
D) 48
E) 54
I couldnot decipher the icelandic part..
P=ponies
H=Horses
5/6p have horshoes. 1/2*5/6p are icelandic. --> 5/12p
3+p=h
min for p must be 12 b/c we have to have a whole number for 5/12p ---> thus 12=p and 15=h
27.
C
Kudos [?]: 528 [0], given: 0
Re: PS - horses and ponies [#permalink] 28 May 2008, 08:38
Display posts from previous: Sort by | 911 | 2,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2017-47 | latest | en | 0.893941 |
http://acm.scu.edu.cn/soj/problem/1009/ | 1,642,739,989,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320302723.60/warc/CC-MAIN-20220121040956-20220121070956-00455.warc.gz | 1,827,872 | 1,539 | New Zealand currency consists of \$100, \$50, \$20, \$10, and \$5 notes and \$2, \$1, 50c, 20c, 10c and 5c coins. Write a program that will determine, for any given amount, in how many ways that amount may be made up. Changing the order of listing does not increase the count. Thus 20c may be made up in 4 ways: 1 20c, 2 10c, 10c+2 5c, and 4 5c.
## Input
Input will consist of a series of real numbers no greater than \$50.00 each on a separate line. Each amount will be valid, that is will be a multiple of 5c. The file will be terminated by a line containing zero (0.00).
## Output
Output will consist of a line for each of the amounts in the input, each line consisting of the amount of money (with two decimal places and right justified in a field of width 5), followed by the number of ways in which that amount may be made up, right justified in a field of width 12.
```0.20
2.00
0.00```
## Sample output
``` 0.20 4
2.00 293``` | 279 | 958 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-05 | latest | en | 0.928194 |
http://www.helpteaching.com/questions/Physics/College | 1,511,244,320,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806317.75/warc/CC-MAIN-20171121055145-20171121075145-00039.warc.gz | 419,020,596 | 11,507 | Looking for Physics worksheets?
Check out our pre-made Physics worksheets!
Tweet
You are browsing College questions. View questions in All Grades.
# College Physics Questions
You can create printable tests and worksheets from these College Physics questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.
Previous Next
College Light and Optics
What is a fixed quantity of light energy?
1. Photon
2. Light reaction
3. Photoautotroph
4. Autotrophs
College Quantum Physics and the Atom
Which range of wavelength is involved in the visible spectrum?
1. $10^-12 m$
2. $4 xx 10^-7 "m to 7" xx 10^-7 m$
3. $10^-2 m$
4. $10^4 m$
College Quantum Physics and the Atom
Which of the following correctly describes the changes in frequency and energy, in moving from radio waves to gamma rays?
1. Energy and frequency both decrease
2. Energy and frequency both increase
3. Energy increases, and frequency decreases
4. Energy decreases, and frequency increases
College Forces and Motion
The sum of all the external forces on a system of particles is zero. Which of the
following must be true of the system?
1. The total mechanical energy is constant.
2. The total potential energy is constant.
3. The total kinetic energy is constant.
4. The total linear momentum is constant.
5. It is in static equilibrium.
College Forces and Motion
If a particle moves in a plane so that its position is described by the functions
$x=Acosomegat$ and $y=Asinomegat$, the particle is
1. moving with constant speed along a circle.
2. moving with varying speed along a circle.
3. moving with constant acceleration along a straight line.
4. moving along a parabola.
5. oscillating back and forth along a straight line.
College Thermodynamics
Which of the following can be used to calculate entropy changes in reactions?
1. $∆Gº_{reaction}=∑n_{r}∆Gº_f{"reactants"}-∑n_{p}∆Gº_f{"products"}$
2. $∆Gº_{reaction}=∑n_{r}∆Gº_f{"reactants"}+∑n_{p}∆Gº_f{"products"}$
3. $∆Gº_{reaction}=∑n_{p}∆Gº_f{"products"}-∑n_{r}∆Gº_f{"reactants"}$
4. None of the above
College Quantum Physics and the Atom
Which of the following describes electron spin quantum number?
1. An orbital holds two electrons, and they have identical spin
2. An orbital holds three electrons, and they have identical spins
3. An orbital holds two electrons, and they have opposite spins
4. An orbital holds three electrons, and they have opposite spins
College Matter
Metals, minerals, water and air are examples of:
1. natural alloys
2. inorganic substances
3. compound gases
4. proteins
College Forces and Motion
A football is tossed up into the air in the +y direction. Which of the following is true at the point where the football reaches the ground?
1. the velocity of the ball is negative and the acceleration is negative
2. the velocity of the ball is negative and the acceleration is positive
3. the velocity of the ball is positive and the acceleration is negative
4. the velocity of the ball is positive and the acceleration is positive
5. the velocity of the ball is zero and the acceleration is negative
College Quantum Physics and the Atom
College Thermodynamics
Which of the following correctly describes the Second Law of Thermodynamics?
1. The universe is constantly decreasing in disorder
2. The entropy in the universe is equal to zero
3. The universe is constantly increasing in disorder
4. None of the above
College Quantum Physics and the Atom
To which of the following elements does the Bohr model apply to?
1. helium, only
2. hydrogen and helium
3. hydrogen, only
4. hydrogen, helium, and lithium
College Thermodynamics
Which of the following correctly represents when the equilibrium point occurs?
1. When the value of ∆Gº=1, only
2. When the value of ∆Gº<0, only
3. When the value of ∆Gº>0, only
4. At the lowest value of free energy available to the system
College Quantum Physics and the Atom
Which of the following correctly describes the Bohr Model?
1. The electron exists in triangular regions called orbitals
2. Electrons are distributed randomly throughout an atom
3. Electrons are distributed in a dense region known as an orbital
4. Electrons are distributed in a circular region known as orbits
College Thermodynamics
College Thermodynamics
Which of the following represents ∆Gº, in terms of temperature?
1. $∆Gº=∆Hº+T∆Sº$
2. $∆Gº=∆Hº-T∆Sº$
3. $∆Gº=∆Hº-T/{∆Sº}$
4. $∆Gº=-∆Hº-T∆Sº$
Previous Next
You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges. | 1,158 | 4,558 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2017-47 | latest | en | 0.834185 |
http://www.defaultlogic.com/learn?s=Point_(typography) | 1,544,624,728,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823895.25/warc/CC-MAIN-20181212134123-20181212155623-00381.warc.gz | 367,399,607 | 23,712 | Point (typography)
Point
Unit systemtypographic unit
Unit oflength
Conversions
typographic units picas
imperial/US units in
metric (SI) units0.3528 mm
In typography, the point is the smallest unit of measure. It is used for measuring font size, leading, and other items on a printed page. The size of the point has varied throughout the history of printing. Since the 18th century, the point's size has varied from 0.18 to 0.4 millimeters. Following the advent of desktop publishing in the 1980s and 1990s, digital printing has largely supplanted the letterpress printing and has established the DTP point (desktop publishing point) as the de facto standard. The DTP point is defined as of an international inch (about 0.353 mm) and, as with earlier American point sizes, is considered to be of a pica.
In metal type, the point size of the font described the height of the metal body on which the typeface's characters were cast. In digital type, letters of a font are designed around an imaginary space called an em square. When a point size of a font is specified, the font is scaled so that its em square has a side length of that particular length in points. Although the letters of a font usually fit within the font's em square, there is not necessarily any size relationship between the two, so the point size does not necessarily correspond to any measurement of the size of the letters on the printed page.[1][2]
## History
The point was first established by the Milanese typographer, Francesco Torniella da Novara (c. 1490 - 1589) in his 1517 alphabet, L'Alfabeto. The construction of the alphabet is the first based on logical measurement called "Punto," which corresponds to the ninth part of the height of the letters or the thickness of the principal stroke.[3][4]
## Notations
A measurement in points can be represented in three different ways. For example, 14 points (1 pica plus 2 points) can be written:
• (12 points would be just "")--traditional style
• 1p2 (12 points would be just "1p")--format for desktop
• 14pt (12 points would be "12pt" or "1pc" since it is the same as 1 pica)--format used by Cascading Style Sheets defined by the World Wide Web Consortium.[5]
## Varying standards
### Comparison table
Various point definitions
Name Year mm inch
Fournier[6] 1737 ? 0.345
American 1886
Japanese[7] 1962
TeX `pt` 1982 = 0.35145980 =
PostScript, CSS `pt`, TeX `bp` 1984 = 0.3527 = 0.0138 =
Didot 1783
Berthold 1878 ? 0.376
German actual,[8] TeX `dd` 1964
German nominal[8] 1984
Other
Truchet 1694 ? 0.188
L'Imprimerie Nationale 1810 = 0.400
German,[9] Japanese, CSS `q` 1999
There have been many definitions of a "point" since the advent of typography. Traditional continental European points at about are usually a bit larger than English points at around .
### French points
The Truchet point, the first modern typographic point, was of a French inch or of the royal foot. It was invented by the French clergyman Sébastien Truchet. During the metrication of France amid its revolution, a 1799 law declared the meter to be exactly 443.296 French lines long. This established a length to the royal foot of m or about 325 mm, which made the Truchet point equal to mm or about . It has also been cited as exactly 0.188 mm.
The Fournier point was established by Pierre Simon Fournier in 1737.[10][11][12]:60-66 The system of Fournier was based on a foot, 1 foot equals 12 inches, 1 inch (pouce) was divided into 12 lines (lignes) and 1 line was further divided into 6 typographic points (points typographiques). 1 point Fournier = 0.0135 inches.
The Fournier scale: two inches in total, divided into four half-inches, the medium intervals are one line ( inch), and the smallest intervals are inch; no intervals for the point is given, though
Fournier printed a reference scale of 144 points over two inches; however, it was too rough to accurately measure a single point.[11]
The Didot point, established by François-Ambroise Didot in 1783,[13] was an attempt to improve the Fournier system. He did not change the subdivisions (1 inch = 12 lines = 72 points), but defined it strictly in terms of the royal foot, a legal length measure in France: the Didot point is exactly of a French foot or of a French inch, that is (by 1799) mm or about . Accordingly, one Didot point is exactly two Truchet points.
However, 12 Fournier points turned out to be 11 Didot points,[11]:142-145 giving a Fournier point of about ; later sources[12]:60-61 state it as being . In Belgium the Fournier system was used until the 1970s and later. It was called the "mediaan"-system. To avoid confusion between the new and the old sizes, Didot also rejected the traditional names, thus parisienne became corps 5, nonpareille became corps 6, and so on.[11]:143 The Didot system prevailed because the French government demanded printing in Didot measurements.[14][better source needed]
The Fournier point did not achieve lasting popularity despite being revived by the Monotype Corporation in 1927.[] It was still a standard in Belgium, in parts of Austria, and in Northern France at the beginning of the 20th century.[12]:66
### Other European points
Approximations were subsequently employed, largely owing to the Didot point's unwieldy conversion to metric units (the divisor of its conversion ratio has the prime factorization of 3×7×1979).
In 1878 Hermann Berthold defined 798 points as being equal to 30 cm, or 2660 points equalling 1 meter: that gives around to the point.[15][16][17][18] A more precise number,, sometimes is given;[16] this is used by TeX as the `dd` unit. This has become the standard in Germany[8] and Central and Eastern Europe.[19] This size is still mentioned in the technical regulations of the Eurasian Economic Union.[20]
### Metric points
TeX also supports a new Didot point (nd) at mm or and cites a 1978 redefinition for it.[] The French National Print Office adopted a point of mm or in about 1810 and continues to use this measurement today (though "recalibrated" to ).[21][22][23]
Japanese[24] and German[9][16][18] standardization bodies instead opted for a metric typographic base measure of exactly mm or , which is sometimes referred to as the quart in Japan. The symbol Q us used in Japanese after the initial letter of quarter millimeter. Due to demand by Japanese typesetters, CSS adopted Q in 2015.[25][26]
### American points
The basic unit of measurements in American typography was the pica,[27][12][28] usually approximated as one sixth of an inch, but the exact size was not standardized, and various type foundries had been using their own.[12]
After the American war of Independence Benjamin Franklin was sent as commissioner (Ambassador) for the United States to France (December 1776 to 1785).[29] Whilst there he had intimate contact with the Fournier family, including the father and Pierre Simon Fournier. Franklin wanted to teach his grandson printing and typefounding, and arranged him to be trained by Francois Ambroise Didot. Franklin bought also matrices and more equipment in order to set up a type-foundry for Bache and brought this with him, when he returned to Philadelphia. Around 1790 Bache published a specimen sheet with some Fournier types. [30][31] After the death of Franklin, the matrices and the Fournier mould were acquired by Binny and Ronaldson, the first permanent type-foundry in America. In 1833 this plant was merged into the firm that in 1860 was renamed in Mackellar, Smith and Jordan. The Fournier cicero mould was used by them to cast pica-sized type.
Nelson Hawks proposed, like Fournier, to divide one American inch exactly into six picas, and one pica into 12 points. However, this saw an opposition because the majority of foundries had been using picas less than one sixth of an inch. So in 1886, after some examination of various picas, the Type Founders Association of the United States approved the pica of the MacKellar, Smiths, & Jordan Co. foundry of Philadelphia (previously L. Johnson & Co., hence the Johnson pica) as the most established.[27] The official definition of one pica is 0.166044 inches (4.2175 mm), and one point is 0.013837 inches (0.3515 mm). That means 6 picas or 72 points constitute standard inches. A less precise definition is one pica equals 0.166 inches (4.2 mm), and one point 0.01383 inches (0.351 mm).[27][32] It was also noticed that 83 picas is nearly equal to 35 cm, so the Type Founders Association also suggested using a 35 cm metal rod for measurements, but this was not accepted by every foundry.[27]
This has become known as the American point system.[32][27] The British foundries accepted this in 1898.
In modern times this size of the point has been approximated as exactly (0.01383700013837) of the inch[33] by Donald Knuth for the default unit of his TeX computer typesetting system and is thus sometimes known as the , which is 0.35145980 mm.
### Desktop publishing point
The desktop publishing point (DTP point) or PostScript point is defined as or 0.0138 of the international inch, making it equivalent to 0.3527 mm. Twelve points make up a pica, and six picas make an inch.
This specification was developed by John Warnock and Charles Geschke when they created Adobe PostScript. It was adopted by Apple Computer as the standard for the display resolution of the original Macintosh desktop computer and the print resolution for the LaserWriter printer.[34][35]
In 1996, it was adopted by W3C for Cascading Stylesheets (CSS) where it was later related at a fixed 4:3 ratio to the pixel due to a general (but wrong) assumption of 96 pixel-per-inch screens.
## Font sizes
In lead typecasting, most font sizes commonly used in printing have conventional names that differ by country, language and the type of points used.
Desktop publishing software and word processors intended for office and personal use often have a list of suggested font sizes in their user interface, but they are not named and usually an arbitrary value can be entered manually. Microsoft Word, for instance, suggests every even size between 8 and 28 points and, additionally, 9, 11, 36, 48 and 72 points, i.e. the larger sizes equal 3, 4 and 6 picas. While most software nowadays defaults to DTP points, many allow other units, especially code-based systems like TeX and CSS.
## References
1. ^ Phinney, Thomas (16 August 2012). "Point Size and the Em Square: Not What People Think". Phinney on Fonts. Retrieved 2018.
2. ^ "15.7. Font size: the 'font-size' property", Cascading Style Sheets Level 2 Revision 2 (CSS 2.2) Specification, World Wide Web Consortium, 12 April 2016, retrieved 2018
3. ^ Giovanni Mardersteig (1971). The alphabet of Francesco Torniello da Novara [1517]: Followed by a comparison with the alphabet of Fra Luca Pacioli. Officina Bodoni.
4. ^ Healey, Robin (2011). Italian Literature Before 1900 in English Translation: An Annotated Bibliography, 1929-2008. University of Toronto Press. ISBN 9781442642690.
5. ^ "4.3.2. Lengths", Cascading Style Sheets, level 2 CSS2 Specification, World Wide Web Consortium, 12 April 2016, retrieved 2018
6. ^ Various sources give different sizes, namely , ? , ? , (exactly) , ? , ? .
7. ^ JIS Z 8305. ?. Dimensions of Printing Types.
8. ^ a b c DIN 16507-1:1998 and its predecessors, at least since 1964, for lead typecasting defined 2660 points to measure 1000.333 mm at 20 °C, but for public communication it later introduced a rounder value.
9. ^ a b DIN 16507-2 (1984, 1999) does not specify a custom unit for electronic typography, but measures using a module.
10. ^ Fournier, Pierre Simon (1764). Manuel typographique. pp. 125-138.
11. ^ a b c d De Vinne, Theodore Low (1900). The practice of typography. 1. New York: Century Co. pp. 133-145.
12. Legros, Lucien Alphonse; Grant, John Cameron (1916). Typographical Printing-Surfaces. London and New York: Longmann, Green, and Co. pp. 57-60.
13. ^ Baines, Phil; Haslam, Andrew (2005). Type & Typography. Laurence King Publishing. p. 93. ISBN 978-1-85669-437-7.
14. ^ L. Ronner, Van leerling tot Zetter, 1913, N.V.De nieuwe Tijd, Amsterdam, pag 30.
15. ^ Smalian, Hermann (1899). "Type Systems of To-day". The British Printer. XII (68): 130-131. They commissioned for this purpose the well-known Berlin brass rule manufacturer, H. Berthold, who supplies brass rules not only to most of the German foundries but also to many foreign houses, and he, in conjunction with Prof. W. Fürster, the chief director of the Berlin Observatory, agreed that 2660 typographical points of the Didot system should correspond to one metre. Accordingly the Standard Gauge Commission in Berlin in 1879 arranged a standard measure of 30 centimetres = 133 nonpareil or 798 typographical points, and gave a copy to all the German foundries, and since that time disputes about the Didot depth were unknown in Germany.
16. ^ a b c Brekle, Herbert E. (1994). "Typographie". Schrift und Schriftlichkeit / Writing and its Use. Walter de Gruyter. p. 210ff. ISBN 978-3-11-020323-3.
17. ^ Funke, Fritz (1998). Buchkunde. De Gruyter. p. 194. ISBN 978-3-11-094929-2.
18. ^ a b Blana, Hubert (1999). Die Herstellung: Ein Handbuch für die Gestaltung, Technik und Kalkulation von Buch, Zeitschrift und Zeitung. Walter de Gruyter. p. 101. ISBN 978-3-11-096787-6.
19. ^ (in Russian) "§1.3". GOST 3489.1-71. Printing types (Russian and Roman graphic bases). Group arrangement. Indexing. Base line. Characters per 4 picas ? 3489.1-71. ( ? ? ?). . ?. . ?. ? ? ?. 0,376 .
20. ^ (in Russian) 8. 11. // 007/2011. ? (? ? ?) , ?-? .
21. ^ Mosley, James (1997). "French academicians and modern typography: designing new types in the 1690s". Typography papers (2): 5-29. The point in current use at the Imprimerie Nationale measures 0.39877 mm. This appears to be the result of a 'recalibration', for which no date can be given, of the point of 0.4 mm.
22. ^ Bulletin du bibliophile. 2002. p. 73. These latter figures give the size in the 'points millimétriques' of about 0.4 mm that are said to have been introduced at the Imprimerie impériale by Firmin Didot and which are the basis for the 'point IN' used today at the Imprimerie nationale.
23. ^ "Type bodies compared". Typefoundry. 30 April 2008.
24. ^ JIS X 4052:2000, JIS Z 8125:2004
25. ^ "CSS Values and Units Module Level 3". World Wide Web Consortium. 29 September 2016.
26. ^ "CSS Values and Units Module Level 3". World Wide Web Consortium. 11 June 2015.
27. De Vinne, Theodore Low (1900). The practice of typography. 1. New York: Century Co. pp. 145-156.
28. ^ Hyde, Grant Milnor (1920). Newspaper Editing: A Manual for Editors, Copyreaders, and Students of Newspaper Desk Work. New York and London: D. Appleton and Company. pp. 226-227.
29. ^ Benjamin Franklin papers, Kislak Center for Special Collections, Rare Books and Manuscripts, University of Pennsylvania
30. ^ Updike, I, p. 257, II pp. 152-3
31. ^ Allen Huet, Fournier the compleat typographer, 1972, London, Frederik Muller Ltd, page 3, 4, 62, 63
32. ^ a b "The American Point System". American printer and lithographer. 11: 89. 1890.
33. ^ Knuth, Donald E. (1990). The TeXbook (17th revised ed.). Addison-Wesley. p. 58.
34. ^ Tucker, H. A. (1988). "Desktop Publishing". In Ruiter, Maurice M. de. Advances in Computer Graphics III. Springer. p. 296. ISBN 3-540-18788-X.
35. ^ Spring, Michael B. (1991). Electronic printing and publishing: the document processing revolution. CRC Press. p. 46. ISBN 0-8247-8544-4.
Connect with defaultLogic
What We've Done
Led Digital Marketing Efforts of Top 500 e-Retailers.
Worked with Top Brands at Leading Agencies.
Successfully Managed Over \$50 million in Digital Ad Spend.
Developed Strategies and Processes that Enabled Brands to Grow During an Economic Downturn. | 4,252 | 15,766 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2018-51 | latest | en | 0.913727 |
https://www.netlib.org/lapack/explore-html-3.6.1/da/dce/ztpqrt2_8f_source.html | 1,713,880,107,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818711.23/warc/CC-MAIN-20240423130552-20240423160552-00280.warc.gz | 819,052,842 | 8,489 | LAPACK 3.6.1 LAPACK: Linear Algebra PACKage
ztpqrt2.f
Go to the documentation of this file.
1 *> \brief \b ZTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztpqrt2.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztpqrt2.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztpqrt2.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZTPQRT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDA, LDB, LDT, N, M, L
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> ZTPQRT2 computes a QR factorization of a complex "triangular-pentagonal"
37 *> matrix C, which is composed of a triangular block A and pentagonal block B,
38 *> using the compact WY representation for Q.
39 *> \endverbatim
40 *
41 * Arguments:
42 * ==========
43 *
44 *> \param[in] M
45 *> \verbatim
46 *> M is INTEGER
47 *> The total number of rows of the matrix B.
48 *> M >= 0.
49 *> \endverbatim
50 *>
51 *> \param[in] N
52 *> \verbatim
53 *> N is INTEGER
54 *> The number of columns of the matrix B, and the order of
55 *> the triangular matrix A.
56 *> N >= 0.
57 *> \endverbatim
58 *>
59 *> \param[in] L
60 *> \verbatim
61 *> L is INTEGER
62 *> The number of rows of the upper trapezoidal part of B.
63 *> MIN(M,N) >= L >= 0. See Further Details.
64 *> \endverbatim
65 *>
66 *> \param[in,out] A
67 *> \verbatim
68 *> A is COMPLEX*16 array, dimension (LDA,N)
69 *> On entry, the upper triangular N-by-N matrix A.
70 *> On exit, the elements on and above the diagonal of the array
71 *> contain the upper triangular matrix R.
72 *> \endverbatim
73 *>
74 *> \param[in] LDA
75 *> \verbatim
76 *> LDA is INTEGER
77 *> The leading dimension of the array A. LDA >= max(1,N).
78 *> \endverbatim
79 *>
80 *> \param[in,out] B
81 *> \verbatim
82 *> B is COMPLEX*16 array, dimension (LDB,N)
83 *> On entry, the pentagonal M-by-N matrix B. The first M-L rows
84 *> are rectangular, and the last L rows are upper trapezoidal.
85 *> On exit, B contains the pentagonal matrix V. See Further Details.
86 *> \endverbatim
87 *>
88 *> \param[in] LDB
89 *> \verbatim
90 *> LDB is INTEGER
91 *> The leading dimension of the array B. LDB >= max(1,M).
92 *> \endverbatim
93 *>
94 *> \param[out] T
95 *> \verbatim
96 *> T is COMPLEX*16 array, dimension (LDT,N)
97 *> The N-by-N upper triangular factor T of the block reflector.
98 *> See Further Details.
99 *> \endverbatim
100 *>
101 *> \param[in] LDT
102 *> \verbatim
103 *> LDT is INTEGER
104 *> The leading dimension of the array T. LDT >= max(1,N)
105 *> \endverbatim
106 *>
107 *> \param[out] INFO
108 *> \verbatim
109 *> INFO is INTEGER
110 *> = 0: successful exit
111 *> < 0: if INFO = -i, the i-th argument had an illegal value
112 *> \endverbatim
113 *
114 * Authors:
115 * ========
116 *
117 *> \author Univ. of Tennessee
118 *> \author Univ. of California Berkeley
119 *> \author Univ. of Colorado Denver
120 *> \author NAG Ltd.
121 *
122 *> \date September 2012
123 *
124 *> \ingroup complex16OTHERcomputational
125 *
126 *> \par Further Details:
127 * =====================
128 *>
129 *> \verbatim
130 *>
131 *> The input matrix C is a (N+M)-by-N matrix
132 *>
133 *> C = [ A ]
134 *> [ B ]
135 *>
136 *> where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
137 *> matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
138 *> upper trapezoidal matrix B2:
139 *>
140 *> B = [ B1 ] <- (M-L)-by-N rectangular
141 *> [ B2 ] <- L-by-N upper trapezoidal.
142 *>
143 *> The upper trapezoidal matrix B2 consists of the first L rows of a
144 *> N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
145 *> B is rectangular M-by-N; if M=L=N, B is upper triangular.
146 *>
147 *> The matrix W stores the elementary reflectors H(i) in the i-th column
148 *> below the diagonal (of A) in the (N+M)-by-N input matrix C
149 *>
150 *> C = [ A ] <- upper triangular N-by-N
151 *> [ B ] <- M-by-N pentagonal
152 *>
153 *> so that W can be represented as
154 *>
155 *> W = [ I ] <- identity, N-by-N
156 *> [ V ] <- M-by-N, same form as B.
157 *>
158 *> Thus, all of information needed for W is contained on exit in B, which
159 *> we call V above. Note that V has the same form as B; that is,
160 *>
161 *> V = [ V1 ] <- (M-L)-by-N rectangular
162 *> [ V2 ] <- L-by-N upper trapezoidal.
163 *>
164 *> The columns of V represent the vectors which define the H(i)'s.
165 *> The (M+N)-by-(M+N) block reflector H is then given by
166 *>
167 *> H = I - W * T * W**H
168 *>
169 *> where W**H is the conjugate transpose of W and T is the upper triangular
170 *> factor of the block reflector.
171 *> \endverbatim
172 *>
173 * =====================================================================
174 SUBROUTINE ztpqrt2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
175 *
176 * -- LAPACK computational routine (version 3.4.2) --
177 * -- LAPACK is a software package provided by Univ. of Tennessee, --
178 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
179 * September 2012
180 *
181 * .. Scalar Arguments ..
182 INTEGER INFO, LDA, LDB, LDT, N, M, L
183 * ..
184 * .. Array Arguments ..
185 COMPLEX*16 A( lda, * ), B( ldb, * ), T( ldt, * )
186 * ..
187 *
188 * =====================================================================
189 *
190 * .. Parameters ..
191 COMPLEX*16 ONE, ZERO
192 parameter( one = (1.0,0.0), zero = (0.0,0.0) )
193 * ..
194 * .. Local Scalars ..
195 INTEGER I, J, P, MP, NP
196 COMPLEX*16 ALPHA
197 * ..
198 * .. External Subroutines ..
199 EXTERNAL zlarfg, zgemv, zgerc, ztrmv, xerbla
200 * ..
201 * .. Intrinsic Functions ..
202 INTRINSIC max, min
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input arguments
207 *
208 info = 0
209 IF( m.LT.0 ) THEN
210 info = -1
211 ELSE IF( n.LT.0 ) THEN
212 info = -2
213 ELSE IF( l.LT.0 .OR. l.GT.min(m,n) ) THEN
214 info = -3
215 ELSE IF( lda.LT.max( 1, n ) ) THEN
216 info = -5
217 ELSE IF( ldb.LT.max( 1, m ) ) THEN
218 info = -7
219 ELSE IF( ldt.LT.max( 1, n ) ) THEN
220 info = -9
221 END IF
222 IF( info.NE.0 ) THEN
223 CALL xerbla( 'ZTPQRT2', -info )
224 RETURN
225 END IF
226 *
227 * Quick return if possible
228 *
229 IF( n.EQ.0 .OR. m.EQ.0 ) RETURN
230 *
231 DO i = 1, n
232 *
233 * Generate elementary reflector H(I) to annihilate B(:,I)
234 *
235 p = m-l+min( l, i )
236 CALL zlarfg( p+1, a( i, i ), b( 1, i ), 1, t( i, 1 ) )
237 IF( i.LT.n ) THEN
238 *
239 * W(1:N-I) := C(I:M,I+1:N)**H * C(I:M,I) [use W = T(:,N)]
240 *
241 DO j = 1, n-i
242 t( j, n ) = conjg(a( i, i+j ))
243 END DO
244 CALL zgemv( 'C', p, n-i, one, b( 1, i+1 ), ldb,
245 \$ b( 1, i ), 1, one, t( 1, n ), 1 )
246 *
247 * C(I:M,I+1:N) = C(I:m,I+1:N) + alpha*C(I:M,I)*W(1:N-1)**H
248 *
249 alpha = -conjg(t( i, 1 ))
250 DO j = 1, n-i
251 a( i, i+j ) = a( i, i+j ) + alpha*conjg(t( j, n ))
252 END DO
253 CALL zgerc( p, n-i, alpha, b( 1, i ), 1,
254 \$ t( 1, n ), 1, b( 1, i+1 ), ldb )
255 END IF
256 END DO
257 *
258 DO i = 2, n
259 *
260 * T(1:I-1,I) := C(I:M,1:I-1)**H * (alpha * C(I:M,I))
261 *
262 alpha = -t( i, 1 )
263
264 DO j = 1, i-1
265 t( j, i ) = zero
266 END DO
267 p = min( i-1, l )
268 mp = min( m-l+1, m )
269 np = min( p+1, n )
270 *
271 * Triangular part of B2
272 *
273 DO j = 1, p
274 t( j, i ) = alpha*b( m-l+j, i )
275 END DO
276 CALL ztrmv( 'U', 'C', 'N', p, b( mp, 1 ), ldb,
277 \$ t( 1, i ), 1 )
278 *
279 * Rectangular part of B2
280 *
281 CALL zgemv( 'C', l, i-1-p, alpha, b( mp, np ), ldb,
282 \$ b( mp, i ), 1, zero, t( np, i ), 1 )
283 *
284 * B1
285 *
286 CALL zgemv( 'C', m-l, i-1, alpha, b, ldb, b( 1, i ), 1,
287 \$ one, t( 1, i ), 1 )
288 *
289 * T(1:I-1,I) := T(1:I-1,1:I-1) * T(1:I-1,I)
290 *
291 CALL ztrmv( 'U', 'N', 'N', i-1, t, ldt, t( 1, i ), 1 )
292 *
293 * T(I,I) = tau(I)
294 *
295 t( i, i ) = t( i, 1 )
296 t( i, 1 ) = zero
297 END DO
298
299 *
300 * End of ZTPQRT2
301 *
302 END
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine zlarfg(N, ALPHA, X, INCX, TAU)
ZLARFG generates an elementary reflector (Householder matrix).
Definition: zlarfg.f:108
subroutine zgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERC
Definition: zgerc.f:132
subroutine ztpqrt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
ZTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Definition: ztpqrt2.f:175
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:149 | 3,544 | 9,338 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-18 | latest | en | 0.371148 |
https://wiki.haskell.org/index.php?title=99_questions/Solutions/39&oldid=38299 | 1,495,859,066,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608773.42/warc/CC-MAIN-20170527040600-20170527060600-00013.warc.gz | 998,773,647 | 6,050 | # 99 questions/Solutions/39
Jump to: navigation, search
(*) A list of prime numbers.
Given a range of integers by its lower and upper limit, construct a list of all prime numbers in that range.
Solution 1:
```primesR :: Integral a => a -> a -> [a]
primesR a b = filter isPrime [a..b]```
If we are challenged to give all primes in the range between a and b we simply take all number from a up to b and filter the primes out.
Solution 2:
```primes :: Integral a => [a]
primes = let sieve (n:ns) = n:sieve [ m | m <- ns, m `mod` n /= 0 ] in sieve [2..]
primesR :: Integral a => a -> a -> [a]
primesR a b = takeWhile (<= b) \$ dropWhile (< a) primes```
Another way to compute the claimed list is done by using the Sieve of Eratosthenes. The
primes
function generates a list of all (!) prime numbers using this algorithm and
primesR
filter the relevant range out. [But this way is very slow and I only presented it because I wanted to show how nicely the Sieve of Eratosthenes can be implemented in Haskell :)] | 285 | 1,014 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2017-22 | latest | en | 0.848304 |
https://math.stackexchange.com/questions/3026333/can-an-undirected-graph-be-disconnected/3026345 | 1,718,245,578,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861319.37/warc/CC-MAIN-20240612234213-20240613024213-00447.warc.gz | 362,502,365 | 37,709 | # Can an undirected graph be disconnected?
This may be a rather trivial question but I am still trying to get the hang of all the graph theory terms. Nonetheless, I haven't found a source that explicitly says that an undirected graph can only be connected so is it possible to have an undirected graph that is disconnected? And if so, may I have an example one?
Much thanks!
• if they are made of separate pieces.
– hbm
Commented Dec 4, 2018 at 23:30
• Here's an example of (the diagram of) a disconnected undirected graph: $$\huge ○\,\,\,\, ○$$ Commented Dec 4, 2018 at 23:30
## 4 Answers
Undirected just mean The edges does not have direction. connected means that there is a path from any vertex of the graph to any other vertex in the graph. so take any disconnected graph whose edges are not directed to give an example. following is one:
Yes. The simplest such graph is just two vertices (no edges).
The definition of graph that I know is the following: A graph consists of two sets $$(V,E)$$ where $$V$$ is the set of vertices and $$E$$ is the set of edges.
The elements of $$E$$ are subsets (or multisets in the case of loops) of cardinality $$2$$ of $$V$$.
A graph is undirected if $$\{x,y\}=\{y,x\}$$ where $$\{x,y\},\{y,x\}\in E$$ and it is directed if $$\{x,y\}\neq \{y,x\}$$.
Therefore, by taking $$V=\{a,b,c\}$$ and $$E=\{\{a,b\}\}$$, you obtain a disconnected undirected graph.
I believe, since you can define a graph $$G = (E,V)$$ by its edge and vertex sets, it is perfectly ok to have a disconnected graph (i.e. a graph with no path between some vertices). In fact, taking $$E$$ to be empty still results in a graph. | 449 | 1,645 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-26 | latest | en | 0.963273 |
https://primes.utm.edu/curios/page.php?number_id=97 | 1,585,777,727,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370506121.24/warc/CC-MAIN-20200401192839-20200401222839-00513.warc.gz | 656,441,761 | 5,792 | # 163
A prime whose reversal is another prime (19) squared. [Trigg]
In the April 1975 issue of Scientific American, Martin Gardner wrote (jokingly) that Ramanujan's constant (e^(π*sqrt(163))) is an integer. The name "Ramanujan's constant" was actually coined by Simon Plouffe and derives from the above April Fool's joke played by Gardner. The French mathematician Charles Hermite (1822-1901) observed this property of 163 long before Ramanujan's work on these so-called "almost integers." [Aitken]
The largest Heegner number. [Croll]
163 = "is a prime number" by adding the letters in the alphabet code, i.e., a = 1, b = 2, c = 3, etc. [Necula]
163 is the smallest prime number that is a factor of more than one number of the form p# - 1 (163 divides both 67# - 1 and 79# - 1).
Let the cs(p) be the cumulative digit sum of all the primes 2 to p (e.g., cs(11)=2+3+5+7+1+1=19). There are the only four known primes such that cs(p)=2p; they are 5, 23, 47 and 163. [Vrba]
163 = 1+2*3^4. [Oliver-Lafont]
163 is the only known number m (up to 3*10^10) such that m + 4*n^2 for n = 0, 1, 2, ... , 19 are prime. [Firoozbakht]
Conjectured to be the largest prime that can be represented uniquely as the sum of three squares (1^2 + 9^2 + 9^2). Note that squares are allowed to be zero. [Noe]
The smallest score impossible to make using up to but not more than 3 darts. [Geach]
The sum 37 + 59 + 67 of all 2-digit irregular primes. [Poo Sung]
The smallest prime p whose pth power pp contains a pandigital substring: 163163 = 38599...(5941863207)...95547. Note that π(163) is a semiprime with larger prime factor 19 which is the smallest prime q whose qth power qq is pandigital, and that the concatenations 16319 and 19163 are also primes. [Beedassy]
According to Cam McLeman, 163 is the coolest number in existence.
163 is the least number k such that decimal representation of 1/k has period of length 81. It is one of a few exceptions to the rule that k=3^(n+2) is the least number with 1/k having period 3^n. [Noe]
The smallest 3-digit prime whose absolute value of the differences between any two of its digits are also prime. [Green]
Some Major League Baseball seasons consists of 163 games. [Post]
Monument Valley is accessible from U.S. Highway 163.
The largest squarefree integer n such that the ring of integers of the field Q(sqrt(-n)) has unique factorization. [Luen]
The prime number 163 contains only the three positive triangular digits, as does the 163rd triangular number (13366). [Gaydos]
CD163 is a protein encoded by the CD163 gene in humans. [Ford]
If A=1, B=2, C=3, ..., Z=26, then COUSIN PRIMES is a cousin prime. [Homewood]
Buying 163 lottery tickets in a 49 number lottery guarantees at least a 3-match. [Homewood]
(There are 7 curios for this number that have not yet been approved by an editor.) | 824 | 2,834 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2020-16 | longest | en | 0.915916 |
https://chess.stackexchange.com/questions/28742/variant-in-which-two-pieces-can-occupy-a-single-square/28897 | 1,716,198,098,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058254.21/warc/CC-MAIN-20240520080523-20240520110523-00014.warc.gz | 139,979,662 | 43,110 | # Variant in which two pieces can occupy a single square
A friend and I tried playing this variant yesterday. My question is:
Surely someone has looked at this before. Does it have a standard name? Or is there something obviously wrong with it that my friend and I missed?
Sometimes this kind of drastic change to the rules produces a game that is obviously no good. (Consider the variant in which the board is turned into a torus; White has already lost, or perhaps wins immediately with 1. QxK, depending on how you look at it.) This variant didn't seem to have an obvious failure, and we had a good time playing one game and seeing how the tactics differed.
Specifically, the variant we played was:
1. All pieces move and capture the same as in standard chess, except:
2. Up to two pieces may occupy the same square.
3. A piece may move into an occupied square, but not through it.
4. A piece moving into a square occupied by two pieces of the opposite color may capture either, but not both.
5. Pieces of opposite colors sharing a square do not threaten one another.
So for example, it was legal for White to open with 1. Rh2, and have the rook and pawn sharing h2. Having done this they could then continue on the following move with 2. Rh4. But 1. Rh4 was illegal.
Since every chess variant imaginable has been tried out, I expect this one has also. I'd like to read about it, but I don't know what to search for.
• The set we were playing with had enough room for two pieces on a square, with no stacking. Mar 3, 2020 at 19:54
• If there is white pawn on e5 and Black plays Ne5, this is not a capture and both pieces remains on e5 ? If White then play Bxe5, she captures the bN and both the wB and the wP remain on e5 ? (just to make sure I understand the rules correctly) Mar 5, 2020 at 10:58
• Yes @Evargalo. Capturing a piece on a location that is doubled up by opponent meant that you got to choose which (one) piece of the two is captured. Then the space is occupied by a single piece from both players at once. This means the king isn't really protected by stacking. Capturing both pieces seemed to make the technique too weak (the capture too strong). Mar 10, 2020 at 21:44
• OK, another question then : after, from the starting position, 1.Nf3 e5 2.Ne5, can White capture the bP or does he has to share square e5 with the bP? Can you choose between double occupation and capture, or is double occupation mandatory when possible? Mar 10, 2020 at 21:51
• You have the choice. It seems that one usually wants to make the capture, but not always. I can imagine there are situations where capture might produce stalemate rather than checkmate. Mar 10, 2020 at 22:00
Pierre-Françoys Brousseau found a similar variant on Guy T Shafer's blog “Insane Chess”. It says:
### Crowded chess
Requires standard chess set & board. Pieces setup, and capture as normal.
Pieces move as normal, except any 2 non-pawn pieces of the same color may share the same square. Men cannot pass through an occupied square: pieces are blocked by men as usual. But you may pass your own piece in 2 turns (one to move onto the occupied square, another to move off that square). Pawns may never share a space with any piece.
This is a little different from our variation, in which pieces of opposite colors may share space, and pawns may share space.
Unfortunately there is no real discussion there.
Ralph Betza has a series of "crowd" games, but they don't quite match what you have in mind. The closest is the note in "Multiple Occupancy Miscellany", section "Crowd Capture":
What happens when you make a capturing move that ends on a square where there is more than one enemy piece? Many rules are possible.
The simple cases are that you capture
• one enemy piece, chosen by the attacker (in this case multicolored crowds are common),
• all enemy pieces, as in Troll Chess
• All pieces, friend or foe,
• No pieces at all.
Other Betza games where multi-occupancy shows up, but isn't perhaps the main attraction:
https://www.chessvariants.com/other.dir/pasgl312-chess.html
https://www.chessvariants.com/diffmove.dir/firefighter-chess.html
This sounds similar to a variant from the Netherlands known as Paco Ŝako ("peace chess"). In Paco Ŝako captured pieces are not removed from the board; instead, they become "merged" and occupy the same square. Merged pieces move as a unit according to the rules for the current player's piece, and cannot capture. However, they can be captured, in which case the capturing piece replaces the same-color piece from the merged pair, which then immediately moves to a new location. This allows a player to move multiple pieces in the same turn. Checkmate occurs when any piece merges with the opponent's king. This implies that the king cannot capture other pieces. Otherwise the rules for movement, castling, en passant, etc. work as in traditional chess. There is a YouTube video which illustrates the basic concepts.
I did not find any information about this variation you are proposing which is interesting, but i do think it is equivalent to a 3D chess game where the board is 8x8x2 and the third dimension will be the "stacking" of the two pieces together on the same square. Then when a piece moves, say for capturing one piece out of the two on the e5 square, it could choose between capturing on e5,1 or e5,2 .
By the way, just a thought on a thing to consider when playing it: if there is a situation where white has king on a1,1 and queen on b2,1 and black with a king on e5,1 and a knight on e5,2 - if Qxe5,2 then it will be a stalemate.
• "if there is a situation where white has king on a1,1 and queen on b2,1 and black with a king on e5,1 and a knight on e5,2 - if Qxe5,2 then it will be a stalemate." I believe this would actually not be stalemate because the queen on e5,2 doesn't deliver check to the king on e5,1 Dec 2, 2020 at 16:12
• It doesn't deliver check - and that's exactly why in black's move he won't have anywhere to go with the king (stalemate). That's considering that the variation allows same dimension to cast checks in other dimensions also (that's because you can also capture in other dimensions). Also need to consider what about moving only dimension up or down - in that case the king is now in check and can capture the queen. Dec 3, 2020 at 13:16
• It's not very much like 8×8×2 chess, because in our game a pawn on the upper part of e4 blocks all movement on the e file and the fourth rank, but in 8×8×2 it wouldn't normally block movement on the lower board. Jul 1, 2023 at 16:44 | 1,606 | 6,563 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-22 | latest | en | 0.983599 |
http://www.kidzworld.com/forums/homework-help/t/928527-im-expert-on-science | 1,524,270,745,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944848.33/warc/CC-MAIN-20180420233255-20180421013255-00127.warc.gz | 444,721,379 | 46,665 | im expert on science
Posted By:
Posts: 1039
need help on science but dont know who is good at it. Well ur question is answered. im the one who can help u. I got all a plus on my grades. so dont be worried to ask me. i got lots of questions for me when i was 7. Im still good at it. just ask me. love ya
Visit my post, If your a new user, post here and i will add you!
Posted By:
Posts: 949
So... The maximum kinetic energy of photoelectrons ejected from a tungsten surface by monochromatic light of wavelength 248nm was fround to be 8.6*10^-20. Find the work function of tungsten? Planck constant = 6.6*10^-34 Js Speed of light = 300,000,000ms-1 Electronic charge = -1.6*10^-19 C Its Physics...
Posted By:
Posts: 391
dont you think thats a bit difficult to work out?
HELLO ALL YOU KW USERS!
Peace & Justice
Posted By:
Posts: 949
"iluvmrmen" wrote:
dont you think thats a bit difficult to work out?
Its only AS level. It isn't crazy university Physics. it was posted mainly as a joke due to the claim of being an "expert in science"...
Posted By:
Posts: 257
i need help with atoms
Posted By:
Posts: 949
Posted almost 7 years ago
Posted By:
Posts: 5
"Mahatama" wrote:
So... The maximum kinetic energy of photoelectrons ejected from a tungsten surface by monochromatic light of wavelength 248nm was fround to be 8.6*10^-20. Find the work function of tungsten? Planck constant = 6.6*10^-34 Js Speed of light = 300,000,000ms-1 Electronic charge = -1.6*10^-19 C Its Physics...
E= φ - KE ∴ φ= KE + E c= λf ∴ f= c/λ E=hf ∴ E = h * c/λ E= KE + h * c/λ Substituting values for 〖KE〗_e = 8.6*10^-20 J, c = 3.00 * 10 ^ 8 m/s, h = 6.63 * 10 ^ -34 J∙s, and λ = 2.48 * 10 ^ 7 m, you should get the result of 8.9 * 10 ^ -19 J, or 5.6 eV, a 24.4% error from the established work function of tungsten, 4.5 eV.
Posted almost 7 years ago
Posted By:
Posts: 7149
"Eddward28" wrote:
"Mahatama" wrote:
So... The maximum kinetic energy of photoelectrons ejected from a tungsten surface by monochromatic light of wavelength 248nm was fround to be 8.6*10^-20. Find the work function of tungsten? Planck constant = 6.6*10^-34 Js Speed of light = 300,000,000ms-1 Electronic charge = -1.6*10^-19 C Its Physics...
E= φ - KE ∴ φ= KE + E c= λf ∴ f= c/λ E=hf ∴ E = h * c/λ E= KE + h * c/λ Substituting values for 〖KE〗_e = 8.6*10^-20 J, c = 3.00 * 10 ^ 8 m/s, h = 6.63 * 10 ^ -34 J∙s, and λ = 2.48 * 10 ^ 7 m, you should get the result of 8.9 * 10 ^ -19 J, or 5.6 eV, a 24.4% error from the established work function of tungsten, 4.5 eV.
Wow. Considering you're only 12 you're very smart.
If you read this you lose the game. | 890 | 2,620 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2018-17 | latest | en | 0.875109 |
https://forums.space.com/threads/question-about-big-bang-theory.53298/ | 1,721,120,588,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514742.26/warc/CC-MAIN-20240716080920-20240716110920-00168.warc.gz | 231,127,902 | 39,231 | # Question about big bang theory
#### Suhana
How did that singular particle get its energy to initiate big bang??
#### Helio
How did that singular particle get its energy to initiate big bang??
This is a complete unknown. The limit of physics may not be able to go all the way to time = 0, though physics can get incredibly close.
BBT begins not at t=0, but a short time before that. This keeps the theory testable and avoids metaphysics and religion, for that matter.
#### billslugg
As I read somewhere "there is no net positive energy in the universe". The positive energy of the matter is exactly balanced by the negative potential energy of the expansion. I don't understand it so I can't answer any challenges, I just read it somewhere.
#### Atlan0001
As I read somewhere "there is no net positive energy in the universe". The positive energy of the matter is exactly balanced by the negative potential energy of the expansion. I don't understand it so I can't answer any challenges, I just read it somewhere.
One place to look, and there are several others, in books and on the web:
Negative energy - Wikipedia
I remember a long time ago reading that when many of his physicist colleagues finally realized this total of energy and worried over it as the totality of energy in the universe (what it might mean), Stephen Hawking told them to quit being bothered with it . . . it was nothing to bother with since the universe was already there (zero balanced between positive and negative energy).
My picture:
I make it that the Cosmological Constant is Base2 binary base, '0' and/or '1' . . . the Universe (U), the Big Mirror. Infinity = '1' (constant!).
The Universe (U) mirrors itself to infinities ('1') and/or ('0' ('-1')) | mirrors itself to infinities ('-1') and/or ('0' ('1')).
Multiverse = (Planck) Big Crunch (M) | Big Vacuum (C = C , , , squaring (C^2)) | (Planck) Big Bang (E) | Simultaneous Equivalents (M) (E).
Is it particle or wave? | Is it point or plane?
It's a multi-dimensional Multiverse Universe.
---------------------------
Try to imagine it if you can: In an infinity of universes (u), how many black holes? In an infinity of space (spaces), how many black holes? In an infinity of time (times), how many black holes? The 'Black Hole' simultaneously everywhere and nowhere.
And then, simultaneously, there is the other, also simultaneously everywhere and nowhere.
----------------------------
I repeat: It's a multi-dimensional Multiverse Universe.
Last edited:
#### voidpotentialenergy
No real answer to how the universe came into being from a particle.
Seems like an unlikely scenario for it to happen then expand into nothing from nothing.
Easier solution is that (nothing) was unstable or carried a potential energy.
Fluctuation was the result of that and energy balance of fluctuations particle creation did the rest.
A BB might be some very long time scale away from nothing=fluctuation=particles= mergers=to much E=BB.
Smoother line of natural processes than a mystery particle just happened.
JMO
#### iconoclastmax
As I read somewhere "there is no net positive energy in the universe". The positive energy of the matter is exactly balanced by the negative potential energy of the expansion. I don't understand it so I can't answer any challenges, I just read it somewhere.
This is very close to the current understanding. Space containing a gravitational field has a negative energy density due to the gravitational field (read Alan Guth's book). Mass with positive energy creates a gravitational field with a negative energy; creation of the negative energy also releases the positive energy that shows up as the mass-energy. A chicken-and-egg situation but since quantum mechanics is fuzzy we have:
initial vacuum with zero energy as an initial state -> final state with total energy zero, positive energy in real mass-energy and negative energy contained in the gravitational field created by that mass-energy.
#### Wind Angel
This question is one of the reasons I signed up here. That magical singularity makes no sense. Why would a singularity with infinite density and no mass form spontaneously in an infinite vacuum that contains zero energy? I can see energy forming spontaneously all over the place in a vacuum but I can't imagine it forming a singularity that could expand and become such a massive universe. My logical mind just can't accept the Big Bang model as the absolute beginning of everything, I think eating cement would be easier.
The only way I can make this make any sense, without adding a creator deity into the equation (and I couldn't imagine why one would create it that way), is to imagine that singularity came from a collapsed ancient universe that got sucked down black holes which absorbed one another until it could go no further and re expanded to become this one.
This makes that pesky Methuselah star and those galaxies that are almost as old as this universe fit smoothly into the big picture (and I predict they're going to find one that is just too old to fit in). I think that our little known universe sits in a void like the little cluster of galaxies in the Bootes Void, and we simply haven't come into contact with the outer universe yet.
I know I sound crazy. And I admit I am eccentric. But there are other theories out there that back up what I think might be true. If only I were better at math and could work one of those amazing equations, maybe I could "prove" my hypothesis mathematically.
#### billslugg
Two points to clarify.
1) Big Bang Theory does not address anything before 10^-43 seconds, therefore BB Theory does not include a singularity.
2) From the beginning there was no "creation of energy from nothing". The books were balanced at "net zero energy" from the start. The energy in the universe has always been exactly balanced by the negative energy due to the expansion.
#### Wind Angel
Two points to clarify.
1) Big Bang Theory does not address anything before 10^-43 seconds, therefore BB Theory does not include a singularity.
2) From the beginning there was no "creation of energy from nothing". The books were balanced at "net zero energy" from the start. The energy in the universe has always been exactly balanced by the negative energy due to the expansion.
Please explain. Every article and science show (including Nova) I have come into contact with all talk of this mysterious singularity that has no explanation. Now you say there is no singularity. Then what was it that expanded?
Now as for this balance of energy- I just went through a month of researching energy in science (which as a terrible definition, btw) and was under the impression that there is no way to actually measure energy itself. So how do they know positive and negative energy is actually balanced? And where did this energy come from in the first place to be balanced ? Something had to have originally come from nothing, didn't it?
I not trying to be argumentative. I am just tired of arguing with my computer screen and getting no response. Googling my questions hasn't worked either!
Helio
#### Helio
Please explain. Every article and science show (including Nova) I have come into contact with all talk of this mysterious singularity that has no explanation. Now you say there is no singularity. Then what was it that expanded?
The use of "singularity" adds "sizzle" to any article. It is ad hoc. We have no evidence infinite density can form with finite mass. Twisted math might do it, but I'm not convinded.
Oddly enough, I just finished typing how the founder of the Big Bang never mentions a point beginning (see the Lemaitre thread). BBT came from Lematire applying the known, but limited, redshift data from Slipher (not Hubble) and the distance measurements from Hubble, and crunching his GR equations to reveal and expanding universe.
Given today's expanding universe, he and others, take BBT to be a theory that addresses the conditions for space as we shrink it by reversing the clock. How far can we go is what Bill mentioned? This trillionith of a second is as far as the best lab can take us, and this too isn't robust with answers. The laws of physics, according to physicists, is that their equations have their wheels flying off the wagon before they reach the first Planck unit of time (10^-43 sec.). Thus, stuffing the singularity into the BBT is like adding a jalapeno to the center of a jumbo shrimp -- the shrimp should be seen as independent of the spicy jalapeno, IMO.
Now as for this balance of energy- I just went through a month of researching energy in science (which as a terrible definition, btw) and was under the impression that there is no way to actually measure energy itself. So how do they know positive and negative energy is actually balanced? And where did this energy come from in the first place to be balanced ? Something had to have originally come from nothing, didn't it?
I would be shocked if there is any objective evidence that some sort of negative labeled energy could be combined with positively labeled energy to zap them out of the universe without any effects. This seems to be more about side-stepping a religious point of view for an initial creation, or whatever one wants to call it. Perhaps I'm wrong, but show me the tests, not the, seemingly ad hoc, math.
Wind Angel
#### Wind Angel
The use of "singularity" adds "sizzle" to any article. It is ad hoc. We have no evidence infinite density can form with finite mass. Twisted math might do it, but I'm not convinded.
Oddly enough, I just finished typing how the founder of the Big Bang never mentions a point beginning (see the Lemaitre thread). BBT came from Lematire applying the known, but limited, redshift data from Slipher (not Hubble) and the distance measurements from Hubble, and crunching his GR equations to reveal and expanding universe.
Given today's expanding universe, he and others, take BBT to be a theory that addresses the conditions for space as we shrink it by reversing the clock. How far can we go is what Bill mentioned? This trillionith of a second is as far as the best lab can take us, and this too isn't robust with answers. The laws of physics, according to physicists, is that their equations have their wheels flying off the wagon before they reach the first Planck unit of time (10^-43 sec.). Thus, stuffing the singularity into the BBT is like adding a jalapeno to the center of a jumbo shrimp -- the shrimp should be seen as independent of the spicy jalapeno, IMO.
I would be shocked if there is any objective evidence some sort of negative labeled energy could be combined with positively labeled energy to zap them out of the universe without any effects. This seems to be more about side-stepping a religious point of view for an initial creation, or whatever one wants to call it. Perhaps I'm wrong, but show me the tests, not the, seemingly ad hoc, math.
Are there any theories out there that you think are better than the BBT? CERN has discovered how particles form spontaneously in a vacuum (or at least claim they have, and I believe them) and I am wondering how this might effect cosmology theories. I've read arguments for and against the Bang and what sits best for me is that it's part of the equation, but isn't the entire equation itself. But then again I want to go beyond a belief that makes me comfortable- I want to know. I want evidence.
Helio
#### billslugg
BB Theory does not address the beginning. There is no singularity in BB Theory. The Big Bang theory only goes as far back as it can given our physics. Our physics stops at 10 to the minus 43 of a second. At that point, in order to go any further back, we would have to exceed the highest possible temperature that there can be. This is called the Planck temperature and is 10^32 K. At this point the wavelength of the particles is smaller than the mean free path between them such that they cannot communicate. Another way of looking at it is they are tiny black holes. Black holes cannot communicate with each other. Communication between them is needed to exchange heat. Can't exchange heat thus can't get any hotter.
There are many theories as to what might have happened at the beginning but those theories are separate from the Big Bang. The Big Bang is nothing more than an extrapolation backwards from the currently observed expansion of the universe.
One theory is there was a "fluctuation in the vacuum" that resulted in space being torn apart and mass and negative energy being created at the same time and flying apart. The energy of the mass and the negative energy always balance such that conservation of mass/energy was never violated.
Another theory is that the universe contracted and bounced.
#### Helio
Are there any theories out there that you think are better than the BBT?
Nothing comes close. The abundance of evidence that matches the predictions has given great strength favoring BBT.
Any new theory must be able to explain, and unify, all the hard observations found in our universe. The following thread lists most of the important ones: Big Bang Bullets
billslugg
#### billslugg
Pre-eminent among the observations any theory must explain is the Cosmic Background Radiation. It is a red-shifted fireball. We are literally looking at a fireball. We can literally see the Big Bang at age 378,000 years.
Helio
#### Helio
Pre-eminent among the observations any theory must explain is the Cosmic Background Radiation. It is a red-shifted fireball. We are literally looking at a fireball. We can literally see the Big Bang at age 378,000 years.
Yes. The CMBR discovery, as predicted by BBT, is stated to have been the final nail in the coffin of the only true competitor to BBT — the Steady State theory.
billslugg
#### Wind Angel
What do you guys think of Penrose's theory of a universe before this one? His evidence involves hotspots in the CBR, but other scientists say they don't see them there.
#### billslugg
His work is pretty much over my head. I understand he says the end of the universe occurs when all matter ends up being sucked into black holes and the black holes eventually evaporate, the universe becomes nothing but photons. Photons do not experience time or space. Their clock is at zero, they see the universe foreshortened into a point. Time stops. Entropy resets to zero. This is then equivalent to a new start to the universe, a new Big Bang. It just cycles over and over.
Wind Angel
#### Wind Angel
His work is pretty much over my head. I understand he says the end of the universe occurs when all matter ends up being sucked into black holes and the black holes eventually evaporate, the universe becomes nothing but photons. Photons do not experience time or space. Their clock is at zero, they see the universe foreshortened into a point. Time stops. Entropy resets to zero. This is then equivalent to a new start to the universe, a new Big Bang. It just cycles over and over.
Yes, that's the one. I rather like it because it makes more sense. But maybe those black holes didn't evaporate but instead became one massive white protuberance ( science calls them white holes, but a hole isn't the opposite of a hole) and that is the "singularity" of the Bang.
Of course until there is actual evidence it's all conjecture. It makes me feel more comfortable, though.
#### billslugg
I don't know that black holes do anything but evaporate. It takes some time though. A solar mass black hole (2e30 kg) containing 1e54 atoms, would emit one photon of Hawking radiation every 1e10 years and would last for 1e64 years. A supermassive black hole (1e14 solar masses) would take 2e106 years to evaporate.
Source: Wiki article on Hawking radiation
#### Wind Angel
I don't know that black holes do anything but evaporate. It takes some time though. A solar mass black hole (2e30 kg) containing 1e54 atoms, would emit one photon of Hawking radiation every 1e10 years and would last for 1e64 years. A supermassive black hole (1e14 solar masses) would take 2e106 years to evaporate.
Source: Wiki article on Hawking radiation
The problem is we don't know if they do eventually evaporate entirely from Hawking radiation, only that they emit it. That slow of a death almost seems meaningless for us. This will be an interesting subject to keep an eye on. It's a shame none of us will live long enough to observe it.
#### billslugg
We have never measured Hawking Radiation, it is only theoretical. However if it is emitted then the Black Hole must eventually disappear. This would be due to conservation of mass.
#### Wind Angel
Why have I read about Hawking radiation as if it is proven? This sort of thing gets so confusing! This isn't the first subject this has happened with . This is starting to irritate me.
If the amount of energy emitted is far less than what the black hole takes in, it wouldn't disappear, though. The energy has to go somewhere, it's not going to magically cease to exist.
#### billslugg
You may have fallen prey to an overzealous headline copy editor. "Steven Hawking was Right, Black Holes Can Evaporate, Weird New Study Shows". Read a bit further and you find out they did not look at a black hole, they simulated one in a laboratory with sound waves. The experiment lends credence to his theory but does not prove it. If you read the Wiki article on Hawking Radiation, it is termed "theoretical" in the lead sentence.
Stephen Hawking Was Right: Black Holes Can Evaporate, Weird New Study Shows | Live Science
You are correct, a black hole will decrease in size only when the amount of mass and radiation it takes in is less than what it gives off. This is part of the theorized process. Currently only a black hole with a mass less than our Moon will evaporate. Any larger than that and its temperature is less than the CMBR and it will gain mass. CMBR will have to red shift to a very low temperature in order for large black holes to dissipate.
Wind Angel
#### Wind Angel
You may have fallen prey to an overzealous headline copy editor. "Steven Hawking was Right, Black Holes Can Evaporate, Weird New Study Shows". Read a bit further and you find out they did not look at a black hole, they simulated one in a laboratory with sound waves. The experiment lends credence to his theory but does not prove it. If you read the Wiki article on Hawking Radiation, it is termed "theoretical" in the lead sentence.
Stephen Hawking Was Right: Black Holes Can Evaporate, Weird New Study Shows | Live Science
You are correct, a black hole will decrease in size only when the amount of mass and radiation it takes in is less than what it gives off. This is part of the theorized process. Currently only a black hole with a mass less than our Moon will evaporate. Any larger than that and its temperature is less than the CMBR and it will gain mass. CMBR will have to red shift to a very low temperature in order for large black holes to dissipate.
Yes, it was definitely articles like this that got me thinking it was fact over theory. I read too many like that and I respect Hawking's work so much I just took it for granted.
I tend to think that like stars, black holes will probably die in many different ways. I am particularly drawn to white hole theory, which if true might have led to that 'singularity' that became our known universe. This is really what I was getting at in the first place. If that is possible the Bang starts to make sense.
I hate feeling crazy when what was pounded into my head in school doesn't make any sense when scrutinized. Finding other theories similar to what I envision makes me feel better. I don't know why it's so important to me to know how we got here, it just is.
Helio and billslugg
#### Unclear Engineer
The problem with the BBT "not explaining the univese before "10^-43 seconds" is that it then needs to explain why the theory doesn't go to times before that.
Yes, doing so would get us into dimensions so tiny that the Heisenberg Uncertainty Principle tells us we cannot know the full set of parameters for things of such small dimension.
But, considering that the whole BBT is an extrapolation backwards in time from the astronomy observations we make today, that seems more like a cop-out than an actual reason to not have to explain how "something" can possibly come from "nothing". At best, that cop-out leaves room for some sort of pre-existing form of the universe, perhaps the inflection point after a "Big Crunch". But, the same theorists who argue for the BBT argue against the BC. To me, they have no basis for doing that if they can't get the BBT back to a singularity.
But, I have other problems with the BBT, and so do others who point out "tensions" and "paradoxes" like problems with "missing" anti-matter and magnetic monopoles.
My main problem with the BBT is where it needs to transition from things we observe in our macro world to where we can only try to imagine things in the tiny quantum world that the BBT theoretically compresses everything into as it extrapolated backwards in time. The main actor in the BBT at that point is called "inflation", and it seems to just do whatever makes the BBT work, without regard to how that could happen. In particular, trying to get theorists to address what actually happens to something like a photon as it is inflated from the quantum world into a macro world microwave seems to be beyond their capability to conceive adequately, or at least attempt to explain adequately.
And, failing to do that, I have no faith in the various arguments about the total net energy balance of the universe through the "inflation" period.
I think the problem is that quantum theorists are far too comfortable with thinking about things in inconsistent ways, such as particles being waves and vice versa, and fields being independent things that make particles, rather than particles make fields of effects in space. When we try to bring those concepts through "inflation" from quantum level to macro level, the theory does not seem to hold together when I look at the details. Maybe some day, there will be a theory that can unite what we think we understand about gravity and the other forces, and that will make sense of the full effects of "inflation". But, that is not where we are at, today. So, I am not to the poinit of "believing" that the BBT has everything right, at this point in its development.
I get really dubious about the BBT about at the point where the cosmic microwave background radiation is fitted into the theory. I am hoping to see some better analyses of the CMBR and some better observations of the universe between the time of the farthest gallaxies we can see, today, and the hypothesized time of the origin of the CMBR being received now on Earth.
Wind Angel
Replies
2
Views
599
Replies
39
Views
3K
Replies
18
Views
1K
Replies
26
Views
2K
Replies
29
Views
2K | 5,023 | 22,955 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2024-30 | latest | en | 0.943142 |
https://lms.aotawhiti.school.nz/?q=node/196344 | 1,656,720,085,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103947269.55/warc/CC-MAIN-20220701220150-20220702010150-00376.warc.gz | 399,586,153 | 5,157 | # HB Hawk Stage 6 Maths Group Term 3 2018
• Posted on: 7 August 2018
• By: GinaHarrison
Stage 6 maths group will attend workshops 4x per week.
This term we will be focusing on addition and subtraction strategies including large numbers and decimals. We will use Maths Buddy for Must Dos, some lessons and at home practice.
Number Strategies and Knowledge:
- Use a range of multiplicative strategies when operating on whole numbers.
- Understand addition and subtraction of fractions, decimals, and integers.
- Apply simple linear proportions, including ordering fractions.
- Know the relative size and place value structure of positive and negative integers and decimals to three decimals.
I can:
- Read and order decimals to 3 places
- Know some equivalent fractions
- Know how many tenths, tens, hundreds and thousands are in whole numbers up to 1,000,000
- Know all basic facts must/div up to 10x10
Learning Area:
Key Competencies:
To Do List:
Learn my times tables
Learn part whole strategies such as standard place value, compensating tidy numbers, reverse operations, doubling and halving, splitting into parts, reversing for division
Know basic facts to 20 by heart
Come to my maths group and participate positively
Complete must dos on Maths Buddy on time.
LA Code:
Levels:
2
Year: | 284 | 1,295 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2022-27 | latest | en | 0.850127 |
http://forum.arduino.cc/index.php?topic=143103.0;prev_next=next | 1,475,144,178,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738661781.17/warc/CC-MAIN-20160924173741-00270-ip-10-143-35-109.ec2.internal.warc.gz | 96,218,598 | 11,071 | Go Down
### Topic: How many LED's on Pin 13 that already powers the on-board Green L-LED? (Read 988 times)previous topic - next topic
#### Andy_Cool
##### Jan 17, 2013, 11:29 am
Hi
The max pin output current on an Arduino is 40 mA.
So I can put in 2 LED's (with appropriate resistors) on a single pin.
(Each LED will source upto 20 mA)
However pin-13 is already connected to the on-board L - LED (green).
Does this mean I cannot connect 2 normal LED's on Pin 13?
Thank you.
#### fungus
#1
##### Jan 17, 2013, 12:32 pm
Hi
The max pin output current on an Arduino is 40 mA.
So I can put in 2 LED's (with appropriate resistors) on a single pin.
(Each LED will source upto 20 mA)
However pin-13 is already connected to the on-board L - LED (green).
Does this mean I cannot connect 2 normal LED's on Pin 13?
Yes.
PS: Aiming for exactly 20mA with resistors is a BAD idea. This forum has a loooong history of the reasons why.
Short version:
a) At the "20mA" point on an LED output curve (see datasheet) even a tiny error in voltage can produce a large error in current.
b) The variation in voltage between individual LEDs is enough to make sure that the error in part (a) will happen.
Solution: Either aim for 15mA (which won't be much dimmer) or use a constant-current circuit (eg. LED driver chip)
No, I don't answer questions sent in private messages (but I do accept thank-you notes...)
#2
##### Jan 17, 2013, 07:26 pm
"Does this mean I cannot connect 2 normal LED's on Pin 13?"
Recent Uno's have a buffer (LM358) on D13 that drives the onboard LED. Older Unos have a 1K resistor to the LED, which consumes ~3mA of current when driving High.
Both early and later have recommended Absolute Max of 40mA both high & low. However, high voltage drops down as current exceeds 20mA, and low voltage rises up as current exceeds 20mA.
There is also a limit on how much current a port will support, and an overall limit on how much current the Vcc/Avcc & Gnd pins can support. (200mA/pin) See Section 29 of the datasheet, excerpted below.
Depending on Vf of your LEDs, you might be able to run them at 20mA by putting both in series with a single resistor.
ATmega328P:
DC Current per I/O Pin ................................................ 40.0mA
DC Current VCC and GND Pins................................. 200.0mA
3. Although each I/O port can source more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady state
conditions (non-transient), the following must be observed:
1] The sum of all IOH, for ports C0 - C5, D0- D4, ADC7, RESET should not exceed 150mA.
2] The sum of all IOH, for ports B0 - B5, D5 - D7, ADC6, XTAL1, XTAL2 should not exceed 150mA.
If IIOH exceeds the test condition, VOH may exceed the related specification. Pins are not guaranteed to source current greater than the listed test condition.
4. Although each I/O port can sink more than the test conditions (20 mA at VCC = 5V, 10 mA at VCC = 3V) under steady state
conditions (non-transient), the following must be observed:
1] The sum of all IOL, for ports C0 - C5, ADC7, ADC6 should not exceed 100 mA.
2] The sum of all IOL, for ports B0 - B5, D5 - D7, XTAL1, XTAL2 should not exceed 100 mA.
3] The sum of all IOL, for ports D0 - D4, RESET should not exceed 100 mA.
If IOL exceeds the test condition, VOL may exceed the related specification. Pins are not guaranteed to sink current greater than the listed test condition.
Designing & building electrical circuits for over 25 years. Screw Shield for Mega/Due/Uno, Bobuino with ATMega1284P, & other '328P & '1284P creations & offerings at my website.
#### retrolefty
#3
##### Jan 17, 2013, 07:48 pm
Nothing magic about running standard leds at 20ma, run them at 10 to 15ma and you will be fine. I have some 3mm red leds that at even at 3 ma are bright as heck, too bright for just a always on power indicator.
Lefty
Go Up
Please enter a valid email to subscribe | 1,099 | 3,930 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2016-40 | longest | en | 0.92015 |
https://excelformulas.net/2019/07/30/max-function-excel/ | 1,582,966,823,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875148850.96/warc/CC-MAIN-20200229083813-20200229113813-00205.warc.gz | 367,990,902 | 6,962 | # Max Function Excel
Maximum is a widely used function in Excel. Very often we need to know the maximum number of a specific range. Yes, MAXIMUM is the function which can easily show you the maximum number of a range. But this function is very easy to use.
=MAX (NUMBER1:NUMBERn)
Now let’s see the practical use of MAXIMUM function:
Above image shows a simple range of some people’s names and their respective salary. We find the maximum salary of the all-employee is \$ 940 by using the formula =MAX(C3:C14) . So, finding the maximum value of a data set is very easy. | 134 | 572 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2020-10 | latest | en | 0.890425 |
http://gmatclub.com/forum/three-cards-are-drawn-from-a-52-card-deck-no-replacement-what-is-th-101417.html | 1,484,990,696,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281001.53/warc/CC-MAIN-20170116095121-00532-ip-10-171-10-70.ec2.internal.warc.gz | 120,070,489 | 52,535 | Three cards are drawn from a 52 card deck - no replacement. What is th : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack
It is currently 21 Jan 2017, 01:24
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Three cards are drawn from a 52 card deck - no replacement. What is th
Author Message
TAGS:
### Hide Tags
Manager
Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 103
Concentration: Social Entrepreneurship, Social Entrepreneurship
GPA: 3
WE: Consulting (Insurance)
Followers: 2
Kudos [?]: 146 [0], given: 15
Three cards are drawn from a 52 card deck - no replacement. What is th [#permalink]
### Show Tags
21 Sep 2010, 01:55
00:00
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct 0% (00:00) wrong based on 0 sessions
### HideShow timer Statistics
Three cards are drawn from a 52 card deck - no replacement. What is the probability that the last two draws are aces if the first was an ace?
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 105
Kudos [?]: 957 [0], given: 25
Re: Three cards are drawn from a 52 card deck - no replacement. What is th [#permalink]
### Show Tags
21 Sep 2010, 02:03
vanidhar wrote:
Three cards are drawn from a 52 card deck - no replacement. What is the probability that the last two draws are aces if the first was an ace?
After the first draw, 51 cards left in the desk, of which 3 are aces. (Since first draw was an ace).
So probability of drawing an ace in the second draw = 3/51
Now, there are 50 cards left and 2 aces
So probability of drawing an ace in the third draw = 2/50
Hence probability of drawing 2 aces after the first one is an ace = 3/51 * 2/50 = 1/425
_________________
Re: Three cards are drawn from a 52 card deck - no replacement. What is th [#permalink] 21 Sep 2010, 02:03
Similar topics Replies Last post
Similar
Topics:
In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 11 Jul 2016, 11:41
6 If 3 cards are selected at random from the deck of 52 cards then What 2 27 Jul 2015, 05:05
If 2 cards are selected at random from the deck of 52 cards then What 1 27 Jul 2015, 04:45
If you are drawing one card from a regular deck of cards (52 cards 4 14 Jun 2015, 01:04
1 Two cards are drawn successively from a standard deck of 52 8 08 Jan 2010, 16:29
Display posts from previous: Sort by | 820 | 2,920 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2017-04 | latest | en | 0.910114 |
https://learntofish.wordpress.com/2010/02/18/data-structures-and-algorithms-books-and-videos/ | 1,500,877,883,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549424756.92/warc/CC-MAIN-20170724062304-20170724082304-00392.warc.gz | 687,614,006 | 36,076 | # Learntofish's Blog
## Data Structures and Algorithms – Books and Videos
Posted by Ed on February 18, 2010
This post is about data structures and algorithms. I will give some book recommendations and links to video lectures.
Recently, I’ve become interested in data structures and algorithms. Given a problem it is fun to think about how to solve it with the computer. You need an algorithm but you also need to know how to implement it, i.e. you have to teach the computer what you actually intend to do.
For example, there are these GPS navigation systems that calculate a shortest route between two cities. You can model this using graphs and Dijkstra’s algorithm. But how do you save a graph on a computer. What kind of data structure do you use? Another example is getting out of a maze. Naturally, you would try something like Depth First Search. Again, how do you tell the computer to search for a way out of a maze?
Below is a list of books and video lectures that get you started. For me, the field of data structures and algorithms is fascinating. I also want to learn more about it to solve complex problems on projecteuler and to compete in topcoder.
Books
1) Introduction to Algorithms by Cormen, Leiserson, Rivest, Stein
Hands down, this book also known as CLRS (the initial letter of the authors’s names) is the bible for algorithms. My first encounter with it was when I tried to understand Dijkstra’s algorithm. After this I just fell in love with the book. The pseudo codes are clear and tell you what data structures are involved. If you had to buy a book then it would be this one.
2) Introduction to the Design and Analysis of Algorithms by Anany V. Levitin
For a total beginner, this book might be better suited. I liked the section on combinatorics, e.g. how to generate permutations and combinations. The solution of the knapsack problem with dynamic programming is very well described.
3) Algorithm Design by Kleinberg, Tardos
This book is rather wordy. But I liked the section on NP completeness, a topic every computer scientist has to know.
4) The Algorithm Design Manual by Skiena
This book sheds some light on the practical side of algorithms, containing code in C++. It is not a standalone book, though. But what I really like are the “war stories”. These are stories illustrating the application of the right data structures. For example, the author tells about a problem on DNA sequences and how he worked together with his student to solve the problem. The author also describes his work on Combinatorica, a package included in Mathematica for discrete mathematics and graph theory. Moreover, you’ll find an extensive list of references at the end of each chapter.
5) Algorithms by S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani
You can view a draft of the entire book if you click on the link above. The section on dynamic programming is nice.
Video Lectures
1) Data Structures and Algorithms (UNSW)
Prof. Buckland is a great teacher. Look at this funny presentation of Bubble Sort during his lecture.
2) Introduction to Computer Science and Programming
This MIT course illustrates algorithms using Python.
3) Introduction to Algorithms (MIT OpenCourseWare)
This course is based on the book by CLRS I mentioned in the beginning.
4) Data Structures and Advanced Programming (UC Berkeley)
These lectures by Prof. Shewchuk illustrate algorithms using Java. Very good lectures.
5) Introduction to Data Structures and Algorithms (IIT Delhi)
A series of 36 lectures, each one lasting for almost an hour!
6) Skiena’s Algorithm Lectures
Lectures by Prof. Skiena, the author of the fourth book from above.
7) Data Structures, Algorithms, and Applications in Java
Lectures by Sartaj Sahni
8) Algorithms
Excellent lectures by Shai Simonson
At last, a step by step explanation on how quicksort works. This video helped me alot to understand this wonderful sorting algorithm. | 857 | 3,922 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2017-30 | longest | en | 0.952017 |
https://stat.ethz.ch/pipermail/r-sig-finance/2009q1/003797.html | 1,657,082,011,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104660626.98/warc/CC-MAIN-20220706030209-20220706060209-00150.warc.gz | 568,657,971 | 2,856 | # [R-SIG-Finance] help (regarding block bootstrap)
Brian G. Peterson brian at braverock.com
Tue Mar 17 13:25:30 CET 2009
```Yana Roth wrote:
> Hello,
> I am trying to do block reasampling to rearrange my data and not succeed to do random permutation and assugnement.
> I would like to divide original time series to subsamples and then to rearange this subsamples randomly.
>
> Function tsboot works only if I need to check statistic, I am interested in just rearranging the data while keeping its structure.
>
> The problem is defined as follows.
> 1. I define llentgh of block , b.
> 2.Divide an original time series by b and receive k=n/b subsamles.
> 3. I need to generate random vector of integers from 1 to k
> 4 Let Z*(j) be for j=1....k be the j th row of a matrix with num of rows equal to number of blocks and number of columns equal to number of simulations.
> 5. Assigne to each Z*(j) the blocks according to generated random vector(each column of matrix is a different order of permutations)
For future reference, please provide reproducible code as per the posting guidelines. It makes it easier for others to help you. Also, please use a desciptive subject, as we all get a quite a lot of mail.
Your procedure appears incorrect.
Your steps 3-5 look like a homework assignment, so I'm going to ignore those and focus on the block bootstrap, which has some applicability to other members of this list in financial time series analysis.
I suspect that you simply misunderstood the "statistic" parameter of tsboot(). I expect that you do indeed intend to use the bootstrapped data to calculate one or more statstics, this is what the statistic parameter is for.
Block bootstrapping works by randomly sampling blocks of length l from your original series. The tsboot function also applies one or more statistics to the bootstrapped data, and uses the multiple samples to calculate the bias and standard error for those statistics, providing you with a sensitivity analysis for those statistics on your data.
Using the data series "acme" included with R, you would do something like:
library(boot)
library(PerformanceAnalytics)
data(acme)
#calculate the sensitivity of standard deviation on the data:
tsboot(tseries=acme[,2],statistic=sd,R=1000,l=12,sim="fixed",endcorr=FALSE,n.sim=1000)
# use blocks of length 12 (one year) to
# create 1000 bootstrapped time series
# each of length 1000 observations
#Returns:
#Bootstrap Statistics :
# original bias std. error
#t1* 0.05362889 0.0001614213 0.001925484
# calculate sensitivity of VaR:
tsboot(tseries=acme[,2],statistic=VaR.CornishFisher,R=1000,sim="fixed",l=12,endcorr=FALSE,n.sim=1000)
#Returns:
#Bootstrap Statistics :
# original bias std. error
#t1* 0.227064 0.009412978 0.007284343
Normally, this is what you want. The random bootstrapped series itself is not useful to you, except to calculate a statistic or statistics of interest, and understand their sensitivity. If you want the bootstrapped series returned, you can modify the code of the tsboot function to do what you want.
If you want to apply your steps 3-5 to the bootstrapped data, see the documentation of tsboot() for an example of defining a function to use as the statistic parameter.
Regards,
- Brian
--
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock
``` | 853 | 3,367 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2022-27 | latest | en | 0.890188 |
https://starrmatica.com/september-friday-favorites-math-resources/ | 1,716,936,458,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059160.88/warc/CC-MAIN-20240528220007-20240529010007-00368.warc.gz | 459,651,720 | 33,809 | # THE SOURCE FOR SCIENCE AND READING INSPIRATION
Each Friday on Facebook and Twitter, we share a curated digital resource from our library that is one of our favorites. In September, we focused on math resources. Here’s what we shared:
Place Value Game
Students are challenged to create the largest number possible, yet once they place a number they aren’t able to move it. This causes them to think ahead about possible future digits.
http://education.jlab.org/placevalue/
Evil Robots Shape Short
Here’s a center idea for practicing identifying shapes! Place the shapes in the right containers before being caught by the evil robots!
http://mathematics.hellam.net/maths2000/shapes.html
Shape Guess
This is a fun game for discussing shape attributes.
http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SHAP&lesson=html/object_interactives/shape_classification/use_it.html
Place Value Machine
Want to try a new place value manipulative? Try using this place value machine to let your students discover what happens to a number’s place value when you multiply or divide by 10.
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/activities/thenumbersystem.swf | 293 | 1,222 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-22 | latest | en | 0.788557 |
https://medium.com/@william456821/454-4sum-ii-d55a6925e57b | 1,513,637,259,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948627628.96/warc/CC-MAIN-20171218215655-20171219001655-00546.warc.gz | 605,785,877 | 19,941 | # 454. 4Sum II
Given four lists A, B, C, D of integer values, compute how many tuples `(i, j, k, l)` there are such that `A[i] + B[j] + C[k] + D[l]` is zero.
To make problem a bit easier, all A, B, C, D have same length of N where 0 ≦ N ≦ 500. All integers are in the range of -228 to 228–1 and the result is guaranteed to be at most 231–1.
``public int fourSumCount(int[] A, int[] B, int[] C, int[] D) { Map<Integer, Integer> map = new HashMap<>(); for(int i=0; i<C.length; i++) { for(int j=0; j<D.length; j++) { int sum = C[i] + D[j]; map.put(sum, map.getOrDefault(sum, 0) + 1); } } int res=0; for(int i=0; i<A.length; i++) { for(int j=0; j<B.length; j++) { res += map.getOrDefault(-1 * (A[i]+B[j]), 0); } } return res;}Time complexity: O(n^2)Space complexity: O(n^2)``
One clap, two clap, three clap, forty?
By clapping more or less, you can signal to us which stories really stand out. | 325 | 988 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2017-51 | latest | en | 0.535363 |
http://www.weegy.com/?ConversationId=661DHXMJ | 1,369,263,369,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368702454815/warc/CC-MAIN-20130516110734-00063-ip-10-60-113-184.ec2.internal.warc.gz | 800,231,239 | 14,449 | View the question
where is the fuse box on a 96 ford aspire? ...
There are 2 fuse boxes. Your Aspire has a main fuse block under the hood and a regular fuse box mounted in the instrument panel behind a ...
Complete Conversation
User: where is the fuse box on a 96 ford aspire?
Weegy: There are 2 fuse boxes. Your Aspire has a main fuse block under the hood and a regular fuse box mounted in the instrument panel behind a cover. There are diagrams and charts in the owners manual that can explain and show you exactly where they are and which one has what fuses. The chapter about fuses begins on page 215. If you don't have a manual, you can download one for free from this site: http://www.motorcraftservice.com/vdirs/retail/default.asp?pageid=&gutsid=&kevin=rules Just scroll to the tab on left that says "Owner Guides" and submit your vehicle Year/Model. No subscription nor registration is needed. I hope this helps.
Weegy: Ford Aspire Questions including "How do you repair or change the clutch in a 1997 Ford Aspire" and "How do you remove the front brake rotor on a 1995 Aspire"
All Categories|No Subcategories|Auto answered|3/14/2011 3:03:27 AM
Rating
Ask a question and get an instant answer from an advanced search engine and a team of really smart live experts. It's free. No kidding!
Popular Conversations
Solve this equation: 80 = 3y + 2y + 4 + 1. A. y = 15 B. y = ...
Weegy: 80 = 3y + 2y + 4 + 1 80 = 5y + 5 80 - 5 = 5y -5y = -75 y = 15 User: Given the formula D = ABC, what is ...
what does the name Gautrain mean
Note: The minimum frequency between Johannesburg and the airport will initially be five trains per hour per direction ...
Planners should assign ___________________ to events that are ...
Weegy: Planners should assign (D.) public transportation to events that are expected to draw very large crowds and ...
At the beginning of â??If I Forget Thee, Oh Earthâ?¦,â? how would ...
Weegy: D. suspensful
Solve the equation. 0.6(y + 3) = 4.8 A. 5 B. 3 C. 13 D. ...
Weegy: Solve equation by factoring X ... A)1/2 B)2/3 C)1 D)3/2 E)2; Use factoring to solve the Quadratic Equation. ... ...
When most vehicles are driven at a speed higher than 55 mph, A. fuel ...
Note: d decreased Note: I'm sorry that that wasn't a good answer. Please hold on while I contact an expert. Weegy: ...
The growth of the service economy caused A. an increase in American ...
Weegy: A. an increase in American blue-collar jobs
President Truman sent a fleet of ships to this island in 1949 to ...
Weegy: 3.Taiwan 4.Philippines
soliloquy
Weegy: A soliloquy (from Latin: "talking by oneself") is a device often used in drama whereby a character speaks to ...
S
Points 687 [Total 714]| Ratings 6| Comments 612| Referrals 3|Offline
P
S
L
L
L
C
1
C
M
P
C
C
P
C
1
P
C
L
P
C
1
P
C
1
P
C
P
C
1
P
C
P
C
C
C
P
C
C
P
C
P
C
P
C
P
C
P
C
1
P
C
1
P
C
Points 680 [Total 47162]| Ratings 12| Comments 560| Referrals 0|Offline
S
L
P
C
Points 622 [Total 1639]| Ratings 2| Comments 602| Referrals 0|Offline
S
L
P
C
1
R
P
1
L
P
C
1
P
1
M
P
1
P
1
L
P
1
P
1
P
1
P
1
P
1
P
C
1
P
C
P
C
1
P
C
P
C
P
C
1
P
C
1
Points 617 [Total 21923]| Ratings 17| Comments 447| Referrals 0|Offline
S
M
L
P
C
P
C
P
C
Points 561 [Total 4243]| Ratings 3| Comments 531| Referrals 0|Offline
S
P
C
L
P
C
Points 365 [Total 3160]| Ratings 7| Comments 295| Referrals 0|Offline
S
L
1
Points 277 [Total 1495]| Ratings 9| Comments 187| Referrals 0|Offline
S
1
L
1
Points 223 [Total 3954]| Ratings 12| Comments 103| Referrals 0|Online
S
L
1
P
C
M
P
C
1
L
P
1
P
1
P
1
1
1
1
1
1
1
Points 205 [Total 9743]| Ratings 20| Comments 5| Referrals 0|Offline
S
Points 199 [Total 199]| Ratings 8| Comments 9| Referrals 22|Offline | 1,277 | 3,661 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2013-20 | longest | en | 0.895361 |
http://www.openwetware.org/index.php?title=TUT_07/16/2012_-_07/20/2012&diff=prev&oldid=614950 | 1,481,437,055,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698544140.93/warc/CC-MAIN-20161202170904-00283-ip-10-31-129-80.ec2.internal.warc.gz | 620,062,167 | 7,228 | TUT 07/16/2012 - 07/20/2012
(Difference between revisions)
Revision as of 14:33, 20 July 2012 (view source)← Previous diff Current revision (14:34, 20 July 2012) (view source) Line 4: Line 4:
Although she recognized that the goal-setting image was a speedometer, her interpretation of the numbers in the odometer were incorrect. She correctly guessed price because she knew that the text in black was a set number. However, she believed that the 694 and \$90.09 were the ceiling in which people were allowed to consume. Only after thorough examination would people recognize that the series of numbers were actually variables in an equation; therefore, it might be a good idea to play around with this. The fact that the red marker was in the yellow threw her off because she thought it meant that she over-consumed from the 694 kWh "ceiling." She did not know what the numbers on the speedometer meant either, which means we need to rethink what kind of information we want this graphical display to present. I suggest that the numbers on the speedometer match the daily ceiling in which people are allowed to consume. This means where the yellow meets the red, we have 37.2 kWh and where the green meets the yellow we have 33.48 kWh (the difference being 3.72). The numbers will be explained on a separate summary page and the numbers on the speedometer will change every month (depending on the goal, etc).
Although she recognized that the goal-setting image was a speedometer, her interpretation of the numbers in the odometer were incorrect. She correctly guessed price because she knew that the text in black was a set number. However, she believed that the 694 and \$90.09 were the ceiling in which people were allowed to consume. Only after thorough examination would people recognize that the series of numbers were actually variables in an equation; therefore, it might be a good idea to play around with this. The fact that the red marker was in the yellow threw her off because she thought it meant that she over-consumed from the 694 kWh "ceiling." She did not know what the numbers on the speedometer meant either, which means we need to rethink what kind of information we want this graphical display to present. I suggest that the numbers on the speedometer match the daily ceiling in which people are allowed to consume. This means where the yellow meets the red, we have 37.2 kWh and where the green meets the yellow we have 33.48 kWh (the difference being 3.72). The numbers will be explained on a separate summary page and the numbers on the speedometer will change every month (depending on the goal, etc).
An interesting note I had about this participant was that she really liked the idea of social comparison. She believed that it provided her with a benchmark of what is acceptable use, and she even went further in saying that it provided her with more motivation to conserve. She mentioned that the dorms at her university participated in energy reduction contests, which proved effective. She also mentioned that her family was very environmentally conscious and possibly more than the average household. I think that this fact played a role in her enthusiasm about social comparison because most people we've talked to, surveyed, or interviewed had not liked the idea. If social comparison in energy consumption became more widespread (i.e. with Opower's contracts with multiple utilities) we could use this goal setting method to help people consume less than their comparative baseline. Including goal-setting with social comparison might lead to higher reduction than just social comparison alone.
An interesting note I had about this participant was that she really liked the idea of social comparison. She believed that it provided her with a benchmark of what is acceptable use, and she even went further in saying that it provided her with more motivation to conserve. She mentioned that the dorms at her university participated in energy reduction contests, which proved effective. She also mentioned that her family was very environmentally conscious and possibly more than the average household. I think that this fact played a role in her enthusiasm about social comparison because most people we've talked to, surveyed, or interviewed had not liked the idea. If social comparison in energy consumption became more widespread (i.e. with Opower's contracts with multiple utilities) we could use this goal setting method to help people consume less than their comparative baseline. Including goal-setting with social comparison might lead to higher reduction than just social comparison alone. + + =====Navigation===== + *[http://openwetware.org/wiki/Technology_Usability_Testing Go back to TUT]
Technology Usability Testing Report – 07/20/2012
After the participant was asked to scan through the slides, while imagining the information would be displayed through some sort of device, she revealed that the goal-setting slide was the most confusing. I suggest that we change the order of the slides so that they're presented with either the calendar or summary page first. Leading with the summary page (or the calendar) would allow participants to walk through the device in a more cohesive manner. I say this because it was not until she was exposed to the calendar that she knew the technology was going to be used for electricity feedback. However, even with this in mind, I do not think it would be smart to start off with the calendar. The reason I propose this is because the color coding seen on the page will not be interpreted as related to the goal. Even when the she saw the goal-setting page first, she did not know that the colors on the goal and on the speedometer were related until I told her. Her interpretation of the colors was usage as related to her monthly consumption, not her goal. She suggested that we include a summary page, which should contain important information relating to the goal.
The device as it is now is spacious and not text heavy. I think this is great in terms of attractiveness and usability; however, I believe we need to include important information on a separate page. Creating a separate slide for usage and goal summaries would preserve the attractiveness of the current layout, yet give the participant information that would be useful as goal attainment feedback. The main pieces of information that are missing: the total amount (kWh or \$) in which the reduction percentage is referring to, the total consumption ceiling to attain the goal, and the daily consumption ceiling to attain the goal. While it is clear, on the calendar, which days you are under, close, or over the consumption limit—they are never actually told what that limit is. They would have to take an extra step to figure out what the ceiling is by comparing the green, yellow, and red days; even then, they would not have a clear idea of where the line is actually drawn. I think it is important we tell the participant whether their reduction goal is a reduction from the previous month's usage, or if it was the previous year's (same month) usage. She easily recognized that if people were trying to reduce consumption in August compared to July that we would be setting them up for failure. We need to be sure that we help people set a goal that is actually attainable.
Although she recognized that the goal-setting image was a speedometer, her interpretation of the numbers in the odometer were incorrect. She correctly guessed price because she knew that the text in black was a set number. However, she believed that the 694 and \$90.09 were the ceiling in which people were allowed to consume. Only after thorough examination would people recognize that the series of numbers were actually variables in an equation; therefore, it might be a good idea to play around with this. The fact that the red marker was in the yellow threw her off because she thought it meant that she over-consumed from the 694 kWh "ceiling." She did not know what the numbers on the speedometer meant either, which means we need to rethink what kind of information we want this graphical display to present. I suggest that the numbers on the speedometer match the daily ceiling in which people are allowed to consume. This means where the yellow meets the red, we have 37.2 kWh and where the green meets the yellow we have 33.48 kWh (the difference being 3.72). The numbers will be explained on a separate summary page and the numbers on the speedometer will change every month (depending on the goal, etc).
An interesting note I had about this participant was that she really liked the idea of social comparison. She believed that it provided her with a benchmark of what is acceptable use, and she even went further in saying that it provided her with more motivation to conserve. She mentioned that the dorms at her university participated in energy reduction contests, which proved effective. She also mentioned that her family was very environmentally conscious and possibly more than the average household. I think that this fact played a role in her enthusiasm about social comparison because most people we've talked to, surveyed, or interviewed had not liked the idea. If social comparison in energy consumption became more widespread (i.e. with Opower's contracts with multiple utilities) we could use this goal setting method to help people consume less than their comparative baseline. Including goal-setting with social comparison might lead to higher reduction than just social comparison alone. | 1,904 | 9,564 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2016-50 | latest | en | 0.987147 |
http://www.acmerblog.com/uva-11722-joining-with-friend-1963.html | 1,502,976,358,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886103316.46/warc/CC-MAIN-20170817131910-20170817151910-00202.warc.gz | 479,521,426 | 12,777 | 2013
12-11
# Uva-11722-Joining with Friend-[连续概率]
### Joining with Friend
You are going from Dhaka to Chittagong by train and you came to know one of your old friends is going from city Chittagong to Sylhet. You also know that both the trains will have a stoppage at junction Akhaura at almost same time. You wanted to see your friend there. But the system of the country is not that good. The times of reaching to Akhaura for both trains are not fixed. In fact your train can reach in any time within the interval [t1, t2] with equal probability. The other one will reach in any time within the interval [s1, s2] with equal probability. Each of the trains will stop for w minutes after reaching the junction. You can only see your friend, if in some time both of the trains is present in the station. Find the probability that you can see your friend.
Input
The first line of input will denote the number of cases T (T < 500). Each of the following T line will contain 5 integers t1, t2, s1, s2, w (360 ≤ t1 < t2 < 1080, 360 ≤ s1 < s2 < 1080 and 1 ≤ w ≤ 90). All inputs t1, t2, s1, s2 and w are given in minutes and t1, t2, s1, s2 are minutes since midnight 00:00.
Output
For each test case print one line of output in the format “Case #k: p” Here k is the case number and p is the probability of seeing your friend. Up to 1e-6 error in your output will be acceptable.
Sample Input
2
1000 1040 1000 1040 20
720 750 730 760 16
Output for Sample Input
Case #1: 0.75000000
Case #2: 0.67111111
#include <string.h>
#include <stdio.h>
int cas, t1, t2, s1, s2, w;
double area(int w){
int lc = t1+w, rc = t2+w, uc = s2-w, dc = s1-w;
if (lc >= s2) return 0;
if (rc <= s1) return (t2-t1)*(s2-s1);
bool bl = (lc>=s1 && lc<=s2);
bool br = (rc>=s1 && rc<=s2);
bool bu = (uc>=t1 && uc<=t2);
bool bd = (dc>=t1 && dc<=t2);
if (bl&&bu) return (lc-s2)*(lc-s2)*0.5;
if (bl&&br) return (t2-t1)*(s2-lc+s2-rc)*0.5;
if (bd&&bu) return (s2-s1)*(uc-t1+dc-t1)*0.5;
if (bd&&br) return (t2-t1)*(s2-s1)-(rc-s1)*(rc-s1)*0.5;
return 0;
}
int main(){
scanf("%d", &cas);
for (int ca = 1; ca <= cas; ca++) {
scanf("%d%d%d%d%d", &t1, &t2, &s1, &s2, &w);
printf("Case #%d: %.7f\n", ca, (area(-w)-area(w))/(t2-t1)/(s2-s1));
}
return 0;
}
1. 约瑟夫也用说这么长……很成熟的一个问题了，分治的方法解起来o(n)就可以了，有兴趣可以看看具体数学的第一章，关于约瑟夫问题推导出了一系列的结论，很漂亮
2. 第二块代码if(it != mp.end())应改为if(it != mp.end() && (i+1)!=(it->second +1))；因为第二种解法如果数组有重复元素 就不正确 | 885 | 2,387 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2017-34 | longest | en | 0.819738 |
http://gmatclub.com/forum/gmat-data-sufficiency-ds-141/?sk=er&sd=a&tov=rank | 1,472,702,859,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982958896.58/warc/CC-MAIN-20160823200918-00115-ip-10-153-172-175.ec2.internal.warc.gz | 101,658,263 | 61,548 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 31 Aug 2016, 21:07
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# GMAT Data Sufficiency (DS)
new topic Question banks Downloads My Bookmarks Reviews Important topics Go to page 1 2 3 4 5 6 7 8 9 10 11 ... 165 Next Search for:
Topics Author Replies Views Last post
Announcements
108
150 Hardest and easiest questions for DS Tags:
Bunuel
3
16675
07 Dec 2015, 09:09
443
DS Question Directory by Topic and Difficulty Tags: Coordinate Geometry
bb
0
127891
07 Mar 2012, 08:58
Topics
20
Jeff is painting two murals on the front of an old apartment
chiragr
16
5004
29 Aug 2016, 21:05
4
Company R's annual profit has increased by a constant amount each
Bhai
12
3966
17 Jun 2016, 18:50
1
If k is an integer greater than 1, is k wqual to 2^r for Tags:
coffeeloverfreak
11
3567
05 Oct 2005, 20:04
1
What is the probability that events A and B both occur? Tags: Poor Quality
hallelujah1234
7
4472
17 Jan 2012, 21:44
x^2 + y^2 + z^2| < 4, is |x^2 + z^2| < 1 1. |x^2 + Tags: Inequalities
hallelujah1234
7
1574
29 Jul 2010, 07:56
aleph777
1
Rectangle ABCD is inscribed in a circle as shown above. What
cloaked_vessel
9
4802
26 Aug 2012, 13:48
2
What digit does t represent in the decimal 0.t73 ?
MA
4
3198
08 Aug 2014, 11:44
Is the standard deviation of ages of students in class A
anandnk
6
1957
06 May 2010, 06:10
4
Linda, Robert, and Pat packed a certain number of boxes with
BG
12
3782
07 Apr 2016, 02:27
6
Martin has worked for the last 30 years. If his average (ari
dinesh8
3
2456
19 Dec 2015, 13:13
11
If x and y are integers greater than 1, is x a multiple of Go to page: 1, 2, 3 Tags: Difficulty: 600-700 Level, Divisibility/Multiples/Factors, Source: GMAT Prep
themagiccarpet
45
4522
01 Oct 2011, 01:59
In what year was Ellen born? (1) Ellen s brother Pete, who
dr_sabr
5
1549
20 Nov 2010, 17:07
15
A bowl is filled with consecutively numbered tiles from 1 to x. Joe
crackgmat750
8
2096
24 Jul 2016, 09:07
8
x, y, and z are consecutive even numbers. What is the average of x, y,
gamjatang
10
1702
15 Jul 2016, 00:15
1
In 1990 850 million movie tickets were sold in the United States. One
tyagel
7
2188
20 Jul 2016, 05:57
3
x is a positive integer. Is x even?
cbrf3
4
1665
25 Nov 2014, 06:38
5
The cost of a taxi fare consists of an initial fee of \$3 plu
bewakoof
9
3101
08 Jul 2016, 04:05
3
What is the circumference of the circle above? (1) The Tags: Geometry
JAI HIND
18
3825
30 Jan 2011, 12:08
8
On his trip from Alba to Benton, Julio drove the first x
sandalphon
12
5674
27 Feb 2016, 17:40
10
Is x > y ?
GMATT73
16
2923
21 Jul 2016, 07:46
3
If a and b are positive integers, what is the value of a + b
joemama142000
9
5413
22 Jul 2011, 01:33
55
The point A, B, C, and D are on the number line, not necessa
ronybtl
18
18064
14 Jun 2016, 11:19
1
In PQR, if PQ = x + 2, and PR = y, which of the three
saurya_s
10
3174
09 Nov 2011, 07:40
If x is negative, is x < -3? (1) x2 > 9 (2) x3 < -9 Tags: Inequalities
Guest
5
2467
30 Nov 2011, 14:14
13
When a rectangular label, 21.5 centimeters long, is wrapped
wonder_gmat
13
3034
01 Jun 2016, 10:43
If 1 < d < 2 , is the tenths' digit of the decimal Tags:
wonder_gmat
5
2871
09 Nov 2003, 18:32
Find a nonzero integer R. (1) R^3=R^R (2) |R^R|=1 Tags:
stolyar
4
1853
20 Mar 2011, 07:47
A coal company can choose to transport coal to one of its
shahnandan
7
1624
11 Jan 2010, 07:31
Is x/m(m^2 + n^2 + k^2) = xm + yn + zk? (1) z/k = x/m (2)
ValleyBall1
4
2006
18 Nov 2011, 05:19
11
In Quadrilateral WXYZ, is XY perpendicular to YZ?
mbassmbass04
9
4975
23 Aug 2016, 21:57
6
A certain calculator is able to display at most 10 digits,
cpcalanoc
10
3854
26 Apr 2016, 18:02
3
Find F/|G|, where F and G are nonzero integers. (1) |F|=|G| Tags:
stolyar
5
2455
22 Mar 2011, 21:02
Is a nonzero integer Z prime? (1) |Z|^|Z|=4 (2) |Z^Z|=Z^2 Tags:
stolyar
8
1997
22 Mar 2011, 20:50
What is the ratio of x : y : z? (1) z = 1 and xy =32 (2) x/y
ValleyBall1
7
2253
24 Aug 2011, 11:06
10
Find an integer F
stolyar
4
4100
05 Aug 2016, 09:23
What is the remainder when the positive integer n is divided Tags:
sperumba
10
1310
20 Apr 2015, 12:07
12
If P and R were solutions of water and ammonia and if
chunjuwu
4
3377
15 Dec 2015, 16:36
1
Is x the square of an integer? (1) x = 12k + 6, where k is a Tags:
AkamaiBrah
4
1976
20 Mar 2011, 07:45
20
What is the value of x given that |x - y| = |x - z|
AkamaiBrah
11
2971
08 Jul 2016, 22:56
4
What is the value of the two-digit number XY, where X
araspai
5
2109
16 Jul 2016, 08:04
1
If d denotes a decimal, is d >= 0.5?
blshah
16
2088
05 Apr 2011, 02:52
23
If a number is drawn at random from the first 1000 positive
GMATT73
14
8418
12 Jul 2016, 22:53
3
If a rope is cut into three pieces of unequal length
mciatto
4
3752
31 Mar 2016, 16:28
There are two solids 1 & 2. These solids are not of the Tags: Geometry
mistdew
6
1599
26 Jul 2010, 07:09
Is it true that a > b? (1) 2a > 2b (2) a + c > b + c
briozeal
7
1653
29 Mar 2012, 06:11
In a sequence of numbers in which each term after the first Tags:
Curly05
4
2509
22 Mar 2011, 20:42
8
The shape of a flower bed is a combination of semicircle and Go to page: 1, 2 Tags: Difficulty: 600-700 Level, Geometry, Source: GMAT Paper Tests
gayathri
21
4697
19 Dec 2015, 20:59
2
A small factory that produces only upholstered chairs and
Curly05
5
3487
09 Jun 2016, 10:12
9
What is the cube root of w ? Go to page: 1, 2 Tags: Difficulty: Sub-600 Level, Roots, Source: Official Guide
Guest
29
11539
10 May 2011, 04:58
1
Steve took 5 history exams during a semester. Each score was
Paul
8
2170
28 Aug 2011, 13:11
new topic Question banks Downloads My Bookmarks Reviews Important topics Go to page 1 2 3 4 5 6 7 8 9 10 11 ... 165 Next Search for:
Who is online In total there are 2 users online :: 0 registered, 0 hidden and 2 guests (based on users active over the past 15 minutes) Users browsing this forum: No registered users and 2 guests Statistics Total posts 1526375 | Total topics 185451 | Active members 460732 | Our newest member kdinesh322
Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2,482 | 6,656 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2016-36 | longest | en | 0.801525 |
https://www.enotes.com/homework-help/my-homework-am-given-parabola-says-give-equation-476702 | 1,490,307,544,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218187225.79/warc/CC-MAIN-20170322212947-00648-ip-10-233-31-227.ec2.internal.warc.gz | 906,181,307 | 13,431 | # In my homework I am given a parabola and it says to give the equation of the parabola in standard form. It gives me the Vertex, the y intercept and the zeros. I understand that y=ax2 +bx+c. C is...
In my homework I am given a parabola and it says to give the equation of the parabola in standard form. It gives me the Vertex, the y intercept and the zeros.
I understand that y=ax2 +bx+c. C is the y intercept, but I do not know how to get a or b. Please help me understand.
embizze | High School Teacher | (Level 2) Educator Emeritus
Posted on
Let us consider a specific example: Given the vertex of the parabola is at (3,-2), the y-intercept is (0,16), and the zeros are 2 and 4 find the equation of the quadratic in standard form.
Note that a quadratic function in one variable can be written in many forms:
(1) Intercept or factored form y=a(x-p)(x-q) where p,q are the zeros of the function.
(2) Vertex form `y=a(x-h)^2+k ` where the vertex is at (h,k).
(3) Standard form `y=ax^2+bx+c ` : here c is the y-intercept, and the x-coordinate of the vertex is `x=(-b)/(2a) ` .
We can move from one form to another using algebraic techniques -- to get from factored form to standard form you multiply the factors. To get from standard form to vertex form you can complete the square. To get from vertex form to standard form you expand the binomial term, etc...
If you are given the vertex, the zeros, and the y-intercept there are many ways to get to the standard form.
(1) Using the example above: find the factored form and multiply to get the standard form. Since 2 and 4 are zeros we have y=a(x-2)(x-4). Since (0,16) is a point on the curve, substitute for x and y to solve for a:
16=a(0-2)(0-4) ==> a=2 so y=2(x-2)(x-4). Now multiply to get:
`y=(2x-4)(x-4)=2x^2-12x+16 `
Note that we could have used the point (3,-2) to solve for a, but it is computationally easier to use the intercept since x=0.
(2) Again using the example above, find the vertex form and then expand to get the standard form.
The vertex is (3,-2) so h=3 and k=-2. So `y=a(x-3)^2-2 ` . Use a known point to solve for a: we can use any of (0,16),(2,0), or (4,0). Using (4,0) we substitute 4 for x and 0 for y to get:
`0=a(4-3)^2-2 ==> a=2 `
Then `y=2(x-3)^2-2=2[x^2-6x+9]-2=2x^2-12x+16 `
(3)We only need three noncollinear points to determine a parabola (assuming it is a function.). Here you know (3,-2),(2,0) and (4,0). So you could develop and solve simultaneously three linear equations of the form `y=ax^2+bx+c ` for the coefficients a,b, and c.
` a(0)^2+b(0)+c=16 ==> c=16 `
`a(2)^2+b(2)+16=0 ==> 4a+2b=-16 ==> 2a+b=-8 `
`a(4)^2+b(4)+16=0 ==> 16a+4b=-16 ==> 4a+b=-4 `
Then solving the last two equations we get 2a=4 or a=2 and b=-12.
So `y=2x^2-12x+16 ` as before.
There are other methods.
Sources: | 893 | 2,804 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2017-13 | longest | en | 0.870404 |
http://www.blufftontoday.com/savvy-shopper/2013-02-17/savvy-strategy-leads-bigger-savings | 1,531,957,602,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590362.13/warc/CC-MAIN-20180718232717-20180719012717-00408.warc.gz | 422,946,999 | 15,050 | Being a savvy shopper is much more than looking for the lowest advertised prices or the highest percentage of savings. There are many other things that you need to take into consideration. The key question is this: How do you know where to shop to get the best prices for items you buy regularly?
Percentage of savings - the store offering the highest percentage of savings isn't necessarily the best deal.
As a savvy shopper, it is fun to watch those numbers go down at the register. With each coupon that the cashier scans, the total drops lower and lower. I love to calculate the percentage saved.
• To calculate the percent saved, you take the amount that you saved and divide it by the total before savings.
• For example if I paid \$50 for \$250 worth of groceries I would have saved \$200. Take the \$200 that I saved and divide it by the \$250 the groceries would have cost and you will get 80 percent.
An 80 percent savings is awesome, but don't be fooled. It is possible that you could have purchased the same items at another store whose everyday prices are less. Don't fall into the trap of basing your purchases on the percentage of savings you will receive at the register. I try to save at least 50 percent on almost every item that I purchase; however, I am very knowledgeable about prices and will not purchase an item that is 50 percent off unless the price is still an awesome price after the discount.
Here's an example:
• Michelle's Market has cereal on sale for \$2; the price is normally \$6.
• Amazing Market has cereal on sale for \$2; the price is normally \$5.
• If I purchase the cereal at Michelle's Market, my percentage of savings will be 66.67 percent.
• If I purchase the cereal at Amazing Market, my percentage of savings will be 60 percent
• Michelle's Market has a higher percentage of savings, yet the products are the same price at both stores.
Now, let's look at what the percentage of savings would be if each store had a slightly different price.
• Michelle's Market has laundry detergent on sale for \$2.50, normally \$8.
• Amazing Market has the same laundry detergent on sale for \$2, normally \$5
In this case, the store with the higher percent of savings does not have the lower price. Michelle's Market will show 68.75 percent savings, and Amazing Market will only have 60. Amazing Market definitely has a better deal because the price is lower.
Coupon policies can make a huge difference in the price of the item.
Do they double coupons?
Another contributing factor to determine the best final price will be the store's coupon policy. A store that doubles coupons will have a lower price than a store that doesn't. Let's assume that I have a 50 cent coupon for the cereal that I mentioned earlier.
• Michelle's Market does not double coupons. \$2-50 cent coupon = \$1.50. My percentage of savings is now 75 percent. (Savings of \$4.50 divided by \$6)
• Amazing Market doubles coupons. \$2-(50 cents coupon+ 50 doubled amount) = \$1. My percentage of savings is now 80 percent (\$3 savings divided by \$5)
Even though both stores had the same sales price, the coupon policy of Amazing Market allowed the shopper to score a better deal.
Do they allow overage?
When a coupon is valued at more than the cost of the item, the difference is called overage. Not many stores allow this; most of them will adjust the coupon down to the price of the item. In our area, Walmart and Publix both allow overage. Sometimes overage will determine where you need to shop to get the best deal.
• Michelle's Market has aspirin on sale for \$2. You have a \$3 coupon for Bayer Aspirin. Michelle's Market allows overage. You will receive the item for free plus \$1 toward the rest of your groceries or you can receive the \$1 back at the register.
• Amazing Market has aspirin on sale for \$2, and you have a \$3 off coupon for aspirin. Amazing Market does not allow overage. They will adjust the coupon down to \$2, and you will still receive the item for free.
In this case, Michelle's Market is the best place to shop because it allows overage.
Combine price-matching and overage to score an even better deal!
• Amazing Market has aspirin on sale for \$2, and you have a \$3-off coupon for aspirin. You will receive the item for free, but you will lose the \$1 overage.
• Michelle's Market has aspirin on sale for \$3, and with your \$3-off coupon you will receive the item for free. Amazing Market has a lower price on the item. Michelle's Market matches competitor prices. You can take Amazing Market's ad to Michelle's Market and price-match the \$2 price and then use the coupon to get overage on the item. (Walmart is the only store in our area that price matches and allows overage.)
Do they allow you to stack coupons?
Some stores allow you to combine their store coupons and a manufacturer coupon on the same item.
• Amazing Market and Michelle's Market both have laundry detergent on sale for \$10.
• I have a \$1 Amazing Market store coupon for the laundry detergent and a \$1 manufacturer coupon. If I can stack these coupons, I will save \$2.
• Amazing Market does not allow you to combine a store coupon and a manufacturer coupon. I will have to choose either the store coupon or manufacturer coupon. My final price for the laundry detergent will be \$9.
Do they take competitor coupons?
Sometimes you will have a store coupon that is not allowed to be stacked at the issuing store. However, if a store accepts the other store as a competitor, you will be allowed to stack the coupons.
• Michelle's Market allows you to combine a store coupon and a manufacturer coupon.
• It will also take competitor coupons and you can stack a competitor coupon with a manufacturer coupon.
• I can use the Amazing Market \$1 coupon at Michelle's Market and combine it with the \$1 manufacturer coupon to end up paying \$8 for the laundry detergent.
Do you want to know who doubles coupons, who allows you to stack coupons, and who takes competitor coupons?
Sign up for one of my coupon classes and you will learn all of this and much more.
Send your tips or questions to Savvy Shopper Michelle Rubrecht at savvyshopper@savannahnow.com or post them to Facebook at Savannah Savvy Shopper. | 1,364 | 6,256 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2018-30 | latest | en | 0.958556 |
https://www.coursehero.com/file/9769323/91/ | 1,632,364,991,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057416.67/warc/CC-MAIN-20210923013955-20210923043955-00712.warc.gz | 740,661,516 | 49,755 | # 9.1 - Anonymous Student Assignment Section 9.1 due at...
• Test Prep
• 2
• 100% (4) 4 out of 4 people found this document helpful
This preview shows page 1 - 2 out of 2 pages.
Anonymous StudentBrewerMAT266Spring2012Assignment Section9.1 due 04/25/2012 at 11:59pm MST2.(1 pt)Consider the parametric curve:x=2sinθ,y=2cosθ,0θπ3.(1 pt)Consider the parametric curve:x=12cosθ,y=7sinθ,-π2θπ2 | 140 | 389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-39 | latest | en | 0.684572 |
https://askworksheet.com/math-worksheets-for-kids-domain-and-range/ | 1,718,521,161,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861643.92/warc/CC-MAIN-20240616043719-20240616073719-00855.warc.gz | 91,071,551 | 28,787 | # Math Worksheets For Kids Domain And Range
Some of the worksheets for this concept are functions domain and range review date block domain and range work domain and range es1 name class date 2 6 work work domains and ranges of relations and functions domain and range work 1 name. The pdf exercises are curated for students of grade 3 through grade 8.
Algebra 2 Domain And Range Match Activity Teaching Algebra Learning Mathematics Algebra
### Function worksheets for high school students comprises a wide variety of subtopics like domain and range of a function identifying and evaluating functions completing tables performing arithmetic operations on functions composing functions graphing linear and quadratic functions transforming linear and quadratic functions and a lot more in a nutshell.
Math worksheets for kids domain and range. Domain and range and tables displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are domain and range es1 work domains and ranges of relations and functions functions domain and range review date block work 1 precalculus review functions and inverse pre calculus work name section period domain and range work 1 name domain and range work answer key. 1 f x 3 2 x.
Interesting word problems are included in each section. Domain and range and tables. These domain and range worksheets are a good resource for students in the 9th grade through the 12th grade.
Identifying domains and ranges from graphs worksheets these algebra 1 domain and range worksheets will produce problems for finding the domain and range of graphed sets. Domain and range table sheet 1 7 4 2 8 10 19 12 9 11 17 6 5 1 x y domain. 19 6 1 2.
Domain and range function l1s1 write the range of each function for the given domain. Sample some of these worksheets for free. Mean median mode and range worksheets contain printable practice pages to determine the mean median mode range lower quartile and upper quartile for the given set of data.
Some of the worksheets for this concept are work 2 on functions part i identifying domain and range of a function work domain and range es1 name date ms functions domain and range review date block 7 functionswork. Displaying top 8 worksheets found for domain and range. Domain and range displaying top 8 worksheets found for this concept.
Domain 13 3 6 10 13 18 range. Some of the worksheets for this concept are functions domain and range review date block domain and range work domain and range es1 name class date 2 6 work work domains and ranges of relations and functions domain and range work 1 name. Domain and range puzzle displaying top 8 worksheets found for this concept.
This compilation of domain and range worksheet pdfs provides 8th grade and high school students with ample practice in determining the domain or the set of possible input values x and range the resultant or output values y using a variety of exercises with ordered pairs presented on graphs and in table format.
Relations Functions And Domain And Range 7th 10th Grade Worksheet Functions Algebra Worksheets Graphing
This Is A Double Sided Practice Page Over Functions Domain Range And Function Notation The Front Asks The Student To Det Functions Math Notations Math Blog
Identifying Functions From Ordered Pairs Worksheets Algebra Worksheets Identifying Functions Math Exercises
Functions Domain And Range Math Guided Notes Functions Math Practices Worksheets
Domain And Range Worksheet 1 Elegant Function Domain And Range Worksheet Free Printable In 2020 Algebra Worksheets Worksheets Math Worksheets
Domain And Range Foldable Notes Math Formulas Life Hacks For School Advanced Mathematics
Domain And Range From Graph Khan Academy Solving Quadratic Equations Chemistry Worksheets Interpreting Motion Graphs
Algebra 1 Worksheets Domain And Range Worksheets Algebra Algebra Worksheets Practices Worksheets
Draft Webitou Images Domain Range Function Worksheet Algebra Worksheets Math Worksheets Algebra 1
Domain Range Of Linear Functions Using Graphs Math Tutoring Activities Summer School Math Activities Summer School Math
Domain Range Continuous Discrete Flashcards Pp Studying Math Teaching Algebra Teaching Math
Pin On Printable Chart And Graph Template
Function Worksheets Practices Worksheets Graphing Functions Linear Function
Http Www Mathworksheets4kids Com Function Domain Range Large Png Practices Worksheets Graphing Algebra Worksheets
Function Worksheets Graphing Linear Equations Linear Function Quadratic Functions
Domain And Range Of Polynomials Functions Excellent Sheet Polynomial Functions Functions Algebra Polynomials
Custom Algebra 2 Worksheets Designed To Develop Mastery Of Functions Through Function Notation Analyzing Graphs Form Quadratics Graphing Algebra 2 Worksheets | 916 | 4,799 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2024-26 | latest | en | 0.847976 |
https://www.physicsforums.com/threads/can-you-find-roots-with-the-power-series-inverse.328922/ | 1,531,878,299,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589980.6/warc/CC-MAIN-20180718002426-20180718022426-00145.warc.gz | 950,064,799 | 14,120 | # Can you find Roots With The Power Series Inverse?
1. Aug 4, 2009
### John Creighto
The following link outlines a method to find the inverse of a power series. I was wondering what would happen if you try this on a polynomial. Since polynomials aren't one to one, I presume that it wouldn't give you all the roots, but might it give you the nearst root. Or will this technique not work on this type of function?
http://www.mathpages.com/home/kmath625/kmath625.htm
Edit: Looking further at the solution, to find the coefficients you have to be able to find the roots. Therefor we could only find at most say around the first five coefficients in general without using numeric techniques.
Edit 2: Although maybe it is better to find the derivative of the inverse more directly, then suggested in the above link. For instance we could chose some point, where we know the inverse, and then use the functions for the derivative of the inverse as outlined here:
http://en.wikipedia.org/wiki/Inverse_functions_and_differentiation#Higher_derivatives
Last edited: Aug 4, 2009 | 241 | 1,074 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2018-30 | latest | en | 0.928521 |
http://www.traditionaloven.com/tutorials/distance/convert-china-small-li-unit-to-fingers-fingerbreadth-measure.html | 1,513,136,602,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948521188.19/warc/CC-MAIN-20171213030444-20171213050444-00216.warc.gz | 501,919,700 | 11,727 | Convert 釐 or 厘 to finger | Chinese lí to fingerbreadths
# length conversion
## Amount: 1 Chinese lí (釐 or 厘) of length Equals: 0.0098 fingerbreadths (finger) in length
Converting Chinese lí to fingerbreadths value in the length units scale.
TOGGLE : from fingerbreadths into Chinese lí in the other way around.
## length from Chinese lí to fingerbreadth Conversion Results:
### Enter a New Chinese lí Amount of length to Convert From
* Whole numbers, decimals or fractions (ie: 6, 5.33, 17 3/8)
* Precision is how many numbers after decimal point (1 - 9)
Enter Amount :
Decimal Precision :
CONVERT : between other length measuring units - complete list.
Conversion calculator for webmasters.
## Length, Distance, Height & Depth units
Distance in the metric sense from any two A to Z points (interchangeable with Z and A), also applies to physical lengths, depths, heights or simply farness. Tool with multiple distance, depth and length measurement units.
Convert length measuring units between Chinese lí (釐 or 厘) and fingerbreadths (finger) but in the other reverse direction from fingerbreadths into Chinese lí.
conversion result for length: From Symbol Equals Result To Symbol 1 Chinese lí 釐 or 厘 = 0.0098 fingerbreadths finger
# Converter type: length units
This online length from 釐 or 厘 into finger converter is a handy tool not just for certified or experienced professionals.
First unit: Chinese lí (釐 or 厘) is used for measuring length.
Second: fingerbreadth (finger) is unit of length.
## 0.0098 finger is converted to 1 of what?
The fingerbreadths unit number 0.0098 finger converts to 1 釐 or 厘, one Chinese lí. It is the EQUAL length value of 1 Chinese lí but in the fingerbreadths length unit alternative.
How to convert 2 Chinese lí (釐 or 厘) into fingerbreadths (finger)? Is there a calculation formula?
First divide the two units variables. Then multiply the result by 2 - for example:
0.00984251968504 * 2 (or divide it by / 0.5)
QUESTION:
1 釐 or 厘 = ? finger
1 釐 or 厘 = 0.0098 finger
## Other applications for this length calculator ...
With the above mentioned two-units calculating service it provides, this length converter proved to be useful also as a teaching tool:
1. in practicing Chinese lí and fingerbreadths ( 釐 or 厘 vs. finger ) values exchange.
2. for conversion factors training exercises between unit pairs.
3. work with length's values and properties.
International unit symbols for these two length measurements are:
Abbreviation or prefix ( abbr. short brevis ), unit symbol, for Chinese lí is:
Abbreviation or prefix ( abbr. ) brevis - short unit symbol for fingerbreadth is:
finger
### One Chinese lí of length converted to fingerbreadth equals to 0.0098 finger
How many fingerbreadths of length are in 1 Chinese lí? The answer is: The change of 1 釐 or 厘 ( Chinese lí ) unit of length measure equals = to 0.0098 finger ( fingerbreadth ) as the equivalent measure for the same length type.
In principle with any measuring task, switched on professional people always ensure, and their success depends on, they get the most precise conversion results everywhere and every-time. Not only whenever possible, it's always so. Often having only a good idea ( or more ideas ) might not be perfect nor good enough solution. If there is an exact known measure in 釐 or 厘 - Chinese lí for length amount, the rule is that the Chinese lí number gets converted into finger - fingerbreadths or any other length unit absolutely exactly.
Conversion for how many fingerbreadths ( finger ) of length are contained in a Chinese lí ( 1 釐 or 厘 ). Or, how much in fingerbreadths of length is in 1 Chinese lí? To link to this length Chinese lí to fingerbreadths online converter simply cut and paste the following.
The link to this tool will appear as: length from Chinese lí (釐 or 厘) to fingerbreadths (finger) conversion.
I've done my best to build this site for you- Please send feedback to let me know how you enjoyed visiting. | 949 | 3,984 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2017-51 | latest | en | 0.795915 |
https://www.physicsforums.com/threads/simple-integration-u-sub-ln.213147/ | 1,531,980,721,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590559.95/warc/CC-MAIN-20180719051224-20180719071224-00108.warc.gz | 973,811,527 | 13,399 | # Simple Integration (U-sub/LN)
1. Feb 4, 2008
### acurtiz
Hey everyone. One of the steps at the end of this problem is confusing to me. I'll point it out.
$$\int \frac{1}{1+ \sqrt{2x}} dx$$
Setting u equal to $${1+ \sqrt{2x}}$$ and du equal to $$\frac {1}{\sqrt(2x)}$$ and taking the derivative, I get
$$\int \frac {sqrt(2x)}{u} du$$
The answer to the problem is apparently as follows -
$$\equiv \sqrt{2x} - ln|1+ \sqrt{2x}| + c$$
As far as I'm aware there is no step in between those last two. I'm not sure how it works and I'm 90% sure that I'm just missing something extremely obvious. I'd appreciate any help. Thank you!
Last edited: Feb 4, 2008
2. Feb 4, 2008
### cemar.
okay so here your biggest problem is your u.
When you have a value under a square root your best bet is usually to set u = what is under that square root.
And i am very confused with your answer as it includes both variables u and x.
You must also remember to find a way to sub du into the value of dx.
3. Feb 4, 2008
### acurtiz
Sorry about that; hopefully my edited post is a little more clear. In my class we usually do set the value(s) under the square root as the u. However, in this particular problem, the directions are to set the entire denominator as u. I'm not sure how to do it even if I was to set u=2x. I'm new to the whole syntax thing. dx = sqrt(2x)du after going through everything.
4. Feb 4, 2008
### awvvu
$$u = 1 + \sqrt{2x} => \sqrt{2x} = u - 1$$
Does that help you? You need the integral to have the same variable.
5. Feb 5, 2008
### HallsofIvy
After you have substituted "u" for "x", you cannot have an x remaining in the integral! I'm not sure how in the world you would integrate
$$\int \frac {sqrt(2x)}{u} du$$
with the x in there while differentiating with respec to u.
Fortunately, as awvvu said, since $u= 1+ \sqrt{2x}$, $\sqrt{2x}= u- 1$. You integral, after the substitution is really
$$\int \frac {u-1}{u} du = \int (1- \frac{1}{u}) du$$
That gives the answer you have. | 624 | 2,001 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.984375 | 4 | CC-MAIN-2018-30 | latest | en | 0.942884 |
https://healthiersteps.com/how-many-tablespoons-in-a-cup/ | 1,725,722,976,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650883.10/warc/CC-MAIN-20240907131200-20240907161200-00758.warc.gz | 280,376,459 | 64,223 | # How Many Tablespoons In A Cup?
## How many tablespoons in a cup?
A new baker or cook is likely to be learning how to measure ingredients exactly so that they don’t wind up being used in excess or insufficient amounts in the recipe. If this is the case, read on for additional information. An important step is to be able to calculate how many tablespoons in a cup.
Have you ever become completely immersed in a complicated recipe only to find you were missing a measuring cup?
Although the temptation to eyeball the amount of an item is great, occasionally using too much or too little of an ingredient can ruin a dish.
Instead of asking yourself, “How many tablespoons are in a cup?” employ this simple trick to ensure that the amount is accurate every time!
Using tablespoons is not only extremely convenient, but it also decreases the amount of cleanup that needs to be done.
To save time and effort, utilize some of the tablespoons you already have on hand instead of breaking out the measuring cups. This will result in fewer dishes to clean up afterwards.
So, how many tablespoons are there in a cup of something? The correct answer is that 16 tablespoons equals one cup. Let’s have a look at our post for a more in-depth guidance and cooking suggestions!
## In what countries are tablespoons and cups different?
Technically, there are four different forms of measurements used around the world: the international metric system, the imperial cup system, the United States metric system, and the United Kingdom metric system (in that order).
As an illustration, consider the following discrepancies in tablespoons and cups used around the world in different countries.
In the United States, there are two primary sizes of cups available: the legal cup and the customary cup; therefore, the type of cup you use before converting it to tablespoons is dependent on the size of the cup you use.
Now, the usual cup is the measuring cup that is used for traditional American foods such as pies and bread, and one customary cup is equal to 16 tablespoons in US measurements.
One cup is equal to 16.24 tablespoons in the legal cup, which is primarily used by food and drug authorities as well as manufacturers of consumer goods to label their nutritional information.
## What is the difference between dry and wet measurements?
To be clear, dry and wet cups are the same thing. When cooking with dry ingredients such as sugar, flour, or cocoa powder, one cup equals 16 tablespoons. The same is true for liquid substances such as water, cooking oil, syrup, and so on.
When measuring wet components, it’s important to use liquid measuring cups. They frequently include a handle and measurement lines, allowing you to achieve the desired measurement without spilling.
When you use dry measuring cups to measure liquid components, you will either spill them or receive too little (to avoid spilling). These cups retain a precise amount and are leveled with a flat edge.
## How many tablespoons are there in a cup?
Sit back and relax if you worried and searched the terms ‘how many tbsp in a cup’ midway through cooking. Once you’ve cracked the code, any cup-to-teaspoon conversion becomes second nature.
A cup has 16 tablespoons.
So, the next time you’re baking and a recipe calls for a cup of flour, measure 16 level tablespoons instead of eyeballing it or hoping your regular teacup will suffice.
How much tbsp are there in a 3/4 cup? You’ll need to do some arithmetic for this. It’s multiplying 16 by 34 in this example. Because 16×34=12, there are 12 tablespoons in a 34 cup.
From here, most recipes’ calculations become straightforward. Simply halve the amount to get how many tablespoons are in a half-cup. Half a cup is 8 tablespoons for most substances.
Now that you know how many tbsp are in 1/2 cup, you can proceed to scale things down. Divide 16 by 4 to get the number of tablespoons in a quarter cup. A quarter cup of dry ingredients, such as rice or flour, contains 4 tablespoons.
You can take it a step farther. How many tablespoons are there in an eighth cup? Divide 16 by 8 to get the answer. One-eighth cup is two tablespoons.
### Let’s keep it going!
Now let’s move on to some more difficult conversions. Most people struggle to figure out how many teaspoons are in 2/3 cup.
So, how much tbsp are there in a third cup? 13 divided by 16 = 5.333, a fraction. While you can approximate the amount and use just a little more than 5 tablespoons, there is a better approach. Instead, use 5 tablespoons Plus 1 teaspoon, which is a more precise amount.
Similarly, to convert 23 cups to tablespoons, use 10 tablespoons plus 2 teaspoons of a specific component.
## Other methods of conversion:
While remembering these dimensions will come in handy in a pinch, there’s a lot more where they came from. Another important conversion that comes in handy is ounces to spoons.
So, how many tablespoons are there in an ounce? 1 ounce is equivalent to 6 teaspoons or 2 tablespoons. In other terms, 18 cup equals one ounce of a component.
But how much is half a tablespoon? Converting it to tablespoons is an easy way to do this because they are commonly found in every kitchen. When measuring dry products, half a tablespoon = 1.5 teaspoons.
## How to simplify?
There are a number of tools available to make these calculations easier. If you need to be more particular, most sticks of butter contain marks on the wax paper wrapping that indicate how much butter is in each ounce or half-cup.
Aside from that, several solid kinds of shortening are available as sticks that may be easily cut into precise portions for use in baking recipes.
## Measuring solids:
When working with any solid (or dry) product, weighing the product before adding it to your mixing bowl is a much more accurate approach of adding it to your mixing bowl.
Consider the following examples: one cup of milk weighs 8 ounces, while a cup of whole wheat flour weighs 4.5 ounces and a cup of cake flour weighs 4 ounces.
Powdered sugar weighs about the same as cake flour, despite the fact that brown sugar is heavier than white sugar.
Now that we understand why our most recent batch of oatmeal cookies turned into aromatic blocks, we can fix the problem and get back to creating delicious cookies again.
The use of a kitchen scale that will zero out is essential if you intend to measure your dry goods by weight in the kitchen.
## Tips for new bakers on measuring
When it comes to creating the most delectable desserts, it all comes down to how you utilize your tablespoon. Here’s a list of what they are:
Making certain that your measuring cups and spoons are level is essential to getting the most out of any dish you make.
Half-filled or heaping utensils will result in the use of either too much or too few ingredients, which can negatively impact the taste of whatever you’re producing in the process!
When you are cooking your favorite dishes, aerate the components such as flour, cocoa powder, and other dry items to give them more volume.
This procedure will prevent the finished result from becoming too dense while also providing it with an incredible texture!
It is not recommended to use tea or coffee cups when measuring by volume because you will not receive consistent cooking results.
It is especially crucial while baking, since it might result in unevenly cooked baked items if not done correctly!
When measuring dry items such as flour, sugar, or spices, make sure to fill the jar to the brim. Make use of the back of your knife to scrape across the surface of the surface and level it off.
When measuring liquids, don’t rely on dry ingredient cups to get the job done! In lieu of this, use a liquid measuring cup and place them on an even surface, then position yourself so that you can easily observe the measurement findings.
When measuring, it is critical to always use the proper-sized cups or spoons for the task at hand. Different recipes call for different serving sizes, so be sure to select one that is appropriate for your needs.
Don’t only rely on the measuring cups to get things done! Kitchen scales can offer you the most precise results in milliliters or grams because they are small and portable.
## Conclusion
Cooking is enjoyable, creative, and provides numerous opportunity for individual expression. Baking is also enjoyable, but it is chemistry that heats your home and makes it smell wonderful. Learning to cook can be difficult, especially if you start with recipes that require new measurements.
It will be much easier to prepare consistent, tasty baked items that taste fantastic from batch to batch if you weigh and measure your dry and wet materials precisely.
This post should have provided some helpful advice and tips for measuring ingredients. It’s time to start cooking now that we can quickly convert tablespoon quantities to cups!
## More cooking measurement tips:
How Many Teaspoons In A Tablespoon?
How Many Grams In An Ounce
Celsius To Fahrenheit Chart
How Many Ounces In A Cup?
How Many Cups In A Gallon?
If you enjoyed this post about How Many Tablespoons In A Cup and would love to see more, join me on YoutubeInstagramFacebook & Twitter!
Get discounted copies of my cookbook here.
Fortunately, because of the Ads on our website, readers and subscribers of Healthier Steps are sponsoring many underprivileged families. | 1,958 | 9,413 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2024-38 | latest | en | 0.95016 |
https://www.thedriller.com/articles/90227-for-drilling-jobs-combating-lost-circulation | 1,719,044,923,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862310.25/warc/CC-MAIN-20240622081408-20240622111408-00347.warc.gz | 879,418,294 | 19,556 | I have stated that drilling is 80 percent knowledge and 20 percent luck. Bad luck happens when a driller encounters a loss zone, thus preventing the driller from finishing the hole. In these situations, it is up to the driller to create luck. Loss zones need to be dealt with quickly and efficiently. The following steps help prevent losing the borehole when drilling into a loss zone.
### 1. Sample Logs, Geology and Experience
As a young mud engineer, I was invited by Ortman Drilling to help drill a geothermal test hole in downtown Indianapolis, at a site that would become a nature center. After evaluating the sample logs for the area, we expected to lose circulation at a depth of 88 feet and again at 105 feet. We removed the “luck factor” by having basic geologic knowledge of the area. I worked with this very same talented drill team at Ball State, and we encountered many lost circulation zones together. These guys were lost circulation experts for central Indiana. The team prepared to lose circulation once they drilled to 80 feet in the ground. At 88 feet, the drill bit encountered fractured limestone that immediately caused partial fluid loss. The experienced drill team agreed that understanding the loss zone, along with preparation, would be the key to drilling past the zone and completing the borehole.
### 2. Hole Volume and Required Drilling Volume
First, the drill team prepared 2.5 times the total borehole fluid volume. The hole design:
• 6.25-inch diameter hole to a total depth of 400 feet
• 6.25-inch diameter bit uses a borehole fluid volume of 1,593 gallons per foot
• 400 feet x 1.593 gallons per foot = 637.23 total gallons
• 637.23 x 2.5 = 1,593 total gallons
Note that you can take the drill rod diameter out and reduce the fluid volume by 300 gallons, but it is a good practice to build in a safety factor.
Using 2.5 times the fluid volume allows the operator to explore into the loss zone before losing all of the fluid on the surface. When drilling into a fractured zone for the first time, it is important to note how much fluid is lost and at what depth it is lost. The idea is to drill beyond the loss zone back into competent formation. The team could have started with a 300-gallon mud pan or a 600-gallon small mud managing system, but we expected the loss zone to take more fluid than either of the smaller options could provide. There is a fine line between stopping a partial loss and creating a huge loss circulation area. The goal is to shut the partial loss down as quickly as possible. That is hard to do with only 300 to 600 gallons of drilling fluid. There has to be enough volume to create a patch and have enough volume to put pressure against the new plug.
### 3. Visualize the Loss Zone
The good thing about having enough fluid volume to drill into the loss is that you have the chance of drilling beyond the zone back into a competent formation. You have time to learn about the loss or fracture zone. The bad thing about having enough fluid volume to drill into the loss formation is that you can do more damage if you do not stop the loss. If you drill into a fractured loss zone and immediately lose 50 percent of your fluid, it is time to stop drilling, raise the rods off the bottom, shut off the mud pump and prepare for WAR. Yes, there is a possibility that you could open the valve to the water truck or hydrant, mix some mud while drilling and get through the zone. However, in reality, every gallon of fluid that goes into a loss zone opens up a bigger loss zone. The drilling fluid is washing out any matrix that Mother Nature had deposited over the last 10,000 years. To get past the partial loss zone, we need that delicate matrix to stay intact.
We plan our attack by selecting the right drilling fluid and plugging media. Drillers’ notes can help recreate the encountered loss zone; go back and review how much fluid was lost and at what depth. Consider how the bit reacted to the loss zone. Did the bit have lots of rattling or chatter? Did the rods fall several feet? The goal is to build a mental picture of the loss zone. Fractured rock drills differently than glacial till and radically different than drilling into a void. At 88 feet, if the bit encounters a zone that lost 5 to 10 percent of your fluid then it is possible the loss zone is small fractures. If that 88 feet formation takes 80 percent of your fluid, and the rate of penetration met no resistance for 5 feet, then you have a huge void. Start to create a picture of the loss zone. What does it look like? Downhole cameras and logging tools are great ways to see what is going on downhole. However, realize that it is very hard to analyze downhole video, and logging tools are very expensive to lose in the hole. Your imagination works great at visualizing the downhole conditions.
### 4. Selecting the Right Lost Circulation Media
In Indianapolis, we hit the loss zone, pulled up off the bottom and discussed what the drill had encountered. The situation seemed simple at first. The bit started to chatter as the team penetrated the fractured limestone. The mud pit lost 10 percent of the fluid volume between 88 and 91 feet. As the team drilled to 95 feet, another 25 percent of the fluid was lost. The team had a partial loss zone but not a total loss zone. They mixed up 600 gallons of drilling fluid, ensuring that the viscosity and filtrate were within recommended parameters. If the base fluid transporting the Lost Circulation Material (LCM) to the fractured zone is of poor quality or has bad properties, then the chance of the LCM working is less.
Next, the team discussed which LCM to select. At 88 feet, we understood that the zone took little fluid, but as the team drilled into the fractured limestone, the fluid loss increased. We decided to use a combination of Baroid IDP’s N-Seal, Diamond Seal and Benseal. The team visualized a loss zone with small fractures on top and larger cracks toward the middle and bottom of the zone. To shut down the variety of loss zones encountered, the team selected products with a variety of size. Each LCM is designed to patch fracture zones differently. N-Seal is intended to build stability in the drilling fluid, creating a webbinglike matrix with the fluid over the small fractures. Diamond Seal slowly absorbs water, increasing in size over time. It can be pumped into a larger void space and swell, closing the loss zone over time. Benseal is a product used for grouting water wells. It hydrates rapidly and can fill fracture spaces. It is a great product because it can be easily pumped downhole and create a strong patch. Granular bentonite as an LCM is always a smart option. The combination of three different sizes of materials working together shut down the loss zone encountered from 88 feet to 100 feet. Beyond 100 feet, the fractures became total loss zones, and the team had to evaluate the entire project. The job could be drilled, but estimating cost and time was impossible.
### Other Factors to Combating Loss Circulation
Sometimes the best way to combat loss zones is to assess the project; question the drilling method and techniques used to drill the hole. Many loss zones are drilling induced or, better yet, driller induced. Poor drilling fluid properties, such as excessive mud weights or high viscosity, can cause loss zones. Couple poor drilling fluids with bad drilling techniques, and loss zones are inevitable. Solids control can help maintain proper drilling fluid parameters. Changing drilling methods can help. For example, drilling with foam can be a better option in fragile zones. Think of the downhole conditions like your first woodworking project. Your instructor told you to predrill the hinge holes for the cherry music box you were making. It seemed like one extra step that was not necessary, so you drove the screw into the wood and split it. You had broken the fracture gradient of your Mother’s Day gift. You could patch it with putty, but it would never have been as strong as it was before the wood split. Downhole conditions are the same way; sometimes moving is a better option than continuing the fight.
It is always important to be environmentally responsible and have the groundwater’s best interests in mind when drilling. The project in Indianapolis was downtown, and we did not have to worry about water wells in the area. Always ask, where did my drilling fluid go? The fluid took the path of least resistance. That path could be impacting a water source or water well. When drilling water wells use NSFapproved loss circulation material and products that can be produced back out of the formation. Your loss zone could be another person’s water source. | 1,850 | 8,723 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-26 | latest | en | 0.930768 |
https://www.assignmentexpert.com/homework-answers/chemistry/inorganic-chemistry/question-164020 | 1,718,573,758,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861671.61/warc/CC-MAIN-20240616203247-20240616233247-00404.warc.gz | 579,151,387 | 67,250 | 107 763
Assignments Done
100%
Successfully Done
In June 2024
# Answer to Question #164020 in Inorganic Chemistry for Rashika
Question #164020
1) How many mg of hcl are in 20/ml of the juice with ph 2 molar mass of hcl is 36.5 what is OH minus ions concentration in a solution with PH 2 ?
2) what is physiological range of blood pH ? How the increase of carbon dioxide can influence pH of the blood ? What should be the ratio between the components of the bicarbonate buffer to keep pH of the blood in physiological range ?
3) 0.9% (m/v) Nacl ( 58.5G/mole ) solution is physiological solution . Explain in words or calculation if 10 %of (m/v) saccharose (sucrose) (342g/m) solution can be treated as physiological solution
4 ) There are two water solutions 2 moles/dm*3 glucose (180g/mole ) and 2 moles /dm*3 kcal 74.5G/mole a) explain if the solution is isotonic b) which has lower melting melting point
1
2021-02-16T07:49:09-0500
1.
pH = - log1 0[ H+]
2 = - log10 [H+]
H+ = 10-2
= 0.01
OH- = 14 - 0.01 = 13.99
2. To maintain homeostasis, the human body employs many physiological adaptations. One of these is maintaining an acid-base balance. In the absence of pathological states, the pH of the human body ranges between 7.35 to 7.45, with the average at 7.40.
So CO2 in the bloodstream lowers the blood pH. When CO2 levels become excessive, a condition known as acidosis occurs. This is defined as the pH of the blood becoming less than 7.35. The body maintains the balance mainly by using bicarbonate ions in the blood.
Ideally, the pH of the blood should be maintained at 7.4. ... Fortunately, we have buffers in the blood to protect against large changes in pH. ... the body) H+ ions and other components of the pH buffers that build up in excess.
I
3.Concentrations of solutions are sometimes given as "percentages." This refers to the mass of solute, in grams, dissolved in a solvent to a volume of 100 ml. "Normal saline" is an aqueous solution of 0.9% NaCl. This means that normal saline can be prepared by measuring out 0.9 g of NaCl and diluting this amount of NaCl to a final volume of 100 ml's in water. This would be the same as diluting 9 g of NaCl to a final volume of 1 liter in water. Normal saline is also known as "physiological saline." Normal saline (0.9% NaCl) is the basis (starting fluid) for intravenous fluid therapy. Normal saline can be directly administered to the bloodstream as it has the same osmolarity as plasma.
4. They are not isotonic because they have different osmotic pressure due to their weight.
The second solution
Need a fast expert's response?
Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS! | 743 | 2,727 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-26 | latest | en | 0.893952 |
https://www.effortlessmath.com/math-topics/mcas-grade-3-math-free-sample-practice-questions/ | 1,624,402,651,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488525399.79/warc/CC-MAIN-20210622220817-20210623010817-00500.warc.gz | 671,330,064 | 15,312 | # 3rd Grade MCAS Math FREE Sample Practice Questions
Preparing your student for the 3rd Grade MCAS Math test? To succeed on the MCAS Math test, students need to practice as many real MCAS Math questions as possible. There’s nothing like working on MCAS Math sample questions to measure your student’s exam readiness and put him/her more at ease when taking the 3rd Grade MCAS Math test. The sample math questions you’ll find here are brief samples designed to give students the insights they need to be as prepared as possible for their 3rd Grade MCAS Math test.
Check out our sample 3rd Grade MCAS Math practice questions to find out what areas your student needs to practice more before taking the 3rd Grade MCAS Math test!
Start preparing your student for the 2021 MCAS Math test with our free sample practice questions. Also, make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions students need to practice.
## 10 Sample 3rd Grade MCAS Math Practice Questions
1- Which number correctly completes the subtraction sentence
$$8000 – 658 =$$_____ ?
A. 7,342
B. 7,452
C. 742
D. 7,458
2- Jason packs 14 boxes with flashcards. Each box holds 40 flashcards. How many flashcards Jason can pack into these boxes?
A. 56
B. 480
C. 540
D. 560
3- Which of the following statements describes the number 24,589?
A. The sum of two thousands, 4 thousands, five hundreds, eighty tens, and nine ones
B. The sum of forty thousands, 2 thousands, five hundreds, eight tens, and nine ones
C. The sum of twenty thousands, 4 thousands, fifty hundreds, eighty tens, and nine ones
D. The sum of twenty thousands, 4 thousands, five hundreds, eight tens, and nine ones
4- What is the value of “A” in the following equation?
$$21 + A + 9 = 44$$
A. 10
B. 12
C. 14
D. 20
5- Mr. smith usually eats four meals a day. How many meals does he eat in a week?
A. 21
B. 24
C. 28
D. 30
6- What is the value of A in the equation $$72 ÷ A = 8$$
A. 2
B. 6
C. 7
D. 9
7- Use the models below to answer the question.
$$\img{https://appmanager.effortlessmath.com/public/images/questions/taar322d.JPG}$$
Which statement about the models is true?
A. Each shows the same fraction because they are the same size.
B. Each shows a different fraction because they are different shapes.
C. Each shows the same fraction because they both have 3 sections shaded.
D. Each shows a different fraction because they both have 3 shaded sections but a different number of total sections.
8- To what number is the arrow pointing?
$$\img{https://appmanager.effortlessmath.com/public/images/questions/taar3228.JPG}$$
A. 36
B. 38
C. 40
D. 42
9- Emily has 108 stickers and she wants to give them to nine of her closest friends. If she gives them all an equal number of stickers, how many stickers will each of Emily’s friends receive?___________
10- The following models are the same size and each divided into equal parts.
The models can be used to write two fractions.
$$\img{https://appmanager.effortlessmath.com/public/images/questions/taar330.JPG}$$
Based on the models, which of the following statements is true?
A. $$\frac{2}{8}$$ is bigger than $$\frac{4}{16}$$.
B. $$\frac{2}{8}$$ is smaller than $$\frac{4}{16}$$.
C. $$\frac{2}{8}$$ is equal to $$\frac{4}{16}$$.
D. We cannot compare these two fractions only by using the models.
## Best 3rd Grade MCAS Math Prep Resource for 2021
1- A
$$8000 – 658 = 7342$$
2- D
$$14 × 40 = 560$$
3- C
24,589 is the sum of $$20,000; 4,000; 500; 80;$$ and 9
4- C
$$A = 44 – (21 + 9)$$
$$A = 14$$
5- C
In 1 day 4 meals so $$4 × 7 = 28$$ meals a week.
6- D
$$A = 72 ÷ 8$$
$$A= 9$$
7- D
the model for the first fraction is divided into 6 equal parts. We shade 3_6 to show the same amount as 1_2. The model for the second fraction is divided into 8 equal parts. We shade 3_ 8 that it shows this two model are different fractions.
8- C
Arrow shows exactly the middle of two numbers 35 and 45,so the answer is 40
9- 12
$$108 ÷ 9 = 12$$
10- C
the model for the first fraction is divided into 8 equal parts. We shade 2_ 8 to show the same amount as 1_ 4. The model for the second fraction is divided into 16 equal parts. We shade 4_ 16 to show the same amount as 1_ 4.
36% OFF
X
## How Does It Work?
### 1. Find eBooks
Locate the eBook you wish to purchase by searching for the test or title.
### 3. Checkout
Complete the quick and easy checkout process.
## Why Buy eBook From Effortlessmath?
Save up to 70% compared to print
Help save the environment | 1,318 | 4,568 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2021-25 | longest | en | 0.925594 |
https://studysoup.com/tsg/10938/elementary-statistics-12th-edition-chapter-4-5-problem-5bsc | 1,576,359,771,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575541294513.54/warc/CC-MAIN-20191214202754-20191214230754-00007.warc.gz | 552,298,555 | 11,861 | > > > > Problem 5BSC
# Describing Complements. In Exercises, provide a written
## Problem 5BSC Chapter 4.5
Elementary Statistics | 12th Edition
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants
Elementary Statistics | 12th Edition
4 5 0 320 Reviews
29
2
Problem 5BSC
Describing Complements. In Exercises, provide a written description of the complement of the given event, then find the probability of the complement of the given event.
Five Girls When a couple has five children, all five are girls. (Assume that boys and girls are equally likely.)
Step-by-Step Solution:
Step 1 of 3
Solution 5BSC
=...
Step 2 of 3
Step 3 of 3
##### ISBN: 9780321836960
This full solution covers the following key subjects: girls, complement, given, Event, equally. This expansive textbook survival guide covers 121 chapters, and 3629 solutions. The full step-by-step solution to problem: 5BSC from chapter: 4.5 was answered by , our top Statistics solution expert on 03/15/17, 10:30PM. The answer to “Describing Complements. In Exercises, provide a written description of the complement of the given event, then find the probability of the complement of the given event.Five Girls When a couple has five children, all five are girls. (Assume that boys and girls are equally likely.)” is broken down into a number of easy to follow steps, and 45 words. Since the solution to 5BSC from 4.5 chapter was answered, more than 281 students have viewed the full step-by-step answer. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12th.
#### Related chapters
Unlock Textbook Solution
Describing Complements. In Exercises, provide a written
×
Get Full Access to Elementary Statistics - 12th Edition - Chapter 4.5 - Problem 5bsc
Get Full Access to Elementary Statistics - 12th Edition - Chapter 4.5 - Problem 5bsc
I don't want to reset my password
Need help? Contact support
Need an Account? Is not associated with an account
We're here to help | 534 | 2,149 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2019-51 | latest | en | 0.910732 |
https://www.physicsforums.com/threads/why-su-2-times-u-1-for-the-sm.846099/ | 1,529,385,261,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267861899.65/warc/CC-MAIN-20180619041206-20180619061206-00049.warc.gz | 922,179,828 | 19,725 | # Why $SU(2) \times U(1)$ for the SM?
1. Dec 2, 2015
### ChrisVer
Just a question that had always been bugging me, yet I didn't have the chance to ask...
How was WGS model of $SU(2) \times U(1)$ come into the game as the theory of leptons? in other words, what led them (gave them hints) in choosing this successful group combination instead of some other?
2. Dec 2, 2015
Staff Emeritus
U(1) looks like electromagnetism, SU(2) looks like isospin. Why not start from what you already know?
3. Dec 2, 2015
### samalkhaiat
For simplicity let us focus just on the electron and its neutrino. It was known that the weak interaction is governed by an IVB theory with $(A-V)$-type charged current
$$J^{\mu} = \bar{\nu}_{e}\gamma^{\mu}(1-\gamma_{5}) e ,$$ with two corresponding weak charges
$$T_{+} = \frac{1}{2} \int d^{3}x \ \nu^{\dagger}_{e}\gamma^{\mu}(1-\gamma_{5}) e = T_{-}^{\dagger} .$$ On the other hand there was the electromagnetic interaction $j^{\mu}A_{\mu}$ of these leptons with the em-current and its charge was given by
$$j^{\mu} = \bar{e}\gamma^{\mu}e , \ \ \ Q = \int d^{3}x \ e^{\dagger}e .$$
As far back as 1957 and based on the vectorial nature of both interactions, Schwinger suggested the idea of weak and electromagnetic unification. Now, the simplest gauge group with 3 generators is $SU(2)$. However, the 3 charges $(T_{\pm},Q)$ do not form a closed algebra. Indeed, it is easy to show that
$$[T_{+},T_{-}] = \frac{1}{2}T_{3} \neq Q . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$$ The fact that $Q$ cannot be a generator of $SU(2)$ with only two leptons is easy to see: (1) The generators of $SU(2)$ are traceless. So, in order for $Q$ to be a generator the electric charges of an irreducible multiplet must add up to zero. Clearly, the doublet formed out of $\nu_{e}$ and $e$ does not satisfy this condition. (2) $Q$ corresponds to purely vector current, while the weak charges $T_{\pm}$ correspond to $V-A$ type currents.
(i) The unification group is $SU(2)$. This requires adding new fermions to the multiplet and, therefore, modify the currents so that the new charges $t_{\pm}$ and $q$ form a closed $su(2)$ algebra. In the case at hand, a new positively charged lepton $E^{+}$ was needed to form an electrically neutral $SU(2)$-triplet. And another neutral lepton $N$ was also needed to obtain the $V-A$ nature of the weak current at low energies. In fact, Georgi & Glashow (1972) had formulated such model with 2 triplets and a singlet
$$\frac{1}{2}(1-\gamma_{5}) \left( \begin{array}{c} E^{(+)} \\ \nu_{e} \\ e^{(-)} \end{array} \right) , \ \ \frac{1}{2}(1+ \gamma_{5}) \left( \begin{array}{c} E^{(+)} \\ N \\ e^{(-)} \end{array} \right) , \ \ \frac{1}{2}(1+\gamma_{5}) N .$$
This model leads to 2 (electrically) charged weak currents (therefore they couple to charged vector bosons) with the corresponding weak charges $t_{\pm}$ given by
$$t_{+} = \frac{1}{2} \int d^{3}x \ \left( E^{\dagger} (1-\gamma_{5}) \nu_{e} + \nu_{e}^{\dagger}(1-\gamma_{5})e + E^{\dagger}(1+\gamma_{5})N + N^{\dagger}(1+\gamma_{5})e \right) ,$$
and a single neutral current (which could couple to the photon field) with charge given by
$$q = \int d^{3}x \ (E^{\dagger}E - e^{\dagger}e) .$$
It is simple exercise to show that the algebra of these charges is indeed isomorphic to $su(2)$
$$[t_{+} , t_{-}] = 2q .$$
This model was ruled out because it could not account for the weak neutral-current which was observed in 1973. Notice that the only neutral-current in this model is the electromagnetic current.
(ii) The gauge group is $SU(2) \times U(1)$. To achieve this, one only needed to introduce another gauge field to couple to the weak charge $T_{3}$ as given in equation (1). The four generators, $T_{\pm}, T_{3}$ and $Y \propto (Q - T_{3})$ can now generate the Lie algebra of $SU(2) \times U(1)$. Note that the crucial relation here is
$$[T_{i} , Q - T_{3}] = 0 , \ \ i = 1, 2 , 3 . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)$$
This option was eventually adopted by Weinberg, Salam and Glashow and you should know the rest of the success story of this particular choice for the gauge group, namely anomaly cancellation, unitarity etc.
Okay, that was history and phenomenology, but one can derive the $SU(2) \times U(1)$ model from pure field theoretical arguments. I will do that for you if I find spare time tomorrow.
Last edited: Dec 2, 2015
4. Dec 16, 2015
### samalkhaiat
Not exactly “tomorrow” but “better late than never”. Okay, I hope you will enjoy the story that is if I can get the LaTex to work.
Let $\Psi_{1}$ and $\Psi_{2}$ be two free fermion fields. If $m_{1}=m_{2}$, we can treat $\Psi = \begin{pmatrix}\Psi_{1} \\ \Psi_{2} \end{pmatrix}$ as a vector in 2-dimensional (internal) complex vector space $\mathcal{V}^{(2)}$. Since the group $SU(2)$ acts naturally on $\mathcal{V}^{(2)}$, we can use $\Psi$ and its (Dirac) conjugate $\bar{\Psi}$ to form the following $SU(2)$ invariant Lagrangian
$$\mathcal{L} = \bar{\Psi}\left(i \gamma^{\mu}\partial_{\mu} + m I_{(2)} \right) \Psi .$$
Since a mass term does not alter the form of Noether currents, we will set $m = 0$ and take
$$\mathcal{L}_{0} = i \bar{\Psi}\gamma^{\mu}\partial_{\mu}\Psi ,$$
to be our free Lagrangian. The invariance of $\mathcal{L}_{0}$ under the infinitesimal $SU(2)$,
$$\begin{equation*} \delta \Psi_{i} = -i \epsilon^{a}\left( \frac{\tau^{a}}{2} \right)_{ij} \Psi_{j} , \ \ i = 1,2 \end{equation*}$$
or,
$$\delta^{a} \Psi_{i} = -i \left( \frac{\tau^{a}}{2} \right)_{ij} \Psi_{j} , \ \ \ a = 1,2,3$$
leads to the following (conserved) Noether currents
$$\begin{equation*} J^{a\mu} = \frac{\partial \mathcal{L}_{0}}{\partial(\partial_{\mu}\Psi_{i})} \delta^{a}\Psi_{i} , \end{equation*}$$
$$J^{a\mu} = \bar{\Psi}_{i} \gamma^{\mu}\left(\frac{\tau^{a}}{2}\right)_{ij}\Psi_{j} .$$
The corresponding time-independent charges are, then, given by
$$T^{a} = \int d^{3}x J^{a0}(x) = \int d^{3}x \ \Psi^{\dagger}_{i}\left(\frac{\tau^{a}}{2}\right)_{ij} \Psi_{j} .$$
Okay, let me pause for a minute and ask you to do the following exercise:
The canonical formalism (for fermions) rest on the following equal-time anti-commutation relations
$$\big\{ \Psi^{\dagger}_{i}(t,\mathbf{x}) , \Psi_{j}(t,\mathbf{y}) \big\} = \delta_{ij}\delta^{3}(\mathbf{x} - \mathbf{y}),$$
$$\begin{equation*} \big\{ \Psi_{i}(t,\mathbf{x}) , \Psi_{j}(t,\mathbf{y}) \big\} = \big\{ \Psi^{\dagger}_{i}(t,\mathbf{x}) , \Psi^{\dagger}_{j}(t,\mathbf{y}) \big\} = 0 . \end{equation*}$$
Show that the canonical Noether charges $T^{a}$ generate the correct infinitesimal transformations on the fields
$$\left[iT^{a} , \Psi_{i}(x)\right] = \delta^{a}\Psi_{i}(x) ,$$
and form a representation of the Lie algebra of $SU(2)$
$$\left[T^{a} , T^{b}\right] = i \epsilon^{abc} T^{c} .$$
And finally, show that the Noether current $J^{a\mu}$ transforms in the adjoint representation of $SU(2)$
$$\delta^{a} J^{b}_{\mu}(x) = \left[iT^{a} , J^{b}_{\mu}(x)\right] = - \epsilon^{abc} J^{c}_{\mu}(x) .$$
Hint: use the algebra
$$\left[\frac{\tau^{a}}{2} , \frac{\tau^{b}}{2}\right] = i \epsilon^{abc} \frac{\tau^{c}}{2} ,$$
and the identity
$$\begin{equation*} \left[AB , C \right] = A \big\{ B , C \big\} - \big\{ A , C \big\} B . \end{equation*}$$
For later use, let’s define the “ladder” currents by
$$J^{\mu}_{\pm} = J^{1\mu} \pm i J^{2\mu}.$$
The corresponding ladder charges are, then, given by
$$T^{\pm} = T^{1} \pm i T^{2} .$$
Indeed, using the anti-commutation relations (5), it is easy to show that $T^{\pm}$ and $T^{3}$ form, as they should, a closed ladder algebra
\begin{align*} \left[ T^{+} , T^{-} \right] &= 2 \ T^{3} \\ \left[ T^{\pm} , T^{3} \right] &= \mp T^{\pm} . \end{align*}
Notice that
$$\begin{equation*} T^{+} = \int d^{3}x \ \Psi_{1}^{\dagger}(x) \Psi_{2}(x) = \left(T^{-}\right)^{\dagger} , \end{equation*}$$
destroys type-2 fermion and creates type-1 fermion.
Of course, any $SU(2)$-invariant Lagrangian is also invariant under independent global $U(1)$ transformations. Infinitesimally,
$$\delta \Psi_{i} = i \theta \Psi_{i} ,$$
with $\theta$ being an arbitrary constant, leads to a conserved $U(1)$ current
$$j^{\mu} = \bar{\Psi}_{i} \gamma^{\mu} \Psi_{i} ,$$
and time-independent charge
$$Y = \int d^{3}x j^{0}(x) = \int d^{3}x \ \Psi^{\dagger}_{i}(x)\Psi_{i}(x) .$$
Since we don’t yet know the nature of this $U(1)$ symmetry, we will call its charge, $Y$, the fermion number.
So, the global symmetry group of our theory is the non semi-simple group $SU(2) \times U(1)$. Indeed, using the anti-commutation relations (5), you can easily show that the $U(1)$ charge $Y$ commutes with the $SU(2)$ charges $T^{a}$
$$[ Y , T^{a}] = 0 , \ \ \forall a (= 1,2,3) .$$
This means that the two particles described by the fields $\Psi_{1}$ and $\Psi_{2}$ must have the same fermion number $Y$. Using this fact for all possible $U(1)$ groups, one can determine, almost uniquely, the particles content of all possible $SU(2)$ doublets.
Since we are at it, let us gauge our global symmetry group $SU(2) \times U(1)$. The detail of how to gauge the global symmetry of a generic field theory is explained in the PDF below. However, the details are irrelevant for our discussion here. All what we need to know is the fact that gauging $SU(2) \times U(1)$ forces us to introduce four real massless gauge fields: an $SU(2)$ triplet $W_{\mu}^{a}$, transforming in the adjoint representation, to couple to the matter current $J^{a\mu}$ of $SU(2)$, and a $U(1)$ gauge field $B_{\mu}$ to couple with the $U(1)$ matter current $j^{\mu}$. That is to say that we need to modify our free Lagrangian $\mathcal{L}_{0}$ by adding the following interaction terms
$$\mathcal{L}_{1} = gW^{a}_{\mu}J^{a\mu} + \frac{\bar{g}}{2} B_{\mu}j^{\mu} ,$$
where $g$ and $\bar{g}$ are the coupling parameters and the factor $1/2$ is for convenience.
Of course for a complete dynamical model, we also need to include the kinetic terms for the gauge fields. However, this is, again, an irrelevant issue for us.
Now, from the definition of the ladder currents (10), we have
\begin{align*} J^{1\mu} &= \frac{1}{2}(J^{\mu}_{+} + J^{\mu}_{-}) \\ J^{2\mu} &= \frac{1}{2i}(J^{\mu}_{+} - J^{\mu}_{-}) . \end{align*}
Inserting these currents in (16), we obtain
$$\begin{split} \mathcal{L}_{1} =& \frac{g}{\sqrt{2}} J^{\mu}_{+} \left[ \frac{1}{\sqrt{2}}\left( W^{1}_{\mu} - i W^{2}_{\mu} \right)\right] + \frac{g}{\sqrt{2}} J^{\mu}_{-} \left[ \frac{1}{\sqrt{2}}\left( W^{1}_{\mu} + i W^{2}_{\mu} \right)\right] \\ & + g W^{3}_{\mu} J^{3\mu} + \frac{\bar{g}}{2} B_{\mu}j^{\mu} . \end{split}$$
Notice that the first line in (17) contains complex (hence electrically charged) vector fields, and in the second line only real (i.e., electrically neutral) vector fields enter. In other words, the first line represents the charged current interaction Lagrangian $\mathcal{L}_{CC}$, and the second line is the neutral current interaction Lagrangian $\mathcal{L}_{NC}$.
Now, we define the complex (i.e., charged) fields
$$W^{\pm} = \frac{1}{\sqrt{2}}( W^{1}_{\mu} \mp i W^{2}_{\mu} ) ,$$
and rewrite $\mathcal{L}_{1}$ as $\mathcal{L}_{CC} + \mathcal{L}_{NC}$, where
$$\mathcal{L}_{CC} = \frac{g}{\sqrt{2}} \left( W^{+}_{\mu} J^{\mu}_{+} + W_{\mu}^{-} J^{\mu}_{-} \right) ,$$
and
$$\mathcal{L}_{NC} = g W^{3}_{\mu} J^{3\mu} + \frac{\bar{g}}{2} B_{\mu}j^{\mu} .$$
Let us redefine the neutral fields by
$$\begin{pmatrix} W^{3}_{\mu} \\ B_{\mu} \end{pmatrix} = \begin{pmatrix} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{pmatrix} \begin{pmatrix} Z_{\mu} \\ A_{\mu} \end{pmatrix} .$$
Since fields redefinition should not increase the number of parameters, $\theta$ must be a function of the couplings $g$ and $\bar{g}$. Mathematically, $\theta (g , \bar{g})$ can be any (arbitrary) function of its arguments. However, if our $SU(2)\times U(1)$ model contains, beside the fermion doublet $\Psi$, a doublet $\Phi$ of complex scalar fields which can develop non-zero vacuum expectation value $\langle \Phi \rangle_{0}$, remarkable physical consequences follow when we choose
$$\tan \theta = \frac{\bar{g}}{g} .$$
Indeed, with this choice only the $A_{\mu}$ field remains massless. This means that (22) determines the following pattern of symmetry breaking
$$SU(2) \times U_{Y}(1) \to U_{em}(1) .$$
To see this, consider the gauge invariant kinetic part of the scalar field Lagrangian, $(D_{\mu} \Phi)^{\dagger}(D^{\mu}\Phi)$, where the covariant derivative is given by
$$\begin{equation*} D_{\mu}\Phi = (\partial_{\mu} - i \frac{g}{2} W^{a}_{\mu}\tau^{a} - i \frac{\bar{g}}{2} B_{\mu}) \begin{pmatrix} 0 \\ v + h(x)/ \sqrt{2} \end{pmatrix} , \end{equation*}$$
or
$$D_{\mu}\Phi = \begin{pmatrix} -i \frac{g}{\sqrt{2}} W_{\mu}^{-} \\ \partial_{\mu} + \frac{ig}{2}( W^{3}_{\mu} - \frac{\bar{g}}{g}B_{\mu}) \end{pmatrix} \left(v + \frac{h(x)}{\sqrt{2}}\right) ,$$
with $\frac{h(x)}{\sqrt{2}}$ represents a small perturbation (the Higgs field) on the chosen physical vacuum $\langle 0|\Phi|0 \rangle \equiv \langle \Phi \rangle_{0} = (0 , v)^{T}$.
In terms of the fields $(Z_{\mu},A_{\mu})$, as given by (21), we find
$$W^{3}_{\mu} - \frac{\bar{g}}{g}B_{\mu} = Z_{\mu}( \cos \theta + \frac{\bar{g}}{g} \sin \theta ) + A_{\mu}( \sin \theta - \frac{\bar{g}}{g} \cos \theta ) .$$
So, choosing $\theta$ as in (22) we find that
$$W^{3}_{\mu} - \frac{\bar{g}}{g}B_{\mu} = \frac{Z_{\mu}}{\cos \theta} .$$
Thus, the field $A_{\mu}$ drops out of the covariant derivative,
$$D_{\mu}\Phi = \begin{pmatrix} - i \frac{g}{\sqrt{2}}W_{\mu}^{-} \\ \partial_{\mu} + \frac{i g}{2 \cos \theta}Z_{\mu} \end{pmatrix} \left(v + \frac{h(x)}{\sqrt{2}} \right) ,$$
and, therefore, it (the $A_{\mu}$) remains massless. The masses of the other vector bosons, $(W^{\pm}_{\mu},Z_{\mu})$, are obtained by expanding the kinetic term
$$\begin{split} (D_{\mu}\Phi)^{\dagger}(D_{\mu}\Phi) =& \left(\frac{g^{2}v^{2}}{2}\right) \eta^{\mu\nu}W_{\mu}^{-}W^{+}_{\nu} + \frac{1}{2}\left(\frac{g^{2}v^{2}}{2 \cos \theta}\right) Z_{\mu}Z^{\mu} \\ & + \eta^{\mu\nu}\partial_{\mu}H \partial_{\nu}H + \mathcal{L}_{int}(W,H) + \mathcal{L}_{int}(Z,H) . \end{split}$$
From this we can read off the masses of the IVB
$$M_{W^{\pm}} = \frac{gv}{\sqrt{2}}, \ \ M_{Z} = \frac{M_{W}}{\cos \theta} .$$
Okay, now let’s go back to the neutral current interaction lagrangian $\mathcal{L}_{NC}$ of (20). Substituting (21) and the choice (22) in (20), we obtain
$$\begin{split} \mathcal{L}_{NC} =& \frac{g}{\cos \theta} Z_{\mu} \left( J^{3\mu}\cos^{2}\theta - \frac{1}{2} j^{\mu} \sin^{2}\theta \right) \\ & + g \sin \theta A_{\mu} \left( J^{3\mu} + \frac{1}{2} j^{\mu} \right) . \end{split}$$
If $A_{\mu}$ is to be the massless photon field, then the second line in (30) must be the pure electromagnetic interaction $eA_{\mu}J^{\mu}_{em}$. Thus, we are led to the following identifications of the couplings
$$e = g \sin \theta ,$$
and currents
$$j^{\mu} = 2 (J^{\mu}_{em} - J^{3\mu}) .$$
Setting $\mu = 0$ in (32) and integrating, we obtain an expression for the generator $Y$ of the original $U(1)$ group
$$Y = 2 (Q_{em} - T^{3}) .$$
This relation is exactly the Gell-Mann-Nishijima relation relating the (strong) hypercharge to the electric charge and the third isospin component of hadrons. This is why we call $Y$ the weak hypercharge.
Now, substituting (31) and (32) in (30) leads to
$$\mathcal{L}_{NC} = e A_{\mu} J_{em} + \frac{g}{\cos \theta} Z_{\mu} J^{\mu}_{NC} ,$$
where
$$J^{\mu}_{NC} \equiv J^{3\mu} - J^{\mu}_{em} \sin^{2} \theta ,$$
is the weak neutral current.
The last thing I would like to do is to calculate the size of (vev) the vacuum expectation value $v$. Using (19), we can write down the charged IVB amplitude
$$\mathscr{M}^{CC} = \left( \frac{g}{\sqrt{2}} J^{\mu}_{+} \right) \left( \frac{\eta_{\mu\nu} - \frac{q_{\mu}q_{\nu}}{M_{W}^{2}}}{M_{W}^{2} - q^{2}} \right) \left(\frac{g}{\sqrt{2}} J^{\nu}_{-} \right) .$$
At very low energies $q^{2}_{\mbox{max}} \ll M_{W}^{2}$, the amplitude
$$\mathscr{M}^{CC} \approx (\frac{g}{\sqrt{2}}J^{\mu}_{+}) (\frac{\eta_{\mu\nu}}{M^{2}_{W}}) (\frac{g}{\sqrt{2}}J^{\nu}_{-}) ,$$
should be comparable with the charge current weak amplitude of $V-A$ (4 fermions) theory
$$\mathscr{M}^{CC} = \frac{4 G_{F}}{\sqrt{2}} \eta_{\mu\nu}J^{\mu}_{+}J^{\nu}_{-} ,$$
where $G_{F} \sim 10^{-5}/m^{2}_{p}$ is the Fermi coupling constant with $m_{p}$ being the proton mass.
Thus, we can make the identification
$$\frac{g^{2}}{8M^{2}_{W}} = \frac{G_{F}}{\sqrt{2}} .$$
Using (29), this implies that the vacuum expectation value has the size
$$v \sim \sqrt{\frac{5}{\sqrt{2}}} 10^{2}m_{p} \approx 176 \mbox{GeV} .$$
File size:
343.6 KB
Views:
107 | 5,977 | 16,537 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2018-26 | latest | en | 0.912755 |
https://uk.mathworks.com/matlabcentral/cody/problems/21-return-the-3n-1-sequence-for-n/solutions/676278 | 1,566,344,437,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027315681.63/warc/CC-MAIN-20190820221802-20190821003802-00047.warc.gz | 681,077,812 | 15,585 | Cody
# Problem 21. Return the 3n+1 sequence for n
Solution 676278
Submitted on 27 May 2015 by Jose Fernandez
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
%% n = 1; c_correct = 1; assert(isequal(collatz(n),c_correct))
2 Pass
%% n = 2; c_correct = [2 1]; assert(isequal(collatz(n),c_correct))
3 Pass
%% n = 5; c_correct = [5 16 8 4 2 1]; assert(isequal(collatz(n),c_correct))
4 Pass
%% n = 22; c_correct = [22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1]; assert(isequal(collatz(n),c_correct)) | 221 | 622 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2019-35 | latest | en | 0.49015 |
https://oeis.org/A137338 | 1,627,105,880,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046150129.50/warc/CC-MAIN-20210724032221-20210724062221-00427.warc.gz | 443,124,590 | 4,975 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137338 Triangle read by rows: T(n,k), 0 <= k <= n, gives the coefficients of the Charlier polynomials (with parameter a=1), ordered by rising powers. 3
1, -1, 1, 0, -3, 1, 3, 6, -6, 1, -12, -9, 26, -10, 1, 45, 3, -109, 71, -15, 1, -198, 81, 501, -475, 155, -21, 1, 1071, -786, -2663, 3329, -1455, 295, -28, 1, -6984, 6711, 16510, -25495, 13729, -3647, 511, -36, 1, 53217, -60309, -117912, 216004, -135961, 43897, -7994, 826, -45, 1, -462330, 589197, 953711 (list; table; graph; refs; listen; history; text; internal format)
OFFSET 1,5 COMMENTS Row sums are 1, 0, -2, 4, -4, -4, 44, -236, 1300, -8276, 61484, etc. Matrix inverse is A216916. - Peter Luschny, Sep 21 2012 LINKS Carl V. L. Charlier, Über die Darstellung willkürlicher Funktionen, Arkiv För Matematik, Astronomi Och Fysik, Band 2, No. 20 (Meddelande från Lunds Astronomiska Observatorium, Series I, No. 27), 1905, 1-35. [Accessible only in the USA via the HathiTrust Digital Library.] M. Dunster, Uniform asymptotic expansions for Charlier polynomials, J. Approx. Theory, 112 (2001), pp. 93-133. Wikipedia, Carl Charlier. Wikipedia, Charlier polynomials. FORMULA Charlier polynomials: C_{n}(a; x) = Sum_{k=0..n} binomial(n,k)*binomial(x,k)*k!*(-a)^(n-k). EXAMPLE [0] 1, [1] -1, 1, [2] 0, -3, 1, [3] 3, 6, -6, 1, [4] -12, -9, 26, -10, 1, [5] 45, 3, -109, 71, -15, 1, [6] -198, 81, 501, -475, 155, -21, 1, [7] 1071, -786, -2663, 3329, -1455, 295, -28, 1, [8] -6984, 6711, 16510, -25495, 13729, -3647, 511, -36, 1, [9] 53217, -60309, -117912, 216004, -135961, 43897, -7994, 826, -45, 1. MAPLE with(PolynomialTools): C := (n, x) -> if n>0 then expand((x-n)*C(n-1, x)-n*C(n-2, x)) elif n = 0 then 1 else 0 fi: A137338_row := n -> CoefficientList(C(n, x), x); for n from 0 to 7 do A137338_row(n) od; # Peter Luschny, Sep 21 2012 MATHEMATICA Ca[x, -1] = 0; Ca[x, 0] = 1; Ca[x_, n_] := Ca[x, n] = (x - (n - 1) - 1)*Ca[x, n - 1] - n*Ca[x, n - 2]; Table[ExpandAll[Ca[x, n]], {n, 0, 10}]; a = Table[CoefficientList[Ca[x, n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Cf. A216916. Sequence in context: A033789 A109532 A264584 * A176106 A302867 A058659 Adjacent sequences: A137335 A137336 A137337 * A137339 A137340 A137341 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Apr 07 2008 EXTENSIONS Edited by Peter Luschny, Sep 21 2012 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified July 24 01:41 EDT 2021. Contains 346269 sequences. (Running on oeis4.) | 1,206 | 2,938 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-31 | latest | en | 0.277636 |
https://2109.medium.com/how-integers-are-stored-in-memory-using-twos-complement-30ad89a0d801?source=author_recirc-----42a8f276f5ec----1---------------------39310afc_a60c_4eff_9fbf_04c02d534bc1------- | 1,709,504,022,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476399.55/warc/CC-MAIN-20240303210414-20240304000414-00481.warc.gz | 67,576,924 | 29,093 | # How integers are stored in memory using two’s complement.
## But, what’s an integer?
--
According to Wikipedia “An integer (from the Latin integer meaning “whole”) is colloquially defined as a number that can be written without a fractional component.
That means that numbers such as “21”, “189” or “-1824” are integers, while “8.5” , “13 1/2” or “√4” are not. The number “0” (zero) is also an integer.
As we know, computers, in order to understand and store data (such as integer numbers) have to encode such data as binary numbers, which are numbers expressed in the base-2 numeral system. This system is known as base-2 because it only uses two symbols (typically 0 and 1), instead of the 10 symbols used by the decimal system.
A binary number is a sequence of bits. The specific position of the 0’s and 1’s within the sequence of bits creates the representation of the number’s value.
## Bit what?
Now, a bit is the most basic unit of the computer memory. Going back to Wikipedia: “The bit is a basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either “1”or”0", but other representations such as true/false, yes/no, +/−, or on/off are common.
Physically, there are several ways to store a bit, but ultimately, it depends on the physical device capability to differentiate between two states. Whatever the physical implementation, the important thing to know about a bit is that, like a switch, it can only take one of two values: it is either “on” or “off”.
Eight bits placed together are called a byte. In a 32-bit or 64-bit computer, an integer value is stored in a collection of 4 bytes, or 32 bits.
So, if we consider the integer value “50”, the computer will store it in memory within a collection of bits of value 0 or 1.
The image of the Windows calculator above is actually filtering out all the leading 0’s in the binary value. The actual value stored would be something like this:
# 00000000 00000000 00000000 00110010
But what happens when representing negative integers such as -50?
Well, negative and positive are the two possible states of an integer value. In binary, each state can be represented by what is called the Most Significant Bit (MSB). The MSB will be the value of the first bit to the left of the binary number. If the integer number is positive, the MSB will have a value of 0, but if the number is negative, the bit is 1.
So -50 will be:
# 10000000 00000000 00000000 00110010
The problem is that using MSB to represent negative numbers has some important disadvantages, starting with the fact that reserving one bit to represent the negative/positive value of the number reduces the amount of available numbers by one half.
At the same time, using MSB would allow us to represent a value that actually doesn’t exist on decimal numeration such as “-0”. Like this:
# 10000000 00000000 00000000 00000000
## Enters one’s complement:
A possible work around to the reduction of the range of numbers is to utilize the method called one’s complement.
This method represents negative numbers by inverting the values of bits of the number magnitude. In plain English this means to flip all the bit values within the binary number to its opposite. A 1 is placed whenever there was a 0 and vice versa. The signed binary number obtained from the inversion is called complement.
So, again, 50 and -50:
00000000 00000000 00000000 00110010
11111111 11111111 11111111 11001101
While this significantly increases the amount of available numbers, it still has the issue of allowing the representation of a negative 0, which again, doesn’t actually exists:
11111111 11111111 11111111 11111111 (-0???).
## What about two’s complement then?
Wikipedia (again): “Compared to other systems for representing signed numbers (e.g., ones’ complement), two’s complement has the advantage that the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers (as long as the inputs are represented in the same number of bits as the output, and any overflow beyond those bits is discarded from the result). This property makes the system simpler to implement, especially for higher-precision arithmetic. Unlike ones’ complement systems, two’s complement has no representation for negative zero, and thus does not suffer from its associated difficulties.
## But how?
In a nutshell:
1- Find the binary equivalent for any given decimal.
2- Find the one’s complement of the binary by inverting 0's and 1’s.
3- Add 1 to the one’s complement.
Let’s start again with the integer 50 in binary:
00000000 00000000 00000000 00110010
Now let’s calculate -50 with the one’s complement method:
11111111 11111111 11111111 11001101
Finally we are going to add one (+1 in binary, of course) to -50.
11111111 11111111 11111111 11001101 +
00000000 00000000 00000000 00000001 (this is the binary representation of the decimal integer “1”).
Result:
11111111 11111111 11111111 11001101
The fact that the first bit on the left is a “1” indicates that the number is negative.
The range of integers obtained from using the two’s complement method is the same as the obtained from the one’s complement, but by using the two’s method a negative zero value will not be represented, as “1” it is always added to the complement of zero.
Decimal “0” — 00000000 00000000 00000000 00000000
“-0” (not a thing) — 11111111 11111111 11111111 11111111
addition of 1 -00000000 00000000 00000000 00000001
Result: 00000000 00000000 00000000 00000000 (actually 0!).
So, that are the reasons why computers use two’s complements to deal with negative values.
Hope you enjoyed! | 1,418 | 5,828 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2024-10 | latest | en | 0.922161 |
https://runestone.academy/runestone/books/published/thinkcspy/Lists/FunctionsthatProduceLists.html | 1,579,862,518,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250619323.41/warc/CC-MAIN-20200124100832-20200124125832-00032.warc.gz | 638,430,102 | 9,600 | # 10.21. Functions that Produce ListsΒΆ
The pure version of doubleStuff above made use of an important pattern for your toolbox. Whenever you need to write a function that creates and returns a list, the pattern is usually:
initialize a result variable to be an empty list
loop
create a new element
append it to result
return the result
Let us show another use of this pattern. Assume you already have a function is_prime(x) that can test if x is prime. Now, write a function to return a list of all prime numbers less than n:
def primes_upto(n):
""" Return a list of all prime numbers less than n. """
result = []
for i in range(2, n):
if is_prime(i):
result.append(i)
return result
You have attempted of activities on this page
Next Section - 10.22. List Comprehensions | 184 | 777 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2020-05 | longest | en | 0.755546 |
https://mathexpressionsanswerkey.com/math-expressions-grade-5-unit-8-lesson-13-answer-key/ | 1,714,010,157,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296820065.92/warc/CC-MAIN-20240425000826-20240425030826-00798.warc.gz | 335,836,201 | 42,886 | # Math Expressions Grade 5 Unit 8 Lesson 13 Answer Key Volume of Composite Solid Figures
## Math Expressions Common Core Grade 5 Unit 8 Lesson 13 Answer Key Volume of Composite Solid Figures
Math Expressions Grade 5 Unit 8 Lesson 13 Homework
Find the volume of each composite solid figure.
Volume Of Composite Figures Worksheet Math Expressions Grade 5 Pdf Question 1.
Volume Of Composite Figures Answer Key Math Expressions Grade 5 Unit 8 Question 2.
Composite Figures Volume Math Expressions Grade 5 Unit 8 Question 3.
The volume of the figure is 204 cu in.
Explanation:
Here, we will divide the figure into rectangles, and then we will find the volume of each rectangle, then we will add them. So the volume of the rectangle is
V = l × w × h,
V1 = 4 × 13 × 3
= 156 cu in.
V2 = 3 × 4 × 4
= 48 cu in.
So the volume of the solid figure is 156 + 48
= 204 cu in.
Volume Of Composite Figures Pdf Math Expressions Grade 5 Unit 8 Question 4.
The exterior of a refrigerator is shaped like a rectangular prism, and measures 2$$\frac{2}{3}$$ feet wide by 5$$\frac{1}{2}$$ feet high by 2$$\frac{1}{2}$$ feet deep. What amount of space does the refrigerator take up?
The amount of space does the refrigerator take-up is 36 $$\frac{2}{3}$$ cu ft.
Explanation:
Given that the exterior of a refrigerator is shaped like a rectangular prism, and measures 2$$\frac{2}{3}$$ feet wide by 5$$\frac{1}{2}$$ feet high by 2$$\frac{1}{2}$$ feet deep. So the amount of space does the refrigerator take-up is 2$$\frac{2}{3}$$ × 5$$\frac{1}{2}$$ × 2$$\frac{1}{2}$$
= $$\frac{8}{3}$$ × $$\frac{11}{2}$$ × $$\frac{5}{2}$$
= $$\frac{440}{12}$$
= 36 $$\frac{2}{3}$$ cu ft.
Volume Of Composite Math Expressions Grade 5 Unit 8 Question 5.
In the space below, draw a composite solid of your own design that is made up of two prisms. Write the dimensions of your design, and then calculate its volume.
Math Expressions Grade 5 Unit 8 Lesson 13 Remembering
Divide.
Volume Of Composite Figures Math Expressions Grade 5 Unit 8 Question 1.
= 70.
Explanation:
Here, we will change the divisor 0.7 to a whole number by moving the decimal point 1 place to the right, and then we will move the decimal point in the dividend to the same 1 place right.
Question 2.
= 1000.
Explanation:
Here, we will change the divisor 0.05 to a whole number by moving the decimal point 2 places to the right, and then we will move the decimal point in the dividend to the same 2 places right.
Question 3.
= 0.8
Explanation:
Here, we will change the divisor 0.8 to a whole number by moving the decimal point 1 place to the right, and then we will move the decimal point in the dividend to the same 1 place right.
Question 4.
= 600.
Explanation:
Here, we will change the divisor 0.06 to a whole number by moving the decimal point 2 places to the right, and then we will move the decimal point in the dividend to the same 2 places right.
Question 5.
= 3,132.
Explanation:
Here, we will change the divisor 0.3 to a whole number by moving the decimal point 1 place to the right, and then we will move the decimal point in the dividend to the same 1 place right.
Question 6.
= 455.
Explanation:
Here, we will change the divisor 0.06 to a whole number by moving the decimal point 2 places to the right, and then we will move the decimal point in the dividend to the same 2 places right.
Solve.
Question 7.
A fish tank is 20 feet long, 12 feet wide, and 10 feet deep. What is the volume of the fish tank? | 962 | 3,469 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.8125 | 5 | CC-MAIN-2024-18 | longest | en | 0.802906 |
https://www.jiskha.com/display.cgi?id=1320980303 | 1,503,202,844,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886105970.61/warc/CC-MAIN-20170820034343-20170820054343-00268.warc.gz | 904,499,252 | 3,765 | # physics grade 12
posted by .
we have a trebuchet. if the arm of the trebuchet fires in a circular motion with a radius of 2.0 m and the mass is 50kg on the other end of the arm. what will the speed of the 4 kg boulder be as it is launched into the air? assuming it is launched parallel to the ground at a height of twice the radius, how far will the boulder travel before hitting the ground.
## Similar Questions
1. ### Physics
When you release the arm of a trebuchet and the projectile is released, I know that energy is lost/wasted. Can someone give me some good examples of what happens to this energy?
2. ### physics (projectile motion)
A cow on a trebuchet is catapulted toward a castle wall. The cow is released with an inital velocity of 50 m/s at a 60 degree angle above the horizontal. At its release the cow is 8 m above the ground. The castle wall is 100 m from …
3. ### physics (projectile motion)
A cow on a trebuchet is catapulted toward a castle wall. The cow is released with an inital velocity of 50 m/s at a 60 degree angle above the horizontal. At its release the cow is 8 m above the ground. The castle wall is 100 m from …
4. ### Physics
a modified U-tube: the right arm is shorter than the left arm. The open end of the right arm is height d = 10.0 cm above the laboratory bench. The radius throughout the tube is 1.60 cm. Water is gradually poured into the open end of …
5. ### physics
a modified U-tube: the right arm is shorter than the left arm. The open end of the right arm is height d = 10.0 cm above the laboratory bench. The radius throughout the tube is 1.60 cm. Water is gradually poured into the open end of …
6. ### Physics
A ballistic pendulum consists of an arm of mass M and length L = 0.52 m. One end of the arm is pivoted so that the arm rotates freely in a vertical plane. Initially, the arm is motionless and hangs vertically from the pivot point. …
7. ### physics grade 12
we have a trebuchet. if the arm of the trebuchet fires in a circular motion with a radius of 2.0 m and the mass is 50kg on the other end of the arm. what will the speed of the 4 kg boulder be as it is launched into the air?
8. ### Physics HELP!
A war-wolf, or trebuchet, is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling pumpkins and pianos. A simple trebuchet is shown in the figure. Model it as a stiff rod of negligible mass …
9. ### Physics
A ballistic pendulum consists of an arm of mass M and length L = 0.485 m. One end of the arm is pivoted so that the arm rotates freely in a vertical plane. Initially, the arm is motionless and hangs vertically from the pivot point. …
10. ### physics
A war-wolf, or trebuchet, is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling pumpkins and pianos. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible …
More Similar Questions | 742 | 2,932 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2017-34 | latest | en | 0.905857 |
https://learn.careers360.com/ncert/question-what-is-the-density-of-water-at-a-depth-where-pressure-is-800-atm-given-that-its-density-at-the-surface-is-103-103-kg-m3/ | 1,716,615,227,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058773.28/warc/CC-MAIN-20240525035213-20240525065213-00339.warc.gz | 292,622,797 | 35,763 | #### Q13 What is the density of water at a depth where pressure is 80.0 atm, given that its density at the surface is ?
Water at the surface is under 1 atm pressure.
At the depth, the pressure is 80 atm.
Change in pressure is
Bulk Modulus of water is
The negative sign signifies that for the same given mass the Volume has decreased
The density of water at the surface
Let the density at the given depth be
Let a certain mass occupy V volume at the surface
Dividing the numerator and denominator of RHS by V we get
The density of water at a depth where pressure is 80.0 atm is . | 139 | 588 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-22 | latest | en | 0.918741 |
https://studysoup.com/tsg/10477/elementary-statistics-12-edition-chapter-11-3-problem-19bsc | 1,656,552,054,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103646990.40/warc/CC-MAIN-20220630001553-20220630031553-00058.warc.gz | 600,943,227 | 15,286 | ×
Get Full Access to Elementary Statistics - 12 Edition - Chapter 11.3 - Problem 19bsc
Get Full Access to Elementary Statistics - 12 Edition - Chapter 11.3 - Problem 19bsc
×
# Clinical Trial of Lipitor Lipitor is the trade name of the
ISBN: 9780321836960 18
## Solution for problem 19BSC Chapter 11.3
Elementary Statistics | 12th Edition
• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants
Elementary Statistics | 12th Edition
4 5 1 280 Reviews
31
4
Problem 19BSC
Problem 19BSC
Clinical Trial of Lipitor Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. (Until its patent expired in 2011, this was the largest-selling drug in the world, with annual sales of \$13 billion.) Adverse reactions have been studied in clinical trials, and the table below summarizes results for infections in patients from different treatment groups (based on data from Parke-Davis). Use a 0.01 significance level to test the claim that getting an infection is independent of the treatment. Does the atorvastatin treatment appear to have an effect on infections?
Placebo Atorvastatin 10 mg Atorvastatin 40 mg Atorvastatin 80 mg Infection 27 89 8 7 No Infection 243 774 71 87
Step-by-Step Solution:
Solution 19BSC
Step 1 of 1
We are given a data set of infections among people given different groups of treatments. We have to test the claim that getting an infection is independent of the treatment.
Step 1: To test the claim we need to fulfil certain assumptions.
1. We assume that the sample has been randomly selected because of the structure of the study.
2. The results are tabulated as frequencies.
3. The expected frequencies are more than five in every column.
Step 2 of 4
Step 3 of 4
## Discover and learn what students are asking
Calculus: Early Transcendental Functions : Integration Techniques, LHpitals Rule, and Improper Integrals
?In Exercises 49-56, find the indefinite integral using any method. $$\int \theta \sin \theta \cos \theta d \theta$$
#### Related chapters
Unlock Textbook Solution | 544 | 2,162 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2022-27 | latest | en | 0.870669 |
https://espanol.libretexts.org/Humanidades/Arte/Historia_inteligente_del_arte/08%3A_Europa_1800_-_1900/8.08%3A_Posimpresionismo | 1,719,337,727,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198866218.13/warc/CC-MAIN-20240625171218-20240625201218-00024.warc.gz | 214,152,969 | 114,106 | Saltar al contenido principal
# 8.8: Posimpresionismo
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vectorC}[1]{\textbf{#1}}$$
$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$
$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$
$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
## Post Impresionismo
Cézanne, Seurat, Van Gogh y Gauguin son todos post-impresionistas, aunque sus estilos varían ampliamente.
c. 1880 - 1900
## Una guía para principiantes
### Introducción al Neo-Impresionismo, Parte I
por y
Apenas una docena de años después del debut del Impresionismo, el crítico de arte Félix Fénéon bautizó a Georges Seurat como el líder de un nuevo grupo de “Neo-Impresionistas”. No pretendía sugerir el resurgimiento de un estilo desaparecido —el impresionismo seguía siendo fuerte a mediados de la década de 1880— sino una modificación significativa de las técnicas impresionistas que exigían un nuevo sello.
Fénéon identificó un mayor rigor científico como la diferencia clave entre el neoimpresionismo y su predecesor. Donde los impresionistas eran “arbitrarios” en sus técnicas, los neoimpresionistas habían desarrollado un método “consciente y científico” a través de un cuidadoso estudio de teóricos del color contemporáneos como Michel Chevreul y Ogden Rood [1].
#### Un método científico
Este mayor rigor científico es inmediatamente visible si comparamos el neoimpresionista Grande Jatte de Seurat con el impresionista Moulin de la Galette de Renoir. El tema es similar: una escena al aire libre de gente en el ocio, descansando en un parque junto a un río o bailando y bebiendo en la terraza de una cafetería. El objetivo general también es similar. Ambos artistas están tratando de capturar el efecto de la luz moteada en una tarde soleada. No obstante, la escena de Renoir parece haber sido compuesta y pintada espontáneamente, con las figuras capturadas a mitad de gesto. La técnica floja y pictórica de Renoir refuerza este efecto, dando la impresión de que la escena fue pintada rápidamente, antes de que la luz cambiara.
Por el contrario, las figuras de La Grande Jatte son prematuramente inmóviles, y la pincelada también se ha sistematizado en un minucioso mosaico de diminutos puntos y guiones, a diferencia de los trazos y frotis fortuitos de Renoir. Los pintores neoimpresionistas empleaban reglas y un método, a diferencia de los impresionistas, que tendían a confiar en “el instinto y la inspiración del momento” [2].
#### Puntillismo y mezcla óptica
Una de estas reglas era utilizar únicamente los colores “puros” del espectro: violeta, azul, verde, amarillo, naranja y rojo. Estos colores podrían mezclarse solo con el blanco o con un color adyacente en la rueda de colores (llamados “colores análogos”), por ejemplo para hacer más claros, verdes amarillos o violetas más oscuras y rojas. Sobre todo, los neoimpresionistas no mezclarían colores opuestos en la rueda de colores (“colores complementarios”), porque hacerlo da como resultado marrones fangosos y grises opacos.
Las variaciones de color más sutiles fueron producidas por “mezcla óptica” en lugar de mezclar pintura en la paleta. Por ejemplo, examinar la hierba al sol. Seurat entremezcla el campo general de verdes amarillos con motas de crema tibia, verde oliva y ocre amarillo (en realidad amarillo cromo descolorido). Vistas desde la distancia estas motas se mezclan para ayudar a aclarar y calentar el verde, como cabría esperar cuando la hierba es golpeada por la luz amarillo-anaranjada del sol de la tarde. Fue esta técnica de pintura en pequeños puntos (“puntos” en francés) la que le dio al neoimpresionismo el apodo popular de “Puntillismo” aunque los artistas generalmente evitaron ese término ya que sugería un artilugio estilístico.
Para la hierba en las sombras, Seurat utiliza verdes más oscuros entremezclados con motas de azul puro e incluso algo de naranja y granate. Estos son colores muy inesperados para el pasto, pero cuando retrocedemos los colores se mezclan ópticamente, dando como resultado un verde más fresco, más oscuro y más opaco en las sombras. Este verde es, sin embargo, más vibrante que si Seurat hubiera mezclado esos colores en la paleta y los hubiera aplicado en una franja uniforme.
De igual manera, ¡mira la cantidad de colores que conforman las piernas de la pequeña! Incluyen no sólo los esperados rosas y naranjas de carne caucásica, sino también cremas, azules, cimarrones, e incluso verdes. Sin embargo, retírese de nuevo y la “mezcla óptica” los mezcla en un color carne convincente y luminoso, modelado con luz cálida y sombreado por su vestido blanco. (Para obtener más información técnica sobre este tema, consulte Teoría del color neoimpresionista).
#### Rigor composicional
Los neoimpresionistas también aplicaron rigor científico a la composición y al diseño. El amigo y compañero pintor de Seurat, Paul Signac, afirmó:
El Neo-Impresionista... no iniciará un lienzo antes de que haya determinado el trazado... Guiado por la tradición y la ciencia, él... adoptará las líneas (direcciones y ángulos), el claroscuro (tonos), [y] los colores (tintes) a la expresión que desea hacer dominante. Paul Signac, Delacroix al Neo-Impresionismo, en Nochlin, ed., p. 121.
Numerosos estudios para La Grande Jatte dan testimonio de cuán cuidadosamente Seurat decidió la pose de cada figura y las arregló para crear una recesión rítmica en el fondo. Esta práctica es muy diferente a la de los impresionistas, quienes enfatizaron las visiones momentáneas (impresiones) al crear composiciones intencionalmente haphazar-parecidas, como Moulin de la Galette de Renoir.
El Desfile de Cirque de Seurat es aún más rigurosamente geométrico. Está dominado por líneas horizontales y verticales, y el espaciado apenas ligeramente fuera rítmico de las figuras y la estructura arquitectónica crea una cuadrícula sincopada. Los estudiosos han debatido si la composición se basa en la Sección Dorada, una proporción geométrica que fue identificada por los matemáticos griegos antiguos como intrínsecamente armoniosa.
Los neoimpresionistas también intentaron sistematizar las cualidades emocionales que transmitían sus pinturas. Seurat definió tres herramientas expresivas principales a disposición del pintor: el color (los tonos del espectro, de cálido a frío), el tono (el valor de esos colores, de claro a oscuro) y la línea (horizontal, vertical, ascendente o descendente). Cada uno tiene un efecto emocional específico:
La alegría del tono viene dada por el dominio de la luz; del color, por el dominio del calor; de la línea, por las líneas por encima de la horizontal. La calma del tono viene dada por una equivalencia de luz y oscuridad; de color por una equivalencia de cálido y frío; y de línea, por horizontales. La tristeza del tono viene dada por el dominio de la oscuridad; del color, por el dominio de los colores fríos; y de la línea, por las direcciones descendentes.
Georges Seurat, Carta a Maurice Beaubourg, 28 de agosto de 1890, en Nochlin, ed., p. 114 (traducción modificada para mayor claridad).
Chaut (Can-Can) de Seurat parece diseñado para ejemplificar estas reglas, empleando mayormente colores cálidos, claros y líneas ascendentes para transmitir un ambiente de alegría apropiado al baile.
El estilo neoimpresionista tuvo un apogeo relativamente breve; muy pocos artistas continuaron el proyecto hasta el siglo XX. Sin embargo, un gran número de artistas experimentaron con él y tomaron porciones de su método en su propia práctica, desde van Gogh hasta Henri Matisse. En términos más generales, el deseo neoimpresionista de conformar la creación artística a las leyes universales de percepción, color y expresión resuena a lo largo del Modernismo, en movimientos tan diversos como el Simbolismo, el Purismo, De Stijl y la Bauhaus.
Hasta el momento nos hemos concentrado en el estilo del Neo-Impresionismo. En la segunda parte, examinaremos el tema favorecido por los artistas, y discutiremos su relación con el contexto social y político de finales del siglo XIX.
#### Notas:
1. Félix Fénéon, “Les Impressionnistes en 1886”, traducido en Linda Nochlin, ed., Impresionismo y post impresionismo, 1874-1904: Fuentes y documentos (Englewood Cliffs, N.J.: Prentice-Hall, 1966), p. 108.
2. Paul Signac, De Eugène Delacroix al Neo-Impresionismo (1899), traducido en Nochlin, ed., p. 122.
### Introducción al Neo-Impresionismo, Parte II
por y
En la primera parte de esta introducción al neoimpresionismo examinamos el estilo del movimiento, concentrándonos en el intento de los artistas de sistematizar un método de pintura de acuerdo con las leyes científicas de percepción, color, composición y expresión. Aquí, nos referiremos al tipo de tema típicamente elegido por los neoimpresionistas y discutiremos su relación con la historia social y política de finales del siglo XIX.
#### Escenas de ocio
En su mayor parte, los neoimpresionistas continuaron describiendo los tipos de temas preferidos por los impresionistas: paisajes y escenas de ocio. Además de su famoso cuadro de gente descansando en el parque de la isla de La Grande Jatte, muchas de las pinturas de Georges Seurat retrataban entretenimientos como los circos y salas de música que contribuyeron a la reputación de París de espectáculos masivos a finales del siglo XIX.
Las pinturas paisajísticas de Paul Signac revelan de manera similar una concentración en las escenas de ocio. Un marinero mismo, Signac pintó decenas de escenas portuarias dominadas por las velas y mástiles de pequeñas embarcaciones de placer. La costa mediterránea de Francia, donde Signac pasaba sus veranos, tenía fama tanto por la calidad de su luz —un interés clave de los neoimpresionistas en general— como por un estilo de vida relajado y lleno de sol. En los lienzos de Signac, los colores brillantes favorecidos por los neoimpresionistas complementan perfectamente esta reputación.
Si bien estos temas sugieren un placer despreocupado, hay matices de crítica social en algunas pinturas neoimpresionistas. El Circo de Seurat muestra las estrictas distinciones de clase en París tanto por ubicación, con los mecenas más ricos sentados en los niveles inferiores, como por vestimenta y postura, que se vuelve marcadamente más informal cuanto más lejos están los espectadores de la orilla del ring.
Un crítico contemporáneo también comentó que la rigidez de las poses en La Grande Jatte de Seurat le recordó “la rigidez del ocio parisino, prim y exhausto, donde incluso la recreación es cuestión de poses llamativas” [1] Mientras examinamos a los personajes en La Grande Jatte en detalle, hay algunas inclusiones y yuxtaposiciones sorprendentes. En primer plano izquierdo, un hombre de clase trabajadora con mangas camiseras se superpone a un caballero de clase media mucho más formal con un sombrero de copa que sostiene un bastón. Un trompetista en el medio-suelo toca directamente en los oídos de dos soldados parados en la atención de fondo. Una mujer con un mono mascota ostentosamente excéntrico a la derecha y otra de pesca a la izquierda han sido interpretadas como prostitutas, una de las cuales está echando señuelos para clientes. Entre ellos, un perro faldero de juguete con una cinta rosa salta hacia un sabueso rangy cuyo pelaje es tan negro como el del caballero burgués con el bastón.
A pesar de estas provocadoras yuxtaposiciones y superposiciones, muy pocas de las figuras en realidad parecen estar interactuando entre sí; cada una se pierde en su propio mundo. A diferencia del estado de ánimo de convivencia entre clases y sexos en el Moulin de la Galette de Auguste Renoir, Grande Jatte de Seurat establece una dinámica de alienación y tensión.
La Grande Jatte forma una pareja implícita con una pintura anterior del mismo tamaño de Seurat, Bathers at Asnières. Asnières era un suburbio industrial de París, justo al otro lado del río Sena desde La Grande Jatte. A diferencia de los mecenas mayoritariamente de clase media de esa isla con sus sombreros de copa y faldas de bullicio, aquí vemos más figuras de clase trabajadora y de clase media baja en mangas de camisa y sombreros de paja o jugadores de bolos. En el fondo las chimeneas de las fábricas de Clichy sirven como recordatorio del trabajo, incluso durante el tiempo libre de los hombres.
Al igual que en la pintura de La Grande Jatte, todas las figuras están aisladas en su propio mundo, pero una sensación de tensión implícita es levantada por su mirada insistente a través del río hacia sus compatriotas más ricos. Una pareja de clase media siendo remada por un remero contratado en un bote con una prominente bandera francesa se suma aún más a las tensiones de clase planteadas por la obra.
#### ¿Revolucionarios políticos?
Quizás fue esta extraña sensación de tensiones de clase no resueltas lo que hizo que Signac sugiriera que incluso las pinturas de Seurat sobre “los placeres de la decadencia” tratan de exponer “la degradación de nuestra era” y dar testimonio de “la gran lucha social que ahora se está dando entre los trabajadores y el capital” [2] Seurat'. su propia política no estaba clara, pero Signac era anarquista social, al igual que otros neoimpresionistas, entre ellos Camille Pissarro y su hijo Lucien, así como Maximilian Luce, Theodore van Rysselberghe, Henri Cross y el crítico Félix Fénéon. Los anarquistas sociales rechazan un gobierno centralizado fuerte en el que el Estado posea los medios de producción y oriente la economía; creen que la propiedad social y la cooperación surgirán naturalmente en una sociedad apátrida.
En tiempos de armonía de Signac se tituló originalmente En el tiempo de la anarquía, pero la controversia política obligó a un cambio. Entre 1892 y 1894 hubo once bombardeos en Francia por parte de anarquistas, y un juicio muy público a presuntos anarquistas que incluyeron a Fénéon y Luce.
La pintura de Signac pretendía mostrar que, a pesar de sus tácticas revolucionarias actuales, el objetivo del anarquismo era una utopía pacífica. En primer plano, los trabajadores ponen sus herramientas para un picnic de higos y champán mientras otros juegan en la petanca. Una pareja en el centro contempla un ramillete, mientras detrás de ellos un hombre siembra y las mujeres cuelgan la ropa. A pesar de que el estado de ánimo es atemporal —con vestimenta diferente, esta pintura podría ser una escena pastoral clásica— a lo lejos el moderno equipamiento mecánico agrícola refuerza el subtítulo de la pintura, “La edad de oro no está en el pasado, está en el futuro”.
Relativamente pocas pinturas neoimpresionistas son tan claramente alegóricas y políticas. Signac argumentó que era la técnica de los neoimpresionistas, no ninguna materia directamente socialista o anarquista, la que estaba más en sintonía con los políticos revolucionarios. El riguroso atractivo de los neoimpresionistas a la ciencia dura, más que a las convenciones muertas, junto con su voluntad intransigente de “pintar lo que ven, como lo sienten”, ayudarán a “dar un duro golpe de pico a la vieja estructura social” y a promover una revolución social correspondiente [3].
#### Notas:
1. Henri Fèvre, “L'Exposition des Impressionnistes”, en Étude sur le Salon de 1886 et sur l'exposition des impressionnistes (París, 1886), p. 43 (nuestra traducción).
2. Paul Signac, “Impresionistas y revolucionarios”, La Révolte, 13 a 19 de junio de 1891, traducido en Nochlin, ed., p. 124.
3. ibíd., pág. 124.
### Teoría del Color Neo-Impresionista
por y
En 1899, el artista Paul Signac rechazó la etiqueta “puntillista” y afirmó: “El neoimpresionista no puntea, divide”. Planteó un argumento de cuatro partes que describe cómo la división logra los objetivos de “luminosidad” y “armonía” por medio de:
1. La mezcla óptica de pigmentos únicamente puros (todos los tintes del prisma y todos sus tonos);
2. La separación de los diferentes elementos (color local, color de la iluminación, sus interacciones, etc.);
3. El equilibrio de estos elementos y sus proporciones (según las leyes del contraste, de la gradación y de la irradiación);
4. La elección de una pincelada acorde con las dimensiones de la pintura. [1]
El argumento de Signac es denso con el vocabulario técnico de la teoría del color de finales del siglo XIX. Los neoimpresionistas se enorgullecieron de aportar rigor científico al proyecto impresionista hasta ahora en gran parte intuitivo. Al comprender los significados contemporáneos de los términos de Signac, podemos rastrear cómo la teoría científica del color afectó la práctica neoimpresionista.
El neoimpresionista utiliza “únicamente pigmentos puros”, que Signac especifica como los colores del “prisma”. Esta redacción ya sugiere una base científica para el uso del color neoimpresionista. En el siglo XVII el físico inglés Sir Isaac Newton utilizó un prisma de vidrio para separar la luz blanca en un arco iris. En términos de los pintores, los colores del prisma corresponden a los colores primarios rojo, amarillo y azul, los colores secundarios naranja, verde y violeta, y los colores terciarios azul-violeta, azul-verde, amarillo-verde, etc.
Los neoimpresionistas mezclarían estos tonos o “tintes” solo con el blanco para producir diferentes valores o “tonos” (todas las gradaciones del azul de claro a oscuro, por ejemplo). Sobre todo, evitaron los colores tierra fangosos que dominaban las paletas de los pintores europeos antes de finales del siglo XIX.
En su búsqueda de colores puros y brillantes, los neoimpresionistas fueron ayudados por nuevos pigmentos creados a través de la síntesis química, a diferencia de los minerales fundados o la materia orgánica de los pigmentos tradicionales. El análisis ha demostrado que la paleta de Seurat de 1889-90 constaba de muchos colores que no estaban disponibles antes del siglo XIX, entre ellos el amarillo cromo (inventado 1797), el azul cobalto (1803-04), el naranja cadmio (1820), el ultramarino francés (1826) y el violeta de manganeso (1860).
El apodo de “Puntillismo” se le dio al movimiento debido a la tendencia de los artistas a pintar en pequeños puntos (puntos en francés). Signac se opuso al término porque sugiere un artilugio estilístico, pero ejecutar pinturas en pinceladas pequeñas y discretas fue crucial para otro concepto clave del movimiento que menciona anteriormente: la mezcla óptica.
Como cualquier pintor se da cuenta rápidamente, cada vez que mezclas dos pigmentos, la mezcla resultante es más opaca que cualquiera de los pigmentos originales. Este efecto opaco se magnifica cuanto más separados estén los colores en la rueda de colores. Mezclar azul y verde da como resultado un azul-verde bastante brillante, pero mezclar azul y naranja crea grises opacos y marrones fangosos.
En lugar de mezclar colores en la paleta, los neoimpresionistas los yuxtaponían sobre el lienzo en pequeños puntos. Vistos desde una distancia adecuada, estos puntos se mezclan en el ojo, y logran los efectos deseados sin perder la intensidad cromática de los pigmentos originales.
Por ejemplo, la carne de las mujeres en The Models de Seurat está conformada por miles de diminutos puntos de colores que van desde los esperados amarillos claros, melocotones y rosas, hasta sorprendentes azules, violetas y verdes. Vistos desde una distancia suficiente, estos colores se mezclan en el ojo para crear una representación convincente y muy luminosa del juego de luces y sombras a través de los cuerpos de las modelos.
Los puntos de color deben ser bastante pequeños para que se produzca la mezcla óptica, aunque como señala Signac, su tamaño podría variar en relación con el tamaño de la pintura. Un mural destinado a ser leído desde una distancia de varios metros podría usar puntos más grandes que un pequeño paisaje destinado a ser visto de cerca.
#### Color local vs. color percibido
El término preferido de Signac “división” se refiere a la forma en que el artista aísla todas las influencias componentes que contribuyen a un determinado color percibido. En el extracto anterior, enumera los dos componentes principales: el color local y el color de la luz, junto con “sus interacciones, etc.” El color local es lo que pensamos como el color real del objeto mismo: un autobús amarillo, una manzana roja, una camisa blanca. Pero simplemente pintar un objeto en su color local ignora los efectos de la luz sobre el objeto.
Uno de los efectos de la luz es, por supuesto, el claroscuro: partes del objeto golpeadas por la luz son más claras que las partes en sombra. El puente de Camille Corot en Narni es un buen ejemplo de un paisaje tradicional pintado en color local y claroscuro. El grueso de la pintura está en tres colores básicos: el verde de la hierba, el bronceado rojizo de la tierra y el puente (y agua fangosa), y el azul del cielo y montañas distantes. Corot ha mezclado valores más oscuros y claros de cada uno de estos colores para mostrar cómo la escena se ve afectada por la luz proveniente del sol en la parte superior derecha.
Lo que Corot no enfatiza, sin embargo, es lo que se llama la temperatura de color de la luz misma. Una camisa blanca vista con una luz cálida parecerá ser de color naranja amarillento, mientras que vista bajo luz fría estará teñida de azul-violeta.
La temperatura de color de la luz exterior se ve afectada por la hora del día, la temporada y el clima. En estas dos pinturas ejecutadas en la localidad costera francesa de Concarneau, Signac presta mucha atención no solo a los colores locales de los objetos, sino también a sus colores percibidos —los colores que realmente vemos ya que se ven afectados por la temperatura de la luz. Una paleta basada en naranja y azul claro representa las cualidades brillantes y claras de la luz matutina, mientras que una atmósfera de color amarillo rosáceo con intensas sombras violetas transmite el efecto del crepúsculo.
#### Divisionismo
El color percibido de cualquier objeto dado es el resultado de múltiples factores, entre ellos el color local del objeto, la temperatura de color de la luz que golpea ese objeto, el posible color reflejado de los objetos cercanos, la perspectiva atmosférica (que hace que los objetos distantes parezcan más azul-gris) y, como deberemos ver, el efecto de “contraste simultáneo” con colores adyacentes. En lugar de mezclar todos estos factores, el divisionismo los mantiene separados. El pasto de primer plano en Evening Calm de Signac incluye puntos de amarillo y naranja —el color de la luz— para mostrar cómo los verdes son calentados por la luz del sol vespertino.
En las porciones sombreadas de la hierba, Signac entremezcla los verdes con puntos de cerúleo y azul ultramarino. Esto se debe a que los colores de sombra son el “complemento” del color de la luz. Los colores complementarios son colores opuestos entre sí en la rueda de colores, por lo que la luz de la tarde amarillo-naranja produce sombras violeta-azul.
#### La ley del contraste
Signac también menciona la necesidad del artista de tomar en cuenta “las leyes del contraste, de la gradación y de la irradiación”. Estas “leyes” se refieren a principios de interacción de color descubiertos por teóricos del siglo XIX como Michel Chevreul, Ogden Rood y Charles Henry, que parecían prometer que la totalidad del arte podría ser subsumida en principios científicos rigurosos.
La contribución más famosa de Chevreul a la teoría del color es la “ley del contraste simultáneo”, que tiene en cuenta cómo cambia nuestra percepción del color en relación con los colores adyacentes. Mira cuán diferente aparece la muestra del mismo color de azul contra un campo de verde brillante versus un campo de naranja opaco, por ejemplo.
La forma general de la ley del contraste simultáneo es que dos colores yuxtapuestos aparecerán al máximo diferentes entre sí. Así el azul aparece a la vez más oscuro y más opaco cuando se ve en un campo de luz, alto croma amarillo-verde a la izquierda, y aparece más claro y más alto en intensidad cromática cuando se ve contra un campo de naranja oscuro, opaco a la derecha.
Visto contra un campo blanco, una muestra de color en realidad ganará un “halo” de su color complementario como resultado de este efecto. Por ejemplo, si miras la muestra verde sin enfocarte durante varios segundos, comenzarás a ver emerger bordes magenta a su alrededor.
Seurat registra este efecto en su cuadro Los modelos. Observe cómo la modelo sentada de la derecha tiene un halo oscuro, violeta-azul alrededor de la carne anaranjada clara de su espalda, y un halo claro contra el lado sombrío azul-violeta oscuro de su estómago y parte superior del brazo. Este efecto natural de “irradiación” es exagerado por Seurat para ayudar a intensificar los colores y valores mediante la yuxtaposición con sus opuestos a través del contraste simultáneo.
#### Percepción del color, armonía del color, expresión del color
Aquí nos hemos concentrado en cómo los neoimpresionistas utilizaron la teoría del color para ayudar a duplicar los efectos perceptuales. Emplearon el divisionismo para mantener sus pinturas lo más luminosas posible mientras registraban cómo el color percibido se ve afectado por factores como la temperatura de la luz, el color reflejado y el contraste simultáneo con los colores adyacentes.
Los objetivos de los neoimpresionistas fueron más allá de la precisión perceptual para incluir también los efectos puramente estéticos del color: cómo pueden ser utilizados para crear agradables armonías de color basadas en ciertos principios. Las “leyes de contraste y gradación” de Signac evocan dos de estos principios: “gradación” es la armonía estética producida por transiciones suaves entre colores en gran parte análogos, y el “contraste” es producido por la yuxtaposición más nítida de los opuestos. Las obras posteriores de Signac parecen más preocupadas por tales armonías que por la precisión perceptual.
Los neoimpresionistas también reconocieron que el color tiene efectos expresivos. Signac afirmó que la “alegría” es evocada por pinturas con tonos cálidos y claros dominantes, mientras que la “tristeza” es evocada por los colores dominantes fríos y oscuros [2] Idealmente, una pintura neoimpresionista tomará en cuenta las tres cualidades: precisión perceptual, armonía formal y expresión emocional. Los artistas creían que todos estos eran susceptibles a leyes científicas rigurosas que apenas estaban siendo reconocidas y sistematizadas en su época.
#### Notas:
1. Paul Signac, De Eugene Delacroix al neoimpresionismo, traducido en Linda Nochlin, ed., Impresionismo y post impresionismo, 1874-1904: Fuentes y documentos (Englewood Cliffs, N.J.: Prentice-Hall, 1966), p. 118. Este pasaje está muy cerca de la formulación propia de Georges Seurat de su método en una carta a Maurice Beaubourg del 28 de agosto de 1890: “El medio de expresión es la mezcla óptica de tonos y colores (tanto del color local como del color iluminador—sol, lámpara de aceite, lámpara de gas, etc.), es decir, de las luces y sus reacciones (sombras) según las leyes del contraste, la gradación y la irradiación” (en Nochlin, ed., p. 114).
2. Ibíd., pág. 121.
La historia de los pigmentos
## Georges Seurat
### Georges Seurat, bañistas en Asnières
por y
Video$$\PageIndex{1}$$: Georges Seurat, Bañistas en Asnières, 1884, óleo sobre lienzo, 6.6 x 9.8 ft (National Gallery, Londres)
### Georges Seurat, Un domingo en La Grande Jatte — 1884
por y
Video$$\PageIndex{2}$$: Georges Seurat, Un domingo en La Grande Jatte — 1884, 1884-86, óleo sobre lienzo, 81-3/4 x 121-1/4 pulgadas (207.5 x 308.1 cm) (El Instituto de Arte de Chicago)
## Vincent van Gogh
### Los comedores de papa
por y
¿A qué debe oler una pintura campesina? Van Gogh tiene una opinión...
Video$$\PageIndex{3}$$: Vincent van Gogh, Los comedores de papa, 1885, óleo sobre lienzo, 82 x 114 cm (Museo Van Gogh, Ámsterdam, Fundación Vincent van Gogh). Una conversación con la Dra. Beth Harris y el Dr. Steven Zucker.
### Vincent van Gogh, autorretrato dedicado a Paul Gauguin
por y
Video$$\PageIndex{4}$$: Vincent van Gogh, Autorretrato Dedicado a Paul Gauguin, 1888, óleo sobre lienzo, 24 x 19-11/16″ (Fogg, Harvard Art Museums, Cambridge, Massachusetts)
Este autorretrato fue pintado para Paul Gauguin como parte del intercambio entre los artistas. Van Gogh optó por representarse a sí mismo con severidad monástica. La otra pintura es Autorretrato de Paul Gauguin Dedicado a Vincent van Gogh (Les Misérables). El título de Gauguin es una referencia al heroico fugitivo, Jean Valjean, en la novela Les Misérables de Victor Hugo. La pintura de Gauguin también contiene un retrato de Emile Bernard que no fue pintado por Gauguin sino por Bernard dentro de la pintura de Gauguin.
A continuación se presenta una carta de Van Gogh a su hermano Theo sobre el intercambio de pintura con Gauguin fechada el 7 de octubre de 1888:
Mi querido Theo,
Muchas gracias por su carta. Qué contento estoy por Gauguin; no voy a tratar de encontrar palabras para decirte — seamos de buen corazón.
Acabo de recibir el retrato de Gauguin por él mismo y el retrato de Bernard de Bernard y en el fondo del retrato de Gauguin está el de Bernard en la pared, y viceversa.
El Gauguin es, por supuesto, notable, pero me gusta mucho la foto de Bernard. Es solo la visión interior de un pintor, unos tonos abruptos, unas pocas líneas oscuras, pero tiene la distinción de un Manet real, real.
El Gauguin es más estudiado, llevado más allá. Eso, junto con lo que dice en su carta, me dio absolutamente la impresión de que representa a un preso. No es una sombra de júbita. Absolutamente nada de la carne, pero uno puede poner eso con confianza en su determinación de hacer un efecto melancólico, la carne en las sombras se ha vuelto un triste azul.
Entonces ahora por fin tengo la oportunidad de comparar mi cuadro con lo que están haciendo los compañeros. Mi retrato, que envío a Gauguin a cambio, tiene el suyo, estoy seguro de eso. Le he escrito a Gauguin en respuesta a su carta que si se me permite enfatizar mi propia personalidad en un retrato, lo había hecho al tratar de transmitir en mi retrato no sólo a mí mismo sino a un impresionista en general, lo había concebido como el retrato de un bonze, un simple adorador del Buda eterno.
Y cuando pongo la concepción de Gauguin y la mía propia al lado de la otra, la mía es tan grave, pero menos desesperada. Lo que me dice el retrato de Gauguin antes de todas las cosas es que no debe seguir así, debe volver a ser el Gauguin más rico de los “Negresses”.
Estoy muy contento de tener estos dos retratos, pues finalmente representan a los compañeros en esta etapa; no se quedarán así, volverán a una vida más serena.
Y veo claramente que el deber que se me ha impuesto es hacer todo lo posible para disminuir nuestra pobreza.
Nada bueno viene el camino en el trabajo de este pintor. Siento que él es más Mijo que yo, pero yo soy más Díaz que él, y como Díaz voy a tratar de complacer al público, para que algunos centavos puedan entrar a nuestra comunidad. He gastado más que ellos, pero no me importa un poco ahora que veo su pintura, han trabajado en demasiada pobreza para tener éxito.
Eso sí, tengo cosas mejores y más vendibles que las que te he enviado, y siento que puedo seguir haciéndolo. Al fin tengo confianza en ello. Sé que hará bien el corazón de algunas personas volver a encontrar temas poéticos, “El cielo estrellado”, “Las vides de hoja”, “Los surcos”, el “Jardín del poeta”.
Entonces creo que es su deber y el mío exigir riqueza comparativa solo porque tenemos artistas muy grandes que mantener vivos. Pero por el momento eres tan afortunado, o al menos afortunado de la misma manera, como Sensier si tienes a Gauguin y espero que esté con nosotros corazón y alma. No hay prisa, pero en todo caso creo que le gustará tanto la casa como un estudio que aceptará ser su cabeza. Danos medio año y mira qué significará eso.
Bernard me ha vuelto a enviar una colección de diez dibujos con un poema atrevido —el conjunto se llama En el Burdel.
Pronto verás estas cosas, pero te enviaré los retratos cuando los haya tenido que mirar desde hace algún tiempo.
Espero que escribas pronto, estoy muy duro por las camillas y marcos que pedí.
Lo que me dijiste de Freret me dio placer, pero me atrevo a pensar que voy a hacer cosas que le gusten mejor, y a usted también.
Ayer pinté una puesta de sol.
Gauguin se ve enfermo y atormentado en su retrato!! Espera, eso no va a durar, y será muy interesante comparar este retrato con el que hará de sí mismo dentro de seis meses.
Algún día verás también mi autorretrato, que envío a Gauguin, porque él lo mantendrá, espero.
Todo es gris ceniciento contra veronese pálido (no amarillo). La ropa es este abrigo marrón con borde azul, pero he exagerado el marrón al morado, y el ancho de los bordes azules.
La cabeza está modelada en colores claros pintados en un grueso empaste contra el fondo claro sin apenas sombras. Sólo he hecho que los ojos se inclinen ligeramente como los japoneses.
Escríbeme pronto y la mejor de las suertes. Qué feliz será el viejo Gauguin.
Un buen apretón de manos, y agradezco a Freret el placer que me ha brindado. Por ahora bien.
Siempre tuyo,
Vicente.
Carta cortesía de Web Exhibes
### Vincent van Gogh, autorretrato con oreja vendada
por
El siguiente reporte apareció en la revista de Arles Le Forum Republicain el 30 de diciembre de 1888:
El domingo pasado, a las 11:30 de la noche, Vincent Vaugogh [sic], pintor de origen holandés, llamó en el Burdel No. 1, pidió a una mujer llamada Rachel y le entregó... su oído, diciendo: 'Guarda este objeto con tu vida'. Después desapareció. Al ser informados de la acción, que sólo podía ser la de un lamentable loco, la policía acudió al día siguiente a su casa y lo descubrió tirado en su cama aparentemente al punto de morir. El desafortunado hombre ha sido trasladado de urgencia al hospital.
Los relatos de lo que ocurrió esa noche varían. Sin embargo, cualesquiera que sean las circunstancias exactas, cualesquiera que sean las motivaciones subyacentes podrían haber obligado a van Gogh a hacerlo, el episodio efectivamente puso fin a una de las relaciones laborales más famosas de la historia del arte, ya que Paul Gauguin abordó el tren a París al día siguiente.
Durante nueve semanas habían vivido juntos compartiendo hospedajes en la Casa Amarilla, a las afueras de las murallas del casco antiguo de Arles en el sur de Francia, estimulándose mutuamente como colaboradores y como rivales también. El sueño había sido montar “un estudio en el Sur”, como lo expresó van Gogh, una comunidad de artistas, consigo mismo y Gauguin, los padres fundadores, todos trabajando en armonía con la naturaleza y, como esperaba, entre ellos.
#### ¿Una cara valiente?
El cuadro, terminado dos semanas después del evento, a menudo se lee como una despedida de ese sueño. Para Steven Naifeh y Gregory White Smith, los biógrafos más recientes del artista, sin embargo, el retrato fue ante todo una súplica a los médicos de van Gogh.
Se muestra al artista de perfil de tres cuartos parado en una habitación de la Casa Amarilla vistiendo un abrigo cerrado y un gorro de piel. Su oreja derecha está vendada. De hecho era su oreja izquierda la que estaba vendada, siendo la pintura una imagen especular. A su derecha hay un caballete con un lienzo sobre él. Apenas visible, un tenue contorno debajo revela lo que parece ser un bodegón que parece haber sido pintado. La parte superior del caballete ha sido recortada por el borde del lienzo y el sombrero de la niñera para formar una forma de tenedor. A su izquierda hay una ventana enmarcada de color azul, y en parte oscurecida por la cresta demacrada de su mejilla, una impresión japonesa en madera muestra dos geishas en un paisaje con el monte Fuji al fondo.
Naifeh y White Smith argumentan que van Gogh, tras su liberación del hospital, estaba ansioso por persuadir a sus médicos de que efectivamente estaba perfectamente en forma y capaz de cuidarse y que, a pesar de su lapso momentáneo, no sería necesario que lo comprometieran, como se había sugerido, a uno de los asilos locos locales; de ahí el abrigo y el sombrero de invierno, para mantener el calor como habían aconsejado, y con la ventana entreabierta todavía recibiendo ese aire fresco tan necesario en su sistema. El vendaje también, que habría sido empapado en alcanfor, sugiere que ambos acepta lo sucedido y está feliz, literalmente, de tomar su medicina. La misma nota de optimismo estoico, si se desea leer la pintura de esta manera, también se encuentra en las cartas a su hermano Theo, en las que van Gogh, lejos de abandonar su sueño de un “estudio en el Sur”, habla de continuar con el proyecto, expresando el deseo de que más artistas vengan a Arles, incluso proponiendo que Gauguin y él podrían “empezar de nuevo”.
Sin embargo, claro, independientemente de que Van Gogh estuviera o no dispuesto a admitirlo, el proyecto definitivamente había llegado a su fin. Y aunque por poco tiempo sí llegó a seguir viviendo en la Casa Amarilla, a las pocas semanas, actuando sobre una petición entregada a las autoridades locales y firmada por 30 de sus vecinos, fue trasladado por la fuerza y llevado al Hospital Arles donde fue encerrado en una celda de aislamiento. En mayo van Gogh se comprometió al asilo privado en Saint-Remy un pequeño pueblo al norte de Arles y en poco más de un año estaba muerto.
#### Una obsesión por el arte japonés
Aunque el argumento de Naifeh y White Smith es convincente, cómo el artista se contabiliza en sus cartas y cómo se expresa en la pintura, son cosas diferentes. Por mi parte, lo más interesante de la imagen es lo que revela sobre la práctica artística de van Gogh y particularmente su obsesión por el arte japonés: “Todo mi trabajo hasta cierto punto se basa en el arte japonés”, escribió en julio de 1888.
Tres años antes, mientras estaba en la ciudad portuaria de Amberes en Bélgica, paseaba por los mercados allí donde estaban fácilmente disponibles grabados en madera de la escuela Ukiyo-e, los llamados “artistas del mundo flotante” y podían comprarse por solo unos pocos centimos. Estos primeros vislumbres del arte de Japón llegaron en un momento crucial de la carrera del artista: a medio camino entre su Holanda natal donde se había educado en la tradición realista de artistas como Jozef Israëls, con su paleta oscura y terrosa y simpatía por los pobres rurales, y París donde se encontraría la colorida urbanidad de los impresionistas.
Para van Gogh, los artistas de Japón ofrecieron el punto de encuentro perfecto de la teoría y la práctica. El más famoso de ellos fue Hokusai, “los Dickens de Japón”, que compartía la pasión del holandés por representar la vida de los pobres. Fue esta dimensión compasiva del arte japonés la que van Gogh esperaba aportar al Impresionismo, un movimiento que —para cuando llegó a París en 1886— ya había absorbido la inventiva visual de la escuela Ukiyo-e.
A medida que pasaba el tiempo, los enlaces iban aún más lejos. En sus dos años de estancia en París, la ciudad de los extraños, era el compañerismo sobre todo lo que anhelaba, y así llegó a imaginar a los impresionistas, entre cuyas filas afirmaba pertenecer, para ser como imaginaba a los japoneses, un cuerpo unido de artistas, compartiendo las mismas metas e ideales. Fue esto lo que impulsó el viaje hacia el sur. Al llegar a Arles le escribió a su hermano, declarando su esperanza de que “otros artistas se levanten en este animado país y hagan por ello lo que los japoneses han hecho por los suyos”. Y de nuevo, mientras decoraba su nueva casa con pinturas de girasoles, le escribió a Theo: “Ven ahora, ¿no es casi una verdadera religión la que nos enseñan los simples japoneses, que viven en la naturaleza como si ellos mismos fueran flores”.
Fue en Arles donde leyó la novela Madame Chrysanthème de Pierre Loti, mejor conocida hoy como la fuente literaria de la ópera Madame Butterfly de Puccini. Si bien su heroína abnegada se abrió paso grácilmente hacia las fantasías orientalistas de van Gogh, la descripción de Loti de los sacerdotes budistas inspiró su propio Autorretrato (Dedicado a Paul Gauguin), una pintura que dibuja la dirección que esperaba que siguieran los dos artistas.
Qué muy diferente es el Autorretrato con Oreja Vendada a este retrato anterior. Con su ambientación formal; los repetidos triángulos, por ejemplo, en la forma de su abrigo, la parte superior del caballete y la vista ofrecida del propio monte Fuji, otorgando a la pintura su calidad aspiracional, su empuje ascendente. Y sin embargo, el sentimiento dominante seguramente es transmitido por los marcos internos: la ventana, el lienzo y la impresión, cada uno de los cuales aparece condensado y algo forzado en la pintura, como si dobladeteara a la niñera.
El estampado japonés como Van Gogh lo pintó en Autorretrato con Oreja Vendada difiere del original. Comparándolos vemos cómo van Gogh desplazó la composición hacia la derecha, descartando deliberadamente una de las figuras a favor de la garza, cuyo pico afilado asoma como para apuñalar la oreja del artista. Frente a ella, la lona apretada a la izquierda con su huella fantasmal de flores coronada por el tenedor del caballete establece un paralelo formalmente satisfactorio pero psicológicamente inquietante. ¿Hay alguna pista en todo esto, aunque inconscientemente expresada, de que el sueño de una comunidad de artistas en Arles se ha vuelto en su contra?
Quizás, pero entonces por supuesto siempre está el color de van Gogh: la alegre aplicación del pigmento sobre la tela, el glorioso uso del empaste, grueso y veloz; esa fabulosa técnica de eclosión, en lugares que evocan las texturas que representa, el tejido del abrigo, los hilos del vendaje, el pelaje del sombrero. Y anotar la matriz tonal de trazos que conforman el rostro: violeta, verde, rojo, marrón, naranja, amarillo pajizo; los negros centrados en esas pupilas penetrantes.
Un anhelo de ser probado cuerdo o un grito de angustia sentido, lo que sea que leamos en la imagen sobre van Gogh el hombre, desde un punto de vista puramente histórico del arte, es aquí en su pincelada y en su paleta donde se descubre la fuente de las “desarmonías deliberadas” de André Derain. Qué apropiado entonces que fue mientras estaba de vacaciones en el sur de Francia, un lugar favorito de ese movimiento modernista temprano al que pertenecía —los fauves— que Derain pintara a su amigo y compañero artista Matisse; suficiente tal vez para decir que la esperanza y predicción de Van Gogh de que “otros artistas se levantarán en este país animado” no estaba tan salvajemente fuera de lugar después de todo.
### Vincent van Gogh, el dormitorio
por y
Video$$\PageIndex{5}$$: Vincent van Gogh, La recámara, 1889, óleo sobre lienzo, 29 x 36-5/8 pulgadas (73.6 x 92.3 cm) (Instituto de Arte de Chicago)
### Vincent van Gogh, La noche estrellada
por DR. NOELLE PAULSON
#### Un raro paisaje nocturno
Las curvas y arremolinadas líneas de colinas, montañas y cielo, los azules y amarillos brillantemente contrastantes, los grandes cipreses llameantes y las pinceladas de capas gruesas de La noche estrellada de Vincent van Gogh están arraigadas en la mente de muchos como expresión del artista estado mental turbulento. El lienzo de Van Gogh es de hecho una obra de arte excepcional, no sólo en términos de su calidad sino también dentro de la obra del artista, ya que en comparación con temas favorecidos como los lirios, girasoles o campos de trigo, los paisajes nocturnos son raros. No obstante, es sorprendente que La noche estrellada se haya vuelto tan conocida. Van Gogh lo mencionó brevemente en sus cartas como un simple “estudio de la noche” o “efecto nocturno”.
Su hermano Theo, gerente de una galería de arte parisina y un talentoso conocedor del arte contemporáneo, no quedó impresionado, diciéndole a Vincent: “Claramente percibo lo que te preocupa en los nuevos lienzos como el pueblo a la luz de la luna... pero siento que la búsqueda del estilo quita el verdadero sentimiento de las cosas” (813, 22 Octubre de 1889). Aunque Theo van Gogh sintió que la pintura finalmente empujó el estilo demasiado lejos a expensas de la verdadera sustancia emotiva, la obra se ha vuelto icónica de expresión individualizada en la pintura de paisajes moderna.
#### Desafíos técnicos
Van Gogh había tenido en mente el tema de un cielo nocturno azul salpicado de estrellas amarillas durante muchos meses antes de pintar La noche estrellada a fines de junio o principios de julio de 1889. Presentaba algunos desafíos técnicos que deseaba enfrentar, a saber, el uso del color contrastante y las complicaciones de pintar en plein air (al aire libre) por la noche, y lo hizo referencia repetidamente en cartas a familiares y amigos como un tema prometedor aunque problemático. “Un cielo estrellado, por ejemplo, bueno —es algo que me gustaría intentar hacer”, confesó Van Gogh al pintor Emile Bernard en la primavera de 1888, “pero ¿cómo llegar a eso a menos que decida trabajar en casa y desde la imaginación?” (596, 12 de abril de 1888).
Como artista dedicado a trabajar siempre que sea posible a partir de grabados e ilustraciones o afuera frente al paisaje que representaba, la idea de pintar una escena inventada desde la imaginación preocupaba a Van Gogh. Cuando sí pintó un primer ejemplo del cielo nocturno lleno en Noche estrellada sobre el Ródano (1888, óleo sobre lienzo, 72.5 x 92 cm, Musée d'Orsay, París), imagen de la ciudad francesa de Arles por la noche, la obra se completó al aire libre con la ayuda de una lámpara de gas, pero la evidencia sugiere que su segunda Noche Estrellada fue creada en gran parte si no exclusivamente en el estudio.
#### Ubicación
Tras el dramático final de su efímera colaboración con el pintor Paul Gauguin en Arles en 1888 y el infame colapso durante el cual mutiló parte de su propio oído, Van Gogh fue finalmente hospitalizado en Saint-Paul-de-Mausole, un asilo y clínica para enfermos mentales cerca del pueblo de Saint- Rémy. Durante su convalecencia allí, Van Gogh fue animado a pintar, aunque rara vez se aventuró a más de unos cientos de metros de las paredes del asilo.
Además de su habitación privada, desde la que tenía una vista panorámica de la cordillera de los Alpilles, también se le dio un pequeño estudio para pintar. Dado que esta sala no miraba hacia las montañas sino que tenía una vista del jardín del asilo, se supone que Van Gogh compuso La noche estrellada utilizando elementos de algunas obras previamente terminadas aún almacenadas en su estudio, así como aspectos de la imaginación y la memoria. Incluso se ha argumentado que la aguja de la iglesia en el pueblo es de alguna manera de carácter más holandés y debe haber sido pintada como una amalgama de varias agujas de iglesia diferentes que van Gogh había representado años antes mientras vivía en los Países Bajos.
Van Gogh entendió también que la pintura era un ejercicio de estilización deliberada, diciéndole a su hermano: “Estas son exageraciones desde el punto de vista del arreglo, sus líneas se contorsionan como las de antiguas xilografías” (805, c. 20 de septiembre de 1889). Similar a sus amigos Bernard y Gauguin, van Gogh estaba experimentando con un estilo inspirado en parte en xilografías medievales, con sus gruesos contornos y formas simplificadas.
#### Los colores del cielo nocturno
Por otro lado, La noche estrellada evidencia la extensa observación de Van Gogh del cielo nocturno. Después de salir de París hacia zonas más rurales del sur de Francia, Van Gogh pudo pasar horas contemplando las estrellas sin interferencias de las luces de las calles de la ciudad a gas o eléctricas, que estaban cada vez más utilizadas a finales del siglo XIX. “Esta mañana vi el campo desde mi ventana mucho tiempo antes del amanecer, con nada más que la estrella matutina, que se veía muy grande” 777, c. 31 de mayo — 6 de junio de 1889). Como le escribió a su hermana Willemien van Gogh de Arles,
A menudo me parece que la noche es aún más rica de color que el día, coloreada con las violetas, azules y verdes más intensos. Si miras con atención, verás que algunas estrellas son limonosas, otras tienen un resplandor rosa, verde, nomeolvides azul. Y sin trabajar el punto, está claro para pintar un cielo estrellado no es suficiente para poner manchas blancas en azul-negro.
(678, 14 de septiembre de 1888)
Van Gogh siguió sus propios consejos, y su lienzo demuestra la gran variedad de colores que percibió en noches claras.
#### Invención, recuerdo y observación
Podría decirse que es esta rica mezcla de invención, recuerdo y observación combinada con el uso de Van Gogh de formas simplificadas, empaste grueso y colores audazmente contrastantes lo que ha hecho que la obra sea tan convincente para las generaciones posteriores de espectadores, así como para otros artistas. Inspirar y animar a los demás es precisamente lo que Van Gogh buscó lograr con sus escenas nocturnas. Cuando la Noche Estrellada sobre el Ródano se exhibió en el Salon des Indécolgantes, un lugar importante e influyente para artistas de vanguardia en París, en 1889, Vincent le dijo a Theo que esperaba que “pudiera dar a otros la idea de hacer efectos nocturnos mejor que yo”. La noche estrellada, su propio “efecto nocturno” posterior, se convirtió en una imagen fundamental para el expresionismo así como quizás en la pintura más famosa de la obra de Van Gogh.
## La Escuela Pont-Aven y el Sintetismo
por y
Cuando los espejos destinados a decorar las paredes del Café des Arts de París no llegaron a tiempo para su apertura en 1889, el propietario accedió a una exposición de arte improvisada en su lugar. Los artistas, entre ellos Paul Gauguin, Emile Bernard, Charles Laval y Emile Schuffenecker, se llamaron a sí mismos el “Groupe Impressioniste et Synthétiste”, pero hoy son más conocidos como la Escuela Pont-Aven, después de un pueblo de la provincia francesa de Bretaña donde muchos de los artistas pintado.
En la exposición Gauguin mostró una pintura de tres niñas bretonas bailando en un prado a las afueras de Pont-Aven, con la torre de la iglesia de San José al fondo. Esta pintura exhibe dos características clave de la Escuela Pont-Aven: temas “primitivistas” con temas rurales y campesinos, y un estilo “sintetizador” consistente en dibujo simplificado, contornos claramente definidos, colores intensificados y espacio aplanado.
#### “La tierra del pintor”
Bretaña había sido un destino popular para los turistas desde que se completó la primera línea ferroviaria de París en la década de 1860. Era famosa no sólo por su accidentado paisaje sino también por sus pintorescos habitantes, especialmente las campesinas bretonas en sus gorras blancas almidonadas. Una popular guía inglesa de la época titulada Breton Folk describió a Bretaña como “la tierra del pintor”, y elogió la atracción particular de la región por los artistas “en busca de disfraces pintorescos y escenas de la vida pastoral” [1].
Los temas rústicos y campesinos fueron populares entre los artistas y mecenas franceses comenzando por la Escuela Barbizon y los pintores realistas franceses de mediados del siglo XIX. Estas escenas rurales “atemporales” ofrecían un sentido tranquilizador de tradición y continuidad durante una época marcada por la rápida industrialización y urbanización.
Mujeres bretonas en un indulto de Pascal Dagnan-Bouveret, mostrada en el Salón Francés de 1889, demuestra la popularidad de las materias bretonas en un estilo académico convencional. Muestra a un grupo de campesinos bretones reunidos en primer plano escuchando leer a una mujer. El fondo representa un ritual bretón característico llamado Perdón, en el que los penitentes procesan descalzos o de rodillas alrededor de la iglesia para ganarse la absolución por sus pecados. A un espectador urbano de clase media, los campesinos bretones habrían parecido pintorescos y anticuados, pero también admirables por su piedad y autenticidad.
#### Sintetismo
Al igual que la pintura de Dagnan-Bouveret del año anterior, la famosa Visión después del Sermón de Gauguin también representa la profunda fe religiosa del pueblo bretón. Un grupo de mujeres en el archivo de primer plano fuera de la iglesia, habiendo escuchado un sermón sobre Jacob combatiendo a un ángel (Génesis 32:24-32). Tan grande es su fe que literalmente “ven” la escena bíblica frente a la iglesia, justo al lado de una vaca que pastaba prosaicamente.
El estilo de las dos obras es muy diferente, sin embargo. El color de Gauguin es brillante y antinatural en comparación con los grises apagados y los tonos tierra de Dagnan-Bouveret, y junto al meticuloso naturalismo del artista académico La técnica de Gauguin parece francamente incompetente. El dibujo es crudo, la anatomía de los rostros de las mujeres es casi infantil, los planos planos de su ropa no logran transmitir por completo una sensación de los cuerpos que se encuentran debajo, y el suelo rojo se levanta como una pared en lugar de retroceder al espacio.
Lejos de ser incompetente, sin embargo, la técnica simplificada de Gauguin, incluso un tanto cruda, fue una elección consciente. Un joven artista llamado Paul Sérusier que estudió con Gauguin relató los consejos del artista mayor mientras estaban pintando juntos en la orilla de un río cerca de Pont-Aven:
¿Cómo ves estos árboles? Son de color amarillo; así que pon un poco de amarillo. Esta sombra, es más bien azul, la pinta con puro ultramarino. ¿Esas hojas rojas? Poner bermellón. [2]
Gauguin le dice a Sérusier que simplifique e intensifique lo que está viendo. En lugar de buscar sutiles matices de color y tono dentro de las hojas amarillentas de otoño, Sérusier las pinta en amarillo puro, no modulado. Los troncos grises fríos de los árboles se renderizan de manera similar como trazos de ultramarino mezclados con blancos, sobre un fondo de rojo bermellón. Cada color se intensifica, y el dibujo y la composición se simplifican en un patrón plano. En otros lugares, Gauguin aconsejó a los artistas pintar desde la memoria en lugar de directamente desde la naturaleza, porque la memoria automáticamente descarta detalles extraños y destila percepciones hasta su esencia.
Este proceso de destilar elementos múltiples y complejos en un todo simplificado es lo que el grupo quiso decir cuando se llamaban a sí mismos “Sintetistas” en la exposición Café des Arts. Insistir en el proceso de síntesis fue un contraste deliberado con el proceso altamente científico y analítico del Neo-Impresionismo. Las dos pinturas anteriores fueron ejecutadas en el mismo año a solo unos kilómetros de distancia en Bretaña. Mientras que los Neo-Impresionistas trabajaron para analizar o descomponer cuidadosamente todos los componentes separados que componen complejas sensaciones de color y luego los renderizaron en innumerables puntos diminutos, los Sintéticos los destilaron en amplias áreas de color puro.
El estilo sintético a veces se llamaba “Cloisonismo”, después de la técnica cloisonné utilizada para decorar objetos fundiendo esmalte coloreado entre contornos de alambre. También tiene similitudes con los grabados japoneses, que eran populares en su momento, así como xilografías de colores medievales y vidrieras. El sintetismo estaba algo antitéticamente asociado tanto con cualidades sensuales/decorativas como con cualidades religiosas/espirituales, pero cualquiera que sea su génesis o propósito, forma un fuerte contraste tanto con el estilo naturalista académico de Dagnan-Bouveret como con el estilo neoimpresionista de Signac.
#### Primitivismo
Hay una lógica en representar la vida campesina con este estilo simplificado. Los colores brillantes y el dibujo crudo del Sintetismo tienen mucho en común con el arte popular rural. Gauguin reconoce implícitamente esta similitud de estilo en su pintura El Cristo Amarillo de 1889, que muestra a un grupo de mujeres bretonas arrodilladas en oración alrededor de un crucifijo de madera en un campo. El crucifijo es una representación de uno de un artista anónimo del siglo XVII que Gauguin vio una pequeña capilla ambientada en los campos fuera de Pont-Aven. Si bien la burda talla y la rígida anatomía de la obra no demuestran facilidad técnica, parecen garantizar la fe sencilla y sincera del escultor anónimo que la creó.
En lugar de colocar el crucifijo en la capilla, Gauguin lo transporta a un campo para conectar aún más la vida de Cristo con los ciclos atemporales de la naturaleza que impulsan la vida tradicional de los campesinos bretones. La luz en el cielo marca la hora como temprano en la tarde, y el color del follaje denota caída. Ambos sugieren un final, pero un final que promete un nuevo comienzo. Cristo, al igual que el sol y los granos de cosecha de otoño, volverán a levantarse.
Tanto el estilo folclórico simplificado como el tema campesino ejemplifican el primitivismo, un retroceso a una forma de vida anterior (preindustrial, precientífica y preurbana) como una forma de buscar una mayor autenticidad y un propósito superior en la vida. Gauguin escribió en una carta a su amigo Emile Schuffenecker: “Me encanta Bretaña. Aquí encuentro cierta rareza y primitividad. Cuando mis zuecos resuenan en este suelo de granito, escucho el tono opaco, mate y poderoso que busco en mi pintura”. [3] A diferencia de Dagnan-Bouveret, quien representaba la vida popular bretona con la técnica sofisticada y el ojo científico de un parisino completamente moderno, Gauguin aspiraba a “volverse primitivo”, como ejemplifica su adopción de zuecos campesinos (sabots) así como el simple estilo folk-art de sus pinturas.
Es fácil romantizar el proyecto de la Escuela Pont-Aven de celebrar la sencilla vida rural y las tradiciones populares de los campesinos bretones. Muchos relatos de la biografía de Gauguin elogian su acto de renunciar a una carrera como corredor de bolsa, junto con todos los placeres y comodidades de la vida moderna, para vivir como pobre pintor entre los campesinos de Bretaña y más tarde en la isla de Tahití en el Mar del Sur.
Una beca más reciente ha problematizado tanto esa biografía como ese proyecto, sin embargo. La visión de Pont-Aven en las pinturas de Gauguin es en gran parte una fantasía romántica. Bretaña se estaba modernizando rápidamente, y las tradiciones populares y los trajes que Gauguin admiraba estaban desapareciendo o exhibían solo para vacaciones y turistas. La guía de 1880 ya señala que
En las tiendas y en los paseos [de Bretaña] la mayoría de las mujeres se visten como en París... Cada año se tiran más gorras blancas a un lado... y cada año los mercados de San Malo y San Servan tienen menos individualidad de vestuario. [4]
Las pinturas de Gauguin de Bretaña son, al final, más fantasías que imágenes precisas de una auténtica cultura campesina.
También vale la pena preguntarse por qué las principales protagonistas de las pinturas de Gauguin son las mujeres, tanto en Bretaña como posteriormente en Tahití. En Visión después del Sermón como en El Cristo Amarillo y El Cristo Verde, se trata de mujeres cuyos trajes pintorescos proporcionan la antítesis a la moda moderna, mujeres cuya profunda fe religiosa proporciona el antídoto a la modernidad ciencia y escepticismo, y mujeres cuya adhesión a la tradición proporciona un respiro de las innovaciones constantes y disruptivas de la vida moderna. Si bien esto eleva a las mujeres a un lugar de honor, también refuerza los estereotipos comunes, sugiriendo que las mujeres preservan la fe y las tradiciones populares simplemente porque son menos adecuadas que los hombres para el nuevo mundo de la ciencia, la tecnología y el cambio constante.
#### Notas:
1. Henry Blackburn y Randolph Caldecott, Breton Folk: An Artistic Tour in Brittany (Boston, 1881), p. 3.
2. El consejo de Gauguin a Sérusier fue grabado por su amigo Maurice Denis, “Paul Sérusier, sa vie, son oeuvre”, en Sérusier, L'ABC de la peinture (París: Harina, 1942), p. 42.
3. Carta, Gauguin a Schuffenecker, febrero de 1888, en M. Malingue, ed, Lettres de Gauguin à sa femme et à ses amis (París, 1946), p. 322 (nuestra traducción).
4. Blackburn, Breton Folk, p. 10.
Paul Gauguin
### Gauguin, Autorretrato con Retrato de Émile Bernard (Les misérables)
por y
Video$$\PageIndex{6}$$: Paul Gauguin, Autorretrato con Retrato de Émile Bernard (Les misérables), 1888, óleo sobre lienzo, 44.5 x 50.3 cm (Museo Van Gogh). Ponentes: Dr. Steven Zucker y Dra. Beth Harris
### Paul Gauguin, Visión después del Sermón (o Jacob Luchando con el Ángel)
por y
Video$$\PageIndex{7}$$: Paul Gauguin, Visión después del sermón (o Jacob Wrestling with the Angel), 1888, óleo sobre lienzo, 2′ 4 3/4″ x 3′ 1/2″ (Galería Nacional de Escocia, Edimburgo)
### Paul Gauguin, Nunca más
por , y
Video$$\PageIndex{8}$$: Paul Gauguin, Nevermore, 1897, óleo sobre lienzo (Courtauld Gallery, Londres)
### Paul Gauguin, La vaca roja
por y
Video$$\PageIndex{9}$$: Paul Gauguin, La vaca roja, 1889, óleo sobre lienzo (LACMA)
Nota: aunque el video afirma que los cipreses sugieren que este lienzo pudo haber sido pintado en el sur, fue pintado en Le Pouldu cerca de Pont-Aven en Bretaña.
### Paul Gauguin, Espíritu de los muertos Observando
por
#### Sé misterioso
Misterios de Soyez”, (sé misterioso), dijo Gauguin. Quizás tenía en mente este mandato cuando produjo la pintura más significativa —según sus propios cálculos— para salir de su primera estancia en Tahití, El espíritu de la observación de muertos. Pocos críticos dudarían de la importancia de esta obra. Su misterio y apertura a la interpretación le han asegurado una posición entre las obras clave de Gauguin.
Gauguin realizó su primera visita a Tahití (una colonia francesa) en marzo de 1891, regresando a París en mayo de 1893. Fue un periodo enormemente productivo en la carrera de Gauguin. “En los dos años que he pasado aquí”, escribió, “con sólo unos meses perdidos, he producido sesenta y seis lienzos más o menos finos y una serie de esculturas ultra-primitivas. Eso es suficiente para cualquier hombre”.
#### Un trasfondo de terror
Para presagiar su regreso a Europa y también para rescatar a su familia de la penura, con la ayuda de su esposa danesa, Mette, Gauguin organizó una exposición de su obra en Copenhague. Entre los nueve lienzos que envió desde Tahití se encontraba El espíritu de los muertos Watching, llevando consigo un precio de venta —el más caro en la venta— de entre mil 500 y 2.000 francos. Claramente muy apreciado por Gauguin, el mejor de dos años de lienzos “finos”, la pintura representa a una adolescente (la modelo era la novia tahitiana de Gauguin, Tehura, que solo tenía catorce años), acostada boca abajo en una cama, su rostro mirando al espectador con una expresión temerosa. La cama está cubierta con un pareo azul (una falda envolvente que llevan los tahitianos) y una sábana de color amarillo cromo claro. Detrás de la cama, siluetada y de perfil, una mujer vigila al niño.
Gauguin creó una cualidad inquietante y sobrenatural al explotar lo que consideraba el potencial emocional del color. Al describir el cuadro a Mette, señala cómo los tonos de púrpura en la pared crean “un fondo de terror” y cómo la hoja “debe ser amarilla, porque, en este color, despierta algo inesperado para el espectador”. Usar colores para despertar sentimientos estuvo muy en línea con el trabajo de otros artistas post-impresionistas, como el contemporáneo y amigo de Gauguin, Vincent van Gogh.
#### El espíritu de los muertos
Aparte del color, la composición es inquietante en sí misma, particularmente la relación entre la niña y la anciana detrás de ella cuya forma simplificada y escala desproporcionada sugieren estatuas o tiki tahitianos. Si ella es una estatua tallada de madera, sin embargo, ¿qué o a quién significa? Si no es así, ¿entonces es real o de otro mundo? ¿Es este el espíritu de los muertos viendo al que se refiere el título? Y si ella es imaginada, ¿entonces por quién? ¿Todo lo que rodea a la niña son los conjuros de su propia imaginación embrujada? ¿O es lo que ella mira, el espacio en el que habitamos nosotros mismos, que es la fuente de su terror? ¿Podría ser, entonces, que somos el espíritu de los muertos vigilando? El idioma tahitiano ciertamente permite tales ambigüedades. La expresión, manao tupapau significa o vigilar el espíritu de los muertos o el espíritu de los muertos vigilando.
Otras características formales de la pintura parecen realzar esta ambivalencia. Observe, por ejemplo, el complejo mirador que tenemos. Nuestra mirada está nivelada con los ojos luminosos de la anciana, mientras que al mismo tiempo, miramos hacia abajo la figura de la joven.
#### Un estudio un poco indecente de un desnudo
También podemos considerar esta pintura dentro de la tradición del desnudo femenino y recordar la Olimpia de Manet (1865). La obra de Manet proporcionó una plantilla para artistas más jóvenes, una que rechazó convenciones de larga data en la representación del desnudo y desafió los valores morales de la burguesía. Gauguin, por ejemplo, admiraba lo suficiente a Olimpia como para haber producido una copia de la misma en 1891.
Estaba ansioso por conmocionar a la burguesía y ciertamente su propio desnudo en El espíritu de los muertos Watching —“ un estudio ligeramente indecente” como él lo describió— es en muchos sentidos tan radical como el de Manet.El cuerpo está torpemente posicionado y desproporcionado. Los pies sobresalen de la cama y las manos son más grandes que los pies. Y lo más impactante de todo, es la edad del modelo.
Igualmente inquietante es el miedo que exhibe. Gauguin describió esto en cartas a su esposa, Mette. Habiendo caminado ese día a un pueblo vecino, Gauguin no regresó a su casa hasta la madrugada. Al entrar, encontró a Tehura desnuda en la cama mirándolo aterrorizado. El motivo de su miedo, según Gauguin, fue que Tehura creía en los tupapaus, los espíritus de los muertos que en la mitología tahitiana habitan el interior de la isla y cuya presencia ilumina el bosque por la noche.
Gauguin se mostró escéptico sobre esta creencia, sosteniendo que estos resplandores nocturnos fosforescentes que los tahitianos tomaron por espíritus eran de hecho un tipo de hongo que crece en árboles muertos. De cualquier manera, para Tehura, caminar por el interior tras la puesta del sol corría el riesgo de perturbar a los tupapaus con consecuencias potencialmente desastrosas; de ahí su miedo y así también esas brillantes formas espectrales que aparecen en el fondo de la pintura y que Gauguin declaró representaban el tupapaus mismos.
#### Lecturas críticas
Dada su construcción de la cultura tahitiana como “primitiva”, la versión de Gauguin de estos eventos ha sido examinada por historiadores del arte que han puesto en duda si Tehura realmente habría sostenido estas creencias (ya que era una cristiana practicante). Gauguin es así acusado de proyectar sobre su tema sus propias ideas preconcebidas primitivistas.
Otra crítica viene de la historiadora del arte, Nancy Mowll Mathews, quien argumenta que no eran los espíritus a los que le daba miedo Tehura, sino al propio Gauguin, el colonialista de mediana edad, blanco, varón contra el que, como depredadora sexual, tenía poco poder para resistir. Esta lectura da un giro inquietante a la imagen con Gauguin tomando placer sádico al representar el miedo que él mismo causó. Vale la pena señalar que en la cuenta de Gauguin, verla en este estado lo conmovió a declarar que nunca se veía tan hermosa, y que él se sintió atraído a consolarla, prometiendo no volver a dejarla nunca más.
El crítico Stephen Eisenman toma una línea de argumento diferente, describiendo la pintura como “un asalto a la tradición del desnudo europeo”. De particular interés para Eisenman es la incertidumbre del espectador respecto al sexo de la figura, las manos grandes y las caderas estrechas que sugieren una forma masculina más que femenina. “La postura y anatomía de Tehura, que enfatiza su infancia, se deriva de diversos prototipos andróginos y hermafroditas”, argumenta Eisenman, citando al hermafrodita Borghese como uno de ellos. Visto a esta luz, la pintura, lejos de ser una imagen de dominio patriarcal sobre el cuerpo colonizado, es en cambio un ataque subversivo a ese patriarcado y a todos los valores de género que mantiene.
Sin embargo elegimos mirar la pintura, provoca un cuestionamiento interminable, en el que nos vemos obligados a encontrarnos con el otro, ya sea en términos de edad, fe, género, espiritualidad, etnia, sexualidad, cultura, lo que quieras, es una pintura que explora la naturaleza heterogénea de la identidad, preguntando preguntas profundas en cuanto a quiénes y qué somos.
### Paul Gauguin, Oviri
por
El regreso de Gauguin a París desde su primera estancia en Tahití en agosto de 1893 no fue del todo como esperaba: sin fanfarria, sin bienvenida de héroe, y lo más decepcionante de todo, sin ventas.
#### Gauguin y “alfarería artística”
A pesar de cierto interés crítico en su obra, el éxito aún parecía eludirlo. Además, después de años de apoyo, su esposa Mette cortó cualquier vínculo con él. En quiebra y sin familia, se fue a Bretaña donde los costos de vida eran más baratos, pero reajustarse a la vida en la Francia “civilizada” resultó un reto. Una pelea de borrachos con un grupo de marineros bretones se destrozó el tobillo, lesión de la que nunca se recuperaría por completo. Ya fue suficiente, al parecer. En junio de 1895 partió hacia Tahití para no volver nunca. Es en este periodo tempestuoso que produjo posiblemente su obra maestra en el medio de la cerámica: Oviri.
Desde tallas de madera y cerámica hasta obras de mármol altamente terminadas, la escultura fue parte integral de la práctica artística de Gauguin. Sus obras en arcilla, todas producidas en París entre mediados de los 80 y mediados de los 90, le deben mucho al gran ceramista Ernest Chaplet que ofreció a Gauguin asistencia en la cocción y el acristalamiento, así como el acceso a su horno en Rue Blomet, Montparnasse. Oviri fue la más grande y la última de estas series.
La cerámica le apeló por varias razones; la primera era financiera, no sólo es barata la arcilla, sino que dados sus usos prácticos, Gauguin esperaba, descarriadamente como resultó, que su alfarería atraería a más compradores que su pintura. Luego estaba su famoso amor por el arte no europeo, como la cerámica inca y precolombina que encontró en su infancia peruana. Gauguin veía tales obras, tanto decorativas como utilitarias, como capaces de expresar emociones profundas tanto como el llamado arte alto, de ahí el término “cerámica artística” que utilizó para describirlas.
Gauguin no estaba del todo solo en el deseo de elevar a este humilde medio. Hacia finales del siglo XIX hubo un notable desmoronamiento de las jerarquías que habían separado al fino artista del artesano, la distinción digamos entre el artista liberal y el mecánico que había dominado desde el Renacimiento. En la cultura tahitiana no había distinciones tan finas, en cambio, el artesano /artista se definió de manera bastante diferente, como Gauguin llegó a descubrir, no siendo ni guerreros ni cazador/ama de casa ni cuidador, allá no era ni completamente masculino ni completamente femenino sino ocupado, socialmente hablando, un término medio andrógino en algún lugar entre los dos. Este sentido ambiguo de identidad de género apeló al espíritu subversivo de Gauguin. Ciertamente el potencial creativo de la androginia lo intrigó y a menudo se comenta en discusiones sobre Oviri.
#### Oviri
Una forma abreviada de Oviri-moe-aihere (el salvaje que duerme en el bosque salvaje), la diosa tahitiana de la muerte y el luto, el nombre mismo fascinó a Gauguin: salvaje, brutal, sediento de sangre. Lo utilizó, como un nom de guerre, para referirse a sí mismo, como si tomara los terribles aspectos de la diosa.
Aquí se para, entonces: bajo sus pies una loba muerta; en sus manos la forma aplastada de su cachorro; el esmalte rojo que sugiere el goteo de su sangre. No hay una fuente conocida para el episodio, que probablemente fue el invento de Gauguin. Esto dejó el camino abierto a diversas interpretaciones: que los lobos representan el salvajismo de la propia diosa; que al matarlos está absorbiendo de alguna manera sus capacidades violentas; incluso que son el mismo Gauguin. En varias letras dibuja la comparación, recordando, por ejemplo, cómo Degas alguna vez lo describió como “el lobo hambriento sin collar”. Otros ven una alusión velada a la práctica del infanticidio, proscrita en el momento de la llegada de Gauguin, que fue llevada a cabo por los Areoi, la élite sacerdotal de Tahití. La imagen evoca nociones de sacrificio o quizás historias del arquetipo vengativo de la madre, dibujando conexiones entre Oviri y Medea A punto de matar a sus hijos de Delacroix de 1838.
Sea cual sea la historia que cuente, sus primeras manifestaciones en términos de diseño se remontan a una obra producida dos años antes durante su primera estancia en Tahití, ¿A dónde vas? Es aquí, en el robusto, escultórico y marcadamente andrógino marco de la figura de primer plano, llevando en sus brazos un cachorro de lobo que obtenemos nuestro primer atisbo de Oviri.
Sin embargo, qué diferente es la cerámica a la pintura. Quizás por la crisis personal que vivió a su regreso a París o quizás por el propio medio con su contacto directo entre la mano y el barro. Oviri es una partida mucho más radical, un atávico asalto a los cánones de la gracia, la armonía y la belleza. Feo parece poco adecuado para describir a este avatar retorcido y condensado de fuerzas primarias y destructivas, los enormes ojos de las gafas flotando inhumanamente alrededor de su cabeza desproporcionada.
La figura en forma de bloque, carente de perforaciones o partes sobresalientes, como la estatuaria egipcia, manda una vista frontal. Cuando se ve desde atrás, sin embargo, se nos presenta una imagen totalmente diferente, otra obra de arte casi. Lo que había parecido desde el frente como pelo aparece ahora como una cubierta parecida a un capullo, la crisálida debajo, incipiente, a punto de estallar. Llama la atención el contraste con Oviri, la asesina.
Desde este ángulo, la obra también tiene un parecido llamativo con el Balzac de Rodin, escultura en la que había estado trabajando desde 1891. Aunque no se exhibió públicamente hasta 1898, Gauguin ciertamente sabía de la comisión y quizás estaba al tanto de la dirección que Rodin estaba tomando con ella. En ambas obras encontramos la misma dramática reducción de la forma, rechazando cualquier referencia al pasado clásico, aprovechando en cambio un impulso más primordial, en el caso de Oviri una fuerza a la vez femenina y masculina, en la que el acto destructivo, de aplastar al cachorro de lobo encuentra su antítesis creativa y vivificante en la forma orgánica, parecida a un budo de su reverso.
Fue esta confusión de la frontera última, la que entre la muerte y la vida, bien pudo haber llevado a Gauguin en 1900, sabiendo que no le quedaba mucho tiempo de vida, a pedirle a un amigo que le enviara su Oviri de París con la intención de que fuera para su lápida. Su amigo nunca llegó a ello; un descuido misericordioso dado el gres no habría resistido bien en ese clima tropical. En cambio, pasó a aparecer en la retrospectiva del artista de 1906, una exposición que Picasso vio y probablemente se inspiró en la hora de componer sus Les Demoiselles d'Avignon.
En 1978, se realizó un molde de bronce de la escultura, la cual fue colocada antes de la tumba de Gauguin en las Marquesas. Reconocida como obra maestra, en 1987 el original entró en la colección del Musée d'Orsay.
Esta escultura en el Musée d'Orsay
Barbara Landy, “El significado de la cerámica 'Oviri' de Gauguin”, Revista Burlington, vol. 109 (1967), pp. 242, 244-246. (JSTOR)
### Paul Gauguin, ¿de dónde venimos? ¿Qué somos? ¿A dónde vamos?
por DR. NOELLE PAULSON
¿De dónde venimos? ¿Qué somos? ¿A dónde vamos? es una obra enorme, de colores brillantes pero enigmática pintada sobre tela de cilicio áspera y pesada. Contiene numerosas figuras humanas, animales y simbólicas dispuestas a lo largo de un paisaje isleño. El mar y las montañas volcánicas de Tahití son visibles al fondo. Es la pintura más grande de Paul Gauguin, y entendió que era su mejor obra.
¿A dónde vamos? representa el manifiesto pintado del artista creado mientras vivía en la isla de Tahití. El artista francés pasó de ser un “pintor dominical” (alguien que pinta para su propio disfrute) a convertirse en un profesional después de que su carrera como corredor de bolsa fracasara a principios de la década de 1880. Visitó la isla del Pacífico Tahití en la Polinesia Francesa permaneciendo de 1891 a 1893. Luego regresó a la Polinesia en 1895, pintó allí este lienzo masivo en 1897, y finalmente murió en 1903, en Hiva Oa en las islas Marquesas.
Gauguin escribió a su amigo Daniel de Monfried, quien manejó la carrera de Gauguin en París mientras el artista permanecía en el Pacífico Sur, “Creo que este lienzo no sólo supera a todos mis anteriores, sino que jamás haré nada mejor, ni siquiera me gustará”. Gauguin completado ¿A dónde vamos? a un ritmo febril, presuntamente dentro del plazo de un mes, e incluso le reclamó a De Monfried que se fue a las montañas para intentar suicidarse una vez finalizada la obra. Gauguin, siempre el maestro de la autopromoción y muy consciente de su imagen como artista de vanguardia, puede o no haberse envenenado con arsénico como alegaba, pero esta leyenda estaba bastante en línea con los temas de la pintura de la vida, la muerte, la poesía y el significado simbólico.
El propio Gauguin proporcionó una descripción reveladora de las imágenes esotéricas de la pintura en la misma carta a De Monfried, escrita en febrero de 1898:
Se trata de un lienzo de cuatro metros cincuenta de ancho, por un metro setenta de altura. Las dos esquinas superiores son de color amarillo cromo, con una inscripción a la izquierda y mi nombre a la derecha, como un fresco cuyas esquinas se estropean con la edad, y que se aplica sobre una pared dorada. A la derecha en el extremo inferior, un niño dormido y tres mujeres agachadas. Dos figuras vestidas de púrpura se confian sus pensamientos el uno al otro. Una enorme figura agachada, fuera de toda proporción e intencionalmente así, levanta los brazos y mira con asombro a estos dos, que se atreven a pensar en su destino. Una figura en el centro está recogiendo fruta. Dos gatos cerca de un niño. Una cabra blanca. Un ídolo, sus brazos misteriosamente levantados en una especie de ritmo, parece indicar el Más Allá. Entonces, por último, una anciana que se acerca a la muerte parece aceptarlo todo, resignarse a sus pensamientos. ¡Ella completa la historia! A sus pies un extraño pájaro blanco, sosteniendo un lagarto en sus garras, representa la inutilidad de las palabras... Así que he terminado una obra filosófica sobre un tema comparable al del Evangélio.¹
El texto de Gauguin no sólo aclara parte de la iconografía abstrusa, idiosincrática de la pintura, sino que también nos invita a “leer” la imagen. Gauguin sugiere que las figuras tienen misteriosos significados simbólicos y que podrían responder a las preguntas que plantea el título de la obra. Y, a la manera de un pergamino sagrado escrito en una lengua antigua, la pintura debe leerse de derecha a izquierda: del bebé dormido —de donde venimos— hasta la figura de pie en el medio —lo que somos —y terminando a la izquierda con la anciana agachada— hacia donde vamos.
Estilísticamente, la composición está diseñada y pintada para recordar frescos o iconos pintados sobre un fondo dorado. Las esquinas superiores han sido pintadas con un amarillo brillante para contribuir a este efecto, y las figuras aparecen desproporcionadas entre sí —“ deliberadamente así” como escribió Gauguin— como si estuvieran flotando en el espacio en lugar de apoyarse firmemente sobre la tierra.
Estas características estilísticas, junto con el enigmático tema de Gauguin, contribuyen a la calidad “filosófica” de la pintura. Y como es común con otras obras simbolistas de este periodo, interpretaciones precisas y completas de ¿De dónde venimos? permanecer fuera de su alcance. La pintura es una mezcla deliberada de sentido universal —las preguntas que se hacen en el título son fundamentales que abordan la raíz misma de la existencia humana— y el misterio esotérico. Aunque ¿de dónde venimos? está pintado a gran escala similar a los paneles públicos decorativos creados por el artista francés Pierre Puvis de Chavannes (un artista admirado por Gauguin), ¿De dónde venimos? es esencialmente una obra privada cuyo significado probablemente sólo era conocido por el propio Gauguin.
A los pocos meses de terminar la pintura, Gauguin la envió a París junto con varias otras obras de arte, con la intención de que se exhibieran juntas en una galería o en el estudio de un artista. Envió a de Monfried instrucciones cuidadosas sobre cómo ¿De dónde venimos? debe enmarcarse (“una franja lisa de madera, de 10 centímetros de ancho, y encalada para parecerse a un mural”) y a quién se le debe invitar a la exposición (“de esta manera, en lugar de multitudes uno puede tener a quien uno quiere, y así ganar conexiones que no pueden dañarte”). La preocupación que Gauguin revela en los detalles indica su continua conciencia del mercado del arte parisino, que siguió siendo un foco central incluso cuando se exilió en una pequeña isla tropical al otro lado del globo.
En noviembre y diciembre de 1898, el grupo de pinturas tahitianas fue exhibido en la galería de Ambroise Vollard, un ex estudiante de derecho convertido en marchante de arte que se especializó en artistas de vanguardia. Vollard parece haber tenido dificultades para vender el “cuadro grande”, como lo llamó Gauguin. Los esfuerzos de los amigos parisinos del artista para adquirir colectivamente la pintura y donarla al estado francés nunca se realizaron. ¿De dónde venimos? se desplazó entre galerías y colecciones privadas en Francia y Noruega hasta que el Museo de Bellas Artes, Boston, la adquirió en 1936.
1. “La sabiduría de Paul Gauguin—Artista”, International Studio, volumen 73, número 291, 69.
## Gauguin y Laval en Martinica
por
Cuando piensas en Paul Gauguin, probablemente pienses en visiones exotizadas del Pacífico Sur o escenas coloridas del campo bretón. Lo que más probablemente no pienses de inmediato es en el Caribe. No obstante, antes de pintar obras famosas como Visión tras el Sermón y Espíritu de los Muertos Watching, el artista pasó varios meses en Martinica, posesión francesa en las Antillas Menores. Mientras estaba en la isla, Gauguin pintó numerosas obras que retratan a Martinica como un exuberante paisaje lleno de mujeres locales y frutas tropicales. Estas coloridas obras proporcionan un vínculo inesperado con el arte caribeño y pueden servir como estudio de caso en la historia de los viajes y representaciones de Martinica en el siglo XIX.
### De Panamá a Martinica
El viaje de Gauguin comenzó el 10 de abril de 1887, cuando él y su amigo Charles Laval abordaron el barco de vapor Canadá rumbo a Panamá. Ambos eran artistas que buscaban algo nuevo, más allá de lo que veían como las limitaciones de la vida moderna en Francia. Gauguin, cuyas finanzas se estaban agotando, estaba particularmente harto de la vida en París, a la que llamó “un desierto para un hombre pobre” [1].
En Panamá, la pareja esperaba encontrar un empleo que les ofreciera nuevos horizontes en los que crear. Desafortunadamente, Panamá no coincidió con sus expectativas idealistas: el paisaje había sido drásticamente alterado por la construcción del Canal de Panamá, la enfermedad era desenfrenada y el trabajo estable era difícil de encontrar. Después de muchas semanas difíciles, Gauguin y Laval salieron de Panamá hacia Martinica con la esperanza de encontrar más condiciones ideales. Llegaron el 11 de junio de 1887 y rentaron una choza en una plantación de azúcar, cerca de la capital cultural y económica de la isla, Saint-Pierre.
### Personas, frutas y paisajes
A pesar de que estaban cerca de la ciudad, los dos artistas se enfocaron en el paisaje tropical, como se ve en The Mango Trees de Gauguin, Martinica. Aquí, Gauguin representa a un grupo de mujeres recogiendo frutos en un bosque de árboles. Gauguin utiliza trazos cortos y diferentes tonos de verde y naranja para pintar la vegetación tropical que incluye un árbol de papaya reconocible en primer plano izquierdo. Las mujeres visten ropa tradicional: vestidos largos, sueltos o faldas, collares con cuentas y pañuelos de madras.
Todas las cifras de la escena son de ascendencia africana, reflejando un importante grupo demográfico en la isla. Al igual que muchas islas del Caribe, Martinica estaba conformada por una economía de plantaciones alimentada por el trabajo forzoso de personas que fueron secuestradas y transportadas desde África durante la trata transatlántica de esclavos. Aunque la esclavitud fue abolida en 1848, los descendientes de personas esclavizadas formaron una gran parte de la clase obrera de la isla, incluidos los trabajadores de las plantaciones, que trabajaban junto a los recién llegados de África y Asia en condiciones a menudo miserables.
Cerca del centro de la composición, una mujer balancea una canasta sobre su cabeza, práctica que fascinó a quienes visitaban el Caribe. En Martinica, las mujeres que transportaban mercancías del campo a los mercados de esta manera eran conocidas como porteusas. Estas mujeres fueron un tema popular para artistas y escritores que viajaban a Martinica, entre ellos Gauguin y Laval. Por donde vivían, los artistas habrían visto a muchas mujeres locales recogiendo frutas o pasando en su camino a Saint-Pierre.
Mujeres junto al mar de Charles Laval también muestra a un grupo de porteos caminando por la costa. Al igual que en The Mango Trees, las mujeres de la escena visten vestidos tradicionales, faldas y pañuelos en la cabeza. En lugar de una arboleda de árboles, Laval ofrece una vista clara de la Bahía de Saint-Pierre con el volcán Monte Pelée elevándose en la distancia. Laval también construye su composición utilizando trazos direccionales de pintura, pero anima sus figuras de una manera más dramática. La porteusa de la izquierda extiende su antebrazo y dedos, mientras que su bandeja de frutas se dobla bajo su propio peso, lo que contrasta con las pacíficas figuras de Gauguin.
Un elemento común en la obra de Gauguin y Laval en Martinica es la representación de mujeres afrocaribeñas trabajadoras, notablemente porteuse s. Aunque ciertamente formaban parte de la Martinica contemporánea, ambos artistas las favorecieron abrumadoramente en sus pinturas. Un catálogo de exhibición reciente señaló que los artistas crearon una visión de una isla habitada casi en su totalidad por porteos. [2]
Las imágenes de estas figuras fueron populares mucho antes de que llegaran Gauguin y Laval. Los pintores de los siglos XVIII y XIX representaban porteos en animados paisajes urbanos y como personal (pequeñas figuras incluidas en pinturas de paisajes, a menudo para marcar escala) en pintorescas vistas para los clientes locales de élite y el público en Francia. En la segunda mitad del siglo XIX, los libros y revistas de viajes caribeños presentaban imágenes de porteuses en sus ilustraciones, las cuales fueron vistas por miles de lectores en Francia y Estados Unidos. Two Years in the French West Indies (publicado en 1890) del escritor estadounidense de viajes Lafcadio Hearn incluyó un capítulo completo sobre porteuses, que presentaba una ilustración grabada. Al igual que las figuras representadas por Gauguin y Laval, la mujer descalza viste un vestido suelto, largo, turbante madras, y balancea una bandeja en la cabeza.
La popularidad de los porteos puede deberse a la naturaleza poco familiar y aparentemente idealizada de su trabajo. Aunque en realidad viajaban decenas de kilómetros por senderos montañosos con cargas pesadas en la cabeza, los porteos podían ser vistos como trabajadores independientes en armonía con la naturaleza, posiblemente realzados por los animales en las composiciones. En comparación con las representaciones de trabajos sobre plantaciones de azúcar, que por cierto están ausentes en gran parte de las imágenes que representan a Martinica, los porteos ofrecieron un tema femenino que complacería al público y lanzaría a la isla como un idilio exótico.
### Gauguin, Laval y las convenciones de representar a Martinica
Si bien Gauguin y Laval se adhirieron a ciertas convenciones de representar a Martinica, su obra también destaca. Los artistas eligieron centrarse exclusivamente en el pueblo afro-martiniquano. Muchas pinturas, fotografías y grabados enfatizaron la diversidad étnica en la isla, especialmente los diferentes tonos de tono de piel. Los libros ilustrados a menudo presentaban imágenes de diferentes “tipos étnicos” (en su mayoría femeninos), desde negrezas de piel oscura hasta mulâtress de piel clara (tenga en cuenta que estos términos tienen connotaciones despectivas en inglés, pero son más descriptivos, aunque aún problemáticos, en un Contexto francés caribeño). En contraste, Gauguin y Laval evitaron en gran medida la representación de diferentes “tipos” raciales y representaron una población exclusivamente de piel oscura. Tanto si se trataba de una elección consciente como por otra razón, las figuras de los artistas van más allá de la tradición del escaparate étnico.
Si bien la elección de Gauguin para centrarse en las mujeres no es sorprendente, el hecho de que las figuras no estén descaradamente erotizadas también es significativo, dada la reputación del artista. A diferencia del descanso, figuras desnudas que Gauguin pintó más tarde en Tahití, las figuras martiniquanas están completamente vestidas, mujeres trabajadoras. En las pinturas paisajísticas de Martinica, parecen habitar una Arcadia tropical que también son escenas de género que representan trabajo y descanso.
### Conclusión
El viaje de Gauguin y Laval a Martinica es un capítulo menos conocido en la historia de la pintura francesa del siglo XIX que conecta con las colonias caribeñas del país. Al igual que muchos artistas que viajaron a Martinica, los dos artistas representaban porteos y exuberantes paisajes tropicales. Sin embargo, destaca el estilo único de sus obras, así como su enfoque casi exclusivo en las figuras afrocaribeñas. Si bien es probable que Gauguin siga siendo recordado por sus coloridas (y cada vez más problematizadas) vistas del Pacífico, tal vez la próxima vez que escuches su nombre pensarás en una pequeña isla francesa en el Caribe.
### Notas:
1. Paul Gauguin, Cartas a su esposa y amigos, ed. Maurice Malingue, trans. Henry J. Stenning (Boston: MFA Publications, 2003), p. 75.
2. Joost van der Hoeven, “Martinica Experimentado”, Gauguin y Laval en Martinica (Bussum: Thoth Publishers, 2018), p. 68.
“Gauguin y Laval en Martinica”, Museo Van Gogh
Maite van Dijk, Joost van der Hoeven, et al. Gauguin y Laval en Martinica (Bussum: Thoth Publishers, 2018).
Paul Gauguin, Cartas a su esposa y amigos, ed. Maurice Malingue, trans. Henry J. Stenning (Boston: Publicaciones MFA, 2003).
Lafcadio Hearn, Dos años en las Indias Occidentales Francesas (Nueva York: Harper & Brothers, 1890).
Kay Dian Kriz , La esclavitud, el azúcar y la cultura del refinamiento: imaginando las Indias Occidentales Británicas, 1700—1840 (New Haven: Yale University Press, 2008).
Joost van der Hoeven, “Martinica Experimentado”, Gauguin y Laval en Martinica (Bussum: Thoth Publishers, 2018), pp. 58—75.
## Paul Cézanne
### Una introducción a la pintura de Paul Cézanne
por y
Categorizar el estilo de la obra de arte de Paul Cézanne (Say-zahn) es problemático. De joven dejó su casa en Provenza en el sur de Francia para unirse a la vanguardia en París. Él también tuvo éxito. Cayó con el círculo de jóvenes pintores que rodeaban a Manet, había sido amigo de la infancia del novelista, Emile Zola, quien defendió a Manet, e incluso se mostró en la primera exposición impresionista, realizada en el estudio de Nadar en 1874.
#### Fuera de lugar en París
No obstante, Cézanne no encajaba del todo con el grupo. Mientras que muchos otros pintores de este círculo se preocupaban principalmente por los efectos de la luz y el color reflejado, Cézanne permaneció profundamente comprometida con la forma. Al sentirse fuera de lugar en París, se fue después de un período relativamente corto y regresó a su casa en Aix-en-Provence. Permanecería en su Provenza natal la mayor parte del resto de su vida. Trabajó en el semiaislamiento que le brindaba el país, pero nunca estuvo realmente fuera de contacto con los avances de la vanguardia.
#### Trabajar al aire libre, pero con un propósito diferente
Al igual que los impresionistas, a menudo trabajaba al aire libre directamente ante sus sujetos. Pero a diferencia de los impresionistas, Cézanne utilizó el color, no como un fin en sí mismo, sino más bien como línea, como una herramienta con la que construir forma y espacio. Irónicamente, es la vanguardia parisina la que eventualmente lo buscaría. En los primeros años del siglo XX, justo al final de la vida de Cézanne, jóvenes artistas harían una peregrinación a Aix, para ver al hombre que cambiaría de pintura.
#### Influencia
Paul Cézanne suele ser considerado como uno de los pintores más influyentes de finales del siglo XIX. Pablo Picasso admitió fácilmente su gran deuda con el maestro mayor. De igual manera, Henri Matisse llamó una vez a Cézanne, “... el padre de todos nosotros”. Durante muchos años El Museo de Arte Moderno de Nueva York organizó su colección permanente para comenzar con una sala entera dedicada a la pintura de Cézanne. El Museo Metropolitano de Arte también le entrega una gran sala entera. Claramente, muchos artistas y curadores lo consideran enormemente importante.
Cézanne's bodegón con manzanas en el MoMA
Biografía del artista de Grove Art en MoMA.org
Cézanne en Provenza
Meyer Shapiro sobre Cézanne de Artchive
### Paul Cézanne, El bañista
por y
#### Una figura en el espacio
El cuadro es de un solo macho en un paisaje ambiguo. La figura es empujada hacia arriba al frente de la lona y la llena casi de arriba a abajo. Detrás de él, se define el espacio profundo, pero hay algo así como un tira y afloja visual sucediendo. Cézanne tiene, como es tradicional, definido tanto los planos de tierra cercanos como los distantes. Sin embargo, inusualmente, deja fuera el plano medio, lo que intensifica la distancia entre el frente y el fondo. El problema comienza cuando colapsa a los dos.
Observa de cerca el contorno que define el borde de la figura. No mires dentro de la línea que define los bordes de su cuerpo, mire justo afuera (vea especialmente al lado de la pierna derecha). Cézanne ha cambiado ligeramente la pincelada y el color. Al parecer, una vez terminados los antecedentes y la figura, regresó y reelaboró la parte del ambiente que rodeaba al bañista. El resultado es un cambio impar en la distancia.
#### La ruptura de la ilusión
La ilusión de profundidad que permite que nuestro ojo viaje de regreso en el espacio se rompe a medida que la pintura reelaborada parece aferrarse a la figura de primer plano. Es como si el fondo se levantara hacia adelante, sujetándose al borde del hombre como un marco.
¿Por qué Cézanne querría destruir las relaciones espaciales que ha rendido cuidadosamente? Esto suena como algo que Edouard Manet podría hacer. Al igual que Manet, es como si Cézanne quisiera que el espectador intentara dar cuenta de esta distorsión y que se involucre activamente en la imagen y su construcción.
#### Asimetría
Tales preguntas se vuelven aún más insistentes si nos fijamos en la representación de la figura. Claramente esta no es obra de Rafael ni de los refinados técnicos académicos asociados al Salón del siglo XIX. De hecho, la cifra es un desastre. Más allá de generalizarse, las partes no parecen estar juntas. Mira los brazos, por ejemplo. El izquierdo no empareja con el de la derecha. Lo mismo ocurre con el pecho y hasta la cara. Las piernas son particularmente incómodas. A pesar de que uno está adelante, sin embargo es demasiado largo en relación con el otro.
¿Qué piensa el observador cuidadoso? ¿El Museo de Arte Moderno ha cometido un terrible error? ¿Los museos de todo el mundo han entregado un precioso espacio de pared a un charlatán? Cézanne pudo dibujar con precisión cuando eligió, pero en esta instancia eligió conscientemente ignorar la tradición y representar el espacio de una manera que invita al espectador a reconocer tanto la ilusión de profundidad como el desmantelamiento de esa ilusión.
### Paul Cézanne, La cesta de las manzanas
por y
En la era neoclásica de David, la naturaleza muerta se consideraba el tipo de sujeto menos importante. Sólo artistas menores se molestaron con lo que entonces se veía como el tema más puramente decorativo y trivial de la pintura. La jerarquía de los sujetos pasó aproximadamente de los temas más importantes, históricos y religiosos (a menudo de gran escala); a retratos importantes (generalmente de escala moderada); menos importante—paisaje y género (temas de la vida común, generalmente de escala modesta); a menos importante— naturaleza muerta (generalmente pequeña lienzos).
#### Un sujeto sin esperanza
Había habido una excepción histórica significativa. En el siglo XVII en el norte de Europa y particularmente en los Países Bajos, floreció la naturaleza muerta. Pero este periodo fue breve y tuvo poco impacto en Francia aparte de la obra de Chardin. Entonces, ¿por qué Cézanne recurriría tan a menudo a este tema desacreditado?
Fue el hecho mismo de que la naturaleza muerta estaba tan descuidada que parece haber atraído a Cézanne hacia ella. Tan anticuada estaba la iconografía (formas simbólicas y referencias) en la naturaleza muerta que este tema bastante desesperado se liberó de prácticamente toda convención. Aquí estaba un tema que ofrecía una libertad extraordinaria, una pizarra en blanco que le dio a Cézanne la oportunidad de inventar un significado sin trabas por la tradición. Y Cézanne reviviría casi sin ayuda el tema de la naturaleza muerta convirtiéndola en un tema importante para Picasso, Matisse y otros en el siglo XX.
La imagen en la parte superior de esta página parece bastante simple, una botella de vino, una canasta volcada para exponer una generosidad de fruta en su interior, un plato de lo que quizás son galletas apiladas o pequeños rollos, y un mantel tanto recogido como drapeado. Nada destacable, al menos no hasta que uno empiece a notar los errores impares en el dibujo. Mira, por ejemplo, las líneas que representan el borde cercano y lejano de la mesa. Recuerdo a un viejo alumno mío comentando a la clase: “¡Nunca lo contrataría como carpintero!” Lo que se había dado cuenta era el extraño paso de una línea que esperamos sea recta.
#### Errores intencionales
Pero eso no es todo lo que está mal. La mesa parece estar demasiado empinada a la izquierda, tanto es así que la fruta está en peligro de rodar fuera de ella. La botella se ve borrosa y las galletas son muy extrañas de hecho. Las galletas apiladas debajo de la capa superior parecen como si se vieran desde un lado, pero en el mismo momento, las dos de arriba parecen estallar hacia arriba como si las estuviéramos mirando hacia abajo. Esta es una clave importante para entender las preguntas que hasta ahora hemos planteado sobre las fotos de Cézanne.
Al igual que Edouard Manet, de quien tanto pidió prestado, Cézanne fue impulsado a repensar el valor de las diversas técnicas ilusionistas que había heredado de los maestros de las épocas renacentista y barroca. Esto se debió en parte al creciente impacto de la fotografía y su transformación de la representación moderna. Mientras Degas y Monet tomaron prestada de la cámara la fragmentación del tiempo, Cézanne vio esta segmentación mecanizada del tiempo como artificial y en desacuerdo con la percepción del ojo humano. Para la época de Cézanne, la cámara sí fragmentó el tiempo en fragmentos al igual que las cámaras no digitales que se pueden configurar para que el obturador esté abierto a la luz por solo 1/1000 de segundo.
#### Vista y memoria
Cézanne empujó esta distinción entre la visión de la cámara y de la visión humana. Razonó que los mismos temas se aplicaban al ilusionismo de los viejos maestros, de Rafael, Leonardo, Caravaggio, etc. Por ejemplo, pensar en cómo funciona la perspectiva lineal. Desde el Renacimiento temprano, la construcción de la ilusión del espacio requería que el artista permaneciera congelado en un solo punto en el espacio para mantener una recesión constante entre todos los ortogonales en retroceso. Este mirador congelado pertenece tanto al artista como al espectador. Pero, ¿es una descripción completa de la experiencia de la vista humana? El bodegón de Cézanne sugiere que no lo es.
Si un pintor renacentista se dispuso a renderizar los objetos bodegones de Cézanne (no es que lo harían, te importa), ese artista se habría colocado en un punto específico antes de la mesa y se habría esforzado mucho en renderizar la colección de objetos de mesa solo desde esa perspectiva original. Cada línea ortogonal permanecería consistente (y recta). Pero esto claramente no es lo que Cézanne tenía en mente. Su perspectiva parece confusa. Cuando miramos con atención por primera vez, puede parecer como si simplemente no pudiera dibujar, pero si pasas más tiempo, se le puede ocurrir que Cézanne está, de hecho, dibujando con cuidado, aunque según un nuevo conjunto de reglas.
Aparentemente simple, la preocupación de Cézanne por representar la verdadera experiencia de la vista tuvo enormes implicaciones para la cultura visual del siglo XX. Cézanne se dio cuenta de que a diferencia de la visión renacentista bastante simple y estática del espacio, la gente realmente ve de una manera que es más compleja, vemos tanto a través del tiempo como del espacio. En otras palabras, nos movemos como vemos. En términos contemporáneos, se podría decir que la visión humana es menos como la visión congelada de una cámara fija y más similar a la visión continua de una cámara de video excepto que trabajó con óleo sobre lienzo que se seca y se vuelve estática.
Entonces muy tentativamente, Cézanne comenzó la destrucción decidida de la imagen unificada. Vuelva a mirar las galletas, o lo que sean, apiladas sobre el plato en la parte superior derecha. ¿Es posible que los suaves desacuerdos que notamos resulten de la representación de dos puntos de vista ligeramente diferentes? No se trata de grandes rupturas, sino que sugieren un descubrimiento cuidadoso y tentativo. Es como si Cézanne simplemente hubiera representado las galletas de fondo mientras las miraba de otro lado y luego mientras miraba más ligeramente hacia abajo a las galletas superiores después de desplazar su peso a su pierna delantera. Además, no estoy seguro de que estuviera tan orgulloso de estos descansos que permiten más de una sola perspectiva. Mira, por ejemplo, en los puntos donde la mesa debe romperse para expresar estas múltiples perspectivas y notarás que cada una de ellas está oculta a la vista. Sin embargo, al hacer esto, Cézanne cambió la dirección de la pintura.
Esta pintura en el Instituto de Arte de Chicago
Gira de bodegones desde la Galería Nacional de Arte
Selección en La canasta de manzanas de Richard Brettell, Post Impresionistas. Chicago (1987, p. 67
### Paul Cézanne, bodegón con yeso Cupido
por , y
Video$$\PageIndex{10}$$: Paul Cézanne, Bodegón con Cupido de yeso, c.1895, óleo sobre lienzo (Courtauld Gallery, Londres)
#### René Descartes
Quiero plantear aquí la filosofía cartesiana. La palabra está en mayúscula porque se refiere a la filosofía del pensador proto-iluminación René Descartes. Aunque nunca hayas oído hablar de este gran racionalista, es probable que reconozcas una de sus frases como “pienso, por lo tanto, lo soy”. Esta extraña frase es el resultado de su esfuerzo por encontrar pruebas irrefutables de que realmente existía. Los filósofos a menudo hacen preguntas que están destinadas a revelar verdades fundamentales. ¿Te imaginas por un momento haciéndote esta misma pregunta: ¿cómo puedo probar realmente que existo? Descartes realizó una solución elegante, su propia capacidad para hacer la pregunta era la prueba de la conciencia independiente y por tanto, de su existencia.
Con tales preguntas, Descartes planteó muchas consideraciones que darían forma al mundo moderno. A veces estas preguntas planteaban, a su vez, conclusiones aparentemente contrarias entre sí, como su escepticismo tanto de la percepción como de la suposición evidente
#### Conocimiento objetivo y subjetivo
Irónicamente, tales pensamientos conducirían eventualmente a una reevaluación de nuestra confianza en el empirismo científico de la sociedad. El empirismo se basa en la objetividad. Recordarás que la palabra “objetivo” significa una verdad que está más allá de la experiencia personal. En contraste, la palabra “subjetiva” está directamente ligada a la experiencia personal.
Aquí hay un ejemplo. Imagina un accidente menor entre un taxi y un autobús urbano. Un patrullero viene a reconstruir el evento. ¿Sólo le pregunta al taxista qué ocurrió o también le pregunta al pasajero en la parte trasera de la cabina y al chofer del autobús y a los pasajeros del autobús? El objetivo del policía es reconstruir lo que “en realidad” sucedió. Pero si tomamos una posición poscartesiana podríamos preguntarnos si realmente hubo un solo evento real (objetivo) o si en realidad había múltiples verdades (subjetivas), cada una resultado de la perspectiva de cada testigo. Tomemos un ejemplo más directamente aplicable. Mira sobre la habitación en la que te encuentras actualmente. Probablemente tiene seis lados: cuatro paredes, un piso y un techo. Cuando un arquitecto dibujó un diagrama de su habitación, habría salido conceptualmente del espacio para que se pudiera entender en total.
Pero, ¿esta visión objetiva es falsa? Ahora en la sala construida, no se puede ver su totalidad en un solo momento. Solo podemos ver pedazos de la habitación en cualquier momento y debemos confiar en la memoria para entender la habitación como un todo. Su experiencia más subjetiva históricamente ha sido considerada menos importante que la concepción objetiva del arquitecto aunque experimente directamente y el arquitecto conozca la habitación solo teóricamente.
#### Cézanne y la experiencia subjetiva
En cuanto a la tradicional relación jerárquica entre objetivo y subjetivo, Cézanne parece preguntar, “¿cuál es más cierto?” y su conclusión refleja un importante desarrollo del modernismo. En Bodegón con Cupido de Yeso, es la visión subjetiva la que construye el espacio. Cézanne ha colocado un yeso (copia) de una antigua escultura romana de un cupido (el hijo de Venus) sobre una mesa para que domine la composición.
Claramente este no es el espacio objetivo del arquitecto. Cézanne ha buscado claramente que la percepción del espacio coincida con el movimiento del cuerpo. Pero, ¿no es eso lo que realmente experimentamos? Cuando entras en una habitación, ¿ves la habitación como un todo objetivo? No. Sólo podemos ver un fragmento a la vez. Pero como ya lo hemos establecido, en realidad no vemos en fragmentos; vemos continuamente y el espacio está conformado por nuestro continuo movimiento a través de él. Pruébalo. Enfócate en cualquier línea recta de la habitación en la que te encuentres ahora. Inclinarse hacia adelante, y como cabría esperar, los ángulos de la habitación cambian. En Bodegón con Cupido de Yeso, vemos el intento de Cézanne de hacer verdadera visión humana, visión subjetiva, continua e informada por la memoria.
### Paul Cézanne, La Roca Roja
por y
Video$$\PageIndex{11}$$: Paul Cézanne, La roca roja, c. 1895, óleo sobre lienzo, 91 x 66 cm (Musée de l'Orangerie, París)
### Paul Cézanne, camino de giro en Montgeroult
por y
Aquí hay una pintura recientemente adquirida por El Museo de Arte Moderno. Fue considerado uno de los pocos grandes lienzos de Cézanne aún en una colección privada. Fue entregado al museo por el señor y la señora John Hay Whitney junto con otras seis obras maestras de van Gogh, Matisse y Picasso. Algún regalo. Aún así, la pintura es un poco difícil de entender. Al principio, la estructura del espacio es sencilla. Como era de esperar, hay un primer plano (el follaje verde en el fondo), un terreno medio (la carretera y las casas) y una zona de profunda recesión (el cielo).
#### Distorsión espacial
Cada una de estas zonas se define en gran medida por el color; verde para los arbustos de frente, un ocre cálido para el plano medio (carretera y casas), y azul para el cielo. Es aquí donde Cézanne comienza a hacer trucos. Habiendo rechazado la clara perspectiva lineal o atmosférica como un medio para construir la ilusión recesiva, Cézanne se basa en las pistas proporcionadas por la escala, la superposición y el color. Sin embargo, por todo esto, el espacio en Turning Road en Montgeroult parece incómodo.
Aun cuando vemos las tres zonas del espacio en relación entre sí, la pintura parece extrañamente plana, como si el cielo se arrastrara hacia adelante y el primer plano se empujara hacia atrás. Por supuesto que todavía vemos la ilusión, pero aún cuando vemos el espacio en el que insiste la línea de Cézanne, la pintura se parece demasiado a tres planos planos descansando uno encima del otro y la pintura comienza a recordarnos que es, de hecho, una cortina vertical.
Hay dos medios por los que Cézanne ha saboteado el espacio de este lienzo (desafortunadamente el efecto está silenciado en la reproducción y más aún en la pantalla de la computadora, así que confía en mí en esto). El primero es la pincelada. En un paisaje del Viejo Maestro, el mayor detalle y la pincelada más delicada existen en primer plano. Los movimientos del pincel se hacen más amplios y generalizados a medida que el espacio retrocede. Aquí, sin embargo, el artista ha tratado todo el lienzo con un nivel consistente de claridad, o falta allí de, nivelando el sentido de cerca y lejos.
En segundo lugar, Cézanne ha entendido el potencial del color, a diferencia del claroscuro y la perspectiva lineal para estructurar o desestabilizar el espacio. ¿Te has dado cuenta de que en medio del cielo, justo a la izquierda del campanario de la iglesia y del árbol, hay una pequeña mancha de pintura marrón? Es el mismo ocre utilizado para renderizar las sombras en la carretera y en los tejados. ¿Qué es esto? ¿Alguna vez has visto una densa mancha marrón que acaba de flotar en el cielo? No lo creo.
#### Errores a propósito
Entonces, ¿qué somos como espectador para hacer de ello? ¿Es un error? ¿Era Cézanne un viejo punteante para 1898, quien accidentalmente golpeó la lona cuando sus brazos se agitaban y luego era demasiado vago para borrarlo y volver a pintar esa sección? No. Entonces, ¿qué es entonces? Bueno, cuando miras la mancha ocre, ¿qué pasa con el espacio profundo del cielo? ¿Te das cuenta de cómo la mancha ocre se niega a sentarse en el espacio profundo sino que empuja hacia adelante hacia el plano medio de las casas?
Cuando se ve en persona, la pintura marrón que cuelga en el cielo en realidad trae consigo el cielo, negando por completo la ilusión del espacio profundo. También, tenga en cuenta los brillantes azules celestes en los arbustos de primer plano. Así como la mancha ocre en el cielo obliga al cielo hacia adelante, así los claros azules que extrañamente aparecen al alcance del espectador, hacen agujeros en la solidez del primer plano. El marrón en la espalda empuja hacia adelante y el azul en el frente empuja hacia atrás. El resultado es un aplanamiento del espacio o quizás una expresión más honesta de la verdadera planitud del lienzo.
Esta pintura en el MoMA
Esta pintura en el Google Art Project
### Paul Cézanne, Mont Sainte-Victoire
por Dr. BEN HARVEY
Video$$\PageIndex{12}$$: Paul Cézanne, Mont Sainte-Victoire, 1902-04, óleo sobre lienzo, 73 x 91.9 cm (Philadelphia Museum of Art)
Ponentes: Dr. Steven Zucker y Dra. Beth Harris
Puede ser difícil estimar, a simple vista, qué tan lejos se encuentra una montaña. Un pico puede dominar un paisaje y llamar nuestra atención, llenando nuestros ojos y nuestra mente. Sin embargo, puede ser una especie de shock descubrir que una característica natural tan prominente todavía puede estar a una larga distancia de nosotros.
#### Una montaña
Con 3317 pies (1011 metros) de altura, el pico de piedra caliza del Mont Sainte-Victoire es un pigmy comparado con los gigantes de, digamos, el monte Fuji y el Monte Rainier. Pero, como ellos, sigue ejerciendo una presencia imponente sobre el país que lo rodea y, en particular, sobre Aix-en-Provence, la ciudad natal de Paul Cézanne. Gracias a sus muchas pinturas al óleo y acuarelas de la montaña, el pintor se ha asociado indeleblemente a ella. Piense en Cézanne y sus bodegones y paisajes vienen a la mente, sus manzanas y sus representaciones del Mont Sainte-Victoire.
Empapada de siglos de historia y folclore, tanto clásica como cristiana, la montaña —o, más exactamente, la cordillera— solo emergió gradualmente como un tema importante en la obra de Cézanne. En la década de 1870, lo incluyó en un paisaje llamado The Railway Cutting, 1870 (Neue Pinakothek, Munich) y unos años después apareció detrás de las figuras monumentales de sus Bathers at Rest, 1876-77 (The Barnes Foundation, Filadelfia), que se incluyó en la Tercera Exposición Impresionista de 1877. Pero no fue hasta principios de la siguiente década, mucho después de su adopción del Impresionismo, que comenzó a presentar consistentemente la montaña en sus paisajes. Escribiendo en 1885, Paul Gauguin probablemente estaba pensando en Mont Sainte-Victoire cuando imaginó que Cézanne pasaba “días enteros en las montañas leyendo a Virgilio y mirando al cielo”. “Por lo tanto”, continuó Gauguin, “sus horizontes son altos, su blues muy intenso, y el rojo en su obra tiene una vitalidad asombrosa”. La leyenda de Cézanne comenzaba a emerger y una montaña la atravesaba.
#### Serie A
Cézanne volvería al motivo del Mont Sainte-Victoire a lo largo del resto de su carrera, resultando en una serie de obras increíblemente variada. Muestran la montaña desde muchos puntos de vista diferentes y a menudo en relación con un elenco en constante cambio de otros elementos (árboles y arbustos de primer plano, edificios y puentes, campos y canteras). De esta serie podemos extraer un subgrupo de más de dos docenas de pinturas y acuarelas. Estos paisajes, que datan de los últimos años de la vida del artista, presentan un lirismo intensificado y, más prosaicamente, un punto de vista consistente. Muestran la montaña como se puede apreciar desde el cerro de Les Lauves, ubicado justo al norte de Aix.
#### A un paseo del estudio
Cézanne compró un acre de terreno en este cerro en 1901 y a finales del año siguiente había construido un estudio sobre él. A partir de aquí, caminaría más cuesta arriba hasta un lugar que ofrecía una vista panorámica del Mont Sainte-Victoire y el terreno que le precedía. El pintor Emile Bernard recordó acompañar a Cézanne en este mismo paseo:
Cézanne recogió una caja en el pasillo [de su estudio] y me llevó a su motivo. Estaba a dos kilómetros de distancia con una vista sobre un valle al pie de Sainte-Victoire, la escarpada montaña que nunca dejó de pintar [...]. Estaba lleno de admiración por esta montaña.
Cézanne cultivó conscientemente su asociación con la montaña y tal vez incluso quiso ser documentado pintándola. Cuando visitaron Aix en 1906, los artistas Maurice Denis y Ker-Xavier Roussel se encontraron siendo conducidos a la misma ubicación. En una pintura al óleo de Denis y en algunas de las fotografías de Roussel, vemos a Cézanne de pie ante su caballete y pintando la montaña. ¡Otra vez! Fue la vista que podemos ver en la mayoría de las vistas tardías de Cézanne del Mont Sainte-Victoire, incluida la pintura que nos ocupa aquí, que ahora se encuentra en el Museo de Arte de Filadelfia.
En esta obra, Cézanne divide su composición en tres secciones horizontales aproximadamente iguales, que se extienden a través del lienzo de tres pies de ancho. Nuestro punto de vista es elevado. Lo más cercano a nosotros se encuentra una banda de follaje y casas; a continuación, ásperas manchas de ocre amarillo, esmeralda y verde viridiano sugieren el mosaico de una llanura expansiva y extienden el esquema de color del primer plano hacia el medio; y arriba, en azules, violetas y grises contrastantes, vemos la “montaña escarpada” rodeada por el cielo. Los azules que se ven en esta sección también acentúan el resto de la obra mientras que, a la inversa, los toques de verde animan el cielo y la montaña.
#### Ajustes sutiles
Es decir, Cézanne introdujo ajustes sutiles para evitar un esquema demasiado simple. Por lo que el pico de la montaña se empuja justo a la derecha del centro, y la línea del horizonte se inclina suavemente hacia arriba de izquierda a derecha. De hecho, se puede encontrar un complicado contrapunto de diagonales en cada una de las bandas de la obra, en los tejados de las casas, en las líneas de la montaña, y en la disposición de los parches en la llanura, que conectan primer plano con fondo y conducen el ojo hacia atrás.
Cézanne evoca una escena profunda, panorámica y la atmósfera que llena y unifica este espacio. Pero es absolutamente característico de su arte que también permanezcamos agudamente conscientes de la pintura como una superficie bastante rugosa, aunque hábilmente, trabajada. La planitud convive con la profundidad y nos encontramos atrapados entre estos dos polos, ahora más conscientes de uno, ahora del otro. El paisaje montañoso está a nuestro alcance, pero muy lejos.
#### Una comparación
Comparar el lienzo de Filadelfia con algunas de las otras vistas de Cézanne del Mont Sainte-Victoire y con fotos de la zona puede ayudarnos a comprender algunas de las sutilezas perceptivas y desafíos de la obra. Toma el lado izquierdo de la montaña. Aunque el contorno más externo es inmediatamente evidente, dentro de él también se puede discernir una segunda línea (o, más exactamente, una serie de líneas y aristas). Los dos convergen apenas tímidos de la cima de la montaña. El área entre este contorno exterior y la línea o cresta interior delimita un plano espacial distintivo; esta pendiente se aleja de nosotros y se conecta con la cordillera más grande que se encuentra detrás de la cara escarpada. Atiende a esta zona, y la montaña parece ganar volumen. Se convierte menos en un triángulo irregular y más en una pirámide complicada.
O vuelve a mirar el foco de interés más obvio de la pintura, la cima de la montaña. Otras obras de Cézanne muestran que la montaña tiene una especie de pico doble, con un punto ligeramente más alto al lado izquierdo y uno inferior a la derecha. A primera vista, el lienzo de Filadelfia parece contradecir esto: el ápice truncado de la montaña parece elevarse ligeramente de izquierda a derecha. Pero una mirada más cercana revela que Cézanne sí respeta la topografía. El pequeño parche triangular de gris claro —en realidad el cebado del lienzo— puede leerse como perteneciente al espacio inmediatamente encima de la montaña o tal vez como una nube detrás de ella. Así son las pinceladas gris y azul claro inmediatamente debajo de este parche las que describen la inclinación hacia abajo de la cima de la montaña.
Curiosamente, en un aspecto, nuestro punto de vista en realidad es un poco engañoso. A una elevación de 3104 pies (946 metros), el pico izquierdo no es el punto más alto, sino que simplemente aparece a partir de Les Lauves. Una enorme cruz de hierro, la croix de Provence, se erigió en este lugar a principios de la década de 1870, la cuarta que se colocó allí. Aunque visible desde lejos, la cruz no aparece en ninguna de las representaciones de Cézanne de la montaña.
Cézanne presumiblemente había estado en esta cumbre, o en estas cumbres, varias veces. Había explorado a fondo el campo alrededor de Aix, primero durante las divagaciones juveniles con sus amigos y más tarde como artista al aire libre en busca de motivos. Y sabemos con certeza que había subido a la cima de la montaña tan recientemente como 1895. Armado con estas experiencias, podría haber estimado la distancia desde Les Lauves hasta la cima del Mont Sainte-Victoire con cierta precisión, es de unas diez millas (16 kilómetros) a medida que vuela el cuervo.
Cuando se paró en la montaña en 1895 Cézanne había entrado, por así decirlo, en uno de sus propios paisajes. Al estar ahí parado, tal vez hizo una pausa para recordar algunas de las pinturas del Mont Sainte-Victoire que ya había realizado. Pero, para volver al idioma de Gauguin, ¿podría haber soñado con las obras que pasaría a pintar en la siguiente década, obras como el paisaje de Filadelfia, con su horizonte alto, blues intenso y una vitalidad asombrosa?
### Paul Cézanne, Los jugadores de cartas
por Dr. BEN HARVEY
#### Una nueva dirección
Escribiendo cerca del final de su vida, Paul Cézanne dijo a un crítico de arte que “uno no se pone en lugar del pasado, uno solo agrega un nuevo vínculo” [1] Es decir, a través de su arte quiso involucrarse con la historia del arte sino también modificarla y llevarla en una nueva dirección. Es un sentimiento bellamente ejemplificado en las cinco pinturas del artista de jugadores de cartas, en las que había trabajado aproximadamente una década antes, a principios y mediados de la década de 1890.
En cuanto a su temática, la serie debe una clara deuda con representaciones anteriores de jugadores de cartas y juegos de artistas barrocos y rococó como Caravaggio (arriba), de la Tour, los hermanos Le Nain y Chardin; dentro de Cézanne propia vida, el tema había sido retomado de nuevo por Daumier, Meissonier, Degas y Caillebotte.
El “nuevo vínculo” de Cézanne radica en la manera en que aleja al tema de su evidente potencial simbólico y dramático: tréboles y corazones, ganadores y perdedores, los tramposos y los engañados. Todo esto ya había sido explorado a fondo. En cambio, Cézanne atiende otros aspectos de la actividad. Destaca el espacio social compartido del juego de cartas, íntimo y familiar, y la atención y concentración que exige el juego. No casualmente, estos son los mismos estados psicológicos que demandan los actos de hacer y mirar el arte.
#### La versión en el Met
La versión de los jugadores de cartas en el Museo Metropolitano de Arte (imagen en la parte superior de la página) ahora generalmente se piensa que es la primera de las cinco pinturas de la serie. Representa figuras algo excéntricamente proporcionadas que rodean una mesa: tres cartas de juego y una cuarta se limita a observar el juego, su pipa indicativa de su actitud contemplativa. Se trata de trabajadores rurales tranquila y sociablemente que pasan el tiempo en una taberna o habitación. Al igual que las otras obras de la serie, el escenario en el lienzo del Met es escaso. Vemos una mesa y tres sillas (dos de ellas más implícitas de lo que se describen completamente); una rejilla completa y un trozo de tela amarilla cuelgan de la pared trasera de la habitación. El tablero de la mesa crea un claro foco de atención dentro de la obra más grande. Apoya los brazos y manos de los jugadores, que a su vez proporcionan un marco para algunos objetos: una pipa, tarjetas y un prominente rectángulo gris, tal vez una bolsa de tabaco u otra carta.
Si bien esta habría sido una escena familiar para Cézanne, no deberíamos imaginarlo montando su caballete frente a un verdadero juego de cartas. En cambio, las obras preparatorias sobrevivientes del artista indican que estudió sus figuras de forma independiente, una a una, y luego incorporó estos estudios a sus composiciones multifiguras. Cézanne realizó estudios al óleo para dos de las figuras de la pintura del Met (ver arriba para un ejemplo), y ambos modelos han sido identificados como manos de granja que trabajaban en la finca de la familia Cézanne cerca de Aix-en-Provence, las Jas de Bouffan. Aun cuando comparten el mismo espacio, las figuras de Cézanne conservan un sentido de independencia y autocontención. Están comprometidos, como dijo acertadamente un historiador del arte, en un juego de “solitario colectivo”.
Y sin embargo, un detalle en la pintura del Met apunta, aunque sutilmente, a una secuencia de eventos y, por lo tanto, a la lógica de un juego real. La figura a la izquierda de la obra (modelada por una Pauleta Paulin) parece estar a punto de extender su dedo índice (ver detalle abajo), como si estuviera a punto de recoger una tarjeta de la mesa. Es un gesto que conecta el pensamiento con la acción, la contemplación de una mano de cartas con el movimiento de una mano. Acciones similares, aunque más enfáticamente renderizadas, se pueden encontrar en una representación anterior de jugadores de cartas de Gustave Caillebotte (abajo), quien fue a la vez colega de Cézanne en el grupo impresionista y coleccionista de su obra.
#### Elementos formales prevalecen sobre consideraciones narrativas
La lógica particular de cualquier juego de cartas determina el valor de cualquier carta dada dentro de él, y así Caillebotte nos proporciona una pista importante en su título (El juego de Bezique) e incluso permite a su espectador discernir los colores y rangos de algunas cartas en su pintura (un as rojo, un siete negro). En contraste, el instinto de Cézanne es retener toda esa información, mantener sus tarjetas cerca de su pecho. Sobre su mesa, hay una tarjeta vuelta hacia arriba que sostiene tres parches aproximadamente rectangulares de pigmento rojo (ver detalle a continuación). Pero estos parches no se parecen mucho a los diamantes y, como para disminuir cualquier parecido, la tarjeta también contiene parches similares de pintura blanca y azulada.
El tricolor de colores se recoge en otra parte de la composición, en el azul de la ropa de los trabajadores, el blanco de sus pipas y camisas, y en el rojo del cravat del hombre de pie (izquierda). Con sus vívidas combinaciones de colores y formas planas, los naipes pueden incluso haber tenido un significado estético para Cézanne, sugiriendo un modelo para su propia práctica. Ya en 1876, le contó a Camille Pissarro sobre un motivo de paisaje en el que estaba trabajando: “Es como una carta de juego”, escribió. “Techos rojos sobre el mar azul”. [2]
Para Cézanne, los elementos formales (color, forma, textura, composición) finalmente superaron las consideraciones narrativas. Las marcas que vemos en la tarjeta crean una cuadrícula de elementos compositivos, y esto coloca la carta en relación con dos cuadrículas análogas. El primero consiste en la colección más grande de objetos sobre la mesa, donde los objetos y los espacios entre ellos forman una especie de patrón tic-tac-toe. El segundo está conformado por las propias cuatro figuras, cada una de las cuales ocupa una de tres zonas espaciales distintas (primer plano, medio, fondo) así como una de tres posiciones laterales diferentes (izquierda, centro, derecha).
Esta conexión entre objetos y figuras es aún más evidente en la obra más grande de la serie de jugadores de cartas ahora en la Colección Barnes en Filadelfia (ver abajo), que Cézanne probablemente hizo poco después de la pintura del Met. Al agregar una quinta figura en la parte posterior derecha, las figuras ahora repiten el esquema X formado por los objetos sobre la mesa.
#### Otras obras de esta serie
Las tres obras restantes de la serie (Galería Courtauld —ver más abajo, Musée d'Orsay, y una colección privada) contienen solo dos jugadores de cartas enfrentándose entre sí en estricto perfil, una idea compositiva que apareció por primera vez en las dos figuras de primer plano de la obra del Met. En estas pinturas posteriores, la mesa es más estrecha y limpia de todos los objetos, a excepción de una botella de vino colocada en el centro. Los dos hombres estudian sus cartas con atención, pero ningún movimiento o movimiento parece inminente. Los detalles del juego han retrocedido aún más y la vida se ha calmado. Los jugadores de cartas de Cézanne, como muchas de sus figuras, ocupan un espacio en algún lugar entre la pintura de figuras y la pintura de objetos. Se desplazan entre diferentes géneros.
Una caricatura neoyorquina explota esta deriva hacia un efecto humorístico. En él, Robert Mankoff permite que los elementos de bodegones y los detalles del juego vuelvan a inundarse en una de las obras de dos figuras del artista. Llena los brazos y la mesa de los jugadores de cartas con montones de manzanas, recordándonos la estrecha asociación de Cézanne con la fruta. “Veo a tu abuela Smith”, corre el pie de foto, “y te crio un Golden Delicious” (ver imagen aquí) Las famosas manzanas de Cézanne son ahora de un tipo específico, como si fueran directamente de un supermercado. Sus cifras ahora no son solo cara de póquer: son jugadores de póquer.
Aunque no parece haber dinero en juego en los juegos de cartas de Cézanne, el comercio estuvo ciertamente involucrado en la creación de la pieza. Para la década de 1890, Cézanne era rico independientemente; podía permitirse pagar cómodamente a sus modelos para que posaran y las obras resultantes estaban hechas de pigmentos producidos industrialmente generalmente aplicados a lienzos de tamaño estándar fabricados comercialmente (un “no. 25” en el caso de la obra del Met). Casi al mismo tiempo que terminó la serie, el artista entabló una relación con un marchante parisino, Ambroise Vollard, quien luego se convirtió en la primera dueña del lienzo del Met. Los libros de registro de negocios de Vollard registran que obtuvo una ganancia ordenada de la obra, comprándola por 250 francos y, a principios de 1900, vendiéndola por 4,500. Sin embargo, el atractivo perdurable de los jugadores de cartas de Cézanne puede deber algo a la forma en que las cinco pinturas proporcionan un claro contraste con el capitalismo moderno que rodeó su creación. Si la vida puede parecer cada vez más rápida, superficial y mercenaria, entonces quizás se pueda encontrar algo de consuelo aquí, en nuestro compromiso prolongado con lienzos hechos a mano que muestran un pasatiempo atemporal, arraigado y sociable.
[1] Carta a Roger Marx, 23 de enero de 1905, citada en John Reward (editor), Paul Cézanne, Letters (Da Capo Press, 1995), p. 313.
[2] Carta a Camille Pissarro, 2 de julio de 1876, citada en John Reward (editor), Paul Cézanne, Letters (Da Capo Press, 1995), p.146.
### Paul Cézanne, Bañistas (Les Grandes Baigneuses)
por y
Video$$\PageIndex{13}$$: Paul Cézanne, Bañistas (Les Grandes Baigneuses), c. 1894-1905, óleo sobre lienzo, 127.2 x 196.1 cm (The National Gallery, Londres)
### Paul Cézanne, Los grandes bañistas
por y
Video$$\PageIndex{14}$$: Paul Cézanne, Los grandes bañistas, 1906, óleo sobre lienzo, 82-7/8 x 98-3/4″/210.5 x 250.8 cm (Philadelphia Museum of Art)
## ¿Por qué esta mujer en la selva? El sueño de Henri Rousseau
por
Video$$\PageIndex{15}$$
El artista Henri Rousseau pintó El sueño en 1910, y su imaginería de una mujer descansando en un sofá en medio de una jungla era tan surrealista entonces como lo es hoy. ¿Qué tiene esta obra de arte que cautivó al público entonces y ahora?
## Henri de Toulouse-Lautrec, en el Moulin Rouge
por y
Video$$\PageIndex{16}$$: Henri de Toulouse-Lautrec, Al Moulin Rouge, 1893-95, óleo sobre lienzo, 48-1/2 x 55-1/2 pulgadas (123 x 141 cm) (Instituto de Arte de Chicago)
### Imágenes Smarthistory para la enseñanza y el aprendizaje:
8.8: Posimpresionismo is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts. | 38,119 | 135,999 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2024-26 | latest | en | 0.191124 |
http://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-7-section-7-3-adding-and-subtracting-rational-expressions-with-the-same-denominator-and-least-common-denominator-exercise-set-page-508/49 | 1,524,173,251,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937045.30/warc/CC-MAIN-20180419204415-20180419224415-00017.warc.gz | 428,760,342 | 14,464 | ## Algebra: A Combined Approach (4th Edition)
$\frac{x+3}{2x-1}$
$\frac{x+3}{4}$$\div$$\frac{2x-1}{4}$= $\frac{x+3}{4}$.$\frac{4}{2x-1}$= $\frac{x+3}{2x-1}$ | 78 | 157 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.890625 | 4 | CC-MAIN-2018-17 | latest | en | 0.276848 |
https://www.creativeakademy.org/2016_06_01_archive.html | 1,521,477,774,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647003.0/warc/CC-MAIN-20180319155754-20180319175754-00301.warc.gz | 794,853,063 | 32,856 | ## Posts
Showing posts from June, 2016
### A Summary of The Corner Shop
Please find below the summary of The corner Shop. Do let me know for change, improvement anything you think. It is often said ‘The best ghost stories don’t have ghosts in them; rather, you see the result of its actions.’ For centuries readers have been attracted to the mysterious air surrounding ghosts and other supernatural beings. It is probably this sense of wonder and fear that makes ghost stories so addictive and hard to put down. An example of such a story is Cynthia Asquith’s The Corner Shop. The Corner Shop starts out as a happy story of a man, Peter Wood who discovers an antique shop filled with vintage trinkets run by two charming, young women. Upon browsing through its offerings, the man purchases a jade frog figurine at a throwaway price. Content with his purchase, Peter decides to make frequent visits to this lovely little shop. However, there is something sinister lurking behind the scenes. On the second visit to the store, Peter is in for an eerie surprise. Gone…
### 3 Commercial Unit Of Electrical Energy Physics Class 10
Th S.I. unit of energy is joul(J).
Let the power (p) of an electrical appliance = P watt
Let it is used for t seconds.
Then Electrical energy consumed (W) = P x t watt-second
i.e. W = Pt Watt-second
or W = Pt Joul (Joul is Mechanical unit equivalent of Watt-second)
In practice bigger unit like Watt-Hour (Wh) or Kilo Watt Hour (KWh) is used for Electrical energy consumption. Watt-Hour : It is the electrical unit consumed by an electrical appliance of P watt that was used for 1 hour. 1 w-hr = 1 watt x 1 hr
= 1 w x (60x60)second
=3600 watt-second
=3600 Joul
1 Whr =3600 J
Kilowatt-Hour: One kilowatt-hour is the electrical energy consumed by an electrical appliance of power rating 1 kw when it used for 1 hour.
1 KWhr = 1 kilowatt x 1 hr
= 1000 w x (60x60)second
=3.6x106 watt-second
=3.6x106 Joul
1 KWhr = 3.6x106 J
The electrical energy consumed in our houses or in industries are measured in KWhr . This is also called ! unit electrical unit consumed. The rate delared by gover…
### 2.Electrical Power and its Expression For Class 10
Electrical Power: Rate of electrical energy supplied by a source e.g. a power station or an alternator or a dc battery etc is called electrical power.
∴ Power = Electrical Energy supplied / Time
if Power = P
Energy supplied = W
and Time = T
Then P = W / T
if W is in Joul
T in second
then unit of power will be Joul/Second (J/S); which is called watt.
∴ watt = j/s
∴Electrical Power, P=W/t=V.I=V2/R=I2.R
You are requested to suggest to make this chapter explanation better. So comment please.
### Love Concern Humanity And Trust are the Eccentric Features of Mankind
Love Concern Humanity And Trust are the Eccentric Features of Mankind . Quoting examples from chapters : "The Last Leaf", Journey by Night", and "God Lives in Panch", Justify the statement . The main element which makes us differ from the rest are the qualities we possess.” Human nature is something which cannot be taught but which is self-existent. We, having an upper hand in the eco system, have something which other creatures lack. It is that object of our conscience which makes us good. Saying simply good is not enough because we are much more than being good. It is this positive quality in us, which makes us good. “The last leaf” by O Henry tells us the tale about unconditional concern which is not bounded by relationship but out of sheer care for one another. It is not only those people who are bounded by relationship care for one another but also those people who understand are not bounded but yet understand the pain of another. This chapter has taugh…
### Ohm's Law of Current Electricity Physics Class 10
Ohm's Law: It can be defined as "The potential difference (P.D.) across a conductor is proportional to the current flowing through it provided that physical conditions remain constant." If V = Potential Difference (P.D.)
I= current
Then we can write V ∝ I
Or V= I. R
R= Constant and it is known as resistance of the conductor.
It also means that
V/I = Constant(R) , If all surrounding conditions are constant.
The resistance of a conductor depends on:
1. Length of the conductor.
2. Area of cross section of the conductor.
3. Type of material of the conductor.
It is because of the type of the material different conductors have different conductance. Copper is more good conductor than iron. Similarly silver is more good conductor than copper. Conductance of silver is slightly more than copper. As silver is costlier than the copper therefore we use copper instead of silver to ignore slight advantage of conductance. 4. Temperature of the conductor.
If the temperat…
### Concept of Phrases and Clauses English Grammar for all higher Class
Concept of Phrases and Clauses are still much more confusing for students. But after going through this topic students will be more confident about phrases and clauses. Phrase: Three most basic elements of phrase are:
-Phrases are Group of words.
-Phrases Can not be used alone as it has got no complete meaning. -Phrases Has no subject and verb.
Examples:
On the hill.to read itIn the north.Have to complete the taskOn the table. Clauses: The Three most basic elements of clauses are:+Clauses are also Group of words.+Clauses Can be used alone as it makes sense by itself. +Phrases Has subject and verb.
Examples of Clauses:
who reach school lateHe is energetic.Til he stop shouting .Which is made up of Gold.Types of Phrases: Noun Phrases:The word group modifies the noun in the sentence. This group of words is called noun phrases.
Examples Noun Phrases:
A bright blue Shirt.Large quantity of water.A sharp knife.An interesting and beautiful place.Verb Phrases: Thre phrase contains helping ver… | 1,363 | 5,821 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.890625 | 4 | CC-MAIN-2018-13 | latest | en | 0.913848 |
http://oeis.org/A134159 | 1,369,432,879,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705097259/warc/CC-MAIN-20130516115137-00068-ip-10-60-113-184.ec2.internal.warc.gz | 190,272,678 | 3,920 | This site is supported by donations to The OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134159 a(n) = 13 + 165 n + 756 n^2 + 1470 n^3 + 1029 n^4. 6
13, 3433, 31591, 130351, 370273, 846613, 1679323, 3013051, 5017141, 7885633, 11837263, 17115463, 23988361, 32748781, 43714243, 57226963, 73653853, 93386521, 116841271, 144459103, 176705713, 214071493, 257071531, 306245611 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,1 COMMENTS A000540(n) is divisible by A000330(n) if and only n is congruent to {1,2,4,5} mod 7 (see A047380) A134158 is case when n is congruent to 1 mod 7 A134159 is case when n is congruent to 2 mod 7 A134160 is case when n is congruent to 4 mod 7 A134161 is case when n is congruent to 5 mod 7 A133180 is union of A134158 and A134159 and A134160 and A134161 LINKS FORMULA a(n) = (3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 2}] G.f.: -(13+3368*x+14556*x^2+6596*x^3+163*x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007 MATHEMATICA 1) Table[(3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7, {n, 0, 100}] 2) Table[Sum[k^6, {k, 1, 7n + 2}]/Sum[k^2, {k, 1, 7n + 2}], {n, 0, 100}] (*Artur Jasinski*) CROSSREFS Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134160, A134161. Sequence in context: A220642 A159357 A221885 * A221851 A221924 A070905 Adjacent sequences: A134156 A134157 A134158 * A134160 A134161 A134162 KEYWORD nonn AUTHOR Artur Jasinski, Oct 10 2007 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.
Content is available under The OEIS End-User License Agreement . | 738 | 1,841 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2013-20 | latest | en | 0.568803 |
http://clay6.com/qa/28382/ratio-of-the-magnetic-field-at-the-centre-of-a-current-carrying-coil-of-rad?show=28384 | 1,537,608,308,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267158279.11/warc/CC-MAIN-20180922084059-20180922104459-00498.warc.gz | 50,090,117 | 28,163 | # Ratio of the magnetic field at the centre of a current carrying coil of radius $R$ and at a distance of $3R$ on its axis is
$\begin {array} {1 1} (a)\;10\sqrt{10} & \quad (b)\;20\sqrt{10} \\ (c)\;2\sqrt{10} & \quad (d)\;\sqrt{10} \end {array}$
The desired ratio is $\Large\frac{\Large\frac{\mu_0i}{2R}}{\Large\frac{\mu_0iR^2}{2(R^2+9R^2)^{\Large\frac{3}{2}}}}$
Ans : (a) | 155 | 374 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2018-39 | longest | en | 0.577301 |
https://www.roseindia.net/answers/viewqa/Java-Interview-Questions/13244-print-100-numbers-using-loops.html | 1,726,110,655,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651420.25/warc/CC-MAIN-20240912011254-20240912041254-00403.warc.gz | 913,780,450 | 16,151 | # print 100 numbers using loops
how to print from 1 to 100 using for loop ?
November 13, 2010 at 11:11 AM
Hi Friend,
You can use the following code:
```class Loop{
public static void main(String[] args){
for(int i=1;i<=100;i++){
System.out.println(i);
}
}
}
```
Thanks
November 13, 2010 at 11:11 AM
Hi Friend,
You can use the following code:
```class Loop{
public static void main(String[] args){
for(int i=1;i<=100;i++){
System.out.println(i);
}
}
}
```
Thanks
November 13, 2010 at 11:13 AM
class Numbers { public satic void main(string args[]_ { for(int a=1;a<=100;a++) { System.out.println("val of a is ="+a); } } }
November 13, 2010 at 11:37 AM
How java is securable ?
November 13, 2010 at 11:38 AM
why java is securable ?
print 100 numbers using loops
print 100 numbers using loops how to print from 1 to 100 using...;=100;i++){ System.out.println(i); } } } Thanks ...{ public static void main(String[] args){ for(int i=1;i<=100;i
print rectangle triangle with ?*? using loops
print rectangle triangle with ?*? using loops * * * * * * i want print like this.what is the code? import java.lang....("*"); } } System.out.print(" "); } } print("code sample"); class
print a-z, A-Z with exact order using loops
print a-z, A-Z with exact order using loops how to print from a-z, A-Z with exact order using for loop? Thanks for all concern
multiply of 100 digits numbers
multiply of 100 digits numbers multiplying 100 digits numbers to eachother
print the sum of even number from 1 to 100
print the sum of even number from 1 to 100 how to print the sum of even number from 1 to 100 using for loops? Thanks
print numbers
print numbers 1234 123 12 1234 1234 123 12 1234
Using Nested loops
Using Nested loops How to use nested loops in java when I want to print the 10 multiples of numbers 2 to 15(in multiplication table) public class MultiplicationTable{ public static void main(String[] args) { int
Application for print pyramid of numbers
Application for print pyramid of numbers What is the code for printing the numbers like 1 1 1 1 2 2 1 1 3 4 3 1 1 4 7 7 4 1
How to list even numbers between 1 and 100?
How to list even numbers between 1 and 100? Hi, I Java to check if a number is even? How to list even numbers between 1 and 100? Thanks ... the numbers between 1 and 100 for (int i=1;i <=num ; i++){ if(i%2==0
print numbers in traingle shape
print numbers in traingle shape 1 22 333 4444 i want output like this please help me class Pyramid { public static void main(String[] args) { for(int i=1;i<=4;i++){ for(int j=1;j<
Generate random numbers from 1 to 100
Generate random numbers from 1 to 100 1)A class Called: RandomNumberGenerator that generate random numbers from 1 to 100 2)A class Test that tests the hierarchy in A) especially the getArea() and getVolume() methods. Use
Prime numbers in Java between 1 and 100
Prime numbers in Java between 1 and 100 Hi, How to display prime numbers in java between 1 and 100? Thanks Hi, Prime numbers... which prints prime numbers between 1 and 100. Here is complete for printing prime
pattern-using loops
pattern-using loops Write a program that displays the following pattern ... (use nested loops) * ** * ** * ** * the correct pattren
print the even numbers between the range 100-200
print the even numbers between the range 100-200 Q ?write an application that print out the even numbers between the range 100-200 ? 1- which aer... prints out the even numbers between the range of 100 and 200 and then determine
Solve using only Javascript loops...
Solve using only Javascript loops... Write a JavaScript code, 1... count will be '4') 2) so that numbers appear in following format, 1 1 2... % 100; tenRem = value % 10; if (hunRem - tenRem == 10
read string - using loops in Java
read string - using loops in Java Write a program to read a string composed of an unknown number of words, then count the number of words in the string, and Display the longest and shortest words, with first letter Uppercase
write an application that print out the even numbers between the range 100-200
write an application that print out the even numbers between the range 100-200 write an application that print out the even numbers between the range 100-200 ? The given code accepts the number from 100 to 200
convert numbers to strings using JavaScript
convert numbers to strings using JavaScript How to convert numbers to strings using JavaScript
How to print a equilateral triangle patren with numbers
How to print a equilateral triangle patren with numbers I figure out how to use for loop to print the triangle but i couldn't get the exact values as this http://im37.gulfup.com/FzrOb.jpg could you please help me
Loops
Loops Write code that uses nested loops to print the following patterns: Pattern1: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 Pattern 2: 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 1 2 3 1 2 1
Loops
Loops Write code that uses nested loops to print the following patterns: Pattern1: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 Pattern 2: 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 1 2 3 1 2 1
Loops
Loops by using drjava q1.Write code that uses nested loops to print the following patterns: Pattern1: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 Pattern 2: 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 1 2 3 1 2 1 q2.Write code
Write a program to print using for loop
Write a program to print using for loop Write a program to print using for loop * * * *
adding two numbers with out using any operator
adding two numbers with out using any operator how to add two numbers with out using any operator import java.math.*; class AddNumbers... BigInteger("100"); BigInteger num2=new BigInteger("50
Loops
Loops ï??Using for loops, Write a program to simulate a clock countdown. The program prompts the user to enter the number of seconds, displays a message at every second, and terminates when the time expires. Use method
add tow numbers with out using arthamatic operaters
add tow numbers with out using arthamatic operaters add tow numbers with out using arthamatic operaters
I need to output number diamond using nested for loops.
I need to output number diamond using nested for loops. How to i output this using nested for loops 1 131 13531 1357531 135797531 1357531 13531 131 1
Java repeat string without using loops
Java repeat string without using loops In this section, you will learn how to repeat string without using for loops. The given example accepts the number... using while loop or any other control statements. Example:ADS_TO_REPLACE_1
how to write a program in java to print numbers in equalateral triangle
how to write a program in java to print numbers in equalateral triangle the output must be 1 324 76589 Here is an example of pattern 1 2 3 4 5 6 7 8 9 Example: public class NumberTriangle{ public
Loops
ADS_TO_REPLACE_3 } Using While loop we can print the counting from 1 to n...3.10. Loops Loops are the essential part of the program that have.... More than one loops can be used several times in a script. Loops makes easy
Java reverse words in a string using only loops
Java reverse words in a string using only loops In this tutorial, you will learn how to reverse words in a string without using any inbuilt methods like split() etc, StringTokenizer functiom or any extra ordinary function Only loops
write program have product - using loops
write program have product - using loops Write a program for a grocery that reads products data and determine and display the product that has the highest price and the average price. A product has three pieces of data: id (int
loops
loops how to print 11 12 22 13 23 33 14 24 34 44 15 25 35 45 55 plz reply fast...EMERGENCY
greatest of 3 numbers using classes and functions.
greatest of 3 numbers using classes and functions. WAP to calculate greatest of 3 numbers using classes and functions with parameters through input..._VALUE; System.out.println("Enter 3 numbers:"); Scanner input
adding two numbers using bitwise operators
adding two numbers using bitwise operators adding two integer numbers with using bitwise opeators Hi Friend, Try the following code: public class AddNumberUsingBitwiseOperators { public static void main(String
loops
loops how to get the sum of 10 number using a loop
loops
loops how to use for loop and while loop in java?/ how to write a code using for or while loop
loops
loops I need the program output 55555 4444 333 22 1 like this by using for loop and if condition only
how to print all colors using awt
how to print all colors using awt how to print all colors using awt
how to print HTML using javascript or Jquery
how to print HTML using javascript or Jquery is there any way to print a document(created using Html and javascript) without using window.print... used Iframe for print, but this only work in chrome, but I have required one
How to print the following output using c program
How to print the following output using c program 1) 4 3 4 2 3 4 1 2 3 4 2) A B C D E F G H I J
Print Matchingwords using Regular expression
Print Matchingwords using Regular expression This Example describe the way to print the matching word from the file using Regularexpression. The steps involved in
Sum of two numbers using command line arguments in Java
Sum of two numbers using command line arguments in Java Hi, How...? The calculate the sum of two numbers using command line arguments in Java... sum = a+b; Check complete example code at Add Two Numbers in Java. Thanks
print from a-z, A-Z with exact order using for loop
print from a-z, A-Z with exact order using for loop how to print from a-z, A-Z with exact order using for loop? Thanks for all concern
Java find prime numbers without using break statement
Java find prime numbers without using break statement In this tutorial, you will learn how to find the prime numbers without using break statement. You all are aware of Prime Numbers, these are the numbers which are either divided
java loops - Java Beginners
java loops Q1-sum the series 2/9-5/13+8/17..... Q2 print first n odd numbers in descending order? Q3 program to input digits and write in words with out using any type of in built function and array program to print truth
how to print fasta file into jtable using netbeans IDE
how to print fasta file into jtable using netbeans IDE mt file is : contig00001 length=586 numreads=4... ctgaggactcctcg now i want to print the lines "contig00001 length=586 numreads=4
To find first two maximum numbers in an array,using single loop without sorting array.
To find first two maximum numbers in an array,using single loop without sorting array. Java program to find first two maximum numbers in an array,using single loop without sorting array
To find first two maximum numbers in an array,using single loop without sorting array.
To find first two maximum numbers in an array,using single loop without sorting array. Java program to find first two maximum numbers in an array,using single loop without sorting array
ask user how many numbers to be inputted and determine the sum and highest number using an array in java
ask user how many numbers to be inputted and determine the sum and highest number using an array in java ask user how many numbers to be inputted and determine the sum and highest number using an array in java | 3,050 | 11,308 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2024-38 | latest | en | 0.613094 |
https://www.dataunitconverter.com/kilobit-per-day-to-zebibyte-per-second/534 | 1,721,488,024,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763515300.51/warc/CC-MAIN-20240720144323-20240720174323-00611.warc.gz | 620,490,261 | 16,961 | # kbit/Day to ZiBps - 534 kbit/Day to ZiBps Conversion
expand_more
S = Second, M = Minute, H = Hour, D = Day
Sec
Min
Hr
Day
Sec
Min
Hr
Day
kbit/Day
label_important RESULT close
534 kbit/Day =0.0000000000000000000006543917734863952272 ZiBps
( Equal to 6.543917734863952272E-22 ZiBps )
content_copy
Calculated as → 534 x 1000 ÷ (8x10247) / ( 60 x 60 x 24 ) smart_display Show Stepsexpand_more
Below chart table shows the amount of data that can be transferred at a constant speed of 534 kbit/Day in various time frames.
Transfer RateAmount of Data can be transferred
@ 534 kbit/Dayin 1 Second0.0000000000000000000006543917734863952272 Zebibytes
in 1 Minute0.0000000000000000000392635064091837136338 Zebibytes
in 1 Hour0.0000000000000000023558103845510228180337 Zebibytes
in 1 Day0.0000000000000000565394492292245476328105 Zebibytes
ADVERTISEMENT
toc Table of Contents
## Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps) Conversion - Formula & Steps
The kbit/Day to ZiBps Calculator Tool provides a convenient solution for effortlessly converting data rates from Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps). Let's delve into a thorough analysis of the formula and steps involved.
Outlined below is a comprehensive overview of the key attributes associated with both the source (Kilobit) and target (Zebibyte) data units.
Source Data Unit Target Data Unit
Equal to 1000 bits
(Decimal Unit)
Equal to 1024^7 bytes
(Binary Unit)
The conversion from Data per Day to Second can be calculated as below.
x 60
x 60
x 24
Data
per
Second
Data
per
Minute
Data
per
Hour
Data
per
Day
÷ 60
÷ 60
÷ 24
The formula for converting the Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps) can be expressed as follows:
diamond CONVERSION FORMULA ZiBps = kbit/Day x 1000 ÷ (8x10247) / ( 60 x 60 x 24 )
Now, let's apply the aforementioned formula and explore the manual conversion process from Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps). To streamline the calculation further, we can simplify the formula for added convenience.
FORMULA
Zebibytes per Second = Kilobits per Day x 1000 ÷ (8x10247) / ( 60 x 60 x 24 )
STEP 1
Zebibytes per Second = Kilobits per Day x 1000 ÷ (8x1024x1024x1024x1024x1024x1024x1024) / ( 60 x 60 x 24 )
STEP 2
Zebibytes per Second = Kilobits per Day x 1000 ÷ 9444732965739290427392 / ( 60 x 60 x 24 )
STEP 3
Zebibytes per Second = Kilobits per Day x 0.0000000000000000001058791184067875423835 / ( 60 x 60 x 24 )
STEP 4
Zebibytes per Second = Kilobits per Day x 0.0000000000000000001058791184067875423835 / 86400
STEP 5
Zebibytes per Second = Kilobits per Day x 0.0000000000000000000000012254527593378187
ADVERTISEMENT
By applying the previously mentioned formula and steps, the conversion from 534 Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps) can be processed as outlined below.
1. = 534 x 1000 ÷ (8x10247) / ( 60 x 60 x 24 )
2. = 534 x 1000 ÷ (8x1024x1024x1024x1024x1024x1024x1024) / ( 60 x 60 x 24 )
3. = 534 x 1000 ÷ 9444732965739290427392 / ( 60 x 60 x 24 )
4. = 534 x 0.0000000000000000001058791184067875423835 / ( 60 x 60 x 24 )
5. = 534 x 0.0000000000000000001058791184067875423835 / 86400
6. = 534 x 0.0000000000000000000000012254527593378187
7. = 0.0000000000000000000006543917734863952272
8. i.e. 534 kbit/Day is equal to 0.0000000000000000000006543917734863952272 ZiBps.
Note : Result rounded off to 40 decimal positions.
You can employ the formula and steps mentioned above to convert Kilobits per Day to Zebibytes per Second using any of the programming language such as Java, Python, or Powershell.
### Unit Definitions
#### What is Kilobit ?
A Kilobit (kb or kbit) is a decimal unit of digital information that is equal to 1000 bits. It is commonly used to express data transfer speeds, such as the speed of an internet connection and to measure the size of a file. In the context of data storage and memory, the binary-based unit of Kibibit (Kibit) is used instead.
- Learn more..
arrow_downward
#### What is Zebibyte ?
A Zebibyte (ZiB) is a binary unit of digital information that is equal to 1,180,591,620,717,411,303,424 bytes (or 9,444,732,965,739,290,427,392 bits) and is defined by the International Electro technical Commission(IEC). The prefix 'zebi' is derived from the binary number system and it is used to distinguish it from the decimal-based 'zettabyte' (ZB). It is widely used in the field of computing as it more accurately represents the storage size of high end servers and data storage arrays.
- Learn more..
ADVERTISEMENT
## Excel Formula to convert from Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps)
Apply the formula as shown below to convert from 534 Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps).
A B C
1 Kilobits per Day (kbit/Day) Zebibytes per Second (ZiBps)
2 534 =A2 * 0.0000000000000000001058791184067875423835 / ( 60 * 60 * 24 )
3
If you want to perform bulk conversion locally in your system, then download and make use of above Excel template.
## Python Code for Kilobits per Day (kbit/Day) to Zebibytes per Second (ZiBps) Conversion
You can use below code to convert any value in Kilobits per Day (kbit/Day) to Kilobits per Day (kbit/Day) in Python.
kilobitsperDay = int(input("Enter Kilobits per Day: "))
zebibytesperSecond = kilobitsperDay * 1000 / (8*1024*1024*1024*1024*1024*1024*1024) / ( 60 * 60 * 24 )
print("{} Kilobits per Day = {} Zebibytes per Second".format(kilobitsperDay,zebibytesperSecond))
The first line of code will prompt the user to enter the Kilobits per Day (kbit/Day) as an input. The value of Zebibytes per Second (ZiBps) is calculated on the next line, and the code in third line will display the result.
## Similar Conversions & Calculators
All below conversions basically referring to the same calculation. | 1,908 | 5,822 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2024-30 | latest | en | 0.746681 |
https://www.geebeephoto.com/this-recreation-shall-be-a-technological-masterpiece-the-amount-of-effort-science-and-knowledge-thats-being-put-collectively-in-it-is-just-past-words.html | 1,597,143,122,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738746.41/warc/CC-MAIN-20200811090050-20200811120050-00111.warc.gz | 667,473,404 | 9,743 | The evolutionary historical past of dogs is controversial and requires full genomes to supply enough resolving power to test hypotheses related to demographic historical past, admixture and choice during dog domestication. Furthermore, a inhabitants genomics strategy to understanding the constraints on variation and the consequences of deleterious mutations is in its infancy, and can profit from wider inhabitants sampling.
## Eat Your Way to a Healthier You, Me, Country, and Planet
If the opposite is true that the gap from the fulcrum to the input point A is lower than from the fulcrum to the output point B, then the lever reduces the magnitude of the enter pressure. This equation reveals that if the distance a from the fulcrum to the purpose A where the enter pressure is utilized is bigger than the space b from fulcrum to the purpose B the place the output drive is utilized, then the lever amplifies the input drive. On the other hand, if the distance a from the fulcrum to the input force is lower than the gap b from the fulcrum to the output pressure, then the lever reduces the input drive. It reveals that if the distance a from the fulcrum to where the enter pressure is applied (point A) is larger than the distance b from fulcrum to where the output pressure is applied (level B), then the lever amplifies the input force.
A lever is a straightforward machine that consists of a inflexible bar supported at one point, generally known as the fulcrum. A drive called the trouble pressure is applied at one point on the lever in order to transfer an object, generally known as the resistance force, positioned at some other level on the lever. A frequent instance of the lever is the crow bar used to move a heavy object corresponding to a rock. To use the crow bar, one finish is placed underneath the bar, which is supported at some point (the fulcrum) near the rock. A particular person then applies a pressure at the reverse finish of the crow bar to raise the rock.
In a 3rd-class lever, the trouble force lies between the resistance drive and the fulcrum. Some kinds of backyard instruments are examples of third-class levers. When you utilize a shovel, for example, you maintain one end regular to act because the fulcrum, and you utilize your other hand to pull up on a load of filth. The second hand is the trouble pressure, and the filth being picked up is the resistance drive.
It has failed in its first effort, as a result of the mobs of the cities, the instrument used for its accomplishment, debased by ignorance, poverty and vice, couldn’t be restrained to rational action. But the world will quickly recuperate from the panic of this first disaster. Chief Seattle, of the Indians that inhabited the Seattle space, wrote a beautiful paper that has to do with placing oneself in tune with the universe. He mentioned, “Why ought to I lament the disappearance of my individuals! All things end, and the white man will discover this out also.†And this goes for the universe.
They actually do it. It doesn’t occur as often as it should, as a result of scientists are human and change is sometimes painful. But it occurs every day. I cannot recall the last time something like that occurred in politics or religion. From Evolution in Science and Religion (1927), fifty eight-59.
The above presentation was partially supported by the ESA/SSA SWE A-EFFort venture, ESA Contract No. 4000111994/14/D/MRP. Special thanks go to the ESA Project Officers R. Keil, A. Glover, and J.-P. Luntama (ESOC), M. Bobra and C. Balmer of the SDO/HMI group at Stanford University, and M.
The knowledge records themselves can be cited with the assistance of a Digital Object Identification (DOI) quantity. In addition, if the info is nicely prepared, different scientists can use them in additional analyses and cite the unique authors of their studies . Prior to sample assortment, all canine homeowners should signal normal Animal Care and Use Consent forms providing signed permission for the collection of a blood pattern, pedigree information and registration number (if out there), demographic history (if relevant), proprietor contact info, consent to re-contact proprietor, medical history and pedigree data for privately owned canines as listed (Table 1). While blood samples are fascinating, samples from some canine could solely be obtainable using buccal swabs. Our research on the genomic impact of canine domestication will depend on intensive sampling across wild canid lineages (Fig. 2). | 951 | 4,524 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2020-34 | latest | en | 0.915923 |
https://www.scribd.com/document/311371757/Chapter-5-Fcp-10jun2014 | 1,576,139,115,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540542644.69/warc/CC-MAIN-20191212074623-20191212102623-00363.warc.gz | 862,571,087 | 71,139 | You are on page 1of 19
# 1
Chapter 5
Overview
Fatigue definition
A material subjected
to a repetitive or
fluctuating stress will
fail at a stress much
lower
than
that
required
to
cause
failure on a single
Failures
occurring
under conditions of
called fatigue failures.
## Fatigue Mechanisms - two steps;
Crack Initiation and
Crack Propagation
Characterisation of Fatigue
There are three commonly
recognized forms of fatigue:
High cycle fatigue (HCF),
Low cycle fatigue (LCF),
Thermal mechanical
fatigue (TMF)
Fatigue strength is
determined by running
multiple specimen tests at a
number of different
stresses.
The objective is to identify
the highest stress that will
produce a fatigue life
beyond ten million cycles.
This stress is also known as the material's endurance limit or fatigue limit.
Gas turbines are designed so that the stresses in engine components do not
exceed this value including an additional safety factor.
## Fatigue Crack Growth LEFM approach
What are the important parameters to characterize a
Mean stress
1
m = ( max + min )
2
Stress range
= max min
Stress amplitude
1
a = ( max min )
2
Stress Ratio
R=
min K min
=
max K max
K Range
K = K max K min
## Fatigue Crack Growth LEFM approach
Frequency, f in units Hz. For rotating machinery at 3000 rpm, f
= 50 Hz. In general only influences fatigue crack growth if
there are environmental effects present, such as humidity or
elevated temperatures.
Waveform, is the stress history a sine wave, square wave or
some other waveform? As with frequency, generally only
influences fatigue crack growth if there are environmental effect.
Key difference between static and cyclic loading:
Static Until applied K reaches Kc (30 MPam for example)
the crack will not grow.
Cyclic K applied can be well below Kc (3 MPam for
example). Over time the crack grows.
The design may be safe considering static loads, but
any cyclic loads must also be considered.
## Fatigue Crack Growth LEFM approach
In 1961 the ideas of LEFM were applied to fatigue crack
growth by Paris, Gomez and Anderson .
For given cyclic loading, define K as Kmax Kmin which
can be found and the geometry of the crack body.
Say that the crack grows an amount a during N cycles.
Paris, Gomez and Anderson said that the rate of crack
growth depends on K in the following way:
a
da
m
= C (K )
N
dN
## Thus plot of log (da/dN) vs. log (K) should be straight
line with a slope m.
The actual relationship between crack growth rate and
K is depicted on the following slide. There are three
7
different regime of fatigue crack growth A, B and C.
## FATIGUE CRACK GROWTH
REGIME
Terminology
A
B
Slow-growth rate Mid-growth rate
(near-threshold) (Paris regime)
C
High-growth rate
Microscopic mode
Stage I, single
shear
Stage II,
(striations)
modes
Fracture surface
features
Faceted or
serrated
Planar with
ripples
microvoid coalescene
Microstructural
effects
Large
Small
Large
Environmental
effects
Large
Large
Small
*
Large
Large
## Stress state effects
Near-tip plasticity
rc < dg
Large
rc > dg
Large
rc >> dg
9
* large influence on crack growth for certain combinations of environment, load ratio and frequency.
rc and dg refer to the cyclic plastic zone size and the grain size, respectively.
## FATIGUE CRACK GROWTH - Regime A
Concept of the threshold stress intensity Kth:
When K is Kth,, where Kth is the threshold stress
intensity factor, the rate of crack growth is so slow that the crack
is often assumed to be dormant or growing at an undetectable
rate.
An operational definition for Kth often used is that if
the rate of crack growth is 10-8 mm/cycle or less the
conditions are assumed to be at or below Kth.
An important point is that these extremely slow crack
growth rates represent an average crack advance of less
than one atomic spacing percycle. How is this possible?
What actually occurs is that there are many cycles with
no crack advance, then the crack advances by 1 atomic
spacing in a single cycle, which is followed again by 10
many cycles with no crack advance.
## FATIGUE CRACK GROWTH - Regime B
When we are in regime B (Paris regime) the following
calculation can be carried out to determine the number of
cycles to failure.
From Paris Law:
K can be expressed in terms of ;
da
m
= C (K )
dN
K = Y a
da
= C Y a
dN
both sides:
a
N
ao
da
f
m m/2
m
= CY ( ) dN
m/2
0
a
11
## FATIGUE CRACK GROWTH - Regime B
CONT
For m > 2:
Nf =
(m 2)CY m ( )m m / 2
1
1
(m 2 )/ 2
(m 2 )/ 2
(
)
(
a
)
a
o
For m = 2:
Nf =
af
1
ln
2
CY 2 ( ) ao
## The constant C and m are material parameters that must
be determined experimentally. Typically m is in the range
2 4 for metals and 4 100 for ceramics and polymers.
For cases where Y depends on crack length, these
integration generally will be performed numerically.
Important: Note that in the Paris regime the rate of
12
crack growth is weakly sensitive to the load ratio R. The
key parameter governing crack growth is K.
CONT
## From those expressions, we need to determine the initial
crack length ao and the final crack length af (some times
called the critical crack length).
How do we determine the initial crack length ao?
Crack can be detected using a variety of techniques, ranging
from simple visual inspection to more sophisticated
techniques based on ultrasonics or x-rays. If no cracks are
detectable during inspection, we must assume that a crack
just at the resolution of our detection system exists.
How do we determine the final crack length af? We know
that eventually the crack can grow to a length at which the
material fails immediately, i.e.
K max K C
or
Y max a f K C
13
CONT
af =
K C2
2
Y 2 max
## A very important idea that comes from this analysis
is the following: even if a component has a
detectable crack, it need not to be removed from
service! Using this framework the remaining life
can be assessed. The component can remain in
service provided it is inspected periodically. This is
the crack-tolerant or damage tolerant design
14
approach.
FATIGUE STRIATIONS
An advancing fatigue crack leaves
characteristic markings called
striations in its wake. These can
provide evidence that a given failure
was caused by fatigue.
The striations on the fracture surface
are produced as the crack advances
over one cycle, i.e. each striation
correspond to da.
Striations are close together
indicating low stress, many cycles.
Widely spaced striations mean high
stress few cycles.
Fatigue failure is brittle in nature,
even in normally ductile materials;
there is very little plastic deformation
associated with the failure.
15
EXAMPLE 5.1
A wide thick plate, K1c = 40 ksi-in0.5, contains an
edge crack 0.1 inch long. The plate is subjected to
alternating stresses between 0 and 20 ksi. Data on
similar material under similar environmental
conditions exhibited Paris law with coefficients m =
4 and C = 7x 10-10 for K in ksi-in0.5. How many
cycles will the plate support before failure?
Solution
It is first necessary to determine the length of the
longest crack the plate can support without
failure. A suitable stress intensity factor is:
K1c = 1.12 max (ac)
40 = 1.12 (20) (ac)
ac = 1.02 inches
16
Solution
For this case, Paris Law has the form
## da/dN = C(K)m = C [1.12)(ac)]m
Substituting this materials Paris law parameters,
we obtain;
## da/dN = 7 x 10-10 (1.12)4(20)42a2
Rearranging the forgoing equations yields
da/a2 = 7 x 10-10 (1.12)4(20)42dN
Thus
1.02
1
2
N=
(
a
da)
10
4
4
2
7 x10 (1.12) (20) 0.1
## Integrate from ai = 0.1 inch to ac= 1.02 inch,
N 5185 cycles
ans
17
EXAMPLE 5.2
A large aluminium alloy plate contains a
central crack of length 10 mm. The plate is
subjected to a constant amplitude tensile cyclic
loading from 6 MPa to 60 MPa. The Paris law
exponent is 3, and K at da/dN = 10-7 m/cycles
is 28 MPam. Assuming that Y is 1.02,
calculate how many loading cycles must be
applied for the crack to grow to 20 mm?
18
Solution
First calculate C in Paris law
C = 10-7/283= 4.55 x 10-11,for crack in m/cycle
Obtain stress range, = 54 MPa
Substitute into the given expression:
2
Nf =
(m 2)CY m ( ) m m / 2
Nf =
1
1
( m2) / 2
( m2) / 2
(a f )
( ao )
2
4.55 x10 111.023 (54) 3 3 / 2
1
1
(0.005)1/ 2 (0.01)1/ 2
19 | 2,277 | 8,219 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2019-51 | latest | en | 0.877916 |
http://codeforces.com/problemset/problem/701/B | 1,653,363,496,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00005.warc.gz | 12,076,819 | 13,529 | B. Cells Not Under Attack
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Vasya has the square chessboard of size n × n and m rooks. Initially the chessboard is empty. Vasya will consequently put the rooks on the board one after another.
The cell of the field is under rook's attack, if there is at least one rook located in the same row or in the same column with this cell. If there is a rook located in the cell, this cell is also under attack.
You are given the positions of the board where Vasya will put rooks. For each rook you have to determine the number of cells which are not under attack after Vasya puts it on the board.
Input
The first line of the input contains two integers n and m (1 ≤ n ≤ 100 000, 1 ≤ m ≤ min(100 000, n2)) — the size of the board and the number of rooks.
Each of the next m lines contains integers xi and yi (1 ≤ xi, yi ≤ n) — the number of the row and the number of the column where Vasya will put the i-th rook. Vasya puts rooks on the board in the order they appear in the input. It is guaranteed that any cell will contain no more than one rook.
Output
Print m integer, the i-th of them should be equal to the number of cells that are not under attack after first i rooks are put.
Examples
Input
3 31 13 12 2
Output
4 2 0
Input
5 21 55 1
Output
16 9
Input
100000 1300 400
Output
9999800001
Note
On the picture below show the state of the board after put each of the three rooks. The cells which painted with grey color is not under the attack. | 438 | 1,555 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2022-21 | latest | en | 0.896988 |
https://www.daniweb.com/programming/web-development/threads/390072/javascript-dice-roller-passing-rolling-output-issues | 1,653,746,172,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663016853.88/warc/CC-MAIN-20220528123744-20220528153744-00451.warc.gz | 823,428,493 | 16,238 | Hello,
I am taking a JavaScript class and I am currently on an assignment where my Professor wants me to create a dice roller program with the following stipulations:
* Users can choose via form how many sides that they can choose from, between 2 and 100.
* Dice are rolled '36000' times and totals are tracked.
* Actual totals and percentages are shown. ie.
2: 2341
3: 4486
4: 6626
5: 9166
6: 6636
7: 4480
8: 2265
2: 6.50%
3: 12.46%
4: 18.41%
5: 25.46%
6: 18.43%
7: 12.44%
8: 6.29%
Now to the problems. I have set up to where it will take the form, pass it to my "sidecheck" function, but I do not think it is passing it to the Die() function to roll the die. As far as the output part of it to show roll totals and percentages, I am lost on that one. Below is my code and what I have so far. Thank you for your help in advance.
``````<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Lab05 - Dice Roller</title>
<script type="text/javascript" >
function sidecheck( ) {
if ( document.getElementById("sides").value < 2 || document.getElementById("sides").value > 100 ) {
alert( "Value you entered is not within range" );
} else if ( isNaN(document.getElementById("sides").value )) {
alert( "Value you entered is not within range" );
} else {
Die( sides );
}
return false;
}
function Die( sides ) {
this.sides = 6;
this.roll = function( ) {
return parseInt((Math.random( ) * 1000) % this.sides) + 1;
}
}
function field_prompt(field_name, prompt) {
var sides = document.getElementById( field_name );
sides.value = prompt;
sides.style.color = "#888";
sides.onfocus = function( ) {
this.style.color = "#000";
if ( this.value == prompt ){
this.value = "";
}
}
sides.onblur = function( ){
if( this.value == "" ){
this.style.color = "#888";
this.value = prompt;
}
}
}
field_prompt( "sides", 12 );
}
</script>
<body>
<h1>Dice Roller</h1>
<hr />
Enter a number of sides for the die between 2 and 100.
<form action="" name="dice_roller" id="dice_roller" />
<p><input type="text" name="sides" id="sides" /></p>
<p><input type="submit" value="Click to roll the Die!" onclick="sidecheck( );" /></p>
</form>
<script type="text/javascript">
var d = new Die( );
d.sides = 12;
var rolled_value = d.roll( );
</script>
<table>
<tr>
<td><b>Rolled Times</b></td>
<td></td>
<td><b>Each Percentage Total</b></td>
</body>
</html>``````
1.You need a loop to do the roll. Currently, you only roll it once and done.
2.You do not have the display part for the value you just row.
3.What does your line 16 `Die(sides)` do? The "sides" variable is unknown in the function. If you want to create a new variable, you could do `Die(document.getElementById("sides").value);` , but there is a problem here. Where do you save the variable at?
Be a part of the DaniWeb community
We're a friendly, industry-focused community of developers, IT pros, digital marketers, and technology enthusiasts meeting, learning, and sharing knowledge. | 877 | 3,126 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-21 | latest | en | 0.602817 |
https://answers.yahoo.com/question/index?qid=20170321203523AA7XNEb | 1,580,234,105,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251779833.86/warc/CC-MAIN-20200128153713-20200128183713-00209.warc.gz | 317,773,295 | 26,261 | Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 years ago
# Math question?
What is an equivalence relation on a set X? (ii) Consider the relations R
and S, defined on the set X = {1, 2, . . . , 99} as follows.
xRy ⇐⇒ x + y is a multiple of 9,
xSy ⇐⇒ x − y is a multiple of 9.
One of R and S is an equivalence relation, the other is not. Determine which is which and
justify your answers. (iii) For the equivalence relation from part (ii), into how many classes
does it partition the set X?
Relevance
• jibz
Lv 6
3 years ago
(i) In general, a relation Q on a set X is a just a subset of X^2. Q being a relation, we conventionally write (a,b) ∈ Q as aQb. An equivalence relation E on a set X is a relation on X that has the following 3 properties:
1) reflexivity: for every element x ∈ X, we have xEx.
2) symmetry: if aEb then bEa.
3) transitivity: if aEb and bEc, then aEc.
(ii) Claim: S is an equivalence relation on X. Proof: take any x ∈ X. Then x - x = 0 = 9*0, so xSx showing that S is reflexive. Check. Next, suppose aSb. That means that a - b = 9k for some integer k. Then b - a = 9(-k). Since -k is also an integer, we have bSa, showing that S is symmetric. Check. Finally suppose aSb and bSc. Then
a - b = 9m and
b - c = 9n,
for some integers m and n. Adding the above 2 equations, we have
a - c = 9(m+n).
Since m+n is also an integer we have aSc, showing that S is transitive, q.e.d.
On the other hand R is not reflexive (e.g. 1+1 is not a multiple of 9, so (1,1) ∉ R), so (even though it is symmetric and transitive) R isn't an equivalence relation.
(iii) S partitions X into 9 equivalence classes, namely its residue classes mod 9.
• 3 years ago
Professional Internet troll posts text alleged to be a technical question about a mathematics topic it probably does not understand:
"Math question? What is an equivalence relation on a set X? (ii) Consider the relations R
and S, defined on the set X = {1, 2, . . . , 99} as follows.
xRy ⇐⇒ x + y is a multiple of 9,
xSy ⇐⇒ x − y is a multiple of 9.
One of R and S is an equivalence relation, the other is not. Determine which is which and
justify your answers. (iii) For the equivalence relation from part (ii), into how many classes
does it partition the set X?"
Likewise for "define your operators and notation".
The troll in question probably copied the text from some book it never read. | 699 | 2,399 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2020-05 | latest | en | 0.921391 |
http://openoffice995.com/standard-error/the-standard-error-of-the-coefficient.php | 1,548,197,960,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583875448.71/warc/CC-MAIN-20190122223011-20190123005011-00621.warc.gz | 164,672,187 | 5,768 | Home > Standard Error > The Standard Error Of The Coefficient
The Standard Error Of The Coefficient
Contents
Use the standard error of the coefficient to measure the precision of the estimate of the coefficient. All rights Reserved.EnglishfrançaisDeutschportuguêsespañol日本語한국어中文（简体）By using this site you agree to the use of cookies for analytics and personalized content.Read our policyOK current community blog chat Cross Validated Cross Validated Meta your communities Adjusted R-squared, which is obtained by adjusting R-squared for the degrees if freedom for error in exactly the same way, is an unbiased estimate of the amount of variance explained: Adjusted The answer to this is: No, strictly speaking, a confidence interval is not a probability interval for purposes of betting. have a peek at these guys
And the uncertainty is denoted by the confidence level. Here is an example of a plot of forecasts with confidence limits for means and forecasts produced by RegressIt for the regression model fitted to the natural log of cases of However, if one or more of the independent variable had relatively extreme values at that point, the outlier may have a large influence on the estimates of the corresponding coefficients: e.g., A technical prerequisite for fitting a linear regression model is that the independent variables must be linearly independent; otherwise the least-squares coefficients cannot be determined uniquely, and we say the regression http://support.minitab.com/en-us/minitab/17/topic-library/modeling-statistics/regression-and-correlation/regression-models/what-is-the-standard-error-of-the-coefficient/
Standard Error Of Regression Coefficient
Return to top of page Interpreting the F-RATIO The F-ratio and its exceedance probability provide a test of the significance of all the independent variables (other than the constant term) taken If either of them is equal to 1, we say that the response of Y to that variable has unitary elasticity--i.e., the expected marginal percentage change in Y is exactly the If it turns out the outlier (or group thereof) does have a significant effect on the model, then you must ask whether there is justification for throwing it out.
Bionic Turtle 95.377 visualizações 8:57 Statistics 101: Simple Linear Regression (Part 1), The Very Basics - Duração: 22:56. Note that s is measured in units of Y and STDEV.P(X) is measured in units of X, so SEb1 is measured (necessarily) in "units of Y per unit of X", the The diagonal elements are the variances of the individual coefficients.How ToAfter obtaining a fitted model, say, mdl, using fitlm or stepwiselm, you can display the coefficient covariances using mdl.CoefficientCovarianceCompute Coefficient Covariance Standard Error Of The Correlation Coefficient Carregando...
The estimated slope is almost never exactly zero (due to sampling variation), but if it is not significantly different from zero (as measured by its t-statistic), this suggests that the mean Standard Error Of Coefficient Formula Find standard deviation or standard error. Thus, Q1 might look like 1 0 0 0 1 0 0 0 ..., Q2 would look like 0 1 0 0 0 1 0 0 ..., and so on. http://stats.stackexchange.com/questions/85943/how-to-derive-the-standard-error-of-linear-regression-coefficient In a multiple regression model with k independent variables plus an intercept, the number of degrees of freedom for error is n-(k+1), and the formulas for the standard error of the
The log transformation is also commonly used in modeling price-demand relationships. Standard Error Coefficient Multiple Regression The standard error of the slope coefficient is given by: ...which also looks very similar, except for the factor of STDEV.P(X) in the denominator. For example, the first row shows the lower and upper limits, -99.1786 and 223.9893, for the intercept, . This means that noise in the data (whose intensity if measured by s) affects the errors in all the coefficient estimates in exactly the same way, and it also means that
Standard Error Of Coefficient Formula
AP Statistics Tutorial Exploring Data ▸ The basics ▾ Variables ▾ Population vs sample ▾ Central tendency ▾ Variability ▾ Position ▸ Charts and graphs ▾ Patterns in data ▾ Dotplots Check This Out Adicionar a Quer assistir de novo mais tarde? Standard Error Of Regression Coefficient If you need to calculate the standard error of the slope (SE) by hand, use the following formula: SE = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) Standard Error Of The Estimate You can change this preference below.
price, part 3: transformations of variables · Beer sales vs. More about the author Select a confidence level. See the beer sales model on this web site for an example. (Return to top of page.) Go on to next topic: Stepwise and all-possible-regressions Linear regression models Notes on standard-error inferential-statistics share|improve this question edited Mar 6 '15 at 14:38 Christoph Hanck 9,76832150 asked Feb 9 '14 at 9:11 loganecolss 50311026 stats.stackexchange.com/questions/44838/… –ocram Feb 9 '14 at 9:14 Standard Error Of Coefficient Excel
With simple linear regression, to compute a confidence interval for the slope, the critical value is a t score with degrees of freedom equal to n - 2. Formulas for R-squared and standard error of the regression The fraction of the variance of Y that is "explained" by the simple regression model, i.e., the percentage by which the regressing standardized variables1How does SAS calculate standard errors of coefficients in logistic regression?3How is the standard error of a slope calculated when the intercept term is omitted?0Excel: How is the Standard check my blog Fazer login 24 7 Não gostou deste vídeo?
The standard error is given in the regression output. Standard Error Coefficient Linear Regression Compute margin of error (ME): ME = critical value * standard error = 2.63 * 0.24 = 0.63 Specify the confidence interval. In a multiple regression model, the constant represents the value that would be predicted for the dependent variable if all the independent variables were simultaneously equal to zero--a situation which may
Join the conversation Linear regression models Notes on linear regression analysis (pdf file) Introduction to linear regression analysis Mathematics of simple regression Regression examples · Baseball batting averages · Beer
Faça login para adicionar este vídeo a uma playlist. In this case, you must use your own judgment as to whether to merely throw the observations out, or leave them in, or perhaps alter the model to account for additional The critical value that should be used depends on the number of degrees of freedom for error (the number data points minus number of parameters estimated, which is n-1 for this Coefficient Of Determination The estimated coefficient b1 is the slope of the regression line, i.e., the predicted change in Y per unit of change in X.
R-squared will be zero in this case, because the mean model does not explain any of the variance in the dependent variable: it merely measures it. In fact, the standard error of the Temp coefficient is about the same as the value of the coefficient itself, so the t-value of -1.03 is too small to declare statistical Note that the inner set of confidence bands widens more in relative terms at the far left and far right than does the outer set of confidence bands. news Sometimes you will discover data entry errors: e.g., "2138" might have been punched instead of "3128." You may discover some other reason: e.g., a strike or stock split occurred, a regulation
Hence, it is equivalent to say that your goal is to minimize the standard error of the regression or to maximize adjusted R-squared through your choice of X, other things being In this case, if the variables were originally named Y, X1 and X2, they would automatically be assigned the names Y_LN, X1_LN and X2_LN. Therefore, the 99% confidence interval is -0.08 to 1.18. If the model assumptions are not correct--e.g., if the wrong variables have been included or important variables have been omitted or if there are non-normalities in the errors or nonlinear relationships
Identify a sample statistic. Rather, a 95% confidence interval is an interval calculated by a formula having the property that, in the long run, it will cover the true value 95% of the time in For large values of n, there isn′t much difference. | 1,834 | 8,396 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2019-04 | latest | en | 0.869658 |
https://softmath.com/algebra-software-2/difference-of-squares.html | 1,685,524,053,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646457.49/warc/CC-MAIN-20230531090221-20230531120221-00653.warc.gz | 473,034,316 | 9,368 | difference of squares calculator
Related topics:
formula preparatory mathematics answers | linear and nonlinear solution manual free download | why are polynomials important in algebra | factoring quadratic equations | equations with rational expressions | algebra and trigonometry test | learn algebra slope | quadratic equations in two unknown | how to solve logarithms calculator | solving like terms calulayor | adding integers fraction example | solving a quadratic model | simplify exponents calculator
Author Message
FarowneTCJ
Registered: 09.09.2002
From:
Posted: Tuesday 30th of Apr 16:20 Hello there I have almost taken the decision to look fora math private teacher, because I've been having a lot of problems with math homework recently . each time when I come home from school I waste hours and hours with my math homework, and in the end I still seem to be getting the wrong answers. However I'm also not certain if a math tutor is worth it, since it's really expensive, and who knows, maybe it's not even so good . Does anyone know anything about difference of squares calculator that can help me? Or maybe some explanations about interval notation,converting fractions or adding matrices? Any ideas will be valued.
espinxh
Registered: 17.03.2002
From: Norway
Posted: Thursday 02nd of May 09:47 There used to be a time when those were the only ways out. But thanks to technology today , we have something known as the Algebrator! It’s quite easy to use, something which even a total newbie would enjoy working on and what’s even better is that it would solve all your questions and also explain the steps it took to reach that solution ! Isn’t that just great ? Well I think it is, and I’m sure after using it trying it, you’ll be on the same page as me.
Techei-Mechial
Registered: 14.10.2001
From:
Posted: Friday 03rd of May 14:46 Even I got help from Algebrator to learn the basic principles of Pre Algebra a month back. It is worth investing in the purchase of Algebrator since it offers qualitytutoring in Algebra 2 and is available at an affordable rate. | 468 | 2,084 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2023-23 | longest | en | 0.961312 |
https://www.teacherspayteachers.com/Product/Least-Common-Multiple-I-have-Who-has-Activity-1950647 | 1,495,991,672,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463610342.84/warc/CC-MAIN-20170528162023-20170528182023-00161.warc.gz | 1,193,364,016 | 20,852 | # Main Categories
Total:
\$0.00
Whoops! Something went wrong.
# Least Common Multiple I have, Who has Activity!
Common Core Standards
Product Rating
4.0
1 rating
File Type
PDF (Acrobat) Document File
1 MB|6 pages
Product Description
Description of product:
Aligns with common core standard 4.0A.B.4:
Find all factor pairs for a whole number in the range 1-100. *Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.* Determine whether a given whole number in the range 1-100 is prime or composite.
This product is designed to be used as a whole class review. You can also turn it into small group practice with each student having more than one card, or teaming students up to work together.
There are 24 total cards- You will need to cut cards apart and pass out. This works best if each student is solving the LCM of each card along the way!
p.s. They are in order as is and will need to be shuffled up
-Emma
Total Pages
6 pages
N/A
Teaching Duration
N/A
• Product Q & A
\$1.00
\$1.00 | 283 | 1,114 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2017-22 | longest | en | 0.91696 |
https://uk.mathworks.com/matlabcentral/cody/players/3001298-shaun-vanweelden/badges | 1,566,644,998,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027320734.85/warc/CC-MAIN-20190824105853-20190824131853-00270.warc.gz | 689,876,268 | 15,750 | Cody
# Shaun VanWeelden
Rank
Score
1 – 60 of 62
#### Solver+10
Earned on 26 Apr 2012 for solving Problem 1. Times 2 - START HERE.
#### Commenter+10
Earned on 27 Feb 2013 for commenting on Problem 9. Who Has the Most Change?.
#### Creator+20
Earned on 8 Oct 2013 for creating Problem 1919. Returning a "greater than" vector.
#### Promoter+10
Earned on 20 Oct 2013 for liking Problem 141. Solve the Sudoku Row.
#### Quiz Master+20
Earned on 30 Nov 2017 for having 50 or more solvers for Problem 1919. Returning a "greater than" vector.
#### CUP Challenge Master+50
Solve all the problems in CUP Challenge problem group.
#### Speed Demon+50
Solve a problem first.
#### Community Group Solver+50
Solve a community group
#### Introduction to MATLAB Master+50
Solve all the problems in Introduction to MATLAB problem group.
Solve a problem with a best solution.
#### Cody Challenge Master+50
Solve all the problems in Cody Challenge problem group.
#### ASEE Challenge Master+50
Solve all the problems in ASEE Challenge problem group.
#### Tiles Challenge Master+50
Solve all the problems in Tiles Challenge problem group.
#### Curator+50
25 solvers for the group curated by the player
#### Scholar+50
Solve 500 problems.
#### Cody5:Easy Master+50
Solve all the problems in Cody5:Easy problem group.
#### Puzzler+50
Create 10 problems.
#### Indexing I Master+50
Solve all the problems in Indexing I problem group.
#### Project Euler I Master+50
Solve all the problems in Project Euler I problem group.
#### Draw Letters Master+50
Solve all the problems in Draw Letters problem group.
#### Indexing II Master+50
Solve all the problems in Indexing II problem group.
#### Matrix Manipulation I Master+50
Solve all the problems in Matrix Manipulation I problem group.
#### Cody Problems in Japanese Master+50
Solve all the problems in Cody Problems in Japanese problem group.
#### Magic Numbers Master+50
Solve all the problems in Magic Numbers problem group.
#### Sequences & Series I Master+50
Solve all the problems in Sequences & Series I problem group.
#### Computational Geometry I Master+50
Solve all the problems in Computation Geometry I problem group.
#### Famous+20
Must receive 25 total likes for the problems you created.
#### Divisible by x Master+50
Solve all the problems in Divisible by x problem group.
#### Strings I Master+50
Solve all the problems in Strings I problem group.
#### Matrix Patterns I Master+50
Solve all the problems in Matrix Patterns problem group.
#### R2016b Feature Challenge Master+50
Solve all the problems in R2016b Feature Challenge problem group.
#### Number Manipulation I Master+50
Solve all the problems in Number Manipulation I problem group.
#### Matrix Manipulation II Master+50
Solve all the problems in Matrix Manipulation II problem group.
#### Cody5:Hard Master+50
Solve all the problems in Cody5:Hard problem group.
#### Indexing III Master+50
Solve all the problems in Indexing III problem group.
#### Matrix Patterns II Master+50
Solve all the problems in Matrix Patterns II problem group.
#### Likeable+20
Must receive 10 likes for a problem you created.
#### Celebrity+20
Must receive 50 total likes for the solutions you submitted.
#### Sequences & Series II Master+50
Solve all the problems in Sequences & Series II problem group.
#### Functions I Master+50
Solve all the problems in Functions I problem group.
#### Matrix Patterns III Master+50
Solve all the problems in Matrix Patterns III problem group.
#### Magic Numbers II Master+50
Solve all the problems in Magic Numbers II problem group.
#### Indexing V Master+50
Solve all the problems in Indexing V problem group.
#### Renowned+20
Must receive 10 likes for a solution you submitted.
#### Card Games Master+50
Solve all the problems in Card Games problem group.
#### Strings II Master+50
Solve all the problems in Strings II problem group.
#### Matrix Manipulation III Master+50
Solve all the problems in Matrix Manipulation III problem group.
#### Sequences & Series III Master+50
Solve all the problems in Sequences & Series III problem group.
#### Computational Geometry II Master+50
Solve all the problems in Computational Geometry II problem group.
#### Indexing IV Master+50
Solve all the problems in Indexing IV problem group.
#### Number Manipulation II Master+50
Solve all the problems in Number Manipulation II problem group.
#### Strings III Master+50
Solve all the problems in Strings III problem group.
#### Computational Geometry IV Master+50
Solve all the problems in Computational Geometry IV problem group.
#### Word Puzzles Master+50
Solve all the problems in Word Puzzles problem group.
#### Computational Geometry III Master+50
Solve all the problems in Computational Geometry III problem group.
#### Computer Games I Master+50
Solve all the problems in Computer Games I problem group.
#### Logic Master+50
Solve all the problems in Logic problem group.
#### Combinatorics I Master+50
Solve all the problems in Combinatorics - I problem group.
#### Fundamentals of robotics: 2D problems Master+50
Solve all the problems in Fundamentals of robotics problem group.
#### Modeling & Simulation Challenge Master+50
Solve all the problems in Modeling and Simulation Challenge problem group. | 1,242 | 5,337 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2019-35 | latest | en | 0.771797 |
https://www.mmo-champion.com/threads/1400125-Probability/page2?p=23711159 | 1,521,617,782,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647584.56/warc/CC-MAIN-20180321063114-20180321083114-00338.warc.gz | 861,017,885 | 24,741 | 1. Originally Posted by voidspark
Your chance of getting it your next run is the same as the chance of getting it your first run. That said, it's about a 1% drop rate. If you run the place 458 more times, you will (with a 99% chance) get the mount.
You also don't understand probability. If the chance to drop is 1%, it doesn't matter how many times you run the place. On the 1000th run the chance to drop is still 1%. On the 10,000th run the chance to drop is still 1%.
2. Originally Posted by Daedelus
You also don't understand probability. If the chance to drop is 1%, it doesn't matter how many times you run the place. On the 1000th run the chance to drop is still 1%. On the 10,000th run the chance to drop is still 1%.
You're the one that isn't understanding. I did not say "on the 458th run," I said "in 458 runs."
The chance you get zero drops on run 1, 2, 3, 4, 5, 6, ..., 456, 457, AND 458 is 1%.
3. Originally Posted by voidspark
You're the one that isn't understanding. I did not say "on the 458th run," I said "in 458 runs."
The chance you get zero drops on run 1, 2, 3, 4, 5, 6, ..., 456, 457, AND 458 is 1%.
The previous 457 runs have no bearing on the chance on the 458th run, which remains at 0.0078. As I said, you don't understand probability.
The question is not "What is the chance I get zero drops in 458 runs?". The question is "What is the chance I get the mount this run?", which is 0.0078.
4. Originally Posted by Daedelus
The previous 457 runs have no bearing on the chance on the 458th run, which remains at 0.0078. You don't understand probability.
You're the one that is incorrect factually, there's no "argument" to be had here. Please stop trying to sound so brilliant repeating an obvious fact that has been said at least 20 times in this thread (including by me) when you have no clue what you're talking about.
I am not talking about JUST the 458th run, I am talking about ALL 458 runs. In a similar vein if I flipped a coin 10 times, yes, the chance I get a head on exactly the 10th flip is 0.5, but the chance I get at least one head in ANY of the 10 flips is quite a bit more than 0.5.
Edit: Person I'm quoting is actually not factually incorrect insofar that what he is saying himself is true, but he does suffer from "inability to read" syndrome, so he's wrong when claiming I am Please read my statements carefully!
5. Originally Posted by voidspark
I am not talking about JUST the 458th run, I am talking about ALL 458 runs. In a similar vein if I flipped a coin 10 times, yes, the chance I get a head on exactly the 10th flip is 0.5, but the chance I get at least one head in ANY of the 10 flips is quite a bit more than 0.5.
What's that got to do with anything? The chance of getting a head on the nth flip (substitute any number for n) is 0.5
Why are you labouring under the illusion that previous flips have any effect on the next flip? They don't. Same goes for mount drops.
6. The probability problem you described has tricked numerous people that gamble.
Suppose you are betting on an event that 9 of 10 times comes true.
A gambler might think by progressive betting is going to win if he keeps chasing a 1/10 loss.
However it is possible or probable that even a 9/10 winner will lose 20,30,40,100,1000 times. Suppose your original bet is 1\$ by betting progresively you will be risking thousands or even millions to win 1\$ and risk still losing.
Casinos and bookmakers, because of that, love progressive staking players.
7. Exactly. People can keep doing mount runs thinking that their chance is increasing each time, but it isn't. More fool you.
That said, "you've got to be in it to win it".
8. Well for probability to be understandable you have to realize 2 things. You're not trying to measure your chance to get it but the chance to NOT get it . atm you are at ~54.7% NOT to get the mount.
Doing one run every day reduces that amount until eventually your chance not to get it will be equal to your chance to get it.
X=Chance to drop
Y=Chance to not drop
Z=Number of runs required.
X=Y^Z which gives us a number of Z=619.
This means after 619 runs you have better chances of getting it than not getting it but it's STILL A FUCKING CHANCE !
Go do a sacrifice to the RNG gods ... they will guide you to the path of luck and eventually... to epic mount !
9. Originally Posted by Arian21
Well for probability to be understandable you have to realize 2 things. You're not trying to measure your chance to get it but the chance to NOT get it . atm you are at ~54.7% NOT to get the mount.
Doing one run every day reduces that amount until eventually your chance not to get it will be equal to your chance to get it.
X=Chance to drop
Y=Chance to not drop
Z=Number of runs required.
X=Y^Z which gives us a number of Z=619.
This means after 619 runs you have better chances of getting it than not getting it but it's STILL A FUCKING CHANCE !
Go do a sacrifice to the RNG gods ... they will guide you to the path of luck and eventually... to epic mount !
Wrong. Wrong. Wrong.
If you flip a coin 99 times and get heads every time, what is the probability of you getting tails on the 100th flip?
10. Originally Posted by Daedelus
What's that got to do with anything? The chance of getting a head on the nth flip (substitute any number for n) is 0.5
What it has to do with the OP: If he runs the place 458 more times, he has a 99% chance to get the mount.
What it has to do with you: Either you are deliberately being dense or totally ignorant. Since cumulative probability is quite difficult to understand, I am wholly understanding and sympathetic to your total inability to grasp the concept, if it is the latter.
I'm not going to go in circles about simple facts.
- - - Updated - - -
Originally Posted by Daedelus
Wrong. Wrong. Wrong. If you flip a coin 99 times and get heads every time, what is the probability of you getting tails on the 100th flip?
I'll try to break it down one last time, in case it's really just you understanding:
He. is. not. describing. the. same. problem. you. are. describing.
P.S to Arian21: The 0.0079 came from Wowhead which is only an estimate since only Blizzard knows the true drop chances. Most people believe the actual drop rate is set to 1% (could be 0.8%, could be 1.2% for some similar mounts).
11. Originally Posted by voidspark
He. is. not. describing. the. same. problem. you. are. describing.
Yes he is. Why do his previous runs have any bearing on his next run? There's nothing cumulative about this. Please explain to me how it is, I'm interested to know why you erroneously think that.
I like the way you are trying to make out I don't understand what I'm talking about. The irony is beautiful.
12. Originally Posted by Daedelus
I like the way you are trying to make out I don't understand what I'm talking about.
... because you don't. Anyway I'm through with you, just suggesting that OP and others put this troll on ignore.
@ OP: If you run the place 458 more times, you'll have a 99% chance at the mount. That said theoretically what others have said is right... you could run the place until the servers shut down (you are limited to 5 runs per hour and servers will shut down within your lifetime) and never get the mount, but in the same vein you could theoretically flip a fair coin until you die and never flip tails.
If you run it 5 times a day, you'll have it pretty confidently within a few months
13. Gambler's fallacy.
Whether or not you get the mount on one kill has absolutely no bearing on whether or not you get it on the next kill.
Every single time you kill the monster, there is a 0.78% chance (0.0078 chance) of the mount dropping. You are equally likely the receive the mount on your first kill as you are on your tenth, fiftieth, two-thousandth, and millionth kills.
14. Originally Posted by Daedelus
Yes he is. Why do his previous runs have any bearing on his next run? There's nothing cumulative about this.
I like the way you are trying to make out I don't understand what I'm talking about. The irony is beautiful.
You don't understand what you are talking about.
Assume a 1% drop chance for simplicity's sake. What is the cumulative probability of seeing a drop by the 50th run?
Answer: 1 - (0.99 ^ 50) = 39.5%
What is the cumulative probability of seeing a drop by the 500th run?
Answer: 1 - (0.99 ^ 500) = 99.3%
This is what we are talking about. We are not saying that the drop rate changes with repeated attempts.
15. voidspark, you are the troll, trying to give out bullshit stats. There are plenty of people here who have explained this problem very clearly (including Neganova above) and you still can't understand.
16. Originally Posted by 7seti
Assume a 1% drop chance for simplicity's sake. What is the cumulative probability of seeing a drop by the 50th run?
Right. Most people in statistics are well aware that independent events are independent. That said there's not a whole lot interesting about them. What most people are interested in is cumulative probabilities, for instance, what's the chance that the next week we'll get a storm? (Not the chance of getting a storm the next particular minute, for instance). Not "what's the chance I win a game one time I play it" but rather, what the statistics/odds are long term after several iterations of the same game.
That said it's quite difficult to understand the difference so I have to forgive people for being "dumb" about it... as for being "dense" about it, not so sure.
17. Originally Posted by 7seti
You don't understand what you are talking about.
Assume a 1% drop chance for simplicity's sake. What is the cumulative probability of seeing a drop by the 50th run?
Answer: 1 - (0.99 ^ 50) = 39.5%
What is the cumulative probability of seeing a drop by the 500th run?
Answer: 1 - (0.99 ^ 500) = 99.3%
This is what we are talking about. We are not saying that the drop rate changes with repeated attempts.
THERE IS NOTHING CUMULATIVE ABOUT THIS. Jesus, I give up.
18. Originally Posted by Daedelus
THERE IS NOTHING CUMULATIVE ABOUT THIS. Jesus, I give up.
I advise you to study more probability if you wish to come off as an "expert" but I understand if you give up. It's not for everyone
Here's another justification which could help you "understand" if that is even possible (you don't seem to have a desire to read anything I write): There is a reason I said the next 458 runs, and did not give him credit for the ~40-50 runs he previously did already.
19. I'm really tempted to post the Monty Hall problem and watch people's heads explode.
20. Originally Posted by 7seti
I'm really tempted to post the Monty Hall problem and watch people's heads explode.
Haha, let's keep it relevant!
#### Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• | 2,754 | 10,890 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2018-13 | latest | en | 0.976578 |
https://au.mathworks.com/matlabcentral/cody/problems/43086-recursion-at-variable-input/solutions/2976385 | 1,604,153,037,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107918164.98/warc/CC-MAIN-20201031121940-20201031151940-00256.warc.gz | 193,675,568 | 16,884 | Cody
# Problem 43086. Recursion at variable input
Solution 2976385
Submitted on 21 Sep 2020 by David Hill
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
x = 1; y_correct = 1; assert(isequal(pow2Pow(x),y_correct))
2 Pass
x = 2; y =2; y_correct = 4; assert(isequal(pow2Pow(x,y),y_correct))
3 Pass
x = 2; y= 2; z=3; y_correct = 64; assert(isequal(pow2Pow(x,y,z),y_correct))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 188 | 628 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2020-45 | latest | en | 0.67365 |
https://docest.com/doc/684000/sampling-distributions-chapter-4 | 1,721,667,754,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517890.5/warc/CC-MAIN-20240722160043-20240722190043-00104.warc.gz | 178,092,127 | 9,807 | 9 - Sampling Distributions and Confidence Intervals for m & p
Introduction:
When take a sample of size n from a population and calculate summary statistics like the sample mean , the sample median (med), the sample variance (), the sample standard deviation (s), or the sample proportion ) we must realize that these quantities will ______and hence are themselves ______.
Any random variable in statistics has a probability distribution. We have been talking about three common probability distributions in statistics. When X = # of “successes” in n independent trials we used the binomial distribution to talk about X probabilistically, when X = # of occurrences in a fixed time/space unit we used the Poisson distribution, and finally when X was continuous and had an approximate bell-shaped distribution we used the normal distribution to calculate probabilities and quantiles associated with X.
Because the summary statistics discussed above are random variables they also have a probability distribution that determines the likelihood of certain values of these statistics being obtained. The distribution of a summary statistic, e.g. the sample mean is called the ______.
In this handout we explore the sampling distributions of the sample mean () and the sample proportion ().
Sampling Distribution of
The sample mean () is a random quantity that varies from sample to sample. The probability distribution the sample mean follows is called the sampling distribution of.
The sampling distribution demo I showed in class is found at the following web address:
http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/
The Central Limit Theorem for the Sample Mean (CLT) ~ tells us about the sampling distributions of the sample mean (). There is also a version (which we will see later) that tells us about the sampling distribution of the sample proportion () .
The CLT for says the following:
1.
2.
3. The sampling distribution will be ______if either of the conditions
below are met:
·
or if
·
We now consider applications of the central limit theorem (CLT).
Applications to Decision Making
Example 1: Cholesterol levels of adult males (50-60 yrs. old)
The mean blood cholesterol level of adult males (50-60 yrs. old) is 200 mg/dl with a standard deviation of 20 mg/dl. Assume also that blood cholesterol levels are approximately normally distributed in this population.
a) What is the probability that when taking a sample of size n = 25 that you would obtain sample mean greater than 225 mg/dl?
b) Give a range of values that we would expect the sample mean to fall approximately 95% of the time.
c) Suppose we took sample of adult males between the ages of 50 – 60 who are also strict vegetarians and obtained sample mean of 188 mg/dl. Does this provide evidence that the subpopulation of vegetarians have a lower mean cholesterol level that the greater population of men in this age group? Explain.
Example 2: Mercury Levels Found in Boulder Reservoir Walleyes
Fish consumption guidelines suggest you should limit the number of fish you eat with Hg levels above .25 ppm. Is there evidence to suggest that walleyes from Boulder Reservoir have a mean Hg content exceeding .25 ppm?
Confidence Intervals for the Population Mean (m)
Motivating Example: Suppose we are trying to estimate the mean protein content of zebra mussels, which are becoming an increased part of the diet for ducks on the Mississippi River. A sample of n = 25 zebra mussels are analyzed for their protein content and a sample mean ofunits.
This is called a ______for the population mean (m) because it yields a single value for this unknown quantity.
A better estimate might be 9.14 give or take _____ units, i.e. ______up to ______. This is called an ______ as it gives a range or interval of plausible values for the population mean.
How do we know this if this a good interval estimate? ______
What properties should a good interval estimate have?
· It
· dfk
The central limit theorem states that if our sample size (n) is sufficiently large, then which also implies that after standardizing
This means that when we collect our data the probability our observed sample mean will fall within two standard errors of the mean is approximately .95 or a 95% chance, or being more precise we could use 1.96 standard errors because
Which gives
For a 99% chance we use ______and for 90% we use ______in place of 1.96.
Starting with the statement,
we will perform algebraic manipulations to isolate the population mean m in the middle of this inequality instead. By doing this we will obtain an interval that has a 95% chance of covering the true population mean.
Algebraic Manipulations of the Inequality on the Previous Page:
This says that the interval from up to has a 95% chance of covering the true population mean m. This interval is simply the sample mean plus or minus roughly two standard errors. However, this interval cannot be calculated in practice! WHY?
A “simple fix” to this would be replace ____ by the estimated standard deviation from our data _____.
The problem with our “simple fix” is that the distribution of is not standard normal, i.e. N(0,1) therefore the 1.96 value will not necessarily produce the desired level
of confidence.
FACT: If the population we are sampling from is approximately normal then
has a t-distribution with degrees of freedom df = n – 1.
What does a t-distribution look like?
·
Examples: Using the t-table to find confidence intervals
a) n = 20 and 95% confidence t =
b) n = 20 and 99% confidence t =
c) n = 50 and 90% confidence t =
d) n = 10 and 95% confidence t =
The basic form of most confidence intervals is:
General Form for a Confidence Interval for the Mean
For the population mean we have,
or
The appropriate columns in t-distribution table) for the different confidence intervals are as follows:
90% Confidence look in the .05 column (if n is “large” we can use 1.645)
95% Confidence look in the .025 column (if n is “large” we can use 1.960)
99% Confidence look in the .005 column (if n is “large” we can use 2.576)
Example: Suppose we are trying to estimate the mean protein content of zebra mussels, which are becoming an increased part of the diet for ducks on the Mississippi River. A sample of n = 25 zebra mussels are analyzed for their protein content and a sample mean ofunits with a sample standard deviation of s = 2.98 units.
a) Use this information to find a 95% CI for the mean protein content found in the tissues of zebra mussels, assuming that protein content of zebra mussels has a normal distribution.
Suppose a sample of n = 25 freshwater clams was obtained and similar protein analysis was conducted resulting in a sample mean units with a standard deviation of s = 12.12 units.
b) Find a 95% confidence interval for the mean protein content found in the tissue of freshwater clams.
c) Does this interval in conjunction with the interval obtained for zebra mussels provide evidence that freshwater clams are richer in protein than zebra mussels?
Sampling Distribution of the Sample Proportion ()
Just like the sample mean the sample proportion () is random, as it too varies from sample to sample. The sampling distribution of has the following properties:
1. The mean of the sampling distribution is the population proportion (p)
2. The standard deviation of the sampling distribution or the standard error of
and is given by:
where
3. The sampling distribution is approx. normal provided n is “sufficiently large”.
Note: When estimating proportions large sample sizes are generally used
(e.g. n 100)
APPLICATIONS TO DECISION MAKING
Example: New Method for Treating a Certain Illness/Disease
Suppose the current treatment method for certain disease has 70% success rate. A new method has been proposed that will hopefully have a higher success rate. The new method is administered to a sample n = 50 patient and 40 have successful treatment.
Can we conclude on the basis of this result that the new method has a higher success rate?
Using the Binomial Table (this is called the Binomial Exact Test, see Sec. 11.1)
CONFIDENCE INTERVALS FOR THE POPULATION PROPORTION (Sec. 4.5)
Motivating Example: A study of 200 rainbow trout caught on baited size 8 barbed hooks and released with the line cut at the hook (but the hook not removed from the fish) showed that 58 fish died (from the National Symposium on Catch and Release Fishing).
An estimate of the proportion of trout that die when caught and released in this fashion is .29 or 29%. A better estimate might be 29% give or take 4%, i.e. estimating that the actual percentage of that will die to be somewhere between 25% and 33%. This is called an “interval estimate”, as it gives a range or interval of plausible values for the population proportion/percentage. As with the population mean discussed earlier, we wish this interval to be narrow enough to provide useful information about this unknown percentage, yet have a high probability or chance of covering the actual percentage of trout that will die under this catch and release strategy.
The central limit theorem for proportions states that if our sample size (n) is sufficiently large, then . This means that when we take our sample and find our sample proportion,, the probability our observed sample proportion will fall within approximately two standard errors of the population proportion is roughly 95%, or more precisely
ß Recall:
Starting with this statement we can perform some algebraic manipulations to isolate the population proportion, p, in the middle of the inequality above. By doing this we will see that the resulting interval will have a 95% chance of covering the true population proportion (p).
After a wonderful algebraic manipulation of the equality above :
This says that the interval from up to has a 95% chance of covering the true population proportion p. This interval is simply the sample proportion plus or minus roughly two standard errors, i.e. . However, this interval cannot be calculated in practice! WHY?
A simple fix is to replace ______by our sample based estimate ______. Provided the sample size is sufficient large the resulting interval will still have an approximate 95% chance of covering the true population proportion. This gives what we should technically call the estimated standard error of the proportion, but when we say “standard error of the proportion” it is assumed this estimated version is the one we are talking about because in reality the population proportion p is NOT known. If p were known we would not be conducting a study in first place!
General Form for a CI for Population Proportion (p)
Normal Table Values:
95% Confidence we use z = 1.96
90% Confidence we use z = 1.645
99% Confidence we use z = 2.576
Example: Mortality of Released Rainbow Trout with Barbed Hooks (cont’d)
A study of 200 rainbow trout caught on baited size 8 barbed hooks and released with the line cut at the hook (but the hook not removed from the fish) showed that 58 fish died (from the National Symposium on Catch and Release Fishing). Using this information to construct a 95% confidence interval for the percentage of rainbow trout that will die when caught and released using baited size 8 barbed hooks.
Mortality of Released Rainbow Trout Caught with Barbless Hooks
In a similar study of 855 rainbow trout caught using barbless hooks it was found that 26 of them died. Use this information to construct a 95% confidence interval for the percentage of rainbow trout that will die when caught and released using barbless hooks.
Comparing the Mortality Rates
Does this interval suggest that the mortality rate of rainbow trout is lower when caught and released using barbless hooks as opposed to barbless? Explain.
Construct a 2 X 2 contingency table from the combined results of these studies. Then find the RR and OR associated with using barbed hooks when catching and releasing rainbow trout.
10 – Confidence Intervals for the RR and OR
Recall that the =
The RR can only be calculated when the number individuals with and without the disease in the study are random. If a case-control study is used where these numbers are fixed it is inappropriate to calculate the necessary conditional probability to find the RR.
The OR = =
and gives a measure risk associated with the risk factor in terms a multiplicative statement regarding the odds for the having the disease. We now examine confidence intervals for these quantities.
CI for RR:
1) Take natural logarithm of RR to obtain .
2) Compute SE(ln(RR)) =
3) Find to obtain (LCL, UCL) | 2,685 | 12,652 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2024-30 | latest | en | 0.906918 |
https://forum.codingame.com/t/community-puzzle-euclids-algorithm-with-complex-numbers/201167 | 1,695,674,758,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510085.26/warc/CC-MAIN-20230925183615-20230925213615-00594.warc.gz | 291,150,179 | 4,552 | # [Community Puzzle] Euclid's algorithm with complex numbers
Coding Games and Programming Challenges to Code Better
Created by @Rafarafa,validated by @Edjy,@Diabetos and @DeanTheMachine.
If you have any issues, feel free to ping them.
Does anybody know why test 5 in validator fails?
Does everything else pass, validators and tests ?
If so, the reason probably is because you have useless parenthesis on the line before the last, you should print “2j = …” and you print (or so I think) “(2j) = …” or “(0+2j) = …”, the issue should not appear if you use complex from python, but if you programmed it yourself or used another language it can be not shown as expected. That is the only thing I could see specific to the validator 5.
I don’t think there is any error about parenthesis.
Well if you don’t explain what you’ve done I’m not sure I can’t be of any more help to you,
here are the validators entries so you can look up what’s wrong.
Spoiler
32 733
-351 -455
What are the expected results?
Expected result
``````(32+733j) = (-351-455j) * (-1-1j) + (136-73j)
(-351-455j) = (136-73j) * (-1-4j) + (77+16j)
(136-73j) = (77+16j) * (2-1j) + (-34-28j)
(77+16j) = (-34-28j) * (-2+1j) + (-19-6j)
(-34-28j) = (-19-6j) * (2+1j) + (-2+3j)
(-19-6j) = (-2+3j) * (2+5j) + -2j
(-2+3j) = -2j * (-1-1j) + 1j
-2j = 1j * (-2+0j) + 0j
GCD((32+733j), (-351-455j)) = 1j
`````` | 476 | 1,368 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2023-40 | latest | en | 0.797658 |
https://www.nuclear-power.net/nuclear-engineering/materials-science/material-properties/strength/hookes-law/youngs-modulus-of-elasticity/ | 1,618,725,726,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038468066.58/warc/CC-MAIN-20210418043500-20210418073500-00383.warc.gz | 1,012,668,667 | 53,393 | # Young’s Modulus of Elasticity
The Young’s modulus of elasticity is the elastic modulus for tensile and compressive stress in the linear elasticity regime of a uniaxial deformation and is usually assessed by tensile tests. Young’s modulus is named after the 19th-century British scientist Thomas Young.
Most polycrystalline materials have within their elastic range an almost constant relationship between stress and strain. In 1678 an English scientist named Robert Hooke ran experiments that provided data that showed that in the elastic range of a material, strain is proportional to stress. Robert Hooke concluded that the force F in any spring is proportional to the extension (the deformation from the relaxed state) x as follows:
F = k · x
where the term k is the stiffness of the spring and x is small compared to the total possible deformation of the spring. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state.
In case of tensional stress of a uniform bar (stress-strain curve), the Hooke’s law describes behaviour of a bar in the elastic region. In this region, the elongation of the bar is directly proportional to the tensile force and the length of the bar and inversely proportional to the cross-sectional area and the modulus of elasticity. Up to a limiting stress, a body will be able to recover its dimensions on removal of the load. The applied stresses cause the atoms in a crystal to move from their equilibrium position. All the atoms are displaced the same amount and still maintain their relative geometry. When the stresses are removed, all the atoms return to their original positions and no permanent deformation occurs. According to the Hooke’s law, the stress is proportional to the strain (in the elastic region), and the slope is Young’s modulus. Young’s modulus is equal to the longitudinal stress divided by the strain.
The elastic moduli relevant to polycrystalline materials:
• Young’s Modulus of Elasticity. The Young’s modulus of elasticity is the elastic modulus for tensile and compressive stress in the linear elasticity regime of a uniaxial deformation and is usually assessed by tensile tests. Young’s modulus is named after the 19th-century British scientist Thomas Young.
• Shear Modulus of Elasticity. The shear modulus, or the modulus of rigidity, is derived from the torsion of a cylindrical test piece. It describes the material’s response to shear stress. Its symbol is G. The shear modulus is one of several quantities for measuring the stiffness of materials and it arises in the generalized Hooke’s law.
• Bulk Modulus of Elasticity. The bulk modulus of elasticity is describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions. For example, it describes the elastic response to hydrostatic pressure and equilateral tension (like the pressure at the bottom of the ocean or a deep swimming pool). It is also the property of a material that determines the elastic response to the application of stress. For a fluid, only the bulk modulus is meaningful.
References:
Materials Science:
1. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
2. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 2 and 2. January 1993.
3. William D. Callister, David G. Rethwisch. Materials Science and Engineering: An Introduction 9th Edition, Wiley; 9 edition (December 4, 2013), ISBN-13: 978-1118324578.
4. Eberhart, Mark (2003). Why Things Break: Understanding the World by the Way It Comes Apart. Harmony. ISBN 978-1-4000-4760-4.
5. Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing. ISBN 978-1-56032-992-3.
6. González-Viñas, W. & Mancini, H.L. (2004). An Introduction to Materials Science. Princeton University Press. ISBN 978-0-691-07097-1.
7. Ashby, Michael; Hugh Shercliff; David Cebon (2007). Materials: engineering, science, processing and design (1st ed.). Butterworth-Heinemann. ISBN 978-0-7506-8391-3.
8. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
Hooke’s law | 1,001 | 4,364 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-17 | latest | en | 0.918889 |
https://blogs.mathworks.com/loren/?p=3845/? | 1,627,527,688,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153814.37/warc/CC-MAIN-20210729011903-20210729041903-00220.warc.gz | 161,461,343 | 36,147 | # Automatic Differentiation in Optimization Toolbox™
This column is written by Alan Weiss, the writer for Optimization Toolbox documentation. Take it away, Alan.
Hi, folks. You may know that solving an optimization problem, meaning finding a point where a function is minimized, is easier when you have the gradient of the function. This is easy to understand: the gradient points uphill, so if you travel in the opposite direction, you generally reach a minimum. Optimization Toolbox algorithms are based on more sophisticated algorithms than this, yet these more sophisticated algorithms also benefit from a gradient.
How do you give a gradient to a solver along with the function? Until recently, you had to calculate the gradient as a separate output, with all the pain and possibility of error that entails. However, with R2020b, the problem-based approach uses automatic differentiation for the calculation of problem gradients for general nonlinear optimization problems. I will explain what all of those words mean. In a nutshell, as long as your function is composed of elementary functions such as polynomials, trigonometric functions, and exponentials, Optimization Toolbox calculates and uses the gradients of your functions automatically, with no effort on your part.
The "general nonlinear" phrase means that automatic differentiation applies to problems that fmincon and fminunc solve, which are general constrained or unconstrained minimization, as opposed to linear programming or least-squares or other problem types that call other specialized solvers.
Automatic differentiation, also called AD, is a type of symbolic derivative that transforms a function into code that calculates the function values and derivative values at particular points. This process is transparent; you do not have to write any special code to use AD. Actually, as you'll see later, you have to specify some name-value pairs in order not to have the solver use AD.
### Contents
#### Problem-Based Optimization
The problem-based approach to optimization is to write your problem in terms of optimization variables and expressions. For example, to minimize the test function ${\rm fun}(x,y) = 100(y-x^2)^2 + (1-x)^2$ inside the unit disk $x^2+y^2\le 1$, you first create optimization variables.
x = optimvar('x');
y = optimvar('y');
You then create optimization expressions using these variables.
fun = 100*(y - x^2)^2 + (1 - x)^2;
unitdisk = x^2 + y^2 <= 1;
Create an optimization problem with these expressions in the appropriate problem fields.
prob = optimproblem("Objective",fun,"Constraints",unitdisk);
Solve the problem by calling solve, starting from x = 0, y = 0.
x0.x = 0;
x0.y = 0;
sol = solve(prob,x0)
Solving problem using fmincon.
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
sol =
struct with fields:
x: 0.7864
y: 0.6177
The solve function calls fmincon to solve the problem. In fact, solve uses AD to speed the solution process. Let's examine the solution process in more detail to see this in action. But first, plot the logarithm of one plus the objective function on the unit disk, and plot a red circle at the solution.
[R,TH] = ndgrid(linspace(0,1,100),linspace(0,2*pi,200));
[X,Y] = pol2cart(TH,R);
surf(X,Y,log(1+100*(Y - X.^2).^2 + (1 - X).^2),'EdgeColor','none')
colorbar
view(0,90)
axis equal
hold on
plot3(sol.x,sol.y,1,'ro','MarkerSize',10)
hold off
#### Effect of Automatic Differentiation
To examine the solution process in more detail, solve the problem again, this time requesting more solve outputs. Examine the number of iterations and function evaluations that the solver takes.
[sol,fval,exitflag,output] = solve(prob,x0);
fprintf('fmincon takes %g iterations and %g function evaluations.\n',...
output.iterations,output.funcCount)
Solving problem using fmincon.
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
fmincon takes 24 iterations and 34 function evaluations.
The output structure shows that the solver takes 24 iterations and 34 function counts. Run the problem again, this time enforcing that the solver does not use AD.
[sol2,fval2,exitflag2,output2] = solve(prob,x0,...
'ObjectiveDerivative',"finite-differences",'ConstraintDerivative',"finite-differences");
fprintf('fmincon takes %g iterations and %g function evaluations.\n',...
output2.iterations,output2.funcCount)
plot([1 2],[output.funcCount output2.funcCount],'r-',...
[1 2],[output.funcCount output2.funcCount],'ro')
ylabel('Function Count')
xlim([0.8 2.2])
ylim([0 90])
legend('Function Count (lower is better)','Location','northwest')
ax = gca;
ax.XTick = [1,2];
Solving problem using fmincon.
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
fmincon takes 24 iterations and 84 function evaluations.
This time the solver takes 84 function counts, not 34. The reason for this difference is automatic differentiation.
The solutions are nearly the same with or without AD:
fprintf('The norm of solution differences is %g.\n',norm([sol.x,sol.y] - [sol2.x,sol2.y]))
The norm of solution differences is 1.80128e-09.
#### What Is Automatic Differentiation?
AD is similar to symbolic differentiation: each function is essentially differentiated symbolically, and the result is turned into code that MATLAB runs to compute derivatives. One way to see the resulting code is to use the prob2struct function. Let's try that on prob.
problem = prob2struct(prob);
problem.objective
ans =
function_handle with value:
@generatedObjective
prob2struct creates a function file named generatedObjective.m. This function includes an automatically-generated gradient. View the contents of the function file.
function [obj, grad] = generatedObjective(inputVariables)
%generatedObjective Compute objective function value and gradient
%
% OBJ = generatedObjective(INPUTVARIABLES) computes the objective value
% OBJ at the point INPUTVARIABLES.
%
%
% Auto-generated by prob2struct on 06-Oct-2020 09:01:35
%% Variable indices.
xidx = 1;
yidx = 2;
%% Map solver-based variables to problem-based.
x = inputVariables(xidx);
y = inputVariables(yidx);
%% Compute objective function.
arg1 = (y - x.^2);
arg2 = 100;
arg3 = arg1.^2;
arg4 = (1 - x);
obj = ((arg2 .* arg3) + arg4.^2);
if nargout > 1
arg5 = 1;
arg6 = zeros([2, 1]);
arg6(xidx,:) = (-(arg5.*2.*(arg4(:)))) + ((-((arg5.*arg2(:)).*2.*(arg1(:)))).*2.*(x(:)));
arg6(yidx,:) = ((arg5.*arg2(:)).*2.*(arg1(:)));
end
end
While this code might not be clear to you, you can compare the AD gradient calculation to a symbolic expression to see that they are the same:
$\nabla({\rm fun}) = [-400(y-x^2)x - 2(1-x);\ 200(y-x^2)]$
The way that solve and prob2struct convert optimization expressions into code is essentially the same way that calculus students learn, taking each part of an expression and applying rules of differentiation. The details of the process of calculating the gradient are explained in Automatic Differentiation Background, which describes the "forward" and "backward" process used by most AD software. Currently, Optimization Toolbox uses only "backward" AD.
To use these rules of differentiation, the software has to have differentiation rules for each function in the objective or constraint functions. The list of supported operators includes polynomials, trigonometric and exponential functions and their inverses, along with multiplication and addition and their inverses. See Supported Operations on Optimization Variables and Expressions.
#### What Good is Automatic Differentiation?
AD lowers the number of function evaluations the solver takes. Without AD, nonlinear solvers estimate gradients by finite differences, such as $(f(x+\delta e_1) - f(x))/\delta ,$ where $e_1$ is the unit vector (1,0,...,0). The solver evaluates n finite differences of this form by default, where n is the number of problem variables. For problems with a large number of variables, this process requires a large number of function evaluations.
With AD and supported functions, solvers do not need to take finite difference steps, so the derivative estimation process takes fewer function evaluations and is more accurate.
This is not to say that AD always speeds a solver. For complicated expressions, evaluating the automatic derivatives can be even more time-consuming than evaluating finite differences. Generally, AD is faster than finite differences when the problem has a large number of variables and is sparse. AD is slower when the problem has few variables and has complicated functions.
So far I have talked about automatic differentiation for supported operations. What if you have a black-box function, one for which the underlying code might not even be in MATLAB? Or what if you simply have a function that is not supported for problem-based optimization, such as a Bessel function? In order to include such functions in the problem-based approach, you convert the function to an optimization expression using the fcn2optimexpr function. For example, to use the besselj function,
fun2 = fcn2optimexpr(@(x,y)besselj(1,x^2 + y^2),x,y);
fcn2optimexpr allows you to use unsupported operations in the problem-based approach. However, fcn2optimexpr does not support AD. So, when you use fcn2optimexpr, solving the resulting problem uses finite differences to estimate gradients of objective or nonlinear constraint functions. For more information, see Supply Derivatives in Problem-Based Workflow.
Currently, AD does not support higher-order derivatives. In other words, you cannot generate code for a second or third derivative automatically. You get first-order derivatives (gradients) only.
#### Final Thoughts
AD is useful for increased speed and reliability in solving optimization problems that are composed solely of supported functions. However, in some cases it does not increase speed, and currently AD is not available for nonlinear least-squares or equation-solving problems.
In my opinion, the most useful feature of AD is that it is utterly transparent to use in problem-based optimization. Beginning in R2020b, AD applies automatically, with no effort on your part. Let us know if you find it useful in solving your optimization problems by posting your comment here.
Published with MATLAB® R2020b
| | 2,418 | 10,925 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2021-31 | longest | en | 0.934815 |
https://cupdf.com/document/mat-594cm-s10fundamentals-of-spatial-computingangus-forbes-week-4-curves.html | 1,695,740,174,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510214.81/warc/CC-MAIN-20230926143354-20230926173354-00550.warc.gz | 208,640,325 | 30,465 | MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes Week 4 : Curves Topics: parametric curves, Bezier curves, Hermite curves, b-splines/NURBS curves, NURBS surfaces
30
# MAT 594CM S10Fundamentals of Spatial ComputingAngus Forbes Week 4 : Curves Topics: parametric curves, Bezier curves, Hermite curves, b-splines/NURBS curves,
Dec 19, 2015
## Documents
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Week 4 : Curves
Topics: parametric curves, Bezier curves, Hermite curves, b-splines/NURBS curves, NURBS surfaces
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Families of curves
“Parametric Curves” - you have an explicit function for generating the curve
“Cubic Curves” (Bezier, Hermite, Catmull-Rom) - curves defined generally by particular geometric constraints, a basis matrix, and the cubic polynomials, Parameterized between 0 and 1.
“b-splines” (uniform b-splines, non-uniform b-splines, and NURBS, or non-uniform rational b-splines) - curves defined by a set of control points, a knot vector, and (for NURBS) weights for the control points. Parameterized between 0 and 1.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Parametric curves
A “parametric” curve is a curve that is parameterized by a function with a independent variable t, which defines the curve as it changes.
That is, for a function P(t), providing a number t results in a unique position vector P
ex: Linethe equation y = mx + b can be parameterized by t like so:Px = x0 + vxt
Py = y0 + vyt
where x0 and y0 are the intial values of x and y
v is a vector that is parallel to the line
Using these equations we can determine the position of a point on the line at any specific t value.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Parametric line
example, if you have the line equation:y = 2x + 2
you can parameterize it:
A vector parallel to this line would be v = (1, 2)And we can set the initial x value to 0 and the initial y value to the y-intercept = 2;
Px = 0 + 1t
Py = 2 + 2t
so for the values t = {0, .25, .5, .75, 1} we get the points P = {(0, 2), (.25, 2.5), (.5, 3), (.75, 3.5), (1, 4)}
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Parametric curves
ex: circle
(x – a)2 + (y – b)2 = r2
where (a, b) = the center of the circle and r = the radius
can be parameterized by t using sine and cosine like so:x(t) = a + r cos(t)y(t) = b + r sin(t)
If we step through values of t between 0 and 2pi we will approximate a circle.(the smaller the steps through t, the closer the approximation)
If we add another parametric equation for the 3rd dimension, we get a helixx(t) = a + r cos(t)y(t) = b + r sin(t)z(t) = rt
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Cubic curves
“Cubic Curves” (Bezier, Hermite, Catmull-Rom) - curves defined generally by particular geometric constraints, a basis matrix, and the cubic polynomials.
Cubic curves are defined most generally by the following equation:
Q(t) = a + bt + ct^2 + dt^3 , where t moves between 0 and 1
This can also be written in matrix notation as
Q(t) = Q’(t) =
[ 1 t t^2 t^3 ]
[ ax, bx, cx, dx
ay, by, cy, dy
az, bz, cz, dz ]
[ ax, bx, cx, dx
ay, by, cy, dy
az, bz, cz, dz ]
[ 0 1 2t 3t^2 ]
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Cubic Curves
In practice, we don’t generally know what the cubic polynomial is, and we create it by specifying control values and providing a basis matrix which “blends” these control points in a specific way, depending on what kind of cubic curve it is.
Q(t) = GMT(t) , where t moves between 0 and 1
That is, where G contains the geometric information (either vectors of points or points and tangents), M contains the “basis” matrix used to interpolate through G over time and T is the vector [1, t, t^2, t^3].
The different kinds of cubic curves expect different geometric information and use each use a different basis matrix for blending.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Bezier curves
Bezier curves are simple parametric curves that are defined by two endpoints and some number of control points.
They are usually found in one of two flavors: quadratic (with a single control point) or cubic (with two control points), although there is no reason you couldn’t have more control points.
The control point(s) define the position function of the curve as the variable t changes.
An algorithm created by DeCasteljau provides a simple mechanism for creating these curves parametrically.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
DeCasteljau’s algorithm
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Bezier curves
Bezier curves with 2 control points are called cubic curves, because the mathematical “blending” function that defines the curve from the control points is a cubic polynomial.
(1 – t)3 P0 + 3t(1 – t)2 P1 + 3t2(1 – t) P2 + t3 P3
Where t is between 0 and 1.
That is, this equation defines the amount each point contributes to the curve as t moves from 0 to 1.
At t = 0, P0 contributes 100%
At t = 1, P1 contributes 100%
At t = .5, P0 contributes 12.5%, P1 cs 37.5%, P2 cs 37.5%, P3 cs 12.5%
etc.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Bezier curves
And it turns out that at each point the total sum of the contribution is 100%.
Moreover, at time 0 and time 1 a single point account for the full contribution of the curve, which means that the curve begins and end on a control point.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Bezier curves
Since we know the blending functions we can shorten our equation to:
P(t) = B0(t) P0 + B1(t) P1 + B2(t) P2 + B3(t) P3
or just P(t) = ΣBiPi
In practice, you can calculate each dimension of the curve separately. I.e. :
Px(t) = (1 – t)3 Px,0 + 3t(1 – t)2 Px,1 + 3t2(1 – t) Px,2 + t3 Px,3
Py(t) = (1 – t)3 Py,0 + 3t(1 – t)2 Py,1 + 3t2(1 – t) Py,2 + t3 Py,3
Pz(t) = (1 – t)3 Pz,0 + 3t(1 – t)2 Pz,1 + 3t2(1 – t) Pz,2 + t3 Pz,3
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Bezier curves
Or, returning to our generalization Q(t) = GMT(t)
we can encode G using our 4 points (the start point, the two control points, and the end points) and M by extracting out the coefficients of the blending function.
G = [Pstart, Pcontrol1, Pcontrol2, Pend]
M = T = M’ = T’ =
[ 1 -3 3 1
0 3 -6 3
0 0 3-3
0 0 0 1 ]
[ 1 t t^2 t^3 ]
[ -3 6-3
3 -12 9 0 6
-9 0 0
3 ]
[ 1 t t^2 ]
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Hermite curves
A similar curve that also lets you create a curve around set endpoints is called a Hermite curve. In the Bezier curve you move the two control points to influence the curve. In a Hermite curve you instead adjust the tangents at the endpoints to control the curve.
Hermite curves are also known as “the pen tool” in Illustrator.
The curve is parametrically defined by the following equation:
Q(t) = (2t3 – 3t2 + 1)P0 + (t3 – 2t2 + t)T0 + (t3 – t2)T1 + (-2t3 + 3t2)P1
where P0 and P1 are the endpoints of the curve, and T0 and T1 are tangent vectors for P0 and P1 respectively.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Hermite curves
Here is the graph of the blending function for the two endpoints. (The red and blue indicate the blending for the points and the green and turquoise for the tangents)
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Hermite curves
G = [Pstart, Pend, Tstart, Tend]
M = [ 1 0 -3
2 0 0 3
-2 0 1 -2
1 0 0 -1
1 ]
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Continuity
Obviously both these simple cubic parametric curves suffer from the fact that you are limited to the kinds of curves you can generate. That is, they have at most one inflection point. You can keep track of the tangents of the curves at the end points and stitch them together.
To increase the range / loopiness of your curve you can either increase the order/complexity of your curve by adding more control points.
Or you can stitch together a series of simpler curves. One common solution to do this is to use a Catmull-Rom spline.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Catmull-Rom splines
Nice because the curve actually goes through the points that define the curve and is easy/cheap to calculate (often used for camera animations).
G = [Pi-1, Pi, Pi+1, Pi+2]
M = (1/2)
Except for the first and last point, the curve goes through every point.
The tangent of the curve at each point is defined by 1/2 (Pi+1 - Pi-1)
(can’t find an image of this-- draw on board)
[ 0 -1 2 -1
2 0 -5 -3
0 1 4 -3
0 0 -1 1 ]
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Continuity
When stitching together curves there is generally a trade-off between ease of use and flexibility. A simple naming scheme is used to describe the power of the different techniques to join together curve pieces;
C0 = the curves share an end point, but the end point may look discontinuous, sharp
G1 = the curves share an end point and those end points have the same tangent.
C1 = same as G1 except that the tangent vector is also required to have the same magnitude
C2 = the curves share an end point, the tangent is the same, and also the second derivative (representing curvature or acceleration) is the same.
C∞ = all derivates of the curve are the same.
Generally, strive for C2 as it looks good and if we are using the curve for animation it guarantees that both the velocity and the acceleration are the same.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
B-splines
B-splines are a more general way to think about curves. The “B” stands for the basis which defines the blending functions. The phrase “b-spline” is often used to describe a certain category of continuously connected curve pieces.
B-splines guarantee C2 continuity, but at the price of a increased complexity and the loss of some control (none of the points go through the control points!)
B-splines come in three flavors: Uniform, Nonuniform, and Nonuniform Rational.
The latter is also called NURBS (NonUniform Rational B-Splines)
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Uniform b-splines
The basic b-spline is defined like so:
Given a set of n+1 control points, the b-spline curve is composed of n-2 cubic curves pieces.
Each piece is defined again by a blending of 4 points, where for each piece Qi, Qi(t = 1) = Qi+1 (t = 0)
Q’i(t = 1) = Q’
i+1 (t = 0)
Q’’i(t = 1) = Q’’
i+1 (t = 0)
That is, the joins are C2 continuous. These joins are called internal knots.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Uniform b-splines
For each curve piece Qi,
Qi(t) = B0(t) + B1(t) + B2(t) + B3(t)
where the blending functions are the following:
B0(t) = [ (1 – t)3 / 6 ] * P0
B1(t) = [ (4 – 6t2 + 3t3) / 6 ] * P1
B2(t) = [ (1 + 3t + 3t2 + 3t3) / 6 ] * P2
B3(t) = [ t3 / 6 ] * P3
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Uniform b-splines
B0(t) = [ (1 – t)3 / 6 ] * P0
B1(t) = [ (4 – 6t2 + 3t3) / 6 ] * P1
B2(t) = [ (1 + 3t + 3t2 + 3t3) / 6 ] * P2
B3(t) = [ t3 / 6 ] * P3
which looks like this:
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Uniform b-splines
G = [Pi-1, Pi, Pi+1, Pi+2]
M = (1/6)[ 1 -3 3
1 4 0 -6
3 1 3 3
-3 0 0 0
1 ]
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Nonuniform b-splines
In uniform b-splines, the knots are automatically positioned at equal distances along the curve.
In a nonuniform b-spline, we can space the knots at nonuniform locations along the curve, which can change the curve in various ways. For instance, we can create looped curves, and perfect circle arcs.
To create a nonuniform cubic b-spline we need to define a knot-vector to describe the knot spacing.
If our curve uses 7 control points, then we will need (# of control points + degree of curve + 1) knots = 7 + 3 + 1 = 11 knots
If the knot vector is (0,1,2,3,4,5,6,7,8,9,10) then the curve will reduce to the uniform b-spline.
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Cox-deBoor algorithm
Each piece is defined like so:
Qi(u) = ΣBi+k-1,d(u)Pi+k-1
(sum as k goes from 0 to 3, ie the previous point Pi-1 Pi+2)
Where the range of u is defined by the knot vector (the val at t0 -> val at t#knots)
d = the degree parameter (which is the degree + 1, or 3 + 1 for cubic b-spline)
The blending functions are recursively defined like so:
Bi,0(u) = 1 if ti-2 <= u <= ti-1, otherwise 0
Bi,k(u) = (u – ti-2) [Bi,k-1(u) / ti+k-2 – ti-2] +
(ti-+k-1 – u) [Bi+1,k-1(u) / ti+k-1 – ti-1]
(ie, input Bi+k-1,d(u) from curve algo above and calc from reduced dimensionality)
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
NURBS
Similar to nonunifrom b-splines, except that you can specify a weight to every control point.
Pi = <wixi, wiyi, wizi, wi>
Qi(u) = ΣBi+k-1,d(u)Pi+k-1
The weight is thought of as 4th component to the point, making it a point in homogeneous coordinates.
The weights have the effect of shifting the curve in the direction of the weighted control point
(whereas moving knots close together has the effect of causing the curve to converge upon a control point.)
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
NURBS
With a nonuniform b-spline you can insert new control points as desired and update the knot-vector appropriately. This will let you have more control over a specfic range, while leaving the curve controlled by points further away the same.
Also, you can repeat the beginning and end values of your knot vector (order) times which will force your curve to line up with the control point endpoints
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
Curves in OpenGL / GLU
1. create a NURBS object gluNewNurbsRenderer()
2. indicate that you are using the NURBS renderergluBeginCurve(nurbsObj)
3. draw the curvegluNurbsCurve(
lengthOfKnotVector, //how many knotsknotVectorArray, //the knotsstride, //the stride through the controlArray, either 3 or 4
generallycontolPointsArray, //the control pointscurveOrder, //cubic = 3, can be higher but requires more knotsGL_MAP1_VERTEX_3 //use _3 for unweighted points, _4 if you
weight);
MAT 594CM S10 Fundamentals of Spatial Computing Angus Forbes
NURBS surfaces
defined by a mesh of control points, which define two sets of curves – a column of curves and a row of curves...
(demo)
Related Documents
##### Lecture Notes #9 - Curves · Bezier curves -- general class...
Category: Documents
##### Curves and Surfacesadair/CG/Notas...
Category: Documents
##### Bezier Curves, B-Splines, NURBS
Category: Documents
##### Hermite/Bezier Curves, (B-)Splines, and NURBS By Ulf … and...
Category: Documents
##### Lecture 24: Bezier Curves and Surfaces
Category: Documents
##### THE CONDITION OF QUADRATIC AND CUBIC BEZIER CURVES … ·.....
Category: Documents
##### B-Spline & NURBS Curves
Category: Documents
##### Securing Password File Using Bezier Curves
Category: Documents
##### Non-Uniform Rational B-Splines NURBS. NURBS Surfaces NURBS.....
Category: Documents
##### Subdivision of Bezier curves
Category: Documents
##### Curve Modeling-Bezier Curves
Category: Documents
##### Snap Rounding of Bezier´ Curves - Max Planck Society
Category: Documents | 4,477 | 15,582 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2023-40 | latest | en | 0.815787 |
http://www.expertsmind.com/library/calculate-phi-for-these-data-51371563.aspx | 1,611,731,272,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704821253.82/warc/CC-MAIN-20210127055122-20210127085122-00722.warc.gz | 140,344,814 | 11,366 | ### Calculate phi for these data
Assignment Help Basic Computer Science
##### Reference no: EM131371563
1. A poll of 80 state legislators finds that 30 Republicans favor an income tax rebate, while 5 Republicans do not favor it. Similarly, among 45 Democrats, 20 favor the tax rebate and 25 do not. Calculate phi for these data.
2.Calculate phi adjusted for the data in question number 3. Compare phi adjusted to phi What can you conclude?
#### Problem regarding the saturating arithmetic
Assume 161 and 214 are signed 8-bit decimal integers stored in two's complement format. Calculate 161 - 214 using saturating arithmetic. The result should be written in deci
#### Define a fraction adt to represent and store rational number
The ADT should include all of the common mathematical and logical operations. In addition, your ADT should provide for the conversion between floatingpoint values and fracti
#### The program must use a loop
The program MUST use a loop to read in the series of integers from the user. The output is then displayed after the loop. Algorithm or Pseudo Code (as an outline): At the b
#### Proposal to your current-previous company
Write a 4- to 5-page proposal to your current or previous company's executives discussing how analytics can be used in your company to improve sales through your retail outl
#### Annotated bibliography assignment
This week (Part I) you are to create a complete Annotated Bibliography for 2 academic scholarly sources, which include your introduction and thesis, publication details, and
#### Create query in design view to return records from table
Create a query in Design view to return records from the Items table where the value of the Category field is Software and the value of the Cost field is greater than or equ
#### The development process includes planning
The development process includes planning, coding and debugging of code to create the programs that solve real-world applications. Before embarking on a project, one must do a
#### What is the diameter of each screen point
Suppose we have a video monitor with adisplay area that measures 12 inches across and 9.6 inches high. If the resolution is 1280 by 1024 and the aspect ratio is 1, what is t | 477 | 2,244 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2021-04 | latest | en | 0.877966 |
https://discusstest.codechef.com/t/how-to-handle-numbers-larger-than-the-range-of-long-long-unsigned-int/6795 | 1,685,423,338,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224645089.3/warc/CC-MAIN-20230530032334-20230530062334-00428.warc.gz | 236,422,243 | 5,671 | # how to handle numbers larger than the range of long long unsigned int??
How can manipulate numbers larger than the range of long long unsigned integer?
Maybe create your own base system to handle larger numbers. (We work in base 10 in decimal representation system)
I want to save a number containing 10^16 1s. That is 111111…10^16 times. Can you help?
Prefer taking i/p as a string in such cases and do the required manipulations.
Try using Big Integer
i/p. can you explain. I am new at it.
You cant take input as a string with length 10^16.
you can break your number into two parts of an array one containing the upper part and one containing the lower part half
eg…
987654321987654321 can b stored as
a=987654321 and b=987654321
any changes in the lower part resulting in a carry have to be reflected in the upper part also
You can use array storing element as each digits of the large number. For example if we have to store 391 then we will create an array of size 3 and then store 3,9 and 1 as its elements.
So if we have to calculate factorials of large number like 100 we can use this method - https://discuss.codechef.com/questions/7349/computing-factorials-of-a-huge-number-in-cc-a-tutorial | 296 | 1,214 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2023-23 | latest | en | 0.870186 |
https://www.physicsforums.com/threads/rearranging-formula-make-e-the-subject-10b-5be-3e-7c.383072/ | 1,713,035,517,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816832.57/warc/CC-MAIN-20240413180040-20240413210040-00410.warc.gz | 897,276,174 | 15,471 | # Rearranging Formula: Make e the Subject | 10b + 5be - 3e + 7c
• Gringo123
In summary, the individual needs to use parentheses and make sure their starting equation is set equal to zero in order to correctly rearrange the formula to make e the subject.
Gringo123
I need to rearrange this formula to make e the subject. Have I done it correctly?
10b + 5be - 3e + 7c
10b + 5be - 3e = 7c
5be - 3e = 7c - 10b
e(5b - 3) = 7c - 10b
e = 7c - 10b / 5b - 3
Gringo123 said:
I need to rearrange this formula to make e the subject. Have I done it correctly?
You're not starting with an equation! Without the first line below being an equation, you can't solve for anything.
Gringo123 said:
10b + 5be - 3e + 7c
10b + 5be - 3e = 7c
5be - 3e = 7c - 10b
e(5b - 3) = 7c - 10b
e = 7c - 10b / 5b - 3
Assuming that this is your starting equation -- 10b + 5be - 3e = 7c -- your work following it is fine, EXCEPT that you need to use parentheses. You should write e this way:
e = (7c - 10b) / (5b - 3)
Thanks a lot Mark
Mark44 said:
You're not starting with an equation! Without the first line below being an equation, you can't solve for anything.
Assuming that this is your starting equation -- 10b + 5be - 3e = 7c -- your work following it is fine, EXCEPT that you need to use parentheses. You should write e this way:
e = (7c - 10b) / (5b - 3)
Well if we assume that the first line is an equation (set equal to zero): 10b + 5be - 3e + 7c=0, then the second line changes:
10b + 5be - 3e = -7c, and that would change the rest of the steps which follow...
## 1. How do I make "e" the subject of the formula?
To make "e" the subject of the formula, we need to isolate it on one side of the equation by moving all other terms to the other side. This can be done by using basic algebraic operations such as addition, subtraction, multiplication, and division.
## 2. What is the purpose of rearranging a formula?
Rearranging a formula allows us to solve for a specific variable or unknown value. It also makes it easier for us to manipulate and use the formula in different situations.
## 3. Can we rearrange a formula in any way we want?
No, we cannot rearrange a formula in any way we want. We need to follow the rules of algebra and maintain the equality of the equation. This means that whatever operation we do to one side of the equation, we must also do to the other side.
## 4. What is the first step in rearranging a formula?
The first step in rearranging a formula is to identify the variable that we want to make the subject. Then, we need to move all other terms to the other side of the equation using algebraic operations until the variable is isolated on one side.
## 5. Can we use the same method to rearrange any formula?
Yes, we can use the same method to rearrange any formula as long as we follow the rules of algebra and maintain the equality of the equation. However, the specific steps may vary depending on the complexity of the formula.
• Precalculus Mathematics Homework Help
Replies
16
Views
892
• Introductory Physics Homework Help
Replies
22
Views
936
• Precalculus Mathematics Homework Help
Replies
3
Views
2K
• Nuclear Engineering
Replies
5
Views
343
• General Math
Replies
1
Views
836
• Calculus and Beyond Homework Help
Replies
2
Views
968
• General Math
Replies
5
Views
771
• Set Theory, Logic, Probability, Statistics
Replies
8
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
3
Views
1K
• Biology and Chemistry Homework Help
Replies
12
Views
5K | 1,010 | 3,486 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2024-18 | latest | en | 0.887182 |
https://issuu.com/ijcer/docs/ay03303170322 | 1,519,598,530,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891817437.99/warc/CC-MAIN-20180225205820-20180225225820-00531.warc.gz | 691,252,996 | 24,221 | International Journal Of Computational Engineering Research (ijceronline.com) Vol. 3 Issue. 3
Discrimination of Fault from Non-Fault Event in Transformer Using Concept of Symmetrical Component 1,
Mr. R.V.KATRE, 2, Prof. Mr. D. S. Chavan, 3,Prof.S.S.Sardey
Abstract In this paper a overcurrent protection using concept of symmetrical component for power transformer is presented .first we review the concept of symmetrical component. Secondly we investigate how the concept of symmetrical component can be used to improve the transformer protection scheme and how it helps to discriminate the fault and non fault events. For this an algorithm and discrimination criteria is analysed for various fault condition and switching event.
Keywords : Fault, overcurrent relay, symmetrical Components, type of Faults, Transformer energizing, PSCAD, Switching event
1. Introduction The Concept of symmetrical components provides a practical technology for understanding and analyzing power system operation during unbalanced conditions such as those caused by faults between phases and/or ground, open phases, unbalance impedances, and so on. Also, many protective relays operate from the symmetrical component quantities. Thus a good understanding of this subject is of great value and a very important tool in protection. 1.1 Methodology For Improved Protection Schemes: For any unbalanced or nonsymmetrical network, such as unsymmetrical fault occurs or having unbalanced load, symmetrical component conversion can decouple three-phase system into three independent sequence equivalent networks, namely positive, negative and zero sequence network. Therefore these three sequence networks can be analyzed separately. Then we can convert the sequence value back into phase variables. This analysis procedure is commonly used in analyzing the unbalanced system network, including fault. Symmetrical components can be viewed as a mathematical tool on which we can entirely based to analysis system without converting back to phase variable. For example, the amplitude of zero sequence signifies the degree of unbalance, and therefore can be used to detect the unbalanced fault. 1.2 Theoretical background The symmetrical component transformation for an arbitrary three-phase set of variables (balanced or unbalanced), for example the three-phase current, and inverse transformation is given in (1) and (2). -------- (1)
Here I1 , I2 and I0 denote the positive, negative and zero sequences respectively. And α =1∟1200 = − 0.5 + j0.866 In general application in power system analysis, we typically begin with information in “phase variables” denoted by subscripts a, b, and c. Note that phase variables corresponds to actual physical quantities. The value of converting physical quantities to symmetrical components is in visualizing and quantization the degree of unbalanced system network. For a balanced three-phase system, it won’t be difficult to calculate that the zero and negative sequences are zero, and the positive sequence is equal to phase a, no matter current or voltage.
2. Operation And Principle Of Overcurrent Relays There are two characteristics for overcurrent relays: 1) definite- time characteristic and 2) inverse-time characteristic. In the definite-time characteristic relays, if the current amplitude exceeds a pre-defined value, the relay trips after a definite time. In the protection of motors, these relays are used to prevent the unbalanced operation of the motors. According to IEC standard [19], the characteristic of inverse time overcurrent relays (excluding induction type) is depicted by the following expression:
317 ||Issn||2250-3005|| (Online)
||March||2013||
||www.ijceronline.com||
Discrimination Of Fault From Non-Fault Event In Transformer… ----- (2) T- the relay operation time; C- constant for relay characteristic; Is-current setting threshold; I- current detected by relay (normally the effective value) ; I > Is α- constant representing inverse-time type α> 0 By assigning different values to α and C, different types of inverse characteristics are obtained. 2.1 Proposed Algorithm Any three-phase voltage and current consist of three components in sequence space which are related to each other as follows:
Here I1 ,I2 and I0 denote the positive, negative and zero sequences respectively. And α =1∟1200 = − 0.5 + j0.866 Also 1+α+α2=0 if currents Ia,, Ib and Ic are balanced (i.e., Ia,= I∟0, Ib = I ∟ -1200 and Ic = I ∟ +1200 ). So existence of the negative components means that the system is unbalanced. except over a transient period that may be as a result of different switching method or non identical saturated case of three-phase transformers, three phases are almost affected simultaneously during switching event. Consequently, the negative component is not considerably changed in this case. On the other hand, faults are classified into symmetrical and asymmetrical parts. The major feature of these faults is the large value of the negative component, such that there are the theoretical following casesFor phase–ground fault
…… (4) Where Zf is the fault impedance between the line and ground Z0, is the zero component impedance Z1, is the positive component impedance, and Z2 is the negative component impedance. For phase-phase fault: ….. (5) For phase-phase- ground fault: …… (6) Therefore, the negative component in the asymmetrical faults is considerable. For symmetrical faults the negative component tends to zero. Not often, the three-phase fault occurs and the negative component of the current is negligible and almost equal to zero similar with the switching case. The criterion function for discriminating fault from nonfault switching is defined as follows . The criterion function for discriminating fault from non fault switching is defined as follows: ----- (7) Since there is a considerable negative component in the asymmetrical fault case, according to criterion function the value of R is close to zero. In the switching case, the negative component is very small and R is close to 1. In the switching case, the negative component is very small and R is close to 1. Except over a transient period that may be as a result of different switching methods or a non identical saturated case of three-phase transformers, three phases are almost affected simultaneously and the three-phase network has not a major
318 ||Issn||2250-3005|| (Online)
||March||2013||
||www.ijceronline.com||
Discrimination Of Fault From Non-Fault Event In Transformer‌ unbalance, during the switching event. In the calculation of I2 and I1 in equation (1), Ia ,Ib , and Ic are phasor value (amplitude of the fundamental harmonic). Therefore, dc values and its harmonics are largely eliminated. So the difference in dc value in the current is not important. According to the above, R<0.35 indicates the fault; otherwise, over current is the result of switching. The suggested criterion is based on the different behavior of the current components during fault and non fault conditions and is independent of the amplitude of the current which is advantageous. The reason is that it operates based on the relative difference between the negative and positive component of the current. Another advantage of the suggested criterion function is that its proper operation is independent of the power system balancing. Actually, the suggested criterion function in the asymmetrical distribution networks also operates properly. The reason is that during the asymmetrical fault, the negative component of current increases and the value of R is much smaller than that before fault event. Thus, it is enough that the threshold value be lower than at the value of R in the normal state of the network.
3. Simulation To show the advantage of the proposed algorithm, a part of a distribution system shown in Fig.1 is modeled; using the EMTDC/ PSCAD package. The network parameter of the 2-bus distribution system is illustrated in this figure. Several nonfault events are applied to this system along with some short circuit events at different times. The simulation results show that how the proposed algorithm could help the overcurrent relay to discriminate fault from nonfault events. The following cases are presented here: • Transformer energizing; • Induction motor starting;
4. Transformer Energizing When the primary winding of an unloaded transformer is switched on to normal voltage supply, it acts as a nonlinear inductor. In this situation there is a transient inrush current that is required to establish the magnetic field of the transformer. The magnitude of this current depends on the applied voltage magnitude at the instant of switching, supply impedance, transformer size and design. Residual flux in the core can aggravate the condition. The initial inrush current could reach values several times full load current and will decay with time until a normal exciting current value is reached. The decay of the inrush current may vary from as short as 20 cycles to as long as minutes for highly inductive circuits. The inrush current contains both odd and even order harmonics.In order to study a transformer energizing, various inrush current conditions were simulated at different parts of the power system. Various parameters which have considerable effect on the characteristic of the current signal (e.g., core residual magnetization, nonlinearity of transformer core and switching instant) were changed and the current signal was analyzed by the proposed method. In all cases, correctness of the proposed algorithm has been proved. Malfunctioning of transformers is mainly because of following reasons: Due to magnetizing inrush current, Harmonics generated due to occurrence of internal faults, Short Circuit in core winding, Symmetrical or Asymmetrical Faults Symmetrical components consist of three quantities: positive-sequence (exists during all system conditions, but are prevalent for balanced conditions on a power system including three-phase faults); negative-sequence (exist during unbalanced conditions); zero-sequence (exist when ground is involved in an unbalanced condition). Negative and zero-sequence components have relatively large values during unbalanced fault conditions on a power system and can be used to determine when these fault conditions occur. Negative-sequence components indicate phase-to-phase, phase-to-ground, and phase-to-phase-to-ground faults. Zero sequence components indicate phase-to-ground and phase -to-phase-toground faults 4.1 Inrush due to switching-in Initial magnetizing due to switching a transformer in is considered the most severe case of an inrush. When a transformer is de-energized (switched-off), the magnetizing voltage is taken away, the magnetizing current goes to zero while the flux follows the hysteresis loop of the core. This results in certain remanent flux left in the core. When, afterwards, the transformer is re-energized by an alternating sinusoidal voltage, the flux becomes also sinusoidal but biased by the remanence. The residual flux may be as high as 80-90% of the rated flux, and therefore, it may shift the flux-current trajectories far above the knee-point of the characteristic resulting in both large peak values and heavy distortions of the magnetizing current A detailed study of a typical case is presented below. In this case transformer at busbar 1-2 is switched on at instant t= 0.25s and three-phase currents are measured at busbar 7. Fig. 2 shows these three-phase currents. As shown in Fig. 3, except over a transient period, R is close to 1 and is larger than setting R= 0.35s that shows nonfault case. In this case tripping signal is prevented.
319 ||Issn||2250-3005|| (Online)
||March||2013||
||www.ijceronline.com||
Discrimination Of Fault From Non-Fault Event In Transformer‌ 4.2 Fault In this case a phase-ground fault (A-G) occurs at busbar 1 at instant t= 0.25s and three-phase currents are measured at busbar 7. Fig. 4 shows these three-phase currents. As shown in Fig. 5, R is close to zero that shows a fault case in which the tripping signal is issued. Bus 2
#1
#2
A V
RL
A->G
Bus 3 Ea
Bus 1
bus 4
#1
#2 Ia
flt
RL
Bus 5
40.0 [MVAR] 80.0 [MW] 280.0 [MVAR] 800.0 [MW]
Fig 1. 5-bus system model
Fig.2. 3- phase current due to transformer energizing
y
Fig 3. Value of R versus time due to transformer Energizing 80 70 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 -80
Ia1
Fig. 4 Three phase current due to fault (A-G)
320 ||Issn||2250-3005|| (Online)
||March||2013||
||www.ijceronline.com||
Discrimination Of Fault From Non-Fault Event In Transformer‌
Fig. 5 Value of R versus time due to fault (A-G) Three-phase currents are measured at the busbar 1 Fig. 4 shows these currents is close to zero which indicates that there is a fault and the relay trips. In fact, one more advantage of the suggested algorithm is that, in addition to the diagnosis of the fault in the individual occurrence from the nonfault case, it enables to discriminate a fault from simultaneous switching properly. This is necessary because, if in the case of fault, the operation of the relay is prevented and it is assumed switching case, it may lead to a serious damage.
5. Theoretical Analysis
6. Conclusion In this paper, from simulations results it indicates that enhanced sensitivity can be achieved with a symmetrical component based overcurrent protection. Also the paper presents a new algorithm- overcurrent protection based on symmetrical component and shows vastly improved performance over conventional techniques, to discriminate fault and non fault events like switching and magnetizing inrushes in transformer. Undesirable operation of relay due to the switching is prevented. The capability of the new method has been demonstrated by simulating various cases on a suitable power system for various types of asymmetrical faults.
7. Future Scope Here only the fault cases related to Transformer is studied but in future it can be studied for Alternator, Turbo-generators etc.
321 ||Issn||2250-3005|| (Online)
||March||2013||
||www.ijceronline.com||
Discrimination Of Fault From Non-Fault Event In Transformer… Reference [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
F. Wang and M. H. J. Bollen, “Quantification of transient current signals in the viewpoint of overcurrent relays,” in Proc. Power Eng. Soc. General Meeting, Jul. 13–17, 2003, vol. 4, pp. 2122–2127. “Classification of component switching transients in the viewpoint of protection relays,” Elect. Power Syst. Res., vol. 64, pp. 197– 207, 2003. J. H. Brunke and H. J. Frohlich, “Elimination of transformer inrush currents by controlled switching-Part II: Application and performance considerations,” IEEE Trans. Power Del., vol. 16, no. 2, pp. 281–285, Apr. 2001. M. A. Rahman and B. Jeyasurya, “A state-of-the-art review of transformer protection algorithms,” IEEE Trans. Power Del., vol. 3, no. 2, pp. 534–544, Apr. 1988. P. Liu, O. P. Malik, C. Chen, G. S. Hope, and Y. Guo, “Improved operation of differential protection of power transformers for internal faults,” IEEE Trans. Power Del., vol. 7, no. 4, pp. 1912–1919, Oct. 1992. T. S. Sidhu, M. S. Sachdev, H. C. Wood, and M. Nagpal, “Design, implementation and testing of a micro-processor-based highspeed relay for detecting transformer winding faults,” IEEE Trans. Power Del., vol. 7, no. 1, pp. 108–117, sJan. 1992, . K. Yabe, “Power differential method for discrimination between fault and magnetizing inrush current in transformers,” IEEE Trans. Power Del., vol. 3, no. 3, pp. 1109–1117, Jul. 1997. P. Bastard, M. Meunier, and H. Regal, “Neural network-based algorithm for power transformer differential relays,” Proc. Inst. Elect. Eng. C, vol. 142, no. 4, pp. 386–392, 1995. M. C. Shin, C. W. Park, and J. H. Kim, “Fuzzy logic-based for large power transformer protection,” IEEE Trans. Power Del., vol. 18, no. 3, pp. 718–724, Jul. 2003. A. T. Johns and S. K. Salman, Digital Protection for Power Systems. Stevenage, U.K.: Peregrinus, 1995. S. Emmanouil, M. H. J. Bollen, and I. Y. H. Gu, “Expert system for classification and analysis of power system events,” IEEE Trans. Power Del., vol. 17, no. 2, pp. 423–428, Apr. 2002. W. A. Elmore, C. A. Kramer, and S. E. Zocholl, “Effects of waveform distortion on protective relays,” IEEE Trans. Ind. Appl., vol. 29, no. 2, pp. 404–411, Mar./Apr. 1993. J. F. Witte, F. P. Decesaro, and S. R. Mendis, “Damaging long-term over voltages on industrial capacitor banks due to transformer energization inrush currents,” IEEE Trans. Ind. Appl., vol. 30, no. 4, pp. 1107–1115, Jul./Aug. 1994. R. Rudenberg, Transient Performance of Electric Power System. Cambridge, MA: MIT Press, 1965. Improved Overcurrent Protection Using Symmetrical Components Saeed Lotfi-fard, Student Member, IEEE, Jawad Faiz, Senior ion of Member, IEEE, and Reza Iravani, Fellow, IEEE Overcurrent Protection Solution based on symmetrical component Method; Mr. K. K. Rajput, Mrs. K. D. Thakur Mrs. C. H. Chavan, Journal of Information ,knowledge and research in electronics and communication engineering, ISSN 0975-6779,Nov 10 to Oct 11 ,Vol-01,issue-02.
Rohit Katre: M.Tech Student in Electrical Power Systems, Bharati Vidyapeeth Deemed University College of Engineering, Pune, Maharashtra, India
Prof.D.S.Chavan: Ph D (Registered), ME (Electrical), BE (Electrical), DEE Associate Professor, Co-Ordinator (R&D Cell), Co-Ordinator (PH.D.Programme Management) Bharati Vidyapeeth Deemed University College Of Engineering Pune 411043. He Is Pursuing Ph D. He Received ME (Electrical)(Power Systems) Achieved Rank Certificate In Pune University For ME Prof. S.S.sardey.: ME (Electrical Power system), BE (Electrical), Assistant Professor, Bharati Vidyapeeth Deemed University College Of Engineering Pune 411043.
322 ||Issn||2250-3005|| (Online)
||March||2013||
||www.ijceronline.com||
AY03303170322
AY03303170322 | 4,256 | 18,015 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2018-09 | latest | en | 0.88529 |
https://www.ncbi.nlm.nih.gov/books/NBK482501/ | 1,726,371,304,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651614.9/warc/CC-MAIN-20240915020916-20240915050916-00585.warc.gz | 867,637,926 | 17,586 | An official website of the United States government
NCBI Bookshelf. A service of the National Library of Medicine, National Institutes of Health.
StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.
Show details
# Physiology, Lung Dead Space
; ; .
Author Information and Affiliations
Last Update: July 4, 2023.
## Function
Ventilation is the manner by which air enters the lungs. There are two equations needed to calculate the volume that enters the lungs and the volume that reaches the alveoli. The volume that enters the lung per minute is known as minute ventilation (VE). The equation states VE equals tidal volume (VT) multiplied by respiratory rate (RR). This equation demonstrates that the total volume entering the lung is not equivalent to the total volume of gas reaching the alveoli because it does not factor in the gas in the anatomical dead space resting in the conductive airway. Thus, to know the volume of gas that reaches the alveoli per unit time we use the alveolar ventilation equation which states; alveolar ventilation (VA) equals VT minus physiologic dead space (VD) multiplied by RR. From this equation, clinicians can determine that the total volume gas inspired is not being fully utilized in the gas exchange due to the constant anatomical dead space.[4][5][6]
## Mechanism
The Bohr equation can be used to calculate the amount of dead space in a lung. Understanding the equation will simplify the concept of dead space greatly. The equation states VD is equal to VT multiplied by the partial pressure of arterial carbon dioxide (PaCO2) minus partial pressure of expired carbon dioxide (PeCO2) divided by PaCO2.
Breaking down this equation, there is the tidal volume which is the normal amount of inspired and expired gas equivalent to 500 mL. This inspired air is assumed to contain a relatively zero amount of carbon dioxide. The second half of the equation is representative of the fractional amount of dead space. Simply translating to the amount of carbon dioxide (CO2) exchanged for oxygen (O2). The exchange of gases through the respiratory membrane is so rapid that we can assume the arterial CO2 partial pressure is equal to that in the alveoli. The exchanged CO2 will now become PeCO2. PeCO2 will always have a smaller value than arterial CO2 due to the mixture and dilution of CO2 gases with the 150 mL of anatomical dead space sitting in the conductive airway that is assumed to be free of CO2. Thus, by subtracting PeCO2 from PaCO2 and dividing by the PaCO2 one has you have determined a fractional equivalent of the lung is not contributing to gas exchange. Multiply that value by the normal amount of air inspired (VT) you achieve a value for physiologic dead space.
## Pathophysiology
Until now, clinicians have assumed the patient is a healthy individual with properly functioning alveoli. In disease states where alveoli have lost function, there will be a decrease in gas exchange and an increase in alveolar dead space. This can be seen most rapidly with sudden decreases in perfused to ventilated alveoli. This is usually seen in an abrupt decrease in cardiac output, hypotension, or pulmonary embolism, due to fat, air, or amniotic fluid. While obstruction can cause decreased perfusion in PE, the greatest decrease in pulmonary blood flow is due to vasoconstriction caused by locally released vasoactive substances. In these situations, a lack of gas exchange at the alveolar level results in a decrease of PaCO2 gas being exchange by the remaining healthy alveoli and ultimately a lower PeCO2. Looking back at the equation, a lower PeCO2 will result in an increase in the physiologic dead space value for that individual. When an area of the lung is properly ventilated, but poorly perfused, there is an increase in physiologic dead space.[7][8]
## Clinical Significance
Clinically, disease states and environmental factors, such as smoking, all play a major role in the increase of dead space. Increases in dead space can be seen in lung disease states including emphysema, pneumonia, and acute respiratory distress syndrome (ARDS). Emphysema results in the enlargement of air spaces and decreases in the diffusing capacity of the alveolar membrane due to the destruction of alveolar walls. In ARDS there is endothelial damage leading to an increase in the alveolar-capillary permeability, thereby leading to leakage of protein-rich fluid into the alveolar. This results in the formation of intra-alveolar hyaline membranes, which decrease the exchange of CO2 and O2 in the lung contributing to a larger dead space. Studies looking at the causes of death in this disease have shown an increase in dead space in the non-survivors versus survivors. The strongest association of an increased volume of dead space with mortality risk is seen in patients with ARDS.[9]
Clinicians use the understanding of dead space to manage mechanically ventilated patients. Even in a healthy patient, ventilation via an endotracheal tube will increase the dead space volume because the breathing circuit does not participate in gas exchange. During mechanical ventilation, capnography is used; this records the volume of expired CO2, a value used to determine the physiologic dead space in patients. Adjustments in ventilation rates and the use of positive end-expiratory pressure (PEEP) are used to decrease dead space. Although multiple studies have failed to show this expected effect consistently, it is still widely used in cases of ARDS. Proper use of mechanical ventilation, as well as PEEP, is important considering both have been implicated in causing lung injury. Also, the use of high-flow nasal cannula has been shown to decrease dead space in patients with acute and chronic respiratory diseases. This is largely due to decreasing rebreathing in the existing anatomic dead space. Understanding dead space and being able to calculate it is a vital tool for physicians dealing with ventilated, critically ill patients.
## References
1.
Coppola S, Froio S, Marino A, Brioni M, Cesana BM, Cressoni M, Gattinoni L, Chiumello D. Respiratory Mechanics, Lung Recruitability, and Gas Exchange in Pulmonary and Extrapulmonary Acute Respiratory Distress Syndrome. Crit Care Med. 2019 Jun;47(6):792-799. [PubMed: 30908313]
2.
Huang B, De Vore D, Chirinos C, Wolf J, Low D, Willard-Grace R, Tsao S, Garvey C, Donesky D, Su G, Thom DH. Strategies for recruitment and retention of underrepresented populations with chronic obstructive pulmonary disease for a clinical trial. BMC Med Res Methodol. 2019 Feb 21;19(1):39. [PMC free article: PMC6385381] [PubMed: 30791871]
3.
Kiefmann M, Tank S, Tritt MO, Keller P, Heckel K, Schulte-Uentrop L, Olotu C, Schrepfer S, Goetz AE, Kiefmann R. Dead space ventilation promotes alveolar hypocapnia reducing surfactant secretion by altering mitochondrial function. Thorax. 2019 Mar;74(3):219-228. [PubMed: 30636196]
4.
Plantier L, Delclaux C. Increased physiological dead space at exercise is a marker of mild pulmonary or cardiovascular disease in dyspneic subjects. Eur Clin Respir J. 2018;5(1):1492842. [PMC free article: PMC6314086] [PubMed: 30627360]
5.
Ferluga M, Lucangelo U, Blanch L. Dead space in acute respiratory distress syndrome. Ann Transl Med. 2018 Oct;6(19):388. [PMC free article: PMC6212367] [PubMed: 30460262]
6.
Frat JP, Coudroy R, Thille AW. Non-invasive ventilation or high-flow oxygen therapy: When to choose one over the other? Respirology. 2019 Aug;24(8):724-731. [PubMed: 30406954]
7.
Quinn M, St Lucia K, Rizzo A. StatPearls [Internet]. StatPearls Publishing; Treasure Island (FL): Feb 19, 2023. Anatomy, Anatomic Dead Space. [PubMed: 28723045]
8.
Godinas L, Sattler C, Lau EM, Jaïs X, Taniguchi Y, Jevnikar M, Weatherald J, Sitbon O, Savale L, Montani D, Simonneau G, Humbert M, Laveneziana P, Garcia G. Dead-space ventilation is linked to exercise capacity and survival in distal chronic thromboembolic pulmonary hypertension. J Heart Lung Transplant. 2017 Nov;36(11):1234-1242. [PubMed: 28666570]
9.
Gogniat E, Ducrey M, Dianti J, Madorno M, Roux N, Midley A, Raffo J, Giannasi S, San Roman E, Suarez-Sipmann F, Tusman G. Dead space analysis at different levels of positive end-expiratory pressure in acute respiratory distress syndrome patients. J Crit Care. 2018 Jun;45:231-238. [PubMed: 29754942]
Disclosure: Sal Intagliata declares no relevant financial relationships with ineligible companies.
Disclosure: Alessandra Rizzo declares no relevant financial relationships with ineligible companies.
Disclosure: William Gossman declares no relevant financial relationships with ineligible companies.
This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.
Bookshelf ID: NBK482501PMID: 29494107
### Related information
• PMC
PubMed Central citations
• PubMed
### Similar articles in PubMed
See reviews...See all...
### Recent Activity
Your browsing activity is empty.
Activity recording is turned off.
Turn recording back on
See more... | 2,231 | 9,364 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-38 | latest | en | 0.861981 |
http://www.slideshare.net/mcdirector/5-7-standard-form | 1,477,173,419,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719045.47/warc/CC-MAIN-20161020183839-00139-ip-10-171-6-4.ec2.internal.warc.gz | 708,838,190 | 34,115 | Upcoming SlideShare
×
# 5 7 Standard Form
2,054 views
Published on
Published in: Technology
2 Likes
Statistics
Notes
• Full Name
Comment goes here.
Are you sure you want to Yes No
• Be the first to comment
Views
Total views
2,054
On SlideShare
0
From Embeds
0
Number of Embeds
43
Actions
Shares
0
16
0
Likes
2
Embeds 0
No embeds
No notes for slide
### 5 7 Standard Form
1. 1. Standard Form Ax + By = C Section 5.7
2. 2. Standard form in General <ul><li>Standard form is tricky </li></ul><ul><li>Some textbooks will give you </li></ul><ul><ul><li>Ax + By = C </li></ul></ul><ul><li>Others will give you </li></ul><ul><ul><li>Ax + By + C = 0 </li></ul></ul><ul><li>Others may give you some slightly different variation </li></ul><ul><li>Focus on the A, B, C for Standard Form. </li></ul>
3. 3. Ax + By = C <ul><li>A, B, C must be integers </li></ul><ul><li>A, B, C can NOT be decimals or fractions </li></ul><ul><li>Ax & By must be on the same side of the equation </li></ul><ul><li>It is preferred that A be positive (not necessary, but preferred) </li></ul><ul><li>That means that 4x - 3y = 6 is the same thing as -4x + 3y = -6 </li></ul>
4. 4. Example 1- Find x & y intercepts of equations <ul><li>To find the x-intercept, replace y with 0 & solve for x. </li></ul><ul><li>To find the y-intercept, replace x with 0 & solve for y. </li></ul><ul><li>This works because: </li></ul><ul><ul><li>x-intercept is (x, 0) </li></ul></ul><ul><ul><li>y-intercept is (0,y) </li></ul></ul>
5. 5. Example 1- Find x & y intercepts of equations <ul><li>You can use the x & y intercepts to graph. </li></ul><ul><li>Just plot the two intercepts and draw the line through the two points. </li></ul>
6. 6. Example 2 - Graph equations in standard form <ul><li>Use inverse operations to move the equation into slope intercept form. </li></ul><ul><li>Change of instructions above problem 17 on the back: </li></ul><ul><li>Rewrite the equation to slope-intercept form </li></ul>
7. 7. Example 3 - Word Problems <ul><li>We are going to do Example 4 before we do Example 3. </li></ul><ul><li>We’ll come back to Example 3. </li></ul>
8. 8. Example 4 - Find Standard Form from a point and the slope <ul><li>You will be given a point & the slope </li></ul><ul><li>We found slope-intercept form from a point and the slope in lesson 5-5. </li></ul>
9. 9. Example 4 - Find Standard Form from a point and the slope <ul><li>After you find slope intercept form: </li></ul><ul><li>Multiply the equation by an LCD to get rid of any denominators. </li></ul><ul><li>Use inverse operations to move any terms one at a time until the equation is in Ax + By = C form. </li></ul>
10. 10. One Last Thing <ul><li>If you are given two points and told to put it in Standard Form: </li></ul><ul><li>Find the slope </li></ul><ul><li>Use the slope and one of the points to find slope-intercept form. </li></ul><ul><li>Then follow the instructions on the previous screen to move the equation into standard form. </li></ul>
11. 11. Review <ul><li>What is Standard Form. </li></ul><ul><li>How do you find the x & y intercepts? </li></ul><ul><li>How do you use the intercepts to graph an equation? </li></ul><ul><li>How do you graph an equation from standard form? </li></ul>
12. 12. Review <ul><li>What steps do you take to solve a word problem? </li></ul><ul><li>What steps do you take to write a standard form equation given a point and the slope? </li></ul><ul><li>What steps do you take to write a standard form equation given two points? </li></ul> | 1,110 | 3,508 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2016-44 | latest | en | 0.637927 |
https://en.sorumatik.co/t/in-a-group-of-6-boys-and-4-girls-four-children-are-to-be-selected-in-how-many-different-ways-can-they-be-selected-such-that-at-least-one-boy-should-be-there/394 | 1,679,485,860,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00649.warc.gz | 275,050,415 | 5,547 | # In a group of 6 boys and 4 girls, four children are to be selected. in how many different ways can they be selected such that at least one boy should be there?
in a group of 6 boys and 4 girls, four children are to be selected. in how many different ways can they be selected such that at least one boy should be there?
To find the number of ways to select 4 children from a group of 6 boys and 4 girls such that at least one boy should be there, we can use the principle of inclusion-exclusion.
The number of ways to select 4 children from a group of 6 boys and 4 girls is given by:
C(10,4) = 10! / (4! * (10-4)!) = 210,
The number of ways to select 4 children from only the 4 girls is given by:
C(4,4) = 4! / (4! * (4-4)!) = 1,
So, the number of ways to select 4 children such that no boy is included is 1.
To find the number of ways to select 4 children such that at least one boy is included, we subtract the number of ways in which no boy is included from the total number of ways:
C(10,4) - C(4,4) = 210 - 1 = 209,
Therefore, there are 209 different ways to select 4 children from a group of 6 boys and 4 girls such that at least one boy should be there. | 330 | 1,172 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2023-14 | latest | en | 0.949902 |
https://alpynepyano.github.io/healthyNumerics/posts/gradient-descent-algorithm.html | 1,670,351,187,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00804.warc.gz | 122,922,227 | 8,454 | .
.
.
.
.
# HealthyNumerics
HealthPoliticsEconomics | Quant Analytics | Numerics
# MachineLearning: Gradient descent from Nobel Laureates to chocolate consumption
We present a solution method, the Stochastic Gradient Descent (SGD). Our approach is based on this repos:
• https://github.com/elizavetasemenova/amld-2019
which we have slightly modified.
This is an iterative approach, in which the desiered solution is successively approached with every iteration. The gradient of the loss or error function gives the direction to control the development of the solution of the algorithm.
As an example we choose a linear 1-dimensional function to approach the data, which corresponds to a linear interpolation. The aim is to evaluate the model parameters $$\theta_0$$ and $$\theta_1$$ as slope and intercept.
The data we use is from a paper published in New England Journal of Medicine. The author Franz Messerli reports a highly significant correlation between a nation's per capita chocolate consumption and the rate at which its citizens win Nobel Prizes. He reported "a close, significant linear correlation (r=0.791, p<0.0001) between chocolate consumption per capita and the number of Nobel laureates per 10 million persons in a total of 23 countries."
import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt
import random
from matplotlib import rc
rc('text', usetex=True)
print('\n\n\n')
nd = data_df.shape[0]
with plt.style.context('seaborn'): # 'fivethirtyeight'
fig = plt.figure(figsize=(20,8)) ;
for i in range(nd):
x = data_df.loc[i,data_df.columns[1]]
y = data_df.loc[i,data_df.columns[2]]
tx= data_df.loc[i,data_df.columns[0]]
plt.plot(x, y, marker='o',ms=29, c='orange',alpha = 0.6)
plt.text(x,y, tx, fontsize=18)
plt.title('Nobel Laureates vs Chocolate Consumption', fontweight='bold',fontsize=35)
plt.margins(0.1)
plt.show()
### 1. Target function with parameters
We define the linear function f(x) that will approximate our dataset. It depends on two unknown parameters that we want to find out: $$\theta_0$$ and $$\theta_1$$:
$$f(x)=\theta_0 + \theta_1x$$
In matrix notation we can write
$$\mathbf{f}(\mathbf{x}) = \theta_0 + \theta_1 \mathbf{x}$$
### 2. Loss function
We define the loss or error function as the squared distance between the observed data $$y$$ and its approximated value $$f(x)$$
$$L(\theta)=\sum_{i^{(i)}\in data} (f(x^{(i)}) - y^{(i)})^2$$
In matrix notation we can express this as a scalar product of the difference $$\mathbf{\delta} = \mathbf{f}(\mathbf{x})-\mathbf{y}$$ which can be used for an implementation in vectorized form
$$L(\theta)=<\mathbf{\delta},\mathbf{\delta}>$$ , scalar product
### 3. Derivatives of the loss function
They will be used for the descendent gradient algorithm
$$\frac{\partial L}{\partial \theta_0} = 2\sum_i (f(x^{(i)}) - y^{(i)})$$
and
$$\frac{\partial L}{\partial \theta_1} = 2\sum_i (f(x^{(i)}) - y^{(i)})x_{1}^{(i)}$$
We implement these as
$$L_{\theta_0} = 2\cdot sum(\mathbf{\delta})$$
$$L_{\theta_1} = 2\cdot <\mathbf{\delta} , \mathbf{x} >$$ , scalar product
### 4. Algorithm
It's a marching algorithm. Starting with some intitial values for $$\theta_0$$ and $$\theta_1$$ these are updated recursively:
$$\theta_0^{n+1} = \theta_0^n + \epsilon \frac{\partial L}{\partial \theta_0}$$
$$\theta_1^{n+1} = \theta_1^n + \epsilon \frac{\partial L}{\partial \theta_1}$$
We apply the standard approach where all data are used at each time step. There are variations in using only a subset of the data that are randomly picked out at each time step.
### 5. Solution
The rate of convergance depends on the choice of $$\epsilon$$. With a low value the convergence is slow and many iterations are needed. With a large value to soltuion might oscillate or even diverge. This phenomena is well known in computational fluid dynamics where the Courant–Friedrichs–Lewy (CFL) condition is a necessary condition for convergence.
In playing around with this example we can see, that the convergence for the intercept is slower than for the slope. We have chosen $$\epsilon$$ as large as possible, so that an oscillatory behaviour can be seen, which in this case is still benefical and supports a faster convergence.
A Runge-Kutta schema might improve the convergence properties.
def f(x,θ):
return θ[0] + θ[1]*x
def f_loss(xs, ys,θ):
delta = f(xs,θ) - ys
return np.dot(delta,delta)
def f_dθ0(xs, ys,θ):
return 2 * np.sum(f(xs,θ) - ys)
def f_dθ1(xs, ys,θ):
delta = f(xs,θ) - ys
return 2*np.dot(delta,xs)
data_df = pd.read_csv('data.csv') # get the data
xs = np.array(data_df.values[:, 1],dtype=float)
ys = np.array(data_df.values[:, 2],dtype=float)
ε = 0.001 # choose the time step
θ = np.array([4.0, 1.0]) # initialize the parameters theta
dLs, dT0, dT1 = [], [], []
loss_old = 1.0
print('\n\n\n')
with plt.style.context('seaborn'):
fig = plt.figure(figsize=(20,10))
x0, x1 = 0, 14 # 2 x-points of the straight line in the graphics
for i in range(300): #------------- run the algorithm -----------
dθ0 = f_dθ0(xs, ys, θ) # compute the gradients of theta
dθ1 = f_dθ1(xs, ys, θ)
dT0.append(dθ0)
dT1.append(dθ1)
θ[0] -= ε * dθ0 # update theta
θ[1] -= ε * dθ1
loss_new = f_loss(xs, ys, θ) # check the development of the error
dL = (loss_new-loss_old)/loss_old
dLs.append(np.sqrt(dL*dL))
loss_old = loss_new
# ----- Graphics -------------------------------------------------
plt.plot([x0, x1], [f(x0,θ), f(x1,θ)], 'k-', lw=1, alpha=0.3)
plt.plot([x0, x1], [f(x0,θ), f(x1,θ)], 'r-', lw=3, alpha=0.93)
for i in range(nd):
x = data_df.loc[i,data_df.columns[1]]
y = data_df.loc[i,data_df.columns[2]]
tx= data_df.loc[i,data_df.columns[0]]
plt.plot(x, y, marker='o',ms=29, c='orange',alpha = 0.6)
plt.text(x,y, tx, fontsize=18)
plt.xlabel(data_df.columns[1],size=30);
plt.ylabel(data_df.columns[2],size=30)
plt.title('Nobel Laureates vs Chocolate Consumption', fontweight='bold',fontsize=35)
plt.margins(0.1)
plt.show()
#---- compare with linear regression ---------
theta1, theta0,_,_,_ = stats.linregress(xs,ys)
fp = np.polyfit(xs,ys,1)
print('\n\n\n')
print("The parameters θ =",θ[1],θ[0])
print("The parameters with linear regression: =",theta1, theta0)
print("The parameters with np.polyfit: =",fp[0],fp[1])
print('\n\n\n')
The parameters θ = 2.501848008865261 -3.448185705127312
The parameters with linear regression: = 2.548736915671354 -3.792170212097653
The parameters with np.polyfit: = 2.548736915671355 -3.792170212097653
with plt.style.context('seaborn'):
fig = plt.figure(figsize=(20,8)) ;
plt.plot(dLs[1:], lw=2)
plt.xlabel('Iteration',size=30); plt.ylabel('rel. change of Loss',size=30)
plt.title('Convergence',fontweight='bold', fontsize=30);
plt.show()
fig = plt.figure(figsize=(20,8)) ;
plt.plot(dT0); plt.title(r'$\frac{\partial L}{\partial \theta_0}$',fontsize=35);plt.show()
fig = plt.figure(figsize=(20,8)) ;
plt.plot(dT1); plt.title(r'$\frac{\partial L}{\partial \theta_1}$',fontsize=35);plt.show()
# The data
data_df
country chocolate consumption (kg/yr/capita) Nobel laureates per 10M population
0 France 6.3 8.0
1 Denmark 8.5 25.1
2 Finland 7.2 7.3
3 Brazil 2.9 0.0
4 Italy 3.8 3.0
5 Poland 3.6 2.9
6 Switzerland 12.0 32.4
7 China 0.7 0.0
8 Belgium 4.2 8.0
9 Japan 1.8 1.0
10 Greece 2.6 1.2
11 United States 5.4 10.1
12 Norway 9.1 23.0
13 Portugal 1.9 1.3
14 United Kingdom 9.5 18.0
15 Spain 3.7 1.2
16 Austria 8.7 24.5
17 Ireland 8.8 12.5
18 Germany 11.4 12.4
19 The Netherlands 4.3 11.0 | 2,341 | 7,611 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2022-49 | latest | en | 0.713833 |
https://vi.scribd.com/document/245589507/Mech-Dynamics-15-0-L08-Random | 1,561,479,136,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627999853.94/warc/CC-MAIN-20190625152739-20190625174739-00231.warc.gz | 636,453,854 | 63,309 | You are on page 1of 44
# Lecture 8
Random Vibration
15.0 Release
ANSYS Mechanical
Linear and Nonlinear Dynamics
2012 ANSYS, Inc.
February 5, 2014
Release 15.0
## Random Vibration Analysis
Topics covered
A. What is random Vibration
B. Power Spectral Density PSD
C.
Theory Overview
## 2012 ANSYS, Inc.
E.
Analysis Settings
F.
Workshop 8
February 5, 2014
Release 15.0
## A. What is Random Vibration Analysis
Random vibration analysis is another spectral method
The purpose of a random vibration analysis is to determine some
statistical properties of a structural response, normally the standard
deviation (1) of a displacement, force, or stress.
(1) is used to determine fatigue life of a structure
February 5, 2014
Release 15.0
## We have already seen sinusoidal vibration (free and forced)
This is vibration at one predominant frequency
## A more common type of vibration is random vibration
This is vibration at many frequencies at the same time
February 5, 2014
Release 15.0
## Parts on a manufacturing line
Airplanes flying or taxiing
Spacecraft during launch
Courtesy: NASA
February 5, 2014
Release 15.0
## If the amplitude is constantly changing, how can a random
excitation be evaluated?
## Key observation: at a given frequency, the amplitude of the
excitation does constantly change, but for many processes, its
average value tends to remain relatively constant.
This gives us the ability to easily characterize a random excitation.
February 5, 2014
Release 15.0
## Random excitation can be characterized statistically in terms of
a Power Spectral Density plot
PSD amplitude versus frequency
## PSD spectra plots are generally supplied
design spec, building code, etc.
ANSYS does not provide tools for generating PSD spectra plots,
but general approach will be described in next several slides
February 5, 2014
Release 15.0
Random Vibration
## B. Power Spectral Density15.0
PSD
Release
ANSYS Mechanical
Linear and Nonlinear Dynamics
2012 ANSYS, Inc.
February 5, 2014
Release 15.0
## The total frequency range
is split into individual
ranges (called bins).
this can be done using
bandbass filters
real analyzers typically
have hundreds of bins
February 5, 2014
Release 15.0
## The excitation is squared
and the average is
calculated for each bin.
called the mean square
gives (units RMS)2
February 5, 2014
10
Release 15.0
## Power Spectral Density
If a wider bin were used, the average value would be larger
a consistent definition is needed to account for different bin sizes
## Consequently, the average squared amplitudes are divided by
the bin bandwidth
gives (units RMS)2/Hz
leaves units2/Hz
acceleration
velocity
displacement
force
February 5, 2014
## e.g. [(mm/s2)2/Hz] or [G2/Hz]
e.g. [(mm/s)2/Hz]
e.g. [(mm)2/Hz]
e.g. [N2/Hz]
11
Release 15.0
## The value (units2/Hz) is plotted as a function
of the bin frequency.
each bin is referred to by its center frequency.
graph.
plot.
## Although the process is truly random, it obeys
the limits defined in the plot.
February 5, 2014
12
Release 15.0
## The representation of the random excitation is called its Power
Spectral Density (PSD).
## By comparison, a singe sinusoid would result in a narrow flat PSD.
For a bandwidth of 1 Hz, the PSD value would be the RMS amplitude
squared. PSD=(6/sqrt(2))^2=18
40 Hz
February 5, 2014
13
Release 15.0
## We can easily convert between acceleration (including G acceleration),
velocity, and displacement spectra by multiplying or dividing by the
square of the frequency.
remember to convert frequency units; rad/s = 2f Hz
S a S d 2f
S d S v / 2f
S a / 2f
S v S d 2f
S v 2f
S a / 2f
SG S a / g 2
2012 ANSYS, Inc.
February 5, 2014
14
Release 15.0
Random Vibration
C. Theory Overview
15.0 Release
ANSYS Mechanical
Linear and Nonlinear Dynamics
2012 ANSYS, Inc.
February 5, 2014
15
Release 15.0
## Assumptions & Restrictions
The structure has
no random properties
no time varying stiffness, damping, or mass
no time varying forces, displacement, pressures, temperatures, etc applied
light damping
damping forces are much smaller than inertial and elastic forces
## stationary (does not change with time)
the response will also be a stationary random process
## 2012 ANSYS, Inc.
February 5, 2014
16
Release 15.0
Excitation Distribution
A key concept is the fact that many random processes follow a Gaussian
distribution.
## The mean value of a Gaussian probability curve is defined as the
standard deviation (or sigma value) of the distribution.
By taking multiples of sigma, we can account for a greater percentage of all
possible excitations.
## 2012 ANSYS, Inc.
February 5, 2014
17
Release 15.0
Excitation Distribution
1 sigma:
~ 68.27 %
2 sigma:
~ 95.951 %
3 sigma:
~ 99.737 %
## 2012 ANSYS, Inc.
February 5, 2014
18
Release 15.0
Excitation Distribution
## Because the distribution is assumed to be normal, we can never
account for 100% of the possible excitations.
In reality, the distribution of excitations is more likely truncated.
Furthermore, high-sigma excitations occur very rarely.
3 2 1
1 2 3
## Important property of Gaussian distribution:
if the excitation of a linear system is a Gaussian process, then the
response is generally a different random process, but still a normal one
February 5, 2014
19
Release 15.0
Random Vibration
excitation
## We can describe the dynamic characteristics of a linear system by
determining its steady-state response to a sinusoidal input
February 5, 2014
20
Release 15.0
Random Vibration
= 30 Hz
ain = 40 mm/s2
## e.g. output motion
= 30 Hz
aout = 119 mm/s2, = 116
## Information about the amplitude ratio (output/input) and the phase
angle defines the dynamic characteristics of the system at this one
frequency.
this is also called the transmission or transfer function
the input and output could be any quantity, not only acceleration
February 5, 2014
21
Release 15.0
Random Vibration
## We can sweep across a range of frequencies to determine how the
response (amplitude and phase angle) changes with frequency.
## Theoretically, sweeping from a frequency of zero to infinity completely
defines the dynamic characteristics.
February 5, 2014
22
Release 15.0
Random Vibration
## We have described amplitude and phase angle separately, but they
can also be described as a single complex number, called the
(complex) frequency response function H() (FRF).
H A iB
By definition
the magnitude of the FRF is equal to the amplitude ratio, and
the ratio of FRF imaginary part to its real part is equal to the tangent of the
phase angle.
aout
H A B
ain
2
ImH B
tan
ReH A
2012 ANSYS, Inc.
February 5, 2014
23
Release 15.0
Random Vibration
## According to the theory of random vibration, the response of the
system to a single input PSD is
Sout H Sin
2
or
a
Sout out Sin
ain
Where:
Sout
Sin
aout
ain
## = spectral density response (conventional terminology)
= spectral density input (value from PSD curve)
= calculated sinusoidal output
= sinusoidal input
Note: within ANSYS the spectral density response is typically called the
response PSD (RPSD) and the spectral density input is typically called the
input PSD.
2012 ANSYS, Inc.
February 5, 2014
24
Release 15.0
Random Vibration
## To calculate the response PSD (RPSD), multiply the input PSD
by the response function
2
aout
Sin
Sout
ain
aout
input PSD
RPSD
ain
or
2012 ANSYS, Inc.
February 5, 2014
25
Release 15.0
Random Vibration
## As stated earlier, we are typically interested in the average
response of the system.
The area under the RPSD curve gives the mean square response.
the square root of the mean square is the root mean square (RMS)
the RMS is the average, or one standard deviation (1-sigma), response
RMS
S d
0
## integration in log-log space
(requires special consideration)
## 2012 ANSYS, Inc.
February 5, 2014
26
Release 15.0
Random Vibration
We dont know exactly what the response will look like, but we do
know that it will respond to the given input with the RMS response,
on average.
Given our assumptions that (1) the input is Gaussian and (2) the
system is linear, then our output must also be Gaussian.
3 2 1
1 2 3
## 1 x RMS (1-sigma) accounts for ~ 68.27 % of the total response
2 x RMS (2-sigma) accounts for ~ 95.951 % of the total response
3 x RMS (3-sigma) accounts for ~ 99.737 % of the total response
2012 ANSYS, Inc.
February 5, 2014
27
Release 15.0
Random Vibration
For multiple PSDs in the same model, the results are combined
We could alternatively perform separate analyses and manually
February 5, 2014
28
Release 15.0
Random Vibration
## D. PSD Curve Fitting
15.0 Release
ANSYS Mechanical
Linear and Nonlinear Dynamics
2012 ANSYS, Inc.
February 5, 2014
29
Release 15.0
## The PSD is defined as a piecewise linear frequency table and plotted as
such in log-log space.
## A curve-fitting polynomial is used for the closed-form integration of
the curve.
For a good fit, the PSD values between consecutive points should not
change by more than an order of magnitude
February 5, 2014
30
Release 15.0
## PSD Curve Fitting
Once load entries are entered, the graph provides one of the
following color-code indicators per segment:
Green: Values are considered
reliable and accurate.
Yellow: This is a warming
indicator. Results produced are
not considered to be reliable and
accurate.
Red: Results produced are not
considered trustworthy. It is
recommended that you modify
solution process.
February 5, 2014
31
Release 15.0
## To resolve goodness-of-fit issues:
Click the fly-out of the Load Data option and choose Improved Fit.
## Interpolated points are displayed if they are available from the
goodness of fit approximation.
## 2012 ANSYS, Inc.
February 5, 2014
32
Release 15.0
Random Vibration
E. Analysis Settings
15.0 Release
ANSYS Mechanical
Linear and Nonlinear Dynamics
2012 ANSYS, Inc.
February 5, 2014
33
Release 15.0
Setup
Setup a random vibration analysis in the schematic by linking a modal system to a
random vibration system at the solution level.
## 2012 ANSYS, Inc.
February 5, 2014
34
Release 15.0
Analysis Settings
Analysis Settings > Options
1.
## Number of Modes To Use:
It is recommended to include the modes whose frequencies span 1.5 times the
maximum frequency defined in the input PSD.
2.
## Insignificant Modes:, If set to Yes,
Model Significance Level:
0 (all modes selected), and
1 (no modes selected).
Any term whose significance level is
less than significance Level is considered
insignificant and is not contributed to the mode combinations
## 2012 ANSYS, Inc.
February 5, 2014
35
Release 15.0
Analysis Settings
Analysis Settings > Output Controls
Controls to No.
February 5, 2014
36
Release 15.0
## Support boundary condition must be defined in the modal analysis
itself.
The only applicable load is a PSD Base Excitation of spectral value vs.
frequency.
PSD Acceleration,
PSD G Acceleration,
PSD Velocity, and
PSD Displacement.
## Multiple PSD excitations (uncorrelated) can be applied; however,
correlation between PSD excitations is not supported.
February 5, 2014
37
Release 15.0
Results
## Applicable results are directional (X/Y/Z)
displacement, velocity and acceleration.
## Since the directional results are statistical in nature,
they cannot be combined in the usual way.
If strain/stress are requested, applicable results are normal strain and stress,
shear strain and stress, and equivalent stress.
February 5, 2014
38
Release 15.0
Results
## Displacement results are:
relative to the base of the structure (the fixed supports).
## Velocity and acceleration results:
include base motion effects (absolute).
February 5, 2014
39
Release 15.0
Results
## Force Reaction and Moment Reaction probes can be scoped to a Remote
Displacement boundary condition to view Reactions Results.
February 5, 2014
40
Release 15.0
Results
## For real models with multiple DOFs
RPSDs are calculated for every node in every free direction at each
frequency
RPSDs can be plotted for each node in a specific direction versus frequency
a RMS value (sigma value) for the entire frequency range is calculated
for every node in every free direction
Z direction
2012 ANSYS, Inc.
February 5, 2014
41
Release 15.0
Results
The default output results are one sigma (1) or one standard deviation values
(with zero mean value).
## These results follow a Gaussian distribution.
The interpretation is that 68.3% of the time the response will be less than the
standard deviation value.
You can scale the result by 2 times to get the 2 sigma (2) values.
The response will be less than the 2 sigma values 95.45% of the time and 3
sigma values 99.73% of the time.
## 2012 ANSYS, Inc.
February 5, 2014
42
Release 15.0
Response Spectrum
Workshop 8.
15.0 Release
ANSYS Mechanical
Linear and Nonlinear Dynamics
2012 ANSYS, Inc.
February 5, 2014
43
Release 15.0
## In workshop 8, you will determine the displacements and stresses in a girder
assembly due to an acceleration PSD.
WS8: Random Vibration (PSD) Analysis of a Girder Assembly
February 5, 2014
44
Release 15.0 | 3,471 | 13,230 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2019-26 | latest | en | 0.8703 |
https://www.pw.live/question-answer/if-a-and-b-are-natural-numbers-36805 | 1,670,470,619,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00538.warc.gz | 1,012,715,311 | 17,387 | . If a and b are natural numbers
If a and b are natural numbers. If a + b = 2020 then what will be the value of (– 1)a + (– 1)b
1. 1 OR – 1
2. 2020 OR – 2020
3. 1010 OR – 1010
4. 2 OR – 2 | 84 | 192 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2022-49 | latest | en | 0.427509 |
https://www.turito.com/learn/physics/a-longitudinal-wave-grade-8 | 1,713,674,616,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817729.0/warc/CC-MAIN-20240421040323-20240421070323-00540.warc.gz | 966,349,511 | 28,355 | #### Need Help?
Get in touch with us
# Sound – A longitudinal Wave
Aug 20, 2022
## Key Concepts
1. Sound – A longitudinal Wave
2. Transverse waves
3. Differentiation between longitudinal and Transverse waves
## Introduction: A longitudinal Wave
Sound waves originate from a vibrating body, which in turn sets its neighboring particles of the medium into vibration. These vibrating particles set their neighboring particles in motion. This process continues until the disturbance reaches the ears of the listener. As the sound requires a material medium for its propagation, it is called a mechanical wave. We can categorize sound under one more category based on the comparison between the direction of motion of the sound wave and the direction of vibration of the particles of the medium when it propagates through the medium.
## Explanation:
### Sound – A Mechanical Wave:
The movement of the particles of the medium when a sound wave propagates through it is shown below.
Here, it can be noticed that the direction of vibration of particles of the medium is parallel to the direction of propagation of the sound wave. The waves in which the direction of vibration of particles of the medium of propagation is parallel to the direction of propagation of the waves are called longitudinal waves
Sound waves in air or any fluid medium travel by disturbing the particles in the same way. Sound waves are longitudinal waves in any fluid medium.
### Transverse waves:
There is another category of waves wherein the direction of vibrations of the particles of the medium of propagation is perpendicular to the direction of motion of the waves. Such waves are called transverse waves
The ripples on the surface of water and the vibration of a string are examples of transverse waves
These waves are also mechanical as they involve the movement of particles of the medium, i.e., water and string, respectively.
Some transverse waves are not mechanical in nature. It means they do not require a material medium for their propagation. Light waves come under this category. In light waves, the oscillations are not of the particles of the medium or their density or pressure, but the electric and magnetic fields.
### Activity:
To model the way in which various waves propagate through a medium, the following activity can be performed.
For this, a slinky is taken, and one of its ends is fixed to a rigid object such as a wall, and its body rests on a table.
Now, the free end of the slinky is held and moved forward and backwards. The motion of the loops of the slinky is observed.
Now, the free end of the slinky is moved up and down. The motion of the loops is observed.
When the slinky is moved to and fro, the loops move in the way in which a longitudinal wave moves through a medium forming compressions and rarefactions.
When the slinky is moved up and down, the loops move the way in which a transverse wave moves through a medium forming.
## Summary
1. The waves in which the direction of vibration of particles of the medium of propagation is parallel to the direction of propagation of the waves are called longitudinal waves.
2. Sound waves are longitudinal waves.
3. The waves in which the direction of vibration of the particles of the medium of propagation is perpendicular to the direction of propagation of the waves are called transverse waves.
4. The ripples on the surface of water and the vibration of a string are the examples of transverse waves.
5. Light waves are transverse waves which are not mechanical in nature.
6. When the free end of a slinky is moved to and fro the loops move in the way in which a longitudinal wave moves through a medium forming compressions and rarefactions.
7. When the free end of a slinky is moved up and down the loops move the way in which a transverse wave moves through a medium forming.
#### Different Types of Waves and Their Examples
Introduction: We can’t directly observe many waves like light waves and sound waves. The mechanical waves on a rope, waves on the surface of the water, and a slinky are visible to us. So, these mechanical waves can serve as a model to understand the wave phenomenon. Explanation: Types of Waves: Fig:1 Types of waves […]
#### Dispersion of Light and the Formation of Rainbow
Introduction: Visible Light: Visible light from the Sun comes to Earth as white light traveling through space in the form of waves. Visible light contains a mixture of wavelengths that the human eye can detect. Visible light has wavelengths between 0.7 and 0.4 millionths of a meter. The different colors you see are electromagnetic waves […]
#### Force: Balanced and Unbalanced Forces
Introduction: In a tug of war, the one applying more force wins the game. In this session, we will calculate this force that makes one team win and one team lose. We will learn about it in terms of balanced force and unbalanced force. Explanation: Force Force is an external effort that may move a […] | 1,012 | 4,984 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-18 | latest | en | 0.901145 |
https://math.stackexchange.com/questions/3067045/prove-that-n-lfloorn-p-rfloor-lfloor-fracp-1p-leftn-1-right | 1,560,634,415,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627997335.70/warc/CC-MAIN-20190615202724-20190615224724-00540.warc.gz | 543,855,512 | 33,555 | # Prove that $N - \lfloor{N/p}\rfloor = \lfloor{\frac{p-1}{p}\left({N + 1}\right)}\rfloor$ for positive $N$ and prime $p$
I am counting the number of positive integers less than or equal to some positive integer $$N$$ and not divisible by some prime $$p$$. This gets generalized for $$k$$ primes where I use the principle of inclusion-exclusion for this result. The simple result for a single prime is $$N - \lfloor{\frac{N}{p}}\rfloor$$. However, I have noticed by experiment that this is also equal to $$\lfloor{\frac{p-1}{p} \left({N + 1}\right)}\rfloor$$. I am looking for a proof of this relation if true.
Consider that $$N$$ may be expressed as $$N = ap + b$$ for an integer $$a$$ and integer $$0 \le b \le p - 1$$. Using this, the left side of your equation becomes
$$N - \lfloor N/p \rfloor = ap + b - a \tag{1}\label{eq1}$$
Consider the numerator of the right side of your equation, i.e.,
$$\left(p - 1\right)\left(N + 1\right) = \left(p - 1\right)\left(ap + b + 1\right) = ap^2 + \left(b + 1 - a\right)p - \left(b + 1\right) \tag{2}\label{eq2}$$
Since $$0 \leq b \leq p - 1$$, then $$1 \leq b + 1 \leq p$$. As such, for any integer $$M$$, including $$M = 0$$, we have that
$$\lfloor \frac{Mp - \left(b + 1\right)}{p} \rfloor = M - 1 \tag{3}\label{eq3}$$
Using $$\eqref{eq2}$$ and $$\eqref{eq3}$$ in the right side of your equation gives
$$\lfloor \frac{\left(p - 1\right)\left(N + 1\right)}{p} \rfloor = ap + \left(b + 1 - a\right) + \lfloor \frac{-\left(b + 1\right)}{p} \rfloor = ap + b - a \tag{4}\label{eq4}$$
As such, the LHS (from \eqref{eq1}) is always equal to the RHS (from \eqref{eq4} above), so your equation always holds. Note, this is true not only for primes $$p$$, but for all positive integers $$p$$, as I didn't use any particular properties of primes anywhere in the proof above.
let $$f(N) = N - \lfloor \frac{N}{p} \rfloor$$
then $$f(N+1) - f(N) = 1 - \bigg(\lfloor \frac{N+1}{p} \rfloor - \lfloor \frac{N}{p} \rfloor \bigg)$$
thus when $$N$$ is incremented by 1, $$f(N)$$ is also incremented by 1 except when $$N \equiv_p -1$$. in this case $$f(N+1) = f(N)$$
if now we let $$g(N) = \lfloor{\frac{p-1}{p} \left({N + 1}\right)}\rfloor$$ a little rearrangement gives $$g(N) = \lfloor N+1 - \frac{N+1}p \rfloor= N+1 + \lfloor -\frac{N+1}p \rfloor$$ and $$g(N+1) - g(N) = 1 + \bigg(\lfloor -\frac{N+2}{p} \rfloor - \lfloor -\frac{N+1}{p} \rfloor \bigg)$$
since $$N$$ is positive we again find that when $$N$$ increases by 1 the increment of $$g$$ is 1 except when $$N \equiv_p -1$$.
since $$f(1)=g(1)=1$$ the result is demonstrated | 952 | 2,573 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2019-26 | latest | en | 0.794045 |
http://mathhelpforum.com/trigonometry/82005-radical-simplification.html | 1,481,470,595,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698544679.86/warc/CC-MAIN-20161202170904-00126-ip-10-31-129-80.ec2.internal.warc.gz | 177,446,091 | 10,193 | hello can someone please show how to simplify this
20√3-40
---
√2
to 20(√3-√2)
2. Originally Posted by jepal
hello can someone please show how to simplify this
20√3-40
---
√2
to 20(√3-√2)
$20\sqrt{3} - \dfrac{40}{\sqrt{2}}$
$20\sqrt{3} - \dfrac{40}{\sqrt{2}} = 20\sqrt{3} - \dfrac{40 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = 20\sqrt{3} - \dfrac{40 \cdot \sqrt{2}}{2} = 20\sqrt{3} - 20 \cdot \sqrt{2}$ | 184 | 406 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2016-50 | longest | en | 0.655998 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.